James L. Throne
Technology of Thermoforming
Hanser Publishers, Munich Vienna New York Hanser/Gardner Publications, Inc., Cincinnati
The Author: Dr. James L. Throne, Sherwood Technologies, Inc., 158 Brookside Blvd., Hinckley, OH 44233-9676, USA
Distributed in the USA and in Canada by Hanser/Gardner Publications, Inc. 6600 Clough Pike, Cincinnati, Ohio 45244-4090, USA Fax: (513) 527-8950 Phone: (513) 527-8977 or 1-800-950-8977 Distributed in all other countries by Carl Hanser Verlag Postfach 86 04 20, 81631 Miinchen, Germany Fax: +49 (89) 98 12 64 The use of general descriptive names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. While the advice and information in this book are believed to be true and accurate at the date of going to press, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.
Library of Congress Cataloging-in-Publication Data Throne, James L., 1937Technology of thermoforming / James L. Throne. p. cm. Includes bibliographical references and index. ISBN 1-56990-198-8 1. Plastics-Molding. I. Title. TP1150.T48 1996 668.4' 12-dc20
96-24175
Die Deutsche Bibliothek-CIP-Einheitsaufnahme Throne, James L.: Technology of thermoforming / James L. Throne.-Munich ; Vienna ; New York : Hanser ; Cincinnati : Hanser / Gardner, 1996 ISBN 3-446-17812-0 All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying or by any information storage and retrieval system, without permission in writing from the publisher. © Carl Hanser Verlag, Munich Vienna New York, 1996 Typeset in Ireland by Datapage International Ltd., Dublin Printed and bound in Germany by Kosel, Kempten
Preface I completed the monograph, Thermo forming, in 1985 and Carl Hanser Verlag published it in 1987. At the time it was written, there were no up-to-date monographs devoted solely to thermoforming. Two monographs devoted to thermoforming appeared about the same time as the Thermoforming monograph. They are: J. Florian, Practical Thermoforming: Principles and Applications, Marcel Dekker, Inc., New York (1987). G. Gruenwald, Thermoforming: A Plastics Processing Guide. Technomic Publishing Co., Inc., Lancaster PA (1987). Reviewers of the three monographs remarked at the time that while there was some overlap, the three monographs provided separate and unique insights to the industry and that technologists would do well to have access to all three. In the preface to that monograph, I stated that: "Thermoforming is not an easy process. It just looks easy."
In many respects, the industry has verified this over and over in the last decade. I further stated that: " . . . [Thermoforming] is becoming challenging as newer process variations, newer materials, tighter sheet and part tolerances, more critical applications and more sophisticated controls are developed."
In the last decade, the industry has successfully tackled many of these very difficult problems. The core business has been helped greatly by improved heaters, more accurate process controls, cooperative interaction between extruders and formers, more easily thermoformable polymers, advanced trimming techniques, and to a great degree, the acceptance of thermoforming as a process by OEMs. In addition, thermoforming has gained the attention of many universities, technical writers, consultants and software companies. And the industry has grown dramatically in size. As an example, the Society of Plastics Engineers Thermoforming Division held a fall conference in Wisconsin in 1991. About 100 people attended. In Midland MI in 1992 more than 200 attended. In South Bend IN in 1993, more than 400 attended, in Atlanta in 1994, more than 600 attended, and in Cleveland in 1995, nearly 700 attended. And plans are being made for nearly 800 in Cincinnati in 1996. There are more than 200 custom thermoformers in the US today and some estimate that a new thermoforming company is born every week. The industry seems to have come of age in the last ten years. This work was intended to be a revision and update of the 1987 monograph. Readers of that monograph will note that this book is much larger. This book is also an overview of the technical aspects of thermoforming and generally follows the outline of the Thermoforming monograph. However, I have included worked-out examples and many guidelines to illustrate and support the technical aspects. As with the 1987 monograph, the material in each chapter of this book moves from relatively simple concepts to more technical, in-depth considerations. This book has ten chapters:
Chapter 1, "Thermoforming—Definitions, History, Methods and Equipment", is a proper introduction to the subject. The chapter includes some history, some market information, a glossary of definitions, the traditional methods of forming and some technical considerations about the machinery. Chapter 2, "Polymeric Materials", briefly reviews the nature of thermoformable polymers and their adducts. General concepts of polymer response to applied loads and temperatures are considered. Some important new information on infrared energy absorption is detailed. Chapter 3, "Heating the Sheet", reviews the three general ways of heating sheet—conduction, convection and radiation. Since infrared radiation is the most popular and efficient means of heating sheet, fundamental aspects are discussed. This chapter becomes quite technical with general guidelines for determining heating cycles and a new section on computer-genera ted prediction of sheet temperature. Chapter 4, "Stretching the Sheet", is concerned with fundamentals of multiaxial sheet deformation. Polymer hot strength is related to tensile characteristics of rubbery solids and viscosity of elastic liquids. Sheet sag is shown to be strongly related to polymer hot strength. Again, the material is quite technical. Chapter 5, "Cooling and Trimming the Sheet", deals with heat removal from the sheet while against the mold surface. Some new material on computer-generated mold temperature prediction is given. The mechanics of cutting the molded part from the web are considered in detail. Chapter 6, "Thermoforming Molds", considers mold materials and mold designs. Vacuum or vent hole sizes and numbers are arithmetically determined and plug materials and designs are also discussed. Chapter 7, "Parts Design", first considers the economics of parts design. Draw ratios are then defined and wall thickness prediction methods discussed. Regrind and material property loss are considered in detail, and an extensive section on part design guidelines follows. Chapter 8, "Producing Sheet and Film", is a new chapter. Since the thermoformer is the customer of the extruder, he/she should know some rudimentary extrusion concepts. This chapter is a brief summary of the extrusion process, with emphasis on sheet quality and quality control. A sheet quality checklist is discussed in detail. Chapter 9, "Newer Thermoforming Technologies", is also a new chapter, written in response to many requests for forming information in several new processing areas. In the 1987 monograph. I said: " . . . [EJngineers seeking the latest information on pressure forming, the heating of foam sheet or forming crystallizing PET will be disappointed."
This is no longer the case. Chapter 9 presents vignettes on the following forming techniques: • • • •
CPET, Pressure forming, Forming filled and reinforced polymers, Laminated sheet forming,
• • • •
Twin-sheet forming, Forming PP, Thermoforming foam sheet, and Other semi-thermoforming technologies.
Chapter 10, "Set-Up Protocols, Troubleshooting, and the Economics of Thermoforming", is an assemblage of production and economic issues that were scattered through several chapters of the 1987 monograph. Guidelines to setting up a new mold, forming a new polymer and troubleshooting both the thin-gage and heavygage forming process are found here. Thermoforming is an energy intensive process that uses only a portion of its raw material, sheet, to make the part. To be competitive, the thermoformer must know what things cost, in detail. This chapter focuses on this theme. Caveats are in order. Some of the engineering details are quite technical. The monograph is designed to provide a technical foundation for the industry. Nevertheless, the casual reader should find ample guidelines, protocols, tips and rules-ofthumb to help him/her with specific processing problems or new product planning. The decade or so since I wrote the Thermoforming monograph has been marked by retirement and deaths of many thermoforming leaders. Most notably, Dr. Herman "Dick" Osmers, SPE Thermoformer-of-the-Year, fellow PhD chemical engineer-consultant-teacher and critical reviewer of the 1985 book, died shortly after it was published. I will always miss his technical accuracy, his thoroughness, and his up-beat enthusiasm. This book is dedicated to his memory. January 1996
James L. Throne, PhD
Contents
Preface ......................................................................................... 1.
v
Thermoforming – Definitions, History, Methods and Equipment ............................................................................
1
1.1
Introduction ...............................................................................
2
1.2
History .......................................................................................
3
1.3
Markets .....................................................................................
4
1.4
Some Definitions .......................................................................
11
Gage .................................................................................
12
Clamping of Thin-Gage Sheet ...........................................
12
Clamping of Heavy-Gage Sheet ........................................
13
Heating of Thin-Gage Sheet ..............................................
13
Heating Heavy-Gage Sheet ...............................................
14
Shaping Thin-Gage Sheet .................................................
14
Shaping Heavy-Gage Sheet ..............................................
14
Trimming the Thin-Gage Sheet ..........................................
15
Trimming the Heavy-Gage Sheet .......................................
15
Depth-of-Draw ...................................................................
15
Methods of Forming ..................................................................
16
One-Step Forming .............................................................
17
Two-Step Forming with Prestretching ................................
19
Multi-Step Forming ............................................................
22
Other Variations .................................................................
25
1.5
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ix
x
Contents 1.6
2.
Thermoforming Machinery .......................................................
29
Heating Source ..................................................................
29
Forming Platform ...............................................................
31
Vacuum System ................................................................
32
Pressure System ...............................................................
36
Process Control .................................................................
36
Trimming and Cut Parts Handling ......................................
38
1.7
Heavy-Gage Thermoforming Machinery Specifics ..................
38
1.8
Thin-Gage Thermoforming Machinery Specifics .....................
46
1.9
References ...............................................................................
52
Polymeric Materials .............................................................
54
2.1
Introduction ...............................................................................
55
2.2
Network Nature of Polymers ....................................................
55
2.3
Addition and Condensation Polymerization .............................
57
2.4
Aromatic and Aliphatic Polymers .............................................
58
2.5
Molecular Weight and Molecular Weight Distribution ..............
58
2.6
Molecular Weight and Properties .............................................
61
2.7
Morphology and Properties ......................................................
63
2.8
Molecular Orientation ...............................................................
70
2.9
Chain Mobility and Polymer Stiffness .......................................
70
2.10 Stress-Crack Resistance ..........................................................
72
2.11 Gas Permeation ........................................................................
72
2.12 Copolymerization ......................................................................
73
2.13 Blends .......................................................................................
74
2.14 Adducts .....................................................................................
74
Plasticizers ........................................................................
74
Other Additives ..................................................................
76
Fillers and Reinforcing Fibers ............................................
77
2.15 Laminates .................................................................................
78
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Contents
xi
2.16 Stress-Strain Behavior of Plastics ............................................
78
2.17 Thermal Properties ...................................................................
82
Heat Capacity ....................................................................
82
Thermal Conductivity .........................................................
84
Thermal Diffusivity .............................................................
84
Thermal Expansion Coefficient ..........................................
87
2.18 Infrared Spectra ........................................................................
87
2.19 Summary ..................................................................................
96
2.20 References ............................................................................... 103
3.
Heating the Sheet ................................................................ 105 3.1
Introduction ............................................................................... 106
3.2
Energy Absorption by Sheet ..................................................... 106
3.3
Heat Transfer Modes ................................................................ 110
3.4
Incorporating Formability and Time-Dependent Heating ......... 115
3.5
Conduction ................................................................................ 121
3.6
Convection Heat Transfer Coefficient ...................................... 124
3.7
3.8
3.9
The Biot Number ...............................................................
125
Effective Radiation Heat Transfer Coefficient ....................
126
Constant Heat Flux ............................................................
127
Radiation Heating ..................................................................... 128 Black Body Radiation .........................................................
129
Gray Body – Emissivity ......................................................
134
Radiant Heater Efficiency – Constant Heat Flux Application ...................................................................
138
Real Heaters – Efficiencies ...................................................... 140 Radiative Heat Transfer Coefficient ...................................
144
Convection and the Heat Transfer Coefficient ...................
145
Rod Heaters ......................................................................
150
Long-Term Radiant Heater Efficiencies ................................... 151
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xii
Contents 3.10 Edge Losses – View Factor ...................................................... 152 Local Energy Input .............................................................
155
Pattern Heating ..................................................................
159
Zone, Zoned or Zonal Heating ...........................................
161
Heater to Sheet Distance ...................................................
162
3.11 Thin-Gage Sheet – Approximate Heating Rates ..................... 164 Constant Environmental Temperature Approximation ........
164
Constant Heat Flux Approximation ....................................
167
Thin-Gage Approximations – Comments ...........................
167
3.12 Heavy-Gage Sheet – Internal Temperature Control ................ 168 Constant Environmental Temperature ...............................
168
The Constant Heat Flux Case ............................................
172
The Thickness Effect .........................................................
174
Summary ...........................................................................
175
3.13 Equilibration .............................................................................. 176 Convection Heating ...........................................................
177
Constant Heat Flux ............................................................
179
Computed Equilibration Times ...........................................
180
The W-L-F Equation ..........................................................
181
The Arrhenius Equation .....................................................
182
Relating Shift Factors to Sheet Thickness .........................
182
3.14 Infrared-Transparent Polymers ................................................ 182 3.15 Computer-Aided Prediction of Sheet Temperature ................. 188 The Radiant Boundary Condition .......................................
192
3.16 Guidelines for Determining Heating Cycles ............................. 192 The Biot Number ...............................................................
193
Thin-Gage Guidelines ........................................................
193
Heavy-Gage Guidelines .....................................................
193
Intermediate-Gage Guidelines ...........................................
194
3.17 References ............................................................................... 194
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Contents 4.
xiii
Stretching the Sheet ............................................................ 197 4.1
Introduction ............................................................................... 198
4.2
The Stretching Concept ............................................................ 202
4.3
Polymer Hot Strength ............................................................... 208
4.4
4.5
Standard Tensile Tests ......................................................
208
Hot Tensile Tests ...............................................................
212
Hot Creep Tests ................................................................
213
Other Stretching Tests .......................................................
215
Temperature-Dependent Viscosity for Amorphous Polymers ......................................................................
216
Dynamic Mechanical Testing .............................................
222
Stress-Strain-Rate of Strain – Theory ...................................... 226 Elasticity – a Rationalization ..............................................
233
Strain Energy Function ......................................................
235
The Rivlin Form for the Strain Energy Function .................
236
The Ogden Form for the Strain Energy Function ...............
239
Viscoelastic Models ...........................................................
240
Available Stress-Strain Data .................................................... 242 Sensitivity of Models ..........................................................
247
4.6
The Importance of Polymer Material Properties ...................... 248
4.7
Practical Aspects of Stretching ................................................. 257 Funnel Test .......................................................................
260
4.8
Bursting Conditions .................................................................. 264
4.9
Sheet Sag ................................................................................. 266 Initial Sag ..........................................................................
267
Tensile Sag .......................................................................
268
The Catenary Sag .............................................................
269
Parabolic Sag ....................................................................
270
Relating Sag to Hot Sheet Strength ...................................
271
Sag – a Comment ..............................................................
276
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xiv
Contents 4.10 References ............................................................................... 277 Appendix 4.I: Biaxial Stretching of an Elastic Membrane ................... 282
5.
Cooling and Trimming the Part .......................................... 284 5.1
Introduction ............................................................................... 285
5.2
Overall Cooling Heat Balance .................................................. 285
5.3
Cooling the Formed Shape ...................................................... 287
5.4
Steady State Heat Balance ...................................................... 288
5.5
5.6
Interfacial Resistance ........................................................
289
Shape Factor .....................................................................
291
Convection Heat Transfer Coefficient ................................
293
Cyclic Heat Balance ................................................................. 302 Cooling the Free Surface of the Sheet ...............................
303
Cooling Thin Sheet in Ambient Air .....................................
303
Transient Heat Removal from the Sheet ............................
305
Quiescent Ambient Air .......................................................
305
Moving Ambient Air ...........................................................
307
Cooling on Nonmetallic Molds ...........................................
309
Transient Heat Transfer during Sheet Cooling on the Mold Surface – Computer Models ............................................ 314 Interfacial Air .....................................................................
5.7
5.8
5.9
318
Shrinkage .................................................................................. 320 Unconstrained Shrinkage ..................................................
321
Constrained Shrinkage ......................................................
325
Trimming ................................................................................... 329 Trimming Heavy-Gage Parts .............................................
331
Trimming Thin-Gage Parts .................................................
333
Mechanics of Cutting ................................................................ 334 The Trim Region ................................................................
336
Registering the Trim Site ...................................................
337
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Contents
xv
The Nature of the Cut ........................................................
338
Fracture Mechanics ...........................................................
340
Mechanical Chipping .........................................................
340
Multiple-Edged Tool or Toothed Saw Performance ............
342
Abrasive Cut-Off Wheel .....................................................
344
Toothless or Shear and Compression Cutting ...................
347
Fracture Mechanics in Trimming ........................................
347
Nibbling .............................................................................
355
Brittleness, Orientation and Trim Temperature ..................
358
5.10 Steel Rule Die ........................................................................... 359 Resharpening ....................................................................
362
Tabbing and Notching ........................................................
363
5.11 Punch and Die Trimming .......................................................... 364 Forged and Machined Dies ................................................
367
5.12 Drilling ....................................................................................... 367 5.13 Other Cutting Techniques ........................................................ 372 Thermal Cutting .................................................................
372
Water Jet Cutting ...............................................................
374
5.14 Trimming – a Summary ............................................................ 376 5.15 References ............................................................................... 379
6.
Thermoforming Molds ......................................................... 382 6.1
Introduction ............................................................................... 383
6.2
Prototype Molds ........................................................................ 384 Wood .................................................................................
385
Fiberboard .........................................................................
386
Plaster ...............................................................................
387
Plastic ................................................................................
389
White Metal .......................................................................
397
Nickel ................................................................................
400
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xvi
Contents 6.3
6.4
6.5
6.6
Production Molds ...................................................................... 400 Aluminum ..........................................................................
401
Steel ..................................................................................
402
Other Metals ......................................................................
403
Mold Coolant Channels ............................................................ 404 Mold Channel Flow ............................................................
405
Expansion ..........................................................................
406
Contraction ........................................................................
406
Sharp-Edged Orifice ..........................................................
406
Vent Holes ................................................................................ 411 Sizing Vacuum Systems – Steady State ............................
413
Sizing Vacuum Systems – Dynamic ..................................
414
Solenoid Valve Flow Resistance ........................................
416
Vent Hole Resistance to Flow ............................................
417
Vent Hole Diameter ...........................................................
423
Other Types of Vents .........................................................
427
Vent Hole Placement .........................................................
430
Surface Treatments .................................................................. 433 Surface Texture .................................................................
6.7
436
Plug Design Considerations ..................................................... 439 Plug Materials ....................................................................
439
Wood Plugs .......................................................................
441
Plastic Plugs ......................................................................
441
Metal Plugs ........................................................................
441
Plug Design Concepts .......................................................
445
6.8
Sheet Clamping ........................................................................ 448
6.9
Sag Bands and Sheet Supports ............................................... 451
6.10 Other Aspects of Mold Design ................................................. 451 Undercuts ..........................................................................
452
Encapsulation ....................................................................
453
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Contents
xvii
Moving Elements ...............................................................
454
Stripper Plates/Bars ...........................................................
455
Mold Releases ...................................................................
456
Web Breakers, Catchers and Chasers ...............................
457
Moats, Dams and Double Steps ........................................
458
Chamfers and Radii ...........................................................
459
Prestretching Restraints ....................................................
461
6.11 Efficient Use of Sheet ............................................................... 461 Heavy-Gage Sheet ............................................................
461
Thin-Gage Sheet ...............................................................
463
6.12 References ............................................................................... 467
7.
Parts Design ......................................................................... 470 7.1
Introduction ............................................................................... 471
7.2
Elements of Parts Design ......................................................... 471 Material Testing and Its Relevance to Part Performance ................................................................
473
Philosophy of Parts Design ................................................
476
Minimizing the Amount of Sheet to Be Reground ...............
478
Rules for Part Layout on Heavy-Gage ...............................
479
Rules for Multiple Part Layout on Thin-Gage .....................
481
Economics of Buying Sheet of Specific Size ......................
483
7.3
Prototyping as a Justification for Thermoformmg .................... 486
7.4
Draw Ratio ................................................................................ 488 Areal Draw Ratio ...............................................................
489
Linear Draw Ratio ..............................................................
494
H:D ....................................................................................
496
Rim and Lip Sheet for Female Cavities ..............................
499
Draw Ratio Usage – a Rationale ........................................
503
Mechanical Assists – Some Design Features ....................
503
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xviii
Contents Preblowing or Inflation – Comments ..................................
503
Plug Assist – Comments ....................................................
507
7.5
Computer-Aided Design in Thermoforming ............................. 507
7.6
Wall Thickness Prediction – a Justification .............................. 510
7.7
7.8
7.9
Geometric Element Analysis or GEA .................................
513
Finite Element Analysis .....................................................
521
General Comments on Plug Design ...................................
527
Plug Assist Analysis ..........................................................
533
Plug Design – Geometric Element Analysis .......................
536
Plug Design – Finite Element Analysis ..............................
539
Regrind ..................................................................................... 544 Material Property Deterioration on Regrind ........................
545
Property Value Loss – Experiment and Protocol .......................................................................
549
Cascading 100% Regrind ..................................................
553
General Guidelines for Part Design ......................................... 555 General Tips ......................................................................
555
Process Tips ......................................................................
556
Mold Tips ...........................................................................
557
Prestretch Tips ..................................................................
559
Part Design Tips ................................................................
561
Rim and Edge Designs ......................................................
569
Design – a Comment .........................................................
573
References ............................................................................... 574
Appendix 7.I: Draw Ratios for Truncated Cone .................................. 577 Appendix 7.II: Mechanical Property Loss in Regrind .......................... 579
8.
Producing Sheet and Film .................................................. 582 8.1
Introduction ............................................................................... 583
8.2
Forming Thin Films ................................................................... 584
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Contents 8.3
xix
Forming Sheet .......................................................................... 587 Single-Screw Extrusion ......................................................
588
Filtering the Polymer ..........................................................
591
Flow Improvement Devices ................................................
594
Pressure and Temperature in an Extruder .........................
596
Sheet Die Concepts ...........................................................
598
Gage Thickness Monitoring and Control ............................
602
Twin-Screw Extrusion ........................................................
604
8.4
Roll Stacks ................................................................................ 607
8.5
Sheet Trimming ........................................................................ 610
8.6
Take-Off and Take-Up Rolls ..................................................... 611
8.7
Residence Time and Residence Time Distribution through Extruder and Die ......................................................... 614
8.8
Drying ........................................................................................ 617
8.9
Producing Biaxially Oriented Sheet .......................................... 620
8.10 Multilayer Sheet Formation ...................................................... 623 Coextrusion .......................................................................
624
Lamination .........................................................................
628
8.11 Sheet Quality and Quality Control ............................................ 632 Sheet Dimensions .............................................................
637
Orientation .........................................................................
637
Sheet Squareness and Flatness ........................................
639
Moisture ............................................................................
640
Sheet Appearance .............................................................
641
Annoyance Factors ............................................................
642
Lamination .........................................................................
643
8.12 References ............................................................................... 644
9.
Newer Thermoforming Technologies ................................ 648 9.1
Introduction ............................................................................... 649
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xx
Contents 9.2
9.3
Thermoforming Crystallizing Polyethylene Terephthalate ............................................................................ 649 PET Crystallinity ................................................................
650
CPET Patents ....................................................................
652
Characterizing Polyethylene Terephthalate .......................
652
The Effect of Temperature on Crystallization during Sheet Extrusion .................................................
659
Cooling CPET on Chill Rolls ..............................................
662
Heating CPET in Roll-Fed Thermoformers ........................
666
Forming the Sheet .............................................................
666
Cooling the Formed Part ....................................................
668
Trimming Parts from Web ..................................................
670
Troubleshooting CPET Forming ........................................
670
Pressure Forming ..................................................................... 670 Thin Gage ..........................................................................
675
Heavy Gage ......................................................................
677
9.4
Forming Filled and Reinforced Polymers ................................. 679
9.5
Laminated Sheet Thermoforming ............................................. 687
9.6
9.7
Heating Multilayer Sheet ....................................................
687
Forming Multilayer Sheet ...................................................
691
Twin-Sheet Thermoforming ...................................................... 696 Simultaneous Twin-Sheet Forming ....................................
701
Sequential Twin-Sheet Forming .........................................
702
Seal Area – Adhesion ........................................................
704
Seal Area – Compressive Form .........................................
706
Seal Area – Design ............................................................
707
Polypropylene Thermoforming ................................................. 710 Sag Test ............................................................................
711
Modified Polypropylenes ....................................................
717
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Contents 9.8
9.9
xxi
Thermoforming Foam Sheet .................................................... 722 Cell Architecture – Actual v. Ideal ......................................
722
Radiant Energy Transmission ............................................
726
Internal Cell Gas Pressure .................................................
731
Forming Window for Foam .................................................
733
The Forming Equipment ....................................................
736
Other Forming Technologies .................................................... 738 Interdigitation .....................................................................
738
Sealed Air Cushion/Dunnage .............................................
740
9.10 References ............................................................................... 741
10. Set-Up Protocols, Troubleshooting, and the Economics of Thermoforming ............................................ 748 10.1 Introduction ............................................................................... 749 10.2 Setting up a Thermoforming Machine – Protocols .................. 753 A New Polymer ..................................................................
753
Setting up a New Mold .......................................................
758
Setting the Mold Stops .......................................................
761
Dry-Cycling the Mold .........................................................
761
Checking the Vacuum ........................................................
762
Attaching Cooling to the Mold ............................................
763
The Sheet Delivery System ...............................................
764
Setting the Oven Conditions ..............................................
765
Forming Step – Simple Vacuum Forming ..........................
766
Changing Temperature Conditions ....................................
767
Activating the Assists .........................................................
767
Pressure Boxes .................................................................
768
General Objectives ............................................................
768
10.3 Troubleshooting the Forming Process ..................................... 769
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xxii
Contents 10.4 Energy and Materials Cost ....................................................... 783 The Energy Audit ...............................................................
783
Cost of Extrusion ...............................................................
791
Cost of Regrind ..................................................................
793
Competitive Costs of Polymers ..........................................
793
10.5 General Processing Economics ............................................... 794 Rules of Thumb .................................................................
796
Global Production Costs ....................................................
798
Manufacturing Efficiencies .................................................
801
The Learning Curve ...........................................................
806
10.6 Isolated Venture Costs ............................................................. 808 10.7 New Venture Economics .......................................................... 819 Entrepreneurial Risks ........................................................
825
10.8 The Incremental Operation ....................................................... 831 10.9 Comparative Process Economics ............................................ 833 10.10 References ............................................................................... 843
Appendices Appendix A: Abbreviations for Thermoformable Polymers Referred to in Text .................................................................... 844 Appendix B: Typical Conversion Factors Used in Thermoforming (US Customary to Metric, Metric to US Customary) ............................................................................... 847 Appendix C: Glossary of Thermoforming Terms ................................ 849
Author Index ............................................................................... 855 Index ............................................................................................ 862
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1 Thermoforming—Definitions, History, Methods and Equipment
1.1 Introduction 1.2 History 1.3 Markets 1.4 Some Definitions Gage Clamping of Thin-Gage Sheet Clamping of Heavy-Gage Sheet Heating of Thin-Gage Sheet Heating Heavy-Gage Sheet Shaping Thin-Gage Sheet Shaping Heavy-Gage Sheet Trimming the Thin-Gage Sheet Trimming the Heavy-Gage Sheet Depth-of-Draw 1.5 Methods of Forming One-Step Forming Two-Step Forming with Prestretching Multi-Step Forming Other Variations 1.6 Thermoforming Machinery Heating Source Forming Platform Vacuum System Pressure System Process Control Trimming and Cut Parts Handling 1.7 Heavy-Gage Thermoforming Machinery Specifics 1.8 Thin-Gage Thermoforming Machinery Specifics 1.9 References
1.1
Introduction
Thermoforming is a generic term encompassing many techniques for producing useful plastic articles from flat sheet. In its simplest concept, thermoforming is simply the manual draping of a temporarily softened sheet over a simple mold shape. In one of its more advanced forms, it involves automatic high-speed indexing of a freshly extruded sheet having very accurately known temperature into a forming and in-situ trimming station, with integral web regrind and automatic parts counting, packaging and shipping. In another, it involves automatic placement, plug and/or pneumatic stretching and pressure forming, with multi-axis router trimming. Thermoforming is one of a family of processes that deal with the pressing or squeezing of pliable plastic into final shape. More than a century ago, celluloid or camphor-solvated cellulose nitrate, was the only malleable semi-synthetic plastic [I]. It was cut or rolled into sheet and made pliable with steam. When soft, it was squeezed into shape in matched dies or rolled into tubes and inflated against metal walls to produce parts. It was also draped over wooden forms. Cosmetic cases, baby rattles, and piano keys were typical of earliest thermoformed parts. The earliest processing of synthetic plastics, included common types of modern thermoforming, albeit restricted to one polymer and very limited processing conditions. Thermoforming always begins with a contiguous sheet of rubbery plastic. The sheet is produced from: • •
Resin liquid by casting as with PMMA, or Pellets or powder by: Calendering, as with PVC, Biaxially blowing film as with PE and PP, Extruding as with PS and ABS, Compression molding as with cellulosics and high temperature polyimides,
or by similar plastics processing techniques1. Thermoforming is differentiated by other processes in the following ways: •
•
1
From injection molding, where the initial resin state ispellet or powder and the shaping is done on the polymer as a liquid. As a result, the patented Monoblow process that injects a disk of plastic that is then compressed to a shape is not considered as a thermoforming variant [2]. From compression molding, where pressures are substantially higher than those employed in traditional vacuum or low pressure thermoforming and where the polymer is shaped as a liquid between matched metal molds. This differentiation blurs when thermoforming technologies are used to form continuous fiber-reinforced composites. The Allied process described in Chapter 9 is a classic example of this blurring. Glass-reinforced nylon 6 or PA-6 sheet is heated to temperatures Throughout the text, plastics are referred to in abbreviations. Thus PMMA is polymethyl methacrylate and so on. A list of common polymer abbreviations is given as Appendix A, at the end of the book.
above the polymer melt temperature, then forged at relatively high pressures of 150 to 1500 lbf/in2 or 0.1 to 1 MPa [3]. Nontraditional thermoforming processes include the Dow scrapless thermoforming process or STP, where the extruded sheet is cut into squares that are then heated and forged into shapes. Other non-traditional and newer processes are discussed in Chapter 9.
1.2
History
Keratin, as a component in tortoise shell, was probably the first material to be thermoformed [4,5]. Keratin is also found in animal horn and hoof. It can be softened by immersing it in boiling water or oil. The sheet is then manually draped over a form and held until cool. Natural cellulose, primary element in tree bark, was shaped in a similar fashion by native Americans. Although others experimented with natural and extracted cellulosics in the 1800s, J. W. Hyatt is credited with first recognizing the full commercial potential of camphorsolvated cellulose nitrate, which he called "celluloid". Most nineteenth century semi-synthetic plastic products were produced of celluloid or products of similar recipes simply by drape forming softened sheet. Sharps piano keys, formed over captive wooden blocks, are an example. A chronology of the early days in plastics as they pertain to thermoforming is given in Table 1.1. Modern thermoforming began about 60 years ago, shortly before, during, and shortly after the second world war, with major developments in two important areas. Research in thermoplastic resin chemistry led to commercialization of extrusion grade flexible PYC or FPVC, CA and PS and the development of cell-cast PMMA. And continuous forming was achieved with the invention of the screw extruder and the roll-fed thermoformer. These breakthroughs allowed a wide variety of prewar domestic products, particularly thin-gage packages, to be developed. This in turn prepared formers for war product developments such as airplane canopies and war survey relief maps. The packaging industry adopted thermoforming as a basic process in the late 1940s to such an extent that the thermoformed package was considered the most significant packaging development of the 1950s decade [6]. In the 1970s, demand for convenience food containers, ovenable portion servings, and more ductile disposable drink cups spurred development of foam PS, CPET, and PP pressure forming processes. Shower stalls, tub surrounds, and refrigerator liners were thermoformed from heavy-gage sheet. The development of the interstate system led to production of large, light-weight illuminated plastic signs and fast food franchises adopted thermoformed plastics as a way of producing such signs. Engineers developed ways of forming plastic sheets for the transportation industry from reinforced and fire-retardant polymers. Ahead lies further opportunities to replace injection molded plastics in many applications such as packaging lids and containers, welded steel in food cans, glass in jars, aluminum in beverage cans, and hand-laid thermoset
Table 1.1 Chronology on Thermoforming1 Period
Event
Prehistory—Egypt
Heating tortoise shell, keratin, in hot oil, then shaping to produce food containers. Heating tortoise shell, keratin, in hot water, then shaping to produce bowls. Heating tree bark, natural cellulose, in hot water, then shaping to produce bowls, boats, canoes. Extrusion process commercialized from forerunners of today's plastics. Alfred P. Critchlow, Florence MA develops molding presses, dies for gutta-percha, shellacs. Gutta-percha replaces ivory for billiard balls. First moldable plastic, fibrous cellulosic pulp and gum shellac by Peck. Cellulose nitrate solvated with camphor to produce "Parkesine" by Alexander Parkes. Celluloid, molding grade Pyroxylin by John Wesley Hyatt. Hydraulic planer for cutting thin sheets by Charles Burroughs Co., MJ, USA. Celluloid tubes steam-heated, placed in metal form, inflated with steam pressure yielding blow molding, pressure forming. Compression molded phenolic bobbin ends, Richard Seabury, Boonton Rubber, Boonton NJ. Sharps piano keys drape-formed over captive wooden cores. Bottle formed from two thermoformed halves by Fernplas Corp. Relief maps for US Coast & Geodetic Survey. Blister pack of cellulose acetate. Roll-fed automatic thermoformer developed by Clauss B. Strauch Co. Cigarette tips, ice-cube trays automatically thermoformed. Cast PMMA acrylic thermoformed for fighter/bomber windows, gun closures, windscreens. Standard mold bases, Detroit Mold Engineering (D-M-E). Cast PMMA acrylic bathtubs thermoformed by Troman Bros., England. Skin-packaged products shown at Hardware Manufacturers Association, Chicago. Thermoformed ABS automobile body by Borg-Warner.
Prehistory—Micronesia Prehistory—Americas 1845 1850s 1856 1862 1868 1870s 1870s 1907 1910 1930 1930s 1938 1938 1938 1942 1942 1948 1954 1970 1
Adapted from [4,5,32]
composites in aircraft and other transports. The prospects for advanced thermoforming systems are discussed in detail in Chapter 9.
1.3 Markets A best estimate of the entire US consumption of thermoformed shapes in 1992 is about 1181 Mkg or 2600 MIb. About 800 Mkg or 1760 MIb is thermoformed into disposables. The fraction of plastics thermoformed into disposables has dropped steadily in the past decade from about 74% in 1983-1984 to about 68% today [7-9].
Table 1.2 US Polymers Converted via Thermoforming Polymer
Amount thermoformed (Mkg) 1962
1969
1977
1983-1984
ABS PMMA Cellulosics LDPE HDPE PP** PS PVC PET Other*
NA NA 8 NA NA NA 69 4 NA 1
40 21 5 0.7 7 1 166 13 NA NA
70 36 8 0.4 10 8 392 24 NA NA
127 38 4 0.6 26 22 480 45 40 NA
Totals
82
254
544
782
1992 202 42 5 0.7 59 72 640 60 80 20 1181
1995 240 50 5 0.8 87 115 720 72 110 50 1450
Annual growth (%) 1984-1992 6 2 0 0 11 16 4 4 9
5
* Includes K-resin, PAN, XT, TPO polymers ** Does not include stampable PP for automotive applications NA = Not available (not included)
An estimate of the amounts of plastic consumed in thermoforming in the US in the 30 years from 1962 to 1992 is given in Table 1.2. The data are obtained from several sources [8-10]. In 1969, the industry was projected to grow at about 8.5% to 9% per year during the 1970s. It was then estimated that 527 Mkg or 1180 MIb would be consumed by 1978 (Fig. 1.1). About 550 Mkg or 1230 MIb was actually consumed in 1977. In 1969, it was predicted that consumption in 1984 would be 780 to 830 Mkg or 1750 to 1860 MIb. In 1986, it was determined that about 773 Mkg or 1732 MIb were actually consumed in 1983-1984 [H]. In 1986, it was predicted that consumption would reach 1045 Mkg or 2300 MIb in 1992. The prediction is about 13% below actual consumption (Fig. 1.1). The 1986 projection also indicated that 1290 Mkg or 2840 MIb would be thermoformed in the year 2000. From Fig. 1.1, current, 1994 projection indicates 1860 Mkg or 4100 MIb will be consumed in the year 2000. This is a continuing annual growth rate of more than 5%. As seen in Table 1.2, polystyrene accounts for more than half the plastic thermoformed into parts. The growth in this established polymer is less than 3% per year. As expected, PP and PET are experiencing double digit annual growth as new polymers and forming processes are developed. Surprisingly, HDPE growth is also very high, with outdoor products contributing to the growth. As an example, there were no HDPE truck bed liners used in the early 1980s. In 1992, the size of this market alone is approaching 23 Mkg or 50 MIb. Cellulosics continue to lose market share to PP, PVC and PS, particularly in packaging. In 1984, 7 Mkg or 16 MIb thermoplastic polyesters or PETs were thermoformed. Only a very small fraction, less than 1%, was crystallized PET. Since the development of CPET thermoforming processes in the 1980s, CPET has become a staple in the disposable food serving and heating tray and dish markets. In 1984, it was estimated that the development of CPET would spur the consumption of PET to double in five years, to 14 Mkg or
1994 Projection (This Edition)
US Production, Million Ib
1986 Projection (First Edition)
Year Figure 1.1 US Production of thermoformed products. Adapted from [7-11]
Table 1.3 Approximate Conversion Level of Thermoplastic Polymers to Thermoformed Produces1 Polymer
Amount of polymer converted to sheet (%)
Amount of sheet thermoformed (%)
Total amount of polymer formed into product (%)
ABS PMMA Cellulosics HDPE LDPE PP PS PVC
25 50 25 2 0.25 1 30 10
60 30 50 30 5 25 65 20
15 15 12.5 0.6 0.01 0.25 19.5 2.0
1
Adapted from [7,8]
32 MIb. In actuality, in 1992, this market is about 70 Mkg or 154 MIb, a ten-fold increase in less than a decade. In 1992, the consumption of CPET is estimated to be about 19 Mkg or 42 MIb, or about 27% of the total thermoformed PET consumption. About half of all sheet stock is converted to product by thermoforming [12]. The amount of resin converted into sheet varies from about half of all PMMA polymers to less than 1% of all LDPE polymers (Table 1.3). Only about 5% of all LDPE sheet and film is converted to product by thermoforming whereas 65% of all polystyrene sheet is converted. These are mid-1980s data but the percentages have held relatively constant since the 1960s. Similarly, major markets have remained relatively obvious for nearly two decades. Major new packaging markets continue to be in disposables, as illustrated by the development of PP and CPET food packages and the commercial realization of convenience food foam carryout containers. Applications have also broadened to include packaging of heavier items such as power tools and medical items such as critical care emergency packages. Nearly all packaging applications rely on roll-fed thin-gage sheet stock. In heavy-gage discrete sheet forming, the market traditionally has focussed on economic production of a few, large pieces. As a result, applications include: • • •
Major appliance components, such as refrigerator cabinet and door liners, Recreation products such as swimming and wading pools, Vehicles such as snow mobiles and all-terrain vehicles, automotive inner-door panels, truck and tractor cab kick panels, • Home products such as tube and shower stalls that are backed with GR-UPE, luggage shells, and • Display items such as advertising, exterior signs and point-of-purchase stands.
Table 1.4 Markets for Thermoformed Products Packaging and related items Blister packs, point-of-purchase containers Bubble packs—slip sleeve, vacuum carded containers Electronics—audio/video cassette holders Tool cases—hand, power Cosmetics—cases, packages Foams—meat, poultry trays Unit serving—foodstuffs Convenience—carry-out, cooking-box trays Convertible-oven food serving trays Wide-mouth jars Vending machine hot drink cups Cold drink cups—beer, soda Egg cartons Wine bottle protectors Produce separators—apples, grapefruit Portion—medical unit dose Form-fill-seal—jelly, crackers, nuts and bolts (Continued)
Table 1.4 (Continued) Vehicular Automotive door innerliners, headliners Automotive utility shelves, liners Automotive instrument panel skins Aircraft cabin wall panels, overhead compartment doors Snowmobile shrouds, windshields Motorcycle windshields, farings, scooter shrouds, mudguards All-terrain vehicle exterior components Golf cart shrouds, seats, trays Tractor shrouds, door fascia Camper hardtops, interior components such as doors, cabinet tops Truck cab door fascia, instrument cluster fascia Recreational vehicle interior components, window blasters Industrial Tote bins Pallets, single deck, double deck Parts trays, transport trays Equipment cases Building products Shutters, window fascia Skylights, translucent domes Exterior lighting shrouds Storage modules—bath, kitchen, pantry Lavys Bath and shower surrounds, GR-UPE backed Soaking tubs, GR-UPE backed Retrofit shower components, shower trays Others Exterior signs Advertising signs, lighted indoor signs Swimming and wading pools Tray, baskets, hampers, carrying cases Luggage Gun cases, golf club cases Boat hulls, surf-boards, with PUR foams Animal containers Prototype concepts for other plastic processes
The recent rediscovery of pressure forming of sheet against a female mold offers an entre into the economically important market of business machine housings [13]. Some major markets are listed in Table 1.4 [14]. The sizes and annual percent growth rates or APR are given in Table 1.5 for several of these markets. Most of the fully developed, mature thermoforming markets are developed around amorphous polymers such as PVC, PS, ABS and PMMA. These polymers are processed quite successfully over rather wide temperature ranges. Amorphous polymers are usually quite forgiving in this respect. Crystalline polymers and reinforced amorphous polymers, on the other hand, have narrower forming
Table 1.5 Selected Growth Markets for Thermoforming Market
77
Thermoforming machinery (US$ x 106) [35]
22
78 79
80
81 82
83
84
85
86
87
88
89
90
91
91
Rigid plastic packaging (US$ x 109) [36]
92
93
94
95
96
97
98
99 Average annual growth (%) (years)
121
5.9 (94/89)
6.6
Plastic containers ( x l O 9 units) [37]
27.2
38
51
6.5 (95/85)
Multilayer containers ( x l O 9 units) [37]
0.3
11
29
58.0 (95/85)
160
231
Business machine housings ( x l O 6 Ib) [38]
55
115
178
Retortable plastic containers ( x l O 9 units) [39] Automotive sheet stamping ( x 106 Ib) [40]
0.25
4
0.3
0.6
1.1
25
8.6 (90/85) 2.8
62 (91/86)
60
19 (91/86)
Polystyrene in packaging ( x l O 9 16) [41]
2.38
Nucleated PP—sheet extrusion ( x l O 6 Ib) [42]
3.3
2.74
3.1
10
2.8 (95/90)
25 (96/91)
Barrier packaging polymers ( x l O 6 Ib) [43]
940
1475
9.4 (95/90)
Modified atmosphere packaging ( x l O 6 Ib) [44]
800
1400
11.8 (95/90)
Controlled atmosphere packaging ( x 106 Ib) [44]
400
800
14.9 (95/90)
(Continued)
Table 1.5 (Continued) Market
77
78 79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
Average annual growth (%) (years)
PP sheet—non-automotive ( x l O 6 Ib) [45]
44
141
21 (90/84)
PP sheet—auto/appliance ( x l O 6 Ib) [45]
35
125
24 (90/84)
Plastics in appliances ( x l O 6 Ib) [46] Microwavable plastic containers ( x l O 6 units) [47]
96
Non-disposable polyolefin foam ( x l O 6 Ib) [48]
20
Medical plastics ( x l O 9 Ib) [49]
0.65
Plastics in packaging (US$xl0 9 ) [52]
310
1.20
4.8 (92/89) 2.86
1.16
1.19
1.55
6.9 (94/89)
5.4 (94/89)
1.30
7.3
4.1 (97/92)
26 (93/88)
23
2.05
Transport plastics ( x l O 9 Ib) [50] Plastics in appliances (US$xl0 9 ) [51]
1047
888
2.4 (91/86) 8.1
2.1 (94/89)
windows, usually require higher forming pressures, and/or usually cannot be consistently formed on conventional thermoforming equipment. Only recently has the forming industry begun to apply fundamental processing principles to the development of machinery capable of holding accurate sheet temperatures and forming pressures.
1.4
Some Definitions
The technology of thermoforming is rapidly changing. Old ideas about process limitations are being challenged daily. In 1992, one machinery manufacturer said that: "More innovations have been made in thermoforming machinery in the last half-dozen years than in all the years before." [15].
As noted below, machinery innovations include: • • • •
Improved and more reliable ways of clamping sheet, Improved heaters, Improved heat distribution patterns, Adaptation of infrared sensors for monitoring and controlling sheet residence time in ovens, • Improved clamping systems, • New plug assist materials, • Better control of stretching forces and pressures, • Improved trim dies, and • Many new mold materials and mold making techniques. Of course, innovations are not just restricted to machinery. The past decade has seen extensive efforts to produce uniform-property extruded sheet, newer polymers with superior sag resistance and oxidative resistance, regrind monitoring techniques and computer programs to predict time-dependent sheet temperature and local wall thickness. However, there are certain guidelines about the thermoforming process that are relatively generic. For example, thermoforming has become economically important since it offers processing advantages over competitive processes such as: • • • •
Accumulator blow molding, Injection blow molding, Rotational molding, and Injection molding.
Relatively low forming pressures are needed and so mold costs are low and products of relatively large size are fabricated economically. Parts with very small thicknessto-area ratio are fabricated. For thin-walled products, fabrication time is very short, making the process economical for products requiring high multiplication factors.
For a few thick-walled parts, molds are made of wood, plaster or other easily shaped, relatively inexpensive materials. Mold fabrication time and thus lead time are very short. Thermoforming is the method most usually selected for prototype and display products to be made of other processes.
Gage Typical thermoforming steps are: • • • • •
Clamping, Heating, Shaping, Cooling, and Trimming.
The general process of thermoforming is loosely separated by sheet thickness or gage. There are two broad categories—thin-gage and heavy-gage. Recently, sub-categories have been introduced to further classify the process. Thin-gage thermoforming means that the sheet thickness is less than about 0.060 in or 1.5 mm. This category is further classified into: • •
Film forming, where the sheet thickness is less than about 0.010 in or 0.25 mm. Thin sheet forming, where the sheet thickness is between about 0.10 in or 0.25 mm and 0.060 in or 1.5 mm.
Heavy-gage thermoforming means the sheet thickness is greater than about 0.120 in or 3 mm. This category is further classified into: • •
Heavy sheet forming, where the sheet thickness is between about 0.120 in or 3 mm and about 0.400 in or 10 mm. Plate forming, where the sheet thickness is greater than about 0.400 in or 10 mm.
There is a gray area between thin-gage (< 0.060 in or 1.5 mm) and heavy-gage (> 0.120 in or 3 mm). In some instances, sheet in this mid-gage range of 0.060 in to 0.120 in or 1.5 mm to 3.0 mm behaves as if it is thin-gage, and in others, as if it is heavy-gage. This gray area is most apparent during handling of the sheet, heating the sheet and trimming the part from the web. Polystyrene and polyolefln foam sheet thicknesses are usually greater than 0.120 in or 3 mm but these foams are usually treated as thin-gage sheet stock.
Clamping of Thin-Gage Sheet Thin-gage sheet is usually supplied to the former in rolls. The majority of packaging applications such as blister pack, form-fill-seal packaging, foam sheet forming and biaxially oriented forming uses thin-gage sheet. Formers that use roll sheet stock are
called roll-fed or continuous sheet formers. Clamping is by parallel continuous loop chain-fed pins or pin-chains that pierce the sheet at 1 in or 25 mm intervals at about 1 in or 25 mm from each edge. For high-temperature forming of CPET or PP, the rails are shielded from the sheet heating source or are actively cooled. The edges of the sheet and the plastic between the formed product are trimmed, reground and reextruded into sheet for forming. Clamping of Heavy-Gage Sheet Heavy-gage sheet is usually supplied as cut, stacked and palleted sheet. The demand for large numbers of large, heavy-wall parts such as refrigerator door liners and vehicle interior components, has led to the development of an in-line heavy-gage sheet extrusion and thermoforming concept (Fig. 1.2) [16]. The sheet extruder is placed in-line with the thermoformer, thus obviating problems associated with handling cut-sheet materials. Formers that use discrete heavy-gage sheet are called cut-sheet formers. Cut-sheet clamping frames are usually held closed with mechanical spring-loaded toggle clamps or pneumatic hold-down bars. Shuttle clamps are also used. Heating of Thin-Gage Sheet There are three ways of heating sheet: Conduction, where the sheet is placed in direct contact with the heating medium, such as a hot plate, Convection, where the sheet is heated with hot air, and Radiation, where infrared heat from metal wires, ceramic plates, or gas-fired combustion is the primary means of heating the sheet. Thin-gage, roll-fed sheet is usually heated by passing the sheet between banks of infrared radiant heaters. Combinations of radiation and convection heating are used
Figure 1.2 In-line heavy-gage sheet extrusion and thermoforming line—Cannon-Shelly [16]
as well. These are detailed in Chapter 4. Most plastics formed today, such as PS, PVC and ABS, are formed at relatively low temperatures such as 2500F to 4500F or 1200C to 2300C.
Heating Heavy-Gage Sheet Intense energy input from radiant heaters is unwarranted and is potentially a problem for heavy-gage sheet. Conduction of the energy from the surface of the sheet to its interior controls the heating time. As a result, heavy-gage sheet is frequently heated with forced convection hot air or reradiated energy from fine mesh metal screens or hot plates. Heater types and temperatures are selected on the basis of optimizing the amount of energy transferred to the sheet per unit time.
Shaping Thin-Gage Sheet In the earliest days of thermoforming, the rubbery sheet was manually stretched or draped over a male mold. Drape forming or male mold forming, requires no forming pressure and no difference in pressure across the sheet thickness. Certain aspects of drape forming are used today, whenever male portions of female molds are employed. Vacuum forming is the application of differential pressure across the sheet thickness of up to 0.1 MPa or 15 lbf/in2 or one atmosphere absolute. In modern commercial machines, the applied vacuum is on the order of 0.05 to 0.09 MPa or 7.3 to 14 lbf/in2. Since thin-gage sheet surface-to-volume ratio is very large, thin-gage sheet loses heat to its surroundings very rapidly. As a result, thin-gage sheet is usually formed very rapidly (in seconds). Furthermore, more than one part is formed at a time. Special clamps called cavity isolators are used to minimize nonuniformity in individual part wall thickness due to polymer pulling from one cavity to another during forming. Foams are normally very resilient or stiff at their forming temperatures and so matched die molding is used.
Shaping Heavy-Gage Sheet Drape forming and vacuum forming are common ways of stretching heavy-gage sheet as well. Usually the mold has a single cavity. Sheet manipulation or prestretching with air or with mechanical assists called plugs is a common way of redistributing the plastic across the mold surface to minimize thin spots. In addition, pressure forming has been rediscovered. Historically, steam pressure was used to force celluloid against mold surfaces [17]. Air is used today in place of steam [18]. Although forming pressures to 3.5 MPa or 5001bf/in2 are used when shaping continuous fiber-reinforced composites, the pressure forming range of 0.14 to 0.56 MPa or 20 to 80 lbf/in2 is commercial with 1.4 MPa or 200 lbf/in2 considered the practical upper limit. Pressure forming is combined with vacuum forming to gain additional differential
Figure 1.3 Roll-fed thin-gage thermoforming line with in-line trimming station—BattenfeldGlencoe
pressure and to minimize air pockets between the mold and the sheet. Pressure forming is best suited to heavy-gage sheet forming into female molds. Higher forming pressures require more substantial mold construction. This increases the mold cost and the lead time. Trimming the Thin-Gage Sheet Thin-gage sheet can be trimmed in the mold or in a separate in-line hydromechanical trimming device. A camel-back or hump-back trimmer is shown in line with a roll-fed former in Fig. 1.3. Trimming the Heavy-Gage Sheet On occasion, heavy-gage sheet is also trimmed in the press. The more common trimming scenario is the transfer of the sheet from the forming press to a trimming fixture. Trimming follows one of the following: • • • •
Manual with a hook-knife or hand-held router, Manual with a bandsaw, Automatic with a multi-axis trimming fixture, or Automatic with a water jet or laser.
Depth-of-Draw Historically, thermoforming rules-of-thumb are based on the depth-of-draw of a given polymer into a given mold configuration. The depth of draw concept is loosely
understood among formers as the ratio of the depth a sheet could be drawn into a female mold to the minimum dimension at the rim. It is frequently given the notation h\d. Unfortunately, this definition is easily misinterpreted, is vague for non-cylindrical shapes, and does not truly describe the stretching process. Other definitions based on areal draw ratio and linear stretching are more accurate, as discussed in Chapter 7. For reference, the areal draw ratio is the ratio of the area of the formed sheet to that of the unformed sheet. The linear draw ratio is the length of an imaginary line drawn on the formed sheet to its original length.
1.5
Methods of Forming
In its simplest form, thermoforming is the stretching of a heated rubbery sheet into a final shape. As the sheet is stretched against the mold surface, it stops drawing. As a result, the final part has thick walls where the sheet touched the mold first and thin walls where it touched last (Fig. 1.4). In many thin-gage forming applications, the extent of sheet that is stretching is small and so the areal draw ratio is small. The package integrity and durability are therefore uncompromised. Typical applications are in packaging areas such as blister and bubble packs, form/fill/seal packages and fast food containers and picnic plates. If a high degree of stretching is needed, as with disposable drink cups or for heavy-gage sheet forming, simple stretching techniques are insufficient. The methods of forming are divided into the number of sequential steps needed to form the part once the sheet is at the forming temperature.
Figure 1.4 Wall thickness variation during drawdown in simple female vacuum forming
Sheet
Mold
Figure 1.5 Drape forming onto a positive or male mold
Male or Positive Forming
One-Step Forming There are at least five types of one-step forming: •
In drape forming, Fig. 1.5, the clamped, heated rubbery sheet is either lowered onto the male mold or the mold is raised into the sheet. The sheet in contact with the mold does not stretch. For modern drape forming, the air trapped between the sheet and the mold is evacuated as the mold penetrates and stretches the sheet against the mold flange. Either vacuum or air pressure is used to produce the differential pressure needed to force the sheet against the male mold. In drape forming, the formed part has a thick bottom and thin sidewalls. The part is thinnest at the rim. Drape forming is also called male molding. • In vacuum forming, Fig. 1.6, the clamped, heated rubbery sheet is sealed against the rim of the female mold. Vacuum is then applied. The differential pressure presses the sheet against the mold surface. As noted before, the formed part has
Mold Sheet
Figure 1.6 Vacuum forming into a negative or female cavity
Negative or Female Forming
Air Pressure Pressure Box Sheet Clamp Mold
Evacuation or Vacuum Pressure Forming Figure 1.7 Pressure forming
a thick rim and is thinnest in the bottom corners. This is also called cavity forming or female molding. • Pressure forming, Fig. 1.7, is similar to vacuum forming. A pressure box is fitted over the sheet as it is held against the mold rim and positive air pressure is used to push the sheet into the mold corners. Since air pressure to 1.4 MPa or 200 lbf/in2 is used, the pressure box must seal against the free surface of the sheet. Pressure forming is used for difficult-to-form roll-fed thin-gage polymers such as PP and for production of highly detailed heavy-gage parts [18]. • In free blowing, Fig. 1.8, the clamped heated rubbery sheet is stretched with air into a free-form shape. The amount of air pressure is controlled with a photocell that senses the height of the expanding bubble. Since the environmental air is slightly cooler than the sheet, the sheet cools in the free-form shape. This
Lamp
Bubble
Sheet
Photoelectric Eye
Clarnp Mold
Inflating Air Free-Blowing Sheet Figure 1.8 Free-blowing to produce domes
Top Mold Half
Sheet
Clamp
Bottom Mold Half
Matched Molds Advancing on Hot Sheet
Pressure Applied to Shape Part Figure 1.9 Matched die molding with trapped sheet formed at applied pressures less than 1 MPa or 150 lbf/in2
technique was pioneered for aircraft gun enclosures. Since the sheet does not touch a solid surface during forming, it remains mar-free. The bubble wall thickness is quite uniform except near the clamping area. Freely blown roll-fed thin-gage bubbles are used for blister packs. • Matched die molding, Fig. 1.9, is a common way of forming shapes from relatively stiff polymers, such as PS foam or filled polymers. The clamped heated rubbery sheet is positioned between two mold halves. As the mold halves close, vacuum is applied to the female half of the mold to assist with forming. Part wall thickness depends on the mating tolerances of the two mold halves. Appreciable material movement is possible if applied forces are relatively large. Usually the applied pressures do not exceed about 1 MPa or 150 lbf/in2 and are usually about 0.34 MPa or 50 lbf/in2. Two-Step Forming with Prestretching Multi-step forming was developed primarily for heavy-gage sheet where single parts are often quite complex and deep and where cost considerations make wall thickness uniformity a significant design parameter. In thin-gage thermoforming, forming times are very short and shapes are relatively simple. Until a few years ago, thin-gage
forming was restricted to one of the one-step techniques described above. In the 1970s, the development of plug assisted pressure forming of PP below its melting temperature led the way to highly automated multi-step forming of thin-gage roll-fed sheet. The first step in multi-step forming is usually a form of sheet stretching, such as plug assist or billowing. The prestretched sheet is then pressed against the mold surface. Some examples of multi-step forming follow: •
There are many variations of bubble or billow prestretching. The first step is to pneumatically inflate the clamped heated rubbery sheet to a controlled height with internal air pressure. Typically the differential pressure is 0.014 to 0.055 MPa or 2 to 8 lbf/in2 gauge. The bubble height is controlled either by touching a microswitch or by intercepting a photoelectric eye. At this point, the mold can interact with the stretched sheet in one of several ways: • In billow drape forming, Fig. 1.10, the male mold is pressed into the top of the prestretched sheet. This technique yields a part with wall thicknesses that are much more uniform than that obtained with straight drape forming. • When a female mold is used, in billow vacuum forming, Fig. 1.11, the differential pressure that has inflated the bubble is reversed. This causes the prestretched sheet to snap into the female mold. Again, the part wall thickness
Top Platen
Mold
Sheet
Vacuum or Exhaust
Bilow Clamp
Pressure Box
Inflating Air Billow Prestretching With Mold Motion
Pressurized Air Vacuum/Pressure Forming
Figure 1.10 Billow drape forming, with either vacuum or applied air pressure shaping the sheet against the mold surface
Bubble Sheet Gasket Clamp
Mold
Vacuum Inflating Air Billow Prestretching
Vacuum Forming
Figure 1.11 Billow vacuum forming
is much more uniform than that obtained with conventional vacuum forming. The eversion of the bubble can be tricky, so this technique is difficult. • If vacuum is used to pull the bubble, a vacuum box is needed (Fig. 1.12). The male mold is immersed or plunged into the prestretched bubble and the vacuum released and air pressure applied. The bubble then snaps against the mold. The technique is called vacuum snap-back forming. The billow drape forming and the vacuum snap-back forming methods work well as pressure forming techniques as well. • The heated rubbery sheet can also be stretched with a mechanically driven plug. There are several plug assisted methods: Prestretching Into Vacuum Box
Mold Plunged Into Billow
Mold
Clamp
Sheet
Draw Box Billow
Vacuum Figure 1.12 Vacuum snap-back forming
Pressurized Air
Platen Plug
Sheet Clamp Mold Plug Moving Into Hot Sheet
Plug Bottoming Out
Vacuum Forming Vacuum
Figure 1.13 Plug-assisted vacuum forming into a female mold
•
• •
The most common form of plug-assisted thermoforming is plug assisted vacuum forming with a female mold (Fig. 1.13). The sheet is prestretched by pressing the plug into it and forcing the sheet toward the bottom of the female mold cavity. Vacuum is then applied to pull the sheet against the mold surface. If the sheet is forced against the female mold surface with air pressure applied through the plug, the technique is known as plug assist pressure forming (Fig. 1.14). Plug-assisted drape forming onto a male mold (Fig. 1.15) is used when the draped sheet must be tucked into three-dimensional corners or into an undercut. It is also used to stretch plastic sheet away from a male portion of a female mold to minimize webbing.
Multi-Step Forming Billow forming and plug assist forming are occasionally combined with drape forming and vacuum forming to obtain unique wall thickness distributions. One example is reverse draw forming with plug assist. Fig. 1.16 illustrates the multiple step process, where a bubble is blown first. The plug is then plunged into the bubble, everting it under control. Once the plug has stretched the bubble nearly to the female mold bottom, vacuum or pressure is applied to force the sheet against the mold surface. This technique requires much patience since a stable bubble without excessive stretching is key to uniform and consistent part wall thickness distribution. Fig. 1.17 illustrates the male mold variation of this, with the mold initially acting as the plug. This technique is sometimes called pressure bubble immersion forming or just immersion forming. Again, the bubble can be formed with vacuum in a vacuum box that also serves as a pressure box for pressure forming. Table 1.6 [19] summarizes many aspects of the thermoforming process.
Plug Platen
Air Pressure
Gasket Ring Plug Sheet Clamp Mold Exhaust Ring Plug Moving Into Hot Sheet
Pressure Balance During Plugging
Air Pressure
Vacuum Vacuum/Pressure Forming Figure 1.14 Plug-assisted pressure forming, using a ring plug
Individual Plug Travel
Clamp Travel
Male Mold
Figure 1.15 Plug-assisted drape forming, using a wire frame plug
Plug
Bilow Sheet Clamp Mold
Vacuum Inflating Air Plug Immersion Into Billow
Vacuum Forming
Figure 1.16 Reverse-draw forming with plug assist
Mold Perimeter Clamp Sheet Clamp Sheet Pressure Box Sheet Clamp-Down Hot Sheet Between Blow Box and Mold
Inflating Air
Prestretching
Pressurized Air Vacuum/Pressure Forming
Figure 1.17 Pressure bubble immersion forming or immersion forming
Table 1.6 Characteristics of the Thermoforming Process1 Mold configuration
Process
Male Vacuum forming Drape forming Matched mold Inflation-plug assist vacuum forming Plug assist Vacuum snap-back Inflation snap-back Trapped sheet, pressure Slip forming 1
Plug assist
Inflation
X X
X
Female X
X X Plug Plug X
X X X Vacuum Pressure X X
X X Mold Rises
Adapted from [19]
Other Variations In order to form certain types of polymers, techniques other than those discussed above have been devised: •
Trapped sheet forming, Fig. 1.18, is used when: The polymer is thermally sensitive, such as certain types of PVC, The polymer is excessively saggy, as with PP and certain types of LDPE and LLDPE, The polymer sheet is highly oriented, as with oriented PS and PP, The sheet is flocked or metallized on one side, The sheet is laminated with a temperature-sensitive adhesive, Vacuum Blowing Air Electrically Heated Platen
Slotted or Porous Blow Plate
Sheet Gasket
Clamp Mold
Air Pressure Sheet Held Against Heater
Exhaust or Vacuum Sheet Drawn/Blown Into Mold
Figure 1.18 Trapped sheet forming with heating against a slotted or porous heated blow plate
The sheet contains wires or printed circuits that are temperature-sensitive, The sheet is very thin and printed or embossed on one side, or The sheet is less than about 0.005 in or 0.13 mm. The clamped sheet is held against a heated plate until the polymer reaches its forming temperature. Pressure is then applied through holes drilled in the plate, forcing the sheet away from the plate and against the female mold. Alternately, vacuum is applied, sucking the sheet away from the heater and against the mold. The plates are heated with electric rod heaters. Although drilled plate is usually used, there is growing interest in porous bronze or stainless steel plates. Zonal or pattern heating is possible by using insulating plate sections that are heated to different temperatures. • In slip forming, the heated rubbery sheet is not tightly clamped. As the differential pressure is applied, instead of the sheet being stretched, it is drawn from the clamp, over the mold rim and into the cavity. At a predetermined time, the sliding is stopped by increasing the clamp force. This is done by compressing springs as shown in Fig. 1.19, or by using cam-type rockers that squeeze against the sheet after a predetermined amount of rotation. Slip forming parallels deep-draw metal forming practice. It is used to form continuous-fiber reinforced polymer composite sheet. This is described in Chapter 9. • Splitty plastics such as PET and PA or nylon and certain multilayer structures are best formed without splitting using diaphragm forming (Fig. 1.20). A warmed thick-walled neoprene bladder or diaphragm is placed against the clamped heated rubbery plastic sheet. The bladder is inflated with air or with a liquid such as hydraulic fluid or hot water. The inflating bladder stretches the plastic sheet into a female mold. Very uniform wall thicknesses and relatively deep draws are obtained for plastics that cannot be formed in other ways.
Pressure Box Sheet Slip Clamp Spring Spring-Clamp
Cammed Clamp Mold Cam-Clamp
Slip Sheet Moving Onto Mold Sheet Slipping From Clamps Figure 1.19 Slip forming. Spring-loaded sheet clamp on the left and cam-loaded sheet clamp on the right
Female Mold Sheet Clamp Diaphragm
Deformed Diaphagm
Pressure Box Air or Hydraulic Fluid Mold Moving Onto Diaphragm/Sheet
Applied Pressure Diaphragm-Stretched Sheet
Figure 1.20 Diaphragm forming for splitty or weak polymers
•
Twin-sheet thermoforming has been a technically viable process for many years. There are several variations on this process, described in greater detail in Chapter 9. One approach is called simultaneous twin-sheet forming. Two sheets are kept separate while heating, then brought together in a double female mold arrangement (Fig. 1.21). Blow pins are inserted between the sheets. Air inflation begins as the sheets are clamped together and the mold halves close. The air pressure keeps the sheets from initially touching and then provides the force needed to press the sheets against the mold surfaces. Twin-sheet forming produces a relatively flat hollow part that with proper design of kiss-offs and pinch-ofls is light weight and very strong. The hollow cavity can also be filled with PUR foam for additional stiffness and insulation. Tack-Off or Kiss-Off
Kiss-Off Completed
Moving Kiss-Off
Female Mold Sheet Clamp Gasket Female Mold
Blow Pin or Hypodermic Needle Moving Kiss-Off
Heated Sheets Clamped Between Molds
Simultaneous Forming
Inflating Air Actuated PlugLike Kiss-Offs
Figure 1.21 Heavy-gage, simultaneous twin cut sheet thermoforming. Here, blow pins extend through sheet surface and kiss-offs are pneumatically driven during forming
Perimeter Cavity Clamp or Grid
Top Sheet Bottom Sheet
in-Situ Trim
Clamp
Top Sheet Trim Bottom Sheet Trim
Female Mold Vacuum Heated Sheets
Vacuum Draw on Clamped Sheets
In-Place Trimming
Figure 1.22 Thin-gage, simultaneous twin roll-fed sheet thermoforming. Here, sheets are heated separately and brought together at the forming station
For large, heavy-gage parts, the technique competes with blow molding and rotational molding. In roll-fed thermoforming, twin-sheet forming is used in a different way (Fig. 1.22). Packages that provide oxygen and moisture barrier are sought. The most effective barrier materials such as PAN, EVOH and PVDC are usually quite expensive and so are used as thin films between layers of less expensive but durable polymers such as PP, HDPE, PET and PS. The results are usually laminates of essentially incompatible plastics glued together with polymers such as EVA that behave as hot-melt adhesives. The web and trim from coextruded laminates of some of these polymers cannot be reprocessed successfully without degradation and gel formation. As a result, a variation on the twin-sheet thermoforming process was developed wherein separate sheets of the candidate polymers are fed from individual rolls, through sandwich heaters and then brought together right at the forming station. Once the multi-layer formed product has been trimmed, the individual layers in the web and trim are stripped from one another. Each polymer web is therefore "clean" and is recycled to produce new sheet. The diverse layers of material in the formed product are only contact-adhered and so will delaminate through misuse. If the force applied to the sheet increases, thermoforming begins to mimic metal forming techniques. At pressures of 1.73 MPa or 250 lbf/in2, the process is similar to tin metal embossing. At pressures of 6.9 MPa or 1000 lbf/in2, the process resembles coining. At pressures of 13.8 MPa or 2000 lbf/in2, the process is like compression molding or forging [20]. It has been adequately demonstrated in the Dow scrapless thermoforming or STP process, that useful products can be fabricated with high-speed impact forming. High pressure forming is described in detail in Chapter 9. The incentive to achieve more uniform part wall thickness even in very deep draw parts continues to spur development of these multi-step procedures. The more
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sophisticated these procedures become, the more difficult it is to adapt them to high-speed forming without exacting process controls. And yet many new packaging applications, for example, are seeking just such designs. Thermoforming process innovation remains a lively art.
1.6
Thermoforming Machinery
As noted, there are two general thermoforming categories. Typically, heavy-gage sheet is handled as discrete cut sections and the forming equipment are called cut-sheet thermoformers. Thin-gage sheet is handled in continuous rolls and the forming equipment is usually called roll-fed thermoformers. The equipment in both categories includes: • • •
Some form of sheet handling device, A way of moving the sheet from one station to another, A means of controlling the various elements that allow the sheet to be heated, formed and moved from station to station, • A sheet heating oven, • A vacuum system, • A forming press, and • A formed part removal region. In addition, the equipment may include: •
• • •
Some form of prestretching such as: preblowing or plug assist, A pressure system, A trimming press, and Some form of trim removal.
Certain guidelines pertain to both categories of forming equipment. Table 1.7 gives an overview for thermoforming equipment in general [20]. Some of these are summarized below. Heating Source The various heating methods are detailed in Chapter 3. Sheet temperature should be controlled to within + 5°C or + 1O0F. During transfer to the forming station, the sheet temperature drop should not exceed 5 to 100C or 10 to 200F. Infrared heating is most popular today. The various heating methods include [21]: • •
Simple nickel-chrome heating wires, Metal resistance rods, sometimes called calrods,
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sophisticated these procedures become, the more difficult it is to adapt them to high-speed forming without exacting process controls. And yet many new packaging applications, for example, are seeking just such designs. Thermoforming process innovation remains a lively art.
1.6
Thermoforming Machinery
As noted, there are two general thermoforming categories. Typically, heavy-gage sheet is handled as discrete cut sections and the forming equipment are called cut-sheet thermoformers. Thin-gage sheet is handled in continuous rolls and the forming equipment is usually called roll-fed thermoformers. The equipment in both categories includes: • • •
Some form of sheet handling device, A way of moving the sheet from one station to another, A means of controlling the various elements that allow the sheet to be heated, formed and moved from station to station, • A sheet heating oven, • A vacuum system, • A forming press, and • A formed part removal region. In addition, the equipment may include: •
• • •
Some form of prestretching such as: preblowing or plug assist, A pressure system, A trimming press, and Some form of trim removal.
Certain guidelines pertain to both categories of forming equipment. Table 1.7 gives an overview for thermoforming equipment in general [20]. Some of these are summarized below. Heating Source The various heating methods are detailed in Chapter 3. Sheet temperature should be controlled to within + 5°C or + 1O0F. During transfer to the forming station, the sheet temperature drop should not exceed 5 to 100C or 10 to 200F. Infrared heating is most popular today. The various heating methods include [21]: • •
Simple nickel-chrome heating wires, Metal resistance rods, sometimes called calrods,
Table 1.7 General Specifications for Thermoformers1 Platen size, W x L (in x in or mm x mm) Maximum depth of draw (in or mm) Forming process (vacuum, pressure, matched mold, plug assist, twin-sheet capability) Platen power drive (pneumatic, hydraulic, mechanical, electric) Indexing power drive (pneumatic, hydraulic, mechanical, electric) Floor space (ft2 or m2) Heater type (metal rod, quartz, ceramic, radiant, gas, nichrome wire) Heater controls (proportioning, percentage timers, timer controlled, zone controlled, programmable controlled, machine controlled) Maximum heater output (kW/ft2 or kW/m2) Special features (purpose, type such as shuttle or rotary, number of stations, number of ovens, etc.) 1
• • • • • • • •
[20] with permission of John Wiley & Sons
Ceramic bricks or tiles, Quartz heaters in rod, spiral or square plate form, Direct gas-fired burners, Indirect gas-fired catalytic burners, Heat lamps, Quartz glass plates, Halogen bulbs, and Wire or rod heated metal plates.
Heater surface temperature is usually measured with thermocouples, thermistors or infrared pyrometric devices. Heating wires and resistance wires are inexpensive but oxidize rapidly and so lose heating efficiency. Quartz heaters are quite efficient, can be turned on and off like light bulbs but are quite expensive and fragile. Quartz is preferred for high temperature and "shaped heating" needs as described in Chapter 3. Sheet is also heated by direct contact with a hot metal plate (trapped sheet heating), by placing the sheet in a hot air oven (convection heating), or by passing it through a high-frequency electromagnetic field (RF or microwave heating). In the last case, the plastic must absorb the high-frequency energy. PVC is heated by radio-frequency energy in the flow-molding embossing process. Other polymers must be doped with "lossy" substances such as inorganic hydrates or even carbon black. There are certain elements that pertain to the ovens for all forming presses. For example: • •
There must be a way of separating the sheet from the heater source at shut-down. Baffles and dampers are used for heavy-gage sheet and fly-open and extracting shuttles are used for thin-gage sheet. There should be adequate means for rapid replacement of burned-out heater elements on both top and bottom heater banks.
Forming Platform The forming station should include all elements necessary to prestretch the sheet, form it, cool it and eject it from the mold. Some of these elements include: • • • •
• • • • • • • •
Substantial guide-rods are needed. For vacuum molds greater than 12 in or 300 mm by 24 in or 600 in dimension and for all pressure forming applications, four guide-rods are recommended. Clamp tonnage should be in proportion to mold size, that is: Typically >100 lbf/in2 or 0.7 MPa for straight vacuum forming, and Typically > 200 lbf/in2 or 1.4 MPa for pressure forming. The press frame pit should not be deeper than 4 ft or 1.3 m. In many areas, pits deeper than this must be entered by people wearing self-contained breathing apparatus. The overhead press frame structure should be robust enough to support such elements as: The entire weight of the mold, if it is desired to mold in an "up" position, In-mold trimming components including cylinders and framework, Ancillary mold elements such as: Plug assist cylinders and frames, Ejector cylinders and frames, and Cavity isolator cylinders and frames, and Pressure boxes. The press should allow for easy mold removal and maintenance. The press platens should allow for easily adjustable mold daylight. There should be adequate headroom for overhead ancillary equipment. There should be adequate space around the presses for vacuum lines, vacuum and air pressure lines, and adequate mold temperature hoses and manifolds. There should be adequate provision for prestretching and billowing, sheet lockdown and stripping and ejecting. There should be allowance for free surface temperature control, including chilled air. The frame should be adequately reinforced and gusseted to carry heavy molds, ancillary hardware, and day-to-day vibration and shaking. There should be adequate provision for part removal and trim or web takeaway.
The drive system that raises and lowers the platens is the key to forming station performance. Depending on the application, the drive unit can be as inexpensive as a simple air cylinder or as complex as the hydromechanical clamps used on injection molding presses. Table 1.8 [21] rates some of the drives used in thermoforming presses. Many high-speed presses use electric toggle clamps and cams. For high-speed pressure forming of polypropylene, double toggle clamps are used. Some straight hydraulic clamps are used in high pressure applications. Electrically driven clamps are being developed that are touted to be more accurate with less maintenance than conventional clamp systems. Most vacuum forming drive systems are designed to close and clamp at maximum pressures of 20 to 40 lbf/in2 or 0.15 to 0.30 MPa. For
Table 1.8 Comparison of Forming Table Drive Units1 Characteristic
Hydraulic Pneumatic Eccentric Pneumatic Geared motor-cams driven motorair toggle cylinder cogwheel
Uniformity Stroke limit control Timing control Repeatability Speed control
0 1 2 0 3/4
5 5 5 5 0/2/5
4 5 4 4 5
0 3 1 0 1
Forming force Clamping force Stability—tracking Energy consumption Trouble-free nature
3 3 0/3 0 3
3 3 3/4 5 5
5 5 0/3 1 0
4 Maintenance 0 Noise level Construction quality 1 5/2 Cost Preblowing capacity 5
5 5 3 4/1 5
0 3 1 0 5
61/65
42/45
Total
30/31
Motor-driven spindle 5 5 4 5 2
0 5 4 0 2
3 3 2 3 0 1 5 4 3 4
2 0 5 3 0
3 4 5 1 0
3 1 5 1 0
26
41
50
5 4 5 2 3
1 From [21: Table 8] by permission of Carl Hanser Verlag Key: 0 = Low or poor; 3 = Moderate or average; 5 = High or excellent
pressure forming, the drive system must clamp against the forming air pressure. Safety factors of 3 to 4 are recommended. If 30 lbf/in2 or 2 MPa air pressure is used in forming, the drive system should be designed to remain closed against 90 to 120 lbf/in2 or 6 to 8 MPa pressure. For a typical mold forming area of 20 x 10 in or 500 x 250 mm, the drive system clamping load is 9 to 12 T or 32 to 107 Mkgf. Platens and guide-rods must be designed to accommodate high bending forces. For forming pressures in excess of 100 lbf/in2 or 0.7 MPa, forming station designs begin to resemble those used in thermoplastic structural foam injection molding [22]. For forming pressures in excess of 200 lbf/in2 or 1.4 MPa, the presses begin to resemble those used in compression molding. Vacuum System The vacuum systems for both categories of forming equipment are quite similar. For stand-alone shuttle and rotary formers, the vacuum pump, surge tank and plumbing is usually an integral portion of the machine (Fig. 1.23). For installations of several forming presses, regardless of the sheet gage, a centrally located vacuum system is frequently used. Even the least expensive vacuum forming press must have adequate means of rapidly drawing the sheet against the mold surface. One critical factor in efficient vacuum draw-down lies in an unencumbered, adequately sized line between the
Pneumatic/Hydraulic Plug Assist
Cooling Fan
Vacuum Tank Platform
Heater Cabinet Clamp Frame
Mold Platen
Forming Table
End View
Side View
Electric/Electronic Cabinet
Figure 1.23 Single station cut sheet shuttle press—Drypoll/Zimco
vacuum surge tank and the mold cavity. Proper vacuum system design requires a vacuum pump capable of drawing down to 710 to 735 mm Hg vacuum1 in the surge tank prior to the beginning of the forming cycle. The path between the surge tank and the cavity between the hot sheet and the mold should have as few constrictions as possible. Long pipes, flow constrictors, quick-disconnects, restrictive valves and large L/D vent holes should be eliminated. Fast-acting rotary ball valves are recommended for vacuum shut-off [23]. Section 6.5 details a method for determining pressure drops through each of the constrictions from the mold cavity to the vacuum pump inlet. A good estimate of the time required to evacuate a mold cavity is obtained from:
where 0 is the pump-down time, V is the total volume of the system to be evacuated, P1 is the initial system pressure (absolute), pf is the final system pressure, and p o is the vacuum tank pressure. S0 is the volumetric evacuation rate. The evacuation rate of the vacuum pump is usually specified by the pump manufacturer, as Sp. The evacuation rate, S0 is given as:
+
h-k h
<12)
where 1/C is the cumulative resistance of the system between the pump and the mold cavity. This resistance includes valves, piping, vent holes, vacuum box baffles and so on. A protocol for calculating the cumulative resistance is given in Section 6.5. The cumulative resistance is comprised, for the most part, of two resistances, the air flow resistance in the plumbing and the surge tank resistance. The resistance to air flow 1
Pumps of this draw-down range may also be listed in vacuum draw-down units such as 25 to 50 torr, 28 to 29 in Hg or 0.5 to 1.0 lbf/in2 absolute.
between the vacuum or surge tank and the mold cavity, 1/Cp, should not exceed the surge tank resistance, 1/Ct. And this combined resistance should not exceed the pump resistance, 1/Sp. This can be written as: 1/C«l/C p +1/C t
(1.3)
1/C p
(1.4)
1/S p
(1.5)
Therefore a good design volumetric evacuation speed is given as: 1/S o ^2/S p ^4/C p
(1.6)
Examples 1.1 and 1.2 illustrate the relevance of vacuum pump capacity to surge tank size and pressure drop through plumbing. Other examples are found in Section 6.5. Example 1.1 Pump-Down Time in Vacuum System A vacuum pump manufacturer lists your vacuum pump capacity at 60 ft3lmin, 0.0283 m31s, or 1700 liter jmin. Determine the expected evacuation rate of a typical pump and surge tank and the evacuation time to pump a 0.1 m3 mold cavity to 50 mm Hg if the pump pressure is 20 mm Hg. Assume that the piping resistance equals the vacuum pump capacity, Equation 1.1. Therefore: 1/SO = 2/SP or S 0 -0.0283/2 = 0.01415 m3/s. According to Equation 1.1, the pump-down time, 0, is: 0.1m3 9
/760 - 2 0 \
t
= 0.01415 m 3 / s H ^ ^ r
^ 22
-7S-
Example 1.2 Pump-Down Time for Surge Tank Consider pumping a surge tank of volume 1.0 m3 from 50 mm Hg to 20 mm Hg using the vacuum pump of Example 1.1. Determine the time to pump it down and compare this with the time to evacuate the mold cavity of Example 1.1. According to Example 1.2, the vacuum pump rate is given as Sp = 0.0283 m3/ s. The evacuation time is given in Equation 1.1: e
Im 3
t
ln
/50-10\
- = 0 0 2 8 3 ^ UrrTo) =49-Os
The time required to evacuate the mold cavity in Example 1.1 is 22.7 s. Therefore 0r > 0 and the surge tank cannot recover in time. The vacuum in
the surge tank at the end of the forming cycle of 22.8 s is obtained from this equation as well: Pf = Po + (p 1 -Po)exp[-9 r S o /V] or: pf = 10 + (40) exp[- 22.8-0.0283/1] = 31 mm Hg Trial-and-error is used to match the pump-down time of the mold cavity with the surge tank recovery time. The time 9r, to recover the surge tank pressure to p o value is determined from Equation 1.1. The surge tank volume is substituted as V and the final tank pressure at the end of draw-down is pi9 the initial pressure. The vacuum pump pressure is p o , and the desired vacuum tank final pressure is p f . Example 1.3 illustrates this. The total vacuum cycle time, 0t, is given as the sum of 0 and 0r. For most cases, 0r < Q and the total cycle time is simply assumed to be equal to twice the draw-down time [24]. Vacuum pumps are either single or double staged. Two-stage vacuum pumps draw pressures down to 10 mm Hg, but evacuation capacity is usually half that for single-stage pumps. Typical pump capacities are given in Table 1.9 [24]. Example 1.3 Piping Resistance in Vacuum Systems Consider piping resistance for a specific thermoformer to be given by [33]: CP = 22D 3 /L e where D is the pipe diameter and Le is the equivalent pipe length (see Chapter 5 for additional details). Determine the equivalent pipe length if the pipe diameter is 4 in = 100 mm and the vacuum system uses the vacuum system in Example 1.1. What is it if the pipe diameter is 6 in = 150 mm? As noted in Equation 1.1, assume 1/Sp = 2/C p . Therefore: So = Cp/2 = ll D3/Le Rearranging, for D = 4: L e = H D 3 / S o = l l . ^ H ^ = 0.78m = 2.6ft For D = 6: Le = 2.6 m = 8.6 ft. Note that the equivalent length is proportional to the cube of the diameter of the vacuum line.
Table 1.9 Typical Vaccum Pump Specifications1 Theoretical pump capacity
Pump specification No of cylinders
Diameter (mm)
Stroke length (mm)
Single stage (m3/min)
Two stage (m3/min)
Pump speed (rpm)
Power required (kW)
Exit pipe diameter (mm)
1 2 2 2 2 3
76 76 102 127 140 140
70 70 70 80 102 102
0.255 0.510 0.906 1.70 2.80 4.22
0.255 0.453 0.850 1.40 2.80
800 800 800 750 900 900
0.56 0.74 1.48 2.2/3.7 3.7 5.6
19 25 32 38 52 52
1
From [21: Table 10], with permission of Carl Hanser Verlag
Pressure System Pneumatic action for air cylinders usually requires working air pressures of 90 lbf/in2 or 0.6 MPa. Air consumption depends on the size of the press and the type of forming being used. Typically maximum airflow range for both roll-fed and cut sheet presses is 35 to 250 ft3/min, 1 to 7 m3/min or 1000 to 7000 liter/min. Air is usually delivered at 100 to 200 lbf/in2 or 0.7 to 1.4 MPa. Air should be very dry with dew-point of — 400F or — 400C. It should be absolutely oil-free, particularly if it is used as instrument air or for free blowing in prestretching, twin-sheet forming or pressure forming. Prestretching air is delivered to the mold cavity at very low pressures of 0.5 to 5 lbf/in2 absolute or 3.5 to 35 kPa. The air volumetric flow rate is controlled very carefully to +0.1%. Pressure forming air is delivered to the pressure box at 20 to 120 lbf/in2 or 0.14 to 0.83 MPa, also at very carefully controlled volumetric flow rates. Twin sheet forming air is delivered at pressures of 5 to 50 lbf/in2 or 35 to 350 kPa at very carefully controlled volumetric flow rates. Twin-sheet forming air is sometimes heated to 2000F or 95°C to prevent chilling around the blow pins that introduce the air to the mold cavity through the plastic sheet surface. Pressure forming air must be carefully exhausted or bled from the pressure box prior to opening the mold. A two-tank system is used on occasion to handle spent air. Air from one tank is used to form the part, then exhausted to a second tank where it is recompressed with incoming air at higher pressure. The cycle then repeats. This system works best when forming at pressures above about 50 lbf/in2 or 0.35 MPa. Process Control Process repeatability is always of concern to thermoformers. The earliest roll-fed presses were equipped with automatic drop-down clock cycle timers. Accurate measurement and control of:
• • • • • • •
Sheet temperature, Mold temperature, Prestretching pressure, Pre-inflation stretch height, Rate of stretching either by: Plug assist, or Pre-inflation, Forming pressure, and Sheet registry
are all desired. Now, control of: • • • •
Rate of change of sheet temperature, Rate of bubble inflation, Time-dependent plug position, and Time-dependent draw-down
are sought. For example, as detailed in Chapter 9, repeatability of the crystalline level of CPET depends on accurate control of the rate of heating crystallizing sheet prior to forming [25,26]. Newer, more accurate processing techniques are replacing less reliable ones. For example: •
Microprocessor-driven servo motors are replacing cam-operated sequencing wheels. • Newer presses may include such features as: Programmable mold height adjustment, Programmable daylight adjustment, Multi-step, programmable mold closing speeds, Programmable roll-fed chain width spacing, and Programmable forming station sequencing including prestretching and postforming sequences. • Sheet gage and pattern registry monitors can now be added. Safety is an ongoing concern. Thermoforming machines have many rotating and sliding elements and many pinch-points. Higher heater temperatures are used to increase throughput and to heat sheet more efficiently, Chapter 4. An emergency line shutdown should not only shut off heaters but shield the stationary sheet from the heaters. Heaters are now designed to automatically swing away or shift horizontally whenever the sheet stops moving. This reduces the chances of fire. Pressure boxes are pneumatic pressure vessels and so must have appropriate safety ratings and overpressure relief diaphragms. Pressure forming stations have pressure interlocks that prevent opening when internal air pressure exceeds a fixed, relatively low level. In many cases, increased production efficiency and substantially reduced labor costs more than offset the substantial costs of these process controls.
Trimming and Cut Parts Handling All formed parts must be removed mechanically from the surrounding trim or web1. Trimming is detailed in Chapter 5. Cut sheet trimming is traditionally done at an off-line station. Trimming is done with pneumatic or hydromechanical steel-rule dies, routers, saws, punches, guillotines, water jets and/or punches. Semi-automatic microprocessor-controlled multi-axis trimming devices are used for many parts. Robots are used occasionally. Manual trimming is common when a few parts with complex trimming lines are fabricated. Band-saw cutting is common when the trimming line is planar. In-line trimming stations are commonly used in roll-fed forming operations. In-situ or in-the-mold trimming requires that the forming press be equipped with a separate pneumatic or mechanical press that drives the cutting knives through the formed sheet and against the mold anvil. The separate in-line trim press is an alternative to in-mold or in-situ trimming. Typically, the press is a cam-action mechanical toggle-clamp platen press with steel-rule die cutters. If the trim press is integral with the former, the sheet with the formed parts intact is guided through the press bed by the integral pin-chain drive. If the unit is separate but in-line, proper sheet indexing must be provided. If the formed polymer shrinks appreciably or the parts show unusual distortion and warping, care must be taken to register the sheet to achieve pattern repeatability. Integral trim presses are much easier to align and register than separate units. They are recommended for roll-fed forming of CPET and PP polymers. Certain other aspects are similar but not identical. For example, sheet handling and clamping during heating and forming is usually a function of sheet thickness and so is covered below. There is no standardization in mold bases as there is with injection molding. As a result, forming presses must have the flexibility to accept many mold configurations. This is true for both general categories of presses.
1.7
Heavy-Gage Thermoforming Machinery Specifics
Table 1.10 gives a check-list of important items to be considered in heavy-gage thermoforming machine design. The check-list focuses on cut-sheet thermoforming machinery requirements and desires. Heavy-gage thermoforming machines have been developed where the sheet is continuously fed from the extruder (Fig. 1.2). These machines incorporate certain features of roll-fed formers, such as web handling and 1
The thermoforming industry has long been concerned about the use of the word "scrap" to describe the non-product portion of the sheet. Thermoforming economics dictate that the non-product should be reground, mixed with virgin resin, and reprocessed into useful product. Only rarely is the trim or web considered to be unsuitable for reprocessing. The two primary examples are in certain biomedical and medical products and in continuous-fiber reinforced high performance composites. Even in these cases, the web or trim is reground and reprocessed into other products. It is estimated that less than 1% of any extruded sheet surface is discarded as scrap.
Table 1.10 Check-List for Important Items for Heavy-Gage Forming Machines (TFS = To-and-
fro shuttle; ILS = In-line shuttle; R = Rotary; OSP = Oven shuttle press; A = All heavy-gage machines) Sheet handler Vacuum must be applied individually to pick-and-place suction cups. Vacuum pick-and-place should support full sheet weight on one or two suction cups. Vacuum pick-up must allow up to two suction cups to engage and lift sheet before other suction cups are activated to provide vacuum break. Smooth deceleration of table lifter as sheet enters clamp [R]. Manual placement in clamp should have center stop just below sheet to avoid drop-through [TFS, R]. Sheet clamp Manual book mold requires lock-over clamps [TFS]. Pneumatic clamp should have barbs, teeth spaced every 1 in or 25 mm for tough sheet such as ABS, PS, every 0.5 in or 12 mm for soft sheet such as HDPE, PP, every 0.25 in or 6 mm for very soft sheet such as TPO or TPE [A]. Pneumatic clamp should have barbs on closing portion, flats on fixed portion [A]. Clamp pressure on cold sheet should be at least 50 lbf/in2 or 0.35 MPa to prevent extrusion during forming [A]. Clamp should hold at least 0.5 in or 12 mm sheet width for sheet less than 0.100 in or 2.5 mm in thickness [A]. Clamp should hold at least 2 in or 50 mm sheet width for sheet greater than 0.400 in or 10 mm in thickness [A]. Clamp frame, pneumatics must withstand at least 8000F or 425°C for 20 minutes for at least 10,000 cycles without sticking, binding, leaking air or oil [A]. Edge clamps must reliably open and close on sheet for at least 10,000 cycles without sticking or binding [ILS]. Pneumatics must be easy to replace quickly [A]. Hoses must be durable enough to withstand bending and elevated temperatures [A]. Rotary air hose connections must withstand vibration and heat [R]. Clamp frame must be rapidly adjustable for various sheet dimensions [A]. Shuttle rails or shuttle clamps must be self-lubricating or sealed to minimize contamination with sheet [TFS, ILS]. Rotary clamp frame arm must be capable of supporting maximum sheet weight in only one clamp without flexure [R]. Rotary clamp frame arm must not oscillate or bounce when rotation cycle ends or when automatic sheet loading is underway [R]. Rotation acceleration, constant speed and deceleration must be smooth and without oscillation or vibration [R]. Rotary clamp should be clamped in place with a drop pin or equivalent when the sheet is at a specific station [R]. Oven Preheat oven recommended for hydroscopic polymers such as ABS, PS, PET, Celluloics [R]. Two-step oven recommended for hydroscopic polymers [ILS, TFS]. Oven baffles should close off sheet and clamp frame while in oven [TFS, R]. Oven must tightly clamp the sheet during the heating cycle so that the edge clamps can be opened and shuttled backwards [ILS]. Rapid disconnect for main electrical to top and bottom oven [A]. Rapid disconnects for individual heater elements [A]. Rapid disconnects for individual heater thermocouples [A]. (Continued)
Table 1.10 (Continued) Open woven wire or chicken wire guards on top and bottom oven heaters [TFS, ILS, R]. Quartz plate between sheet and bottom heater [OSP]. Adequate places to fasten screens for pattern heating [TFS, ILS, R]. Air- or water-insulated ports in top and bottom oven surfaces for infrared pyrometer devices [A]. For very large area sheets, bottom oven should have drop-down side wall to allow the sagging sheet to exit without touching metal [A]. Shuttle rails must be self-lubricating or sealed to minimize contamination with sheet [OSP]. Photo-eye sensor/warning needed for excessive sheet sag [A]. Automatic oven shut-down, baffling or extraction when sheet time in oven exceeds upper limit [A]. Oven equipped with central system for dispensing CO2 or other non-aggressive fire extinguishing material [A]. Easy adjustment of oven height above/below sheet plane to allow: Rapid change in height during sheet set-up, Rapid change during running [A]. Capability to lower bottom oven height during heating to accommodate sagging sheet [optional] [TFS, ILS, R]. Sufficient daylight between top and bottom oven to allow: Heater burn-out inspection and replacement, Individual heater temperature measurement by non-contact means such as infrared pyrometry [A]. Intermittent vacuum or air layer lift of sagging sheet [TFS, ILS, OSP]. Press Smooth-acting, constant velocity press closure [A]. Acceleration/deceleration at end of stroke to minimize banging, chatter as mold enters sheet [A]. Clamping by: Platen locking devices, Mechanical/pneumatic assists, Servo-motor lockout, Pneumatic gland [A]. Self-lubricating or continuous-lubricating platen screws [A]. Enclosed or self-sealing overhead hydraulic/pneumatic lines to prevent oil vapor contamination of formed product [A]. Protected platen locking cogs or screws to minimize contamination from trim dust, chips, dirt, detritus [A]. Sites for laser leveling [A]. Rapid, easy-to-use platen alignment devices [A]. Rapid, easy-to-use horizontal plane positioning for platen on all ancillaries [A]. Configured to easily accept mold changeover [A]. Adequate daylight between platens to allow for: Inspection and maintenance with mold in place [A], Replacement of in-mold trim dies. Adequate space around press to allow for: Adjustment of ancillaries, Proper placement of vacuum box and vacuum lines, Proper placement of water lines [A]. Upper platen frame robust enough to support ancillaries such as: Plug assist carrier, Trim-in-place die platen, if used, Pressure box [A]. Pneumatic interlocks to prevent: Premature air pressurization before pressure box fully engages mold, Premature opening of pressure box while still pressurized,
Table 1.10 (Continued) Pressurization of an empty clamp frame [A]. Sufficient access space below bottom platen to allow for adequate mold travel adjustment [A]. Proper controls on all rate-dependent ancillaries such as: Plug assist platens or individual cylinders, Trim-in-place die platen or individual cylinders, Pressure box [A]. Means for accessing overhead ancillaries for adjustment,, removal, disengagement, repair, maintenance [A]. Plug assist Relatively easy and rapid means for adjusting the travel length, and rate of travel of individual plugs [A]. Capability for internally heating/cooling individual aluminum plugs, including adequate space above the mold bed to allow for heating/cooling lines and thermocouples [A]. Relatively easy removal of individual plugs or at least methods for rendering individual plugs inoperable [A]. Trim-in-placed Rapid means for determining sharpness of individual trim die sections [TFS, ILS]. Rapid means of removing individual trim die sections [TFS, ILS]. Rapid means of adjusting and aligning individual trim die sections for parallelism to the punch surface [TFS, ILS]. Pr e-stretching Pre-blow bubble height monitor with photoelectric eye connected to air pressure [A]. Bubble inflation rate control [A]. Bubble collapse sensor to deactivate air pressure [A]. Prestretching vacuum box mounts on upper or lower portion of press [A]. Prestretching vacuum box drop side to allow exit of prestretched sheet [R]. Load/unload Clamp frame/formed part at operator [A]. Heavy, deep-drawn parts require break-away clamp frame, mechanical assist to remove [A]. Automated pickers/robots expensive, difficult to maintain, restricted to dedicated presses [R, ILS, OSP]. Vacuum box Mold evacuation rate control [A]. Auxiliary dump tank for evacuation of large volume molds [A]. Condition monitors Sheet temperature monitoring via infrared pyrometry: Automatically through oven, both top and bottom [A], Automatically at sheet exit from oven [TFS, IL S, R], Hand-held as sheet exits oven [A]. Mold temperature monitoring with thermocouples in at least one portion of mold cavity [A]. For metal and ceramic heaters, individual thermocouples mounted on or embedded in many heaters on both top and bottom ovens [A]. Air pressure monitor on all pneumatic devices including: a
Trim-in-place is rarely used in heavy-gage thermoforming. When it is used, the trim dies are forged or machined and are mechanically or hydraulically driven (Continued)
Table 1.10 (Continued) Pressure box, Plug assist cylinders, Trim die if pneumatically driven [A]. Time-dependent vacuum monitor at: Vacuum pump, Surge tank Vacuum box [A]. Time monitor on all phases of sheet transfer through the press [A]. Photoelectric cells on sheet in oven and as sheet exits oven [A]. Sheet presence sensor for quartz oven to shut off oven when no sheet is in clamp [R]. Process control Times and sequences for all events [A]. Temperatures for all heaters or heater banks that are independently controlled [A]. Delay times for line stoppage [R]. Storage of all important event values and capability of resetting machine using stored data [A]. Automatic protocol for emergency shutdown for: Fire, Power overload, brownout and outage, Light curtain interrupt, Safety cage security breach [A].
in-line ovens. The simplest heavy-gage, cut-sheet thermoformer consists of a bookmold sheet clamp, stationary single-sided oven, a stationary mold/vacuum box and a simple vacuum system [27]. These thermoformers are used to form shallow draw products such as signs, transparent protective windows and disposable packaging. Shuttle presses are most commonly used in custom thermoforming. While not as cycle time or energy efficient as rotary presses, they offer flexibility in forming as well as rapid mold change and valuable between-shot process parameter adjustment. The most common shuttle press is a single oven press, with the sheet being shuttled between the load/form/unload station and the stationary oven (Fig. 1.23). The oven is sometimes shuttled and the sheet in its clamp frame is stationary. This configuration is quite energy efficient if the oven lamps are quartz and are switched off when not over the sheet. Dual-oven single-press and dual-press, single-oven thermoformers are also used in special cases. Florian believes that these designs "... suffer from the definite misconception that [they are] saving energy..." [28]. In addition, increased labor costs and additional tooling costs usually obviate any improvement in time or energy efficiency. Dual-oven, single-press formers are used in sequential twin-sheet thermoforming, however (Fig. 1.24 and Chapter 9). If production warrants improved cycle times or economics require increased energy efficiencies, rotary presses should always be considered (Fig. 1.25). Rotary presses have some limitations. The overall cycle time is governed by the slowest step in the process, be it loading and unloading, heating, or forming. If the heating step controls the process cycle time, the heater temperatures can be increased or a four-station rotary press used, with the fourth station being a preheater (Fig. 1.26). When the forming step controls the process time, as it does in the majority of cases,
Top Clamp Frame
Top Mold Platen
Top Sheet Heating Oven Electric/Electronic Cabinet
Bottom Sheet Heating Oven
Bottom Clamp Frame
Side View
Bottom Mold Platen
Figure 1.24 Dual heater simultaneous or sequential twin cut sheet shuttle press
heating efficiency suffers. The optimum forming conditions obtained on a shuttle thermoformer cannot be successfully translated to forming conditions on a rotary press. Rotary formers are also used to produce twin-sheet parts. As detailed in Chapter 9, there are several methods for dealing with the second sheet. Some are:
Cooling Fans/Blowers
Plug Assist
Heating Station
Top Heating Oven
Forming Station Formed Part
Bottom Heating Oven Clamp Frame Rotary Clamp Frame
Electric/Electronic Cabinet
Surge Tank Vacuum Pump Plastic Sheet Load/Unload Station Mold Platen
Figure 1.25 Cut sheet three-station rotary press
Heating Zone
Forming Station Hydraulic Well
Preheating Zone Drive Core
Pit
Oven Control Load/Unload Station Rotary Clamp Frame Electric Cabinet
Figure 1.26 Top view of cut sheet four-station rotary press where the fourth station is a preheater oven
• • •
The second sheet is heated and formed sequentially in the same former, The second sheet is simultaneously heated in a second rotary press and simultaneously formed with the first sheet in the first former, with overlapping sheet clamping frames, and The second sheet is clamped in a second tier rotary clamp, is simultaneously heated in a second tier oven on a single rotary press, and is simultaneously formed with the first sheet in a single rotary former.
Two shuttle formers can also be used in similar fashion. Note in Table 1.10 that cut sheet is usually held in place with mechanical or pneumatic clamps. These clamps are toggle-locked and opened with air pressure. On shuttle presses, the clamp frame is indexed by motor-driven rack-and-pinion rails or by push-pull action of pneumatic or hydraulic pistons. The linear indexing of the rotary press carousel should be accurate to within 0.010 in or 0.25 mm. This requires a rotary drive motor accuracy and repeatability to within one arc minute. This is accomplished on large carousels with high-torque, low-rotation motors of about 1 rev/min, limit switches and electronic brakes. On smaller machines, indexing is also
done by driving the rotary table with a cam-arm-linked pneumatic cylinder. Positive position lock-in is achieved by dropping a tapered shot pin into a hardened bushing on the table. The pin is then pneumatically extracted prior to the next index sequence [29]. Ideally, the rotation cycle needs smooth acceleration and deceleration. For heavy-gage forming, the mold is usually quite large, cumbersome and heavy. As a result, the mold is usually mounted to the press platen in the "down" position. Example 1.4 illustrates a method for determining the weight of a mold. There usually is no top "platen", per se. Ancillaries, such as plug assist cylinders or a pressure box, are therefore mounted over the mold on the top of the press framework. One exception to this is when a single press is used for twin-sheet forming. Another is when a vacuum box is used to prestretch the sheet. This box is normally mounted in the down position. As a result, the male mold is mounted in the "up" position and the press therefore has a top platen but no bottom platen. The sheet clamp frame usually travels as well, so that the formed part can be extracted from the vacuum box. Example 1.4 Mold Weight It is desired to thermoform a spa from 0.400 inch PMMA. The spa dimensions are 48 in x 60 in x 36 in deep. The mold outside dimensions are 76 in x 84 in by a bottom thickness of 12 in. What is the weight of the mold if it is made of aluminum? If a safety factor of 4 is used, what is the uniformly distributed static load on the forming press? The density of aluminum is 167 lb/ft3. The volume of the mold cavity is: Spa volume: 48 x 60 x 36 = 103,680 in3 = 60 ft3 The volume of the mold before the mold cavity is formed is: Billet volume: 76 x 84 x (36 + 12) = 306,432 in3 = 177.33 ft3 The mold volume: 177.33 - 60.0 = 107.33 ft3 Mold weight: 107.33 x 167 lb/ft3 = 29,600 Ib - 14.8 T = 13,450 kg Loading level: 29,600/(76 x 84) = 4.64 lb/in2 = 670 lb/ft2 With a safety factor of four, the static load is 4 x 4.64 = 18.6 lb/in2 = 2,670 lb/ft2.
As discussed in detail in Chapter 3 on heating the sheet, for heavy-gage sheet, energy conduction from the sheet surface to its interior usually governs the rate of heating. As a result, heater energy efficiency is of secondary importance to energy distribution across the sheet surface. The local control and shaping of the energy source is called pattern heating or zoned heating. There are two primary ways of controlling local energy input to the sheet. In one, the heating source energy output, in kW/in 2 or kW/m 2 is uniform. Local control is accomplished with patterns or screen placed between the heater and the sheet surface. The heaters are usually wire or metal rods, heated metal or glass plates, heated screens, and direct or indirect gas burners. The second way uses many elements that are individually temperature or
energy controlled, including metal tapes and coils, ceramic tiles and halogen and quartz lamps. For very heavy-gage sheet, hot air convection ovens heat the sheet at a rate that allows adequate energy conduction into the sheet without sheet surface burning.
1.8
Thin-Gage Thermoforming Machinery Specifics
Table 1.11 gives a list of important items to be considered in thin-gage thermoforming machinery design. Typically, roll-fed thin-gage machinery designs are much more restrictive than those for heavy-gage. Thin-gage machines are designed to produce hundreds or thousands of parts per hour. Unlike heavy-gage forming, thin-gage forming appears as a continuous, seamless operation. It is not, even though sheet is supplied to the former from continuous rolls or directly from an extruder. For most roll-fed formers, the forming step is static, requiring the sheet to remain in contact
Table 1.11 Check-List for Important Items for Thin-Gage Forming Machines Sheet takeoff or unwind station Roll stand capable of holding 1000 Ib [454 kg] rolls. Roll stand capable of holding up to 6 ft [2 m] diameter rolls without vibration, instability. Roll stand capable of handling rolls wound on various core diameters. Roll core diameter should be standard such as 3 in or 75 mm, 6 in or 150 mm, or 8 in or 200 mm. Idler take-off to nip roll, or idler take-off to dancer. Passive tension brake, or roll speed governor. Roll weight overload warning. End-of-roll warning. Rapid roll changeover. Pin-chain and Pin-rail Non-stick, no-scratch engagement shoes. Removable pins so that: Pins can be sharpened, Pins can be replaced if damaged, or Pins designed for piercing specific polymers can be installed. Preheated pins for tough polymers. Self-lubricated chain links. Automatic parallel chain adjustment. Segmental chain guides for non-parallel chains. Manual method for adjusting chain non-parallelism during run. Lower pin guide to keep pin vertical. Lubrication that does not contaminate sheet. Pin-rail heating/cooling/temperature control. Chip vacuum at pin-sheet engagement. "Out-of-sheet" detector/warning light/horn. Servo-driven chain advancement, to achieve:
Table 1.11 (Continued) Constant velocity during transfer, ft/s or mm/s, Smooth and constant acceleration/deceleration rate, ft/s2 or mm/s2, at beginning and end of transfer time. Oven Preheat oven for hydroscopic polymers such as ABS, PS, PET, PMMA, Cellulosics. Oven sides that extend to within 1 to 2 in or 25 to 50 mm of the sheet surface at the rail edge, One to 2 in or 25 to 50 mm fiberglass insulation over entire inner surface of oven. Rapid disconnect for main electrical to top and bottom oven. Rapid disconnects for individual heater elements. Rapid disconnects for individual heater thermocouples. Open woven wire or chicken wire guards on top and bottom oven heaters. Adequate places to fasten screens for pattern heating. Air- or water-insulated ports in top and bottom oven surfaces for infrared pyrometer devices. Internal baffles for ovens with more than one shot capacity, with baffles extending to within 1 to 2 in or 25 to 50 mm of the sheet surface. Automatic heater isolation from the sheet when pin-chain rail shuts down, such as: Pneumatically driven fly-open operation, or Horizontal pneumatically driven heater retraction. Photo-eye sensor/warning for excessive sheet sag. Oven equipped with central system for dispensing CO2 or other non-aggressive fire extinguishing material. Adjustment of oven height above/below sheet plane to allow: Rapid change during sheet set-up, Rapid change during running. Sufficient daylight between top and bottom oven to allow: Heater burn-out inspection and replacement, Individual heater temperature measurement by non-contact means such as infrared pyrometry. Press Smooth-acting, constant velocity press closure. Acceleration/deceleration at end of stroke to minimize banging. Clamping by: Platen locking devices, Mechanical/pneumatic assists, Servo-motor lockout, Pneumatic gland. Self-lubricating or continuous-lubricating platen screws. Enclosed or self-sealing overhead hydraulic oil lines to prevent oil vapor contamination of formed product. Protected platen locking cogs or screws to minimize contamination from trim dust, chips, dirt, detritus. Self-leveling press platens. Configured to easily accept mold changeover. Adequate daylight between platens to allow for: Inspection and maintenance with mold in place, Replacement of in-mold dies. Adequate space around press to allow for: Adjustment of ancillaries such as: Plug assist platen, (Continued)
Table 1.11 (Continued) Cavity isolator platen, Trim-in-place die platen, Ejector ring platen. Proper placement of vacuum lines from vacuum box, Proper placement of water lines. Clear identification various elements of the press. Rapid, easy-to-use platen alignment devices. Rapid, easy-to-use horizontal plane positioning for platen and all ancillaries. Pneumatic interlocks to prevent: Premature air pressurization before pressure box fully engages mold, Premature opening of pressure box while still pressurized, and Pressurization of an empty chamber. Pneumatic interlocks to allow rapid venting of the pressure box before pressure box moves. Proper controls on all rate-dependent ancillaries such as: Plug assist platen, Cavity isolator platen, Trim-in-place die platen, and Pressure box. Means for lowering top platen to below pin-chain plane for: Mold installation, and Mold removal. Plug assist Rapid replacement of individual plugs. Capability for internally heating/cooling aluminum plugs, including adequate space above the press to allow for heating/cooling lines and thermocouples. Relatively easy removal of entire plug assist platen, or at least rendering it inoperative. Relatively easy and rapid means for adjusting the travel length, and rate of travel of plug assist platen. Ejector ring Relatively easy means for adjusting travel of ring platen. Cavity isolator Relatively easy means for adjusting travel of isolator platen. Trim-in-place Rapid means for determining sharpness of individual trim die. Rapid means of adjusting individual trim dies in: Concentricity, Parallelism to individual punch. Rapid means of removing individual trim die. Automatic trim dust removal. Automatic part separation from trim web, by: Individual cavity vacuum cups, Shuttle that holds the ejected parts in plane as the mold falls away, then horizontally removes them to sorting table, or Tipping or rotating mold that dumps parts onto sorting table. Rapid means of clearing trim, chip, detritus from individual trim die during maintenance, inspection. Air blow-back to ensure that all cavities are free of parts.
Table 1.11 (Continued) Trim takeup station Tension speed control, or Slave to pin-chain drive. Roll maximum diameter warining. Condition monitors Sheet temperature monitoring via infrared pyrometry either: Automatically through the oven, both top and botton, Automatically at sheet exit from oven, Hand-held as sheet exits oven. Mold temperature monitoring with thermocouples in at least one mold cavity. For metal and ceramic heaters, individual thermocouples mounted on or embedded in many heaters on both top and bottom ovens. Air pressure to all pneumatic devices including: Pressure box, Ejector ring platen, Plug assist platen, Trim die platen, particularly during cutting. Time-dependent vacuum at: Vacuum pump, Surge tank, Vacuum box, At least one mold cavity. Times on all phases of sheet transfer through the press. Photoelectric cells on sheet in oven and as sheet exits oven. Process control Times and sequences for all events. Temperatures for all heaters that are independently controlled. Delay timers for events such as: "Out-of-sheet", Line stoppage, Mold closure for "part in mold". Storage of all important event values and capability of resetting machine using stored data. Automatic protocol for emergency shutdown for: Fire, Power overload, brownout and outage, Light curtain interrupt, Safety cage security breach.
with a stationary mold for several seconds1. As a result, the sheet remains stationary in the oven for a like amount of time. Trimming of the part from the web or trim is also done while the sheet is stationary. The sheet is advanced from station to 1
Special-purpose or dedicated forming machines are available that allow the sheet to move at a fixed constant velocity from the extruder roll-stack through a tempering oven and onto a rotary vacuum molding station. The molding station is a horizontal roll that contains multiple cavities. Evacuation is through traditional vent holes and the roll is evacuated through a rotating coupling. In-line trimming is usually done on a conventional platen-type trim press.
Regrind Bagging Regrinder Stacking/Counting Device
Thermoformer
Cup Printing
Trim
Take-Oft Carton Packer
Extruder
Roll Stack/Take-Up
Stacking/Transfer Unit
Conveyor Rim Rolling Station Counting Device
Sleeve Wrapper
Figure 1.27 Thermoformed cup production scenario [30]
station in a jog or start-stop fashion. In certain areas, roll-fed thermoforming machines are portions of more complex systems such as the cup production schematic (Fig. 1.27) [30] or the form-fill-seal operation (Fig. 1.28) [31]. Sheet is usually transferred from the takeoff roll through the heater, forming press and trim die by means of a pair of endless chains containing regularly spaced pins or other impaling devices. The pin-chains are usually parallel although provisions can be made to allow the chains to diverge throughout their entire path or only Adhesive Application or Heater Heat Sealing Film Forming Station Filling Station
Sealing Station
Heating Station
Pressure Roil
Trim Die Product
Pin-Chain Thin-Gage Roll Figure 1.28 Thermoform, fill and seal production scenario [31]
Conveyor
in certain segments. Chain divergence is considered necessary when forming polymers with excessive sag, such as LDPE, PP and PET. Unlike heavy-gage forming machinery, thin-gage machinery sheet width is usually restricted to less than about 52 in or 1.3 m. For crystalline polymers or polymers that show excessive sag, sheet width is restricted to less than about 32 in or 0.76 m, unless sag bands are used. The sheet in the pin-chain region is usually shielded from the intense radiant heat to minimize sheet pull-out. Electric radiant heat dominates the heating. methods for thin-gage sheet. For decades, metal rod and wire heaters were the common means of heating thin-gage sheet. Ceramic or quartz heaters are used in most new machines. The newer heaters offer greater flexibility in controlling the amount of heat directed to certain portions of the sheet. The absorption of energy by the sheet depends on: • •
The polymer classification, such as PVC, PE, PET or PS, The type and dosage of various adducts in the polymer, particularly colorants, pigments, and • The thickness of the polymer sheet.
The last factor is most critical to the selection of proper equipment. As discussed in Chapter 2, most plastics are semi-transparent to incident infrared radiation. The total amount of energy absorbed is strongly dependent on the thickness of the polymer sheet. For very thin sheet or film, a substantial portion of incident radiant energy may be transmitted completely through the film. As a result, thin sheet and film heat very slowly when infrared heating is used. Direct contact heat transfer is recommended for thin films of thicknesses of less than about 0.005 in or 0.13 mm, for thin-gage sheet where the surface has been printed or metallized, or for thin-gage sheet that is laminated or contains embedded energy absorbers such as carbon or metal fibers. These aspects and others are discussed in detail in Chapter 3 on heating the sheet. As noted above, sheet sag is a serious problem with certain polymers. Sag bands are standard fare for minimizing sag. In certain cases, sag bands cannot be fully utilized, because of mold configuration or the nature of the polymer. Special thermoformers are available that allow the sheet to be heated and formed vertically. The colder portion of the sheet supports the hotter portion of the sheet as it passes through the excessive sag thermal region. Alternatives to this approach, such as solid-phase pressure forming and compounding or reformulating the polymer to yield one with higher melt strength, are usually less expensive in the long haul. The forming station of a typical thin-gage former is substantially more complex than that of a heavy-gage former. Owing to the thinner sheet, events must take place much more rapidly than those for a heavy-gage sheet. In addition: • • •
Molds are much smaller and are usually in multiples, Plugs must be ganged, Multiple molds require special hold-down plates called cavity isolators or holddown grids, to minimize variations in wall thickness, • Stripper plates are needed to uniformly strip the formed parts from the mold without racking, binding, scuffing or jamming.
Plugs dominate the prestretching process. Machines must have the capability of carrying the mold in the "up" or "down" position. This means that the presses should have two platens and both platens must travel. Presses with this capability are useful in pressure forming and matched die forming, as well. For these two technologies, the press clamping capability must be robust. Thin-gage parts are removed from their web either while they reside on the mold or away from the forming press in an in-line stand-alone trimming press. Since the part is locked on the mold, trimming on the mold, or trim-in-place, affords the most dimensional control on the trimming location. If the part is completely cut from the web, it must be picked or removed from the press before the next sheet is indexed to the forming station. There are many ingenious ways to do this. Nevertheless, the picking method must be absolutely infallible. A part that is not picked or a part that is dropped before clearing the mold will cause havoc in the next forming step. Usually the trimming is not complete, with tabs remaining that hold the parts in the web until the sheet is clear of the mold. Mechanical or manual picking is then required. In-line stand-alone trimming is an economically viable alternative for polymers that do not show substantial distortion, shrinkage or "swimming" between the forming press and the trim press. Extensive efforts are made to correctly register the formed part in the trim press, as discussed in Chapter 5. Additional information is found in [34].
1.9
References
1. J. Harry DuBois, Plastics History USA, Cahners Books, Boston, 1972, pp. 38-51. 2. Anon., "Monoformer", Hayssen Mfg. Co., Sheyboygan WL, 1977. 3. A.H. Steinberg, "Stamped Reinforced Thermoplastic Sheet", Design. Engineering Seminar, 33rd SPI RP/C Conference, Washington DC, Feb 1978. 4. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, and Tests for Design, Hanser Publishers, Munich, 1993, Section 1.2 "Introduction to Polymer History". 5. W. McConnell, "The Oldest Infant", in P.F. Bruins, Ed., Basic Principles of Thermo forming, Gordon and Breach, New York, 1971, p. 3. 6. S. E. Farnham, A Guide to Thermoformed Plastic Packaging, Cahners Books, Boston, 1972, p. 8. 7. J.L. Throne, "Thermoforming: Polymer Sheet Fabrication Engineering, Part 1. Solid Sheet Forming", Plast. Rubber: Proc, 4 (1979), p. 129. 8. E.S. Childs, "Thermoforming-Trends and Prospects", in P.F. Bruins, Ed., Basic Principles of Thermoforming, Gordon and Breach, New York, 1971, p. 37. 9. M. Bakker, personal communication, 1 October 1985. 10. Anon., "Thermoforming", Modern Plastics, 62:1 (Jan 1985), p. 59. 11. J.L. Throne, Thermoforming, Carl Hanser Verlag, Munich, 1986, Figure 1.1, p. 15. 12. E.S. Childs, "Thermoforming-Trends and Prospects", in P.F. Bruins, Ed., Basic Principles of Thermoforming, Gordon and Breach, New York, 1971, p. 38. 13. Anon., ''Thermoforming Lustran ABS, Lustrex Polystyrene and Cadon Engineering Thermoplastics", Monsanto Bulletin #6541, Undated, p. 3. 14. E.S. Childs, "Thermoforming-Trends and Prospects", in P.F. Bruins, Ed., Basic Principles of Thermoforming, Gordon and Breach, New York, 1971, p. 40.
15. P.V. Alongi, "Thermoforming", Mod. Plast, 69:13, (Dec 1992), pp. 577-579. 16. R. Wood., "Inline Thermoforming Offers Efficiencies for Packaging and Large Components", Plast. Mach. Equip., 19:1 (JuI 1985), p. 18. 17. G.P. Kovach, "Thermoforming", in Encyclopedia of Polymer Science and Technology, Vol. 13, 1969, p. 832. 18. G. L. Beall, "Designers' Guide to Pressure Forming", Plast. Design. Forum, 10:5 (May 1985), p. 42. 19. J.M. Wooldridge, "Polymer Process Modeling: Thermoforming of Simple Objects Via Finite Element Analysis", MS Thesis, U. Louisville, Louisville KY, 1985, p. 2. 20. Anon., Modern Plastics, 70:12 (Nov 1993), pp. 489-515. 21. A. Hoger, Warmformen von Kunststoffen, Carl Hanser Verlag, Munich, 1971, Chapter 4, "Maschinen zum Warmformen". 22. J.L. Throne, Thermoplastic Foams, Chapman & Hall, New York, 1995. 23. Wm. K. McConnell, Jr., Material Presented, Distributed at SPE Industrial Thermoforming Symposium & Workshop, 12-14 March 1985. Material Copyrighted by McConnell. 24. A. Hoger, Warmformen von Kunststoffen, Carl Hanser Verlag, Munich, 1971, pp. 135-136. 25. J.L. Throne, "Thermoforming Crystallizing PET", SPE ANTEC Tech. Papers, 27(1981), p. 598. 26. J.L. Throne, "Thermoforming Crystallizing Polyethylene Terephthalate (CPET)", Adv. Polym. Tech., 5(1988), pp. 131-171. 27. J. Florian, Practical Thermoforming: Principles and Applications, Marcel Dekker, New York, 1987, pp. 190-191. 28. J. Florian, Practical Thermoforming: Principles and Applications, Marcel Dekker, New York, 1987, Florian pp. 199-201. 29. Anon., "Kostur... The Shape of Performance in Thermo Forming Production", Kostur Enterprises, Inc., Riviera Beach FL, 12 Dec 1983. 30. K.-H. Hartmann, "Wirtschaftliches Fertigen von warmgeformten Verpackungen", Kunststoffe, 75(1988), pp. 398-401, BiId 2. 31. K.-H. Hartmann, "Wirtschaftliches Fertigen von warmgeformten Verpackungen", Kunststoffe, 75(1988), pp. 398-401, BiId 5. 32. G.L. Beall, "A Brief History of the Mold Making and Mold Design Div. of SPE", Plast. Mach. Equip., 27:6 (June 1993), pp. 38-40. 33. J.L. Throne, Thermoforming, Carl Hanser Verlag, Munich, 1987, p. 33. 34. G. Gruenwald, Thermoforming: A Plastics Process, Technomic Publishing Co., Inc., Lancaster PA, 1987, Chapter 6, "Trimming of Thermoformed Parts". 35. Anon., Polymer News, 16 (1991), p. 214. 36. Anon., Polymer News, 76(1991), p. 87. 37. Anon., Polymer News, 12 (1987), pp. 50-51. 38. Anon., Polymer News, 12 (1987), pp. 215-216. 39. Anon., Polymer News, 13 (1988), pp. 20-21. 40. Anon., Polymer News, 13 (1988), pp. 152-153. 41. Anon., Polymer News, /6(1991), p. 313. 42. Anon., Polymer News, 18 (1993), p. 148. 43. Anon., Polymer News, 16 (1991), p. 250. 44. Anon., Polymer News, /6(1991), p. 340. 45. Anon., Polymer News, // (1986), pp. 214-215. 46. Anon., Polymer News, 18 (1993), p. 227. 47. Anon., Polymer News, 14 (1986), pp. 118-119. 48. Anon., Polymer News, /6(1991), p. 86. 49. Anon., Polymer News, /6(1991), pp. 25-26. 50. Anon., Polymer News, /6(1991), p. 186. 51. Anon., Polymer News, 13 (1988), p. 151. 52. Anon., Polymer News, 15 (1990), p. 377.
2 Polymeric Materials
2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9
Introduction Network Nature of Polymers Addition and Condensation Polymerization Aromatic and Aliphatic Polymers Molecular Weight and Molecular Weight Distribution Molecular Weight and Properties Morphology and Properties Molecular Orientation Chain Mobility and Polymer Stiffness
2.10 2.11 2.12 2.13 2.14
Stress-Crack Resistance Gas Permeation Copolymerization Blends Adducts Plasticizers Other Additives Fillers and Reinforcing Fibers Laminates Stress-Strain Behavior of Plastics Thermal Properties Heat Capacity Thermal Conductivity Thermal Diffusivity Thermal Expansion Coefficient Infrared Spectra Summary References
2.15 2.16 2.17
2.18 2.19 2.20
2.1
Introduction
If a polymer can be produced as a sheet, it can be thermoformed into a product [1,2]. Polymers are high molecular weight organic molecules that are produced by combining very pure carbon-based simple molecules under heat, pressure, and catalyst systems. There are more than 20 major classes of polymers available today [3] and many sub-classes, made by combining polymers with polymers, polymers with fillers and reinforcements, and polymers with additive and processing aids [4]. In order to achieve thermoformed parts having commercially interesting combinations of physical properties, it is necessary to understand the way in which basic polymer architecture affects material properties.
2.2
Network Nature of Polymers
There are two general categories of polymers—thermoplastics and thermosets. Commercially, the most important thermosetting polymers are intrinsically crosslinked resins such as epoxies, phenolics, and reacted unsaturated polyester resins. The polymers are formed from relatively simple chemically unsaturated molecules that are usually liquids at the reaction conditions. The unsaturation is seen as isolated, regularly-spaced double bonds regularly spaced along the carbon-carbon backbone, as -R-C = C-R-. The formation of three-dimensional ties is accomplished by opening the double bonds, -C = C-, with chemical aids or sometimes with heat and pressure. At some point during the formation of this three-dimensional network, the material usually becomes infusible and takes a permanent shape. Thermosets usually cannot be reused or returned to their original forms. More than 80% of all polymers used in the world today are thermoplastics. These polymers are characterized by exceptionally long two-dimensional, nearly linear organic molecules, usually having saturated or single covalent bond carbon-carbon backbones, as -C-C-. In their final forms, thermoplastics are thermally and chemically stable at processing conditions. This means that they can be softened or melted, formed into useful articles, then resoftened or remelted and reused. Thermoforming economics depend on the thermal stability and resulting recyclability of polymers, and so nearly all commercially thermoformable polymers are thermoplastics. The toughness of thermosets is due to the rigid three-dimensional network of relatively small building blocks. The toughness of thermoplastics is due mainly to the entanglements of the very long two-dimensional molecules and in certain cases, the formation of crystalline structures. For example, if the ethylene molecule, CH2 = CH2, is scaled in dimension 100 million times, each -CH2- unit would be about 10 mm or 3/8 in long. The single ethylene unit in a polyethylene backbone, -CH2-CH2is called a repeat unit. An olefin grease or oil has about 100 repeat units and on the same expanded scale would be about 2 m or 6 ft long, if the molecular chains are fully extended. Low-density polyethylene (LDPE) has about 1000 repeat
Table 2.1 Comparative Sizes of Polymer Molecules (Fully Extended Chains Scaled 100,000,000:1) Polymer
Epoxy adhesive Melamine Epoxy resin-medium MW Phenolic Alkyd-unsaturated polyester resin Olefin grease Epoxy resin-high MW Polyethylene, low-density Polyethylene, UHMW
(A)
Degree of polymerization
15.9 35.4 110.9 40.1 94.4 200 580.6 2000 91,000
1 5 6.5 8 19 67 34 670 30,000
End-to-end distance
Chain or free segment length Metric (m)
US (ft)
0.159 0.354 1.109 0.401 0.944 2.00 5.81 20.0 910
0.52 1.17 3.64 1.3 3.10 6.56 19.1 65.6 3000
units and would be about 20 m or 65 ft long, with fully extended chains and minimal branching. Ultra-high molecular weight polyethylene (UHMWPE), a nearly intractable polymer used for friction-and-wear applications, has about 100,000 repeat units, and the extended chains would be about 2 km or 1.2 miles in length. On the other hand, the chain lengths between crosslinking or tie points for thermosets are about 10 to 20 repeat units in length. On the same expanded scale, phenol-formaldehyde or phenolic resin would have chain lengths between tie points of about 25 mm or 1 in. More importantly, molecular diameter would be nearly 25 mm or 1 in, as well. Other comparisons are given in Table 2.1 [5]. Some thermoplastic polymers such as polyethylene are further toughened by crosslinking, with either irradiation or peroxide chemicals. Crosslinking is accomplished by removal of a small molecule such as hydrogen from the primary carbon-carbon backbone. Active sites on adjacent chains then react to form a tie point or crosslink. The number of tie points per thousand repeat units is usually quite small. Typically, crosslinked high-density polyethylene (HDPE) has about 0.5 to 1 tie points per thousand backbone carbons. Low-density polyethylene (LDPE) has about 5 to 10 per thousand backbone carbons. These few tie points serve only to partially immobilize the polymer above its traditional melting point. Thus, crosslinked thermoplastics remain very soft, thermoformable solids rather than becoming fluid above their melting points (Fig. 2.1). As expected, crosslinked LDPE, with its greater frequency of tie points, is considerably more difficult to stretch-form than crosslinked HDPE. The reprocessing, regrinding and re-extruding of crosslinked thermoplastics usually result in mechanical and thermal destruction of tie points or backbone carbon-carbon bonds. Furthermore, crosslinking does not allow melt processing and so small amounts of crosslinked polymer form intractable gels in uncrosslinked polymer extrudates. Thermoforming requires biaxial stretching of polymer sheet. Although certain thermosetting polymers such as rubber soften above their glass transition tempera-
Glassy Plateau
Modulus
High Crystallinity
Low Crystallinity
Rubbery Plateau
Crosslinked
Amorphous
Glass Transition Liquid Flow Temperature Temperature
Melt Temperature
Temperature Figure 2.1 Schematic of temperature-dependent modulus for amorphous, crystalline and crosslinked polymers
tures, the tight three-dimensional network of most rigid thermosetting polymers restricts the gross deformation necessary in thermoforming1. However, partially crosslinked polyurethane has been simultaneously drawn, formed, and heat-stabilized to produce fully crosslinked thermoset shapes [7]. Once these molecules are immobilized, very little additional shaping is possible. Additional thermal energy input or regrind then leads to polymer degradation.
23
Addition and Condensation Polymerization
Thermoplastic polymers are produced from monomers in two general ways. Addition polymers are formed by continuous extension of a preexisting polymer chain by 1
Low-density thermosetting and highly crosslinked thermoplastic foams are the exception to this. Foam cell architecture dominates the tensile and compression behavior of the polymer. Bending and stretching occur predominantly at cell strut or plate intersections rather than in the polymer itself [6].
attachment of a monomer containing a reactive double bond. The largest group of addition polymers are called generically vinyl polymers. Table 2.2 [8,9] summarizes the chemical structure of many common addition polymers, including many common thermoformable polymers such as HDPE, LDPE, polypropylene (PP), polyvinyl chloride (PVC), and polystyrene (PS). Condensation polymers are formed by reacting one, two, or more saturated comonomers with active end groups. Such end groups are amines, hydroxyls or carboxyls. The reaction usually results in evolution of a small by-product molecule such as water. This molecule must be removed continuously to continue the reaction. Thermoplastic polyester (PET), nylon (PA), polymethyl methacrylate (PMMA), and polycarbonate (PC) are examples of thermoformable condensation polymers. These and others are summarized in Table 2.3.
2.4
Aromatic and Aliphatic Polymers
Polyethylene and polypropylene are simple, nearly linear polymers consisting of -C-C- building blocks, with no double-bond unsaturation or ring structure. These are aliphatic polymers. Polystyrene has an unsaturated benzyl pendant group on every other backbone carbon, as is considered the simplest form of an aromatic polymer. Higher aromatic polymers such as polyethylene terephthalate and polycarbonate have ring structures such as benzyl groups within the backbone on regular intervals. Polymer properties such as stiffness and thermal stability are strong functions of the degree of aromaticity [10].
2.5
Molecular Weight and Molecular Weight Distribution
The molecular weight of a given polymer molecule is obtained by multiplying the molecular weight of its repeat unit by the number of repeat units, then addition in the molecular weight of the end groups. For example, the molecular weight of the ethylene repeat unit, -CH2-CH2-, is 28. For HDPE of 10,000 repeat units, the molecular weight is 280,30. In all commercial polymers, there is a distribution of polymer chain lengths (Fig. 2.2). The number-average polymer chain length is obtained by calculating the total weight of all polymer chains, w, then dividing by the total number of chains, n:
The weight-average molecular weight is obtained by multiplying the weight of a chain of a given length, w, by the number of these chains, n, then dividing by the total weight of the chains, w: M.- = . w
™ Z N 1 Mj
(2.2.
Table 2.2 Chemical Structure of Vinyl-Type Thermoplastics R 1 R3 R 2 R4 Common name
Ri
R2
Polyethylene
H
H
H
H
Polyethylene
H
H
H
CH3
Polybutene-1 Polybutadiene Polyvinyl chloride (PVC) Polyvinyl dichloride (PVDC) Polyvinyl fluoride (PVF) Polyvinyl difluoride (PVDF) Polytetrafluoroethylene (PTFE)
H H H H H H F
H H H H H H F
H H H Cl H F F
CH2CH3 HC=CH, Cl Cl F F F
Polysytrene (PS)
H
H
H
C6H5
Polyvinyl alcohol (PVOH) Polymethyl methacrylate (PMMA) Polyvinyl acetate (PVAc) Polyacrylonitrile
H H H H
H H H H
H CH3 H H
OH COCH3 00CCH3 CH
1 2 3 4
Melting temperature of pure crystal polymer Commercially amorphous polymer Isotactic melting point Highly oriented fiber
Subspecies
Glass transition temperature (0C)
Crystalline melt temperature (0C)
LOPE (Branched) HOPE (Linear) Atactic Syndiotactic (Isobutylene) (Divinyl)
-70 -110 -15 -5 -70 -55 80 -17 -20 -35 125
112 134 (137)1 A2 165(17O)1 A2 A2 A2 (212)1 A2 A2 A2 326
94
A2 (24O)3
(6)
85 100 30 104
A2 A2 A2 2754 (327)1
Table 2.3 Chemical Structure of Typical Condensation Thermoplastics Common name
Polyethylene terephthalate (PET)
Repeat unit O
O
Il
I l
—(CH 2 ) 2 —O— C —
O
Il
I l
Glass transition temperature (0C)
Crystalline melt temperature (0C)
70
260(26T)1
48
240(265)]
Nylon 66 (PA-66)
-N-(CH2)6-N- C -(CH2J4- C H H O
Nylon 6 (PA-6) (polycaprolactum)
-N-(CH2)6-CH CH3 O
50
210
Polycarbonate (PC)
—O—C —€>—O—C—O—
150
A2
-60
180
40
(?)4
Polyacetal (POM) (polyoxymethylene) Cellulose
3
Il
I
I l
CH3 -CH2-O CH2-R (R = OH) Cellulose CH-O (R = NH 2 ) / \ Cellulose nitrate -HC CH-O— (R = OOCCH3) \ / Cellulose triacetate CH-CH R
R (R = 0OCC3H7) Cellulose tributyrate 1 Melting temperature of pure crystal polymer 2 Commercially amorphous polymer 3 Natural polymer 4 Infusible, degrades before melting O = Benzyl ring
53 70,100(?)
280(?)(305)1
120
180(7XlSS)1
Number of Molecules
Number-Average Molecular Weight Figure 2.2 Typical molecular weight distributions for narrow and broad molecular weight polymers. Figure used by permission of copyright owner
The ratio of weight average to number average molecular weight is known as the dispersity index, DI:
The dispersity index generally represents the shape of the chain length distribution curve. These three terms help to define the molecular characteristics of the polymer. Molecular weight distributions cannot be measured directly. Dilute solution viscosity measurements yield indirect information, as do end group analyses, turbidity and osmotic pressure measurements, and calculations based on infrared analyses [H]. Thus, whenever the phrase "molecular weight distribution" is used, it must be carefully defined.
2.6
Molecular Weight and Properties
A polymer that has a low molecular weight is easier to extrude into a sheet than one with a very high molecular weight. However, high molecular weight yields improved hot strength during forming and improved finished part properties. Figure 2.3 [12] illustrates this for polyethylene. At a low molecular weight of 1000, polyethylene is a waxy solid at room temperature and an oily liquid at temperatures of less than 212°F or 1000C. At a molecular weight of 100,000, it is a tough ductile plastic at room temperature and a highly elastic liquid above its 1100C or 2300F melt
Brittle Wax Hard Plastic Soft Plastic
Soft Wax
Tough Wax Grease, Liquid Molecular Weight Figure 2.3 Relationship between polyethylene molecular weight, crystallinity and nature of polymer [12]. Figure used by permission of copyright owner
temperature. At a molecular weight of 1,000,000, as UHMWPE, it is an extremely tough crystalline solid at room temperature. The molecular chains are so long and entangled that it barely flows even at temperatures far above its melting point of 134°C or 273°F. Polymethyl methacrylate (PMMA) is another example. At a molecular weight of 300, it is a viscous liquid at room temperature that is commonly used as a cell casting liquid to produce higher molecular weight PMMA. At a molecular weight of 30,000, PMMA is a glassy, brittle transparent solid at room temperature. It becomes a rubbery contiguous formable sheet when heated to temperatures of 150 to 2000C or 300 to 3800F or 50 to 1000C or 90 to 1800F above its softening point or glass transition temperature, T g =105°C or 2200F. Increasing the temperature further causes excessive chain mobility, manifested as sheet sag. For some polymers, the molecular weight distribution can be significantly altered during polymerization or afterward in special depolymerization steps. Typically, broad molecular weight distribution polymers have very shear-sensitive viscosities over wide temperature ranges. These are usually easier to process than narrow molecular weight distribution polymers. Broad molecular weight distribution polymers are used in extrusion coating, laminating and heat sealing where high melt strength over a wide processing temperature range is sought. On the other hand, certain narrow molecular weight distribution polymers can be highly oriented and so yield very tough film and thin-gage sheet. Narrow molecular weight distribution polymers usually have better mechanical properties than broad molecular weight distribution polymers. It is difficult to generalize here, however, since other factors such as: • • • • •
Extent of chain entanglements, Extent of short-chain branching, Extent of long-chain branching, Polymer tacticity and isomerism, Pendant group size,
• •
Pendant group frequency, and Molecular level energy interactions such as; Van der Waals forces, Hydrogen bonding forces, Ionic bonding forces, and Dipole interaction,
act to mask and dominate the effect of molecular weight for any given homologous class of polymers.
2.7
Morphology and Properties
Polymer processing in general is concerned with the economic transition between the solid and fluid or semi-fluid states of polymers. It is easy to identify the liquidus phase of nonpolymeric crystalline substances such as metals and ceramics. An abrupt first-order thermodynamic transition from a rigid state to a waterlike fluid state occurs with a measurable absorption of energy, the latent heat of fusion. Crystalline metals and ceramics in the solid state have regular, ordered atomic structures that sharply diffract X-rays in known, repeatable fashions. It is difficult to envision long-chain, highly entangled polymers as having the high degree or thermodynamic order needed to form crystalline domains. Yet certain polymers such as nylons, polyethylene, polyethylene terephthalate and polypropylene readily crystallize when cooled from the melt. Although single polymer crystals are commonly formed in laboratories, polycrystalline structures are formed in commercial processes. Crystalline formation is a kinetic or rate-dependent process. Noncrystalline or amorphous polymers have molecular structures that are unordered. Disorder may be caused by: •
•
Bulk or stiffness or the polymer chain because of; Side chain branching frequency, Side chain branch length, Side chain branch bulk, Large pendant groups, Steric hindrance, Ladder-type backbone morphology, and Extensive aromaticity in backbone, and Rapid quenching of a potentially crystalline polymer from the melt.
Most crystallite regions in commercial crystallizable polymers are mixtures of spherulitic or sphere-like crystals, dendritic or tree-like crystals, and amorphous regions. The extent of crystallinity and to some extent, the size of the crystallites, for any polymer strongly effect such characteristics as: • • •
Its X-ray pattern, Its melting temperature, Its melting temperature range, and
•
Nearly all commonly measured physical properties such as Tensile strength, Yield strength, Elongation at break, Impact strength, and Chemical resistance
For a crystallizable polymer, high molecular weight, narrow molecular weight distribution, low branching, and backbone linearity yield high crystallinity levels. Small amounts of nucleants such as: • • • • •
Pigments, Organic promoters, Catalyst residue, Fillers, and Reinforcing fibers,
enhance the rate of crystallization. Annealing and orientation also enhance crystallization while high shear processing and rapid cooling inhibit it. Crystallization is a rate-dependent process, as shown in Table 2.4 [13,14]. The isothermal time to reach 50% of the ultimate crystallized fractional volume change is known as the crystallization half-time. The temperature-dependent semi-logarithmic half-time curves are characteristically cup-shaped, as seen for PET in Fig. 2.4 [15,16]. These curves are classically fit with the Avrami equation: -lnc|) = Ktn
(2.4)
where cj) is the volume fraction of uncrystallized material, given as: O = I - ^
(2-5)
Table 2.4 Isothermal Rates of Crystallization for Several Polymers at Tempertures 300C or 54°F below Their Reported Melt Temperatures1 Polymer
Crystallization rate (nm/min)
Polyethylene Polyhexamethylene adipamide (PA 66 or nylon 66) Polyoxymethylene (POM or acetal) Polycaprolactam (PA 6 or nylon 6) Polychlorotrifluoroethylene (PCTFE) Isotactic polypropylene (PP) Polyethylene terephthalate (PET) Isotactic polystyrene (iPS) Polyvinyl chloride (PVC)
5000 1200 400 150 30 20 10 0.25 0.01
1
Adapted from [13,14] with copyright permission
Crystallization Half-Time, t1/2, min
0.65 IV With Talc Nucleant
Temperature, 0C Figure 2.4. Crystallization half-time for various types of polyethylene terephthalate, PET [15,16]
where Ar; is the volumetric change determined by dilatometric methods. K and n are empirical coefficients. K is polymer specific and a strong function of temperature and possibly nucleant concentration, if any. The Avrami constant, n, is a measure of the nature of the crystallite formation. For moderate processing conditions, n = 3 for constant nucleation of spherical crystallites or sporadic plate-like growth [17]. As is apparent from Fig. 2.4, slow cooling enhances crystallization and quench cooling inhibits it. Reheating amorphous sheet of a crystalline polymer such as PET to temperatures where appreciable crystallization takes place leads to unwanted haze. It also leads to a method of fabricating crystalline structures from initially amorphous sheet, as described in detail in Chapter 9 [18]. Usually, thermoforming requires highly extensible sheet at relatively low stretching loads. Very few crystalline polymers can be vacuum thermoformed below their melt temperature. Polypropylene can be pressure thermoformed at or just below its melting temperature. The amount of pressure depends on the level of crystallinity and the size of and regularity of spherulites, as discussed in Chapter 9. Figure 2.5 shows a temperature-dependent modulus for polyisobutylene, a crystalline polymer [19]. X-ray patterns for polymers with crystalline levels less than about 30% are difficult to interpret. Amorphous polymers have no X-ray diffraction patterns, no melting point, and thus no latent heats of fusion. When an amorphous polymer is heated, the temperature range over which it changes from a rubbery solid to a flowable fluid can be as broad as 50 to 600C or 80 to 125°F. Polystyrene and nearly all commercial PVCs are amorphous polymers. The temperature at which a polymer changes from a brittle, glass-like polymer to a rubbery one is the glass transition temperature, Tg. This is a second-order thermodynamic temperature where substantial chain segment mobility takes place along the backbone. Under stress, permanent
Temperature, 0C
Glassy Region
Modulus, MPa
Time, h Glass Transition Region Decomposition
Rubbery Region Polyisobutylene Viscous Flow
Normalized Temperature, T/Tg Figure 2.5 Temperature-dependent modulus of polyisobutylene, showing time-dependent glass transition region [19]
chain motion and intermolecular deformation are possible. Since polymers have broad distributions of molecular chain lengths, the glass transition temperature is in reality a temperature range of a few degrees (Fig. 2.6) [20]. Nevertheless a single value is usually given for a specific polymer. The glass transition temperature is the absolute lowest temperature at which the polymer can be formed. As processing temperatures increase above Tg, amorphous polymers become increasingly easier to process. Crystalline thermoplastics, cross-linked thermoplastics, and certain thermosetting polymers have glass transition temperatures, as well. For thermosets, chain mobility is restricted by the three-dimensional molecular network until the thermal degradation temperature is reached. In crystalline polymers, the morphological order in the crystalline regions restrict amorphous chain mobility until the melting temperature is reached (Fig. 2.7). For crystalline polymers, the ratio of melt temperature to glass transition temperature is 1.4 to 2.0 in 0K. For polymer homologs, increasing molecular weight yields increasing crystallinity and melt temperature [21]. The glass transition temperature, Tg, is relatively unaffected by molecular weight. Figure 2.8 [22] shows a typical amorphous polymer phase diagram. Figure 2.9 [23] shows a similar phase diagram for a semicrystalline polymer. Glass transition temperatures for typical thermoformable polymers are given in Tables 2.2, 2.3 and 2.5.
Temperature, 0C Glassy Region A-Transition
Modulus, MPa
Time, h
Glass Transition
Decomposition
Rubbery Region
Viscous Flow Polystyrene
Normalized Temperature, T/Tg Figure 2.6 Temperature-dependent modulus of polystyrene, showing time-dependent glass transition region [20]
Melting Temperature,0K
Polyethylene Terephthalate
Nylon 66 [PA-66 Polyvinylidene Chloride Polyurethane Polyethylene Adipate Polyisobutylene
Polychlorotrifluoroethylene Polyvinyl lsobutylether
Polyethylene Sebacate Polysulfide Rubber Polychloroprene Natural Rubber
Dimethyl Silicones
Glass Transition Temperature,0K Figure 2.7 Relationship between glass transition temperature and melting temperature of several polymers [21]
Molecular Weight
Thermal Decomposition Line Diffuse Transition Zone Viscous Liquid Rubbery Region Glass Transition Line
Glassy Region
Temperature Figure 2.8 Amorphous polymer phase diagram [22]
Thermal Decomposition Line
Molecular Weight
Diffuse Transition Zone R u bbery-Crystall i ne or Leathery Region
Crystalline Melting Line Viscous Liquid
Rigid-Crystalline Region Glass Transition Line Glassy Region
Temperature Figure 2.9 Crystalline polymer phase diagram [23]
Table 2.5 Characteristic Temperatures of Thermoformable Polymers Polymer
Amorphous polymers Polystyrene PMMA PMMA/PVC alloy ABS Polycarbonate Rigid PVC Modified PPO Polysulfone Polyethersulfone (PES) 20% GR PES Polyamide-imide Crystalline polymers LOPE EVA HDPE Cellulose acetate Cellulose butyrate Cellulose propionate Polypropylene, homoPolypropylene, CO40% GR PP Polymethyl pentene PVDC Acrylonitrile PET PBT, neat Nylon 6 (PA 6) Nylon 66 (PA 66) POM, copolymer 30% GR POM PTFE FEP PEEK Foams Polystyrene foam Rigid PVC foam
Glass transition temperature (0C) (0F)
94 100 105 88-120 150 77 104-110 190 230 225 275
Melt temperature (0C) (0F)
200 212 221 190-248 300 170 219-230 374 445 437 527 -13
115 107 -166 134 -110 158, 212 230 70, 100 248 140 120 190 168 41 150-175 -20 -4 168 5 41 235 47 117 160 0 32 135 95 203 255 70 158 -80, 70 -112, 158 245 220 58 136 255 78 169 165 -55 -67 166 -50 -58 327 -55 -67 275 -55 -67 100, 149 212, 300 334 -25
70-85 70
158-185 158
239 225 273 445 284 374 334 302-347 334 455 320 275 490 473 428 491 329 331 621 527 633
Heat distortion temperature (0.46 N/mm 2 / 66 psi) (0C) (0F)
Set and mold temperature (0C) ( 0 F)
Lower forming temperature (0C) (0F)
Orienting temperature (0C) (0F)
Normal forming temperature (0C) (0F)
Upper forming temperature (0C) (0F)
68-96 74-113 81 77-113 138 57-82 110 181 216 216 302
155-204 165-235 177 170-235 280 135-180 230 358 420 420 575
85 85 79 82 132 66 99 163 204 210 232
185 185 175 180 270 150 210 325 400 410 450
127 149 143 127 168 104 165 191 274 279 357
260 300 290 260 335 220 325 375 525 535 675
135 163 154 137 177 118 182 213 293 293 371
275 325 310 280 350 245 360 415 560 560 700
149 177 171 146 191 138 188 246 316 316 404
300 350 340 295 375 280 375 475 600 600 760
182 193 182 182 204 154 204 302 343 357 427
360 380 360 360 400 310 400 575 650 675 800
40-44 62 79-91 52-93 54-108 64-121 107-121 85-104 166 85 68 78 49 185 80 105 110-125 163 46 70 140
104-112 114 175-196 125-200 130-227 147-250 225-250 185-220 330 185 155 172 120 365 176 221 230-257 325 115 158 284
66 77 77 71 79 88 88 88 91 77 66 82 77 177 91 104 99 104 99 149 160
150 170 170 160 175 190 190 190 195 170 150 180 170 350 195 220 210 220 210 300 320
116 127 127 127 127 127 132 143 129 260 163 127 121 260 216 249 163 163 234 232 399
240 260 260 260 260 260 270 290 265 500 325 260 250 500 420 480 325 325 435 450 750
129 138 132 141 138 137 138 177 141 274 177 137 138 274 224 260 177 177 249 246 413
265 280 270 285 280 280 280 350 285 525 350 280 280 525 435 500 350 350 480 475 775
132 146 146 154 146 146 154-163 185 204 277 182 149 149 274 227 274 182 182 260 260 418
270 168 295 182 295 182 310 182 295 182 295 182 310-325 166 365 193 400 232 530 288 360 199 300 182 300 166 525 288 440 238 525 288 360 204 360 204 500 282 500 279 785 427
335 360 360 360 360 360 330 380 450 550 390 360 330 550 460 550 400 400 540 535 800
55-65 65
131-149 149
50 66
122 150
88 110
190 230
96 124
205 255
104 143
220 290
235 340
113 171
Table 2.6 Biaxial Orientation Properties of Thermoformable Polymers1 Polymer
Polystyrene PMMA PP
PET HdPE 1 2
Orientation
Tensile strength
Elongation at break
Impact strength
(MPa)
(lbf/ln2)
(%)
(J/m)
(ft-lb/in)
None Biaxial None Biaxial None Blown Tenter-frame
34.5-62 48.3-83 51.7-70 55.2-75.8 31.4-41.4 207 124-234
5000-9000 7000-12,000 7500-10,000 8000-11,000 4500-6000 30,000 18,000-34,000
1-36 8-18 5-10 25-50 100-600 80 50-130
13.3-27 >160 215 800 530 NA2 NA
0.25-0.5 >3 4 15 10 NA NA
None Biaxial None Blown
48.3-70 207 22.1-31.0 34.5-35.9
7000-10,000 30,000 3200-4500 5000-5200
200-300 100
13.3-37 NA 21.3-213 NA
0.25-0.7 NA 0.4-4.0 NA
600-700 450-500
Adapted from [24-26] Not available
2.8
Molecular Orientation
In some polymers, sheets are biaxially oriented during the extrusion process to obtain improved properties in some polymers. Both crystalline and amorphous polymers can be oriented. For crystalline polymers, unique combinations of properties are achieved by carefully matching levels of mechanical stress to heating and cooling rates. The crystallites formed this way are formed from highly oriented molecules, yielding dramatic reductions in haze level, for example, and equally impressive increases in ultimate tensile strength, albeit at reduction in elongation at break. Thin-gage sheets of amorphous polymers such as PS and PMMA are biaxially oriented as well, to yield substantially increased ultimate elongation and ductility in the heated sheet and in the formed product. Some properties of oriented crystalline and amorphous polymers are given in Table 2.6 [24-26].
2.9
Chain Mobility and Polymer Stiffness
The intrinsic strength of a polymer depends on chain rigidity and ability of polymer-to-polymer intermolecular structure to withstand deformation or disentanglement under load. The ductility, hardness, resistance to impact and stiffness of a plastic product are related to the nature of the polymer molecular structure. Flexibility is a function of the degree of chain segment rotation about the -C-C-
Table 2.7 Effect of Steric Hindrance on Polyethylene Properties [27] Effect Branching: Chain ends per 1000 carbon atoms Attainable crystallinity Elastic modulus [MPa] Relative density [kg/m3] Crystalline melting point (0C)
LDPE
HDPE
25
2
-65% 170 115 115
-85% 1380 131 131
backbone. If double bonds are included in the backbone, stiffness is increased. It is increased further if the occurrence of double bonds is regular, such as -C = C-C = C-. Aromaticity in a pendant group adds stiffness as with PS. Benzene ring inclusion in the backbone as with PC and PET further increases stiffness. If the backbone has only aromatic carbon-carbon bonds, the polymer becomes quite stiff, as with polycyclic diphenyls. Some of the stiffest polymers are the polyimides where backbone bonding occurs at four points on the aromatic ring rather than two. This forms a ladderlike or rodlike structure. Decreasing chain mobility implies increasing difficulty in thermoforming the polymer sheet. The benzyl pendant group on PS stiffens the polymer chain, due to the difficulty in fitting the bulky pendant groups side by side along the backbone. This is called steric hindrance. Not all pendant groups cause stiffening, however. Long-chain branching on LDPE acts to separate main chains, increase free volume or the molecular-level voids in the solid. This reduces the bulk density of the polymer. The lowered density results in greater flexibility, lower tensile strength, lower Tg and Tm, and lower levels of crystallinity (Table 2.7) [27]. The methylene group on every other carbon of isotactic polypropylene represents the limiting case of short side-chain branching. The steric hindrance forces the polymer chain into a helix, stiffening the backbone and at the same time creating even greater free volume. As a result, PP has very low room temperature density and relatively high Tg and Tm. Although not pendant groups, per se, halogen atoms such as chlorine on PVC and the carboxyl group on PMMA are much larger than, say, a hydrogen atom. These groups cause substantial steric hindrance and prevent or at least inhibit crystallization of the polymers. More important is the highly electronegative state of halogen atoms, such as the chlorine on PVC and the fluorine on PTFE or FEP. In very regular polymers, these tend to repel one another, thus stiffening the backbone into a rodlike configuration. Most halogen-substituted polymers without plasticizers are quite difficult to process into sheet. Polymers that have very high hydrogen bonding levels, such as PMMA, certain celluloses and nylons, also have increased stiffness. Secondary hydrogen bonds occur between main chain groups such as amines, -H-NH-, and hydroxyls, -H-OH-. In effect, these increase the effective diameter of the chain segment and reduce its mobility.
Flexural Stress, x 1000 lbf/in2
Air Air
ABS ABS
HIPS HIPS
Vegetable Oil
Time to Failure, min Figure 2.10 Effect of environment on flexural creep rupture of HIPS and ABS [28]
2.10 Stress-Crack Resistance Environmental stress-crack resistance or ESCR is the ability of a strained polymer to withstand aggressive media. Many thermoformed products must withstand environments such as detergents, oils, greases and mild solvents. Solvent molecules tend to be quite small and so readily diffuse into the polymer, moved between adjacent polymer chains and act to separate them. When the polymer-solvent attraction forces exceed the polymer-polymer intermolecular attraction forces, the polymer chains are separated by the solvent. The polymer then dissolves, swells or crazes. Weak solvents act on the polymer chain only when it is strained. Unfortunately, most product stress crack failures occur because the strain polymer failed in a weak solvent over a long period of time (Fig. 2.10) [28]. Classic examples are rubber-impact-modified polystyrene shower stalls that craze when in contact with soap solutions for long times and refrigerator door and cabinet liners that craze or crack when in contact with certain foaming agents used in polyurethane insulation. Surface deglossing and microcrazing on PMMA and PVC are caused by exposure to very mildly aggressive environments. Migration and loss of small molecule plasticizers, erosion and acid rain also lead to microcrazing. UV-embrittlement is probably due to surface crosslinking.
2.11 Gas Permeation Gas transmission through polymers depends on the extent of the free volume in the formed part on the relative order of magnitude of polymer-polymer and polymer-gas
molecule attraction forces. Gases that are chemically similar to the polymer repeat unit tend to migrate readily. Cellulosics transmit water but polyolefins do not. Olefins tend to transmit fluorocarbon gases but styrenics do not. The permeation of a gas through a given plastic is the product of its solubility in the plastic and its diffusivity through the plastic. Solubility is directly related to polymer-solvent affinity [29]. In semicrystalline polymers, the small molecule diffusion rate through amorphous or unordered polymer regions is many times higher than that through highly order crystalline regions. As expected, an increasing degree of crystallinity leads to a decrease in permeability of all small molecules. Orienting any polymer substantially increases the small molecule diffusion path. Orienting a crystalline polymer results in substantially reduced gas permeation. Polymers such as PET and nylon become more efficient gas barriers with increased orientation.
2.12 Copolymerization Polymers made from a single set of monomers are called homopolymers. Frequently, specific end uses or processing conditions dictate properties that are unattainable by homopolymers. A common method of altering polymer properties is by co-reacting small amounts of reactive monomers with the primary polymer molecules. These copolymers can be added in the following fashions, by controlling the nature of the polymerization: •
Randomly along the polymer backbone, as random copolymerization. This results in: Broadening of melt and glass transition temperatures, Reduced stiffness or increased flexibility, Reduction in melt viscosity and crystallinity, and An increase in high temperature rubbery sheet strength and melt strength. Classic examples include ethylene into polypropylene to reduce Tg and increase thermoformability and sodium methacrylate into polyethylene to produce an ionomeric polymer with reduced crystallinity, improved transparency and toughness. • Fit into the polymer backbone as long-chain homopolymer segments, as block copolymerization. This results in main chain flexibility in otherwise brittle polymers. Classic examples include butadiene in polystyrene. The butadiene segments are not cosoluble with PS and so form a separate but chemically linked phase. • As pendant groups, as branched or graft copolymerization. ABS or acrylonitrilebutadiene-styrene is a terpolymer with the acrylonitrile polymer grafted to the block butadiene-styrene copolymer backbone. The acrylonitrile adds improved solvent resistance and high forming temperature toughness to impact-modified polystyrene.
2.13 Blends If two polymers are cosoluble, such as PS and polyphenylene oxide or PPO, or PVC and ABS, or polyvinyl acetate and PMMA, intensive shear melt mixing can yield a true thermodynamic single phase polymer mixture. The resulting polymer properties are nearly identical to those that are obtained through copolymerization. Note that physical blends of homologs such as polyethylenes or vinyls should yield true single phase blends, but may not. Insoluble blends yield macroscopic two-phase systems that might behave as if they are copolymers, as is the case of melt coblending butadiene rubber and polystyrene. However, many insoluble blends yield useless polymers.
2.14 Adducts Nearly all thermoplastics are mixtures of polymers and adducts or nonpolymers added to modify the general characteristics of the polymers. Table 2.8 [29,30] is a short list of some adducts found in thermoplastics. Plasticizers Plasticizers are small molecules of a chemical nature similar to the polymer in which they are dissolved. Their role is to separate the main chains, thus reducing polymerpolymer intermolecular forces and allowing the polymer chains to move past one another during shearing. Plasticized polymers usually exhibit the following characteristics: • •
Lower processing viscosities, Lower stiffness,
Table 2.8 Typical Nonpolymers Added to Polymers [29] Antioxidants Antistatic agents Bulk fillers Colorants and pigments Coupling agents Crosslinking agents Fibrous reinforcements Flame retardants Foaming agents Heat stabilizers
Odor suppressants Plasticizers Processing aids Emulsifiers Internal lubricants Mold release agents Viscosity depressants External lubricants Anti-blocking agents Ultraviolet stabilizers
• • • • • • •
Lower glass transition temperatures, Lower melt temperature, Lower continuous use temperature, Greater flexibility, Higher toughness, Greater tear strength, and Higher elongation at break.
DOP Plasticizer, wt %
These effects are controlled to a great degree by the thermodynamic compatibility of the polymer and plasticizer, and the plasticizer glass transition temperature. The glass transition temperature is also broadened by the plasticizer, with the greatest broadening occurring when the plasticizer is a poor solvent for the polymer. PVC is the most important polymer thermoformed as a plasticized sheet. PVC is nearly intractable in an unplasticized state. The effect of dioctyl phthalate (DOP) on the glass transition temperature of PVC is seen in Fig. 2.11 [31]. At 40% (wt) DOP, the glass transition temperature is lowered from 82°C or 1800F to -60 0 C or -80 0 F. The glass transition region is increased from about 100C or 18°F to 300C or 500F. In order to ensure long-term property retention, plasticizers must have very low vapor pressure at room temperature and must be non-migrating.
Glass Transition Temperature, 0K Figure 2.11 Effect of dioctyl phthalate [DOP] plasticizer concentration on glass transition temperature of polyvinyl chloride, PVC [31]
Other Additives Plasticizers are one very specific category of additives. Many chemicals are added to polymers in order to change specific undesirable characteristics [3]. Surfactants and lubricants are aids used to improve processing quality and extruder production rate or throughput. Antioxidants are added to minimize polymer yellowing during processing and reprocessing. Tints are dyes added to change transparent plastic color from nonwhite to perceived "water-white". Organic dyes color transparent plastics but do not appreciably affect their long-wavelength radiant energy absorption spectra [32]. Organic and inorganic pigments color opaque plastics. The dosage level is usually less than 2% (wt). Titanium dioxide, TiO2, is an opacifier in low dosage, as is carbon black. Carbon black is also used extensively as an ultraviolet light absorber, particularly in
Table 2.9 Common Fillers for Thermoformable Thermoplastics [33] Silica products • Minerals Sand Quartz Novaculite Tripoli Diatomaceous earth T^ , • Dolomite C4.!... u .,. • Synthetic amorphous silica J „, . .r Wet process silica rJ Ii • j i -1Fumed colloidal silica , c.r Silica aerogel Silicates • Minerals Kaolin or china clay Mica • Nepheline silicate Talc Wollastonite Asbestos • Synthetic products Calcium silicate Aluminum silicate
Metallic oxides • Zinc oxide • Alumina • Magnesia • Titania • Beryllium oxide ^ i • • J Other inorganic compounds r» • u- + • Barium sulfate _... ,., • Silicon carbide _ , ,., • Tungsten carbide . ,CA A/r , u , • Molybdenum Adisulnde T> • r v • Barium ferrite Metal powders • Aluminum • Bronze • Lead • Stainless steel • zinc Carbon
* Carbon black Channel black Furnace
black
•
Ground petroleum coke
Glass
•
Pyrolyzed products
• • • •
• Exfoliated graphite Cellulosic fillers
^
Glass flakes Hollow glass spheres Cellular glass nodules Glass granules 1
.
j
Calcium carbonate ^, it • Chalk • Limestone •
Precipitated calcium carbonate
#
.
Wood
flour
Shell flour Peanut
^ Pecan „. , ^ Walnut Comminuted polymers
vinyls and polyolefins. Chemical and physical blowing agents are added to the polymer prior to extrusion to produce foamed sheet [6]. Chemical blowing agents are very fine powders of ultrapure thermodynamically unstable chemicals such as azodicarbonamide, H2N-CO-N = N-CO-NH2. Azodicarbonamide, azobisformamide or AZ decomposes to produce nitrogen. Sodium bicarbonate, NaHCO3, with citric acid buffer, decomposes to produce CO2 and H2O vapor. It is used extensively to produce PS foam sheet. Frequently, hydrocarbons such as pentane and butane and halogenated hydrocarbons such as R123 and R 142b are added to PS and polyethylene to produce low-density closed cell foams for shock mitigation and insulation applications. Fillers and Reinforcing Fibers Although fillers reduce overall resin costs slightly, they are usually not added solely for this reason. Common inorganic fillers such as talc, calcium carbonate and clay or kaolin increase sheet stiffness and processing temperature by interfering with polymer chain segment mobility. Table 2.9 [33] lists some common fillers used in thermoformable thermoplastics. Some increase in stiffness is beneficial. For example, 20% (wt) talc in PP broadens its thermoforming processing window enough to allow forming on conventional roll-fed equipment. Fillers also restrict bulk chain straightening and flexing under load. These restrictions reduce ultimate elongation, tensile strength, impact strength and fatigue strength of the neat polymer. Milled glass fibers, to 30% (wt) provide exceptional strength improvement in rubber-modified styrenics and mPPO, but processing is restricted to pressure forming. Even further improvements in polymer stiffness is obtained by adding reinforcing elements such as those listed in Table 2.10 [34]. Unfortunately, elements such as glass fibers, mica, or Table 2.10 Typical Fibrous Elements in Polymers [34] Cellulose a-cellulose Pulp preforms Cotton Jute o. , Sisal n Rayon o
,
fibers flock
• rii
Whiskers
Synthetic r» 1
fibers -A
i
r>A
UT-T- J
„ Boron
Polyamide, nylon, PA ^ /
Fibrous glass Filaments Chopped strand Reinforcing mat „, Glass yarn _,/ . u u Glass ribbon
_,. tm tm
Polyester, PET, dacron Polyacrylonitrile, PAN, dyneltm, orlontm Polyvinyl alcohol, PVOH Other fibers ^ u ^u Carbon fibers Mineral fibers Asbestos Wollastonite
.
,.
.,
Titanium dioxide
Metallic fibers Aluminum Stainless steel Copper ^
graphite fibers so stiffen the polymer that matched-die forming at pressures near compression molding pressures and temperatures above the polymer melt temperature are required. Nevertheless, commercial parts are thermoformed from glass fiber-reinforced PP, PET and nylon and graphite fiber-reinforced polyimide. More details are given in Chapter 9.
2.15 Laminates Certain end use applications need mechanical or barrier properties that no single polymer can provide. Polymers are therefore laminated, coated or coextruded into multilayer sheet. Examples include: • • • • •
UV and chemical barrier of PMMA on ABS, Fire retardant barrier of PVC on PMMA, Solid impact PS "cap sheets" on PS foam for stiffness and cut resistance, Thermoformable PET-EVOH-PET thin-gage sheet used to produce preforms for high barrier stretch blow-molded containers, and PVDC on PS for gas barrier insulating containers.
Other examples are described in Chapter 9. The control of multilayer thickness is of great concern to the sheet extruder. Mismatched viscosities lead to interlayer thickness variation. Temperatures must be matched to ensure good interlayer bonding. Plasticizers and additives must be nonmigratory and must be carefully monitored to prevent "blooming" at interfaces. Biaxial orientation during thermoforming will reveal poor interlayer adhesion. Orientation must be carefully monitored to minimize formation of microvoids in inherently weak inner layers. Multilayer structures must be carefully heated to prevent innerlayer interface overheating and delamination from mismatched thermal expansion coefficients.
2.16 Stress-Strain Behavior of Plastics Thermoforming is a deformation process on a polymer in its rubbery solid state above Tg. For crystalline polymers, the deformation process occurs near the crystalline melting temperature, Tm. Technically, a nearly uniform force is applied to a two-dimensional membrane to biaxially stretch it. The amount of force required and the extent of stretching are directly related to the stress-strain behavior of the polymer at its process condition. Below, Tg, all polymers are brittle. The stress-strain curve is quite steep and linear and quite steep until fracture at a very low strain level (Fig. 2.12) [35]. In general, the tensile modulus values, or the slopes of the stress-strain curves, of nearly all unfilled or neat amorphous polymers below Tg are about 0.345 GPa or 500,000 lbf/in2 [36]. Within 200C or 400F above Tg, tensile
Break
Stress
Yield Point
Increasing Temperature Strain Hardening
Glass Transition
Eiongational Strain Figure 2.12 Temperature-dependent stress-strain schematic for an amorphous polymer
modulus values drop 3 to 4 decades, to 35 to 350 MPa or 50 to 500 lbf/in2. Ultimate tensile strengths also drop rapidly about the same orders of magnitude. As the sheet temperature increases above Tg, all polymers become increasingly ductile (Fig. 2.12). Some polymers exhibit yielding at modest strain levels. The applied stress is then sustained over ever-increasing strain levels. There is strong indication that the minimum vacuum forming temperature is where the abrupt yield point vanishes. In crystalline polymers, the rubbery region is compromised to a great degree by the crystalline structure, as shown in schematic in Fig. 2.13 [37]. At high
Shear Modulus, GPa
PP SAN
PS HIPS ABS-Low Temp LDPE
ABS-Hi Temp
HDPE
Temperature,
0
C
Figure 2.13 Temperature-dependent shear modulus for several thermoplastics [37]
Storage Modulus, G1, MPa
Temperature, 0F
Loss Factor, G7Gf
G1
G1VG1
Temperature,0C Figure 2.14 Temperature-dependent elastic modulus, G', and mechanical loss factor, G"IG' of polytetrafluoroethylene, PTFE [38]
levels of crystallinity, as with UHMWPE and PTFE, the modulus of the polymer above the glass transition temperature is only slightly less than that below the glass transition temperature (Fig. 2.14) [38]. An increasing level of crystallinity then has the effect of compressing the temperature effect on the stress-strain curves (Fig. 2.15). Further, for homologous crystalline polymer species, yield strength and ultimate tensile strength at a given temperature increase with increasing crystallinity (Fig. 2.16) [39].
Break Increasing Temperature
Stress
Yield Point Strain Hardening Glass Transition
T
-Tm
Elongational Strain Figure 2.15 Temperature-dependent stress-strain schematic for a crystalline polymer
Elastic Modulus, MPa
90% = Degree of Crystallinity
Temperature,0C Figure 2.16 Effect of crystallinity level on temperature-dependent modulus of polytetrafluoroethylene, PTFE [39]
It is apparent that there is a direct relationship between the stress-strain behavior of a given polymer and the process of thermoforming it from sheet form to shaped product. As expected, the normal forming temperature of any polymer is closely related to Tg for amorphous polymers and Tm for crystalline polymers. Forming temperature ranges for many polymers are given in Table 2.5 [40]. The lower forming temperature represents the lowest temperature the polymer can be shaped without cracking or splitting or without using heroic forces. Typically, for amorphous materials, the lower forming temperature is about 20 to 300C or 40 to 55°F above Tg and the normal forming temperature is about 70 to 1000C or 125 to 1800F above Tg. The "set temperature" is the temperature at which a part can be removed from the mold without significant distortion. The set temperature value is about equal to the polymer heat distortion temperature at 0.455 MPa or 66 lbf/in2 or about 10 to 200C or 20 to 400F below the polymer glass transition temperature, Tg. The orienting temperature is the temperature at which the polymer can be uniaxially stretched 375%. The upper forming temperature represents the temperature above which the polymer sags excessively, discolors, bubbles or smokes excessively. The upper forming temperature for a given polymer is usually about equal to the lowest injection temperature for that polymer. The crystalline polymer forming temperature range is usually quite narrow and the recommended forming temperature range is often within a few degrees of the polymer melt temperature. Certain crystalline polymers such as nylon (PA) and homopolymer polypropylene (PP) retain high degrees of order and therefore great strength up to abrupt melting points, then have very low melt viscosities and melt elasticities. As a result, these polymers have normal processing windows as narrow as 2 to 5°C or 5 to 100F. It must be understood,
therefore, that the temperature ranges given in Table 2.5 represent extreme or ideal conditions. Practical forming ranges are usually much narrower. A more thorough analysis of the interaction of temperature-dependent stress-strain behavior, viscoelasticity, applied stress and extent of drawing is given in Chapter 4.
2.17 Thermal Properties Heat capacity or specific heat and thermal conductivity are two important polymer physical properties used extensively in thermoforming. Heat Capacity Heat capacity at constant pressure, cp, is a thermodynamic property, defined as the isobaric change in polymer enthalpy with temperature: c
- y
(2 6)
-
P
Heat capacity values for many polymers are obtained from enthalpic tables [41] or from graphs such as Fig. 2.17 [42,43]. The enthalpic curves for amorphous polymers are usually quite linear with temperature. Heat capacity values or the slopes of the
HDPE
Enthalpy, kcal/kg
MDPE
Acetal, POM. Nylon 6 [PA-6] PP PS.MIPS, ABS1PMMA
LDPE ?PVC,RPVC
Temperature, 0C Figure 2.17 Enthalpies of several thermoplastics [42,43]
Table 2.11 Heat Capacities of Certain Thermoplastics in cal/g°C or Btu/lb°F Polymer
Morphology 1
PS ABS PMMA PC PVC
A A A A A
PP HDPE EP-copoly PTFE PA-6 PA-66 PET mPPO
C C C C C C C A
1
C p from enthalpy (Tg
C p from graph (500C < T < 900C) 0.45 0.45
0.56
Cp from DSC experiments
ecp/8T
0.50 0.54 0.56 0.50
225°C 225°C 225°C 225°C
0.043 0.074 0.048 0.033
@ @ @ @
(per 1000C)
0.65
0.39
0.78 0.58 0.80 0.25
0.47 0.61
0.96 @ 125°C 0.88 @ 800C
0.132 0.597
0.50
0.87 @ 1800C
0.502
0.74 0.45 ^0.50
0.09
A = commercially amorphous polymer, C = Commercially crystalline polymer
enthalpic cures are therefore only slightly dependent on temperature above the glass transition temperature, Tg. On the other hand, crystalline polymer enthalpic curves usually show dramatic changes near the melt temperatures of the polymer and exhibit discontinuities at the melt temperatures. As a result, it is difficult to give specific values for heat capacity of crystalline polymers. This is demonstrated in Table 2.11. Very accurate techniques for predicting heat capacities of simple organic molecules have been extended to polymers by assuming that: • • •
Energy is transmitted by translation of molecules or molecular segments, Each segment acts as a liquid harmonic oscillator, and The polymer is characterized as a semicrystalline solid [44].
The total molecular energy is the sum of its components: • • • • •
Translational, External rotational, Internal rotational, Vibrational, and Electronic.
From established tables of molecular energy contributions for each of the segmental groups of the polymer: • • • • •
Repeat units, End groups, Comonomeric elements, Pendant groups, and The like.
Relatively accurate but tedious calculations yield reasonable predictions of polymer heat capacity. Experimentally, the entire temperature-dependent heat capacity curve for any polymer can be obtained in a few minutes with less than a gram of polymer using standard differential scanning calorimetry, DSC. Basically a known weight of polymer is heated at a constant rate and its time-dependent temperature compared with a standard of known heat capacity. Characteristically within normal thermoforming heating ranges, neat amorphous polymers have heat capacity values of about 0.5 cal/g 0C or 0.5 Btu/lb 0 F. Crystalline polymers have average values of about 0.9 cal/g 0C or 0.9 Btu/lb 0 F. More details and examples are found in Chapter 3 on heating the sheet.
Thermal Conductivity Energy transmission through polymer solids and quiescent liquids is by molecular interaction rather than the electron transfer characteristic of metals. Thus thermal conduction, a measure of the efficiency of energy transfer, is governed by the same energy elements that contribute to heat capacity. Theoretical predictions are based on a linear relationship between thermal conductivity, heat capacity and liquid sonic velocity. The accuracy of prediction is excellent for simple organic molecules. For polymers, processing effects on intermolecular free volume and molecular order in partially crystalline polymers cause the calculated results to deviate substantially from carefully measured experimental values. Further, energy tends to be preferentially transmitted along the molecule backbone rather than between molecular chains. Thus, the nature of the crystalline order and the type of pendant groups influences the values. Thermal conductivity is one of the most difficult transport properties to measure [45]. As a result, very few accurate values of thermal conductivity are available for polymers. Fortunately, thermal conductivity is not strongly temperature-dependent and so evaluation at one temperature is probably sufficient for use at other temperatures. And homologous series of polymers, such as polyolefins, styrenics and vinyls, tend to have similar values, Table 2.12. Typically, thermal conductivity values for amorphous polymer such as PS, PMMA and PVC tend to be in the range of 3 to 5 x 10~4 cal/g cm 0C or 0.07 to 0.12 Btu/ft h 0 F. Owing to the higher degree of order for crystalline polymers, values tend to be about twice those of amorphous values. The exceptions are low-crystallinity celluloses and PP, where the effect of crystalline order is obviated by the high free volume caused by steric hindrance. Typically, metals have thermal conductivity values that are hundreds of times greater than those for polymers. Additional information on thermal conductivity is found in Chapter 3.
Thermal Diffusivity Thermal conductivity is a measure of the extent of energy transmission through the solid polymer. Thermal diffusivity is a measure of the rate at which energy is transferred:
Table 2.12 Thermal Properties of Thermoformable Polymers and Certain Mold Materials at 25°C Polymer
Density (kg/m3)
(lb/ft3)
Thermal conductivity
Heat capacity
(cal/s cm 0C) (Btu/ft h 0F) x 10~4
(cal/g 0C) (Btu/lb 0F) (cm2/s) x 10~4
(ft2/h) x 10-4 29.7 22.8 16.4 18.6-27.5 33.0 27.1-32.5 34.0 39.0 26.7 29.9 70.5
Thermal diffusivity
Amorphous polymers Polystyrene PMMA PMMA/PVC alloy ABS Polycarbonate Rigid PVC Modified PPO Polysulfone Polyethersulfone (PES) 20% GR PES Polyamide-imide
1050 1200 1300 1050 1200 1350 1070 1240 1370 1520 1400
65.5 74.9 81.1 65.5 74.9 84.2 66.8 77.4 85.5 94.8 87.4
4.3 4.3 3.3 2-3 5.0 3.45-4.1 5.5 6.74 4.3 7.8 14.4
0.105 0.105 0.080 0.048-0.073 0.121 0.083-0.100 0.133 0.163 0.105 0.190 0.348
0.54 0.615 0.6 0.4 0.49 0.365 0.585 0.54 0.46 0.67 0.565
0.54 0.615 0.6 0.4 0.49 0.365 0.585 0.54 0.46 0.67 0.565
Crystalline polymers LDPE EVA HDPE Cellulose acetate Cellulose butyrate Cellulose propionate Poypropylene, homoPolypropylene, CO40% GR PP Polymethyl pentene PVDC Acrylonitrile PET PBT, neat
920 940 960 1300 1180 1210 900 910 1220 830 1670 1150 1370 1310
57.4 58.7 59.9 81.1 73.6 75.5 56.2 56.8 76.1 51.8 104.2 71.8 85.5 81.7
7.57-9.6 8.27 9.0-12.1 5.2 5.0 5.0 4.1-4.2 5.0 8.4-8.8 4.1 3.0 6.2 5.7 5.0
0.183-0.233 0.200 0.217-0.292 0.125 0.121 0.121 0.100-0.125 0.121 0.203-0.213 0.100 0.073 0.150 0.138 0.121
0.88-1.05 0.95 0.88-1.15 0.67 0.67 0.71 0.83 0.81 0.77 0.91 0.45 0.6 0.44 0.54
0.88-1.05 0.95 0.88-1.15 0.67 0.67 0.71 0.83 0.81 0.77 0.91 0.45 0.6 0.44 0.54
7.66 5.9 4.2 4.8-7.1 8.5 7-8.4 8.8 10.1 6.9 7.7 18.2 7.85-11.9 9.26 8.1-14.3 5.9 6.33 5.8 5.5-6.92 6.8 8.9-9.3 5.5 4.0 9.0 9.5 7.1
Thermal expansion coefficient
30.4-46.1 35.9 31.5-55.4 23.0 24.5 22.6 21.4-26.8 26.3 34.6-36.2 21.2 15.6 34.8 36.8 27.4
( 0 C- 1 ) x 10-6
( 0 F- 1 ) x 10-6
70 70 79-142 60-130 60-70 70-80 60 54 55 23-32 36
39 39 44-79 33-72 33-39 39-45 33 32 31 13-18 20
250 140 160-200 90-110 200 110 120 67 120 67 110-130 61-72 150 83 120 67 27-32 15-18 117 65 190 106 66 37 70 39 60 33 (Continued)
Table 2.12 (Continued) Polymer
Nylon 6 (PA 6) Nylon 66 (PA 66) POM, copolymer 30% CR POM PTFE FEP PEEK Foams Polystyrene foam Rigid PVC foam Mold materials Alumina Copper/bronze Nickel Steel Maple Plaster Al-epoxy Zinc alloy Syntactic foam—plugs
Density
Thermal conductivity
(kg/m3)
Ob/ft 3 )
1130 1140 1415 1530 2170 2200 1320
70.5 71.1 88.3 95.5 135.4 137.3 82.4
64 64
4.0 4.0
2680 8800 8900 7900 450 900-1100 1700 6700 560
167.2 549 555 493 28.1 56-69 106 418 35
Heat capacity
Thermal diffusivity
Thermal expansion coefficient
(Btu/ft h 0F)
(cal/g 0C)
(Btu/lb 0F)
(cm2/s) x 10-4
(ft2/h) x 10-4
( 0 C- 1 ) x 10-6
( 0 F- 1 ) x 10~ 6
6.9 5.5 5.9-7.2 10.1 5.9 6.0 5.9
0.167 0.133 0.142-0.175 0.244 0.142 0.145 0.142
0.71 0.71 0.61 0.615 0.42 0.465 0.565
0.71 0.71 0.61 0.615 0.42 0.465 0.565
8.6 6.8 6.8-8.4 10.7 8.4 5.86 7.9
33.3 26.3 26.4-32.5 41.5 25.0 22.7 30.5
80 80 90-110 40-50 100 80 47
44 44 50-61 22-28 56 45 23
0.57-0.69 0.57-0.69
0.0139-0.0167 0.5 0.0139-0.0167 0.4
0.5 0.4
17.9-21.5 69.5-83.5 22.4-26.9 86.9-104.4
150-200 140-180
83-111 78-100
72.5 109 53.2 21.3 0.073 0.174 0.484-0.967 60.4 0.07
0.23 0.09 0.112 0.11 0.25 0.26 0.3 0.10 0.5
4865 5690 2210 1010 26.8 25-31 39-78 3730 10
(cal/s cm 0C) x 10~4
3000 4500. 2200 880 3.0 7.2 20-40 2500 2.9
0.23 0.09 0.112 0.11 0.25 0.26 0.3 0.10 0.50
18,850 22,000 8560 3930 104 97-120 152-304 14,450 40
19 18 13 11 60 10 45 27 31
11 10 7.2 6.1 33 5.6 25 15 17
k oc = — pcp cm2 = cal/g cm s 0 C s (g/cm3)(cal/g°C) 2 ft _ Btu/ft h 0 F h " (lb/ft3)(Btu/lb 0 F)
l
'
}
This combination of physical properties arises naturally from considerations of transient heat conduction, as detailed in Chapter 3 on sheet heating and Chapter 5 on cooling. Values for all polymers are typically 5 to 1Ox 10~ 4 cm2/s or 20 to 40 x 10~ 4 ft2/h. Polyolefins show the greatest range in values. Metals have values that are hundreds of times larger than polymers, as seen in Table 2.12.
Thermal Expansion Coefficient As polymers heat, chain mobility increases and molecules tend to move away from one another, increasing free volume. Factors that inhibit chain mobility tend to minimize thermal expansion. Thermal expansion is reduced with: Increasing crystallinity, Orientation, Steric hindrance, Hydrogen bonding, Crosslinking, Rigid fillers, and Molecular polarity as with PVC. Thermal expansion is enhanced with: Plasticizers, Lubricants, Processing aids, Solvents, and Dissolved gases. Flexible polymers tend to have thermal expansion coefficient values of about 100 x 10- 6 0 C - 1 or 50 x 10~6 0 F" 1 . Rigid polymers have values of about 50 x 10"6 0 C - l or 25 x 10"6 0 F - 1 . In contrast, metals have values of 10 to 20 x 10~6 0 C" 1 or 5 to 1Ox 10~6 0 F - 1 .
2.18 Infrared Spectra Certain polymeric molecular elements and chain segment motions are sympathetic to specific energy levels. The presence of these elements is detected by measuring the
Thermoforming Region log [Wavelength, m]
log [Frequency, s1]
Radio Hertzian Waves
Infrared
X-Rays Cosmic Rays Ultraviolet Gamma Rays Visible
Figure 2.18 Electromatic radiation scheme showing relative locations of visible light, ultraviolet and infrared radiation and the normal thermoforming region [46]
intensity and wavelength location of absorbed infrared electromagnetic radiation. The infrared region is a small portion of the total electromagnetic radiation spectrum (Fig. 2.18) [46]. The visible light radiation wavelength range is 0.38 um to 0.71 (am. The ultraviolet or UV light wavelength range is 0.006 jim to 0.38 um. The infrared or IR wavelength range is 0.71 jam to 100 |iim. The near-infrared portion of the IR spectrum is 0.71 jam to 5 um. The far-infrared portion of the IR spectrum is 5 um to 100 um, with the longer wavelength portion overlapping the Hertzian wave range. Thermal radiation important in heat transfer is limited to the wavelength range of 0.1 to 20 um [47]. As discussed in Chapter 3, thermoformer radiant heaters emit energy in the infrared region, with the peak wavelength dependent on the radiant heater temperature. The efficiency of absorption of that radiation by semitransparent polymers depends on the matching of the radiant source peak wavelength to the primary absorption wavelengths of the polymer. Each functional group on the polymer molecule may have more than one absorption wavelength. Most polymers have carbon-hydrogen bonds. The -C-H unit stretching IR band is 3 um to 3.7 um. The bending band is 6.7 um to 7.7 um, and the rocking band is 11 um to 17 um. The combination of functional group absorption bands is called the IR spectrum for that polymer. Polymers yield unique IR spectra. Since the intensity of an absorption band is directly related to the concentration of the functional group absorbing the radiation, IR is used for quantitative analysis of plastics. Absolute measures of the following can be obtained from IR analysis: • • • • • •
Copolymer concentrations, Blend concentrations, Amounts and types of processing aids, Amounts and types of dyes, Amounts and types of plasticizers, and Amounts and types of solvents.
Table 2.13 Characteristic Infrared Absorption Bands for Organics Specific vibrational mode
Wavelength range (urn)
Wavenumber range (cm- 1 )
-OH stretch -NH stretch -CH stretch -C=X stretch -C=O stretch
2.7-3.3 2.7-3.3 3.0-3.7 4.2-4.78 5.4-6.1
3030-3700 3030-3700 2700-3300 2090-2380 1640-1850
-C=N stretch -C=C stretch -NH bend -CH bend -OH bend
5.9-6.4 5.9-6.4 6.1-6.75 6.75-7.7 6.85-8.3
1560-1695 1560-1695 1480-1640 1300-1480 1205-1460
-C-O stretch -C-N stretch -C-C stretch -CH rock -NH rock
7.7-11.1 7.7-11.1 8.3-12.5 11.1-16.7 11.1-14.2
910-1300 910-1300 800-1200 600-900 700-900
Further, the nature of the polymerization is determined by determining the types and amounts of end groups. And the extent of thermal and oxidative degradation are determined by subtracting the IR spectrum of the virgin polymer from that of the processed one, then measuring the intensity of the -C = O stretching band, 5.4 um to 6.1 jim or that of the -C = C stretching band, 5.9 urn to 6.4 urn. Characteristic IR absorption bands are given in Table 2.13. The IR spectra for a few common transparent or translucent thermoformable polymers are given in Figs. 2.19 to 2.32 [48], The strong absorption band at 3.2 um to 3.7 um is -C-H stretching and is found on all carbon-hydrogen based polymers. PTFE has no hydrogen and so shows no absorption in that band (Fig. 2.32). On the other hand, PTFE shows strong absorption in the 8.2 jim to 8.7 jam IR band, for -C-F stretching. The PVC spectrum shows a strong absorption region at about 8.1 fim for -C-Cl stretching. The 2.8 um to 3.0 um for cellulose acetate is the -O-H
Transmission
Cellulose Acetate
Wavelength, jj m Figure 2.19 Infrared transmission spectrum for cellulose acetate [48]
Transmission
Nylon, PA
Wavelength, AJ m Figure 2.20 Infrared transmission spectrum for nylon, PA [48]
Transmission
Polypropylene, PP
Wavelength, JJ m Figure 2.21 Infrared transmission spectrum for polypropylene, PP [48]
Transmission
Polyethylene
Wavelength, pm Figure 2.22 Infrared transmission spectrum for polyethylene [48]
Transmission
Polystyrene, PS
Wavelength, pm Figure 2.23 Infrared transmission spectrum for polystyrene, PS [48]
Transmission
Polyurethane
Wavelength, pm Figure 2.24 Infrared transmission spectrum for thermoplastic polyurethane [48]
Transmission
Polyvinyl Chloride, PVC
Wavelength, jjm Figure 2.25 Infrared transmission spectrum for polyvinyl chloride, PVC [48]
Transmission
Polymethyl Methacrylate, PMMA
Wavelength, jjm Figure 2.26 Infrared transmission spectrum for polymethyl methacrylate, PMMA [48]
Transmission
Polycarbonate, PC
Wavelength, pm Figure 2.27 Infrared transmission spectrum for polycarbonate, PC [48]
Transmission
Polyethylene Terephthalate, PET
Wavelength, pm Figure 2.28 Infrared transmission spectrum for polyethylene terephthalate, PET [48]
Transmission
Fluoropolymer, FEP
Wavelength, jum Figure 2.29 Infrared transmission spectrum for fluoropolymer, FEP [48]
Transmission
Polyimide
Wavelength, urn Figure 2.30 Infrared transmission spectrum for polyimide [48]
stretching mode. In polycarbonate, the -C = O stretching mode is shown as an absorption band of 5.4 (im to 6.1 um. In certain polymers such as polyamides, polyethylenes and PET, orientation and crystallinity are revealed in specific IR absorption bands. The crystalline portion of nylon 66 absorbs at 10.7 |im and 11.7 jim and the amorphous portion absorbs at 8.8 um [49]. The extent of crystallinity is determined by comparing the intensities of these bands. Weak and strong IR absorption bands for common thermoplastics are given in Table 2.14. Absorptivity and transmissivity are related as: oc + x = l 1
(2.8)
The typical radiation units are cm" . The larger the value becomes, the greater the radiation effect becomes. Transmissivity values greater than 1 cm" 1 imply high
Transmissivity, cm
ABS
Wavelength, jum Figure 2.31 Infrared transmission spectrum for ABS [48]
absorption and infrared opacity and absorptivity values less than 0.1 cm^ 1 imply high infrared transparency. The effect of thickness is predicted with Beer's law: 1(X,) = I0(A.) e-°^>x
(2.9)
where I 0 is the incident wavelength-dependent radiation, oc is the absorptivity and x is the thickness of the plastic sheet. Figures 2.19-2.30 show the effect of sheet thickness on IR transmission. As is apparent, as the sheet increases in thickness, the amount of IR energy absorbed increases but the general shape of the IR spectra remains the same. For very thin films of less than 1 urn, surface molecular orientation may distort the absolute values of the IR spectra and therefore the energy absorption characteristics of the films.. The primary effect of organic colorant on polymer should be in the visible wavelength range [0.38 jim to 0.71 um]. Solid inorganic particles such as TiO 2 , carbon black, and talc act as opacifiers by increasing surface absorption of visible light and minimizing the amount of visible light that is transmitted into or through
Transmission
Polytetrafluoroethylene, PTFE
Wavelength, pm Figure 2.32 Infrared transmission spectrum for polytetrafluoroethylene, PTFE
Table 2.14 Characteristic Polymer Infrared Absorption Bands in Wavelength (Values in Parentheses Represent Weak Absorption Bands) Polymer
Primary (|im)
HDPE LDPE
3.2-3.9 3.2-3.9
PP
3.2-3.6
PS ABS PVC
3.2-3.6 2.8-3.6 3.2-3.6
PMMA
3.2-3.6
PA 6
3.0-3.2
Cellulose acetate PET
5.5-6.0 7.8-10.0 3.3-3.6
FEP PEI
7.4-9.0 2.7-3.0
PC
3.2-3.6
Secondary (jim)
(7.0-8.0) 6.7-7.1 7.0-8.0 6.6-7.0 7.1-7.3 (8.4-8.7) (9.8-10.1) 6.4-7.3 6.4-7.3 (1.65-1.8) 2.2-2.5 5.7-6.0 6.8-11.0 1.4-2.2 1.1-1.25 5.7-6.0 6.2-9.5 19.-2.8 (6.0-7.8) 2.7-2.9 5.9-6.0 7.0-9.2 (4.2-4.4) 5.8-6.0 (6.9-9.2) 5.5-6.2 6.6-7.7 7.8-9.5
the polymer. Thus, effective opacifiers should have particle sizes in the 0.1 to 10 jim range. Opacifiers with particle sizes of 3 to 12 (im will also act to block incident infrared radiation and thus change the absorption characteristics of the polymer. The effect of colorant dosage on the polymer IR spectrum is shown in Fig. 2.33 [50]. The general effect is to gradually increase the IR absorptivity with increasing dosage. The nature of the colorant also affects the polymer IR spectrum (Fig. 2.34) [51]. Organic dyes and tints are designed to affect the polymer electromagnetic radiation spectrum in the visible wavelength range (Fig. 2.35), and are usually used in small quantities. Although the spectra of these organics overlay those of the polymers, the small dosages usually do not materially affect the energy absorption efficiencies of the polymers. As discussed in Chapter 3, a sound measure of the amount of energy absorbed by a plastic is obtained by integrating the wavelength-dependent absorption curve over the wavelength range of the incident radiation. This is shown in
Penetration Depth, cm
0.25 wt % Red Pigment
Wavelength, urn Figure 2.33 Effect of colorant dosage on absorption characteristics of polymethyl methacrylate, PMMA [50]
Fig. 2.36 [52] for several colorants. Simply put, IR spectra offer substantial information about relative processing effects such as: The effect of increasing heater temperature on sheet heating rate, The effect of sheet downgaging on energy absorption, and thus on cycle time, sheet surface temperature, and discoloration, • The effect of increasing sheet thickness on sheet surface temperature, • The effect of thin cap-sheeting or film on heating rate of sheet, • The effect of changing pigment type and dosage, and • The effect of printing on sheet heating characteristics.
Penetration Depth, cm
• •
Natural
Translucent Blue
Opaque White
Wavelength, jjm Figure 2.34 Effect of pigment type on absorption characteristics of polystyrene, PS [51]
Absorptivity, cm"1
Undyed Red Dyed
Wavelength, jum
Figure 2.35 Absorptivity of natural and red dyed polymethyl methacrylate, PMMA
Integrated Absorption
Temperature, 0K
Opaque White PS Blue PS PP
Amorphous PET Transparent PS
PMMA
Temperature, 0F Figure 2.36 Heater temperature-dependent total absorption for several natural and pigmented thermoplastics [52]
2.19 Summary Although it was stated at the beginning of this chapter that "If a polymer can be produced as a sheet, it can be thermoformed into a product", this does not mean that all polymers thermoform with equal effort. Typically, amorphous polymers have broader forming windows than crystalline ones. Again, the forming temperatures given in Table 2.5 represent extremes and ideal conditions. Actual forming temperature ranges are usually only a few degrees. Table 2.15 gives some general forming characteristics for many of the polymers listed in Tables 2.5 and 2.12. Special, more expensive polymeric homologs are being developed to circumvent the forming inadequacies of certain polymeric classes.
Table 2.15 Thermoforming Processing Characteristics of Some Formable Polymers. (These characteristics are generic unless otherwise noted) Polymer
PS
Process temperature range (0C)
(0F)
150-190
300-375
Char, maximum draw ratio
Major draw limitation
Comments
Tears at high temperatures
Some yellowing at higher temperatures, long oven times. Trim dust is tenacious. Parts are brittle in 3D corners at deep draw. Sheet is easily marked off in plug assist.
Elongation is limited at high rubber content.
Yellowing at higher temperatures. Tends to be dimcult to form into sharp 3D corners. Needs to be held on mold longer than PS or ABS. This is particularly true for high rubber content. Sheet is easily marked off in plug assist.
8:1 HIPS
163-204
325-400 8:1
ABS
150-204
300-400
10:1
Elongation at high temperature.
Moisture causes pits, bubbles, blisters. Discolors at higher temperatures, long oven times. Can be splitty at low temperatures.
mPPO
163-218
325-425
6:1
Stiff at moderate temperature.
Thermoforms like HIPS but stiffer. Odor can be objectionable. Can yellow at high forming temperature. Sharp corners dimcult to form at modern temperatures. Heavy gage must be trimmed cold. Trim dust can be tenacious. Ideal candidate for pressure forming.
OPS
127-160
260-320
5:1
Very stiff at low temperature. Can lose orientation at high temperature.
Must be very carefully heated to maintain orientation. Birefringence can be used to monitor orientation. Sheet best heated by direct contact. Sharp corners dimcult. Very tough, splitty to trim cold. Superior surface gloss, opticals, impact strength. (Continued)
Table 2.15 (Continued) Polymer
Process temperature range (0C)
(0F)
Char, maximum draw ratio
PMMA
150-204
300-400
12:1
Elongation at high temperature for lightly crosslinked PMMA.
Sheet can scorch, blister at high energy input. Surface can change from glossy to matte at high energy input. Highly stretched sheet can be brittle in 3D corners. Sheet is easily scratched during handling, trimming. Sheet frequently thermoforming with protectivefilmin place. Trim dust can be tenacious, statically charged.
PMMA/PVC
150-190
300-375
8:1
Elongation at high temperature.
Sheet can blister, scorch, yellow at high energy input. Sheet can be brittle during trimming. Sheet can be pressure formed with good results.
FPVC
107-150
225-300
10:1
General weakness at higher temperatures.
Upper temperature limit is discoloration. Plasticizer odor objectionable. Rubbery sheet requires longer mold times to set. Embossings wash at high temperature or draw ratios > 5:1.
General weakness at higher temperatures.
Upper temperature limit is discoloration. Long oven times cause yellowing. Decomposition product is HCl. Difficult to prestretch as heavy gage. Thin gage transparency not as good as PS, ABS. Tends to be tougher in 3D corners than PS, PMMA. Virgin transparent has bluish tint to balance yellowish regrind color.
Melt elasticity low at forming temperatures.
Usually processed above its melt temperature of 115°C. Can exhibit excessive sag very quickly. Sag bands recommended for thin gage. Increased haze at higher temperatures.
121-177 250-350
RPVC
260-350
Comments
6:1
127-177 LDPE
Major draw limitation
6:1
HDPE
138-193
280-380
8:1
Melt elasticity.
Usually processed above its melt temperature of 135°C. Can exhibit excessive sag. Black sheet heats much faster than white. Thin gage sheet can excessively sag very quickly. Increased haze at higher temperatures.
PP
143-166
290-330
6:1
Excessive sag and narrow forming window.
Very difficult to control sag with straight homopolymer. Very narrow forming temperature range. Sag bands should be slipcoated to prevent sticking. Draw frequently shows necking. Sheet easily marked by plug. Thin gage can have high residual stress, can pull out of pins during heating. High energy input increases haze. Sheet does not draw well into sharp corners when cold. Best parts are pressureformed. Trim blades must be sharp to avoid forming whiskers, angel hair. Parts formed at higher temperature onto cold mold are frequently brittle. Can be pressure-formed in thin gage below melt temperature.
EP Copoly.
132-177
270-350
8:1
Sags, necks at high forming temperature.
Forms like HDPE in thin gage. Good elongation at lower forming temperature range. Can be very difficult to trim when very cold.
OPP
143-166
290-330
5:1
Rapidly loses orientation, sages at upper temperature.
Very low haze, excellent surface gloss, high impact strength. Must be heated very carefully to maintain orientation. Thin-gage sheet heated best with direct contact.
EVA
135-177
275-350
8:1
Tears at high temperature.
Not normally used alone. As a tie layer, usually draws well with little resistance. (Continued)
Table 2.15 (Continued) Polymer
Process temperature range (0C)
(0F)
Char, maximum draw ratio
PP-20% talc
149-204
300-400
5:1
Elongation low at moderateto-high temperature.
Stiff at forming temperature. Elongation limited byfillerloading. Deep draw restricted. Matte surface may not be acceptable. Sharp corners difficult to form without plug assist. Plug assist useful primarily at low forming temperature. Pressure forming desired heavy-gage sheet.
PP-40% GR
149-232
300-450
4:1
Very stiff at all forming temperatures.
Best pressure-formed. Deep draws cause splits, polymer-rich areas in corners. Plug assist not always effective owing to low melt strength of base polymer.
PC
177-232
350-450
8:1
Stiffness even at upper forming temperature.
Tends to be stiff at all forming temperatures. Can discolor at high temperature. Moisture causes pinholes, pock marks, bubbles, brittleness. Transparent sheet harder to heat than acrylic. Sharp corners hard to form at low forming temperature. Very tough to trim cold. Routering recommended.
APET
127-166
260-330
6:1
Sags, necks, anneals, orients rapidly at high temperature.
Slowly crystallizing polymer. Rate increases with decreasing molecular weight. Low molecular weight heat sets rapidly. Residual stress problem in thin gage. Necking difficult to avoid in deep drawn parts. Plug assist enhances necking. Bubble prestretching enhances orientation, reduces maximum draw ratio. Hard to form sharp corners on hot mold. Trimming is difficult cold, can cause whiskers or angel hair.
Major draw limitation
Comments
Trim registry difficult owing to high polymer movement. Very thin gage sheet and film best heated by direct contact. 185-199
365-390
5:1
Very stiff if sheet too hot. Sheet tears if too cold.
Requires careful oven temperature control. Mold must be heated to 1800C or 3600F or so. Excessive draw-down leads to brittle corners. Crystallinity in 20% range gives optimum properties. Difficult to control crystallinity in very thin sheet. Normal gage range of 1 mm or 0.040 in or more.
135-177 TPE/TPO (Depends on polymer)
275-350
6:1
Spring-back.
Many versions of thermoplastic elastomers. Those with high natural rubber content more difficult to maintain part shape. Very cold molds required. Hard to maintain long-term dimensions. Pre-stretch must remain on during forming to minimize spring-back.
93-121
200-250
4:1
Cell collapse at high temperature, very stiff at low temperature.
Thin laminatingfilmimproves surface appearance, increases maximum draw, stiffensfinalproduct. Parts mostly restricted to shallow draw. Matched die molding usually required for low temperature forming, preferred to control sheet thickness expansion from oven. Trim dust is statically charged, very tenacious. Sharp corners not desired owing to splittiness, poor impact of foam.
CPET
PS Foam
(Continued)
Table 2.15 (Continued) Polymer
Process temperature range (0C)
(0F)
Char, maximum draw ratio
PP foam
149-166
300-330
4:1
Cell collapse, stickiness, mushiness can occur very rapidly.
Matched die molding preferred. Compression molding sometimes recommended. Processing window very narrow. Cell collapse catastrophic. Crosslinked PP preferred. Deep draw difficult without prestretching. Material elasticity at lowest temperature prevents sharp corners.
XLPE foam
149-204
300-400
4:1
Cell collapse, mold stick at high temperature.
Sheet tends to be rubbery-elastic, like TPE. Some spring-back. Cell rupture at high energy input. Difficult to get deep draw even with aggressive plugging. Foam very soft at low density. Best for shallow draw.
PET foam
185-199
365-390
4:1 (?)
Hot mold and other CPET forming limitations.
Early results show 400 to 900 kg/m3 PET form like unfoamed CPET. Foam sheet crystallinity <20% in 2.5 mm or 0.100 in thicknesses or less. Formed sheet crystallinity - 20% as with CPET. Sheet thickness typically > 1 mm or 0.040 inch).
Major draw limitation
Comments
2.20 References 1. J. Frados, Ed., Plastics Engineering Handbook, 4th Ed., Van Nostrand Reinhold Co., New York, 1976, p. 274. 2. J.L. Throne, "Polymer Properties", in M. Bakker, Ed., Encyclopedia of Packaging Technology, John Wiley & Sons, New York, 1986. 3. J.-M. Charrier, Polymeric Materials and Processing: Plastics, Elastomers and Composites, Hanser Publishers, Munich, 1991. 4. R. Gachter and H. Muller, Eds., Plastics Additives Handbook: Stabilizers, Processing Aids, Plasticizers, Fillers, Reinforcements, Colorants for Thermoplastics, 2nd Ed., Carl Hanser Verlag, Munich, 1985. 5. H.R. Simonds, Source Book of the New Plastics, Vol. II, Van Nostrand Reinhold Co., New York, 1961, p. 21. 6. J.L. Throne, Thermoplastic Foams, Sherwood Publishers, Hinckley OH, 1996. 7. J.L. Throne, "Thermoforming—A Look Forward", SPE ANTEC Tech. Papers, 29 (1983), p. 464. 8. R.D. Deanin, Polymer Structure, Properties, and Applications, Cahners Books, Boston, 1972, p. 154. 9. J.L. Throne, Plastics Process Engineering, Marcel Dekker, New York, 1979, p. 65. 10. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, Tests for Design, Hanser Publishers, Munich, 1993, Chapter 1. 11. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, Tests for Design, Hanser Publishers, Munich, 1993, Table 2.4, pp. 90-91. 12. T. Alfrey and E.F. Gurnee, Organic Polymers, Prentice-Hall, New York, 1967, p. 51. 13. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, Tests for Design, Hanser Publishers, Munich, 1993, p. 129. 14. A. Ziabicki, Fundamentals of Fibre Formation: The Science of Fibre Spinning and Drawing, John Wiley & Sons, New York, 1976, p. 112. 15. J.L. Throne, "Thermoforming Crystallizing Polyethylene Terephthalate (CPET)", Adv. Polym. Tech., £(1988), pp. 131-171. 16. J.L. Throne, "Thermoforming Crystallizing PET", SPE ANTEC Tech. Papers, 27(1981), p. 598. 17. J.A. Brydson, Plastics Materials, IHfTe, London, 1966, p. 58. 18. R.E. Dempsey et al., US Patent 4,127,631, Assigned to Amoco Chemicals Corp., Chicago IL, 28 Nov 1978. 19. H. Saechtling, International Plastics Handbook for the Technologist, Engineer and User, 2nd Ed., Hanser Publishers, Munich, 1987, Figure 82, p. 166. 20. LJ. Gibson and M.F. Ashby, Cellular Solids: Structure & Properties, Pergamon Press, Oxford, 1988, Figure 3.2, p. 47. 21. J.A. Brydson, Plastics Materials, Iliffe, London, 1966, p. 34. 22. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, Tests for Design, Hanser Publishers, Munich, 1993, Figure 2.45, p. 135. 23. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, Tests for Design, Hanser Publishers, Munich, 1993, Figure 2.46, p. 136. 24. L.E. Nielsen, Mechanical Properties of Polymers, Reinhold, New York, 1962, p. 244. 25. R.D. Deanin, Polymer Structure, Properties, and Applications, Cahners Books, Boston, 1972, p. QQ
oo.
26. J.L. Throne, "Polymer Properties", in M. Bakker, Ed., Encyclopedia of Packaging Technology, John Wiley & Sons, New York, 1986, p. 533. 27. R.M. Ogorkiewicz, Ed., Thermoplastics: Properties and Design, Wiley-Interscience, Ltd., London, 1974, p. 28. 28. J.B. Howard, "Fracture—Long Term Testing", in N.M. Bikales, Ed., Mechanical Properties of Polymers, Wiley-Interscience, New York, 1971, p. 73.
29. R.L. Baldwin and K.E. Van Holde, Fortschr. Hochpolym. Forsch., 1 (1960), p. 451. See also J.L. Throne, Plastics Process Engineering, Marcel Dekker, New York, 1979, p. 765. 30. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, Tests for Design, Hanser Publishers, Munich, 1993, p. 12. 31. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, Tests for Design, Hanser Publishers, Munich, 1993, Figure 2.47, p 142. 32. F. Brinken and H. Potente, "Some Considerations of Thermodynamics in Thermoforming", SPE ANTEC Tech. Papers, 29 (1983), p. 467. 33. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, Tests for Design, Hanser Publishers, Munich, 1993, Table 1.4. 34. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, Tests for Design, Hanser Publishers, Munich, 1993, Table 1.3, p. 13. 35. J.L. Throne, "Polystyrene Foam Sheet Expansion During Heating", SPE ANTEC Tech. Papers, 29(1983), p. 1328. 36. J.A. Brydson, Plastics Materials, Uiffe, London, 1966, p. 58. 37. H. Domininghaus, Plastics for Engineers: Materials, Properties, Applications, Hanser Publishers, Munich, 1993, Figure 133, p. 208. 38. H. Domininghaus, Plastics for Engineers: Materials, Properties, Applications, Hanser Publishers, Munich, 1993, Figure 246, p. 316. 39. H. Domininghaus, Plastics for Engineers: Materials, Properties, Applications, Hanser Publishers, Munich, 1993, Figure 241, p. 311. 40. Material adapted from W.K. McConnell, Jr., handout material, "Thermoforming Technology for Industrial Applications", SPE Seminar, 12-14 March 1985, Arlington TX. 41. J.L. Throne, Plastics Process Engineering, Marcel Dekker, New York, 1979, pp. 714-735. Taken from an extensive series of tables published by R.G. Griskey in Modern Plastics, 1966-1967. 42. H. Voigt, "Lehrgang fur Thermoformung", Paul Kiefel Thermoformmaschinen GmbH, Freilassing, Germany, undated. 43. Z. Tadmor and CG. Gogos, Principles of Polymer Processing, John Wiley & Sons, Inc., New York, 1979, pp. 697-703. 44. B.C. Sakiadis and J. Coates, AIChE J., 2 (1956), p. 88. See also J.L. Throne, Plastics Process Engineering, Marcel Dekker, New York, 1979, p. 737. 45. R.C. Progelhof, J.L. Throne and R.R. Ruetsch, "Methods for Predicting the Thermal Conductivity of Composite Systems: A Review", Polym. Eng. Sci., 1(5(1976), p. 615. 46. J.P. Holman, Heat Transfer, 4th Ed., McGraw-Hill Book Company, New York, 1976, Figure 8-1, p. 274. 47. F. Kreith, Principles of Heat Transfer, 2nd Ed., International Textbook Co., Scranton, 1965, p. 199. 48. Anon., "Plastic Film Measurement", Technical Note TN100, IRCON, Inc., Niles IL, 1993, Figures 2-5. 49. I. Kossler, "Infrared-Absorption Spectroscopy", N.M. Bikales, Ed., Characterization of Polymers, Wiley-Interscience, New York, 1971, p. 125. 50. D. Weinand, "Modellbildung zum Aufheizen und Verstrecken beim Thermoformen", DoktorIngenieurs Dissertation, Rheinisch-Westfalische Technische Hochschule, Aachen, Germany, 16 JuIi 1987, BiId 3.10. 51. D. Weinand, "Modellbildung zum Aufheizen und Verstrecken beim Thermoformen", DoktorIngenieurs Dissertation, Rheinisch-Westfalische Technische Hochschule, Aachen, Germany, 16 JuIi 1987, BiId 3.9. 52. D. Weinand, "Modellbildung zum Aufheizen und Verstrecken beim Thermoformen", DoktorIngenieurs Dissertation, Rheinisch-Westfalische Technische Hochschule, Aachen, Germany, 16 JuIi 1987, BiId 2.14.
3 Heating the Sheet 3.1 3.2 3.3 3.4 3.5 3.6
3.7
3.8
3.9 3.10
3.11
3.12
3.13
3.14 3.15 3.16
3.17
Introduction Energy Absorption by Sheet Heat Transfer Modes Incorporating Formability and Time-Dependent Heating Conduction Convection Heat Transfer Coefficient The Biot Number Effective Radiation Heat Transfer Coefficient Constant Heat Flux Radiation Heating Black Body Radiation Gray Body—Emissivity Radiant Heater Efficiency—Constant Heat Flux Application Real Heaters—Efficiencies Radiative Heat Transfer Coefficient Convection and the Heat Transfer Coefficient Rod Heaters Long-Term Radiant Heater Efficiencies Edge Losses—View Factor Local Energy Input Pattern Heating Zone, Zoned or Zonal Heating Heater to Sheet Distance Thin-Gage Sheet—Approximate Heating Rates Constant Environmental Temperature Approximation Constant Heat Flux Approximation Thin-Gage Approximations—Comments Heavy-Gage Sheet—Internal Temperature Control Constant Environmental Temperature The Constant Heat Flux Case The Thickness Effect Summary Equilibration Convection Heating Constant Heat Flux Computed Equilibration Times The W-L-F Equation The Arrhenius Equation Relating Shift Factors to Sheet Thickness Infrared-Transparent Polymers Computer-Aided Prediction of Sheet Temperature The Radiant Boundary Condition Guidelines for Determining Heating Cycles The Biot Number Thin-Gage Guidelines Heavy-Gage Guidelines Intermediate-Gage Guidelines References
3.1
Introduction
The thermoforming process is neatly segmented into four steps: • • • •
Heating the sheet, Stretching the sheet, Cooling the sheet on the mold surface, and Trimming the part from its surroundings.
During the forming and trimming steps, the sheet dimensions are changing but the sheet is essentially at constant temperature. During the heating and cooling steps, the sheet dimensions are essentially constant, but the sheet temperature is changing. Thus the heat transfer process and the mechanical deformation process are best treated separately. This chapter focuses on the ways in which sheet is heated to the stretching or forming temperature. Chapter 4 concentrates on the technical details of sheet stretching. Chapter 5 considers the process of cooling and the trimming step. The material in these chapters is quite technical. However, newer thermoforming technologies mandate a thorough understanding of the basic concepts underlying the general process. And many of the troubleshooting solutions to processing problems are apparent once these concepts are understood. Roll-fed formers have used infrared heating for years owing to its efficiency in heating thin-gage sheet. Heavygage cut sheet formers have used forced convection hot air ovens for heating, in order to minimize sheet surface degradation. There are technical and management reasons behind these decisions. In certain instances, these are not necessarily the optimum choices. Pattern or zone heating is used extensively to produce more uniform part wall thicknesses and so parts designers should be aware of some of the details of this technique. Again, what is important is an adequate understanding of the interaction between the plastic sheet, initially at room temperature but being heated to its proper forming temperature, and the chosen heating medium. The material in this chapter begins with a review of the basic types of heating methods. Then thin-gage heating, particularly infrared heating, and forced convection hot air heating of heavy-gage material are considered in detail. Equilibration time is discussed. This is the time it takes for the sheet to achieve a uniform temperature across its cross-section, once the heating source is removed. Computeraided models are also outlined. And finally, guidelines for determining heating cycle times for both thin-gage and heavy-gage sheet are presented.
3.2
Energy Absorption by Sheet
Thermoforming is an energy intensive plastics process. Economics require the most efficient use of energy. The amount of energy needed to heat a unit mass of sheet
PP HDPE
PS
PB
Specific Heat, kcal/kg-°C
PA-6
PC RPVC PMMA PSO2
PTFE Air
Diamond
Temperature, 0C Figure 3.1 Temperature-dependent heat capacities or specific heats of several thermoplastics
from room temperature, RT, to the forming condition, Tf, is enthalpy increase, Ah, and is obtained from: Q or A h =
c p (T)dT
[cal/g] = [cal/g 0C] • [0C]
(3.1)
JRT
[Btu/lb] = [Btu/lb°F] • [0F] cp(T) is the temperature-dependent heat capacity (Table 2.5 and Fig. 3.1) [I]. The forming temperature is assumed to be the average sheet temperature at the normal forming temperature:
Tf
K0f T ( x ) d x
(32)
-
T(x) is the temperature at position x across the sheet half-thickness, 0 < x < L. If the temperature dependency of heat capacity is unknown, an average value will give a reasonable estimate. If the heat capacity of a specific polymer is unknown, a value of a homologous polymer can be used as a first approximation. The change in enthalpy is a much better method of determining the amount of energy uptake by the sheet. Figure 2.17 provides enthalpy values for several thermoformable polymers. H is the enthalpy at a given temperature, as [cal/g], [kcal/kg], or [Btu/lb]. The energies needed to heat typical polymers to forming temperatures are given in Table 3.1.
Table 3.1 Thin-Gage Heating Efficiencies (Heater Temperature, T 0 0 = 7600C; Heater Output, Q/A = 40 kW/m2) Polymer
LOPE PMMA PVC PS PTFE/FEP2 PA 662 1 2
]
Heating rate
Energy absorbed
Efficiency
Maximum effective heating transfer coefficient
(cal/g°C)
(s/mm)
(kW/m2)
(%)
(kW/m2 • 0C)
(Btu/ft2 • h • 0F)
0.498 0.559 0.265 0.341 0.342 0.479
25 27 21 13-15 13 27
11.5 19.44 15.88 19.03-21.97 25.86 19.84
27.6 48.6 39.7 47.6-54.9 64.7 49.6
0.0182 0.0333 0.0255 0.0310-0.0358 0.0548 0.0370
3.21 5.87 4.50 5.46-6.30 9.65 6.52
Normal forming temperature (0C)
Enthalpy
Density
C
(cal/g)
(g/cm3)
129 177 138 146 288 224
71.7 104.1 55.9 65.0 66.9 105.0
0.92 1.2 1.4 1.05 2.2 1.2
Used only for effective heat transfer coefficient calculation Values from Fig. 3.26
Some of these values are based on assumed values for heat capacity and some are approximate. Example 3.1 compares energy uptake for ABS and HDPE, representing amorphous and crystalline polymers, respectively. As detailed in Chapter 2, additional energy is required to melt a crystalline polymer such as HDPE. If the energy input to both sheet is the same, it requires substantially longer to heat HDPE than ABS. Example 3.2 illustrates this point. Example 3.1 Energy Absorbed by Plastic Sheet Calculate the amount of energy required to heat ABS and HDPE to their respective normal forming temperatures. If the energy input is the same to each sheet, calculate the relative times to heat each sheet to the forming temperature.
From Table 2.5, the normal forming temperature of both of these polymers is 295°F or 146°C. The amount of energy required to heat the plastic from room temperature (say 77°F or 25°C) to the forming temperature is obtained from Fig. 2.17. HDPE: 128 kcal/kg @ 146°C - 8 kcal/kg @ 25°C = 120 kcal/kg ABS: 51 kcal/kg @ 146°C - 7 kcal/kg @ 25°C = 45 kcal/kg The densities of these polymers are obtained from Table 2.12. HDPE: 960 kg/m3 ABS: 1050 kg/m3 The energy required per unit volume is given as: HDPE: 120 kcal/kg • 960 kg/m3 = 0.115 x 106 kcal/m3 ABS: 45 kcal/kg • 1050 kg/m3 = 0.0473 x 106 kcal/m3 Relative to the heating time for ABS, HDPE takes 0.115/0.0473 - 2.43 times longer to heat to the normal forming temperature. Example 3.2 Time to Heat Plastic Sheet Consider the two polymers of Example 3.1. If the plastic is 0.100 inch thick (2.5 mm) and the sheet receives 12.9 W/in2 (2 Wjcm2) heating energy1, determine the time required to heat the sheet to the forming temperature. Assume that the sheet heats uniformly throughout its thickness. IW= 3.413Btujh.
The energy required to raise each polymer to the forming temperature is given as: HDPE: 120 kcal/kg • 1.8 = 216 Btu/lb ABS: 45 kcal/kg • 1.8 = 81 Btu/lb 1
Correctly, this example assumes that the net energy interchange between the heater and the sheet is constant with time. See the section on basic concepts in radiation heat transfer for additional details on this constant heat flux assumption.
HDPE: 216^-0.96-624-0-1 - ^ S = 0 7 4 9 S 1 ABS:
4 5 ^ - 1.05 • 62.4 ^ • 0.1 in- J - ^ = ( U O 7 * ? Ib ft3 1728 in3 in2 Energy input per unit time x time = Total energy uptake HDPE: 12.9 ^ x t (time in h) • 3.413 - ^ - = 0.749 ? z^ nr Wh m HDPE: 12.9 ^ 2 x t (time in h) • 3.413 - ^ - = 0.307 ? 2^ in W •h m Solving for time: HDPE:
t =
0.749 3.413- 12.9 =
0
ABS:
t =
3.4133012.9 =
Q 0Q697h = 25 1S
-017h ~ '
6 L 2 S
'
There are many ways of heating sheet to the forming temperature. No heating process is 100% efficient. Regardless of the nature of the polymers, all heating systems must input more specific energy than the amount indicated in Table 3.1. Economics dictate a balance between the efficiency of net energy interchange between the source of heat and the sheet and the net rate of heating to the forming conditions. Where the heating rate controls the cycle time, process optimization usually calls for lowered energy efficiencies. To a large degree, sheet thickness dictates the type of heating that is most effective. Thin sheets are heated quite efficiently with radiant heaters. Thick sheets are best heated in forced convection hot air ovens.
3.3 Heat Transfer Modes There are three ways of exchanging energy between objects of different temperatures: Conduction Conduction is solid phase contact heat transfer. Conduction is the primary way energy moves through plastic sheet and metal molds. Three thermal properties are important in conduction: • • •
Density, Specific heat, heat capacity or enthalpy, and Thermal conductivity.
These properties have been reviewed in Chapter 2. In addition, thermal diffusivity is important in time-dependent heat conduction. Thermal diffusivity was also reviewed in Chapter 2.
Convection
Convection is fluid phase contact heat transfer. Throughout the thermoforming process, the sheet contacts ambient air. Energy is transferred when the air temperature differs from the sheet temperature. Energy transfer depends on the extent of air movement. As expected, energy transfer is low in quiescent air and relatively high when the air is actively moved across the plastic surface. The proportionality between thermal driving force or temperature differential and the amount of heat transferred is called the convective heat transfer coefficient. Convection is important when water mist or fog is used to cool the free surface of a formed part1. Otherwise, the effect of convection on overall heat transfer is secondary to conduction and radiation. Radiation
Radiation is electromagnetic energy interchange between an energy source or hot element and an energy sink or cold element. Radiation pervades nature. Electromagnetic energy is usually characterized by the wavelength of the energy. As seen in Fig. 3.2 [2], X-rays and gamma rays are characterized by very short wavelengths. Ultraviolet rays have wavelengths less than 0.4 um. Visible light wavelength range is 0.4 to 0.7 jam. Near infrared wavelength range is 0.7 to about 2 um. Far infrared wavelength range is from about 2 um to 8 um. Longer wavelength electromagnetic energy includes microwave, short wave radio frequency, long radio frequency and ultrasonic frequency. Heated metal or ceramic surfaces are used throughout thermoforming to radiantly heat plastic sheet. The majority of energy transfer takes place in the 2 um to 8 um wavelength range, or the far infrared region. There are several aspects of radiant heat transfer that require careful attention. For example, the efficiency of energy transfer depends on the relative abilities of the source and sink to transfer
Thermoforming Region
log [Wavelength, m]
log [Frequency, s1]
Radio Hertzian Waves
X-Rays
Infrared Ultraviolet
Cosmic Rays
Gamma Rays
Visible Figure 3.2 Electromagnetic radiation spectrum, showing radio waves, atomic energy, visible light, ultraviolet and infrared domains. Thermoforming region is also shown [2] 1
Cooling the formed part against the mold is the subject of Chapter 5.
energy efficiently. Absorptivity and emissivity are terms used to describe this efficiency. For most thermoforming applications, the energy interchange is between the heater surface and the plastic sheet surface. In some cases, energy is transmitted into or through the polymer. In addition, even though the sheet is sandwiched between the heaters, the interchanging elements are not infinite in extent. As a result, the efficiency of energy interchange depends on geometric factors as well as material properties. Efficient heating and cooling of thermoplastic sheet depends on the balance between the rate of energy input to the sheet surface and the rate of energy conduction from the sheet surface to the centerline. There are two classic cases of time-dependent conduction that illustrate this. Step Change in Surface Temperature
Consider contact or trapped sheet forming (Fig. 1.5). When the sheet is placed against the isothermal hot plate, its surface temperature immediately increases to the plate temperature (Fig. 3.3). As time increases, energy is conducted to the interior of the sheet. If the sheet is held against the hot surface long enough, the sheet temperature will eventually equal the hot surface temperature everywhere throughout the sheet. If the sheet is heated on both sides as shown in Fig. 3.4, the temperature profile through the sheet will be symmetric about the centerline. Constant Energy Input to the Sheet Surface
The amount of energy the heaters interchange with the sheet surface per unit area is called heat flux (kW/m2 or Btu/h • ft2). If the energy input is constant, the time-dependent temperature profile of Fig. 3.5 is obtained. This case illustrates some basic concepts in radiation heat transfer to plastic sheet. If the energy input is equal on both sides of the sheet, the time-dependent temperature profile through the sheet is symmetric about the centerline (Fig. 3.6). The temperature profile is again symmetric about the centerline when the sheet is heated on both sides. Unlike the previous case, the sheet surface temperature continues to increase with time. Unlike the previous case, the sheet temperature never reaches a constant value.
T
Temperature
oo
Increasing Time
initial Surface
Thickness
Figure 3.3 Time-dependent temperature profile for conduction into polymer sheet, constant surface temperature indicative of contact heating
Temperature
Increasing Time
"•"initial Surface.
Centerline
Surface2
Thickness
Temperature
Figure 3.4 Time-dependent temperature profile for two-sided conduction into polymer sheet, constant surface temperature indicative of contact heating
Temperature
Figure 3.5 Time-dependent temperature profile for conduction into polymer sheet, constant surface heat flux, indicative of radiation heating
Increasing Time
initial
Surface
Thickness
Increasing Time
T
initial Surface ^
Centerline
Surface2
Thickness Figure 3.6 Time-dependent temperature profile for two-sided conduction into polymer sheet, constant surface heat flux, indicative of radiation heating
Temperature
Increasing Time
initial Thickness Figure 3.7 Time-dependent temperature profile for conduction into polymer sheet, very low heat flux, very high polymer thermal conductivity or very thin sheet
Temperature
It is apparent from these two cases that there is an interrelationship or coupling between the energy input to the sheet surface and energy conducted to interior of the sheet. Consider this coupling in concept. Figure 3.7 is an extreme example of very low heat flux to the sheet surface coupled with very high thermal conductivity or diffusivity or very thin sheet (or both). The temperature profile through the sheet is essentially flat and the centerline temperature essentially equals the surface temperature. If the energy input to the sheet surface is very high and the polymer thermal conductivity or diffusivity is very low or the sheet is very thick, the sheet surface temperature will appear to reach a fixed temperature nearly instantaneously, as shown in Fig. 3.8 or Fig. 3.3. Figure 3.9 shows a more typical coupling between sheet surface and internal temperatures.
Increasing Tm ie
T
initial Thickness
Figure 3.8 Time-dependent profile for conduction into polymer sheet, very high energy input to the surface, low polymer thermal conductivity or very thick sheet
Temperature
Increasing Time
T
Figure 3.9 Time-dependent profile for conduction into polymer sheet for typical energy flux, polymer properties and nominal sheet thickness ranges
3.4
inttial Thickness
Incorporating Formability and Time-Dependent Heating
Formability is a key aspect of thermoforming. As seen in Table 2.5, all thermoformable polymers have forming windows, defined by the lower, normal and upper forming temperatures (LFT, NFT and UFT). As noted, the lower and upper forming temperatures form the absolute boundaries on formability. Whether a specific polymer can be formed into a specific shape at temperatures near these boundaries depends on: •
• • • •
The sheet characteristics such as: Intrinsic orientation, Hot strength, Sag tendencies, Thermal sensitivity of the polymer, Sheet geometry and Thickness, Uniformity of heating, Depth of draw, General mold geometry, and Other mechanical aspects such as: Transfer time, Ambient air temperature, Plugging geometry, Plug rate, Plug temperature, etc.
Despite these limitations, the upper and lower forming temperatures are useful in defining the nature of the temperature within the sheet. The upper forming temperature relates to the sheet surface. For example, if the upper forming temperature is set because the polymer is prone to blistering or color change above this temperature, the sheet surface temperature must never exceed this value during forming. If the
Forming Range T
Temperature
upper
normal
lower
Surface
Average Centerline
initial Optimum Heating Time Time Figure 3.10 Ideal relationship between polymer forming temperature range [shaded area] and time-dependent sheet surface, average and centerline temperatures
lower forming temperature is set because the polymer is too stiff to be formed or because it forms microcracks below this temperature, the centerline temperature must exceed this temperature before the sheet can be formed. The forming temperature range is shown as a time-independent band in Fig. 3.10. Figure 3.10 also shows the superimposition of the time-dependent local temperatures from Fig. 3.8 for the ideal case where the surface temperature reaches the upper forming temperature at the same time the centerline temperature reaches the lower forming temperature. And the average sheet temperature just equals the normal forming temperature at the same time1. As an example of the interplay between the sheet characteristics and the time-dependent energy input to the sheet, consider the following examples: Thin-Gage Sheet
As noted, when the sheet is very thin, energy input to the sheet controls. If the sheet of Fig. 3.10 is dramatically reduced in thickness, the temperature profiles of 3.11 are obtained. Although this profile is entirely acceptable, it is apparent that the rate of heating can be increased substantially without affecting the formability of the polymer (Fig. 3.12). 1
The shapes of the temperature curves for sheet surface, average and centerline are representative of profiles for sheet heated by radiant or radiant/convective means. The actual shapes depend on the nature of energy input to the sheet surface and the conductive and geometric characteristics of the sheet. See Section 3.15 on predicting temperature profiles for more details.
Temperature
Forming Range T
upper
^normal T
lower Surface, Average, Centerline
Figure 3.11 Relationship between polymer forming temperature range [shaded area] and timed-dependent sheet surface, average and centerline temperatures for very thin sheet
Time
Heavy-Gage Sheet
When the sheet is very thick, conduction from the sheet surface to the centerline controls. If the sheet of Fig. 3.10 is dramatically increased in thickness, the
Temperature
Forming Range
Time
Increasing Heating Rate
Temperature
Forming Range
Time
Minimum Heating Time
Figure 3.12 Effect of increasing energy input rate on the relationship between polymer forming temperature range [shaded area] and time-dependent sheet surface, average and centerline temperatures for very thin sheet
Temperature
Forming Range
S
A
Time
C
Figure 3.13 Relationship between polymer forming temperature range [shaded area] and time-dependent sheet surface, average and centerline temperatures for very heavy gage sheet
temperature profiles of Fig. 3.13 are obtained. To get the temperatures back into the forming window, the rate of heating must be decreased (Fig. 3.14). Changing Polymer Characteristics Without Changing Sheet Thickness
If the new polymer has a broader forming window than the old polymer, the rate of heating can be increased without affecting the formability characteristics. If the new polymer has a narrower forming window, the heating rate must be decreased as seen in schematic in Fig. 3.15. If the new polymer has a higher thermal conductivity than the old polymer, as is the case when filled polymers are used, the rate of heating can be increased without affecting the formability characteristics. If the new polymer has a lower thermal conductivity, as may be the case when foamed polymers are used, the heating rate must be decreased. Changing Other Aspects of the Forming Process
If the new mold requires greater depth of draw than the old one, the sheet may need to be formed at higher temperatures than before. As a result, the forming window may need to be narrowed or the lower forming temperature value increased. The result is that the rate of energy input may need to be reduced and the time to the forming condition extended. If the sheet requires prestretching, time between exiting the oven and completing the stretching may be longer than with straight forming. As a result, the sheet may need to be heated to higher temperatures than before. The rate of heating may need to be reduced and the time to the forming condition extended to increase the average temperature without exceeding the upper forming temperature. Example 3.3 illustrates the interaction of forming temperatures with heating cycle times for ABS and HDPE.
Temperature
Forming Range
Temperature
Decreasing Heating Rate
Time
Forming Range
Mn im i um Heating Time Time Figure 3.14 Effect of decreasing energy input rate on the relationship between polymer forming temperature range [shaded area] and time-dependent sheet surface, average and centerline temperatures for very heavy gage sheet
Example 3.3 Minimum and Maximum Forming Times Consider the two polymers of Examples 3.1 and 3.2. Determine the times required to reach lower and upper forming temperatures.
The upper and lower forming temperatures are obtained from Table 2.5 for ABS and HDPE. As is apparent, the lower forming temperature for both is 2600F (127°C) and the upper forming temperature is 3600F (182°C). The enthalpy increases to these temperatures are obtained from Fig. 3.1, as before: HDPE: LFT: 62 kcal/kg = 112 Btu/lb UFT: 142 kcal/kg = 256 Btu/lb ABS: LFT: 36 kcal/kg= 65 Btu/lb UFT: 60 kcal/kg= 108 Btu/lb Since all other factors are equal, the times are obtained by ratio with the values of Example 3.2. The values are tabulated here:
Polymer
HDPE ABS
Time (s) to reach Lower forming temperature
Normal forming temperature
Upper forming temperature
31.7 20.1
61.2 25.1
72.5 33.5
Temperature
Forming Range
Time
Minimum Heating Time
Reduction in Forming Range
Old Forming Range
Temperature
New Forming Range
Mn im i um Heating Time Time Figure 3.15 Effect of decreasing forming window on the relationship between polymer forming temperature range [shaded area] and time-dependent sheet surface, average and centerline temperatures
These various interactions and the general concepts of coupling of energy input to the sheet surface and conduction into the sheet interior are bundled into a predicting method in as described in Section 3.15. The various elements of this protocol are discussed below and the details of the protocol follow these discussions.
3,5
Conduction
As noted, conduction is solid phase energy transfer on an atomic or molecular level. Owing to high vibrational and rotational mobility of electrons and regular crystallographic structure, metals achieve high levels of conduction energy transfer. Organic materials, on the other hand, have relatively immobile atomic structures and so are poor thermal and electrical conductors. Polymers have even less molecular mobility and in addition, have high free volumes, allowing chain segments to move without contacting other segments. Polymers are therefore very poor thermal and electrical conductors. This was noted in Chapter 2. Classically, thermoformable sheet is considered as a two-dimensional planar surface with lateral dimensions far greater than its thickness dimension. In the bulk of the analyses that follow, the sheet is assumed to be planar to incident energy. One-dimensional steady-state heat conduction across the sheet thickness is given as: (3.3)
a/A
Steady-State Conduction
Q/A
Transient Conduction
Radiation Through Semitransparent Polymer Figure 3.16 Classical temperature profiles through plastics
Q/A
where Q/A is the heat flux, k the polymer thermal conductivity. AT is the temperature difference and Ax is the sheet thickness (Fig. 3.16). AT/Ax is the thermal gradient across the sheet thickness. The dimensions of these terms are: cal/cm • s •0 C cm 0 C cal/cm2 • s or kW/m2
k Ax AT Q/A
Btu/ft • h • 0 F ft 0 F Btu/ft2 • h
Example 3.4 shows the importance of material thermal conductivity in conduction heat transfer. It is apparent that energy conduction through plastic sheet is an important effect. Example 3.4 Relative Steady-State Temperature Differential Compare the steady-state temperature difference for 0.3 cm (O.Olft) thick polystyrene and aluminum for a thermal heat flux of 0.21 cal/cm2 • s [8.8 kW/m2]. The thermal conductivity for polystyrene =5.8 x 10~ 4 cal/cm • s • 0 C. That for aluminum is 5.8 x 10" 1 cal/cm • s • 0 C. The temperature difference for polystyrene is: AT =
^
k
= 0
Cm . 2 1 ^ 2L ' • g ; ° C -0.3Cm=IO 3 X cm -s 5.8 x 10~4 4 cal
For aluminum, the temperature difference is: AT =
(^) k
= 0
. 2 1 - ^2L - ^ * , — , ° C -0.3Cm = (UO-C cm -s 5.8 x 10" 1 cal
As noted, conduction of energy from the sheet surface to its interior controls the heating rate. The rate at which energy transfer occurs is called transient one-dimensional heat conduction. The time-dependent net energy increase or decrease equals the change in heat flux within the plastic sheet [3,4]: . . 6H 6T 6 / 8T\ 6 /Q\ t , Net enthalpy change per unit time = — « pcp - = - ^k - J = - ^ J
(3.4)
The polymer temperature is now a function of time and position across the sheet thickness, T(6,x). Three boundary conditions are needed to solve this equation in most applications: The Initial Condition The initial temperature throughout the sheet, T(G = 0, x = L) is needed, where L is the half-sheet thickness for equal two-sided heat flux energy input to the sheet surface. Usually the initial sheet temperature is not dependent of thickness for equal two-sided heat flux energy input to the sheet surface. Thus: T(O9L) = T0
(3.5)
A Symmetry Condition When the sheet is heated uniformly from both sides, the centerline forms a plane of symmetry (Fig. 3.5). The energy conducted from one side just equals that conducted from the other side. Thus the heat flux at the symmetry plane is zero, Q/A = 0. The condition at the centerline is described as: ^
=0
(3.6)
The Surface Condition The condition at the sheet surface in contact with the heating environment is also required. There are three characteristic conditions: Conduction, where the sheet directly contacts the heating source. For this condition: T(9, x = L) = TL(0)
(3.7)
Depending on the nature of the heating source, TL(0) can be time-dependent or constant. Convection, where the sheet contacts a fluid environment. For this condition: § A
= " 6,x = L
k
= h [ T ( ° ) " Too(e)l
TT 0X
(3-8)
0,x = L
The term h is the convective heat transfer coefficient. T(G) is the sheet surface temperature and T00(G) is the temperature of the environment. These temperatures can be time-dependent. Radiation, where there is energy interchange between the plastic sheet at absolute temperature T*(6) and the heating source at absolute temperature TJ3(G). The general form for this boundary condition is: = fU*(e),T* (9)] = G[T*4 - T*4]
^ A
(3.9)
e,x = L
The function f [ - ] is highly nonlinear in absolute temperature. The third equality is one representation showing the typical radiation fourth-power relationship, with G including geometry and radiation characteristics of both the heating source and the sheet. Quantification of the term G is given in the radiation section below. Numerical solution of the one-dimensional transient heat conduction equation with the nonlinear radiant heat flux boundary condition is difficult. As discussed below, certain approximations are made to simplify the arithmetic. These approximations also allow more direct comparison of radiation and convetion effects. Of course, combinations of these boundary conditions are significant as well. Figure 3.16 illustrates some of the characteristics of the temperature profiles through plastics for these various modes of energy transfer.
3,6
Convection Heat Transfer Coefficient
The convection heat transfer coefficient, h, is defined in Equation 3.8 as a proportionality constant1. When the energy source is a fluid, energy is transferred between the bulk moving fluid at temperature T00 and the solid surface at temperature T across a thin near-stagnant fluid layer. The heat transfer coefficient is a measure of the resistance to heat transfer across this layer. As the bulk fluid motion increases, the resistance to heat transfer decreases and the value of h increases. Representative ranges for heat transfer coefficients are given in Table 3.2. As is apparent, air is a poor convective heat transfer medium, water is more efficient than air and condensing steam is an excellent heat transfer medium. Example 3.5 shows the linearity between fluid temperature and energy transmitted to the plastic sheet. Table 3.2 Range in Values for Convection Heat Transfer Coefficient Conventional heat transfer coefficient (Btu/ft2 • h • 0F)
(10- 3 W/cm 2 - s-°C)
Fluid Quiescent air Air moved with fans Air moved with blowers Air and water mist Fog Water spray Oil in pipes Water in pipes Steam in pipes, condensing
0.5-1 1-3 3-10 30-60 30-60 30-90 30-180 60-600 600-3,000
0.8-2 2-5 5-20 50-100 50-100 50-150 50-300 100-1,000 1,000-15,000
Example 3.5 Convection Heat Transfer to Plastic Sheet For a sheet at temperature T0 = 1000F in hot air at temperature T00 = 2000F, the heat flux, Q/A, is 200 Btu/ft2 • h. What is the heat flux when the air temperature, T00 = 3000F? The solution uses a ratio of heat flux to temperature difference: (QZA)3OQ = / T 0 0 - T o \ ^_ (300 - 100) (Q/A) 200 V T 0 0 - T 0 ; (200-100)
=
Or: (Q/A) 300 = 2 x 200 = 400 Btu/ft 2 • h.
1
The convection heat transfer coefficient is also important in mold cooling analysis, as detailed in Chapter 5.
The Biot Number An important interrelationship between conduction and convection is useful here in determining the relative importance of convection energy. The Biot number, a dimensionless group, is defined as: Bi = ^
(3.10)
where Bi is the Biot number and L is a characteristic sheet dimension, typically the half-thickness. The range on the Biot number is zero to infinity, 0 < Bi < oo. Consider the following cases: •
Small Biot number occurs when the sheet thickness is very small, the convection heat transfer coefficient is very small, the sheet thermal conductivity is very large or combinations of these are in effect. Convection controls energy transfer into the sheet. For these conditions, Bi < 0.1 or so. • Large Biot number occurs when the sheet thickness is very great, the convection heat transfer coefficient is great, the sheet thermal conductivity is small or combinations of these are in effect. Conduction into the plastic controls energy transfer into the sheet. For these conditions, Bi > 1 or so.
Example 3.6 illustrates the use of this dimensionless group. As expected, the Biot number value for very heavy gage sheet is usually very large. Similarly that for very thin sheet is very small. Usually if the energy transfer between the environment and the sheet surface controls, that is, if Bi is very small, a more efficient means of heating should be sought. Example 3.6 The Biot Number in Convection Heating Consider a 0.240 inch (=2L) sheet heated in a high-velocity forced air convection oven where h = 10Btu/ft2 • h • F. The thermal conductivity, k= 0.1 Btu/ft • h • F. What is the Biot number? Does convection or conduction heat transfer control? Then consider a 0.024 inch (=2L) sheet heated in natural convection air where h = 2 Btu/ft2 • h - F. The thermal conductivity, k = 0.2 Btu/ft • h • F. Does convection or conduction heat transfer control the heating rate of this sheet?
For the first case, from Equation 3.10, hL = i 0 . O 1 2 k 0.1 12 Since Bi is large, conduction probably controls the heating rate. For the second case: .
Bl=s
hL
2 0.012
T = OT "IT =0-01
Since Bi is small, convection controls the heating rate.
Effective Radiation Heat Transfer Coefficient As noted, the radiant heat flux boundary condition, Equation 3.9, is nonlinear. Example 3.7 shows this strong nonlinearity. In certain instances, the nonlinear radiation condition can be approximated by a pseudo-convection condition: Q/A = f(T,T J « hr(T - T00)
(3.11)
where hr is a pseudo-convection heat transfer coefficient or radiation heat transfer coefficient. Methods for obtaining values of hr and ways of combining the value of the radiation heat transfer coefficient with the convection heat transfer coefficient value are detailed below. This approximation is best for high radiant heater temperatures or where T00 > T. Thin-gage roll-fed sheet formed into products such as cookie trays, blister packs and live plant containers are examples where this approximation is useful1. Example 3.7 Radiation Heat Transfer to Plastic Sheet For a sheet at temperature T0 = 1000F being heated radiantly from a hot plate at temperature T00 = 2000F, the heat flux, Q/A, is 200Btu/ft2 • h. What is the heat flux when the plate temperature, T00 = 3000F? The absolute sheet temperature, T0= 100+460= 5600R. The absolute plate temperature is either T00 = 200 + 460= 66O0R or T00 = 300+ 460= 7600R. The solution uses a ratio of heat flux to temperature difference: (QZA)3QO _ (T*J - T4A = (7604 - 5604) _ (Q/A)200 V T r - T 0 - ; (660 4 -560 4 ) ' Or: (Q/A)300 = 2.6 x 200 = 520 Btu/ft2 • h.
1
In even more specific cases, the difference between the heater temperature, T00, and the sheet surface temperature is so large that the difference in the fourth powers of their absolute temperatures is essentially independent of time. In that case, the heat flux, Q/A, to the sheet surface is assumed to be constant. The resulting equation is: ^ f ( T , T J « ^T 00 only)
(3.12)
As seen in Equation 3.9, the temperature gradient at the sheet surface is then constant: - k ^- ^f(T00 only) (3.13) Sx The constant heat flux condition represents one of the two ideal cases described earlier. This condition is approximated when roll-forming very thin-gage sheet exposed to very high radiant heater temperatures.
Constant Heat Flux In certain instances, T00 » T and the heat flux can be considered constant, for at least a short portion of the heating cycle: Q/A ^f(TYT00) ^f(T00)
(3.14)
The determination of radiant heater output efficiency is a practical use for the concept of constant heat flux. This technique is' detailed below. For very thin sheets that are truly opaque to incident radiation, the lumpedparameter approximation is important. If the energy transfer through the sheet is secondary to the energy transfer to the sheet, the partial differential equation, Equation 3.4, is replaced with a simple ordinary differential equation based on a simple time-dependent heat balance. The lumped-parameter approximation is discussed later in this chapter. Plastic sheet can be heated to forming conditions by conduction and/or hot air convection energy transfer. In trapped sheet forming [5], the sheet contacts a heated, porous blow plate only on one side (Fig. 3.17). The energy is conducted through the sheet and convected to the ambient air on the free surface. Trapped sheet forming is used in thin-gage form-fill-seal operations, when the plastic sheet is very thin, 0.13 mm or 0.005 in or less, when the sheet requires very high forming temperature, and/or when the plastic thermally degrades. The arithmetic for predicting sheet temperature is given below. Thick PMMA and PC sheet is held vertically on rails in large forced convection hot air ovens prior to being drape-formed into aircraft canopies [6] and whirlpool spas. Slow convection heating allows very thick sheets to
Vacuum
Slotted or Porous Blowing Plate
Hot Plate Sheet Clamp Urethane or Silicone Gasket Heating
Mold Blowing Air
Forming Air Exhaust or Vacuum
Figure 3.17 Trapped sheet forming, an example of conduction heating of plastic sheet [5]
thoroughly dry, anneal and stress relieve prior to forming. This gentle treatment minimizes distortion, spring-back and impact crazing. Contact heating accounts for about 15% of the surface area of sheet formed. Convection heating accounts for about 5% with radiant heating representing the remaining 80%.
3.7
Radiation Heating
Radiation is electromagnetic energy transfer between a hot source and a cold sink that it sees. Radiation energy transfer does not depend on the distance separating the source and the sink. It is the most energy efficient way of heating planar surfaces but misuse can lead to surface scorching or burn, very uneven temperature distribution through the thickness of the sheet, and energy waste. Most roll-fed and many shuttle thermoformers now heat with radiant sources. Common heating sources are: • • • • • • • • • •
Nichrome spiral wires, Steel rod heaters, Steel or Nichrome tapes, Halogen tube heaters, Ceramic plates with embedded resistance wires, Ceramic bricks with embedded resistance wires, Quartz tube heaters, Steel plates that reradiate combustion energy from gas flames, Steel wire grids that reradiate combustion energy from gas flames, and Direct gas combustion.
Primary radiant heat transfer is correctly a net energy interchange between an energy source and energy sink(s). It is apparent that the hot source radiates energy toward the sink, but the sink also radiates energy, albeit weakly, toward the hot source. The primary radiant energy impinging on any surface is either absorbed, reflected or transmitted (Fig. 3.16). If the incident radiant energy is either reflected or absorbed on the surface, the sink is opaque. Other radiation characteristics of materials are given in Table 3.3. The thermal radiation wavelength range is normally from about 0.1 urn to 20 um. The ultraviolet or UV region is 0.1 urn to 0.38 um. The visible light region is 0.38 um to 0.7 um. Near-infrared is 0.7 um to about 3 um and far-infrared is about 3 um to 20 um. The important wavelength range for most radiant thermoforming processes is a portion of the far-infrared range from about 3 um to about 20 um. As reference, the sun at an effective surface temperature of about 55000C [10,0000F] emits more than 90% of its radiation in the wavelength range of 0.1 um (UV) to 3 um, or the near-infrared region. The efficiency of radiant energy interchange depends on several attributes of the source and sink relationship. Some of these are:
Table 3.3 Radiation Characteristics of Bodies Nature
Definition
Surface reflection, diffuse Surface reflection, specular
Incident radiation reflected evenly in hemisphere Incident radiation reflected preferentially in a given steradian segment of hemisphere Unreflected incident radiant energy absorbed on surface, no transmission All unreflected incident radiant energy transmitted through and out of material All unreflected incident radiant energy transmitted through material, partially reflected back from second surface— sometimes specular Properly, semitransparent Nonreflected incident radiant energy partially absorbed volumetrically, partially transmitted through sheet All radiant energy totally absorbed at all wavelengths, no energy reflected, no energy transmitted Also, a radiant source that emits the maximum amount of energy at all wavelengths In contrast to black body, no radiant energy absorbed at any wavelength, can be either ideally transparent or perfectly reflecting A fixed fraction of radiant energy absorbed, independent of wavelength
Opaque Transparent Transparent with internal reflection—light-piping Translucent Semitransparent Black body—ideal
White body—ideal Gray body—ideal
• • • •
The The The The
efficiencies of the sink and the source in absorbing and emitting radiation, wavelength dependencies of these efficiencies, geometry of the sink and the source and their relative proximities, and absolute temperatures of the sink and the source.
The objective of the sections that follow is to quantify the proportionality constant G in Equation 3.9. An understanding of basic elements of radiation energy interchange is needed to achieve this objective. Black Body Radiation The maximum total energy emitted by any source at all wavelengths at a given absolute temperature T* is that emitted by a black body: Eb = aT*4 (3.15) T* is the source temperature in K = 0C + 273 or 0R = 0 F + 460. a is the StefanBoltzmann constant having the following units: kW [a] = 0.5674 x \Q-">—— m •K -0.1714 x 1 0 -
^
^
Monochromatic Black Body Energy Intensity, E^ Visible
Solar, 65000C
Infrared Wavelength, JJm
Figure 3.18 Temperature- and wavelength-dependent monochromatic black body energy intensity
E b is the total energy emitted for all wavelengths, in kW/m 2 or Btu/ft2 • h. All thermoforming radiant sources are referenced to the amount of energy emitted by a black body source. The wavelength-dependent radiant energy emitted by a black body at temperature T* is given as:
where X is the monochromatic wavelength in jim. The values for C 1 and C 2 are given as: [C1]
=
3.743 x 10« k
W
J
m 4
, 1.187 x 10»
B
4
^
[C2] = 1.439 x 104 K • jam = 2.59 x 104 0 R • jam The wavelength-dependent energy emitted by a black body source at temperature T* is given in Fig. 3.18. The wavelength at which the maximum energy is emitted is given as: U
= a/T*
(3.17)
The specific energy emitted at this wavelength is: Eb,,,max = C 3 -T* 5
(3.18)
Appropriate values for a and C 3 are: [a] = 2897.6 \im • K = 5215.6 jim • 0 R IcW [C 3 ]= 1.287 x 10- 1 4
"Rtii
, *Y = 2.161 x 1 0 ~ 1 3 r 7 , o , L 3J 2 5 m -K -^im ft2-h-°R5-|im Example 3.8 illustrates the energy output from a black body. Nearly 20% of the total emitted energy occurs within 0.5 jim of the peak wavelength value (Equation 3.17). Typical radiant heater temperatures ranges from 400 0 F to 1500 0 F or 200 0 C to 815°C. The total energy emitted by a black body source, the wavelength at m a x i m u m energy
emission and the energy emitted at that wavelength are given in Table 3.4 for several temperatures in this range. Example 3.8 Energy Output from a Black Body A black body is at 8000C. Determine the total amount of energy emitted and the amount emitted at the wavelength of maximum energy emission. The total amount of energy is obtained from Equation 3.15:
Eb,0_ „ = 0.5674 x 1 0 - . (800 + 273)< = ^
= * f £ *
The wavelength of maximum energy emission is given as: ^max = 2897.6/(800 + 273) = 2.7 um E^U^O-^ +W
=^
=
^
Approximately (5.82/75.2) = 7.7% of the total radiant energy emitted over the entire wavelength spectrum is emitted at exactly 2.7 um. Most plastics absorb radiant energy preferentially in specific wavelength ranges as discussed in Chapter 2 and as seen in Table 3.5. To maximize the energy absorbed by the plastic, thermoformer heater temperatures should be set to those correspondTable 3.4 Wavelength of Maximum Energy Transmission Black Body Radiation Temperature
Wavelength
Specific energy at peak wavelength1
(0F)
(0C)
(um)
(kW/m 2 • u m )
(Btu/ft2 • h • Jim)
400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
204 260 316 371 427 482 538 593 649 704 760 816 871 927 982 1038 1093
6.06 5.43 4.92 4.50 4.14 3.84 3.57 3.34 3.14 2.96 2.80 2.66 2.53 2.41 2.31 2.21 2.11
0.32 0.55 0.91 1.43 2.16 3.16 4.52 6.28 8.57 11.5 15.1 19.7 25.2 32.0 40.1 49.8 61.3
102 176 289 454 686 1005 1435 2000 2720 3650 4810 6250 8020 10,200 12,700 15,800 19,500
1
E b X m a x = C 3 T* 5 where C 3 = 1.287 x 10~ 1 4 kW/m 2 • k 5 • um = 2.161 x IO" 1 3 Btu/ft 2 • R 5 • um
Table 3.5 Ideal Radiant Heater Temperature Ranges for Several Thermoformable Plastics Plastic
LDPE HDPE PS PVC PMMA PA-6 PET Cellulose acetate
Ideal wavelength (um)
Temperature range (0C)
(0F)
3.2-3.9 3.2-3.7 3.2-3.7 (6.4-7.4) 3.2-3.6 (5.7-6.0) 3.2-3.6 3.0-3.2 3.3-3.6 (7.0-9.2 5.5-6.0 7.8-10.0
470-630 510-630 510-630 120-180 530-630 210-235 530-630 630-690 605-630 42-140 210-255 15-100
877-1170 950-1170 950-1170 245-355 990-1170 410-455 990-1170 1170-1280 1120-1170 107-285 410-490 60-210
Total Emissive Power Fraction
ing to these wavelength ranges. The practical upper limit for thermoformer heater temperature is about 16500F or 9000C. Above this temperature, special materials of construction are needed for the heaters, special reflectors are required, and the high energy level to the polymer sheet makes its temperature control very difficult. The fraction of energy emitted by a black body source at a given temperature over a given wavelength range is obtained by subtracting values from Fig. 3.19 or Table 3.6 [7]. Examples 3.9 and 3.10 illustrate the usefulness of this approach.
^ M max
Wavelength-Temperature Term, AT, um-°R Figure 3.19 Fraction of total emissive power, E0 _ JE0 _ ^, at or below wavelength
Table 3.6 Radiation Functions [7] Eb,0 - XT*
ax-* 1 0 5
CTT* 4
O 1000 1200 1400 1600 1800 2000
0 0.000394 0.001184 0.01194 0.0618 0.2070 0.5151
0 0 0 0 0.0001 0.0003 0.0009
2200 2400 2600 2800 3000
1.0384 1.791 2.753 3.872 5.081
0.0025 0.0053 0.0098 0.0164 0.0254
3200 3400 3600 3800 4000
6.312 7.506 8.613 9.601 10.450
0.0368 0.0506 0.0667 0.0850 0.1051
4200 4400 4600 4800 5000
11.151 11.704 12.114 12.392 12.556
0.1267 0.1496 0.1734 0.1979 0.2229
5200 5400 5600 5800 6000
12.607 12.571 12.458 12.282 12.053
0.2481 0.2733 0.2983 0.3230 0.3474
6200 6400 6600 6800 7000
11.783 11.480 11.152 10.808 10.451
0.3712 0.3945 0.4171 0.4391 0.4604
7200 7400 7600 7800 8000
10.089 9.723 9.357 8.997 8.642
0.4809 0.5007 0.5199 0.5381 0.5558
1 0 5
CFT* 4
8200 8400 8600 8800 9000
8.293 7.954 7.624 7.304 6.995
0.5727 0.5890 0.6045 0.6195 0.6337
9200 9400 9600 9800 10000
6.697 6.411 6.136 5.872 5.619
0.6474 0.6606 0.6731 0.6851 0.6966
10200 10400 10600 10800 11000
5.378 5.146 4.925 4.714 4.512
0.7076 0.7181 0.7282 0.7378 0.7474
11200 11400 11600 11800 12000
4.320 4.137 3.962 3.795 3.637
0.7559 0.7643 0.7724 0.7802 0.7876
12200 12400 12600 12800 13000
3.485 3.341 3.203 3.071 2.947
0.7947 0.8015 0.8081 0.8144 0.8204
13200 13400 13600 13800 14000
2.827 2.714 2.605 2.502 2.416
0.8262 0.8317 0.8370 0.8421 0.8470
14200 14400 14600 14800 15000
2.309 2.219 2.134 2.052 1.972
0.8517 0.8563 0.8606 0.8648 0.8688
Example 3.9 Energy Emitted in a Narrow Wavelength Range Consider an 8000C= 1472°F black body emitter. Determine the fraction of total energy emitted in the wavelength range of 2 jum to 4 jum. Repeat this for a 7000C= 1292°F source.
The term ^T* = 2 • (1472 + 460) = 3864. From Table 3.6, the fraction of energy emitted between 0 and 2 jim is given as: E b , 0 _ 2 = 9.14% For AT* at 4 jim, the fraction of energy emitted between 0 and 4 jim is: E b , 0 _ 4 = 53.14% Thus the amount of energy emitted between 2 jim and 4 jim is (53.1 — 9.1) = 44% of the total amount. For a 7000C source, the energy fractions at 2 \xm and 4 urn are, respectively: Eb,0_2 = 5.9% E 1 ^ 4 = 45.3% And the amount of energy emitted between 2 jim and 4 jim is (45.3 — 5.9) = 39.4% of the total. Example 3.10 Energy Emitted in The Thermoforming Wavelength Range Consider an 8000F ceramic heater. Assume it emits as a black body. Determine the fraction of total energy emitted in the normal thermoforming wavelength range of 3.5 jum to 9 jum. The term ^T* = 3.5 • (800 + 460) = 4410. From Table 3.6, the fraction of energy emitted between 0 and 3.5 urn is given as: Eb^3.5=15.1% For XT* at 9 urn, the fraction of energy emitted between 0 and 9 um is: E 1 ^ 9 = 76.2% Thus the amount of energy emitted in the 3.5 jim to 9 jim thermoforming wavelength range is (76.2 — 15.1) = 61.1% of the total amount.
Gray Body—Emissivity No practical material emits at black body energy levels. Many materials, including nearly all polymers, emit at 80%) to 95%o of the maximum level, however. A gray body is one that emits energy at a fixed fraction of the total black body energy level: Eg = e-aT* 4 (3.19) where e is emissivity, 0 < e < 1. If the fraction of energy emitted by the material is wavelength-dependent, e = e(k), Emissivities are usually wavelength-dependent for real surfaces (Fig. 3.20). The total energy is obtained from integration: (3.20)
log Monochromatic Black Body Energy Intensity, E^
Figure 3.20 Comparison of wavelength-dependent monochromatic energy intensity for black, gray and real bodies
Black Body, e = 1 Gray Body, e < 1 Real Body, e = f(A)
Wavelength
As an approximation, emissivity can be considered constant over specific ranges in wavelength. The individual energies in each of these range segments are then summed to obtain the total energy: T
Eg.,,,*, = «
*4 n
V^N
7
N-I -
W/
I
e A i
+
. - * i )
<3-21)
j=1
The individual black body energies are obtained from Fig. 3.19. In Table 3.7 [8] are given some wavelength-dependent emissivities and absorptivities for materials found in many thermoforming operations. For many materials, however, only an average value is known. Usually polished or very smooth surfaces emit at much lower energy levels, O < e < 0.3, than pitted, oxidized, rusted, matte or irregular surfaces, 0.8 < e < 0.95. The emissivity of a plastic sheet should be determined at its temperature whereas its energy absorption efficiency or absorptivity, a, should be determined at the emitter temperature. Strictly speaking, a ^ e, but practically a and e are assumed equal. All surfaces radiate energy. The maximum amount of energy absorbed by the plastic sheet is determined from a net radiant energy balance between the gray-body source, emitter or heater and the gray-body sink, the polymer sheet: 5
=
aF g (T* 4 -Tf)
(3.22)
TJ3 is the absolute heater temperature and Tf is the sheet temperature, in K or 0R. Again a is the Stefan-Boltzmann constant. F g is a factor that corrects black-body energy for the gray-body nature of the emitter or heater, eh, and the source or sheet, es. For planar heaters and flat sheet, Fg, the gray body correction factor, is:
F 8 JI + I-IT1 g K es J
(3.23)
F g = 1 when both surfaces are black bodies. Examples 3.11 and 3.12 illustrate the relative effect of F g on the energy interchange efficiency. About 21% of the energy interchange occurs in the absorption wavelength regions of 3.2-3.7 urn and 6.4-7.4 jim that are ideal for styrenics such as PS, HIPS and ABS. Other examples of graybody correction factors are given below.
Table 3.7 Emissivities and Absorptivities for Various Materials Used in Thermoforming1 Material
Emission values at various temperatures and peak wavelength
Absorption values
38°C (1000F) 9.3 Jim
2600C (5000F) 5.4 |^m
538°C (10000F) 3.6 j^m
1371°C (25000F) 1.8 urn
Aluminum Polished Oxidized Anodized
0.04 0.11 0.94
0.05 0.12 0.42
0.08 0.18 0.60
0.19
Chromium Polished
0.08
0.17
0.26
0.40
0.06 0.63
0.08 0.66
0.13 0.76
0.25
0.45
0.42 0.90
0.66 0.89
Iron, steel Polished Cast, oxidized Galvanized New Dirty Steel plate Oxide Steel tube, oxidized Stainless steel Polished Weathered Tungsten filament Paper, white Plaster Enameled steel, white Paints Black lacquer Oil, all colours White, ZnO Water Wood Glass 1
0.23 0.28 0.94 0.96
0.97
0.26
0.34
0.98 0.85
0.74
0.80
0.15 0.85
0.18 0.85
0.22 0.85 0.18 0.25
0.03 0.95 0.91
0.27
0.65 0.82 0.96 0.94 0.95 0.96 0.93 0.90
0.97-0.99
0.98 0.90
0.12-0.26
0.91
From [40] with permission of copyright owner; absorption values for solar radiation from [41]
Example 3.11 Gray-Body Correction Factor—I Consider an 8000C = 1472°F heating source with an emissivity of €^ = 0.95 interchanging energy with ABS at 200C = 68°F. The ABS is semi-matte finish with es= 0.85. Determine the energy interchange and compare it with the black-body energy interchange value.
From Equation 3.23, F g = 0.814. The black-body energy interchange is obtained from Equation 3.22, with F g = 1. Eb,totai = 0-5674 x 100 x [1.0734 - 0.2934] = 74.8 kW/m2 The gray-body energy interchange is: Eg,totai = 0.814 • 74.8 = 60.9 kW/m2. The gray-body energy interchange is 81.4% ,efficient. Example 3.12 Gray-Body Correction Factor—II Using the information of Example 3.9, determine the energy interchange when the sheet temperature is 1500C= 3020F. Then determine the amount of energy absorption in the preferential absorption wavelength ranges of 3.2 /urn to 3.7 jum and 6.4 jum to 7.4 jum. From Equation 3.23, F g = 0.814. The black-body energy interchange is obtained from Equation 3.22 with F g = 1. Eb.totai = 0.5674 x 100 x [1.0734 - 0.4234] = 73.4 kW/m2 The gray-body energy interchange is: Eg,totai = 0-814 • 73.4 = 59.7 kW/m2. The gray-body energy interchange at this temperature is about 98% as efficient as that when the sheet is at room temperature. The energy interchange between the source and the sink follows the details of Example 3.9. Consider the heater first. XT* = 3.2 • (1472 + 460) = 6182 and 3.7-(1472+ 460) = 7148. Then AT* = 6.4 • (1472 + 460) = 12,365 and 7.4 • (1472 + 460) = 14,297. From Table 3.6, the following black-body energies are obtained: Eb,0_3.2 = 36.9% Eb,0_ 3.7 = 47.6% Eb,0_6.4 = 80.0% Eb,0.7.4 = 84.5% The percentage of total black-body energy emitted in these wavelength ranges is: Eb,ranges = (84.5 - 80.0) + (47.6-36.9) = 15.2% The actual amount of black-body energy emitted in these wavelengths is: Eb,heater = 0.152« 56.74 • 1.0734 =11.43 kW/m2 Consider the sheet. A-T* = 3.2 • (302 + 460) = 2438 and 3.7-(302 + 460) = 2819. Then XT* = 6.4 • (302 + 640) = 4877 and 7.4 • (302 + 460) = 5639. From Table 3.6, the following black body-energies are obtained: EKO_3.2 = 6.1% ^0-3.7=17.3% Eb,0_6.4 = 20.8% Eb,0.7.4 = 30.3% The percentage of total black-body energy emitted in these wavelength ranges is: Eb,ranges = (30.3 - 20.8) + (17.3 - 6.1) = 20.7%.
The black-body energy emitted in these wavelengths is: Eb,sheet = 0.207 • 56.74 • 0.4234 = 0.38 kW/m2 The total black-body energy interchange is then: Eb,heater - Eb,sheet =11.43-0.38 = 11.05 kW/m2 The total gray-body energy interchange in these wavelength ranges is: Eg,inter = F g - 11.05 = 9.0 kW/m2 The total efficiency in these wavelength ranges, based on total black-body emitter energy is: Eg,mter
100'9.0
In addition to a correction factor for the nonblack nature of the source and sink, a correction factor is usually needed to compensate for the relative sheet and heater geometries. The radiation correction factor or "view factor", F, is unity when both the heater and sheet surfaces are considered as infinite planar surfaces. The view factor is unity when the sheet can be considered as completely enclosed by the heater. The nonplanar nature of heater surfaces and the energy losses at the sheet edge usually yield values of the view factor, F, that are less than unity. These cases are described below. When gray-body and geometry effects are included, the general net radiant energy balance between the source and the sink is written as: 5 = { a F F g } - (T* 4 -T 8 * 4 )
(3.24)
Radiant Heater Efficiency—Constant Heat Flux Application Consider a square aluminum plate, L units on a side by t units thick (Fig. 3.21). The aluminum plate weight is known, m = p • L2t = (2.7 g/cm3) • L2t. Its heat capacity from Table 2.5 is c p = 0.224 cal/g 0 C [Btu/lb 0 F]. The plate is mounted on a thermally insulated rod such as a broom handle. A thermocouple is embedded in the center of the plate and its output is monitored on a strip chart recorder. The plate is sprayed with matte black oven paint to increase emissivity to approximately unity (e ~ 1). The room temperature plate is put in the radiant oven and its temperature measured for several seconds over a 200C (or so) temperature range near room temperature. A heat balance on the plate is:
m C p =A
S (A)* A { a F F g } T * 4
(3 25)
'
The second approximation is assumed since T 0 0 » T. A is the plate area, A = 2L2. The areas of the plate edges are ignored. T = T 0 when 0 = 0. This equation is integrated to yield:
Aluminum Plate
Wood Handle
TC Figure 3.21 Aluminum plate used to determine heat flux from local heaters
T-T0
+
p j ^ ) - T . L (mc p /A) J
+
r ™ £ > L (P tc p/ 2 ) J
,3.26,
For very short times, 6 < 10 s, the plate temperature increases linearly with time, with the slope of the temperature curve containing information about the efficiency of the radiant heating source. Example 3.13 illustrates the use of this equation in determining the energy output of radiant heaters. Heaters are rated in 'watt density' or Watts per unit area of heater surface. The units of watt density are W/cm2 or W/in2. This is a direct measure of the consumption of electric power. The efficiency of conversion of electricity to heat is illustrated in Example 3.13 as well. The application of the concept of constant heat flux illustrates a practical way of measuring and monitoring radiant heater performance. Example 3.13 Radiant Heater Efficiency Consider a 6-in x 6-in aluminum plate, 0.125 in thick. It is heated on both sides from 100 to 125°F in 9.43 s by exposure to ceramic heaters having a measured temperature of 6000F. Determine the radiant heater efficiency. Determine the efficiency of energy conversion if the heaters are rated as 8 W/in2 at 6000F. The plate mass is given as: m = p • L2t = 0.439 Ib =199 g. The increase in energy in the plate is: q =m . c p d T = 1 9 9 g ^ . < i M
The rate of increase is: q/9 = 619/9.43 s = 65.7 cal/s
-C-,,, cd
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The heat flux to the plate is: f
= 65.7^- - - > 0 . 1 4 2 - ^ L = 0 . 5 9 5 ^ = 1 8 8 5 - ^ = 3.83 ^ A s 2 • 15.22 cm2 cm2 • s cm2 ft2 • h m2 The ideal heat flux from this source temperature is obtained from: § = o T * « = 0.164 - ^ 2i - = 0.685 ^ 5 2 = 2172 ^ 2 = 4 . 4 2 ^2 A cm • s cm ft • h m The radiant heater efficiency is given as: Efficiency = 100 • — = 87% The energy conversion efficiency is given by the ratio of the energy actually emitted by the heater to the rated heater efficiency. For the heater rating of 8 W/in2, the energy conversion efficiency is: Energy Conversion Efficiency = 100 • - ^ - = 47.9% 8
3.8
Real Heaters—Efficiencies
As noted earlier, only a fraction of the energy supplied by utility companies to the thermoforming machine is converted to radiant energy to heat the sheet (Fig. 3.22) [9]. Efficiencies of actual radiant heating sources are given in Table 3.8. The efficiencies of various types of heating sources for various polymers are given in Table 3.9. These values represent net efficiencies. The energy conversion from power source to radiant thermal energy at the heater surface is relatively efficient (Example 3.13). Quartz heaters are more efficient at higher temperatures (Fig. 3.23). About 50% of the electrical power input is converted to radiant energy at 316°C or 6000F. Essentially all is converted at 9000C or 16500F. As seen in Table 3.8, tubular and spiral wire heaters have similar efficiencies at about 50% when new. Gas combustion efficiency at 9000C or 16500F for one type of surface infrared burner is reported to be 82% to 84% [10], with an average heat flux at this temperature of 236.5 kW/m2 or 75,000 Btu/ft2 • h. The ideal black body energy emitted at this temperature is 107.4 kW/m2 or 33,970 Btu/ft2 • h. Other types of surface burners show efficiencies somewhat lower than this. Note in Table 3.8 that the effective surface heat fluxes for most gas-fired burners operating at very high temperatures are substantially greater than the values predicted by black body radiation. Convective energy transfer is apparently a major factor with these burners. Since all radiant heaters operate in an air environment, convection losses from heater surfaces reduce heater efficiency, sometimes by as much as 30% to 50%.
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The heat flux to the plate is: f
= 65.7^- - - > 0 . 1 4 2 - ^ L = 0 . 5 9 5 ^ = 1 8 8 5 - ^ = 3.83 ^ A s 2 • 15.22 cm2 cm2 • s cm2 ft2 • h m2 The ideal heat flux from this source temperature is obtained from: § = o T * « = 0.164 - ^ 2i - = 0.685 ^ 5 2 = 2172 ^ 2 = 4 . 4 2 ^2 A cm • s cm ft • h m The radiant heater efficiency is given as: Efficiency = 100 • — = 87% The energy conversion efficiency is given by the ratio of the energy actually emitted by the heater to the rated heater efficiency. For the heater rating of 8 W/in2, the energy conversion efficiency is: Energy Conversion Efficiency = 100 • - ^ - = 47.9% 8
3.8
Real Heaters—Efficiencies
As noted earlier, only a fraction of the energy supplied by utility companies to the thermoforming machine is converted to radiant energy to heat the sheet (Fig. 3.22) [9]. Efficiencies of actual radiant heating sources are given in Table 3.8. The efficiencies of various types of heating sources for various polymers are given in Table 3.9. These values represent net efficiencies. The energy conversion from power source to radiant thermal energy at the heater surface is relatively efficient (Example 3.13). Quartz heaters are more efficient at higher temperatures (Fig. 3.23). About 50% of the electrical power input is converted to radiant energy at 316°C or 6000F. Essentially all is converted at 9000C or 16500F. As seen in Table 3.8, tubular and spiral wire heaters have similar efficiencies at about 50% when new. Gas combustion efficiency at 9000C or 16500F for one type of surface infrared burner is reported to be 82% to 84% [10], with an average heat flux at this temperature of 236.5 kW/m2 or 75,000 Btu/ft2 • h. The ideal black body energy emitted at this temperature is 107.4 kW/m2 or 33,970 Btu/ft2 • h. Other types of surface burners show efficiencies somewhat lower than this. Note in Table 3.8 that the effective surface heat fluxes for most gas-fired burners operating at very high temperatures are substantially greater than the values predicted by black body radiation. Convective energy transfer is apparently a major factor with these burners. Since all radiant heaters operate in an air environment, convection losses from heater surfaces reduce heater efficiency, sometimes by as much as 30% to 50%.
Energy Supplied to Heaters Energy Loss During Conversion to Radiant Heat Energy Convected From Heaters Radiation Loss to Surroundings Reradiation From Surroundings Reradiation From Heaters Radiation From Sheet to Heaters Convection Heat Loss to Surroundings
Energy Absorbed by Sheet Figure 3.22 Schematic of heat transfer energy distribution in thermoforming operation [9]. Figure used by permission of Society of Plastics Engineers, Inc.
An estimate of the convection heat loss is detailed below. Heaters radiant energy to all visible surfaces, including: • • • • • • • • •
Plastic sheet, Reflectors, Other heaters, Rails, Sheet clamping devices, Heater guards, Objects outside the oven edges, Oven sidewalls, and Shields and baffles.
As much as 20% to 30% of the energy emitted by radiant heaters is lost to the environment in this way. Further, a fraction of net radiant energy absorbed by the plastic sheet is convected to the cooler air environment from the hot sheet itself. Thus, only about 20% to 50% of the power supplied by the utility is converted into increasing the enthalpy of the sheet. The actual efficiency depends on: • • •
Matching source temperature with plastic radiation absorption range, Minimizing all thermal sinks other than the plastic sheet, and Controlling the convective energy losses from heater and sheet surfaces.
Table 3.8 Efficiencies of Commercial Radiant Heating Sources1 Radiant source
Maximum energy
Maximum temperature
Black body energy
Maximum efficienty
(0C)
(0F)
(kW/m2)
(Btu/ft 2 • h)
(%)
Heating (kW/m2) Bulb: R-40 reflector
(Btu/ft 2 • h)
Comments
Response time Cooling
16.1
5120
2200
4000
2140
678,000
<1
3s
10s
6.4
2030
2200
4000
2140
678,000
<1
3s
10s
Ceramic spot Quartz lamp
1.4 310
1535 98295
870 2200
1600 4000
97.3 2140
30,900 678,000
1.4 14.5
5-10 min 3s
5-10 min 10s
Tube: Metal sheated
46.5
14745
870
1600
97.3
30,900
48
5 min
Quartz tube
77.5
24575
980
1800
44,700
55
1 min
Strip: Quartz faced
58.1
18430
760
1400
64.7
20,500
90
2-4 min
2-4 min
Panel: Coated glass
14.1
4555
315
600
6.8
2,200
5 min
5 min
Fiberglass
12.9
4095
595
1100
32.0
10,200
40
5 min
5 min
Metal sheath
31
9830
595
1100
32.0
10,200
97
5 min
5 min
Ceramic faced
31
9830
760
1400
64.7
20,500
48
5-10 min
5-10 min
G-30 bulb
141
5 min
20s
Spot output, color sensitive Needs reflector, color sensitive Spot output Needs reflector, color sensitive, seals may need cooling, must be kept clean
Needs reflector, surface exposed, airflow causes large heat loses, resists shock, vibration Needs reflector
Very even heating, low temperature leads to airflow losses Even heating, can be zoned See comments on metal sheathed tube Available with soft or hard face
Quartz or hard ceramic Exposed foil
62
19660
980
1800
59.2
18770
815
1500
141 79.7
44,700
44
5-20 min
25,300
74
4s
5-20 min 10s
Thermally shock sensitive Shock hazard, convective heat losses can be high
GaS-IR impingment: Ceramic plate
1890
600000
1260
2300
314
99,400
3-53
1-3 min
2-4 min
Efficiency decrease increased output
Gas-IR surface burn: Ceramic plate Screen
252 126
80000 4000
930
1700 1600
117.7
37,300 30,900
20-553 20-553
2-3 min 1 min
2-3 min 1 min
148
47000
34,000
33-652-3
4-8s
4-8s
3,100
20-553
30 min
30 min
Same as above Same as above, screen maintenance can be a problem Emitter can be damaged by force or fluids Low temperature, emitter can be damaged by force or fluids
97.7
870 Ceramic fiber
1650 107.7
900 Catalytic
15.8
700
5000 370
1 2 3
9.8
Adapted from [42], with copyright permission Greater than 100% Listed efficiency, but greater than 100% of black body efficiency for given temperature
Radiative Heat Transfer Coefficient Convective energy losses are determined with an energy balance around all solid surfaces, including the heater and plastic sheet. The effect of radiation heat transfer must be included as well. This is done by examining the surface boundary condition for the transient one-dimensional heat conduction (Equation 3.9): ~= - k ^ ^
0X
=frr,T«,,F,Fg)£h,eJ
(3.27)
(6,L)
For radiation absorption (only) on a solid surface, x = L, the proper form for f[---] is: ITT 5 T 009 F 9 F^eJ = {aFFg}[T* 4 - T*4]
(3.28)
As noted, the radiation boundary condition is nonlinear, unlike the convection boundary condition that is linear with temperature, f[---] = h(Too — T). For certain cases, the radiation nonlinearity can be dealt with by letting T* = a • TJ,, where a is a proportionality. Then {[-••] becomes: IjT5T005F9F89G^eJ « Ji1(T00 - T)
(3.29)
where hr9 a radiation heat transfer coefficient, is given as: hr = {aFFg}T* 3(a + l)(a2 + 1) = FFg • R (3.30) where R is the radiation factor (Fig. 3.24). Note that the proportionality a is not constant but varies with the absolute value of the sheet temperature. If a is very small, or TJ 3 »T* throughout the heating cycle, R is approximately constant. Further if a does not vary much throughout the heating cycle, values of R are determined at the beginning and end of the heating cycle and an average value or R Table 3.9 Radiant Heater Efficiencies for Several Polymers1 Polymer
LDPE HPDE PS PVC PMMA PA-6 Cellulose acetate For the typical gray body thermoforming wavelength range, 1.4 to 3.6 um 1
Adapted from [33]
Heater type Ceramic 5100C (9500F) 4.0 um
Metal rod 5500C (10220F) 3.8 um
Quartz 680°C (1256°F) 3.0 jim
Quartz 7600C (14000F) 2.8 um
13% 13% 13% 5% 0% 30% 18% 28%
15% 15% 15% 5% 2% 28% 28% 33%
17% 17%. 17% 22% 50% 24% 48% 70%
20% 20% 20% 25% 65% 28% 56% 77%
Heater Temperature, 0F
Typical Quartz Heater Output W/in2
Human Body Peak Wavelength, um Figure 3.23 Temperature-dependent peak wavelength and quartz heater output
is used. Example 3.16 illustrates the use of the radiation factor. As is apparent, the value of R increases with increasing heater temperature and increasing sheet temperature. In the example, a 2000F increase in heater temperature results in a 29% increase in the rate of heating. Similarly increasing the sheet temperature to the forming temperature results in a 20% to 30% increase in heating rate. Typically, the average value for R is accurate to within 15% to 20% of the actual value. To obtain a value for the radiation heat transfer coefficient, hr, the average value of R must be corrected for the gray-body interchange factor, F g and the view factor, F. As a result, the actual value for the radiation heat transfer coefficient, hr, can be substantially less than the value for R. Typical values for hr are 1 to 10 times those for moving air convection heat transfer coefficients in Table 3.2. The use of the artificial radiation heat transfer coefficient should be restricted to problems where rapid solutions and approximate answers are acceptable. Convection and the Heat Transfer Coefficient Air trapped between the heater banks and the plastic sheet surfaces is very slow moving or quiescent. It therefore attains a nearly isothermal temperature having a
Radiation Factor, R, Btu/ft2-h-°F
Absorber Surface Temperature, 1000F
Emitting Surface Temperature, 100 0F Figure 3.24 Source and sink temperature-dependent radiation heat transfer coefficient
value somewhere between that of the sheet surface value and that of the radiant source. The nature of energy transfer is by rising, buoyant warm air and settling cool air. This is natural convection. The natural convection heat transfer coefficient is obtained from: (3.31)
Heater Convection Film
Sheet
Heater Figure 3.25 Location of various convection heat transfer coefficients between sheet and top and bottom heaters
Table 3.10 Convection Heat Transfer Coefficients 7 AT \l/4 tion from Flat Plates and Rods h = K — \ G / xv Geometry/attitude metric (h in kW/m2 • 0C) (AT in 0C) (G, D, L in m)
for Natural Convec-
^English
(h in Btu/ft2 • h • 0F) (AT in 0F) (G, D, L, in ft)
Heat plate (G = L) Facing upward Facing downward
0.00149 0.000746
0. 263 0.131
Rod (G = D)
0.001533 0.0028391
0.27 0.501
1
From reference [43]
G is the length of the plate heater or the diameter of a rod heater. G T is the temperature difference between the hot surface and the air. The proportionality constant K depends on the heater geometry G and whether the heater faces up or down (Table 3.10). Example 3.14 illustrates the method of calculation for the convection heat transfer coefficient. The range of 0.5 to 2 Btu/ft2 • h • 0 F or 2.8 x 10~ 3 to 11.3 x 10 ~ 3 kW/m 2 • 0 C is typical of natural convection heat transfer coefficients for quiescent air (Table 3.2). The range is a factor of 10 or so less than the typical range for forced air convection heat transfer coefficients and 20 times less than those for radiation heat transfer coefficients. Note that if the air is hotter than the plastic sheet, energy is convected to the sheet. If the sheet is hotter than the air, as in Example 3.15, energy is convected from the sheet. A combined convection and radiation heat transfer coefficient is written as: heffective = h + h r
(3.32)
Example 3.14 The Radiation Factor Consider heating a plastic sheet initially at 800F to 4000F using a heating source at 8000F. Determine the initial and final values of the radiation factor. Obtain an average value. Increase heater temperature to 10000F and recalculate values.
From Fig. 3.24, at 800 0 F, the initial value of R1 = 6.0 Btu/ft2 • h • 0 F. The final value of Rf = 8.1. The average value of R a = 7.05 Btu/ft2 • h • 0 F. From Fig. 3.24, at 10000F, R1 = 8.15, R f = 10.05 and Ra = 9.1 Btu/ 2 ft • h • 0 F. Example 3.15 Convection Heat Transfer Coefficient Consider 2000F air trapped between a 3000F sheet and a 8000F heater. The sheet is sandwiched between two heaters. Determine the heat transfer coefficients between the air and the sheet and the air and the heaters. G=I.
There are actually four heat transfer coefficients to consider, as shown in Fig. 3.25: Ji1 h2 h3 h4
(heater, facing down) = 0.131 (heater, facing up) = 0.263 (sheet, facing down) =0.131 (sheet, facing up) = 0.263
- (800 • (800 - (300 • (300 -
200)1/4 = 200)1/4 = 200)1/4 = 200)1/4 =
0.65 Btu/ft2 1.30 Btu/ft2 0.41 Btu/ft2 0.83 Btu/ft2
• h •0F • h •0F • h • 0F • h • 0F
The range is 0.4 to 1.3 Btu/ft2 • h • 0 F. Example 3.16 shows how the effective heat transfer coefficient changes in value as the sheet is heated. In this idealized case, the radiation contribution to the overall heat transfer coefficient overwhelms the convection contribution. In practical thermoforming, the radiation contribution is diminished by values of F and F g that are less than unity. Nevertheless, in most cases, radiation heat transfer dominates the overall heat transfer coefficient. Example 3.16 Combined Heat Transfer Coefficient Given the conditions of Examples 3.14 and 3.15, determine the effective heat transfer coefficient. Assume that F= Fg= 1. The initial sheet temperature is 800F with a 2000F air temperature and a radiant heater temperature of 8000F. The final sheet temperature is 4000F with a 2000F air temperature and the same radiant heater temperature. From Example 3.14, the radiation heat transfer coefficients are R1 = 6.0 Btu/ft2 • h • 0 F and Rf = 8.1. There are four initial convection heat transfer coefficients and four final ones. Only the values between the sheet and the air are important here: hu h2'i h3,'i V1
(heater, facing down) = 0.131 (heater, facing up) = 0.263 (sheet, facing down) =0.131 (sheet, facing up) = 0.263
1I1f h2f h3/ h4/
(heater, facing down) (heater, facing up) (sheet, facing down) (sheet, facing up)
• (800 • (800 - (200 • (200 -
= 0.131 • (800 = 0.263 • (800 =0.131 • (200 = 0.263 • (200 -
200)1/4 = 0.65 Btu/ft2 200)1/4 = 1.30 Btu/ft2 80)1/4 = 0.43 Btu/ft2 80)1/4 = 0.87 Btu/ft2 200)1/4 = 20O)1/4 = 400)1/4 = 400)1/4 =
• h • 0F • h •0F • h • 0F • h •0F
0.65 Btu/ft2 • h • 0 F 1.30 Btu/ft2 • h • 0 F -0.49 Btu/ft2 • h • 0 F -0.99 Btu/ft2 • h • 0 F
Note that the signs on the convection coefficients indicate the way in which energy is being transferred. The initial and final effective heat transfer coefficients, he { and he f, are: h ej h^ he/ h ef
(sheet, (sheet, (sheet, (sheet,
facing facing facing facing
up) = down) = up) = down) =
R1 + R1 + Rf + Rf +
h 4 , = 6.0 + 0.87 = 6.87 h3'1 = 6.0 + 0.43 = 6.43 h4,f = 8 . 1 - 0.49 = 7.61 h 3f = 8.1 - 0.99 = 7.11
Btu/ft2 Btu/ft2 Btu/ft2 Btu/ft2
• h •0F • h •0F • h • 0F • h • 0F
An effective heat transfer coefficient can also be obtained from an overall heat balance on a given plastic sheet. Effective values in Table 3.11 are obtained from
Table 3.11 Rod Heater Reflector Efficiencies—Effective Heat Transfer Coefficients1 Material
Emissivity
Heater temperature (0C)
Reflector temperature (0C)
Convection heat transfer (kW/m2 •0C)
Gold, new Gold, aged Stainless steel, new Stainless steel, aged Aluminum, new Aluminum, aged
0.92
690 683 686 668 719 693
320 323 304 352 274 287
0.0244 0.0176 0.0125 0.0142 0.0199 0.0199
1
0.60 0.30
Adapted from [11], with permission
HDPE RPVC CAB
Heating Time, s
PMMA
ABS/PVC FPVC HIPS
Foam PS
Sheet Thickness, mm Figure 3.26 Two-sided quartz heating of sheet. Heat flux = 40 kW/m2 or 12,700 Btu/ft2 • h •0 F, peak wavelength = 2.8 um, heater temperature = 7600C or 14000F. Solid points obtained at heat flux = 43 kW/mm2 or 12,700 Btu/ft2 • h •0 F, peak wavelength = 3.7 urn, heater temperature = 5100C or 9500F
thin-gage heating rate data of Fig. 3.26 and typical forming conditions. Values range from about 4.5 to 9.7 Btu/ft2 • h •0 F or 0.0255 to 0.0548 kW/m2 •0C. If the convection contribution is essentially constant at about 1 Btu/ft2 • h •0 F or 0.005 kW/m2 •0C, the radiation contribution is about 4 to 9 times that of the convection
Energy Fraction Compared With Infinite Plane
Non-Conducting Absorber Two Row Total One Row Total First Row of Two Second Row of Two
Planar Sheet
Rod Spacing to Rod Diameter, d/D Figure 3.27 Radiation between metal rod heaters and planar sheet [41]. Figure used by permission of McGraw-Hill Book Co., Inc.
contribution1. Further, if the average black-body net radiant interchange yields an effective radiation heat transfer coefficient of about 10 to 15 Btu/ft2 • h •0 F or 0.05 to 0.075 kW/m2 •0C, the radiant interchange efficiency is about 40% to 60%. This efficiency is the product of the gray-body factor, Fg, and the view factor, F. This efficiency agrees reasonably well with values that are discussed below. These effective heat transfer coefficient values are typical of experimental data obtained in other ways [H].
Rod Heaters Rod heaters, with or without reflectors, are used to heat sheet in many thermoformers. The energy emitted from rod heaters is related to that emitted by a heated plane. Figure 3.27 assumes that the surface behind the rod heaters is nonconducting. Example 3.17 illustrates how to determine the relative energy efficiency of rod heaters. As is apparent, the closer the heaters are to one another, the more efficient the energy transfer becomes. The gray-body correction factor F g for gray surface radiation between a plane and a tube bank is: F 8 = G 00 -G 8
(3.33)
Example 3.17 Rod Heater Efficiency Consider a single row of rod heaters 0.5 in or 12.7 mm in diameter, spaced 3 in or 76 mm apart. Determine the relative energy efficiency as compared with a flat plate. Change the spacing to 1.5 in or 38 mm and recompute. 1
Note that this assumes that the convection energy transfer is from the air to the sheet, with the air temperature hotter than the sheet temperature. Obviously if the convection contribution is negative, the radiation effect is 6 to 11 times greater.
Fig. 3.27 requires the determination of R, the ratio of center-to-center distance to the diameter. R = 3/0.5 = 6 From Curve B of Fig. 3.27, F = 0.46 or the heating is 46% as efficient as from a flat plate. For R = 1.5/0.5 = 3, F = 0.73 or 73% as efficient. Example 3.18 compares the gray-body correction factors for rod and plate heaters. Usually the gray-body correction factor values are quite comparable. However, the rod heater efficiency is low when compared with the flat plate, as also shown in Example 3.18. Radiant energy loss from the back of rod heaters is minimized by reflectors. New aluminum and gold-fired porcelain enamel give the greatest reflector efficiencies. However efficiencies deteriorate with age. Stainless steel appears to provide the best long-term efficiency (Table 3.11). The effective heat transfer coefficient from the top of the reflector is essentially independent of reflector material and reflector temperature (Fig. 3.28). The range in heat transfer coefficient is about 2 to 4 Btu/ft2 • h • 0 F or 0.01 to 0.02 kW/m 2 • 0 C. Essentially all of this is reradiation from the reflectors. Example 3.18 Gray-Body Correction Factor for Rod Heater Compare the values for Fg for flat plates and rod heaters if €^ = 0.9 and zs= 0.85. Then determine the relative gray-body efficiencies. From Equation 3.33, F g r o d = 0.9 • 0.85 = 0.765 From Equation 3.23, F g ' plate = [1/0.85 + 1/0.9 - I ] " 1 = 0.777 The two factors are essentially the same. From Example 3.17, at 1.5-in spacing of 0.50-in diameter rods, the rod efficiency is 0.73. As a result, Rod efficiency = 0.73 • 0.765 = 0.558 Plate efficiency = 1 • 0.777 = 0.777 Or the hot plate transfers nearly 40% more energy than the rod heaters.
3.9
Long-Term Radiant Heater Efficiencies
Radiant heater efficiency decreases with time as seen in Table 3.12. The values represent overall efficiencies or effective energy conversion for several commercial heaters. Efficiency is thought to decrease exponentially with time as a first-order system response: (3.34)
Convection Heat Transfer Coefficient Btu/ft2-rr°F
Newly Gold-Plated
Oxidized Gold
New Aluminum Stainless Steel
Reflector Temperature, 0F Figure 3.28 Convection heat transfer coefficients for metal rod heaters with reflectors
where a is the time constant of the heater, in month"1. The expected efficiencies of heaters at various times are shown in Table 3.121. Since heater efficiency is directly related to the radiant heat transfer coefficient, any decrease in heater efficiency at constant heater temperature increases the time to achieve sheet forming temperature. Since heater efficiency loss is gradual, cycle times can lengthen imperceptibly over weeks. Usually power input or heater temperature is gradually increased to compensate for the decrease in efficiency. An increase in heater temperature results in a reduction in the peak wavelength and this effect might result in heating in the less efficient regions of the infrared spectrum. Since efficient sheet heating is a key to optimum economic performance, all heater manufacturers now recommend strict, scheduled periodic replacement of all elements, regardless of their apparent performance.
3.10 Edge Losses—View Factor Net radiant energy interchange between ideal infinite parallel heat sources and sinks does not depend on the distance between them. This is not the case for finite dimensions of heaters and sheets. The spacing between the plane of the heater and that of the sheet surface affects the efficiency of energy transfer. So long as the sheet width dimension is much larger than the sheet-to-heater spacing dimension, radiation losses to machinery elements are small. The relative amount of energy actually received by the sheet depends on the ability of the heater to "see" the sheet. In simple terms: What the heater sees is what it heats
1
These values assume that the heaters are still functioning at these times.
Table 3.12 Commercial Radiant Heater Overall Efficiencies1 Heater type
new Coiled wire, nichrome Tubular rod4 Ceramic panel Quartz heater Gas-fired IR panel 1 2 3 4
Average life (h)
r|0, efficiency
16-18 42 62 55 40-45
Time constant a (month- 1 )
after 6 months2 8-10 21 55 48 25
1500 3000 12,000-15,000 8,000-10,000 5,000-6,000
Efficiency at end of life
0.0926-0.1155
11-13
0.1155 0.02 0.0227 0.0926-0.104
19 31-36 33-36 11-12
Adapted from [6], with copyright permission One month = 440 h, assumed for time constant only After 6 months use, 4-8% efficiency can be gained by replacing all reflectors Sanding, polishing increases efficiency by 10-15%
Expected efficiency3 12 mo
18 mo
24 mo
4-4.5
2-2.3
1-1.1
10.5 49 42 13
5.3 43 37 7
2.6 38 32 4
View Factor, F
Total Radiation - Surfaces Connected by Non-Conducting Reradiating Surfaces
Squares Circular Disks
Diameter or Side Dimension to Distance Between Surfaces Figure 3.29 Radiation view factor for radiant interchange between parallel surfaces
The radiant energy interchange between black bodies of equal finite dimension connected by reradiating walls is given as Fig. 3.29. The factor F is called a radiation factor or "view factor" and typically has a value less than one. Furthermore, F varies across the sheet surface. Example 3.19 illustrates the effect of sheet-to-heater spacing on the view factor. To obtain the proper net energy interchange value between gray surfaces, this view factor must then be multiplied by the gray-body correction factor, Fg. Example 3.19 includes the relative effect. The energy that is not transmitted to the sheet is lost to the surroundings and is called "edge losses". In Example 3.19, edge losses amount to 36% for the wide spacing and 23% for the narrow spacing. The edge loss is reduced if the side walls reradiate or reflect. Although spacing is used to control the heating characteristics of the sheet without changing the heater temperature, it is now recognized that this is an inefficient use of energy. Heater spacing is usually governed by sheet sag and minimization of sheet "striping" or local overheating beneath rod and quartz heaters.
Example 3.19 View Factor and Edge Losses Consider a 600 mm x 600 mm sheet being heated with a 600 x 600 mm plate heater. Ignore edges. What is the view factor F, from Fig. 3.29, for sheet-to-heater spacing for 150mm? For 75mm? What are the equivalent values if the sides reradiate? Then consider a gray-body correction factor for €^ = 0.9 and ev = 0.85.
R = side/spacing = 600/150 = 4. From Fig. 3.29, F = 0.64. For R = 600/ 75 = 8, F = 0.77. For reradiating sides, F R==4 = 0.765. F R = 8 = 0.86. An oven with reradiating sides is 19% more efficient at R = 4 than one that has no reradiating sides. It is 12% more efficient at R = 8.
The gray-body correction factor, F g - [1/0.9 + 1/0.85 - I ] " 1 = 0.777. The adjusted efficiencies, r\ — FF g , are now: rjR = 4 = 100 • 0.64 • 0.777 = 49.7%
rjR = 8 = 100 • 0.77 • 0.777 = 59.8%
Local Energy Input The view factor obtained from Fig. 3.29 yields an average radiant energy transfer efficiency. The specific local energy transfer rate is also important. As seen in Fig. 3.30 [12] for uniform energy output from the radiant heaters, the edges of the sheet receive substantially less energy than the center. This is because the heaters in the center see substantially more sheet than those at the edges. In other words, the heaters at the edge radiate to a greater amount of non-sheet than those in the center. Figure 3.31 illustrates this. An accurate estimate of the energy of Fig. 3.30 is
Heater Elements
h/b=0.2
b
Figure 3.30 Energy received by finite sheet from uniform energy output by heaters [12]
Heater
b
Heater
Sheet Radiation Overlap Figure 3.31 Schematic of radiation overlap from heaters to sheet
Z Y A2
X r
Direction Cosine
Direction Cosine
A
1
Figure 3.32 Radiation ray tracing between finite parallel plane elements [13]
obtained from radiant heat transfer theory. Consider energy interchange between two differential surface elements (Fig. 3.32) [13]. The intensity of the energy emitted from surface element dA x is constant in a hemisphere of radius r from the surface. Any element that intersects this hemisphere receives an a m o u n t of energy proportional to its projected area relative to the area of the hemisphere. The projected area depends on the attitude of that element to the source plane. In differential form, the total energy interchange between these elements is: Qi ^2 = crFg(T*e4ater - Ts*h4eet)
(IA1 dA 2 (3.35) ^r The double-integral term on the right side represents the view factor, F . The terms, cos 4>, are direction cosines and r is the solid angle radius between the elements. Figure 3.29 is obtained through proper integration of the double integral of Equation 3.35. Quartz and ceramic heating elements are discrete and isothermal 'bricks'. As a result, the differential form of the view factor that yields the double integral can be replaced with the difference form: JA 2 JA 1
_ /rT ^ 4 _ „ . T ^ ^ cos (J)1 cos 4>2 1 Qi-2 = ^F g (T* e 4 ater - Ts*h4eet) X E AA1 AA 2 (3.36) 2 nv LA1 A2 J where the " 1 " element is the heater and the " 2 " element the sheet 1 . Consider a grid of heater and sheet elements in the X-Y direction separated by a distance z in the Z direction. F o r parallel surfaces z units apart: 1
This assumes that the sheet is made of elements as well. In fact, the sheet should be considered as an infinite number of infinitesimal elements and the double integral replaced with a integrodifferential form. This is not done in this discussion.
COS(J)1 = COSCt)2 = -
(3.37)
The spherical radius between any two heater and sheet element is given as: r = y x 2 + y2 + z2
(3.38)
The amount of energy emitted from a single heater element to all plastic elements is: Qi - Z 2 = a F g [ x rc(x2 + y 2+
z2)2
(Th*e4ater - TJKL)AA1 A A 2 ]
(3.39)
Th is the single heater element temperature and Ts represents one of the many sheet surface element temperatures. Likewise, the amount of energy received by a single plastic element from all heater elements is: q £ ,~a = ° F g [ l
7t(x 2 +
y2 +
z2)2
(Ti£ ter - TSU1)AA1 AA 2 ]
(3.40)
Note that the individual element temperatures are now incorporated within the summation. Individual heater element and sheet element temperatures vary and this expression accommodates these variations. Furthermore note that the summation in Equation 3.39 implies that the [XY] position of the heater element is fixed and the [XY] position of each sheet element is computed relative to that [XY] position. Although Equations 3.35 through 3.40 appear formidable, they are rapidly solved on a computer. Figure 3.33 gives the computer solution for energy input to a sheet containing 49 elements from a heater bank containing 49 elements. The energy
15
16
17
76.8%
14 77.3%
76.8%
74.0%
60.9%
23
24
25
26
27 74.0%
11
12
13
60.9% 21 74.0%
74.0%
22 90.8%
94.4% 95.1% 94.4% 33 35 34 32 76. 8% 94. 4% 98.4% 99.2% 98.4%
31 41
77.3%
42 95.1%
43 44 99. 2% 100%
52 53 51 54 76. 8% 94. 4% 98. 4% 99.2% 61
62
74.0% 71
yu, cvo 72
63
64
94. 4% 95.1% 73 74
60. 9% 74. 0% 76.8%
90.8% 36
37
94.4%
76.8%
45
46
47
99.2%
95.1%
77.3%
56 55 98. 4% 94.4% 65
66
94. 4% 90.8% 76 75
57 76. 8% 67 74.0%
77
77. 3% 76. 8% 74. 0% 60.9%
Figure 3.33 Local heat flux distribution from 7 x 7 uniform 540 0 F heaters. Values based on 100% at element [4,4]. Relative heater-to-sheet spacing, Z = I [14]
Heater Element
h/b=0.2
b b
Figure 3.34 Energy received by finite sheet from zonal energy output by heaters [15]
output is the same from each heater element. The elemental values represent the amount of energy received by a given sheet element relative to that received by the center sheet element [14]. As is apparent, the values of Fig. 3.33 support the proposed scheme of Fig. 3.30. The energy flux from each heater element can be varied to achieve near-uniform energy input to the plastic sheet. Figure 3.34 is one proposed scheme of an optimized heating system where the energy flux is the same to each element [15]. Figure 3.35 is the computer solution obtained by varying the individual heater element temperatures. As is apparent from Equation 3.40 and earlier discussion, small changes in absolute heater element temperatures yield 11 185% 706F 21 130% 608F 31 135% 618F 41 135% 618F 51 135% 618F 61 130% 608F 71 185% 706F
12 130% 608F 22 80% 486F 32 90% 514F 42 90% 514F 52 90% 514F 62 80% 486F 72 130% 608F
14 13 135% 135% 618F 618F 24 23 90% 90% 514F 514F 34 33 90% 95% 527F 514F 44 43 90% 92.5% 514F 521F 54 53 95% 90% 527F 514F 64 63 90% 90% 514F 514F 73 74 135% 135% 618F 618F
15 135% 618F 25 90% 514F 35 95% 527F 45 90% 514F 55 95% 527F 65 90% 514F 75 135% 618F
16 130% 608F 26 80% 486F^ 36 90% 514F 46 90% 514F 56 90% 514F 66 80% 486F 76 130% 608F
17 185% 706F 27 130% 608F 37 135% 618F 47 135% 618F 57 135% 618F 67 130% 608F 77 185% 706F
Figure 3.35 Uniform heat flux everywhere [+1.5%]. Relative heater temperature in 0 F. Relative heater-to-sheet spacing, Z = I
substantial changes in emitted energy. This is apparent in Fig. 3.35 for the 7 x 7 heater by 7 x 7 sheet configuration. The heater temperature profile predicted in Fig. 3.35 mirrors current forming practice, with corner heaters running hotter than edge heaters and center heaters running substantially cooler than peripheral heaters.
Pattern Heating Pattern heating is the placing of welded wire screens between the sheet and the heater in strategic locations to partially block the radiant energy. Radiant screens are frequently used to achieve uniform wall thickness in odd-shaped parts [16-18] when the heater output is fixed, as with plate and rod heaters. Fine welded stainless steel wire mesh is cut to an approximate shape of the blocking region and is placed between the heater plane and the sheet surface (Fig. 3.36). The screens are frequently laid on the wire screen protecting the lower heaters from sheet drop. They are wired in position below the upper heaters. If fs is the fraction of open area in the screen and T*. is its absolute temperature, the energy interchanged between the heater and the sheet beneath the screen is given as: 5= {aF^F^.J-f, -[T^-Tf]
(3.41)
The energy interchanged between the heater and the screen is: (3.42)
Heater Hanger Welded Wire Sheet
Welded Wire Support Heater
Figure 3.36 Examples of attaching welded wire screen for pattern heating on rod heaters
And that interchanged between the screen and the sheet is: —= A
IGF \
w x
F
sc — s A g,sc — s i
I • f • [T*4 — T*41 1
S
Lxsc
A
s
J
(3 43) y~y.-T~>j
Note that there are three view factors and three gray-body correction factors. The sheet-to-heater distance, the sheet-to-screen distance and the screen-to-heater distance have different values and the respective view factors will therefore be different. Furthermore, the emissivities of the screen, sheet and heater are different. Example 3.20 illustrates the extent of reduction in energy interchange. The fraction of open area in the screen is the primary method of controlling energy interchange in pattern heating. Multiple screens are used if necessary (Fig. 3.37). Example 3.20 Pattern Heating—Efficiencies Consider a screen having a 0.030-in wire with a square 0.060-in center-to-center distance. The screen is positioned halfway between a 3Ox 30 in sheet and a 3Ox 30 in heater, spaced 6 inches apart. The heater emissivity is 0.9, the sheet emissivity is 0.85 and the stainless steel screen emissivity is 0.3. The heater temperature is 8000C, the emitter temperature is 5000C and the sheet temperature is 2000C. Determine the efficiency of heat transfer relative to the unscreened sheet. The area of a single square is 0.060 x 0.060 = 0.36 x 10~ 2 in2. The projected area of the wire in the square is 2 x 0.06 x 0.015 + 2 x (0.06 - 2 • 0.015) x 0.15 = 0.027 x 10~ 2 in2. Thus, the wire covers 75% of the surface area. fs = 0.25. For the heater-to-screen interchange, F g = 0.9 • 0.3 = 0.27. The view factor is obtained from Fig. 3.27 for R = 0.060/0.030 = 2, and is F = 0.86. Thus the heater-to-screen efficiency is: r|sc_ ^ = FF g (l - fs) = 0.27 • 0.86 • 0.75 = 0.174 For the screen-to-sheet interchange, F g = 0.3 • 0.85 = 0.255. The view factor is obtained from Fig. 3.29 and is F = 0.86. The screen-to-sheet efficiency is: n s c _ s = FF g (l - fs) = 0.255 • 0.86 • 0.75 = 0.164 For the heater-to-sheet interchange, F g = [1/0.9 + 1/0.85 - I ] " 1 = 0.777. The view factor is obtained from Fig. 3.29 for R = 30/6 = 5 and is F = 0.7. The heater-to-sheet efficiency is: Ti00 _ s = FFg • fs = 0.777 • 0.7 • 0.25 = 0.136 The energy interchange equation is: ^={aFFg}fs[Ts*o4urce-Ts*4k] For the heater-to-screen interchange: 5
= 56>74
. Q 1 7 4 . [ L 0 7 3 4 - 0.7734] = 9.56 kW/m2
For the screen-to-sheet interchange: ^ = 56.74 • 0.164 • [0.7734 - 0.4734] = 2.86 kW/m2 For the heater-to-sheet interchange: ^ = 56.74 • 0.136 • [1.0734 - 0.4734] = 9.84 kW/m2 The total energy transfer is: Y = 9.56 + 2.86 + 9.84 = 22.26 kW/m2 This compares with the unscreened energy transfer: 5
= 56
J 4 . o.7O • 0.777 • [1.0734 - 0.4734] = 31.57 kW/m2
The screen provides a 29.5% reduction in the amount of radiant energy interchange between the heater and the sheet.
Zone, Zoned or Zonal Heating With the advent of discrete heating elements, the effect of shielding or screening certain areas of the sheet has been, for the most part, replaced with local heating element energy output control. The earliest heating stations employed manually set proportional controllers on every heating element. Computer-aided controllers are now used. In certain circumstances, the energy output from every heating element is controllable. For very large ovens and very many heating elements, individual control is impractical. Regional banks of heating elements have a single controller and thermocouple. Thus, for an oven with 100 x 100 elements, top and bottom, requiring 20,000 controlling elements, the oven may have 40 zones, top and bottom. In certain circumstances, individual elements may be transferred from one zone to another electronically. In other cases, hard rewiring is necessary. Usually, zonal conditions are displayed on a CRT screen. As noted in the equipment section, most ceramic and metal plate heaters use PID-based controls and thermocouple temperature is the indicating readout variable. Quartz heaters operate on percentage of the time on and percentage is the indicating readout variable. Technically, of course, these variables are simply measures of intrinsic energy output of the heater or bank of heaters. Zone heating or zonal heating is used to change local energy input to the sheet in much the same way as pattern heating. With pattern heating, the pattern must be some distance from the sheet surface to minimize a sharp edge effect, shadowing or spotlighting where the pattern ends. In zone heating, the heaters are some distance from the sheet surface to begin with. As a result, energy change in a local heater or heater bank not only affects the sheet directly below it but also changes the energy input to the sheet elements in the vicinity. This is seen in the
Uniform Heating Pattern, Local Thickness Shown in Insert Temperature,0F
Top Surface Bottom Surface
Temperature, 0F
Time, s Top Center Top Side
Top Corner
Bottom Center Bottom Side Bottom Corner
Time, s Heating Pattern, Shown in Insert Figure 3.37 Effect of patterning on thermoforming part wall thickness and temperature for polystyrene, PS [16,17]. Initial sheet thickness = 2.1 mm. In lower figure, up to four layers of tissue paper are used as screening. In lower figure, thickness ratio, t/t0 = 0.29 to 0.32 over entire part. Figure used by permission of Krieger Co.
computer-generated energy input scheme of Fig. 3.38 [14]. Increasing a specific heater element energy output 14% results in a 6% increase in energy input to the immediate sheet element neighbors and lesser amounts elsewhere even though energy outputs from neighboring heater elements have not changed. If this is an undesirable effect or the effect sought requires greater focus, the bank of heaters making up the specific zone must be reduced in number. Heater to Sheet Distance As stated earlier, radiation does not depend on fluid or solid medium. Relative heater-to-sheet spacing does affect radiant energy interchange however. This was demonstrated in Fig. 3.29 and is apparent in Equation 3.40. Figure 3.39 shows the effect of a 50% increase in heater-to-sheet spacing relative to the optimum energy
11 O 0.1% 21 0 0.1% 31 0 O 41 0 0 51 0 0 61 0 0 71 0 0
12 0 0.2% 22 0 0,2% 32 0 0.1% 42 0 0.1% 52 0 0.1% 62 0 0 72 0 0
13 0.2% 0.4% 23 0.2% 0.5% 33 0.2% 0.4% 43 0.1% 0.3% 53 0 0.1% 63 0 0.1% 73 0 0
14 0.8% 1.6% 24 1.1% 2.2% 34 0.7% 1.5% 44 0.4% 0.7% 54 0.1% 0,3% 64 0 0.1% 74 0 0
15 3.1% 6.2% 25 6.9% 14.0% 35 3.1% 6.3% 45 0.7% 1.5% 55 0.2% 0.4% 65 0 0.1% 75 0 0
16 7.0% 14.1% 26 28.2% 56.4% 36 6.9% 14.0% 46 1.1% 2.2% 56 0.2% 0.5% 66 0.1% 0.2% 76 0 0.1%
17 3.1% 6.3% 27 7.0% 14.1% 37 3.1% 6.2% 47 0.8% 1.6% 57 0.2% 0.4% 67 0.1% 0.2% 77 0 0.1%
Figure 3.38 Spotlighting effect from two-fold and four-fold increases in heater output at [2,6]. Percentage represents local increase in heat absorption [14]
11
12
13
14
15
73%
83%
85%
85%
85%
16 QQO/
17 73%
21
22
23
24
25
26
27
85%
95%
97%
98%
97%
95%
83%
32
33
34
35
36
37
97%
99%
99. 5%
99%
97%
85%
41
42
43
44
45
46
47
85%
98%
100%
99.5%
98%
31
85%
99. 5%
54
55
56
57
QQ R°/
99%
97%
85%
51
52
85%
97%
61
62
63
64
65
83%
95%
97%
98%
97%
53
99%
85%
W, O/o
66
95%
67
83%
71
72
73
74
75
76
77
73%
83%
85%
85%
85%
83%
73%
Figure 3.39 Effect of heater-to-sheet spacing on energy received by sheet elements. Local percentage of initial energy input for Z = 1.5 as given in Figure 3.35 for Z = I [14]
input profile of Fig. 3.35 [14]. As expected, energy input to edges and corners are most affected. But the overall energy input to the sheet also substantially decreases. The energy output from each of the heaters must be changed to compensate for the change in gap distance. Again, the arithmetic in Equation 3.40 is a most useful aid in this process.
3.11 Thin-Gage Sheet—Approximate Heating Rates For thin-gage sheet, especially roll-fed film for packaging and blister-pack applications, the time-dependent heating model can be significantly simplified. The net enthalpic change in the sheet is simply equated to the rate at which energy in the sheet is interchanged with its environment. As a first approximation, the temperature gradient through the plastic film thickness is assumed to be zero. There are two general approaches to this lumped-parameter approximation—constant environmental temperature and constant heat flux to the sheet surface.
Constant Environmental Temperature Approximation Consider T00 to be the constant environmental temperature. The lumped-parameter approximation then becomes: d(VH) = V • pcp dT = !1A(T00 - T) d9
(3.44)
V is the sheet volume, V = At, A is the sheet surface area and t is its thickness. T is the sheet temperature. T00 can be the radiant heater temperature, with h being the approximate radiation heat transfer coefficient. Or T00 can be air temperature with h being the convection heat transfer coefficient. This ordinary differential equation is written as:
cffM£)" If t0 = T(G = 0), and T00 is constant: ln(I^I)
VT00 - T 0 ;
=
Z^
( 3. 46 )
tpCp
or:
This is a first-order response of a system to a change in boundary conditions. This lumped-parameter transient heat transfer model is valid only where conduction through the sheet thickness is less significant than energy transmission from the environment to the sheet surface. There are two dimensionless groups that define the
Table 3.13 Lumped-Parameter Maximum Sheet Thickness Moving air heat transfer coefficient, Table 3.2: 0.0014cal/cm 2 -s-°C 1 Btu/ft2 • h • 0 F Plastics thermal conductivity, Table 3.12: 4.1 to 8.3 x 10- 4 cal/cm- s • 0C 0.1 to 0.2 Btu/ft2 • h • °F/ft Maximum thickness for Bi = 0.1: 0.025 to 0.5 cm 0.010 to 0.100 in 10 to 100 mils
limits of the lumped-parameter model. One is the Biot number, Bi = ht/k, which is the ratio of internal to external heat transfer. The second is the Fourier number, Fo = k9/pcpL2 = oc0/L2, where a is the thermal diffusivity, a = k/pcp, and L is the half-thickness of the sheet when heated equally from both sides1. The lumpedparameter model should be applied only when Bi < 0.1, or when the internal resistance is low. For air moving over plastic sheet, the sheet thickness should be less than about 0.010 in or 0.3 mm or so, Table 3.13 [19], but can be more than this for higher thermal conductivity and higher air velocity. Figure 3.40 [20] expands the limits of Table 3.13 by demonstrating the relative sensitivity of the sheet thickness to the assumed temperature difference from the sheet surface to its centerline. Example 3.21 explores the use of this figure in determining the appropriateness of the lumped-parameter model for convectively heating one side and both sides of a thin-gage sheet. Practical heating times for various thin-gage polymers over a wide range in sheet thickness are given in Fig. 3.26 [21]. The linear relationship is apparent. The energy source temperature and the sheet temperature at forming time is not given for these data. A radiant heater at T00 = 7600C or 14000F produces an energy spectrum with a peak wavelength of about 2.8 um. The energy source output at this temperature is 40 kW/m2. This energy input produces a near-linear heating rate. A lower source temperature, T00 = 5100C or 9500F, does not produce a forming time that is linear with sheet thickness.
1
Note throughout the discussion on sheet heating that the half-thickness of the sheet is used if the sheet is heated equally on both sides. If the sheet is heated on only one side, as is the case with trapped sheet heating, contact heating, or single-side radiant heating, and if the free surface can be considered as insulated or without appreciable energy transfer to the surroundings, then the proper value for L is the total sheet thickness. If the sheet is unevenly heated on both sides or if one side of the sheet is heated in one fashion, such as contact heating and the other side is heated in another fashion, such as forced convection heating, then the proper value for L is the total sheet thickness. More importantly, models describing non-symmetric heating or one-side heating with an insulated free surface cannot be applied. The proper model requires appropriate boundary conditions on each surface of the sheet.
Fourier Number, Fo
1% Difference
5% Difference
10% Difference
Biot Number, Bi Figure 3.40 Sensitivity of sheet thickness to temperature difference between sheet surface and centerline [20]. Dimensionless time, Fourier number = a6/L2 and relative surface resistance, Biot number = hL/k
Example 3.21 The Limits on the Lumped-Parameter Model A 0.020-in (0.5 cm) PET sheet is radiantly heated equally on both sides, from room temperature, 800F to its forming temperature, 3800F. The combined convection and radiation heat transfer coefficient is 10Btu/ft2 • h •0^F. The thermal dijfusivity of the sheet is 0.002ft2/h and its thermal conductivity is 0.08Btujft • h 0F. Determine the heating time for a 1% difference in temperature between the sheet surface and center. Repeat for a 10% difference. What is the heating time for onesided heating and a 1% or 10% temperature difference? Comment on the relative times. For Fig. 3.40, values for Bi and Fo are required.
Fo - .6,L= - 0.002 £ . J L „ ) . J ± L ft-= = 0.8« « From Fig. 3.40, Fo = 5.2 at 1% AT. Therefore 6 = 5.2/0.8 = 6.5s. From Fig. 3.40, Fo = 2.1 at 10% AT. Therefore 0 = 2.1/0.8 = 2.6s. In other words, to keep the centerline essentally at the surface temperature, the heating rate must be adjusted to achieve the forming temperature in about 6.5 seconds. At the forming temperature of 3800F, the centerline temperature will be 0.99 • (380 - 80) + 80 = 377°F, or 3°F below the surface temperature. If the heating rate is faster than this, the centerline temperature
will lag the surface temperature by more than 1%. If the heating rate is such that the sheet reaches the forming temperature in about 2.6 seconds, the centerline temperature will lag the surface temperature by about 10%. At the forming temperature of 3800F, the centerline temperature will be 0.90 • (280 - 80) + 80 - 3500F, or 300F below the surface temperature. For one-sided heating, L = 0.020 in.
ft2 6 Fo = aB/U = 0.002 _ • _
(s )
144 • _ ft-
= 0.29 (s)
From Fig. 3.40, Fo = 4.05 at 1% AT. Therefore 0 = 4.05/0.2 = 20.25s. From Fig. 3.40, Fo = 1.8 at 10% AT. Therefore 0 = 1.8/0.2 = 9.0s. It takes 20.25/6.5 = 3.1 times longer to heat the one-sided sheet to 1% temperature difference and 3.5 times longer to heat it to 10% temperature difference.
Constant Heat Flux Approximation If the heat flux to a thin sheet is constant, Q/A = constant, then: O dT ^ = constant = tpcp —
(3.48)
dT = ^ — d 9 Atpcp
(3.49)
T T
(3 50)
Rearranging:
Integrating this yields:
- «=xi^
-
For a given set of processing conditions, the constant heat flux approximation indicates that the time to heat a very thin sheet of plastic to a given forming temperature is proportional to the sheet thickness. The data of Fig. 3.26 indicate this linearity, even though no values for forming temperature or heat flux are given. Thin-Gage Approximations—Comments The heating efficiencies for several polymers can be determined by using the normal forming temperatures from Tables 3.1 or 2.5. For a given polymer, the enthalpic change between room temperature and the normal forming temperature is determined from Fig. 2.17. The individual heating rate is determined from the slope of the curve of Fig. 3.26, for example. The net energy increase is then calculated. As seen in
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Table 3.1, most thin-gage polymers absorb 40% to 60% of the energy supplied by the heating source. The relatively low efficiency of LDPE is unexplained. PP heating efficiency is also reported to be low [22]. This indicates that the 7600C source temperature used in the calculation may be improper for efficient heating of olefin materials. This is discussed below. This analysis is restricted to one very specific processing area—thin-gage polymers—and to very stringent conditions—lumped-parameter with linear approximation of the logarithmic function. But it serves to illustrate that only a fraction of the energy emitted by the source, about half in the cases examined, is actually taken up by the polymer sheet. The rest is lost to the environment or passes completely through the sheet unabsorbed.
3.12 Heavy-Gage Sheet—Internal Temperature Control For thin-gage sheet and film, energy transmission to the sheet controls the heating cycle time. Radiant heating is far more efficient than convection heating and so is preferred for thin-gage thermoforming. For heavy-gage sheet however, energy absorbed on the sheet surface must be conducted through the thermally insulating plastic to its centerline1. For very thick sheets, the overall heating cycle time is controlled by the sheet centerline temperature and so the overall heating rate must be controlled to prevent surface overheating. As with the thin-gage discussion earlier, there are two general cases to be considered—constant environmental temperature, T00 = constant, and constant heat flux to the sheet surface, Q/A = constant. Constant Environmental Temperature Usually hot air is used as a heating medium for very heavy sheet. As a result, the T00 = constant case prevails. As with all transient heating problems, the centerline temperature lags the surface temperature. This is seen by reviewing the graphical solution to the one-dimensional time-dependent heat conduction equation with a convection boundary condition (Figs. 3.41 and 3.42) [23,24]. Figure 3.41 gives the conditions at the sheet centerline. Figure 3.42 gives the equivalent conditions at the sheet surface. Similar figures for intermediate points throughout the thickness of the sheet are found in standard handbooks [25]. As with the thin-gage approximation, the dimensionless temperature dependency, Y, for heavy-gage sheet is a function of two dimensionless groups, the Biot number and the Fourier number:
1
Again, symmetric heating is assumed throughout this discussion. The general arithmetic described herein must be modified if the sheet is heated in an unsymmetric fashion or if it is heated only on one side.
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Table 3.1, most thin-gage polymers absorb 40% to 60% of the energy supplied by the heating source. The relatively low efficiency of LDPE is unexplained. PP heating efficiency is also reported to be low [22]. This indicates that the 7600C source temperature used in the calculation may be improper for efficient heating of olefin materials. This is discussed below. This analysis is restricted to one very specific processing area—thin-gage polymers—and to very stringent conditions—lumped-parameter with linear approximation of the logarithmic function. But it serves to illustrate that only a fraction of the energy emitted by the source, about half in the cases examined, is actually taken up by the polymer sheet. The rest is lost to the environment or passes completely through the sheet unabsorbed.
3.12 Heavy-Gage Sheet—Internal Temperature Control For thin-gage sheet and film, energy transmission to the sheet controls the heating cycle time. Radiant heating is far more efficient than convection heating and so is preferred for thin-gage thermoforming. For heavy-gage sheet however, energy absorbed on the sheet surface must be conducted through the thermally insulating plastic to its centerline1. For very thick sheets, the overall heating cycle time is controlled by the sheet centerline temperature and so the overall heating rate must be controlled to prevent surface overheating. As with the thin-gage discussion earlier, there are two general cases to be considered—constant environmental temperature, T00 = constant, and constant heat flux to the sheet surface, Q/A = constant. Constant Environmental Temperature Usually hot air is used as a heating medium for very heavy sheet. As a result, the T00 = constant case prevails. As with all transient heating problems, the centerline temperature lags the surface temperature. This is seen by reviewing the graphical solution to the one-dimensional time-dependent heat conduction equation with a convection boundary condition (Figs. 3.41 and 3.42) [23,24]. Figure 3.41 gives the conditions at the sheet centerline. Figure 3.42 gives the equivalent conditions at the sheet surface. Similar figures for intermediate points throughout the thickness of the sheet are found in standard handbooks [25]. As with the thin-gage approximation, the dimensionless temperature dependency, Y, for heavy-gage sheet is a function of two dimensionless groups, the Biot number and the Fourier number:
1
Again, symmetric heating is assumed throughout this discussion. The general arithmetic described herein must be modified if the sheet is heated in an unsymmetric fashion or if it is heated only on one side.
Dimensionless Temperature
Biot Number, Bi
Fourier Number, Fo Figure 3.41 Time-dependent temperature profile at center of plastic sheet with relative surface resistance as parameter [23,24]. Biot number, Bi = hL/k, Fourier number, Fo = a0/L2. Dimensionless temperature = (T - Tinitial)/(Theater - Tinitia])
The Biot number, Bi = hL/k. It represents the convective boundary condition and is the ratio of external to internal resistance at the environment-sheet interface.
Dimensionless Temperature
•
Biot Number, Bi
Fourier Number, Fo Figure 3.42 Time-dependent temperature profile at plastic sheet surface with relative surface resistance as parameter [23,24]. Biot number, Bi = hL/k, Fourier number, Fo = aO/L2. Dimensionless temperature = (T - Tinitial)/(Theater - Tinitial)
• •
The Fourier number, Fo = ocO/L2. It represents a dimensionless time for conduction of energy. Y is the dimensionless temperature, Y = (T - T0)Z(T00 - T 0 ). Y(G = O) = O. Y(G = oo)= 1.
Examples 3.22 and 3.23 show how these figures are used with heavy-gage sheet. As noted, forced air convection heating yields a lower energy input per unit time than does radiation heating. This lowered energy input enables the centerline temperature to reach the lower limit on the forming window before the sheet surface temperature exceeds the upper forming temperature.
Example 3.22 Transient Heating with Convective Boundary Conditions—I Consider a 0.250-in or 6.4 mm sheet placed in a hot air forced convection oven with an air temperature, T00 = 5000F= 2600C. The thermal diffusivity of the sheet is 0.002 ft2 jh and its thermal conductivity is 0.08Btu/ft - h 0F. The convection heat transfer coefficient is 2Btujft2 - h -0F. Determine the time to heat the centerline from 800F to 3200F, the lower forming temperature. What is the surface temperature at this time? Increase the oven temperature to 6000F and repeat the exercise. The Biot and Fourier numbers are needed for Figs. 3.41 and 3.42. 2 Btu
Bl = h L / k
Fo
0.250 ,
1 ft • h • 0 F
^^
= fH^-il2 'ao8-Bfr = a 2 6
0 002
= -
ft2
ft
Q (s)
144
ir-^ -(o^(V2)^= 0 - 005e(s)
For the condition at the centerline: Y
(320-80) (500-80)
From Fig. 3.41, Fo - 3.6. Therefore 0 = 3.6/0.005 = 720 seconds = 12 minutes. From Fig. 3.42, for the sheet surface at this Fourier number, Y = 0.626. Therefore: Ts = 80 + 0.626 • (500 - 80) = 343°F The surface is 343 - 320 = 23°F hotter than the centerline. For the 600 0 F oven temperature, Y = 0.46, and from Fig. 3.41, Fo = 2.78. The time to heat the centerline to this temperature, 0 = 2.78/0.005 = 556 s = 9.3 minutes. From Fig. 3.42, the dimensionless surface temperature at Fo = 2.78 is Y = 0.52. The surface temperature is now 3500F or 30 0 F above the centerline temperature.
Example 3.23 Transient Heating with Convective Boundary Conditions— II Consider the sheet of Example 3.22. What is the centerline temperature when the sheet surface reaches the upper forming temperature of 3800F? Use an oven temperature of 6000F.
For a surface temperature of 3800F: Y =
(380-80) (600-80) = °- 58
The Fourier number at this value of Y from Fig. 3.42 is Fo = 3.15. The centerline temperature from Fig. 3.41 for this value of Fo is Y = 0.53. The centerline temperature is 0.53 • (600 - 80) + 80 = 355°F or 25°F below the surface temperature.
The average sheet temperature is usually obtained by interpolation for x/L values between zero and one. Table 3.14 shows interpolated values for two cases. The second case also includes an empirical equation that accurately predicts the internal sheet temperatures. The average temperature can also be approximated by: Taverage,approx ~ (1 /3)T surface + (2/3)T centerline
(3.51)
The approximate average temperature for the first case of Table 3.14 is 221°C, or within 2%. The approximate average temperature for the second is 1610C or within 3%.
Table 3.14 Convective and Conduction Heat Transfer Through Heavy-Gage Plastic Sheet At T00 = 8000C Fo = 0.34, 0 = 67.6 s Bi =1.04
At T00 = 7600C Fo = 0.5, 0 = 89 s Bi = 0.52
x/L
Y
Temperature (0C)
Y
Temperature (°C)
Temperature1 (0Q
0 0.2 0.4 0.6 0.8 1.0
0.833 0.82 0.78 0.74 0.65 0.56
150 160 192 223 293 363
0.865 0.84 0.82 0.80 0.75 0.70
120 138 153 168 205 242
120 131 147 169 200 242
= 225°C
-*- average
= 169°C
= 166°C
T x
1
average
Calculated from T = 151.65 • e-°-51x + 90.35 where 0 < x < 3.2 cm
The Constant Heat Flux Case For sheet that is not very heavy or for sheet having a large forming window, the energy input to the sheet surface is supplied by forced convection hot air ovens and radiant heater ovens where indirect radiation is used. For these ovens, the concept of constant heat flux may be applied. In Equation 3.27, the heat flux to the sheet surface was given as: ^f(T 5 T 005 G 5 F)
(3.52)
where G is a geometric factor that might include radiation view factor and F is a gray-body factor. The heat flux to the sheet surface can be considered constant if: • • •
The time of exposure to the heat flux is short, The environmental temperature, T00 » T, or The environmental temperature changes with heating rate such that Q/A is constant.
Figure 3.43 [26] shows the graphical representation for the effect of constant heat flux input to the sheet surface on surface and internal temperatures in a non-thin sheet. The arithmetic again depends on the dimensionless group, Fourier number, Fo = oc6/ L2 and on a dimensionless temperature, Q*, given as:
Q =fr T
(153)
* - °>-yb:]
The dimensionless distance, x/L, is zero at the surface and one at the centerline. Examples 3.24 and 3.25 illustrate the use of this graphic for determining the heating cycle time in a moderately heavy-gage sheet. Note that the time-temperature curves are linear beyond Fo = \. The following equation describes these curves:
Q
*= F o + (£f-(iM :
Fo
^
(3 54)
-
Example 3.24 Heating Rate of Thick Sheets in Constant Heat Flux—I A 0.250-in sheet of PET is heated at the rate of 3000 Btu/ft2 • h1. Determine its surface temperature when its centerline temperature is 3200F. The thermal diffusivity of the sheet is 0.002ft2jh and its thermal conductivity is 0.08 Btu/ft - h - 0F. For Fig. 3.43, the Fourier number is: ft2
B Fo = a9 = 0.002 ¥ • — (S) • ^ 1
144 ^
= 0.0059 (s)
Compare this value with the heat flux, !1(T00 - T2) for Example 3.22. For T00 = 5000F, T = 8O0F, and h = 2 Btu/ft2 • h • 0F, Q/A = 840 Btu/ft2 • h.
The dimensionless temperature Q* is: Q* = (320 - 80) • L0QQ8 Q1^25] = (320 - 80) • 0.00256 = 0.614 From Fig. 3.43, Fo - 0.756. 0 = 0.756/0.005 = 151 seconds or 2.5 minutes. The dimensionless sheet surface temperature at this time is given as Q* = 1.12. Thus Tsurface = 1.12/0.00256 + 80 = 518°F. Thus for this example, the temperature difference between the surface and the centerline is nearly 2000F. At this heating rate, the sheet surface may scorch or discolor before the centerline temperature reaches the minimum forming temperature value.
Example 3.25 Heating Rate of Thick Sheets in Constant Heat Flux—II Consider the data of Example 3.24. Assume that the constant heat flux is 840 Btu/ ft2 • h. Using Equation 3.54, determine the surface temperature when the centerline temperature is 3200F. Compare the results with the constant ambient air case of Example 3.22.
The Fourier number remains 0.0050 (s). The dimensionless temperature, Q* is: Q* = (320 - 80) • [ 8 4 0 ° 8 0 | 2 5 ] = (320 - 80) • 0.00914 = 2.19 This value is beyond the curves in Fig. 3.43. As a result, Equation 3.54 is used:
For x/L = 1, Fo = 2.19 - 1 + 1 - 1/3 = 1.86. Thus 0 = 1.86/0.005 = 371 seconds or 6.2 minutes. At this Fourier number, the dimensionless temperature Q* at x/L = 0 is given as Q* = 2.19 + 1/3 = 2.52. The temperature at the surface is 2.52/ 0.00914 +80 = 356°F. In Example 3.22 for constant 5000F ambient air and a convection heat transfer coefficient, h = 2 Btu/ft2 • h •0 F, the sheet heated to the 3200F centerline temperature in 12 minutes. The surface temperature was 343°F at that time.
When comparing constant heat flux and constant ambient temperature, the discussion of Section 3.12 must be kept in mind. For constant heat flux, the sheet surface temperature increases linearly with time beyond Fo = \, as seen in Fig. 3.43. There is no upper limit to the surface temperature for this concept. For constant ambient temperature, the sheet surface temperature asymptotically approaches the ambient temperature.
Dimensionless Temperature
Fourier Number, Fo Figure 3.43 Time-dependent temperature profile through plastic sheet with constant heat flux to the sheet surface [26], Fourier number, Fo = a0/L2. Dimensionless temperature = (T — Tinitial)/ (Theater-Tinitial)
The Thickness Effect If conduction controls, the effect of sheet thickness on time-dependent temperature is quite dramatic. First note that for the boundary condition, the dimensionless group, Bi = hL/k, doubling the sheet thickness doubles the value of the Biot number. The dimensionless time is given as the Fourier number, Fo = a9/L2. Doubling the thickness increases the Fourier number by a factor of four. Reviewing Fig. 3.42, if the Biot number doubles and the Fourier number is constant, the effect is a dramatic increase in surface temperature1. If the Fourier number increases by four at constant Biot number, there is a dramatic increase in surface temperature2. If the Biot number doubles and the Fourier number increases by four, the result is an even more dramatic increase in surface temperature. Example 3.26 focuses on the relative effect of thickness on temperature. The conduction heat transfer axiom appears applicable here: AU other things equal, heating times increase in proportion to the square of the sheet thickness. 1 2
This has the effect of doubling the heat transfer coefficient. The energy input to the surface doubles. This has the same effect as increasing the cycle time by a factor of four. The same energy input results in an increased surface temperature.
Table 3.15 is an experimental corroboration of this axiom for PMMA and a PVC/PMMA blend. Example 3.26 Thickness Effect—Heavy-Gage Sheet Consider a sheet having a Biot number of 0.2 and a Fourier number of 5.0 at the end of the heating cycle. If the initial sheet temperature is 800F and the centerline temperature at the end of the heating cycle is. 3800F, determine the surface temperature. Now increase the sheet thickness by 20%, keeping the heating cycle the same and recalculate the sheet surface temperature. What is the percentage increase in cycle time needed to get the centerline back to 3800F? From Fig. 3.42, Y = 0.592. Therefore the heater temperature is:
T00 = SSl0F from this expression. From Fig. 3.41, Y = 0.64. The surface temperature is: (587-80) orT s u r f a c e = 404°F. For a 20% increase in sheet thickness, Bi = 0.24 and Fo = 3.47. From Fig. 3.42, Y = 0.50. The ambient temperature remains at 587°F. Therefore the new centerline temperature is: Tcenterlme = 0.5 • (587 - 80) + 80 = 334°F The surface temperature is given from Fig. 3.41 as Y = 0.60, or T surface = 0.6 • (587 - 80) + 80 = 384°F. From Fig. 3.42, the Fourier number when Bi = 0.24 and Y = 0.592 is Fo = 4.0. The cycle time increase is 100 • (4.0 - 3.47)/3.47 = 15%. The sheet surface temperature at this Fourier number from Fig. 3.41 is Y = 0.64 and the surface temperature, Tsurface = 0.64 • (587 - 80) + 80 = 404 0 F. There is essentially no effect on the thermal driving force into the sheet. The major effect is increased cycle time.
Summary Thus if Bi < 0.1, the sheet heating process is probably controlled by the rate at which energy is delivered to the sheet surface. Increasing the rate of energy input will result in reduced heating cycle times. On the other hand, if Bi > 1, the heating process is probably controlled by the rate at which heat is conducted to the interior of the sheet. Increasing the rate of energy input may result in surface melting, scorching, yellowing or blistering. Although the range in values for plastic thermal conductivity
Table 3.15 Thermoforming Heating Cycle Times for Heavy-Gage PVC/PMMA and PMMA Sheet1 Sheet thickness (cm)
X/Xo
0.102 0.152 0.203 0.236 0.254 0.318 0.475 0.635 0.953
1.0 1.49 1.99 2.31 2.49 3.12 4.66 6.23 9.34
1
(X/X0)2
time (s) 1.0 2.22 3.96 5.35 6.20 9.72 21.7 38.8 87.3
PMMA
PVC/PMMA
15 35 61 82 150 324 594
[e/e0]
time (s)
[0/O0]
1.0 2.33 4.07 5.47
13 29 51
1.0 2.23 3.92
80 126 276 495 1122
6.15 9.69 21.2 38.1 86.3
10.0 21.6 39.6
Adapted from [44], with copyright permission. Sheet heated on both sides. Note: Heating time controlled by conduction through plastic is proportional to square of sheet thickness. Compare columns 3, 5, and 7
is relatively narrow, usually no more than a factor of two or so, the effective heat transfer coefficient value range is more than 20. Thus the range in sheet thicknesses where neither conduction nor convection dominate the heating rate is quite broad. Further, this range spans most of the common sheet thermoforming thicknesses. As a result, care must be taken in applying any of the above approximations. Case-bycase analysis is always recommended.
3.13 Equilibration When the sheet has reached its forming temperature, it is removed from the heating environment. Immediately the surface temperature begins to decrease. The centerline temperature continues to increase, albeit at a rate slower than before. A schematic of the time-dependent temperature gradient through the sheet is shown as Fig. 3.44. The sheet temperature approaches the average value. This effect is known as equilibration. The relationship between equilibration time, sheet temperature and the forming window is shown in Fig. 3.45. The time to equilibration is sometimes called the soaking time. Equilibration time values are strongly dependent on the sheet thickness and the sheet temperature profile through the sheet at the time the sheet exits the oven. The shape of the temperature profile through the sheet depends on the method of heating. The exponential form for the temperature profile is the best representation of the shape when the sheet is convectively heated. A more linear form is best when the sheet is heated at constant flux. These cases are detailed below.
Temperature
Ts u rf ace
Increasing Time
"^average T
centerline
Surface
Centerline
Sheet Thickness
Temperature
Figure 3.44 Schematic of time-dependent temperature profile through plastic sheet during equilibration
Forming Range
Surface
Average
Heating
Equilibration
Centerline Time
Transfer
Forming Time
Figure 3.45 Relationship between polymer forming temperature range [dashed area] and time-dependent sheet surface, average and centerline temperatures for heating and equilibration of polymer sheet
Convection Heating When convection heat transfer controls the energy input to the sheet, approximate equilibration times are obtained either from Fig. 3.46 or from: (3.55)
Dimensionless Temperature, (T-a)/c
Thermal Time Constant, bL
Equilibration Line x/L = 0
Fourier Number, Fo Figure 3.46 Adiabatic time-dependent equilibration temperature through sheet thickness [27]. Initial sheet temperature profile, T(x) = a • ebx + c, where a, b, c are curve-fit parameters. Fourier number, Fo = oc0/L2. Figure used by permission of McGraw-Hill Book Co.
This equation and the curves of Fig. 3.46 are determined by assuming that the sheet has a temperature profile T(x) = a • exp(bx) + c at the instant the heat source is removed. This empirical profile has been used previously with good success to calculate the local temperature for heavy-gage sheet in Table 3.14. Theoretically, this empirical profile does not exactly mirror typical heat conduction temperature profiles, but practically it yields useful approximate information. Example 3.27 illustrates the method of calculating equilibration times. Note in Fig. 3.46 that the dimensionless equilibrium time Foeq is essentially constant over a wide range of values of bL (0.5
In order to use Equation 3.55 to calculate Fo equil , the temperature profile through the sheet must be emulated by T(x) = a • ebx + c. From trial and error, the following values for a, b, and c are: a = 29.1°F c = 270.90F b = 1 0 0 ft" 1 T(0.5L) = 318.9°F (compared with 3200F calculated) From Equation 3.55, Fo equil = 0.552. The equilibration time is given as:
° = F ° a = ^ ' (0 '° 1)2 ' 36 °° = "A S Constant Heat Flux
Dimensionless Temperature
For constant heat flux for dimensionless time, Fo > \, the temperature profile is best given by Equation 3.54. The equilibration curves are shown in Fig. 3.47 [27], where the equilibration times begin at specific values of Fo. Example 3.28 compares times for constant heat flux with those for step change in surface temperature.
Fourier Number at End of Heating
Fourier Number From Beginning of Heating, Fo Figure 3.47 Time-dependent temperature profile through plastic sheet with constant heat flux to the sheet surface [27], showing equilibration. See Figure 3.43. Fourier number, Fo = a6/L2. Dimensionless temperature = (T - Tinitial)/(Theater - Tinitial)
Example 3.28 Equilibration Time—II Consider constant flux energy input to the sheet. Assume that the energy input is 1700 Btu/ft2 - h. Determine the surface temperature when the centerline temperature reaches 3000F. Then determine the time required to get the surface and centerline temperatures to within 5°F. Finally determine the time required to get full equilibration.
The dimensionless heat flux, Q*, is given as:
Q* = (300 - 80) - [ y ^ l ^ ] = 1 -035 From Equation 3.54, the Fourier number at x/L = 1 is: Fo = 1.035-1 + 1-1/3 = 0.702 The sheet surface temperature, when x/L = 0, is given as: Q
^ ( T -- 8 0 ) [l70^0r]^ L 3 6 8
Or Tsurf=370°F. From Fig. 3.47, the Fourier number when AQ* less than 5% of the average value for Q* is Fo = 0.333. Fo > 0.5 when AQ* = 0. As a result, the time to reach 5% of average and the full equilibration time are given as:
05% = Fo • ^ = j j m • (0.01)2 • 3600 = 59.9 s T2 Q CQQ O0 = Fo • - = — - • (0.01)2 • 3600 = 90 s OC U.UUZ
Computed Equilibration Times In Section 3.5, the finite difference form for the one-dimensional heat conduction equation was presented, together with appropriate boundary conditions. The simplest way of determining the temperature profile through the sheet during equilibration is to simply "switch off" the surface energy boundary condition. For the effective convective boundary condition, this is written in terms of Equations 3.8 and 3.11 as: § = IwP(T 0 0 - T )
(3.56)
where heff is the combined convection and effective radiation heat transfer coefficients, heff = h + h r and P is the switching factor. So long as the sheet is in the heating portion of the cycle, P = I . When the sheet is removed from the oven and
transferred to the forming press, P = 0. In a practical sense however, heat transfer between the sheet surface and its environment does not cease when the sheet is removed from the oven. Instead, the environmental temperature T00 simply becomes the cool air temperature surrounding the forming press. The effective heat transfer coefficient, heff, becomes just the convection heat transfer coefficient between the environmental air and the hotter sheet1. Computer models of this arithmetic are usually designed to accommodate sheet surface cooling during equilibration. For heavy-gage sheet, the calculated times needed to achieve temperature differences across the sheet of ten degrees (100C) or less are usually longer than the practical time to transfer the sheet to the forming station and begin the forming process. This means that at the time of forming, the sheet temperature and hence the sheet strength varies across the sheet cross-section. As seen in Chapter 4, particularly Fig. 4.5, the sheet strength is quite nonlinear with temperature. As detailed in Chapter 4, temperature dependency is modeled with either the W-L-F equation or an Arrhenius equation. The W-L-F Equation The W-L-F equation is given as: logl0aT=-^r(T~TT8)T
(3.57)
where aT, the shift factor, is the effect of temperature on polymer response to applied load, C lg and C2g are experimentally determined constants, and Tg is the glass transition temperature of the polymer. Table 3.16 gives W-L-F coefficients for several thermoformable polymers. As a first approximation, C lg = 17.44 and C2g = 51.6 are adequate "universal constants" [28]. The W-L-F equation is suitable in the temperature range of Tg < T < Tg + 1000C. Table 3.16 Williams-Landel-Ferry or WLF Constants for Several Polymers—Universal Constants Also Given [45]
1
Polymer
C1
C2
T g (K)
Polyisobutylene (PIB) Natural rubber Polyurethane elastomer Polystyrene (PS) Polyethyl methacrylate (PEMA) Polycarbonate (PC) Universal constant
16.6 16.7 15.6 14.5 17.6 16.14 17.44
104 53.6 32.6 50.5 65.6 56 51.6
202 202 238 373 335 423 -
Technically, the sheet surface also interchanges radiant energy with its surroundings. The linear form for the radiant heat transfer coefficient, Equation 3.29, works well here. Example 3.29 illustrates the relative values for the convective and radiative heat transfer coefficients during the equilibration step.
The Arrhenius Equation For polymers being processed at temperatures in excess of Tg + 1000C, the Arrhenius equation is used: <358)
" - " - T r ( K )
AHa is the viscoelastic activation energy of the polymer, R is the universal gas constant and T0 is the reference temperature where T0 ^ Tg. Relating Shift Factors to Sheet Stiffness The shift factor allows average properties to be determined when the sheet has a nonuniform temperature profile. The stiffness of a beam in flexure, for example, is determined by integrating the local modulus across the beam thickness: [b E(y;T)y2 dy S=
J
^
(3.59) y 2 dy
Jo
where E(y;T) is the temperature-dependent local modulus and b is the sheet halfthickness1. When E(T) is referenced to the reference temperature T0 through aT, the expression becomes: I " E 0 (T 0 )a T y 2 dy E 0 (T 0 ) P a T (y)y 2 dy S = Jo—j-b = j£ y2 dy
Jo
(3.60)
y2 dy
Jo
The relative effect of the nonuniform temperature on the sheet stiffness is obtained by integration, once T(y) is known, either from graphics, Figs. 3.46 or 3.47, or from computation. Similar equations can be derived for tensile and compressive strengths of a nonisothermal sheet.
3.14 Infrared-Transparent Polymers Many thermoformable polymers such as PET, PMMA, PS, PC and PVC, may be transparent in visible light but not transparent in incident radiative interchange. As noted in Chapter 2, the visible light wavelength range is 0.38 urn to 0.7 urn. Less than 1% of the total black body radiation is emitted in the visible region for radiant heater temperatures less than 8000C or 1472°F. For some polymers such as PS, PMMA and PET, however, the transparent region extends into the infrared region. For these 1
This again assumes that the sheet has been heated uniformly and centerline symmetry is valid.
Inbound Energy Surface Absorbing, Opaque Inbound Energy Volumetrically Absorbing, Semitransparent Inbound Energy Scattering, Translucent
Inbound Energy Diathermanous, Semitransparent Figure 3.48 Schematic of radiation energy absorption within a semitransparent sheet
polymers, energy is absorbed volumetrically in the short wavelength far-infrared region (Fig. 3.48). Correctly, these polymers are semi-transparent to incident radiation. The exact determination of the effect of volumetric energy absorption on temperature profiles in semi-transparent sheet has been made using opposing heat flux energy balances [29,30]. Expressions for wavelength-dependent reflectance, r, transmittance, t, and absorptance, a, are obtained. Surface or interfacial reflectance is obtained from:
Example 3.29 Energy Loss for Equilibrating Sheet Consider a 3500F sheet in 800F stagnant air. Determine the energy loss from the sheet surface. Air heat transfer coefficient is 2Btu/ft2 • h • 0F. Fg= 0.7andF= 1.0. Radiation effect is given from Equation 3.24: Y = {aFFg}[0.454 - 0.304] = 56.74 • 0.7 • 1.0 • [0.041 - 0.0081] = 1.31 kW/m2
The air convection coefficient is given as: ^ = 2 • (350 - 80) = 540 ft2 ^
op
' ^ y y (kW/m2) = 1.70 kW/m2
The total heat interchange is: Y
= 1.31 -h 1.70 = 3.01 kW/m2
A total
Approximately 56% of the heat loss is due to air motion and the rest to radiation from the sheet to its environment. where n is the index of refraction of the polymer. Reflectance for most transparent polymers is quite small. Example 3.30 illustrates this for PET. Even with a very large index of refraction of n = 1.65, only 6% of the incident energy is reflected. Transmittance, t, is given as: t = to(l-r)2-e^x (3.62) Example 3.30 Interfacial Reflectance PET has a refractive index of 1.65 when the value for air is n= L Determine the extent of interfacial reflectance.
From Equation 3.61:
r=
(1.65-I) 2
(u*TTr 0 - 06
Or 6% of the incident radiation is reflected. where to is the wavelength-specific transmittance at the polymer surface and |i is the wavelength-dependent Beer's Law absorption coefficient. Examples of wavelengthdependent absorption coefficients are given for several polymers in Chapter 2. Absorption curves are usually not mathematically modeled. Some infrared analyzers produce integrated absorptivity values. Figure 3.49 [31] shows integrated absorptivity for various thicknesses of PMMA. Another approach is to partition the absorption curve, as seen in Table 3.17 for PMMA. An infinite value for the Beer absorption coefficient implies that all the incident energy is absorbed on the sheet surface. Example 3.31 shows the relationship between absorption and volumetric energy uptake. Typically, volumetric absorption accounts for no more than about 10% to 15% of the total net radiant energy interchange. Example 3.31 Short Wavelength Absorption in PMMA For PMMA, the average absorpiton coefficient in the 0.4 pim to 2.2 jum visiblenear-infrared wavelength range is 0.8 cm"1. For a 1.25cm sheet, determine the amount of energy absorbed in this wavelength range. Let reflectance, r = 0.06. If the emitter temperature is 8000C or 1472°F, determine the amount of volumetric energy absorption in this wavelength range.
The amount of energy transmitted in this wavelength is given from Equation 3.62 as: t/to = (1 - r)2 • e ^ x = 0.942 • e" 1 = 0.325 The amount of energy absorbed is given as: a = 1 - r - Vt0 = 1 - 0.06 - 0.325 = 0.615 Or 61.5% of the incident energy in the subject wavelength range is absorbed. The total amount of energy emitted is determined by following Example 3.10 and using Table 3.6. For the wavelength range of 0 < X < 0.4 um, XT* = 0.04 • (1472 + 460) = 772.8. The amount of energy emitted in this region is 0.00030. For the wavelength range of 0 < X< 2.2 um, AT* = 2.2 • (1472 + 460) = 4250. The amount of energy emitted in this region is 0.1159. The net amount of energy emitted is: 100 -(0.1159 -0.0003) =11.56% The maximum amount of energy absorbed in this wavelength range is therefore: 11.56%-0.615 = 7.1% As seen in Figs. 2.19 to 2.30, values for \i, the Beer absorption coefficient, are usually independent of sheet thickness for unpigmented polymers [32]. Average values for pigmented polymers tend to decrease with increasing sheet thickness (Fig. 3.50) [33]. Organic dyes increase the absorption coefficient values primarily in the
Relative Total Absorption
Heater Temperature,0F
5 mm Thick
Heater Temperature,0K Figure 3.49 PMMA sheet thickness-dependent total absorption of radiant energy as a function of heater temperature [31]
Table 3.17 Absorption Coefficient Values— Step-Function Approximation for PMMA1 Wavelength [um]
Absorption coefficient \i (cm"1)
0-0.4 0.4-0.9 0.9-1.65 1.65-2.2 2.2-oo
oo 0.02 0.45 2.0 oo
1
Adapted from [17]
Absorption Coefficient, in1
visible wavelength range. Inorganic pigment particle sizes are usually in the 0.1 urn to 10 um range. These particles interfere with visible light transmission and act to increase scattering within the polymer (Fig. 3.51 and Fig. 2.34). This general effect increases the absorption coefficient values across the entire wavelength spectrum in proportion to the particle concentration. Very fine particles such as talc and TiO 2 cause less scattering, as seen by comparing absorption coefficients of unpigmented PET with carbon- and TiO2-pigmented PET (Fig. 3.51). At heater temperatures of 1000 K, 727°C or 13400F or less, the average absorption for 1 mm thick PS sheet is essentially independent of pigment type or color [34]. At much higher heater temperatures, absorption increases with pigments. Nevertheless, there is strong practical evidence that black sheet heats faster than white or natural sheet, regardless of the particle size or type of polymer. A typical ranking of absorption with color is [35]:
0.05 mm Thick 0.010 mm Thick 0.13 mm Thick
Quartz Heater Flux, Btu/ft 2 -rr°F Figure 3.50 Absorption coefficient for various thicknesses of PET with quartz heaters [33]. Figure used by permission of Society of Plastics Engineers, Inc.
Absorption Coefficient in"1
Carbon Pigment, 0.1 mm Thick Unpigmented, 0.1 mm Thick TiO2 Pigment, 0.11 mm Thick
Quartz Heater Flux, Btu/ft2-h-°F
Figure 3.51 Absorption coefficient for pigmented PET with quartz heaters [33]. Figure used by permission of Society of Plastics Engineers, Inc.
I
oo
•
1
2
3
•
•
•
N
•
•
N+1
Figure 3.52 Nodal characteristics of one-dimensional finite difference method
Black (most absorbing) Red Green Blue Yellow Ecru White Natural (least absorbing) Internal reflectance is considered to be the primary variable in this ranking [36]. The general effect of volumetric energy absorption is the flattening of the temperature profile within the sheet. For thin-gage sheet, low energy absorption implies low heating efficiency1. Pigments increase energy absorption and improve heating rates of thin-gage sheet2. At a given energy input rate, pigments increase sheet surface temperature in an otherwise transparent polymer. Most optically 1
2
For very thin sheets, energy transmission completely through the sheet may control the rate at which the sheet is heated. It is apparent from Fig. 3.49 that increasing heater temperature may actually reduce the efficiency of energy uptake. Care must be taken when heating very thin unpigmented sheet that contains printing. Energy may be preferentially absorbed by the printed section of the sheet, leading to uneven heating and serious local sheet distortion.
transparent polymers are opaque to incident far-infrared radiation and so the effect of volumetric absorption is secondary.
3.15 Computer-Aided Prediction of Sheet Temperature In the 1980s, a software program, TFl, was developed to aid engineers in determining formability conditions for several types of plastics [37]1. The program is based on the solution of the one-dimensional transient heat conduction equation, Equation 3.4:
subject to the initial condition, Equation 3.5, the symmetry condition, Equation 3.6, and the combined convection surface condition:
-kf^
=(h +Iv)(T-T 00 )
(3.64)
OX e,x = L
where h is the convection heat transfer coefficient and hr is the radiation contribution, written as the effective radiation heat transfer coefficient, Equation 3.30. As has been discussed, hr includes geometric and radiative efficiencies as well as sink and source temperatures. The numerical solution uses finite difference methods [38]. The explicit method uses a time step defined as: 86 = ^ ^
(3.65)
where a is the thermal diffusivity, a = k/pcp. Fo is the Fourier number. For mathematical stability of the explicit finite difference equations, Fo ^ \. Figure 3.54 shows the general nodal characteristics of the method. The temperatures of interior elements (2 < n > N — 1) are given as:
Tn(G + 56) = Fo[T n _ M + Tn+1(O) - (l - ^ V n ( G ) I
(3.66)
The Nth element is at the centerline or plane of symmetry. Therefore, T N _ x = T N+ x. The equation for the Nth element is: 1
There are several limitations to the data used and obtained from the TFl software package. For example, the values use the data given in Tables 2.5 and 2.12 for nearly 20 polymers. As noted earlier, constant-value specific heats of crystalline polymers do not accurately reflect the temperature-dependent enthalpic changes with temperature. The "view factor" is obtained from the arithmetic used to obtain Fig. 3.29. While this view factor is appropriate to calculate time-dependent average sheet temperature, it does not incorporate local temperature effects, due either to edge effects or zonal heating. And the software does not allow for time-dependent heater or air temperatures. And as noted below, the convection boundary condition uses a linearized form for the radiant heat flux. As a result, the TFl software should be considered only as a way of understanding the relative effects of the various parameters such as emissivity, air temperature, sheet-to-heater distance.
T N (G + 59) = Fo|~2 • T N _ ,(9) - f 2 - j ^ ) T N ( G ) I
(3-67)
The surface element temperature is given as: T1(G + 80) = Fo[T2(G) + Bi • T00 + ( - ^ - 1 - B i V ( G ) J
(3.68)
where Bi is a differential Biot number: Bi = (h + h r ) - ^
(3-69)
Since the equations are explicit, the method of solution is quite simple with the nodal temperatures at time 0 + 50 being determined from those at time 0. Again, time step 50 is determined from the stability criterion for the Fourier number, Fo. Example 3.32 illustrates the application of these equations to the relative effect of heater temperature on time to heat the sheet. The time associated with the lower forming temperature is the time required for the centerline to reach this temperature. The time associated with the upper forming temperature is the time required for the sheet surface to reach this temperature. Example 3.32 Heating Time for ABS and HDPE Polymers Consider heating either ABS or HDPE sheet 30 in x 30 in x 0.060 in using top and bottom heaters Win from the sheet surface. The heater temperature is 5000F. The quiescent air temperature is 2000F. The initial sheet temperature is 800F. The sheet and heater emissivities are 0.9. Determine the times required for the sheet to reach the lower forming temperature, the normal forming temperature and the upper forming temperature. The lower, normal and upper forming temperatures are 260 0 F, 295°F and 3600F for both ABS and HDPE. From the arithmetic of Section 3.15 or from TFl, the following information is obtained: Polymer
ABS HDPE HDPE/ABS ratio
Times (s) LFT
NFT
UFT
75.3 119.0 1.58
98.9 158.6 1.60
>160 >251 -1.59
Note: In Example 3.2, it was determined that the time required to heat HDPE to these temperatures was approximately 2 to 2\ times that for ABS. For this example, the values are about \\ times. There are two reasons for this discrepancy. The computer model assumes a temperature-independent average specific heat rather than a temperature-dependent enthalpy. And the computer model includes radiation and convection boundary conditions that alter the times required to obtain internal temperatures that exceed the forming temperature conditions.
Example 3.33 shows how air temperature and heater temperature affect overall heating cycle times using the computer-aided program. Note the dramatic effect of oven air temperature on the time required to heat the sheets to the normal forming temperatures. Example 3.34 shows the effect of heater temperature variation of ± 200F on the total heating times. The variation for this example is + 10% on the total time. Example 3.35 illustrates the effect of sheet-to-heater spacing on the total heating times. As noted, the view factor is strongly dependent on this spacing. With increased spacing, the heaters see less of the sheet and so the total heating time increases. Example 3.36 shows the effect of downgaging on total heating time. As expected, heating times are quite dependent on sheet thickness. At relatively low heater temperature, the heating time decreases in proportion to the sheet thickness decrease. At relatively high heater temperature, the effect should be more dramatic1.
Example 3.33 Effect of Heater and Air Temperature on Time-Dependent Heating Rates for ABS and HDPE Using the information of Example 3.33, determine the heating rates for ABS and HDPE for heater temperatures of 5000F and 8000F. Then, with heaters at 5000F, determine the effect of 1000F and 2000F oven air temperature.
The results from Section 3.15 or TFl are tabulated: Times (s) at 2000F Air Temperature
Polymer LFT Heater Temp
5000F
8000F
5000F
8000F
5000F
8000F
ABS HDPE
75.3 119.0
23.4 35.6
98.9 158.9
26.7 42.7
>160 >251
33.3 57.3
Times (s) at 5000F Heater Temperature
Polymer
NFT
LFT
1
UFT
NFT
UFT
Air Temp
2000F
1000F
2000F
1000F
2000F
1000F
ABS HDPE
75.3 119.0
104.9 166.1
98.9 158.9
151.8 243.1
>160 >251
>281 >441
Recall however that the convection heat transfer boundary condition used to generate this arithmetic assumes that the radiant heat flux can be approximated by a linear equation in temperature difference between the radiant heater and the sheet temperature.
Example 3.34 Effect of Small Changes in Heater Temperature on TimeDependent Heating Rates for ABS and HDPE Using the information of Example 3.32, determine the heating rates for ABS and HDPE for heater temperature of 4800E, 5000E and 5200F.
The results from Section 3.15 or TFl are tabulated: Times (s)
Polymer LFT 0
0
UFT
NFT 0
0
0
0
480 F 500°F 5200F
0
Heater Temp
480 F
500 F
520 F
480 F
500 F
520 F
ABS HDPE
83.7 132.1
75.3 119.0
68.2 107.4
112.6 180.4
98.9 158.9
87.9 140.9
>184 >289
>160 >251
>142 >220
Example 3.35 Sheet-to-Heater Spacing for ABS and HDPE Determine the effect on heating time for ABS and HDPE of Example 3.32 if the sheet-to-heater spacing is 5in, 10 in, or 15in.
The results from Section 3.15 or TFl are tabulated: Polymer
Times (s) NFT
LFT
UFT
Spacing
5
10
15
5
10
15
5
10
15
ABS HDPE
65.1 102.2
75.3 119.0
83.5 132.0
84.1 134.6
98.9 158.9
111.3 178.5
>135 >211
>160 >251
>180 >284
Example 3.36 The Effect of Downgaging on Heating Times for ABS and HDPE Using the information of Example 3.32, determine the heating rates for ABS and HDPE for sheets of 0.060 in, 0.054 in (10% reduction in thickness) and 0.048 in (20% reduction in thickness).
The results from Section 3.15 or TFl are tabulated: Polymer
Times (s) NFT
LFT
UFT
Sheet Tk
0.048
0.054
0.060
0.048
0.054
0.060
0.048
0.054
0.060
ABS HDPE
59.5 94.7
67.4 106.8
75.3 119.0
78.6 126.6
88.8 142.5
98.9 158.9
>126 >201
>143 >226
>160 >251
The Radiant Boundary Condition The arithmetic given above and the commercial computer software program, TFl, assumes a pseudo-linear radiant heat transfer coefficient, hr. This assumption is unnecessary [39]. The radiation (only) boundary condition at the surface node " 1 " of Fig. 3.54 is:
pCp
T S = h(T2"
Tl)+ { a F F } ( T 4 T 4)
s - -*
(3 7O)
-
where T^ and Tf are the absolute temperatures of the heater and the surface node, respectively. The term {aFFg} combines the view factor, emissivity constants and Stefan-Boltzmann constant. This equation is nonlinear in T1. For computational purposes, it is locally linearized by writing: Tf4(B + 59) « Tf 3(9) • Tf (9 + 59)
(3.71)
where Tf(B) is the old value of Tf. This allows the finite difference equation for the radiant (only) boundary condition to be written as: T1(B + 50) = 2Fo|T2(9) + L^
- RTf 3(0) - IJT1(O) + RT*4 I
(3.72)
where R = {aFFg}dx/k, with similarities to the Biot number, Bi of Equation 3.10. R is sometimes called the radiation Biot number. If the convection boundary condition is now included, the explicit finite difference version of the boundary condition for the one-dimensional transient heat conduction heat transfer problem is: T1(B + 59) = 2FoPr2(B) + (-L - RTf 3(B) - Bi - 1V1(B) + Bi • Ta + R • T^ 4 I
(3.73)
Again, T* refers to an absolute temperature.
3.16 Guidelines for Determining Heating Cycles Guidelines for setting up processing parameters on a new polymer are presented in Chapter 2. This section focuses on energy management for a new polymer. Estimates of energy consumption, heater temperature and heating cycle time are needed for cost estimation. The best sources for this information are resin suppliers and extruders. Experimental data on homologous polymers are quite useful and may be available from the supplier of the new polymer or its competitors. Carefully documented prior observations, particularly from extruders, are also valuable aids in estimating needed data. If these sources cannot provide the information, certain guidelines can be extracted from the information in this chapter.
The Biot Number Heating rate guidelines depend on whether the sheet is considered thin-gage or heavy-gage. These definitions are partially quantified in terms of the Biot number, Bi = hL/k. The Biot number is the ratio of energy input to the sheet surface to that conducted to the sheet interior. If Bi < 0.1, the sheet is usually considered as thin-gage. If Bi > 1, the sheet is considered as heavy-gage. Thin-Gage Guidelines When Bi < 0.1, the sheet is considered thin from a heat transfer viewpoint. The sheet surface temperature is not significantly greater than either the centerline or average sheet temperature. Surface blistering, degradation and burning are not considered primary concerns. Energy input to the sheet surface controls the cycle time. Therefore, radiant heating provides the most efficient means of heating1. To minimize cycle time, the maximum net energy exchange should occur in a wavelength range where the polymer has the greatest absorptivity. This usually implies high heater temperatures and short cycle times. Technically, the most efficient mode of heating is constant heat flux. The effective heat transfer coefficient is typically in the range of 0.06 to 0.12 kW/m2-°C or 10 to 20 Btu/ft2 • h •0 F. Energy transfer is dominated by radiation that is as much as 10 times the natural convection contribution. As a first approximation, convection effects can be ignored. For thin sheet such as those used in blister and bubble packaging, the heating cycle time is proportional to the film thickness. The lumped-parameter model discussed in Section 3.11 is used to predict average sheet temperature during thin-gage heating. It ignores temperature gradients through the sheet and so yields only average temperature values. Cycle time is determined when the average temperature reaches the normal forming temperature. From net energy balances, about 50% of the electric power supplied to the radiant heaters is actually used to heat the sheet to its forming temperature.
Heavy-Gage Guidelines The rate of heating of heavy-gage sheet is governed by the maximum allowable surface temperature. For heavy-gage sheet, Bi > 1. Energy transmitted to the surface from the environment must be conducted to the sheet interior. If the rate of conduction is low compared with the input energy rate, the sheet surface temperature may reach an undesirable level. Thus, highly efficient heating methods may in fact be undesirable. Constant surface temperature or declining heat flux methods are preferred. Forced hot air convection ovens are used to heat very heavy-gage sheet. 1
However, for very thin sheet, radiant transmission through the sheet may be a controlling feature. As a result, alternate heating means, such as direct conduction, contact or trapped sheet heating, are recommended.
Relatively low surface temperatures imply relatively low input energy levels, manifested as relatively low values of the effective convection heat transfer coefficient. Typical values are on the order of 0.005 to 0.03 kW/m2 •0C or 1 to 5 Btu/ft2 • h •0 F. Cycle times are controlled by conduction into the sheet and therefore are proportional to the square of the sheet thickness. Traditional distributed parameter one-dimensional transient heat conduction equations are used to predict the heating rates. Overall energy efficiency is relatively low at about 20% to 30%. Heat losses to surroundings and low conversion efficiencies when heating air are considered the primary reasons. And equilibration times are also proportional to the square of the sheet thickness. Intermediate-Gage Guidelines If the Biot number value is between 0.1 and 1, the sheet has intermediate gage with regard to heat transfer. Typically, the heating cycle time, 9, is proportional to the sheet thickness, L, to a power, 0ocLn
(3.74)
where l < n < 2 1 . Radiant heating dominates the heating methods, with heater temperatures set substantially below the region where optimum energy absorption occurs. Heater temperature values are usually dictated by the upper forming temperature, sheet blistering, discoloration, degradation and/or burning. The energy conversion efficiency is usually between 30% and 50%. Distributed parameter one-dimensional transient heat conduction equations are used to predict heating cycle times.
3.17 References 1. H. Domininghaus, Plastics for Engineers: Materials, Properties, Applications, Hanser Publishers, Munich (1993), Figure 24, p. 47. 2. F. Kreith, Principles of Heat Transfer, 2nd Ed., International Textbook Co., Scranton PA (1965), Figure 5-1, p. 199. 3. F. Kreith, Principles of Heat Transfer, 2nd Ed., International Textbook Co., Scranton PA (1965), p. 142. 4. F. Kreith, Principles of Heat Transfer, 2nd Ed., International Textbook Co., Scranton PA (1965), pp. 128-132. 5. J. Frados, Ed., Plastics Engineering Handbook, 4th Ed., Van Nostrand Reinhold. New York (1976), pp. 278-281. 6. W. McConnell, "Industrial Thermoforming Symposium and Workshop", SPE Thermoforming Division, Arlington TX, 12-14 March 1985, Distributed Handout. 7. F. Kreith, Principles of Heat Transfer, 2nd Ed., International Textbook Co., Scranton PA (1958), Appendix A-4. 1
Again, for thin-gage heating, n = 1. For heavy-gage heating, n = 2.
8. F. Kreith, Principles of Heat Transfer, 2nd Ed., International Textbook Co., Scranton PA (1965), p. 215. 9. F. Brinken and H. Potente, "Some Considerations of Thermodynamics in Thermoforming", SPE ANTEC Tech. Papers, 24 (1978), p. 65. 10. J.L. Throne, Plastics Process Engineering, Marcel Dekker, New York (1979), pp. 714-715. 11. R.R. Kraybill, "Emission Efficiency of Reflector Materials for an Infrared Tubular Heater", SPE ANTEC Tech. Papers, 29 (1983), p. 466. 12. D. Weinand, "Modellbildung zum Aufheizen und Verstrecken beim Thermoformen", Doctoral Dissertation, Institut fur Kunststoffverarbeitung (IKV), Aachen, 16 JuI 1987, BiId 4.9. 13. J.P. Holman, Heat Transfer, 4th Ed., McGraw-Hill Book Co., New York, 1976, Figure 8.8, pp. 284-288. 14. J.L. Throne, "Radiant Heat Transfer in Thermoforming", SPE ANTEC Tech. Papers, 41 (1995), p. 000. 15. D. Weinand, "Modellbildung zum Aufheizen und Verstrecken beim Thermoformen", Doctoral Dissertation, Institut fur Kunststoffverarbeitung (IKV), Aachen, 16 M 1987, BiId 4.10. 16. N. Platzer, "Rigid Thermoplastic Sheeting", Mod. Plastics, 37:11 (Nov 1954), pp3, 144. 17. N. Platzer, "Sheet Forming", in E.C. Bernhardt, Ed., Processing of Thermoplastic Materials, Reinhold, New York (1959), p. 485. 18. J.L. Throne, Plastics Process Engineering, Marcel Dekker, New York (1979), p. 657. 19. F. Kreith, Principles of Heat Transfer, 2nd Ed., International Textbook Co., Scranton PA (1965), pp. 129-135. 20. PJ. Schneider, "Conduction", in W.M. Rohsenow and J.P. Hartnett, Eds., Handbook of Heat Transfer, McGraw-Hill Book Co., New York, 1973, Figure 21, pp. 3-39. 21. A. Hoger, Warmformen von Kunststoffen, Carl Hanser Verlag, Munich (1971), pp. 36-37. 22. H. Gross and G. Menges, "Influence of Thermoforming Parameters on the Properties of Thermoformed PP", SPE ANTEC Tech. Papers, 28 (1982), p. 840. 23. PJ. Schneider, "Conduction", in W.M. Rohsenow and J.P. Hartnett, Eds., Handbook of Heat Transfer, McGraw-Hill Book Co., New York, 1973, Figure 22e, pp. 3-39. 24. PJ. Schneider, "Conduction", in W.M. Rohsenow and J.P. Hartnett, Eds., Handbook of Heat Transfer, McGraw-Hill Book Co., New York, 1973, Figure 22a, pp. 3-39. 25. V.S. Arpaci, Conduction Heat Transfer, Addison-Wesley Publishing Co, Reading MA, 1966. See also references [2,13,20]. 26. PJ. Schneider, "Conduction", in W.M. Rohsenow and J.P. Hartnett, Eds., Handbook of Heat Transfer, McGraw-Hill Book Co., New York, 1973, Figure 40a, pp. 3-67. 27. PJ. Schneider, "Conduction", in W.M. Rohsenow and J.P. Hartnett, Eds., Handbook of Heat Transfer, McGraw-Hill Book Co., New York, 1973, Figure 40b, pp. 3-67. 28. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes and Tests for Design, Hanser Publishers, Munich (1993), Table 3.4, pp. 250-257. 29. R.C. Progelhof, J. Quintiere, J.L. Throne, "Temperature Distribution in Semitransparent Plastic Sheets Exposed to Symmetric, Unsymmetric, and Pulsed Radiant Heating and Surface Cooling", J. Appl. Polym. ScL, /7(1973), p. 1227. 30. R.C. Progelhof, J. Franey, T.W. Haas, "Absorption Coefficient of Unpigmented Poly(methyl Methacrylate), Polystyrene, Polycarbonate, and Poly(4-methylpentene-l) Sheets", J. Appl. Polym. ScL, 75(1971), p. 1803. 31. D. Weinand, "Modellbildung zum Aufheizen und Verstrecken beim Thermoformen", Doctoral Dissertation, Institut fur Kunststoffverarbeitung (IKV), Aachen, 16 JuI 1987, BiId 3.13. 32. R.C. Progelhof, J. Franey, T.W. Haas, "Absorption Coefficient of Unpigmented Poly(methyl Methacrylate), Polystyrene, Polycarbonate, and Poly(4-methylpentene-l) Sheets", J. Appl. Polym. ScL, 25(1971), p. 1806. 33. A. Hoger, Warmformen von Kunststoffen, Carl Hanser Verlag, Munich (1971), Table 2, p. 31. 34. D. Weinand, "Modellbildung zum Aufheizen und Verstrecken beim Thermoformen", Doctoral Dissertation, Institut fur Kunststoffverarbeitung (IKV), Aachen, 16 JuI 1987, BiId 3.14. 35. J. Florian, Practical Thermoforming: Principles and Applications, Marcel Dekker, New York (1987), p. 39.
36. J. Florian, Practical Thermoforming: Principles and Applications, Marcel Dekker, New York (1987), Chapter 2, "Components of the Thermoforming Process". 37. J.L. Throne, TFl, Integrated Design Engineering Systems, Inc., Laramie WY 82070, 1991. 38. D.R. Croft and D.G. Lilley, Heat Transfer Calculations Using Finite Difference Equations, Applied Science Publishers, London (1977). 39. D.R. Croft and D.G. Lilley, Heat Transfer Calculations Using Finite Difference Equations, Applied Science Publishers, London (1977), pp. 92-94. 40. F. Kreith, Principles of Heat Transfer, 2nd Ed., International Textbook Co., Scranton PA (1965), Table 5-1, pp. 215-216. 41. A.I. Brown and S.M. Marco, Introduction to Heat Transfer, McGraw-Hill Book Co., New York (1951), p. 68. 42. R.W. Singleton, "Electric Infrared: Textile Applications in the 1980's", Proceedings, AATCC National Technical Conference (1980), p. 201. 43. J.H. Perry, Ed., Chemical Engineers' Handbook, 4th Ed., McGraw-Hill Book Co., New York (1963), pp. 10-11 to 10-13. 44. H.R. Osmers, "Industrial Thermoforming Symposium and Workshop", SPE Thermoforming Division, Arlington TX, 12-14 March 1985, Distributed Handout. 45. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes and Tests for Design, Hanser Publishers, Munich (1993), Table 6.17, p. 651.
4 Stretching the Sheet 4.1 Introduction 4.2 The Stretching Concept 4.3 Polymer Hot Strength Standard Tensile Tests Hot Tensile Tests Hot Creep Tests Other Stretching Tests Temperature-Dependent Viscosity for Amorphous Polymers Dynamic Mechanical Testing 4.4 Stress-Strain-Rate of Strain—Theory Elasticity—A Rationalization Strain Energy Function The Rivlin Form for the Strain Energy Function The Ogden Form for the Strain Energy Function Viscoelastic Models 4.5 Available Stress-Strain Data Sensitivity of Models 4.6 The Importance of Polymer Material Properties 4.7 Practical Aspects of Stretching Funnel Test 4.8 Bursting Conditions 4.9 Sheet Sag Initial Sag Tensile Sag The Catenary Sag Parabolic Sag Relating Sag to Hot Sheet Strength Sag—A Comment 4.10 References Appendix 4.1 Biaxial Stretching of an Elastic Membrane
4.1
Introduction
Once the plastic sheet temperature is within the forming window, it is ready to be stretched. There are many ways of stretching and prestretching the sheet, as detailed in Chapter 1. Vacuum, air pressure, mechanical aids such as plugs, rubber diaphragms, and combinations of these are used to shape the rubbery sheet against the mold surface. The extent to which a given polymer at a given temperature can be stretched limits the ways in which it can be thermoformed. Part design, especially local part wall thickness, depends on the extent of polymer deformation. Deep drawing, drawing into sharp corners, and replication of mold surface details such as patterns or lettering, require polymers that can be rapidly and uniformly stretched. Chapter 9 examines part design in greater detail. This chapter focuses on the interaction between the forces available to stretch the rubbery sheet and the inherent nature of the rubbery plastic to resist these forces. This interaction, noted in Chapter 2, is directly related to the stress-strain-rate of strain behavior of the plastic at its forming temperature. Typically, at low temperatures, the plastic is quite stiff, does not stretch easily, and will not faithfully replicate the mold details under the modest forces available with simple vacuum forming. Higher forming forces are required when sheet temperatures are low. On the other hand, cycle times are short when sheet temperature is low, so economics favor low sheet temperatures. At high forming temperatures, the sheet is quite limp, is easily stretched and replicates the mold surfaces well at very modest forming pressures. But sagging and sheet surface discoloration can be serious problems, cycle times are increased, and part wall thickness uniformity is usually compromised. Intuitively knowing when a sheet is hot enough for processing is an acquired skill. Sheet sag and sheet smoke are frequently considered as first-line visual indicators. As a plastic sheet is heated, it undergoes several phases of motion [I]: •
The sheet may momentarily tighten in a drum-head fashion. This tightening may be accompanied by some off-gassing from the sheet surface. The gas is usually vaporizing surface or adsorbed water. Since the sheet temperature at this point is usually only a few degrees above room temperature, the tightening is usually attributed to the last steps in sheet extrusion. In the case of heavy-gage sheet, the last step involves palletizing where the just-extruded and guillotined sheet is stacked on older sheet. Heat retention in the palletized stack can cause residual stresses in the individual sheets that are not attributable to the extrusion process, per se. A similar situation occurs with thin-gage sheet that is rolled. The rolling action may cause residual stresses called curl. This curl is relaxed out when the sheet is first heated. In addition, heat retention in the roll can also cause residual stresses that are not attributable to the extrusion process. • As heating continues, the drum-tight state of the sheet is rapidly replaced by sheet rippling or "swimming". The sheet may also exhibit very rapid droop or sag and the sheet texture may change from glossy to matte at this time. During this time, the sheet temperature is passing through the glass transition temperature for
Specific Volume, cm 3 /g
PS PMMA PC
30% DOP FPVC
RPVC
Figure 4.1 Temperature-dependent specific volume for several thermoplastics
Temperature, 0 C
amorphous polymers. For certain crystalline-tendency polymers such as PET, some surface crystallization may take place1. The swimming effect is apparently due to nonuniform residual stresses imparted in the sheet during the last stages of cooling the sheet. The sag is probably due to the decrease in density as the sheet passes through the glass transition temperature (Fig. 4.1) [3]. • As heating continues, the rippling state is frequently replaced with a second tautness in the sheet. Off-gassing or "smoking" may begin at this time, as well. The sheet temperature is usually above the glass transition temperature at this time. This state is directly attributable to sheet orientation during extrusion. At this time, the sheet may pull from the clamps. Careful observation of sheet tautness at this point may yield clues as to the balance in residual stresses in the MD and TD directions. In heavy-gage sheet forming, this balance may dictate the orientation of the sheet to the mold. The liberated gases may be external lubricants, processing aids, and other low boiling adducts. Since the sheet surface is now substantially hotter than the center, moisture and dissolved gas bubbles appear. • Continued heating produces sheet sag. At this point, the tensile strength of the hot sheet is dropping rapidly and the force of gravity pulls the sheet into a catenary-like shape. As stated above, sag is universally used as an early indicator
1
This crystallization is sometimes called "cold crystallization" [2]. It occurs above the glass transition temperature but below the crystalline melting point.
Heater Sheet Clamp
Heater
Sag
Figure 4.2 Schematic of sheet sag in thermoforming oven
that the sheet is ready to be formed. As seen below, sag is a measure of the temperature-dependent tensile strength of the polymer, in combination with sheet geometry. Since sag is so important to the forming process, it is discussed in detail in Section 4.9. Care must be taken when heating sheet beyond the early stages of sag. As seen in schematic in Fig. 4.2, sag dramatically changes the relationship of the sheet to the top and bottom heaters. The general effect is to change the local view factor between the heaters and the sheet. The center of the sag moves away from the top heaters and toward the bottom heaters. The heat flux becomes unbalanced, with more energy being transferred from the bottom heater. The results are different for thin-gage and heavy-gage sheet. • For heavy-gage sheet, conduction from the sheet surface to its interior controls the general heating condition. As discussed in Chapter 3, energy inputs to the two surfaces of the sheet are usually controlled independently to ensure uniform energy distribution throughout the sheet thickness. Therefore, energy input to each sheet surface must be carefully controlled to prevent overheating or inadequate heating. When the sheet sags, it approaches the lower heater and retracts from the upper heater. Local energy input to the middle of the underside of the sheet increases dramatically and that to the top side decreases dramatically. This shifts the center of energy symmetry toward the lower surface of the middle of the
Temperature Profile
Sheet
Sheet Sag
Figure 4.3 Characteristic shift in temperature profile through heavy-gage sheet during sagging
sheet toward the lower surface while the center of symmetry remains near the center of the sheet (Fig. 4.3). • For thin-gage sheet, where energy input to the sheet surface controls the general heating condition of the sheet, the top-to-bottom energy uniformity is less important than the local change in view factor in the sagging center of the sheet. As the sagging sheet nears the lower heater, the view factor increases toward unity. Energy input is more intense and that area of the sheet heats more rapidly. The local sheet temperature may exceed the upper forming temperature of the polymer. If the polymer melt strength is particularly temperature sensitive, the sheet will flow apart and may drip into the heater. If the polymer degrades rapidly at this temperature, the sheet may blacken or ignite. Since sheet energy uptake is governed by the heater energy output, excessive sag and overheating may occur so quickly with certain polymers that degradation or fire cannot be prevented. Again, sheet distortion and sag during heating is the result of the polymer responding to external forces of temperature and stress. This chapter lays the foundation for a technical understanding of the fundamental nature of polymer material deformation. Thermoplastic sheet at its forming temperature is considered as: • • •
A rubbery elastic solid, A highly viscous liquid, or Something in between.
Owing to the commercial interest in deforming polymers near their melt or softening temperatures, an extensive body of knowledge has been created on this topic. The stretching characteristics of thermoformable sheet are important since understanding the characteristics leads to a very basic understanding of polymer behavior during elongation.
In this chapter, elongational deformation of polymer sheet will be examined in great technical detail. The objective of this examination is a better understanding of the thermoforming process and how that relates to intelligent selection of the proper polymer for a given application. While the parts designer does not necessarily need to understand the specifics of the concepts presented to design quality parts, the material should be reviewed for general concepts.
4.2
The Stretching Concept
Stretching is elongational material deformation. All real materials, such as polymers, steel, wood and even concrete, stretch to some extent when forces are applied. For modest stretching, the extent of stretching or elongation is called strain, e. For solids, strain is the polymer response to the applied force per unit cross-section, or stress, a. For a thin membrane, stretching can be in one direction, uniaxial deformation. Or it can be in two directions or biaxial deformation. If the amount of biaxial stretching is the same in both directions, stretching is equal biaxial deformation. The simplest uniaxial relationship is Hooke's law: G =E - e
(4.1)
The proportionality is the elastic modulus, often called Young's modulus [4]. The units on a and E are the same, either MPa or lbf/in2. The relationship in biaxial stretching is written as:
where v is Poisson's ratio and i is the strain direction (i=l,2). Simply put, a Hookean material responds instantaneously to the applied load. So long as the load remains constant, the material retains a constant strain or elongation. When the load is removed, the material instantaneously returns to its unstrained state. Hooke's law adequately describes the small deformation response of most traditional materials such as metals and wood and is often pictured as a simple spring. For modest deformation levels, most solid materials respond in some fashion similar to that of Equation 4.1. When solids are strained to high levels, they may simply fracture, they may exhibit deviation from the Hookean relationship, or they may yield (Fig. 4.41). Most polymers below their glass transition or melting temperatures show these general characteristics.
1
As an example, if the solid material deforms in a Hookean manner to a given level of deformation, then yields to produce a continuous deformation under constant load, the material is called an elastoplastic solid [5].
Stress
Hookean/Spring
Rigid Tough Yield Point Ductile
Break
Strain Figure 4.4 Characteristic stress-strain curves for thermoformable thermoplastics, compared with the classic purely elastic Hookean spring
Elongation, e
Figure 4.5 Tensile elongation under load [5]
Load, F
For extensive deformation, consider the example of tensile loading (Fig. 4.5) [6]. The weight of the hanging sheet is given as: W = p - hbL
(4.3)
where p is the density of the sheet, h is its thickness, b is its width, henceforth assumed to be unity, and L is its length. The tensile strength is given as: W ao = x (4.4) where A = bh. Therefore the initial stress applied to the top of the sheet at the clamp is: (4.5)
The local deformation, e, per unit length of the sheet is given as: e=
AL i r
(4.6)
The differential strain is uniform everywhere along the vertical sheet axis. Engineering strain, eeng, is given in terms of the initial sheet length, L0:
eeng = ^
= f = X-1
(4.7)
where X is the ratio of instant to initial length, L/L o . Hencky strain or true strain, etrue, is obtained by summing all differential strains over the sheet length:
£true=
T T = l n ( r ) = l n {X)
(4 8)
-
For relatively low values of strain, e « L 0 , engineering strain is a good approximation to true strain. At an engineering strain level of 20%, the error in approximating true strain is about 10%. Example 4.1 illustrates other values for engineering and true strain. The engineering strain value is always smaller than the true strain value. Example 4.1
True and Engineering Strain
Determine values for true and engineering strain for L = 1.1 L0 and L = 2 L0. True strain is given by Equation 4.8. Engineering strain is given by Equation 4.7. For the first case, L = L l L 0 . eeng = 0.1 and e true = 0.095. eeng/etrue = 1.15. For the second case, L = 2 L 0 . eeng=\.O a n d e true = 0.693. eeng/etrue = 1.44. Engineering strain is always greater than true strain. As with strain, there are two ways of defining stress. Engineering stress is the applied force per initial unit area:
<*«, = £
(4.9)
True stress is the applied force per true or actual unit area, A t : <W = -^
(4.10)
The initial stress is fixed by the length of the sheet and its density. As the sheet stretches, the weight remains constant, but L increases and h decreases, in proportion. The true stress on the sheet increases in proportion to its length, and the strain on the sheet increases, as well. It is apparent that engineering stress-strain, based on initial lengths and thicknesses, is easier to use for computational purposes. Regard-
less of whether engineering or true stress-strain relationships are considered, the functional relationship is: a = f(e;E(T)) = g(X;E(T))
(4.11)
where E(T) is some material proportionality, such as tensile modulus or the more complex multi-constant proportionalities of hyperelastic models such as the Ogden and Mooney-Rivlin models, discussed below. The stress-strain proportionality is temperature-dependent, decreasing with increasing temperature. As a result, increasing sheet temperature results in rapid increase in strain in the sheet. In general, all solids behave as: a = f(e)
(4.12)
When fluids are shear-stressed, they continue to deform until the stresses are removed. The simplest relationship is Newton's law: G = [I-E
(4.13)
where e is the time rate of change of strain, also called the strain rate. The proportionality, JI, is called the Newtonian viscosity or shear viscosity. The unit on the strain rate is s - 1 . The units on fi are either MPa • s or lb f • s/in2. For elongational flow, the equivalent uniaxial relationship is written as: a = rj e -e
(4.14)
where r| e is the extensional viscosity or the Trouton viscosity. For deformation-rate independent fluids in uniaxial extension, the Trouton viscosity is three times the Newtonian shear viscosity: r,e = 3 - n
(4.15)
For biaxial extension, the equation becomes: Tie = 6 - M-
(4.16)
Most small molecule fluids are adequately described by Equations 4.4 and 4.5 [7]. As a rule, polymers do not follow Newton's law. In certain instances, polymer fluid response can be described adequately as non-Newtonian: a = Ti(€)-e
(4.17)
For viscous-only polymer fluid response, the viscosity, r|(e) is considered to be deformation rate-dependent. For most polymers, the viscosity decreases with decreasing deformation rate. The intermolecular sliding is inhibited by steric factors and chain entanglements. Polymer fluids are considered to be viscoelastic fluids or elastic liquids. By viscoelasticity, it is meant that the polymer response to applied forces has both elastic and viscous characteristics: a = f(e,e)
(4.18)
The arithmetic relationship between the applied stress, a, and the polymer response, as e and e, is called the material constitutive equation of state. The study of polymer
Table 4.1 Relationship between Polymer Response and Extent of Deformation Polymer behaviour
Small deformation
Large deformation
Small deformation rate
Large deformation rate
Viscosity
Not applicable
Not applicable
Elasticity
Hookean
Newtonian or non-Newtonian Not applicable
Viscoelasticity
Linear
neo-Hookean or rubber Nonlinear
Newtonian or non-Newtonian Not applicable Linear
Nonlinear
response to applied forces is called rheologyl. The realm of viscoelasticity is usually separated into linear and nonlinear viscoelasticity. Linear viscoelasticity is restricted to polymer response to small deformations and small deformation rates. Material responses are usually position- or coordinate-independent. In nonlinear viscoelasticity, deformations and deformation rates are large. During stressing, the polymer is convected or moved far from its original position. As a result, there is great complexity in relating the time-dependent polymer response to the applied stress. Table 4.1 summarizes the general concepts of polymer viscoelasticity. Before beginning the technical details of rubbery polymer sheet response to applied external loads, the following axiom applies: Although hot rubbery polymers exhibit both solid rubbery and rubbery liquid characteristics, in the limit, thermoforming is a solid phase deformation process.
The importance of this axiom is seen in computer-aided design models for wall thickness calculations, discussed in detail in Chapter 9. In thermoforming, the extent of sheet deformation depends on: • • • •
Sheet temperature, Level of applied force, Level of molecular order and orientation, and General material constitutive equation of state.
1
Details about rheology and its application to polymer processing in general can be obtained from many source-books. Some introductory books include: S.L. Rosen, Fundamental Principles of Polymeric Materials, Wiley-Interscience, New York, 1982. R.L. Crawford, Plastics Engineering, 2nd Ed., Pergamon Press, Oxford, 1987. J.A. Brydson, Flow Properties of Polymer Melts, Van Nostrand Reinhold, New York, 1970. More advanced books on rheology include: C D . Han, Rheology in Polymer Processing, Academic Press, New York, 1976. A.G. Fredrickson, Principles and Applications of Rheology, Prentice-Hall, New Jersey, 1964. CJ.S. Petrie, Elongational Flows: Aspects of the Behaviour of Model Elastoviscous Fluids, Pitman, London, 1979. R.B. Bird, R.C Armstrong, and O. Hassager, Dynamics of Polymeric Liquids. Volume 1: Fluid Mechanics, John Wiley & Sons, New York, 1977.
Table 4.2 Type of Viscosity Expected for Several Types of Plastic Processing1 Type of extensional viscosity
Process Uniaxial
Uniform biaxial
Pure shear X
Injection molding, radial flow Blow molding Cylindrical parison Spherical parison
X X
Fiber spinning
X
Converging entry flows Rectangular die Circular die
X
Thermoforming2
X
1 2
X X
X
Adapted from [8], with permission of Society of Plastics Engineers Depends on particular configuration and whether plug assist is used
Above the glass transition temperature, Tg, most amorphous polymers have sufficient chain mobility to deform and even flow under load. For crystalline polymers above Tg, those chain segments that are not involved in the crystallite formations, either in the spherulites or capture in dendritic structures, can deform. The extent of deformation then depends on the polymer level of crystallinity. As an example, HDPE has a very high degree of crystallinity of about 90% and so cannot be thermoformed below its melt temperature. PVC, on the other hand, usually has a very low level of crystallinity of about 10% and so is usually thermoformed above its glass transition temperature just as if it is amorphous. Thermoforming involves a complex mixture of extensional deformation processes, Table 4.2 [8]. In pneumatic sheet prestretching, the stretching is essentially uniform biaxial extension in the center of the bubble (Fig. 4.6) and nearly uniaxial extension at the clamp edge (Fig. 4.7). The deformation in the center of the bubble is essentially unconstrained orientation. Free-form blowing of skylights, blisters and
Figure 4.6 Characteristic biaxial stretching of membrane
Biaxial Stretching
Uniaxial Stretching
Figure 4.7 Characteristic uniaxial or tensile stretching of membrane
bubbles yields mostly biaxially stretched parts. When the sheet is mechanically stretched with plugs or web catchers, the plastic is uniaxially stretched between its solid anchor points. When the sheet contacts a mold surface almost immediately upon initiation of stretching, that portion of the sheet is uniaxially stretched. Under these conditions, the sheet is undergoing constrained orientation. Unconstrained deformation gives the clearest analysis of polymer behavior under load. It also provides a practical means for determining the thermoformability of a polymer and so is examined in detail shortly.
4.3
Polymer Hot Strength
As the polymer temperature increases, tensile strength and modulus decrease and elongation increases. This is true for amorphous and crystalline polymers alike. Simply put, polymer sheets should become rubbery when heated to the forming temperature. Typically, the tensile test is a standard procedure for measuring the strength of solid polymers1. From a uniaxial tensile test on a dogbone-shaped sample, the initial elongation under load yields the tensile modulus, elastic modulus or Young's modulus, E (Fig. 4.8). As the applied load increases, neck-down, yielding and extensive elongation occur. The polymer response becomes one of plastic yielding. The yield point is seen as the point where an abrupt change in strain occurs. Ductile and rubbery polymers continue to bear load while yielding. The sample fails at its ultimate tensile strength and ultimate elongation or elongation at break. Brittle polymers normally exhibit very little yielding before failing.
Standard Tensile Tests According to the standard tensile test, ASTM D638, the test speed must be one of four standard values, according to the type of polymer being tested. And the gage 1
The US standard is ASTM D638 with ASTM D618 as the conditioning procedure. The German standard is DIN 53455 and the international standard is ISO 527.
Stress
Elastic Modulus, E Yield Point
Ductile
Elongational Strain Figure 4.8 Characteristic stress-strain curve for a ductile polymer, showing tangent or elastic modulus
length must be one of two standard values, again according to the polymer. The four speeds are: • • • •
Speed A is 0.05 in/min+ 25% for polymers with gage length of 2 in+ 0.01 in. This is an elongation rate of 2.5%/min or 0.0004 s"1. Speed B is 0.2 in/min + 25% for the same gage length. This is an elongation rate of 10%/min or 0.0017 s"1. Speed C is 2.0 in/min + 10% for polymers with gage lengths of 1 in + 0.005 in or 2 in ± 0.01 in. For the shorter gage, this is an elongation rate of 200%/min or 0.033 s"1. Speed D is 20 in/min + 10% for polymers with gage length of 1 in + 0.005 in. This is an elongation rate of 2,000%/min or 0.33 s~!.
The sample strain rate, e, in s"1, mm/mm • s or in/in • s, is the slope of the elongation-time curve. Thermoforming is a high deformation rate process with momentary strain rates of 0.1 to 10 s~l or higher. As seen above, the highest crosshead speeds on the shortest test specimen yield sustained strain rates of 0.33 s" 1 [9,10]. In other words, even the highest laboratory speeds yield stress-strain data near the low end of the practical process strain rate. The standard ASTM D638 test is a room temperature test. Thermoforming needs tensile data at the forming temperature. Hot tensile tests are difficult to carry out with any degree of reliability or confidence in the data. At elevated temperatures, uniaxial stretching is not confined to the neck-down portion of the dogbone sample. Grip slip or extrusion of the plastic from the grips is common. Sample conditioning at the desired temperature is arduous since the sample is usually quite limp and the grips and even the load cells conduct heat from the sample to the environmental chamber. Conditioning times of 12 minutes are recommended [9]. Appreciable annealing and strain relaxation can occur during thermal conditioning and initial elongation values under load, particularly initial values of Young's modulus, are
PS Tensile Strength, MPa
HIPS CA
PMMA SAN
PP
HDPE RPVC
LDPE
XLPE
Temperature,0C Figure 4.9 Temperature-dependent tensile strength for several thermoplastics. Figure adapted from [11] and used with permission of copyright owner
usually suspect. In short, high temperature tensile tests are difficult to master and may yield suspect data. Nevertheless, hot tensile test data are quite important in the determination of the general formability of polymers. For example, the tendency for abrupt sheet sag is thought to be related to the rapid drop in tensile modulus with temperature [10]. Figures 4.9 and 4.10 [11,12] show the temperature-dependent tensile strengths for several crystalline and amorphous polymers. Figures 4.11 and 4.12 [13,14] show temperature-dependent moduli for several commodity and engineering polymers. It is hard to generalize about temperature-dependent properties of polymers. For example, in Fig. 4.9 [11], the tensile strength of amorphous high-impact polystyrene or HIPS has a relatively linear decrease in value with temperature, whereas amorphous unmodified polystyrene tensile strength decreases rapidly with increasing temperature. A similar comparison can be made for crystalline polychlorotrifluoroethylene or CTFE and crystalline polytetrafluoroethylene or PTFE. Again, although it is hard to generalize, filled polymers have higher low-temperature moduli but exhibit the same temperature dependencies as the unfilled polymers at higher temperatures. It is thought that the filler acts to dilute the polymer and to offer yielding defects at higher temperature. Fibers, on the other hand, reinforce the polymer at higher temperatures. Thus, although the shape of the temperature dependent tensile property is the same as that for the neat polymer, the value is increased as the fiber loading is increased, to a point. The shape of the stress-strain curve is also important, as discussed shortly. If
PA-66 30%GRPA-66
Tensile Strength, MPa
PP POM PA-6^
POM Copolymer PC
PCTFE
PTFE
Temperature,0C Figure 4.10 Temperature-dependent tensile strength for several thermoplastics. Figure adapted from [11,12] and used with permission of copyright owner
the polymer does not exhibit excessive yield, the parts produced from the polymer tend to have consistently uniform wall thicknesses, particularly in deep draw applications [10]. Crystalline polymers seem to process best if formed at temperatures within 100C or 200F of their melt temperatures.
Flexural Modulus, GPa
POM PSO2
PC ABS PBT
Transparent PA
Temperature, 0C Figure 4.11 Temperature-dependent flexural modulus for several thermoplastics. Figure adapted from [13,14] and used with permission of copyright owner
Shear Modulus, MPa
mPPO
PA POM
PE PVC
ABS PC-
PUR
Temperature, C Figure 4.12 Temperature-dependent shear modulus for several thermoplastics. Figure adapted from [13,14] and used with permission of copyright owner
Hot Tensile Tests Despite their problems, hot tensile tests have been used for years to bracket the forming regions of polymers [15]. There are two general approaches to hot tensile tests. The first employs a fixed rate of stretch. The ASTM D638 test run in a high-temperature environmental chamber is an example of a fixed stretching rate test. For this test, e = de/dG = constant and the amount of force required to stretch the sample is measured as a function of deformation, yielding: a = f(e;e
fixed)
(4.19)
If the polymer is simply an elastic solid, the rate of stretching is immaterial to the stress-strain curve. Thus: a = f(e only)
(4.20)
On the other hand, if the polymer is viscoelastic, the generated stress-strain curves are functions of e.
Magnetic Brake
Clamp Weight
Hot Box
Tensile Specimen
Clamp
Figure 4.13 Schematic of hot tensile test apparatus with dogbone test specimen
Hot Creep Tests Hot creep is another uniaxial test that has been used extensively to evaluate polymer candidates for thermoforming. In tensile creep, a fixed load, resulting in a fixed stress, a = constant, is applied to the sample at temperature. The strain level, e and the strain rate, G is then measured. Usually, creep is a long-term test, involving relatively low loads and temperatures [16]. Hot creep is a modification of this test. Here, a fixtured sample is placed in a high-temperature oven without load and allowed to reach isothermal temperature. A very high load is then instantaneously applied and a high speed film or video camera records the time-dependent elongation to break [17]. Figure 4.13 is a schematic of this simple test. Instantaneous strain rates of 5 s"1 or more are routinely measured this way. For this test, the following equation applies: a = constant = f(e;e)
(4.21)
Although the test is simple, interpretation of the results can be difficult. Figure 4.14 is a schematic from an actual test sequence for one applied load value for rigid PVC or RPVC in the forming temperature range of 3000F to 3500F or 149°C to 177°C. As is apparent, the sample did not elongate appreciably at the lowest temperature and showed a very high rate of elongation at the highest temperature. The hot creep test yields temperature-dependent ultimate elongation values as well. In one reported experiment [17], the ultimate elongation or strain for rigid PVC or RPVC increased
Elongation
Increasing Temperature
Time Figure 4.14 Characteristic of temperature-dependent elongation for hot tensile test
linearly from about 120% at 1000C to about 500% or so at 122°C, then dropped to about 300% or so at 1400C to 1800C. This indicates that local draw ratios for this PVC should not exceed about 3:1 to 4:1. The effect of strain hardening, owing to increasing strain rate at a given temperature is implicitly found in the hot creep test. Hot uniaxial creep test data are compromised by the same testing vagarities that occur in hot tensile testing. Nevertheless there is a strong indication that ultimate uniaxial strain can be related to areal draw ratios in simple geometries [17]. A strain rheometer has been developed recently in an effort to circumvent some of the difficulties with grip slip (Fig. 4.15) [18,19]. The device replaces the dogbone tensile bar with an injection molded O-ring. A section cut from an extruded thin-walled tube also works as a sample. The device employs a high-torque variable speed motor. A section of very high modulus aircraft cable connects the pulley attached to the motor to the sample. In turn the sample is attached to the load cell. The original device employed a load cell that was rigidly connected to the motor frame and was immersed in the hot silicone oil bath. A modified device uses a torque meter attached to the motor. The operation of the device is quite simple. The polymer O-ring sample is attached to round pins on the aircraft cable and the load cell. The entire assembly is lowered into hot silicone oil, and it reaches the hot oil temperature in about a minute or so. After a few moments, a slight tension is applied to the sample by the motor. The motor is then shut off and the desired motor speed selected. The motor is then switched on and the sample is stretched at constant strain rate. Elongation rates of up to 500%/s or 5 s - 1 have been achieved although rates of 2.5%/s to 25%/s or 0.025 s - 1 to 0.25 s" 1 yield more reliable stress-strain curves.
Clamping Rod
Constant Speed Motor Aircraft Cable
O-Ring in Cross-Section Oil Bath Thermocouples Specimen Load Cell
Figure 4.15 Tensile strain rheometer and O-ring-shaped test specimen [18,19]
The hot creep test is more sensitive than the hot tensile test to changes in polymer character at a given strain level and temperature. The hot tensile test provides a clearer picture for stress-strain behavior at high strain levels. However, hot creep and hot tensile tests do not predict processing conditions necessary for obtaining accurate mold replication. Prediction of sheet performance in practical draw-down situations cannot be obtained from these tests. Neither test system truly replicates the nature of biaxial sheet stretching so common in even the simplest thermoforming process. As a result, recent studies have focused on the development of biaxial stretching laboratory tests that more closely mirror reality. An important aspect of these efforts is to find and define useful material design parameters that are used to better evaluate the performance of a given polymer in a given stretching situation. Other Stretching Tests In addition to hot creep and hot tensile tests, sheet inflation experiments yield important information on biaxial membrane stretching. Two types of inflation devices have been used. The first uses a carefully gridded circular disk that is inflated at constant pressure [20], as shown in schematic in Fig. 4.16. A high-speed video or film camera is used to measure the biaxial stretching rate at the center or pole position of the disk. The results are used to determine constitutive constants in appropriate stress-strain equations, as discussed in Section 4.4. The second uses a long carefully gridded tube of polymer. The ends of the tube are either clamped in cylindrical fittings or pinched shut (Fig. 4.17). Inflation air at a fixed pressure is
Figure 4.16 Schematic of biaxial stretching of disk by air inflation [20]
Figure 4.17 Schematics of biaxial stretching of tube by air inflation. Left figure shows flattened connection to air source. Right figure shows round connection to air source
introduced through a blow pin and the stretching rate in the middle of the tube is measured on high-speed video or film. This now-commercial device is used to obtain constants for constitutive equations [21,22]. And commercial isothermal tenter frame devices are used to determine forces required to biaxially orient thin films of 0.025 in or 0.64 mm or so [24,25].
Temperature-Dependent Viscosity for Amorphous Polymers As noted earlier, once the temperature of an amorphous polymer exceeds its glass transition temperature, the polymer continues to become less and less rubbery and more and more fluid until it is a true liquid. Again, the relationship of stress to strain rate for a purely viscous fluid is: (4.13)
Table 4.3 Temperature Dependency of Shear Viscosity for Several Commercial Polymers [118] Shear rate
Polymer Polymethyl methacrylate (PMMA) Polymethyl methacrylate (PMMA) Cellulose acetate (CA) Nylon 6 Nylon 66 Polyethylene (LDPE) Polyethylene (HDPE) Polystyrene (PS) ABS Polyvinyl chloride, rigid (RPVC) Polyvinyl chloride, flexible (FPVC)
1/Pf (°C)
Trade name
(S-1)
100 27 100 100 100 100 100 100 100 40 100
24 18 32 60 56 85 70 73 65 51 40
Lucite 140 Plexiglass VlOO Tenite Acetate 036-H2 Plaskin Nylon 8206 Zytel 101 NClO Bakelite DYNH Alathon-10 Styron 475 Cyclolac T Geon 8750 Opalon 71329
where |i is a proportionality known as Newtonian viscosity. For polymers, the relationship is usually written as: a = ne(e) • e
(4.22)
where r|e is the strain-rate dependent elongational viscosity. For most amorphous polymers at low strain rates, the viscosity approaches a constant at low strain rates. This is usually written as: Tle(e)-+r|e,oas€^0
(4.23)
1
where r| eo is the zero-elongational rate viscosity . It is thought that the r| eo viscosity of any amorphous polymer at its glass transition temperature is about 1.0 GPa • s. As the polymer temperature increases, the viscosity decreases in an Arrhenius fashion:
^ = "- • exp [!(iH)]
(424)
Usually the Arrhenius activation energy, E6, is determined from temperature-dependent shear viscosity measurements and so is listed as E t . Figure 4.18 shows stressand temperature-dependent shear viscosity for polymethyl methacrylate [26]. Equation 4.24 is also written in an empirical fashion as an Arrhenius-like equation: TIcI = TIe12-CXp[P^(T2-T1)]
(4.25)
where 1/(^ represents "the number of degrees that the polymer temperature must be raised at constant shear rate in order to decrease the viscosity by a factor of 1/e." [27]. Values for the equivalent l/p t coefficient are given in Table 4.3 for several 1
Zero-extensional rate viscosity is the asymptotic elongational viscosity. Zero-shear rate viscosity is the asymptotic shear viscosity. Shear viscosity is easier to measure than elongational viscosity. The elongational viscosity is usually considered to be proportional to the shear viscosity, particularly at zero-state conditions. Since it is the zero-state condition that is most important, it is assumed that this proportionality is in effect in the rest of this section.
Apparent Viscosity, GPa-s
Shear Stress, MPa Figure 4.18 Temperature- and shear stress-dependent viscosity for polymethyl methacrylate, PMMA [26]
polymers. The WLF equation is an alternate to the Arrhenius temperature dependency. It is written as: U T ) = _Cr(T-Tg) % e , o (T g ) C2 + (T-T g ) where C1 and C2 are the WLF constants for a given polymer, Table 3.16. Example 4.2 illustrates the application of these expressions for prediction of temperaturedependent zero-state viscosity. The zero-state viscosity of a polymer at its glass transition temperature cannot be accurately measured. Instead, the values are extrapolated using the Arrhenius-like equation or WLF expression. Example 4.2 The Hypothetical Zero-Strain Rate Viscosity of Polymethyl Methacrylate at Its Glass Transition Temperature From Fig. 4.18, determine the 1 jP^ factor for the molding grade of PMMA. Then, determine the C1 and C2 constants of the WLF equation. Finally, determine the zero-shear viscosity for PMMA at 1050C for each of these equations.
From Fig. 4.18, the zero-shear viscosities at three temperatures are: r|o(270°C) = 310Pa-s r|o(230°C) = 4,400 Pa • s r| o (190°C)= 102,000 Pa -s The Arrhenius-like Equation 4.25 is written as: In[WTi6J = P4(T2-T1) In [102000/310] = 5.80 = p,(270 - 190) = 80 • p, 1/P,= 13.8 Table 4.3 shows a range in values for equivalent 1/P^ from 18 to 24 for shear rates of 27 to 100 s~\ The WLF coefficients are obtained from Equation 4.26: log
r!k, i l l ] = _ C,-(T-T8) LiUo(T8)J
C2+ (T-T8)
0
At 190 C: •.eio[l02«^T,)]=-c^90^, At 230 0 C: •o8l,[4400/,.№-cCfg^ At 270 0 C:
•og.oPIO/WT.)]= - I ' ^ Z These are written as: 5.0086 = A - 85 • C1Z[C2 + 85] 3.6435 = A - 125 • C1Z[C2 + 125] 2.4914 = A - 165 • CJ[C 2 + 165] Eliminating A from the first two and the first and third: 1
8 5 ^ 1 - C " C 2 +125"C2TSS 165-C1 85-C 1 C2 + 165 C2 + 85
1 3 6 5 1 1 3 6 5 1
2
5
Solving each for C 1 : 125 85 1 c f 1.3651 - c i Lc 2 + 1 2 5 - c~T85 J 1 3 6 5 1
„,„
r
f
165
85 I
Eliminating C 1 :
r
165
*J_~\ =
[C 2 +165
C2 + 85J
I" 125
'
L C 2+125
85_] C2 + 85 J
C2 = 347.7 Substituting: C1 = 20.08 These values are compared with C1 = 17.7, C 2 = 52.6 for PMMA from Table 3.16. The value of A = log10 [r|e o(Tg)] is obtained by substitution: 85 C ' > A 85'2Q-Q8 ' - " C 2 T 8 5 - A " 347.7 +85 A = 8.953 or 55 00008866- AA
r|e o(Tg) = 0.897 x 109 Pa • s = 0.897 GPa • s For the Arrhenius-like results, the hypothetical viscosity at T g = 1050C is: rje 105 = 4400 • exp[230 - 105)/13.8] r| el05 = 37.8 MPa • s = 0.038 GPa • s [It is reported that r|e o (T g ) « 1 GPa • s for all amorphous polymers at their glass transition temperatures. It is apparent that the WLF equation yields a viscosity value similar to the expectation. The Arrhenius-like expression does not.] Keep in mind that in thermoforming, stretching is primarily a solid polymer deformation action. The elastic character of the polymer dominates. Nevertheless, the hot rubbery strength of the polymer is frequently compared with its hot melt strength. The actual viscosity value of a polymer is less important than the temperature dependency of the viscosity. If the value of l/p d is very small, the polymer viscosity drops very rapidly with temperature. Since a wide rubbery plateau is sought for thermoforming, polymers with small 1/(3^ values should have narrower forming windows than those with large 1/(3^ values. Examples 4.3, 4.4 and 4.5 illustrate how the zero-state viscosity might be used for thermoforming. Example 4.3 Determination of the Viscosity for Polystyrene in the Thermoforming Window Determine the zero-state viscosity of polystyrene at its lower, average, and upper forming temperatures. Use the Arrhenius-like Equation 4.25. The Arrhenius-like equation is: TWi = 1 V 2 ' exp[P,(T2 - T1)] The relevant temperatures for PS are: T g = 1050C, T L = 127°C, T A = 149°C, T 0 = 182°C. The viscosity of PS at 2100C is 9000 Pa • s and \j% for polystyrene from Table 4.3 is 73.
Tle,i27 = ^ 2 1 0 • exp[(210 - 127)/73] = 28,060 Pa • s 1
IcI 49 = i!e,2io ' exp[(210 - 149)/73] = 20,760 Pa • s
TU.182 = 1Ic2Io • exp[(210 - 182)/73] = 13,210 Pa • s
Example 4.4 Comparison of Polystyrene and ABS Viscosities in the Thermoforming Window Determine the zero-state viscosity of ABS at its lower, average, and upper forming temperatures. Use the Arrhenius-like Equation 4.45. Then compare the results with Example 4.3 for PS. The Arrhenius-like equation is: Tlci = ^,2 * exp[P,(T2 - T1)] The relevant temperatures for ABS are: T g = 1050C, T L = 127°C, T A = 146°C, Tu = 182°C. The viscosity of ABS at 1900C is 43,000 Pa • s and l/|3e for ABS from Table 4.3 is 65. Tlc.127 = Tie,i9o • exp[(190 - 127)/65] = 113,300 Pa • s TIcI46 = 1IcI9O • exp[(190 - 146)/65] = 84,600 Pa • s Tle,i82 = Tle,i9o " exp[(190 - L82)/65] = 48,600 Pa • s ABS has about four times the viscosity of PS across the entire forming window. This implies that the forming forces need to be about four times greater for ABS and that ABS sag should be less of a problem than PS sag. Example 4.5 Predicting the Forming Window From Viscosity Measurements A new polymer is known to have a IJp1 value of 200C. If its viscosity at 3000C is 2,000 Pa • s, determine its approximate forming temperature range. Assume that "best forming viscosity" is 40,000 Pa • s and that the "forming range for viscosity" is a factor of 2. From the information given, the approximate viscosity at the upper forming temperature is about 25,000 Pa • s and that at the lower forming temperature is about 50,000 Pa • s. The Arrhenius-like equation is: 1
Hd = ^U2 ' exp[(3,(T2 - T1)]
Applying this equation three times and solving for the temperatures: 2,000 = 25,000 • exp[(Tu - 300)/20] 2,000 = 40,000 • exp[(TA - 300)/20] 2,000 = 50,000 • exp[(TL - 300)/20] 0
T1J = 250 C, T A = 2400C, T L = 235°C. Potentially, this polymer has a very narrow forming window of 15°C.
E
1
1e1
1
E
W
Stress
2
Figure 4.19 Maxwell-Voigt mechanical analog of linear viscoelasticity [29]
Dynamic Mechanical Testing Dynamic mechanical testing is used to determine the relative importance of the elastic and viscous aspects of polymers [28]. If the polymer response to applied load can be considered as linear viscoelastic, then simple spring-and-dashpot models serve to illustrate the response. The spring represents the elastic or fully recoverable portion of the response and the dashpot represents the viscous or fully dissipative portion of the response. Figure 4.19 [29] is an example of a fourparameter element, having the Maxwell viscoelastic model of a spring and dashpot in series, in series with a Voigt-Kelvin model of a spring and dashpot in parallel. The response of the four-element model to an instantaneously applied constant stress, a, is shown in Fig. 4.20 [30]. When the load is applied in a periodic, sinusoidal fashion, the elastic portion of the model responds instantaneously. The phase angle between the input and response is therefore zero. The phase angle for the purely viscous portion is always TI/2 radians or the viscous portion is always 90° out of phase (Fig. 4.21) [31]. The four-element model, representing linear viscoelastic response, shows a response with a phase angle that is somewhere between 0° and 90°. The sinusoidal strain displacement of the polymer is given as: a = ao sin (©9)
(4.27)
Stress
Time
Strain
Retarded Elastic Strain Viscous Flow
Permanent Set Elastic Strain Time Figure 4.20 Response of Maxwell-Voigt mechanical analog of Fig. 4.19 to step-change in applied tensile load [30]
where a o is the amplitude of the displacement, co is the frequency, and 0 is time. The response to the strain displacement is usually written in complex terms as: T* = T ' + i • T"
(4.28)
where T* is the complex stress, T' is the real component of the stress and x" is called the imaginary component of the stress. Four functions are associated with polymer response to sinusoidal load.The complex modulus, G* is given as: G* =
(T*/OC) =
(T'/a) + i • (x'Voc)
(4.29)
This is also written as: G* = G' + i • G"
(4.30)
The real or in-phase portion of the modulus, G', is called the storage modulus. It represents that portion of the inputted energy that is elastically recovered. The imaginary or out-of-phase portion of the modulus, G", is called the loss modulus. It represents that portion of energy that is dissipated. The ratio of the loss modulus to storage modulus is the loss tangent, loss factor or tan S. It is written as: (4.31)
Y
COt
Applied Sinusoidal Strain GY' cot
Elastic Element Response ricoY1
cot
Viscous Element Response Figure 4.21 Response of elastic and viscous portions of Maxwell-Voigt mechanical analog to sinusoidal tensile load [31]
At constant temperature, polymer response changes with changing frequency. At very high loading frequencies, co-» large, most polymers appear glassy. Thus, the storage modulus, G' is large, the loss modulus, G" is small and tan 8 is small. At very low loading frequencies, oo-> small, many polymers appear rubber-like. Thus, G' is small, G" is small, and tan 5 is moderately small. At intermediate frequencies, the storage modulus, G' is decreasing with increasing frequency. The loss modulus, G' on the other hand, goes through a maximum. The value of tan 6* also goes through a maximum, as shown in Fig. 4.22 [32]. This analysis holds for constant frequency, changing temperature conditions as well. At very low temperatures, polymers appear glassy. At elevated temperatures, polymers appear rubbery. At intermediate temperatures, polymers exhibit loss in rigidity and increased viscous dissipation. The test used to obtain the temperaturedependent complex modulus is called dynamic mechanical analysis or thermomechanical analysis, DMA or TMA [33]. Typically, only G', the storage modulus and tan 5, the loss factor are measured. G", the loss modulus is obtained from Equation 4.31. Figure 4.23 shows classic TMA curves for polycarbonate [34]. As is expected, 30% glass-reinforced PC has a much greater modulus than that for unreinforced PC. However, at or about 1400C, both materials experience rapid drops in G'. Simultaneously, tan 5 for both polymer species shows a rapid increase, indicating a
Loss and Storage Moduli, GPa
Rubbery
Viscoetastic
Glassy
Frequency, O), Log Scale Figure 4.22 Frequency-dependent response of elastic and viscous portions of Maxwell-Voigt mechanical analog to applied sinusoidal tensile load [32]. The loss tangent, tan 5 = G"/G'
PC
Loss Factor
Shear Modulus, G1, MPa
30% GR PC
PC
30% GR PC
Temperature,0C Figure 4.23 Temperature-dependent shear modulus and loss factor for unreinforced and 30% glassreinforced polycarbonate, PC. Figure redrawn from [34] and used by permission of copyright owner
rapid increase in G". In a word, in this temperature range, the polymer is becoming more viscous and less elastic. The glass transition temperature of PC is listed as 1500C. Figure 4.24 shows the effect of molecular weight on transitions for PS [35] and Fig. 4.25 shows the effect of crystalline level on transitions for polyethylene [36].
4.4
Stress-Strain-Rate of Strain—Theory
The time-dependent elastic nature of polymers at the thermoforming temperature is understood in terms of solid or fluid behavior. There are two acceptable ways of including time dependency in the typical stress-stain analysis of a solid. One method is to alter conventional rheological stress-strain rate viscosity models to include solid-like behavior at high strain rates [37]. The other is to include some time dependent factor in a typical stress-strain relationship of a solid. Both are simplified approaches to the general cases of viscoelastic mechanical analyses [38-40]. The common methods for determining polymer strain-strain rate response to applied stretching stresses include extensional rheometry [37,41], biaxial or bubble inflation of a tube or sheet [21-23,42], biaxial stretching of a blown film [43], free blowing of a preform [44], uniaxial stretching of fibers [41], and creep experiments [9,17,45]. Creep experiments are the easiest tests to conduct. These tests yield information on polymer response to constant low-level load at isothermal conditions [9,14,45-47]. Rate-dependent terms are considered negligible. At room temperature, many polymers follow a near-ideal strain-hardening ductile material creep rupture response to constant load: o = a0 exp(m • e) = ao • em • X
(4.32)
where a is instant stress, a o is the initial stress, e is the elongational strain, and m is the straining-hardening factor. If the polymer is ideally ductile, m = 1. It has been shown that 0.92 < m < 1.6 for many polymers at strain-rate levels of less than 0.0333 s"1, Table 4.4 [47]. At high loading levels and/or elevated temperatures, creep rates are so high that measuring and conditioning errors make accurate interpreta-
Table 4.4 Strain Hardening Constants for Several Polymers1 a - a o e me Polymer
POM, Delrin POM, Delrin PA-66, nylon mPPO, Noryl PVC PE PP PE PTFE PTFE 1
Strain rate
From plot [47]
(S-1)
(MPa)
(lbf/in2)
0.00027 0.0027 0.0027 0.0027 0.0027 0.0333 0.0133 0.0333 NR NR
67.9 68.95 49.6 48.3 38.6 7.93 12.93 13.5 10.34 12.41
9850 10000 7200 7000 5600 1150 1875 1960 1500 1800
Adapted from [47], by permission of copyright owner NR = Not reported
From least squares m 1.12 1.19 0.919 1.061 0.974 1.182 1.103 1.182 1.58 1.203
(MPa)
(lbf/in2)
65.8 68.3 51.5 48.8 38.0 8.26 13.0 13.4 10.3 12.51
9539 9910 7468 7079 5518 1198 1889 1943 1495 1815
m 1.312 1.257 0.894 1.06 1.029 1.144 1.102 1.169 1.603 1.203
MFl = 15 MFI = 9 and 26
Loss Factor
Shear Modulus, G', GPa
MFI = 15
MFI = 9 and 26
Loss Factor MFI = 15
Temperature,0C Figure 4.24 Temperature-dependent shear modulus and loss factor for two molecular weights of polystyrene, PS. Figure redrawn from [35] and used by permission of copyright owner
tion difficult or impossible [9,17]. Time-dependent behavior has been added to the creep model as [48-50]: G = G0- f(e) • g(G)
(4.33)
For amorphous polymers such as PMMA and HIPS, at normal forming temperatures, the data favor an ideal elastic or non-strain-hardening, model, Table 4.5 [49]: a = GO • em • 6n
(4.34)
HIPS appears to have little time-dependent behavior, with n « 0. On the other hand, ABS/PVC and PVC exhibit substantial strain-hardening at processing temperatures (Fig. 4.26) [17]. Recent studies on polypropylene show that the time-dependent coefficient can be either positive or negative, depending on the nature and size of spherulites (Fig. 4.27) [51]. So long as the polymer deforms uniformly during uniaxial stretching, its isothermal ultimate tensile strength is obtained from: (4.35)
Dynamic Shear Modulus, G1, GPa
UHMPE
Loss Factor
HDPE
LDPE
LDPE HDPE UHMWPE
Temperature,0C Figure 4.25 Temperature-dependent shear modulus and loss factor for three types of polyethylene. Figure redrawn from [36] and used by permission of copyright owner
where ef is the true strain at fracture. If m « I5 as is the case for most polymers in Table 4.3, T* « ao. As noted in Figs. 4.9 and 4.10, polymer tensile strength decreases with temperature. Tensile strength values for most polymers at normal vacuum forming temperatures are in the 0.07 to 0.7 MPa or 10 to 100 lbf/in2. For truly elastic polymers, the classic temperature-dependent stress-strain curves usually appear as shown in Fig. 4.28. At low temperatures, the polymer is purely elastic. Its modulus is very high and its ultimate strain is very low. As the temperature increases, a small amount of plastic deformation occurs before the polymer breaks. The modulus decreases with increasing temperature. At a slightly higher temperature, the polymer may show a distinct yielding. The higher strain regions beyond the yield point are characterized by localized drawing or necking.
Table 4.5 Stress-Strain Behavior of Two Plastics in Biaxial Extension1 -.
G
=
_
c mnn
CJQE
U
Polymer
n
m
PMMA HIPS
-0.05 -0.33
1.0 1.1
1
Adapted from [49], with permission
Strain, %
Temperature = 116°C
Time, s Figure 4.26 Temperature-dependent strain rate for rigid polyvinyl chloride, RPVC [17]
Growth Function > 1
Viscosity, GPa*s
Growth Function = 1
Growth Function < 1
Time, s Figure 4.27 Schematic of time-dependent viscosity for polyolefin polymers that exhibit various strain rate effects [51]
Increasing Temperature
Stress
Break
Yield Point
Elongational Strain Figure 4.28 Characteristic temperature-dependent stress-strain curves
Not all polymers neck. As the temperature increases, the ultimate elongation increases rapidly. There is an upper limit to the temperature of course. When the polymer cannot sustain any applied force without extensive plastic deformation and fracture, it is considered a fluid. Figure 4.29 shows the interrelationship between the polymer response to applied load and the forming window. As expected, the amount of force required to draw the polymer sheet to a given extent is highest at the lower forming temperature. This implies that the depth of draw or areal draw ratio increases with increasing
Stress
Increasing Temperature
Forming Region
Elongational Strain Figure 4.29 Characteristic overlay of forming temperature on temperature-dependent stress-strain curves
Viscosity, MPa»s
Strain Rate = 1.15 s
Time, s Figure 4.30 Strain-rate dependent extensional viscosity for high-density polyethylene, HDPE, at 18O0C. Figure adapted from [37]
temperature. At the upper forming temperature, draw uniformity gives way to localized flow and the areal draw ratio then abruptly decreases with increasing temperature. When the processing temperature is substantially above Tg for an amorphous polymer or Tm for a crystalline one, the polymer is a fluid. Behavior under load is correctly considered in terms of elongational viscosity. Isothermal elongational viscosity usually increases with increasing time (Fig. 4.30). At very low strain rates, r|eoc0n, where n < 1, Table 4.6 [49]. Isochronous biaxial elongational viscosities of olefins at forming temperature and very low strain rates of 0.000015 to 0.006 s" 1 are inversely proportional to strain rate [46]. As the strain rate increases, the apparent viscosity deviates from the asymptote at earlier and earlier times. As seen in Fig. 4.31 [17], for LDPE at 2 seconds, the polymer has a viscosity about 15 times greater at a strain rate of e = 1 s"1 than at e = 0. At this same rate at 10 s, the elongational viscosity is about 1000 times greater. In short, the polymer is rapidly becoming solid-like in its response to applied load. Example 4.6 continues this analysis. In terms of true stress and true strain, e = e • 0, the data show an initial linear region, a yield region, then strain hardening and fracture (Fig. 4.32) [37]. In other words, both amorphous and crystalline polymers behave as elastic liquids at typical thermoforming temperatures [52]. The extent of elasticity is important in determining the formability of the polymer in question.
Table 4.6 Biaxial Extensional Viscosities for Olefins at Very Low Strain Rates1 Polymer PP, 0.003 in Unoriented2 PP, 0.0015 in Unoriented PP, 0.003 in Ethylene-propylene copolymer, 0.003 in 1
Viscosity, MPa-s
2
(XlO-6S-1)
Viscosity (GPa • s)
2310 196 19.1 2260 219 15.1 5110 262 28.8 181 24.3
4.99 71.6 762 6.51 50.9 719 28.1 496 4150 890 6310
Strain rate, e
Adapted from [49], with permission Least squares fit, r) = 0.015/e
Strain Rate = 1.0 s"1
Time, s Figure 4.31 Comparison of experimental and theoretical strain-rate dependent extensional viscosity for low-density polyethylene, LDPE. Solid lines are theory. Dashed lines are experiment. Figure adapted from [39], and used with permission of John Wiley and Sons, Inc.
Example 4.6 Time-Dependent Strains for LDPE From Fig. 4.31, at a strain rate of ' £= 0.1 s~\ determine the time required to achieve the same level of stiffness as is achieved for e= 1 s"1 in 2s. Repeat for a strain rate of e=0.01 s-L From Fig. 4.31, the stress at e = 0.1 s" 1 is about 15 times greater than that for e = 0 at 12 s. The stress at e = 0.01 s" 1 is about 15 times greater than that for e = 0 at about 100 s.
Stress
Fracture Strain Hardening Yield Linear
Figure 4.32 Schematic of various stages in the straining of a ductile polymer. Figure adapted from [37], and used with permission of John Wiley and Sons, Inc.
True Elongational Strain
Elasticity—A Rationalization When a thermoformed shape is placed in an environment having a temperature substantially greater than Tg and a temperature typically approaching that of its forming temperature, the shape returns to a flat sheet. A recovery rate of 90% in less than 0.002 s has been measured [53]. It is argued therefore that thermoforming is a solid phase deformation process. A contrary argument [40,54] is that this response is proper for a highly strained elastic liquid as well as a purely elastic membrane. Sheet stretching behavior is best viewed in terms of relative orders of magnitude of process times and polymer memory. Consider the simple series spring-and-dashpot model of a linear viscoelastic material, the Maxwell fluid (Fig. 4.33) [55]. If this simple model is strained to a fixed value, e = eo, and e = 0, the Maxwell element response is: a = ao-exp[-E6/Tie]
(4.36)
where E is the tensile or elastic modulus of the spring, r|e is the elongational viscosity of the dashpot and a o = E • eo. The retardation time, 9p = r|e/E, is a characteristic of the polymer. Creep data are used to obtain values for this retardation time. At low strain rates, e « 0 , the tensor stress-strain-rate-of-strain elastic liquid equation reduces to a simple relationship between stress and retardation [56]: a = 6G9p • e • [1 - exp( - 9/9p)]
(4.37)
For long times, 9 -» oo and: a-+6G9 p -e = ^i-e
(4.38)
The model yields the Trouton-Newton form for a purely viscousfluid.At high strain rates, on the other hand, e-*oo: a -> G | 7 I + ^V exp(2e9) - ^ • exp(4e9)l
(4.39)
The term 5 is proportional to the ratio of second to first normal stress difference of the polymer and its value is always negative or zero [40]. The model predicts that
Maxwell Model Stress Off
Strain
Stress On Elastic Element Viscous Element Voigt Model
Strain
Time
Stress Off Stress On
Elastic Element Viscous Element Time Figure 4.33 Responses of the Maxwell series mechanical analog of polymer linear viscoelasticity [top] and Voigt parallel mechanical analog of polymer linear viscoelasticity [bottom] to instantaneous change in applied tensile load
under constant deformation rate, stress increases exponentially with time. In other words, at high strain rates, the rate of stress increase is greater than the rate of internal material stress relaxation. The polymer therefore behaves as if it is an elastic solid [40,57]. It is highly unlikely that constant biaxial deformation can be sustained or is desirable in conventional thermoforming. Deformation rates have been measured that, for the most part, decrease with time [40]. For constant velocity stretching, deformation rate decreases with time [40]. This helps stabilize the initially rapidly growing stress. As noted, retardation times are obtained from creep experiments. Usually these values decrease monotonically with increasing temperature, as seen schematically in Fig. 4.34. discontinuity in the retardation time curve for PP occurs at 1100C or 2300F [45]. This is attributed to a deformation mechanism change on the molecular level. The importance of creep data in parts design has produced a substantial library of information [58]. If temperature-dependent retardation times are not available for a given polymer, approximate values can be obtained at any temperature [48] from: Gp(T)=
§m
(4 40)
-
where r\o is the zero-shear viscosity and G is the tensile modulus or the initial slope of the stress-strain curve. If the processing time is less than 0p by a factor of about 10, the material behaves as an elastic membrane. Snap-back thermoforming depends on elastic membrane response, for instance. If the processing time is greater than 0p by a factor of about 10, the polymer should behave as an elastic liquid. Pressure
Logarithmic Retardation Time Figure 4.34 Characteristic temperature-dependent retardation time for linear viscoelastic polymers
T
m
Temperature
forming, coining, and high surface replication depend to some degree on plastic or anelastic polymer response. Example 4.7 illustrates some of these aspects. As a point of reference, instantaneous stretching rates of 2.4 s~l are recorded for 0.100 in or 2.5 mm HIPS sheet [59] and rates up to 26.8 s" 1 are reported for 0.060 in or 1.25 mm PP [60]. Example 4.7
Stretching Rate and Retardation Time for ABS
Determine the retardation time for ABS at 1200C. The tensile modulus of ABS at 1200C is 80 lbf/in2 = 0.55 MPa. The viscosity for ABS is obtained from Example 4.4: Tle,i2o = 1Ie5I90 ' exp[(190 - 120)/65] = 126,200 Pa • s The retardation time, 0p(120°C) = 126200/(0.55 x 106) = 0.23. If the stretching rate is substantially greater than l/0 p = 4.4 s" 1 , ABS should behave as an elastic solid. If the stretching rate is substantially less than 4.4 s" 1 , ABS should behave as an elastic liquid.
Strain Energy Function1 Principal stresses in elastic solids are defined in terms of the strain energy function, W:
«-w
(4 41)
-
The stress-strain analysis that follows is applicable to large elongational levels. As a result, the analysis is sometimes called hyperelastic analysis, in contrast with linear models used to describe elastic solid response to low elongation levels typically found in structural analysis.
where X{ is the extension ratio in the ith direction (i = 1,2,3). 9W is the incremental amount of work done by the solid when it is stretched an incremental amount dX under stress, a. In general, the strain energy function is written in terms of three principal invariants of the Cauchy strain tensor [40,45,61], as: W = W(I9II9III)
(4.42)
where: I = X2 + Xl + Xl
(4.43)
H = V 2 + K2 + K2 2
2
III = X -X -X
(4.44)
2
(4.45)
A stress-strain energy expression is written in terms of these invariants as: /6WVdI \
/6W\/6II\
/8WV8III\
,A
Ars
F o r a n incompressible solid, X1 -X2 -X3 = 1, o r I I I = 1. T h e last t e r m of E q u a t i o n 4.46 is zero. F o r uniaxial stretching, X1 = X, X2 = X3 = X~l/2. Therefore, this e q u a t i o n is written as: < * - H ) [ < £ H © ] In this equation, <JX is the tensile stress and a is the force per unit area of unstrained cross-section. For equal biaxial stretching, X1 = X2 = X, X3 = X~2. The equation is written as:
The bracketed terms in Equations 4.47 and 4.48 represent the specific elastic solid response, in this case polymeric response, to applied load. The exact form for W(IJI) depends to a great degree on curve-fitting elongational data. Several models follow.
The Rivlin Form for the Strain Energy Function Fifty years ago, the following simple power-law form for W was proposed, to predict elongational response of rubber to stress [62,63]: W(IJI) = X QJ (I - 3)1' (H - 3 ^
(4.49)
The neo-Hookean solid yields one of the simplest forms for W: W = 0^(1 - 3 ) = C10(I - 3 )
(4.50)
The second strain invariant is usually added in one of several ways. The Rivlin-Saunders1 version is the most general form [64]: 1
This is sometimes just called the Rivlin model.
W = Qj(I-S)H-F(II-B)
(4.51) 1
The Mooney version assumes a linear function for F(II) : W = C 0 1 (I-3)+ C 10 (II-3)
(4.52)
Other Rivlin-type forms are found in Table 4.7. Representative strain energy function coefficients for several polymers are given in Table 4.8. The uniaxial and biaxial forms for the elastic stress-strain equation are obtained by differentiating the W-function and substituting into Equations 4.47 and 4.48, respectively. Consider the simple Mooney version. 9W/9I = C01 and 9W/9II = C10. The Mooney stress-strain functions for uniaxial and equal biaxial extension are:
aX = (^2 - i y ^2 • C01 + ^ • C10J GX
= ( ^ - ^ V P • C01 + 2 • ^2 • C10]
(4.53) (4.54)
These equations are used to curve-fit rubbery elastic sheet deformation, and C01 and C10 are the curve-fitting constants. Further, since stress-strain relationships are temperature-sensitive, C01 = C01(T) and C10 = C10(T). In the limit, as the strain goes to zero, the constants are defined in terms of an elastic modulus [59]: E 9W 9W
6 = ^r + 9ir
(4 55)
I = C 0 1 + C10
(4.56)
-
For the Mooney form for W:
For the Schmidt model, Table 4.7, E/6 = C01, where the prime denotes a different value for the first constant [59,131,132]. For HIPS and PS, predicted modulus values range from 427 to 1192 MPa or 62 to 173 lbf/in2. Measured values range from 310 to 3900 MPa or 45 to 566 lbf/in2, with errors ranging from -100% to 4-50%. If the temperature dependency of the polymer modulus is known or is accurately measured, a good approximation of the temperature dependencies of the strain function coefficients can be obtained. For many polymers, 9W/9I»9W/9II [69]. For the Mooney model, as an example, C01 » C10. The curves are approximated best with the new-Hookean model (Fig. 4.35). For vulcanized natural rubber, the value for C10 is about 0.05 to 0.15 times the value for C01 [70]. If C01 = 0, C10 equals the elongational, tensile or elastic modulus, G. The neo-Hookean model works best at low levels of deformation, at or just above the linear viscoelasticity region [59,71]. The Schmidt, Mooney and higher order versions of the Rivlin model work best at very high levels of deformation. Schmidt recognized that although his sheet was being deformed rapidly to large deformation, it was not isothermal and was not being deformed at a constant rate. Funt, on the other hand, correlated PP isochronous creep data best with C10 = 0 [45]. 1
This is sometimes called the Mooney-Rivlin model.
Table 4.7 Strain Energy Density Forms for Polymers and Elastomers Name
Form
Material
Source of data
Comments
Neo-Hookean
W = C 10 (I-3) W = C10(I -3) + C01(II -3)
Funt Schmidt
W = C01 (II-3) W = C10(I -3) + C02(II -3)2
Treloar [63] Williams [65] Mooney [66] Treloar [63] Schmidt [59] Funt [5] Schmidt [59]
Uniaxial stretching
Mooney
Natural rubber PMMA Vulcanized natural rubber HIPS PP HIPS
Mooney-Rivlin Three-parameter Signiorini
W = C10(I -3) + C01(II -3) + C 11 (I-3) (II-3) W = C 1 0 (I-3)+ C 01 (II-3) + C 20 (I-3) 2 W = C 1 0 (I-3)+ C 01 (II-3) + C11(I - 3) - ( H -3) + C20(II -3)2
PVC
Warnecke/Frankenhauser [67]
Creep Bubble inflation (gross) Uniaxial tensile
EPDM
Warnecke/Frankenhauser [67]
Uniaxial tensile
PVC, EPDM
Warnecke/Frankenhauser [67]
Uniaxial tensile
Third-order
Uniaxial stretching
Table 4.8 Typical Strain-Energy Function Coefficients for Rubbery Solids C 1 = C 10 = 9W/SI
C2 = C01 = ew/en C 3 = C 02 - 2(6W/8II) • (II - 3) C2 (MPa)
C 3 x 106 (MPa)
Source Comments
Polymer
Temperature C 1 (0C) (MPa)
HIPS HIPS HIPS Vulcanized Natural rubber PP Cellulose acetate
123.31 124.7 124.4 25.0
0.0758 0.08598 0.14445 0.1618 0.01472
0.001179] 0.001331 f [68] 0.002234J [63]
A=165-T NR
0.0 0.1236
3400
0.080 • A
[45] [68]
No representative values for Mooney C2 given Data on rubber, by Rivlin and Saunders Creep data is source No temperature given, C3 value seems high
1
About 29°C higher at pole than at edge Average value. Range is 0.010 to 0.022. Value decreases with increasing value of II NR = Not reported 2
Strain Rate = 2.5 min "•
Figure 4.35 Tensile stress-strain behavior of polymethyl methacrylate, PMMA, at 1600C. Theory assumes tensile modulus =130 lbf/in2 or 0.9 MPa and Mooney-Rivlin model with C2 = 0. Figure adapted from [69], and used with permission of Ellis Horwood Ltd., copyright owner
Theory
The Ogden Form for the Strain Energy Function It is apparent that the more constants that are available for curve-fitting, the more accurate the model will be in imaging the data. Figure 4.36 compares several Rivlin-type models with experimental data on PVC and EPDM [72, 129-130]. The agreement with experimental data is only satisfactory, even with a three-constant model. Ogden [61,73-75] proposed replacing the general Rivlin strain energy function model, Equation 4.49, with:
Stress, MPa
Model 1 Model 2 Model 3 Experimental
Compression
Tension
Strain, % Figure 4.36 Comparison of experimental stress-strain data with several types of Rivlin constitutive equations. Figure adapted from [72]
(4.57)
Here ocn and [In are the Ogden curve-fitting constants. Although m is unbounded, its value is practically restricted to no more than 3, thus yielding 2, 4 or 6 constants. It has been shown that bubble dynamics are stable for n = 1 when Oc1 > 3. When n = 2, (X1 = 2 and oc2 = —2, the result is the Mooney model (Equation 4.52). Although the Ogden model is based on the strain energy function relationship to principal invariants, the values of ocn are not restricted to integer values, as with the Rivlin version. There is some theoretical justification for the integer values of ocn [63,76]. However, the primary justification for the Rivlin version of a sum of principal invariant effects on the strain energy function is "[a] considerable simplification of the theory..." [77]. Certainly if the linearized Rivlin model is acceptable, the semi-empirical Ogden model is also acceptable.
Viscoelastic Models Models for viscoelasticity are much more complex than elastic models. Most models employ coordinates that translate, rotate and distort with the fluid element under stress. As noted above, Equations 4.33 and 4.34 describe one simple way of including time-dependent polymer properties with traditional stress-strain relationships [48-50]: (4.33) or: (4.34)
Correctly, the constitutive equation for a viscoelastic fluid must contain the concept of an imperfect or fading memory [78]. The general integral form for fading memory viscoelasticity is [79]: re CT(9) =
n(0 - 9') h(I,II) B(9,9') d9'
(4.58)
Jo where JLX(0 — 6') is the relaxation factor or memory function: p.(9 - 9') = Z ^ exp[-(9-9')/XJ
(4.59)
i = i ^i
and G1 and X{ are material parameters. h(I,II) is a damping function of the two strain invariants, usually written as the Wagner form [80]: h(I,II) = [1 + a y ( I - 3 ) - ( I I - 3 ) ] - 1 / 2
(4.60)
In biaxial stretching, h(I,II) is written as: h(e) = [a exp(2e) + (1 - a)exp(me)]-{
(4.61)
where e(0) = In L(O), a = exp( — 2eo), and eo and m are measured constants for a given polymer. L(O) is the stretch ratio, related to time 0'. B(0,0') is the Finger strain tensor for deforming coordinates [81]. Temperature is included in the G1 material parameters as: G1(T) = G1(T0) • exp[ - P(T - T0)]
(4.62)
where T 0 is a reference temperature and p is an Arrhenius-like parameter. The K-BKZ constitutive equation is used to describe the biaxial deformation of a viscoelastic sheet [82,83,119-123]. For biaxial plane stretching, the principal stresses in the i = 1,2 directions are given as: CJ11 =
fe
|4.(9 - 9') • h(e) • [Lf(9,9') - L|(9,9')] d9'
Jo + h(e(9)) • [L?(9) - L|(9)] • P *i(9 - 9') d9' J-OO
(4.63)
where L1(O9O') is the stretch ratio at time 0 related to time 0'. The K-BKZ model is used to shape the time-dependent elongational viscosity curves of the type shown in Figs. 4.26 and 4.30. Typically, only the first term of the memory function is needed: ji(9 - 90 = ^ exp[ - (9 - 90A]
(4.64)
A,
This simplifies Equation 4.63 and allows strain recovery experiments to be used to obtain the necessary parameters [84].
Next Page
As will be seen in Chapter 9, the viscoelastic characteristics of polymers are secondary to their pure elastic characteristics when predicting wall thickness variation in thermoforming1.
4.5
Available Stress-Strain Data
Stress, 1000 lbf /in2
Although there is a plethora of models to predict large deformation of solid and viscoelastic membranes, there is a dearth of temperature-dependent stress-strain-rate of strain data. This section records some of the available data. Typical room temperature data are shown in Fig. 4.37 [87]. The relationship between creep data and stress-strain curves is shown in Fig. 4.38 [88]. Typically, tensile strain or sample elongation is determined as a function of time for a given load or stress. When the data are replotted in terms of stress and strain, time is the parameter and the data are referred to as isochronous stress-strain. Figures 4.39 [89], 4.40, 4.41, and 4.42
PMMA
PA-6 PC ABS
PP HDPE PUR LDPE
Strain, % Figure 4.37 Room-temperature stress-strain data for several thermoplastics [87]
1
Wineman [85,86] notes that if the membrane is an elastoviscous solid under fixed applied pressure, the membrane dimensions eventually reached fixed equilibrium values. If it is a viscoelastic fluid, on the other hand, the polymer will continue to creep. Since practical processing times are usually very small when compared with viscoelastic material times, longterm fluid effects are usually ignored in all but certain plug-assist conditions.
Previous Page
As will be seen in Chapter 9, the viscoelastic characteristics of polymers are secondary to their pure elastic characteristics when predicting wall thickness variation in thermoforming1.
4.5
Available Stress-Strain Data
Stress, 1000 lbf /in2
Although there is a plethora of models to predict large deformation of solid and viscoelastic membranes, there is a dearth of temperature-dependent stress-strain-rate of strain data. This section records some of the available data. Typical room temperature data are shown in Fig. 4.37 [87]. The relationship between creep data and stress-strain curves is shown in Fig. 4.38 [88]. Typically, tensile strain or sample elongation is determined as a function of time for a given load or stress. When the data are replotted in terms of stress and strain, time is the parameter and the data are referred to as isochronous stress-strain. Figures 4.39 [89], 4.40, 4.41, and 4.42
PMMA
PA-6 PC ABS
PP HDPE PUR LDPE
Strain, % Figure 4.37 Room-temperature stress-strain data for several thermoplastics [87]
1
Wineman [85,86] notes that if the membrane is an elastoviscous solid under fixed applied pressure, the membrane dimensions eventually reached fixed equilibrium values. If it is a viscoelastic fluid, on the other hand, the polymer will continue to creep. Since practical processing times are usually very small when compared with viscoelastic material times, longterm fluid effects are usually ignored in all but certain plug-assist conditions.
Strain
Creep Curve
Strain
Time of Load Time Diagram
Stress
Stress
Isochronous Stress-Strain Curve
Time of Load Figure 4.38 Interrelationship between isochronous stress-strain, creep and time-dependent stress [88]
[90-92] show isochronous stress-strain curves for amorphous RPVC and PMMA, and crystalline HDPE, LDPE and PP, respectively. These curves are for temperatures below Tg for the amorphous polymers and Tm for the crystalline ones. Stress-strain curves at elevated temperatures for several polymers are given in the attached figures: • • • • • • • • • • • • •
SAN in Fig. 4.43 [93], P homopolymer in Fig. 4.44 [94], PMMA in Fig. 4.45 [95], PET in Fig. 4.46 [96], ABS in Fig. 4.47 [97], PS in Fig. 4.48 [98], ASA terpolymer in Fig. 4.49 [99], PTFE in Fig. 4.50 [100], FEP in Fig. 4.51 [101], Nylon 6 or PA-6 in Fig. 4.52 [102], Nylon 66 or PA-66 in Fig. 4.53 [103],' PBT in Fig. 4.54 [104], and Polyimide in Fig. 4.55 [105].
As is apparent, most of the data are for engineering and high performance polymers. There are few data for commodity polymers such as PVC and PE. Unfortunately, commodity polymers make up the bulk of the polymers thermoformed today.
Temperature = 400C
Temperature
Temperature = 20°C PMMA Flow Zone
Flow Zone
RPVC
Strain, % Elongation, % Figure 4.39 (left) Time-dependent isochronous stress-strain for rigid polyvinyl chloride, RPVC. (right) Polymethyl methacrylate, PMMA. Figures redrawn from [89] and used with permission of copyright owner
Stress, MPa
HDPE
Failure Curve
Elongation, %
Stress, MPa
Figure 4.40 Time-dependent stress-strain curve for high-density polyethylene, HDPE at 65°C. Figure redrawn from [90] and used with permission of copyright owner
LDPE
Elongation, % Figure 4.41 Time-dependent stress-strain curve for low-density polyethylene, LDPE at 400C. Figure redrawn from [91] and used with permission of copyright owner
Stress, MPa
PP
Failure Curve
Elongation, % Figure 4.42 Time-dependent stress-strain curve for polypropylene, PP at 1100C. Figure redrawn from [92] and used with permission of copyright owner
Stress, MPa
SAN
Elongation, %
Figure 4.43 Temperature-dependent stress-strain curves for SAN. Figure redrawn from [93] and used with permission of copyright owner
Stress, MPa
PP Homopolymer
Strain Rate = 0.025 s~1
Elongation Figure 4.44 Temperature-dependent stress-strain curves for polypropylene, PP, homopolymer [94]
The method of fitting a model to the stress-strain data depends on the method used to obtain the data [106,124-128,133]. It is apparent that fitting uniaxial data with a neo-Hookean model is substantially easier and less arduous than fitting nonuniform biaxial data with a 4- or 6-constant Ogden model.
Sensitivity of Models Two aspects of polymer response to applied load remain for discussion: •
The first deals with the sensitivity of the values of the curve-fit constants for any model to stress-strain prediction and then to the variation in wall thickness of the formed part. This will be addressed in Chapter 9 on the design of thermoformed parts.
Stress, MPa
PMMA
Elongation, % Figure 4.45 Temperature-dependent stress-strain curves for polymethyl methacrylate, PMMA. Figure redrawn from [95] and used with permission of copyright owner
•
The second deals with the accuracy required of the models in the prediction of wall thicknesses of production quality thermoformed parts. This will be addressed in Chapter 10, on production quality control.
Obviously, if the day-to-day forming process conditions are not under control, the accuracy of wall thicknesses of formed parts will be poor. As a result, substantial effort to achieve great accuracy in the prediction of wall thicknesses is unwarranted. However, even with the most carefully controlled forming operation, it appears that no single rubbery solid model can describe the behavior of a polymer sheet undergoing nonisothermal high-speed, large scale deformation. Some guidelines are obtained, however, by beginning with the simplest model, the neo-Hookean model, for illustration.
4.6
The Importance of Polymer Material Properties1
A typical thermoforming process applies near-instantaneous, near-constant differential pressure to the rubbery sheet to deform it. If the pressure is insufficient or if the 1
In [135], this section was titled "A Material Parameter, (J)(T)". Although 4>(T) was identified as a material parameter related to the derivative of the strain energy function with respect to the first principal invariant of the Cauchy strain tensor, the analysis that followed used the neo-Hookean version of this derivative. More importantly, the relationship between <\>(T) and the Mooney constants was not clear.
Stress, MPa
PET
Strain Rate = 0.025 s ~1 Figure 4.46 Temperature-dependent stress-strain curves for polyethylene terephthalate, PET [96]
Elongation
sheet is not soft enough, the sheet will not distort fully to fill the mold or will not replicate the mold details. Earlier sections focused on the basic polymer response to applied load. There is a logical solid mechanistic approach to development of the parameters that are used to determine proper processing conditions for a given material [69,107]. As seen in Appendix 4.1, the neo-Hookean relation between the elongational or tensile elastic modulus, G, and the inflation pressure, P, for a uniform disk of radius a and initial thickness ho, forming a dome of 5 units above the horizontal is [107]: Pa 4C10(8/a) 2h o ~l+(5/a) 2
4G(5/a) l+(5/a) 2
l
"
;
The modulus G is temperature-dependent, G(T), and has the units of MPa or lbf/in2. G(T) is determined by heating a sheet of radius a and initial thickness ho to a fixed, uniform temperature, then measuring the extent of bulging, (5/a), as a function of applied pressure. The analysis is dependent on all neo-Hookean assumptions and is inaccurate at the clamped sheet edge [107]. If the deforming sheet has a constant thickness everywhere:
Stress, MPa
ABS
Elongational Strain, % Figure 4.47 Temperature-dependent stress-strain curves for ABS. Figure redrawn from [97] and used with permission of copyright owner
Stress, 1000 lbt /in2
PS
Strain, % Figure 4.48 Temperature-dependent stress-strain curves for polystyrene, PS. Figure redrawn from [98] and used with permission of copyright owner
Stress, MPa
ASA T e r p o l y m e r
Elongation, % Figure 4.49 Temperature-dependent stress-strain curves for ASA terpolymer. Figure redrawn from [99] and used with permission of copyright owner
V = [l+(5/a)- 2 ]
(4.65)
^ = [l+(5/a)2]
(4.66)
At a maximum value of ^ = 2.59, (5/a)=1.26, and an approximate relationship between the applied pressure and the neo-Hookean modulus becomes:
pmax-y3-G(T)(v)
(4 67)
-
Unfortunately, experiments indicate that biaxially stretched sheet does not have constant thickness, a fundamental assumption in Equation 4.1.10 [50,68]. This analysis is extended to constrained biaxial deformation as sheet draw-down into a cone or funnel of wall angle oc. The polymer not in contact with the wall is biaxially stretching as A1 = XQ and ro = a: (4.68) The thickness is: (4.69)
The pressure is: (4.70) where: (4.71) Note that g(oc) is a geometric factor. If s is the distance down the cone side from the cone opening to the point where the sheet leaves the cone wall (Fig. 4.56): (4.72) (4.73) (4.74)
Examples 4.8 and 4.9 derive the expressions for commercial funnels where a = 60° and cylindrical or straight walled molds, where a = 90°. Example 4.8 Neo-Hookean Draw-Down into a 60° Funnel Determine the pressure-modulus relationship for a neo-Hookean polymer being drawn into a 60° funnel. From Equation 4.71, g(oc) = 0.5. The dimensionless radius is given by Equation 4.72 as:
I = 1-0.577 P ) The wall thickness is given by Equation 4.73 as:
And the pressure-modulus relationship from Equation 4.74 is:
Example 4.9 Neo-Hookean Draw-Down into a Straight-Wall Can Determine the pressure-modulus relationship for a neo-Hookean polymer being drawn into a can having 90° walls.
The wall thickness is given by Equation 4.73 as: h
ex
/
2s\
hr VirJ And the pressure-modulus relationship from Equation 4.74 is:
Stress, MPa
PTFE
Elongation, % Figure 4.50 Temperature-dependent stress-strain curves for polytetrafluoroethylene, PTFE. Figure redrawn from [100] and used with permission of copyright owner
The general form for the pressure equation is: P= G(T)-^Vg
(4.75)
where g is the general form for the geometry of the mold. The deformation pressure is directly proportional to both the neo-Hookean modulus and the relative sheet thickness, ho/a. If the pressure is fixed by the process, as with vacuum forming where P <0.1 MPa or 15 lbf/in2, the ability to deform a sheet of specific thickness into a specific shape or depth of draw, s/a, depends entirely on the temperature-dependent modulus: G(T)=
P
(4.76) (ho/a) • g As seen in Figs. 4.11 and 4.12, G(T) decreases with increasing temperature. To form thicker sheets in the same mold and with the same pressure as thinner sheet, the sheet temperature must be increased. This is true for any geometry and any predetermined applied pressure (Fig. 4.57). As shown in Example 4.10 for a straight-walled mold, there is good agreement between the forming pressure, measured modulus and the temperature where extensive elongation begins. This supports the view that the simple neo-Hookean model has value in determining the minimum forming temperature. Note also that if the polymer type, sheet thickness, mold geometry and applied pressure are known, G(T) establishes a minimum value for the forming temperature. Example 4.11 illustrates the minimum value for the straight-walled mold.
Example 4.10 Comparison of Calculated and Experimental Moduli for PVC Determine the maximum value for the neo-Hookean modulus for vacuum forming PVC into an oc = n/2 straight-walled can and compare the results with the experimental data of Table 4.9. For the data in Table 4.9, the applied stress, a = 426 lbf/in2 or 2.9 MPa. The initial sheet thickness, ho = 0.040 in or 1 mm and the mold diameter, a = 1 in or 25 mm. For a straight-walled cavity, from Example 4.9, the depth of draw is no longer an important element once s/a > 0.5. As a result, the equation is written as:
p* 4GCn-(I) For simple vacuum forming, P < 0 . 1 MPa or 15 lbf/in2. As a result: G(T) = ^ 1 ^
= 0.626 MPa = 91.9 lbf/in2
As seen in Table 4.9, the modulus of PVC at 1100C is 93.6 lbf/in2 or 0.65 MPa and the measured elongation at this temperature is substantially greater than that at 1000C. Example 4.11 The Minimum Forming Temperature for PVC Determine the minimum forming temperature for PVC for the data in Example 4.10.
The maximum applied pressure occurs when the geometric parameter, g, is maximum. This occurs when s/a = 0. At this condition: Pmax = 4G(T)(^) -0.875 Again, for the vacuum forming case, Example 4.10, P<0.1 MPa or 14.7 lbf/in2. 0
^ = 4 - 0 ^ / 2 S ) = 0 - 71 ^ =
1 0 5
1
^
As seen in Table 4.9, if the sheet temperature is less than 1100C, the sheet will not begin to draw since the experimental G(T) is greater than 105 lbf/in2.
Stress, MPa
FEP
Elongation, % Figure 4.51 Temperature-dependent stress-strain curves for fluoroethylene polymer, FEP. Figure redrawn from [101] and used with permission of copyright owner
Stress, MPa
PA-6
Elongation, % Figure 4.52 Temperature-dependent stress-strain curves for nylon 6, polycaprolactam, PA-6. Figure redrawn from [102] and used with permission of copyright owner
One definition for the thermoforming window then is: The minimum thermoforming window is the temperature range from the value below which the sheet is too stiff to deform under applied pressure to that above which the sheet can be easily deformed to a draw ratio, s/a, greater than 0.5.
In the examples, the forming window using this definition is a few degrees, at best. Increasing the temperature above this minimum forming window allows the sheet to be formed at much lower pressure. The practical upper limit on formability is still the point where the sheet is plastically drawn to rupture. Table 4.9 Creep Data and Measured Modulus for PVC [17] (PVC at stress, G = 426 lbf/in2 or 2.9 MPa) Temperature (0C)
e (measured)
Modulus G(T) (lbf/in2) (MPa)
98 100 110 118
1.2 1.45 3.6 3.6
1.5 1.6 0.65 0.65
214 187 93.6 93.6
Stress, MPa
PA-66
Elongation, % Figure 4.53 Temperature-dependent stress-strain curves for nylon 66, polyhexamethylene adipamide, PA-66. Figure redrawn from [103] and used with permission of copyright owner
4.7
Practical Aspects of Stretching
As noted, there are many ways of generating stretching data on plastics. G(T), the neo-Hookean modulus, is one material property extracted from an analysis that uses a simple isothermal stress-strain model. Several precautions are important. Creep data over a relatively wide range in temperatures are easy to obtain, but normally yield uniaxial stretching data at fixed stress. The effect of strain-rate-dependency is masked or missing. Further Treloar [108] cautions against using uniaxial data to predict biaxial performance. He notes that for rubber, experiments that "...cover only one type of strain may, and usually do, appear to conform to [a given strain-energy function] equation. [However,] they provide very little real evidence regarding the form of the strain energy function in general strain, and any use of them is an unwarranted extrapolation."
Stress, MPa
PBT
Elongation, % Figure 4.54 Temperature-dependent stress-strain curves for polybutylene terephthalate, PBT. Figure redrawn from [104] and used with permission of copyright owner
Example 4.12 shows the relationship between uniaxial and uniform principal invariants for a Mooney-type solid at a fixed strain. It is apparent that the importance of curve-fitting constants changes from one stretching mode to another. For one very specific type of fluid, called a "simple fluid" [20], a relationship between uniaxial extension and uniform biaxial extension is obtained. Example 4.12 Uniaxial and Uniform Biaxial Strain for a Mooney-Type Solid Consider uniaxial extension of a Mooney-type solid, where A= 7. Determine values for the first and second strain invariants and their ratios, at the same stress level. For uniaxial stretching, ^ 1 = X, X2 = X3 = X~1/2. I and II are: I - ^ 2 + 2 - ^ - 1 =49.29 H = IA 2 + 2 -X, = 14.02 I/II = 3.52
For uniform biaxial stretching, X1 = X2 = X, X3 = I/X2. I and II are: I = 2 'X2 +1/X4 = 98.0
II = 2A2 + X4 = 2401 I/II = 0.041
In order for biaxial extension data to be relevant [109], inflation experiments must be at isothermal, uniform constant rate conditions. Practical stretching rates are rarely achieved under these conditions. When practical rates are used [46,49,59], inflation rates are not constant and the sheet may not be isothermal. It has been cautioned [110] that the natural process time for inflation may be so short
a s
r
Stress, MPa
H
Figure 4.56 Geometric factors for a conical female mold
PI
Elongation, % Figure 4.55 Temperature-dependent stress-strain curves for polyimide, PL Figure redrawn from [105] and used with permission of copyright owner
Applied Pressure, lbf/in2 Inflation Height to Disk Radius, h^a
Figure 4.57 Elastic deformation as a function of inflation pressure for polyisobutylene [46]. Redrawn figure used by permission of Society of Rheology
that the polymer may never behave as a fluid in dynamic steady state elongation. It appears, then, that elastic liquid and viscoelastic solid models serve only as clues or signposts in thermoforming. No current analytical model should be used a priori to predict the thermoformability of a given polymer. Even with advent of finite element analysis to the solution of the large deformation, the thin membrane problem today cannot yield forming ranges. Practical methods of comparing the performance of one polymer with another must remain relatively empirical for the time being.
Funnel Test Biaxially constrained stretching into a funnel is a relatively simple way of obtaining qualitative information about G(T). Figure 4.58 is the coordinate for thermoforming into a cone of diameter d and angle, a, at time 9, as a sheet of initial thickness ho is being drawn into a cone to a depth of h. The sheet is in contact with the cone surface for a diagonal distance or slant height, s. The sheet is divided into a frustum of a cone and spherical cap. That portion of the sheet that is not in contact with the cone surface forms a spherical cap of radius R = d/2 and r is the indeterminate radius at the bottom of the frustum of the cone. The frustum area is: (4.77)
where h = R tan a and hf is given as: (4.78)
R = d/2
h
1
h H
s a; r
Figure 4.58 Geometric factors for draw-down into a conical female mold
The area of the spherical cap is: (4.79) where 5 is given as: (4.80) Therefore: (4.81) Now r = a cos a and 8 = a(l — sin p). As a result: (4.82) The total area in terms of r is: (4.83) The reduced thickness of the sheet at the frustum-spherical cap intersection, at s, is given as:
For a cone angle of a = 60° or TT/3:
(4.84)
(4.85)
Reduced Thickness
0.014 inch White Geon 87651 340 to 3900F
Distance Down Side, cm Figure 4.59 Measured thicknesses of 0.014-inch polyvinyl chloride, PVC sheet drawn into a 60° conical female mold. Initial sheet temperature range is 3400F to 3900F
Figure 4.59 shows the repeatability of reduced thickness as a function of slant distance, s, for 0.014 in or 0.36 mm RPVC sheet formed into a 2.5 in or 64 mm diameter, 60° cone at sheet temperatures from 340 to 3900F or 171 to 199°C. The thickness shown is (4t/3to). As expected, the reduced thickness is linear with s/d with the data scattering about the linear line and the intercept at about 6.4 cm. The experimental procedure is as follows. An isothermal sheet is stretched using either vacuum or positive air pressure (Fig. 4.60). Sheet temperature and differential pressure are accurately measured. Positive air pressure is easier to control than vacuum [21]. The funnel temperature should be substantially below the polymer Tg so that the sheet freezes instantaneously on contact with the funnel surface. The surface should be relatively smooth to allow good seal between the sheet and the surface. In practice, once the sheet contacts the surface, it does not slide [111]. At a given temperature and applied differential pressure, deformation occurs to a depth s/a, where s is the point along the funnel surface where the sheet last touches it. If s cannot be determined, s + 5 is measured and 5 is calculated from 5 = a(l — sin a).
Convection Oven
Hot Sheet
Book Mold Funnel or Metal Cone Support Stand Vacuum System
Figure 4.60 Laboratory-scale draw-down apparatus
Furthermore, t/to is easily measured at every point along the part surface and compared with s/a at any set of conditions. All polymer in the cone should be accounted for with a simple material balance: Volume =
fs 2nvt
dr + 27iR5t(s)
(4.86)
Jo
If the measured values of t/to do not exactly agree with calculated values, the measured values should be used. G(T) is determined once P, T, t/to, and to/a are known. Figure 4.61 shows the reduced thickness of the cap as a function of sheet temperature for 0.014 in or 0.36 mm thick RPVC drawn into a 60° or n/3 cone. The data in Fig. 4.62, where the applied vacuum was fixed at 9 lbf/in2 or 0.06 MPa, show the characteristic Arrhenius temperature dependency of G(T) for two types of RPVC polymer. Note that extension ratios for draw down into a 60° cone are initially rather small with XQ and X1 values of only 2.4 when the sheet has been drawn a distance of h/a = 1. Values rapidly increase as the polymer is drawn into the tip of the cone. Maximum values of X ~ 11 are achieved when h/a > 1.5. A straight-walled cylinder has been used as a test mold [112], but draw-down is extreme. High pressure and rapid rate-of-pressurization of the sheet on the funnel can lead to premature diaphragm rupture. Results from these types of experiments should be used only to roughly define processing parameters such as pressure and temperature for any given polymer grade, for a given ratio of sheet thickness to part dimension. These experiments suffer many of the same limitations on interpretation as fiber spinning and film blowing processes [41,113].
Reduced Bottom Thickness
0.014 inch White Geon 87651 PVC
Oven Temperature,0F Figure 4.61 Measured temperature-dependent bottom free-surface sheet thickness for 0.014-in polyvinyl chloride, PVC sheet drawn into 60° conical female mold
4.8
Bursting Conditions
Rapid biaxial stretching is common thermoforming practice for thin-gage sheet. Instantaneous strain rates of up to 30 s"1 have been reported at the pole during bubble blowing. As noted earlier, for elastic liquids at constant stress or constant applied pressure, polymer deformation rate increases without bound. This can result in membrane rupture. An interesting relation between applied pressure and bursting time has been proposed in terms of an elastic liquid response to applied stress, a [22]: a = Tie-e
(4.87)
where r|e is the biaxial extensional viscosity and e is the principal biaxial strain rate. Now: (4.88)
Modulus/Applied Pressure, Dimensionless
Geon 87651
Geon 87313
Reciprocal Temperature, 1000/lT + 273],0C1 Figure 4.62 Comparison of temperature-dependent tangent modulus-to-applied pressure ratio for two polyvinyl chlorides, PVCs
e*(cb-^)
(4.89)
R is the radius of the cap of the bubble, h is the membrane thickness, P is the constant applied pressure, Gb is the time to burst, and subscripts o and b represent the initial and bursting conditions. This is rewritten as:
l2ho
+
2hb|J_
Note that (l/0 b ) is a strain-rate-like term with units of s~l and (P9b) is a viscosity-like term with units of MPa • s of lbf • s/in2. If the term in the large brackets [• • •] in Equation 4.90 is essentially constant, (PGb) is proportional to r|e, the biaxial extensional viscosity. A comparison of bursting time data and viscosity data for room-temperature bubble inflation of polyisobutylene rubber is given in Fig. 4.63. If the biaxial extensional viscosity is essentially inversely proportional to strain rate
Viscosity, MPa*s
Applied Pressure x Bursting Time, lbf«s/in2 Strain Rate, s"1 or Reciprocal Bursting Time, s ~1
Figure 4.63 Comparison of bursting time with viscosity for polyisobutylene rubber [46]. Redrawn figure used with permission of society of rheology
[46], the bursting time is independent of applied pressure. Moreover, even if a direct comparison is fortuitous, the effect of sheet temperature on bursting time is found by applying an Arrhenius-type temperature correction factor: (PGb)(T) = A exp[-Evls/RT]
(4.91)
where A is a pre-exponential constant, Evis is a viscous energy of activation for biaxial extension and R is the gas constant. Bursting should be of concern only in the early stages of bubble deformation. At later stages, the process approaches one of constant velocity, and the falling sheet temperature helps to stabilize the bubble against rupture. Sheet splitting is a similar problem seen in constrained deep drawing into rather sharp corners. Perforation of sheet nibs or nipples during draw-down into oversized vacuum holes can also be analyzed in terms of this bursting phenomenon.
4.9 Sheet Sag When a polymer sheet is clamped in a frame and heated, it begins to sag. If the extruded sheet has some residual stress, the initial sag will be reduced as the sheet temperature increases. If the sheet has substantial residual stress, the initial sag is
L NA Figure 4.64 Geometric factors for initial sheet sag for a linear sheet element
minimal and the sheet may be pulled from its frame. This initial stage has been discussed earlier in this chapter. When the sheet is quite hot, sag is appreciable, as shown in schematic in Fig. 4.2. The mechanics of sag are divided into initial sag, where the neutral axis remains in the sheet, and tensile sag, where the sag is appreciable. Initial Sag For initial sag, the neutral axis or the boundary between compressive stress and tensile stress, remains in the polymer sheet, as shown in Fig. 4.64. Maximum tensile strain occurs on the lower sheet surface and maximum compressive strain occurs on the upper sheet surface. There are two general cases: •
For an rectangular sheet clamped along all edges, Fig. 4.64, the initial sag is given as [114]: - ^ l _ (4 92) 3 ( j E(T)h 2 where y is the extent of sag, in mm or in, q is the weight of the sheet, in kg/m or lb/in2, L is the sheet span in inches or mm, E(T) is the temperature-dependent modulus, in MPa or lbf/in2, h is the sheet thickness, in mm or in, and (3 is a function of the sheet length to width, Table 4.10. The sheet weight, q = ph where p is the density of the polymer, kg/m3 or lb/ft3. The sheet width is temperaturedependent, L = L(T), since all polymers have finite thermal expansion coefficients. However this effect is small when compared with the temperature dependency of the modulus (Figs. 4.11 and 4.12). Since b increases with temperature and E decreases with temperature, the overall effect is an increase in initial sag with increasing temperature. For continuous sheet clamped along two edges, p = 0.1421. For a square sheet clamped along four edges, P = 0.0444. The initial sag for the square sheet, as found in cut-sheet forming, is less than one-third that of the continuous sheet, as is typical of roll-fed forming. y = Y
Example 4.12 illustrates the method of calculating initial sag. •
For a circular disk clamped along the radius, Fig. 4.65, the initial sag is given as [115]: (4.93)
Table 4.10 Scale Factor for Sheet Sag Equation [114] Sheet length Sheet width 1.0 1.2 1.4 1.6 1.8 2.0 3.0 4.0 5.0 oo
0.0444 0.0616 0.0770 0.0906 0.1017 0.1110 0.1335 0.1400 0.1417 0.1421
d Y Figure 4.65 Geometric factors for initial sheet sag for a circular disk
where v is Poisson's ratio. This example is most useful when determining the extent of draw-down into vacuum or vent holes. A form of this equation is used in Chapter 6 to predict the initial draw of sheet into a vent hole of diameter d.
Tensile Sag When the neutral axis is no longer within the sheet thickness, the entire sheet is under tension. As described above, the polymer elongates under tensile loading according to: a = f(e;E(T))
(4.94)
If the polymer is simply hanging vertically, as seen in Fig. 4.5, the engineering stress is given as: W aeng = ^ -
(4.95)
where A 0 = bh o , where b is the unit width and h o is the initial sheet thickness. W is the weight of the sheet, W = pbh o L o . If the sheet stretches uniaxially as would be the case if the vertical sheet is heated, the weight of the polymer remains fixed and
so does the engineering stress. The elongation increases and the temperature-dependent proportionality, E(T) decreases in proportion. The analysis of a sagging sheet follows this logic but includes the important fact that the sheet is supported on both ends. There are two models used for suspended elements. Both are developed for the hanging of cable in civil engineering and are adapted here for an infinitely long sheet supported on two edges. The arithmetic follows. The Catenary Sag The classic one-dimensional strength of materials case, typical of a roll-fed sheet held along two sides, is the catenary (Fig. 4.66) [116]. The sheet has a horizontal T0 tension at its origin (x = 0,y = 0). T is its tension at coordinates (x,y) along the sheet surface. The vertical supported load is the weight of the section of sheet length s. For a sheet of unit width and length weighing JI kg/m or lb/ft, the load is (is. The sheet unit weight, \i is related to the sheet thickness by: |i (per unit width and length) = ph 3
(4.96)
3
where p is the sheet density, lbf/ft or kg/m and h is the sheet thickness in inches or mm. This is resolved as: T sin 6 = |is
(4.97)
T cos 9 = T0
(4.98)
The extent of deflection, y, below the horizontal is given as:
where x is the distance from the center of the catenary. Since (ds)2 = (dx)2 + (dy)2, this is written as: (4.100) The arc length then is: (4.101)
L X
T
S
h
y
To W = ^s
Figure 4.66 Geometric factors for catenary sag of a linear sheet element. Figure adapted from [116]
The extent of deflection, y, is given as: (4.102) And the tension on the sheet is given as: (4.103) The total sheet length, S, is given as: (4.104) where L is the initial sheet span. Although the solution is quite compact, there is difficulty applying Equations 4.102 through 4.104 to sagging sheet in thermoforming. For example, as the sheet begins to sag, its span, given as S, increases. Since the total sheet weight remains constant, the sheet must therefore thin. As the sheet thins, the local unit weight of the sheet, given as JI, decreases in proportion.
Parabolic Sag The parabolic model is simpler than the catenary model but less exact. It assumes that the load, JI, is uniformly applied along the horizontal plane of the sheet (Fig. 4.67) [117]. Again, Ji= ph is assumed. The describing equations are: T s i n 9 = |ix
(4.105)
T cos O = T0
(4.106)
The equation describing the curve of the sheet under these conditions is: (4.107) with the parabolic solution being: (4.108)
L x
T
h y T0 W = wx Figure 4.67 Geometric factors for parabolic sag of a linear sheet element. Figure adapted from [117]
The tension at the origin (x = 0,y = 0) is: (4.109) where Y is the maximum sag. The maximum tension in the sheet is: (4.110) Note that it requires an infinite force to hold a sheet of finite thickness in the horizontal plane, Y = O. And the value for the sagged length of the sheet is obtained from: (4.111) When the sag-to-span ratio, Y/L, is small, the parabolic sag equations are satisfactory approximations to the catenary equations and substantially easier to manipulate. Plots of Y/L and S/L as functions of JLIL/2TO are given in Fig. 4.68. The curves deviate at JIL/2T O > 1 or so. A cross-plot of the ratio of S/L to Y/L for parabolic and catenary sag shows essentially identical shapes for values of Y/L greater than about 0.1 (Fig. 4.69). S/L approaches a value of 2(Y/L) for sag levels greater than Y/L = 2.
Relating Sag to Hot Sheet Strength The catenary relationship between Tmax, the tension at the gripped edge of the sheet, and T0, the tension at (x = 0,y = 0) is obtained from: Tmax = T0 + nS = T0 + ( ^ )
•( ^ )
= T0 + phoL
(4.112)
or Tmax is a constant factor greater than T0, regardless of the extent of stretching. On the other hand, for the parabolic relationship: U2T2
TL x = T2 + ^ -
(4.113)
Again, JI = jdo • (h/ho) and (h/ho) = (S/L)"1 as before. Since Tmax is assumed to be constant and equal to the tensile stress of the polymer, this equation is solved for T0 as: T 2
/ T \ 2
T2 = T2 -'u 2 — I -
(4 114)
Unlike Equation 4.112 for the catenary, T0 is not constant but a function of the length of the sagged sheet, which in turn is a function of the vertical extent of sag, Y/L, according to Equation 4.107. So long as S/L is small, the effect of sag on the value of T0 is small and u «jao. As the sag becomes more significant, the basic premises used to develop the parabolic equations are no longer valid.
Dimensionless Sag, y/L or Dimensionless Sagged Sheet Length, s/L
s/L, Catenary y/L, Catenary
s/L, Parabola
y/L, Parabola
Dimensionless Weight, WL/2TO Figure 4.68 Dimensionless extent of sag as function of sheet dimensionless weight for catenary and parabolic sag
From Equation 4.113: (4.115) Again, since T max is constant, Equation 4.114 is written as: (4.116) This relationship also shows T 0 as a function of Y/L. The hot strength of the polymer, in terms of the engineering stress at the grip, is written as a = T max /A where A is the initial cross-section of the sheet, A = h o • b. As a result, a measured property, the tensile strength of the polymer, is directly related to the measured response, sag, for both the catenary and parabolic models [134]. Example 4.14 illustrates the relationship between the catenary and parabolic models. Examples 4.15 and 4.16 illustrate the effect of sheet temperature on sheet sag.
Dimensionless Sagged Sheet Length,S/L
Dimensionless Sag,Y/L Figure 4.69 Dimensionless sheet length as function of dimensionless extent of sag. Catenary and parabolic curves coincide
Example 4.13 Initial Sag of Polypropylene Sheet Consider a 0.250-in thick polypropylene sheet at 1000C. The modulus of the sheet is 10 MPa or 1500 lbf/in2 and its Poisson's ratio is 0.35. Determine the extent of sag if a Wx 10 in sheet is clamped on all sides and then only on two sides. Determine the equivalent sag if a 10-in disk is being heated. The extent of sag is obtained from Equation 4.92. The density of PP is 0.91 g/cm3 = 56.8 lb/ft3 = 0.0329 lb/in3. q = 0.0329 • h. Therefore for the sheet clamped on all sides, (3 = 0.0444: y =
0.0444 • 0.0329 • h • 104 0.0444 • 0.0329 • 104 = 1500^ 1500-0.25*
= a i 5 6 m
For the sheet clamped on two sides, P = 0.1421, and y = 0.500 in1. The extent of sag of a disk is obtained from Equation 4.93: y
1
3 • 0.0329 • h • 100 • (5 + 0.35) . = 542 m = 16 • 1500-h' °-°
Correctly, when the value of y calculated using this equation exceeds the half-thickness of the sheet, the equation should not be used to predict sag.
Example 4.14 Parabolic and Catenary Sag Consider the sag of a 0.100 in thick by 48 in wide plastic sheet having a density of 62.4 Ib I ft3. The tensile stress on the sheet at the grip is 10 Ib/in2. Determine the sag as given by the parabolic and catenary sag equations. Consider the sag in catenary terms first. The tension in the sheet at the grip is given in Equation 4.112 in terms of the tension, T 0 at (x = 0, y = 0), written as:
For the catenary sag model, (Y/L) c a t « 0.0265 and Y cat = 1.27 in. For the parabolic sag concept:
As seen in Fig. 4.72, the S/L-to-Y/L ratio for the catenary model has nearly the same dependency on Y/L as the parabolic model. If (Y/L) para « 0.0265 and if \i « \io:
Note that 2Tmax/jioL - 2 T O / J I L = 11.54 - 9.43 = 2.11 or approximately the same value as for the catenary problem 1 . In other words, for this case, there probably is not a substantial difference in the sag predicted by parabolic and catenary equations.
1
The reader is warned that this may be a self-fulfilling prophecy in that an incorrect value is used for Y/L. Please review the comments in the text at this point.
Example 4.15 Effect of Temperature on Sheet Sag Consider the polymer of Example 4.14. Consider the stress given in the example to be at 2000C. The polymer elongational energy of activation is 20,000 kcal/mol. Determine the tensile stress at 2300C and determine the extent of sag at 2300C. Repeat the analysis for a sheet temperataure of 2400C. The Arrhenius form is given as:
where the temperatures are absolute. From the values given:
° - = 1 0 • e x p [ i ^ ferbs - 200T273)]=10 •exp(-L269) = 2.81 lb/in2 ^ HL
2 2 81 " -2=1.243 0.0361 • 48
^=(TKT'=0-
8 0 4
For catenary sag, Y/L « 0.215 and Ycat « 10.3 in. From Fig. 4.73, S/L « 5.12 (Y/L) or S/L « 1.10 = (Wh0)-1. For parabolic sag, assume: ^ = £ * 1.243 ^L 4Y Therefore, Y/L « 0.201 and Ypara « 9.65 in1. The sheet sag has increased by about 700% in 300C. Now consider the effect at 235°C. Q235 = 2.31 lb/in2. For catenary sag, 2To/^iL = 0.663 and r| = 1.508. For catenary sag, Y/L « 0.463 or Ycat = 22.2 in. For parabolic sag, Y/L « 0.36 or Ypara «17.3 in. The extent of sag has more than doubled in 5°C. 1
This value is suspect since \i has not been adjusted by the 10% decrease in sheet thickness
Example 4.16 The Importance of Temperature-Dependent Hot Strength on Sag Consider two polymers exhibiting the same extent of sag of 9.65 in for a 48-in sheet span at 2300C as given in Example 4.15. Assume that Polymer A has an elongational energy of activation value of 20,000 and B has a value of 10,000. Determine the extent of sag at 235°C.
a
A,235 = 2.31 in Example 4.15. For catenary sag, 2To/uL = 0.663 and r| = 1.508. For catenary sag, Y/L ^ 0.463 or Ycat = 22.2 in. <jB235 = 2.55 from Example 4.15
For catenary sag, Y/L w 0.305 and Ycat « 14.6 in. The results are tabulated as follows:
Polymer A Polymer B
(Y/L) 230
(Y) 230
(Y/L) 2 3 5
0.201 0.201
9.65 9.65
0.463 0.305
(Y) 235 22.2 14.6
It is apparent that Polymer B is substantially stiffer at 235°C than Polymer A and that this should be visibly apparent in the relative extents of sag. Some interesting insights to sheet sag are obtained by reviewing the parabolic and catenary models. For example, the tension on the sheet increases in proportion to the sheet thickness—through the value for JJ,—and in proportion to the square of the span1. S/L varies between 1.0 and 2Y/L as Y/L varies between 0 and oo (Fig. 4.69). Note that the thickness of the sheet decreases from a value of h for Y/L = 0 to a value of h/2 or S/L = 2 at a value of Y/L « 0.82. When Y/L « 1.9, S/L « 4 and the sagged sheet thickness is about 1/4 its original thickness. But, minor sagging does not appreciably reduce the sheet thickness. Even when the sheet has sagged Y/L = 0.2, S/L is just 1.1 and the sagged sheet thickness is still more than 90% of its original thickness. Sag—A Comment The parabolic model is simpler to use than the catenary model and satisfactory for small values of Y/L. For larger values of Y/L, the catenary model is more accurate. The catenary and parabolic sag models are simplistic. They assume that the sheet is 1
2
As noted in Equation 4.85 for initial sheet sag, the extent of sag was proportional to the fourth-power of the span. Note that this assumes that the sheet is thinning uniformly across the sagging span. In reality, the tension on the sheet is varying from the minimum at mid-span to maximum at the clamped edges. As a result, an isothermal sheet should stretch more in the clamped edges. In general, the sheet tends to be cooler in the vicinity of the clamped edges, and so uniform sheet stretching is a reasonable assumption.
essentially infinite in length. Large deformation of two-dimensional sheet and axisymmetric sheet is best solved using finite element analysis, as described in Chapter 7, on part design.
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48. P.I. Vincent, "Short-Term Strength and Impact Behaviour", in R.M. Ogorkiewicz, Ed., Thermoplastics: Properties and Design, John Wiley & Sons, Ltd., London (1974), p. 72. 49. M.O. Lai and D.L. Holt, "The Extensional Flow of Poly(Methyl Methacrylate) and High-Impact Polystyrene at Thermoforming Temperatures", J. Appl. Polym. Sci., 19 (1975), p. 1209. 50. M.O. Lai and D.L. Holt, "Thickness Variation in the Thermoforming of Poly(Methyl Methacrylate) and High-Impact Polystyrene Sheets", J. Appl. Polym. Sci., 19 (1975), p. 1805. 51. D. Hylton, Laboratory Techniques for Predicting Material Thermoformability: A Review, SPE ANTEC Tech. Papers, 57(1990), pp. 580-583. 52. A.S. Lodge, Elastic Liquids, Academic Press, London (1964), p. 99. 53. L.R. Schmidt and J.F. Carley, "Biaxial Stretching of Heat-Softened Plastic Sheets: Experiments and Results", Polym. Eng. Sci., 75(1975), p. 51. 54. T. Alfrey, Jr., "Plastics Processing and Fabrication Problems Involving Membranes and Rotational Symmetry", SPE Trans., 5:4 (Apr 1965), p. 68. 55. J.A. Brydson, Flow Properties of Polymer Melts, Van Nostrand Reinhold, New York (1970), pp. 18-19. 56. R.B. Bird, R.C. Armstrong and O. Hassager, Dynamics of Polymeric Liquids, Vol. 1, John Wiley & Sons, New York (1977), p. 83. 57. C.J.S. Petrie, Elongational Flows, Pitman, London (1979), p. 65. 58. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, Tests for Design, Hanser Publishers, Munich (1993), p. 655. 59. L.R. Schmidt, Biaxial Stretching of Heat-Softened Plastic Sheets, PhD Thesis, University of Colorado, Boulder CO (1972). 60. H. Gross and G. Menges, "Influence of Thermoforming Parameters on the Properties of Thermoformed PP", SPE ANTEC Tech. Papers, 28 (1982), p. 840. 61. R.W. Ogden, "Large Deformation Isotropic Elasticity—on the Correlation of Theory and Experiment for Incompressible Rubberlike Solids", Proc. Roy. Soc. London A326 (1912), pp. 565-584. 62. L.R.G. Treloar, "Elasticity of a Network of Long-Chain Molecules", Trans. Faraday Soc, 39 (1943), pp. 241f. 63. L.R.G. Treloar, The Physics of Rubber Elasticity, Oxford University Press, Oxford (1958). 64. R.S. Rivlin and D.W. Saunders, "Free Energy of Deformation of Vulcanized Rubber", Trans. R. Soc. Lond., A243 (1951), pp. 25If. 65. J.G. Williams, "A Method of Calculation for Thermoforming Plastics Sheets", J. Strain Anal., 5(1970), p. 49. 66. M. Mooney, "Theory of Large Elastic Deformations", J. Appl. Phys, 11 (1940), pp. 582-592. 67. HJ. Warnecke and B. Frankenhauser, "Montage von Kunststoffschlauchen mit Industrierobotern", Kunststoffe, 78 (1988), pp. 440-444. 68. L.R. Schmidt and J.F. Carley, "Biaxial Stretching of Heat-Softened Plastic Sheets Using an Inflation Technique", Int. J. Engng. Sci., 13 (1975), p. 563. 69. J.G. Williams, "A Method of Calculation for Thermoforming Plastics Sheets", J. Strain Anal., 5(1970), p. 52. 70. L.R.G. Treloar, The Physics of Rubber Elasticity, Oxford University Press, Oxford (1958), p. 162. 71. L.R.G. Treloar, The Physics of Rubber Elasticity, Oxford University Press, Oxford (1958), p. 169. 72. HJ. Warnecke and B. Frankenhauser, "Montage von Kunststoffschlauchen mit Industrierobotern", Kunststoffe, 78 (1988), Figure 5, pp. 440-444. 73. R.W. Ogden, Non-Linear Elastic Deformations, Ellis Horwood Ltd., West Sussex, England (1984). 74. W. Song, "Large Deformation Finite Element Analysis for Polymer Forming Processes", PhD Dissertation, McMaster University, Hamilton ON Canada (1993), Section 4.2.1. 75. K. Kouba, O. Bartos, and J. Vlachopoulos, "Computer Simulation of Thermoforming in Complex Shapes", Poly. Eng. Sci., 32 (1992), pp. 699-704. 76. A.E. Green and J.E. Adkins, Large Elastic Deformations and Non-Linear Continuum Mechanics, Oxford (1960), p. 26. 77. A.E. Green and J.E. Adkins, Large Elastic Deformations and Non-Linear Continuum Mechanics, Oxford (1960), p. 85.
78. B.D. Coleman, H. Markovitz and W. Noll, Viscometric Flows of Non-Newtonian Fluids, Springer, New York (1966), pp. 37-41. 79. K. Kouba and J. Vlachopoulos, T-FORMCAD: A Finite Element Software Package for Thermoforming and Blow Molding, Accuform Co., Ltd, and CAPPA-D, McMaster University, Hamilton ON Canada L8S 4L7. 80. M.H. Wagner, "A Constitutive Analysis of Extensional Flows of Polyisobutylene", J. Rheol., 34 (1990), pp. 943-958. 81. R.B. Bird, R.C. Armstrong and O. Hassager, Dynamics of Polymeric Liquids. Volume 1. Fluid Mechanics, John Wiley & Sons, New York (1977), p. 430. 82. K. Kouba and J. Vlachopoulos, "Modeling of 3D Thermoforming", SPE ANTEC Tech. Papers, 3* (1992), pp. 114-116. 83. R.I. Tanner, Engineering Rheology, Clarendon Press, Oxford (1985). 84. R.B. Bird, R.C. Armstrong, and O. Hassager, Dynamics of Polymeric Liquids. Volume 1. Fluid Mechanics, John Wiley & Sons, New York (1977), p. 107. 85. A. Wineman, "On Axisymmetric Deformations of Nonlinear Viscoelastic Membranes", J. Non-Newt. Fluid Mech., 4 (1978), pp. 249-260. 86. A. Wineman, "On the Simultaneous Elongation and Inflation of a Tubular Membrane of BKZ Fluid", J. Non-Newt. Fluid Mech., 6(1979), pp. 111-125. 87. H. Saechtling, International Plastics Handbook for the Technologist, Engineer and User, 2nd Ed., Hanser Publishers, Munich (1987), Figure 109, p. 416. 88. H. Saechtling, International Plastics Handbook for the Technologist, Engineer and User, 2nd Ed., Hanser Publishers, Munich (1987), Figure 111, p. 418. 89. H. Saechtling, International Plastics Handbook for the Technologist, Engineer and User, 2nd Ed., Hanser Publishers, Munich (1987), Figure 112, p. 419. 90. H. Domininghaus, Plastics for Engineers: Materials, Properties, Applications, Hanser Publishers, Munich (1993), Figure 14. 91. H. Domininghaus, Plastics for Engineers: Materials, Properties, Applications, Hanser Publishers, Munich (1993), Figure 15. 92. H. Domininghaus, Plastics for Engineers: Materials, Properties, Applications, Hanser Publishers, Munich (1993), Figure 42. 93. H. Domininghaus, Plastics for Engineers: Materials, Properties, Applications, Hanser Publishers, Munich (1993), Figure 129, p. 206. 94. D. Weinand, "Modellbildung zum Aufheizen und Verstrecken beim Thermoformen", DoktorIngenieur Dissertation, Rheinisch-Westfalische Technische Hochschule Aaachen (Institut fur Kunststoffverarbeitung (1987), BiId 5.2. 95. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, Tests for Design, Hanser Publishers, Munich (1993), Figure 6.25. 96. D. Weinand, "Modellbildung zum Aufheizen und Verstrecken beim Thermoformen", DoktorIngenieur Dissertation, Rheinisch-Westfalische Technische Hochschule Aaachen (Institut fur Kunststoffverarbeitung (1987), BiId 5.3. 97. H. Domininghaus, Plastics for Engineers: Materials, Properties, Applications, Hanser Publishers, Munich (1993), Figure 153, p. 228. 98. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, Tests for Design, Hanser Publishers, Munich, 1993, Figure 6.29. 99. H. Domininghaus, Plastics for Engineers: Materials, Properties, Applications, Hanser Publishers, Munich (1993), Figure 171, p. 245. 100. H. Domininghaus, Plastics for Engineers: Materials, Properties, Applications, Hanser Publishers, Munich (1993), Figure 242, p. 313. 101. H. Domininghaus, Plastics for Engineers: Materials, Properties, Applications, Hanser Publishers, Munich (1993), Figure 260, p. 328. 102. H. Domininghaus, Plastics for Engineers: Materials, Properties, Applications, Hanser Publishers, Munich (1993), Figure 295, p. 374. 103. H. Domininghaus, Plastics for Engineers: Materials, Properties, Applications, Hanser Publishers, Munich (1993), Figure 296, p. 374.
104. H. Domininghaus, Plastics for Engineers: Materials, Properties, Applications, Hanser Publishers, Munich (1993), Figure 403, p. 456. 105. H. Domininghaus, Plastics for Engineers: Materials, Properties, Applications, Hanser Publishers, Munich (1993), Figure 492, p. 534. 106. R.H. Finney and A. Kumar, "Development of Material Constants for Nonlinear Finite-Element Analysis", Rubber Chem. Tech., 61 (1988), pp. 879-891. 107. J.G. Williams, Stress Analysis of Polymers, John Wiley & Sons, New York (1973), pp. 211-220. 108. L.R.G. Treloar, The Physics of Rubber Elasticity, Oxford University Press, Oxford (1958), p. 170. 109. CJ.S. Petrie, Elongational Flows, Pitman, London (1979), p. 90, p. 210. 110. S. Middleman, Fundamentals of Polymer Processing, McGraw-Hill Book Co., New York (1977), p. 48. 111. R. Allard, J.-M. Charrier, A. Ghosh, M. Marangou, M.E. Ryan, S. Shrivastava and R. Wu., "An Engineering Study of the Thermoforming Process: Experimental and Theoretical Considerations", Paper presented at First Annual Meeting, Polym. Proc. Soc, Akron OH, 28-29 March 1984. 112. MJ. Stephenson and M.E. Ryan, "Experimental Study of Thermoforming Dynamics", SPE ANTEC Tech. Papers, 40 (1994), pp. 844-849. 113. S. Middleman, Fundamentals of Polymer Processing, McGraw-Hill Book Co., New York (1977), p. 49. 114. R J . Roark and W.C. Young, Formulas for Stress and Strain, Fifth Ed., McGraw-Hill Book Co., New York (1975), Table 26, p. 386. 115. R J . Roark and W.C. Young, Formulas for Stress and Strain, Fifth Ed., McGraw-Hill Book Co., New York (1975), p. 363, Example 10b. 116. J.L. Meriam, Mechanics: Part I Statics, John Wiley and Sons, Inc., Chapman & Hall, Ltd., London (1952), Figure 52, p. 184. 117. J.L. Meriam, Mechanics: Part I Statics, John Wiley and Sons, Inc., Chapman & Hall, Ltd., London, (1952), Figure 51. 118. J.M. McKelvey, Polymer Processing, John Wiley & Sons, New York (1962), p. 41. 119. M.C. Boyce and E.M. Arruda, "An Experimental and Analytical Investigation of the Large Strain Compressive and Tensile Response of Glassy Polymers", Polym. Eng. ScL, 30 (1990), pp. 1288-1298. 120. H.G. DeLorenzi and H.F. Nied, "Finite Element Simulation of Thermoforming and Blow Molding", in A.I. Isayev, Ed., Modeling of Polymer Processing, Carl Hanser Verlag, Munich (1991), Chapter 5. 121. W.N. Song, F.A. Mizra and J. Vlachopoulos, "Finite Element Analysis of Inflation of An Axisymmetric Sheet of Finite Thickness", J. Rheol., 35(1991), pp. 93-111. 122. K. Kouba, O. Bartos and J. Vlachopoulos, "Computer Simulation of Thermoforming in Complex Shapes", Polym. Eng. Sci., 32 (1992), pp. 699-704. 123. H.F. Nied, CA. Taylor and H.D. DeLorenzi, "Three-Dimensional Finite Element Simulation of Thermoforming", Polym. Eng. Sci., 30(1990), pp. 1314-1322. 124. S.D. Batterman and J.L. Bassani, "Yielding, Anisotropy, and Deformation Processing of Polymers", Polym Eng. Sci., 30 (1990), PP. 1281-1287. 125. S. Bahadur, "Strain Hardening Equation and the Prediction of Tensile Strength of Rolled Polymers", Polym. Eng. Sci., 13 (1973), pp. 266-272. 126. MJ. Miles and N J . Mills, "The Deep Drawing of Thermoplastics", Polym. Eng. Sci., 17 (1977), pp. 101-110. 127. G.W. Halldin, "Solid-Phase Flow Behavior of Polymers", Polym. Eng. Sci., 25 (1985), pp. 323-331. 128. K. Nakamura, K. Imada and M. Takayanagi, "Solid State Extrusion of Isotactic Polypropylene Through a Tapered Die. I. Phenomenological Analysis", Int. J. Polym. Mat., 2(1972), pp. 71-88. 129. G. Menges and D. Weinand, "Modellierung des Verstreckprozesses beim Warmformen", Kunststoffe 78 (1988), pp. 456-460. 130. K. Kouba, M.O. Ghafur, J. Vlachopoulos and W.P. Haessly, "Some New Results in Modelling of Thermoforming", SPE ANTEC Tech. Papers, 40 (1994), pp. 850-853.
131. L.R. Schmidt and J.F. Carley, "Biaxial Stretching of Heat-Softened Plastic Sheets: Experiments and Results", Polym. Eng. Sci., 75(1975), pp. 51-62. 132. L.R. Schmidt and J.F. Carley, "Biaxial Stretching of Heat-Softened Plastic Sheets Using an Inflation Technique", Int. J. Eng. Sci., 13 (1975), pp. 563-568. 133. D. Hylton, "Laboratory Techniques for Predicting Material Thermoformability: A Review", SPE ANTEC Tech. Papers, 37(1990), pp. 580-583. 134. C. Cruz, Jr., "The Sag Process in Modified Polypropylene", SPE ANTEC Tech. Papers, 40 (1994), pp. 854-858. 135. J.L. Throne, Thermo forming, Carl Hanser Verlag, Munich (1987), pp. 110-112.
Appendix 4.1 Biaxial Stretching of an Elastic Membrane1 Consider the biaxial extension of a rubbery solid membrane of initial thickness ho and radius a, inflated with a differential pressure P. The extensional stress-strain equations for a Mooney-type polymer are:
a, = 2(C10+ Q 1 - A l ) - ( V - J ^ i ) CT6 = 2(C10+ C 0 1 - V ) - ( ^ - 5 ^ 1 )
(4.1.1) (4-1-2)
C01 and C10 are the Mooney constants, and 1 and 0 are the in-sheet or meridional and angular or hoop direction coordinates (Fig. 4.70). N is the force acting on the membrane, N = a • h, a is the local stress and h is the local thickness. The radius from the center axis is r, ^h = h/ho, Xe = r/ro, and X1 = (kh- Xd)~l. The angle of the membrane from the horizontal is p and 5 is the cap height above the horizontal plane. Thus r/R = sin (3, where R is the radius of the spherical cap (Fig. 4.71). At the top of the dome: (4.1.3) For C01 « C 1 0 and Xh Xh» 1, or for large deformations of a neo-Hookean solid: (4.1.4) (4.1.5) The forces acting on the membrane are: (4.1.6) (4.1.7) Now N1 • N 0 = (2C10ho)2 = N 0 , a constant. Further, stress equilibrium yields N1 = N 0 . Therefore, N 0 = N1. A hoop stress condition is: (4.1.8) 1
Adapted from Williams [107], by permission of Ellis Horwood, Ltd., copyright owner.
Figure 4.70 Membrane stretching geometry. Adapted from [107] and used with permission of Ellis Horwood, Ltd., copyright owner
Figure 4.71 Geometry of stretched cap or dome. Adapted from [107] and used with permission of Ellis Horwood, Ltd., copyright owner
As a result: (4.1.9)
And since R = R(a,5) above: (4.1.10)
where G is the elastic modulus of the new-Hookean polymer, G = C10. This is the neo-Hookean relationship between applied pneumatic pressure, P, and the extent of deformation, given as 5/a.
5 Cooling and Trimming the Part 5.1 5.2 5.3 5.4
5.5
5.6 5.7
5.8
5.9
5.10
5.11 5.12 5.13
5.14
Introduction Overall Cooling Heat Balance Cooling the Formed Shape Steady State Heat Balance Interfacial Resistance Shape Factor Convection Heat Transfer Coefficient Cyclic Heat Balance Cooling the Free Surface of the Sheet Cooling Thin Sheet in Ambient Air Transient Heat Removal From the Sheet Quiescent Ambient Air Moving Ambient Air Cooling on Nonmetallic Molds Transient Heat Transfer During Sheet Cooling on the Mold Surface—Computer Models Interfacial Air Shrinkage Unconstrained Shrinkage Constrained Shrinkage Trimming Trimming Heavy-Gage Parts Trimming Thin-Gage Parts Mechanics of Cutting The Trim Region Registering the Trim Site The Nature of the Cut Fracture Mechanics Mechanical Chipping Multiple-Edged Tool or Toothed Saw Performance Abrasive Cut-Off Wheel Toothless or Shear and Compression Cutting Fracture Mechanics in Trimming Nibbling Brittleness, Orientation and Trim Temperature Steel Rule Die Resharpening Tabbing and Notching Punch and Die Trimming Forged and Machined Dies Drilling Other Cutting Techniques Thermal Cutting Water Jet Cutting Trimming—A Summary
5.15 References
5.1
Introduction
Once the part has been heated and formed to shape by contact with the cool mold surface, it must be cooled and rigidified. Then the part and its web must be separated by trimming. When thermoforming a reactive polymer such as thermosetting polyurethane or a crystallizing one such as nucleated CPET1, the formed shape is rigidified by holding it against a heated mold to continue the crosslinking reaction or crystallization. In most cases, rigidifying implies cooling while in contact with a colder mold. For automatic thin-gage formers, the molds are usually actively cooled with water flowing through channels. Free surfaces of medium- and heavy-gage sheet are frequently cooled with forced air, water mist or water spray. For amorphous polymers, cooling of the formed part against a near-isothermal mold rarely controls the overall thermoforming cycle. For crystalline and crystallizing polymers such as PET, PP and HDPE, the cooling cycle can be long and can govern overall cycle time. When the sheet has cooled sufficiently to retain its shape and, to a large extent, its dimension, it is stripped from the mold and transferred to a trimming station, where the web is separated from the product. Requisite holes, slots and cut-outs are drilled, milled or burned into the part at this time. Thin-gage roll-fed sheet can be either trimmed on the mold surface immediately after forming or on an in-line mechanical trimming press. Heavier-gage formed sheet is usually removed from the mold and manually or mechanically trimmed on a remote station. Trimming is really a solid phase mechanical process of crack propagation by brittle or ductile fracture. Care is taken when trimming brittle polymers such as PS or PMMA to minimize microcracks. With brittle polymers, the very fine sander, saw or microcrack dust generated by mechanical fracture can be a serious problem. Other polymers such as PP and PET are quite tough and require special cutting dies. Dull steel-rule dies cause fibers or hairs at the cutting edge of thin-gage fiber-forming polymers such as PET and PP. Slowly crystallizing polymers pose registry problems when in-line trimming presses are used. The speed of trim cutting and the nature of the cutting surface control the rate of crack propagation through the plastic. There are no exhaustive studies of the unique trimming and cutting characteristics of thermoformed polymers and so much information must be inferred from other sources including extensive studies on the machining of plastics.
5.2
Overall Cooling Heat Balance
As a first approximation, as the sheet touches the mold, it is assumed to be at an average, equilibrated temperature, Tequil, as described in Section 3.13. When the 1
The unique processing conditions for crystallizing polyethylene terephthalate (CPET) are described in detail in Chapter 9, Advanced Thermoforming Processes.
average sheet temperature reaches the set temperature, Tset, as given in Table 2.5, the sheet is assumed to be sufficiently rigid to be removed from the mold surface. Typically, the amorphous polymer set temperature is about 200C or 400F below its glass transition temperature, Tg. The crystalline polymer set temperature is about 200C or 400F below its melting temperature, Tmelt. During the cooling time, the mold temperature is assumed to be essentially constant at Tmold. The amount of heat to be removed by the coolant flowing through the mold is given as:
(5.1) where V* is the volume of plastic, p is its density and cp is its heat capacity1. Heat is removed from the free sheet surface by convection to the environmental air. Heat is removed from the sheet surface against the mold surface by conduction through the mold to the coolant. The coolant fluid removes the heat by convection. The heat load at any point on the mold surface depends on the sheet thickness, tlocal, at that point. Sheet thickness, as noted in Chapter 4, is not uniform across the mold surface. The heat load at any point is given as: (5.2)
This is the heat to be removed from a given region during the cooling portion of the total cycle, 9cool. The local heat flux then is: (5.3)
The units on q['ocal are kW/m2 or Btu/ft2 • h •0 F. The total heat load during this time is given as: (5.4)
The total heat load per unit time on a steady-state process is given as: (5.5) where N is the number of parts produced per unit time. The units on Qsteady state are kW or Btu/h. At steady-state conditions, this energy is removed by the coolant system and by convection to the environmental air. Mold, coolant and air temperatures increase until the steady state is reached.
1
The last equality relates the amount of heat removed to the differential enthalpy, AH, of the polymer. This expression should be used if the polymer is crystalline and molten during the forming step and is solidifying during the cooling step.
5.3
Cooling the Formed Shape
Consider a typical cooling step. The sheet of variable thickness but known temperature is pressed against a slightly irregular surface of a mold. The properties of the mold material are known and uniform throughout its volume, Chapter 6. Coolant of known properties flows through uniformly spaced channels in the mold. The free surface of the part is also cooled. At any instant, the temperature profile through the various layers of material is as shown in schematic in Fig. 5.1. The rate at which the energy is removed from the plastic to ambient air and coolant depends on the sum of resistances to heat transfer through each of these layers. Heat removal by the coolant is the primary way of cooling the formed part. Transfer to the environmental air is a secondary method but it can be quite important when trying to optimize cycle time. There are two aspects to heat removal from the formed polymer sheet to the coolant. The first deals with the overall heat transfer at steady state conditions. The second focuses on certain aspects of cyclical transient heat transfer. Mold Surface Irregularities
Plastic Sheet
Coolant Film Resistance
Air Gap
Coolant * Tp
T0
Free Surface Film Resistance
T
L
o
Ambient Environment Mold
Series Thermal Resistances Figure 5.1 Schematic of various thermal resistances for sheet cooling against thermoforming mold
Baffle
Mold Insert
Flow Channel
Mold Base
Coolant
Figure 5.2 Typical serpentine coolant flow channel through thermoforming mold
5.4
Steady State Heat Balance
Consider the limiting case where all the energy is transferred directly to the mold and thence to the coolant. Typically, coolant lines are drilled or cast on a discrete, regular basis parallel to the mold surface (Fig. 5.2). Heat removal by coolant depends on convection heat transfer, or fluid motion1. The total amount of energy removed by the coolant embedded in the mold is given as: Q = UA AT
(5.6)
where U is the overall heat transfer coefficient, A is the coolant surface area and AT is the increase in coolant temperature between inlet and outlet portions of the flow channel. The overall heat transfer coefficient includes all flow resistances between the sheet and the coolant. It is usually written as:
where R1 represents the ith resistance to heat transfer. As seen in Fig. 5.1, for flowing fluids, there is a convective film resistance at the conduit surface, l/7iDhc, where TTD is the circumference of the conduit. If the coolant fluid is not kept clean, the coolant channel can become coated with residue, thus increasing thermal resistance. This 1
This section deals only with the convection heat transfer coefficient of coolant flowing through lines in the mold. Section 6.4 considers coolant pressure drop-flow rate relationships for the specification of coolant line size.
Table 5.1 Fouling Factors for Coolant Lines1 Coolant
Condition
Fouling factor (Btu/ft-h^F)-1 Velocity < 3 ft/s
Velocity > 3 ft/s
Treated make-up cooling tower water
Water < 125°F
0.001
0.001
Treated make-up cooling tower water City water City water River water River water Treated boiler feedwater Treated boiler feedwater Industrial heat transfer oil Ethylene glycol Glycerine-water Brine Brine Steam
Water > 125°F
0.002
0.002
Water Water Water Water Water
125°F 125°F 125°F 125°F 125°F
0.001 0.002 0.002 0.003 0.001
0.001 0.002 0.001 0.002 0.0005
Water > 125°F
0.001
0.001
0.001
0.001
0.001 0.002 0.002 0.003 0.001
0.001 0.001 0.001 0.002 0
1
< > < > <
Temperature < 125°F Temperature > 125°F
Information extracted from [1] by permission of copyright holder
resistance is called a fouling factor, ff. Fouling factors are given in Table 5.1 [I]. The resistance through the mold depends on the relative shapes of the mold surface and the coolant channels, and is usually described as 1/Skm, where S is a shape factor and km is the thermal conductivity of the mold material. Since polymer sheet does not press tightly against the mold surface, there is a conductive resistance owing to trapped air, l/ha. Although there may be other thermal resistances, these are the primary ones. So the overall heat transfer coefficient, U, is written as:
Interfacial Resistance In most heat transfer processes, intimate or perfect contact between the hot and cold solids is assumed. Imperfect contact causes resistance to heat flow. Mold surface waviness and microscopic roughness or asperities reduce physical contact (Fig. 5.3). Increasing pressure against the sheet increases physical contact and reduces the resistance to heat transfer. In general, energy is transmitted across the interstices by a combination of:
Cold, Rigid or Heavy-Gage Sheet Trapped Air
Cold Mold
Hot, Flexible or Thin-Gage Sheet
Moid Asperities
Hot Mold
Figure 5.3 Interfacial resistance between sheet and thermoforming mold surface. Left shows substantial thermal resistance owing to large air gap. Right shows reduced thermal resistance
• • •
Conduction at the asperities, Conduction through the interstitial fluid, and Radiation.
The resistance is thus a function of: •
• •
The contacting material properties such as Relative hardness, Thermal conductivity, Surface roughness and Flatness, The conductivity and pressure of the interstitial fluid, and The pressure applied against the free surface of the sheet.
The interface coefficient, ha, is a measure of thermal resistance across the gap. It is similar in concept to the confection heat transfer in that resistance to heat flow decreases with increasing value of ha. For perfect contact, h a -» oo. In thermoforming, the interstitial fluid is air, perhaps at a substantially reduced pressure. If the interface is a uniform air gap of 8 = 0.025 cm or 0.010 in and air thermal conductivity is kair = 0.029 W/m •0C or 0.0167 Btu/ft • h •0 F, the value for ha is about 114 W/m2 •0C or 20 Btu/ft2 • h •0 F. Contact heat transfer coefficient values between flowing polymer melts and mold surfaces of about ha = 568 W/m2 •0C or 100 Btu/ft2 • h •0 F have been reported in injection molding [2-4]. Similar values are expected here. For two surfaces in contact, ha = h ao p n , where p is the applied pressure and hao depends on the relative waviness and roughness of the two surfaces, Table 5.2 [5]. As seen, n has a value of about 2/3 for both rigid-rigid and rigid-flexible material contact in vacuum. Values for hao are typically 50 times greater in air than in hard vacuum. There are no available data for interfacial resistance during thermoforming of softened plastic sheet against various types of mold surfaces. For hot sheet pressed against a relatively smooth, heated mold surface at a relatively high differential pressure, it is expected that an appropriate value for ha would be about 568 W/m2 •0C or 100 Btu/ft2 • h •0 F. For rapidly cooling and rigidizing plastic sheet pressing against a highly textured, cold mold surface with a modest differential pressure, an appropriate value range for ha of 114 to 284 W/m2 •0C or 20 to
Table 5.2 Contact Resistance and Conductance [5] Ji0 = Ii00P11
(Units on h c = W/m 2 • 0 C or Btu/ft2 • h • 0 F) (Units on p are MPa or lbf/in2) Material contact
Inner layer
Elastic deformation theory Hard-to-hard Hard-to-hard Hard-to-soft
None Vacuum Air Vacuum
n
Contact coefficient, Ji00 (W/m2 • C)
(Btu/ft2 • h • 0F)
35.8 113.6 5680 170
6.3 20 1000 30
2/3 2/3 1/6 2/3
50 Btu/ft2 • h •0 F should be considered for first cooling time estimates. Section 5.6 on computer simulation of the cooling process explores the relative effect of interfacial resistance on time-dependent sheet cooling. Shape Factor For thin metal molds, heat is conducted very rapidly from the plastic to the coolant. For relatively thick molds of: • • • • • •
Plaster, Wood, Epoxy, Glass fiber-reinforced unsaturated polyester resin (FRP), Pressed fiberboard, or Any other nonmetallic material,
heat transfer is slowed by low mold material thermal conductivity. If the coolant system is considered to be coplanar with the mold surface (Fig. 5.4), the resistance to heat transfer per unit length (L = 1), across a mold D units thick is given as: Rn, = ^ -
(5.9)
where km is the mold material thermal conductivity. Thermal conductivity values for many mold materials are given in Table 2.7. For round discrete conduits (Fig. 5.5) [6], a shape factor, S, is used: (5.10) where S is given by: (5.11)
Mold
Mold
Coolant
Figure 5.4 Schematic of coplanar coolant flow channel and mold surface, concept frequently called flooded cooling
Hot Sheet
Coolant Channel
P
D
Mold
d Figure 5.5 Geometric factors for mold shape factor analysis
Figure 5.6 gives this equation in graphic form. It is apparent that the thermal resistance of the mold decreases with increasing value of S, which is achieved with many large-diameter coolant lines placed relatively close to the mold surface. The typical value range for S is 2 < S < 3. Example 5.1 illustrates the relative effects of these parameters on mold thermal resistance. Example 5.1 Shape Factors and Mold Thermal Resistance Determine the relative thermal resistances for the following two molds: Mold 1: Thin-walled aluminum mold with km = 131 Btu/ft h 0F, having d= 1/2-in water lines on P = 2 in centers, with the center line being D=I in from the mold surface.
Mold 2: Thick-walled plaster mold with km= LO Btu/ft h 0F, having d= 1/2-in water lines on P = 4 in centers, with the centerline being D = 2 in from the mold surface. Mold 1 P/d = 4, D/d = 2. From Fig. 5.6, S = 2.
Mold 2 P/d = 8, D/d = 4. From Fig. 5.6, S = 1.6.
^ i = U T T o = 0-625 The plaster mold has more than 160 times the thermal resistance to heat transfer than the aluminum mold.
Shape Factor, S
D/d = 1
Coolant Channel Spacing to Diameter Ratio, P/d Figure 5.6 Effect of coolant line location on mold shape factor
Convection Heat Transfer Coefficient The metal molds on automatic, roll-fed thin-gage thermoformers and on many heavy-gage forming operations are actively cooled, with water being the primary
coolant. There is a thermal resistance between the cool bulk flowing fluid and the warmer tube wall (Fig. 5.1). The primary dimensionless group used in fluid mechanics is the Reynolds number, Re: Re = ^ P
(5.12)
where D is the tube diameter, v is the fluid velocity, p is the density of the fluid and |i is its Newtonian viscosity [7]. The Reynolds number is the ratio of inertial to viscous forces for the fluid. Slowly moving fluids are laminar when Re < 2000. Convection heat transfer to slowly moving fluids is poor. Rapidly flowing fluids are fully turbulent when Re > 10,000 and heat transfer is very rapid. Example 5.2 illustrates the interaction between flow rate and Reynolds number. Example 5.2 Water as Coolant—Flow Rates Consider 21° C or 700F water flowing through 0.5-in or 1.27-cm diameter coolant channels. Determine the Reynolds number and the flow characteristic if the velocity is a) 0.52 ft I s or 0.16 m/s and b) 2.6 ft/s or 0.79 m/s. What are the volumetric flow rates at these velocities?
The water density is 62.4 lb/ft3. The viscosity is 0.658 x 10"3 lbm/ft • s. The Reynolds number is:
«,^_£ft.4^._l_£_3*,.v For v = 0.52 ft/s: Re = 2050 and the water is laminar. For v = 2.6 ft/s: Re = 10,300 and the water is turbulent. The volumetric flow rate is given as: V =^ ! . 4
v = 0 .00136-v^
s
= 0.612-v-^mm
For v = 0.52 ft/s, the flow rate is 0.32 GPM. For v = 2.6 ft/s, the flow rate is 1.6 GPM.
As discussed in Section 3.6, energy interchange between solid surfaces and flowing fluids is by convection. The proportionality between heat flux and thermal driving force is the convection heat transfer coefficient. The convection heat transfer coefficient is obtained from standard heat transfer theory and experiments. There are many methods for calculating values of hc. In general, however, the Chilton-Colburn analogy between resistance to fluid flow and resistance to thermal energy flow yields adequate results [8]. The analogy states: St
.Pr2/3
=
f / 8
( 5
1 3 )
where St is the Stanton number, Pr is the Prandtl number and f is the coefficient of friction or friction factor. The Stanton and Prandtl numbers are:
Table 5.3 Prandtl Number Values For Several Coolants [9,10] Prandtl no.
Coolant
Temperature (0F) (0C)
Air Air
32 100
0 38
0.72 0.72
Steam Steam
212 400
100 204
0.96 0.94
Water Water Water Water Water
32 70 100 150 200
0 21 38 66 93
13.7 6.82 4.52 2.74 1.88
SAE SAE SAE SAE SAE SAE
60 100 150 200 250 300
16 38 66 93 121 149
1170 340 122 62 35 22
Glycerine Glycerine Glycerine Glycerine Glycerine
50 70 85 100 120
10 21 29 38 49
31,000 12,500 5,400 2,500 1,600
Air Air Air
32 300 600
0 150 315
105 150 250 300
40 65 120 150
Light Light Light Light
30 Oil 30 Oil 30 Oil 30 Oil 30 Oil 30 Oil
Oil Oil Oil Oil
0.72 0.71 0.685 340 62 35 22
(5.14) (5.15) where h is the convective heat transfer coefficient, p is the fluid density at the appropriate temperature, cp is the fluid heat capacity, v is the average fluid velocity, v = u/p, is the kinematic viscosity, and a = k/pcp, is the fluid thermal diffusivity. In essence, Pr is the ratio of inertial to thermal properties and St is the ratio of fluid to thermal resistances. Table 5.3 gives appropriate Prandtl number values for several coolants [9,10]. As examples, Pr ^ 7 for room temperature water and Pr « 300 for
10O0C oil coolant. Examples 5.3 and 5.4 show the relative effectiveness of convection heat transfer to water and oil, respectively, as coolants 1 . Example 5.3 Water as Coolant—Temperature Increase A 3 ft x 3 ft x 0.125-in thick plastic sheet is initially at 31 5°F and is to be cooled to 2000F. The sheet specific heat is 0.5 Btu/lb • 0F and the density is 70 Ib I ft3. Twelve sheets are thermoformed per hour. Determine the increase in coolant temperature. Heat load from sheet: Q (per cycle) = pcpV*AT = 574 Btu/cycle Q = 574 • 12 = 6888 Btu/h to be removed by coolant. 0
Consider 70 F water flowing through a 3/4-in diameter coolant channel at v = 4 ft/s. From Example 6.1, the Re = 50,000. The flow is turbulent and f = 0.0248. Pr = 7.02. St • Pr2/3 = f/8 h
^ R ^ = 770Btu/ft2 - h -° F
Consider a 3 ft x 3 ft aluminum mold containing four waterlines spaced evenly. Consider the water lines to be I^ in from the mold surface. Thus P/d = 12 and D/d = 2. From Fig. 5.6, the shape factor, S « 3. The thermal conductivity of aluminum, from Table 2.12, km = 72.5 Btu/ft • h • 0 F. Consider h a = oo. As a result, the total thermal resistance, U is given as: U = 0.75Tr.770 + 3 ^ 7 l 5 2
= 0 0112
-
0
or: U = 89.3 Btu/ft • h • F. Surface area of coolant channels, A = TtDLN, where D is the coolant diameter ( = 3/4-in), L is the channel length ( = 1 0 ft), and N is the number of channels ( = 4). A = 7.85 ft2. The increase in coolant temperature is given as: _ ^ = _6888_ UA 89.3-7.85 This is considered to be a typical temperature increase for turbulent coolant flow.
1
These examples use fluid flow data of Examples 6.1 and 6.2 discussed in detail in Chapter 6 on mold design.
Example 5.4 Oil as Coolant—Temperature Increase A 3 ft x 3 ft x 0.125-in thick plastic sheet is initially at 375°F and is to be cooled to 2000F. The sheet specific heat is 0.5 Btu/lb •0 F and the density is 70 Ib I ft3. Twelve sheets are thermoformed per hour. Determine the increase in coolant temperature. Comment on the results. Heat load from sheet: Q (per cycle) = pcpVAT = 574 Btu/cycle Q = 574 • 12 = 6888 Btu/h to be removed by coolant. Consider 1500F SAE 10-like oil flowing through a 3/4-in diameter coolant channel at v = 4 ft/s. From Example 5.2, the Reynolds number, Re = Dvp = 1925. The flow is laminar and f = 0.0333. From Table 5.3, the Prandtl number, Pr = 290 and Pr 2/3 = 44. St • Pr2/3 = f/8 hc - (pCpV) 2 3 - 38 Btu/ft2 • h • 0 F ~ 8 • (29O) / "" ' Consider a 3 ft x 3 ft aluminum mold containing four waterlines spaced evenly. Consider the water lines to be \\ in from the mold surface. Thus P/d = 12 and D/d = 2. From Fig. 5.6, the shape factor, S « 3. The thermal conductivity of aluminum, from Table 2.12, k m = 72.5 Btu/ft • h • 0 F. Consider h a = oo. As a result, the total thermal resistance, U is given as: U = 0.757T • 38 + 3 • 72.5 = ° ' ! 3 9 or: U = 7.22 Btu/ft2 • h • 0 F. Note that this value is less than one tenth that of water flowing at the same velocity. Surface area of coolant channels, A = 71DLN, where D is the coolant diameter ( = 3/4-in), L is the channel length ( = 1 0 ft), and N is the number of channels ( = 4). A = 7.85 ft2. The increase in coolant temperature is given as:
±_
6888
UA
7.22-7.85
Since the sheet must be cooled to 200 0 F, this is an unacceptable increase in oil temperature. One solution is to increase the oil flow rate. Doubling the flow rate will increase the pressure drop by a factor of just less than four. A second alternative is to increase the number of coolant lines. Doubling the number of coolant lines will increase the coolant surface area but the oil velocity will drop to half its current value, thus driving the flow even deeper into the laminar region. Since the friction factor is inversely proportional to the fluid velocity, the friction factor will double. However, since the heat transfer coefficient is essentially independent of velocity, the heat transfer coefficient will not be affected. In addition, the decreased spacing will
increase the shape factor value, S. As a result, doubling the number of coolant lines results in a more than double increase in the overall heat transfer coefficient and a resulting more than halving of the increase in oil temperature. More exact calculations require knowledge of the roughness and geometric characteristics of the flow channel. In general, the Nusselt number, Nu, a dimensionless convective heat transfer coefficient is a product of the Reynolds number and the Prandtl number, as: Nu = ^ = C Rem Prn
(5.16)
For fully developed turbulent flow in very smooth tubes, C = 0.023, m = 0.8 and n = 0.4, and the equation is called the Dittus-Boelter equation. For developing turbulent flow in smooth tubes, m = 0.8, n = 0.33 and C is given as: / D \0.055
C = 0.036 -
(5.17)
where D is the channel diameter, L is the channel length and 10 < L/D < 400. This equation is usually called the Nusselt equation. For laminar flow in smooth tubes, the Sieder-Tate version is frequently used. It is much more dependent on entrance length effects and so has m = 1/3, n = 1/3 and C as: /DY/3 C =1.86 (5.18) where Re • Pr • (d/L) > 10. Example 5.5 illustrates heat transfer coefficient values obtained from these equations for a relatively simple flow channel design. For noncircular channels, the diameter is replaced with the hydraulic diameter, Dh, given as: Dh=^
(5.19)
where A is the cross-sectional area of the flow channel and P is the wetted perimeter. Example 5.5 Convective Heat Transfer Coefficients for Serpentine Mold Channel Figure 5.7 shows an example of a serpentine mold channel that has a roughness value, e = 0.001 D. Two coolants are to be evaluated—water at 700F and oil at 1500F. Determine the relative heat transfer effectiveness of these coolants in this flow channel. Water as a coolant
v, kinematic viscosity= 1.06 x 10~5 ft2/s p, density = 62.4 lb/ft3
Plug
Mold Base Coolant
Mold Cavity Flow Channel
Figure 5.7 Coolant flow channel around mold insert
k, thermal conductivity = 0.35 Btu/ft • h • 0 F v, average velocity = 4 ft/s Prandtl number = 7 Reynolds number, R e = 15,700 Flow is turbulent The friction factor-Reynolds number equation is: f = 0.0204 + 4.212 • R e " 0 6 4 2 = 0.0289 •
Stanton/Colburn analogy: (P^)_ f p r 2 /3 8 h, convective heat transfer coefficient = 886 Btu/ft2 • h • 0 F Nu, Nusselt number = hD/k = 106 Dittus-Boelter fully developed flow: Nu = 0.023 • Re0-8 • Pr0-4 = 114. h = 958 Btu/ft2 • h • 0 F Nusselt developing flow (L = 20): h =
• e
/ I \0.055
Nu = 0.036 • Re 0 8 • Pr0-33 • —
\4oy
• •
h = 1061 Btu/ft2 h - 0 F Nusselt developing flow (L = 6): N u = 136, h = 1137 B t u / f t 2 - h - 0 F Weighted average: Nu = 131, h = 1095 Btu/ft2 • h • 0 F
= 127.
The effect of developing flow is higher convective heat transfer. Oil as a coolant v, p, k, v,
kinematic viscosity= 1.35 x 10~ 4 ft2/s density = 54.5 lb/ft3 thermal conductivity = 0.082 Btu/ft • h • 0 F average velocity = 4 ft/s
Prandtl number, Pr = 290 Reynolds number, Re = 1235 Flow is laminar The friction factor-Reynolds number equation is: f = 16/Re = 0.0518 •
Stanton/Colburn analogy: 8 h, convective heat transfer coefficient = 58 Btu/ft2 • h • 0 F Nu, Nusselt number = hD/k = 29.5
• • •
Sieder-Tate for developing flow (L = 20): Nu = 1.86 • [Re • Pr • (D/L)] 2/3 = 20.8 h = 41 Btu/ft2 • h - 0 F Sieder-Tate for developing flow (L = 6): Nu = 46.4, h = 91 Btu/ft2 • h • 0 F Averaged developing flow: Nu = 32.1, h = 63 B t u / f t 2 - h - 0 F
Again, convective heat transfer in developing flow is higher than with fully developed flow. The arithmetic is considerably simplified for water at 210C or 70 0 F. For laminar flow, the heat transfer coefficient is obtained from [H]:
hlam = 3.52 ^-j Re 1 / 2 (j-J
(5.20)
where k is the thermal conductivity of the fluid, and D and L are the diameter and length of the flow channel, respectively. For turbulent flow in water at 210C or 70 0 F, the heat transfer coefficient is: /k\
/ r > \ 0.055
hturb = 0.068(^-jRe O8 ^ r J
(5.21)
The relative values for laminar and turbulent water flow in a typical mold are given in Example 5.6.
Example 5.6 Laminar and Turbulent Heat Transfer Determine the relative effect on heat transfer coefficient when the flow rate is increased so that flow moves from laminar to turbulent flow. Consider a serpentine coil imbedded in an epoxy mold, where Lid— 100. From Equations 5.20 and 5.21, determine the relative effect on the Biot number, the relative heat transfer coefficient. Then determine the actual heat transfer coefficients for water flowing in a 0.500-in or 1.27 cm diameter coil. The thermal conductivity of water is 0.35 Btu/ft - h -0F. Then, determine the heat transfer coefficient in the transition region, 2000 < Re < 10,000. For laminar flow, Re < 2000. Consider Re = 2000. From Equation 5.20, the Biot number, Bi = hD/k is given as: hD /D\1/2 Bi = — = 3.52 • Re1/2 • = 3.52 • 20001/2 • (0.01)1/2 = 15.7
k
Vw
¥ or fully turbulent flow, Re > 10,000. Consider Re = 10,000. From Equation 5.21, the Biot number is: hD /£)\0.055 Bi = —- = 0.068 • Re0-8 • = 0.068 • 10000° 8 • (0.0I) 0 - 055 = 83.7
k
VW
Note that increasing the flow rate by a factor of five increases the relative heat transfer coefficient by a factor of 83.7/15.7 = 5.3. The dimensional convection heat transfer coefficient for the coolant is given as: l W i a m = 15.7 - 0.35
ft
. h . o F • Qjjt = 132
hwater,turb = 83.7 • 0.35 • 12 = 700
ft2
^
ft2 fa o p
op
= 750 ^ - ^
= 4000
^ ^
Approximate values for heat transfer coefficients in the transition region, 2000 < Re < 10,000 are obtained by averaging. For example, for Re = 5000, the approximate heat transfer coefficient is:
Since the heat is conducted perpendicular to the mold plane, the fluid resistance must be corrected for the flow channel diameter and the number of flow channels in a given mold area (Fig. 5.1). If there are N flow channels of diameter d, then the area ratio is TTDNL/L 2 , and the effective resistance is:
R
»=s^
<5 22)
-
or (l/7iDNh conv ) per unit area. This resistance is small for turbulent water flowing in many closely-spaced large-diameter flow channels. It is quite significant for laminar oil flowing in widely-spaced small-diameter flow channels.
5.5
Cyclic Heat Balance
The total amount of energy to be removed from the plastic sheet by the coolant is easily determined for any given cycle from Equation 5.1. At steady state, this energy is usually transferred to: • • • •
The metal mold, and thence to the coolant, Cooler metal surfaces such as stripper bars and sheet clamps, and thence to surrounding air, Surrounding air, and/or Sprayed liquids such as water mist that then evaporate.
Consider the limiting case where a plastic sheet of uniform temperature Tp and uniform thickness tp is brought in contact with a mold having an initially uniform temperature Tm and thickness tm. Consider the mold to be made of a high thermal conductivity metal that is in contact with a coolant having a uniform temperature Tm. The free surface of the plastic sheet is insulated. The time-dependent temperature profile through the mold and the plastic sheet are shown in schematic in Fig. 5.8. Typically, the initial interfacial temperature between the sheet and the mold is much closer to that for the mold than that for the plastic. As cooling proceeds, the interfacial temperature falls.
Initial Sheet Temperature
Temperature
Thickest Section on Free Surface
Mold Surface Temperature Sheet Contacting Mold Surface
Thin Section on Free Surface
Time Figure 5.8 Characteristic time-dependent temperature profiles of thermoformed part cooling against a metal mold
Cooling the Free Surface of the Sheet There are four general methods for cooling the free surface of the sheet: • • • •
No cooling. In this case, the surface is essentially insulated from the environment, Natural air cooling. That is, no fans or forced air cooling methods are used. Forced air cooling. This can be as simple as clock-timer actuated shop floor fans or as complex as special-purpose high-velocity blowers, and Water fog or mist cooling. The mist is usually clock-timer controlled to shut off some time prior to sheet removal from the mold surface. This allows the fine water drops to evaporate before the part is removed.
Free surface cooling effectiveness increases as one progresses down this list. The measure of effectiveness of heat removal is the convective heat transfer coefficient, h. Table 5.4 summarizes the relative values of convective heat transfer coefficients for the last three free surface cooling methods. The convective heat transfer coefficient for an insulated surface is h = 0. Matched metal molds are used if the sheet is foam, reinforced or highly filled, or if close tolerance is needed in certain regions. In this case, the effective heat transfer coefficient, h eff = oo. These methods are shown in schematic in Fig. 5.9.
Cooling Thin Sheet in Ambient Air When a thin sheet of plastic is heated to the forming condition, it must be quickly transferred to the mold surface to minimize heat loss to the surrounding air. For very thin sheet, less than 0.005 in or 0.01 cm in thickness, the sheet is usually heated by
Table 5.4 Cooling a Part on the Mold—Relative Values of Thermal Resistance Physical resistance Free surface cooling Ambient air Forced air Water spray Interface gap** Mold Aluminum Plaster Coolant Laminar water (L/7idNhCOOI) Turbulent water (L/7tdNhcool)
Form for resistance
Typical reciprocal value (W/m2 •0C)
(Btu/ft2 • h • 0F)
1/hair 1/hair
l/hmist l/hc
2.84 28.4 284 114
0.5 5 50 20
D*/km dto
34,330 21
6000 3.7
454 4000
80 700
D* is the effective mold thickness and includes shape factor ** See Table 5.2 for these values
to to to to
5.68 56.8 568 284
to to to to
1 10 100 50
Cool Air
h=O,lnsulated Increasing Tm ie
Temperature
Initial Sheet Temperature
Mold Surface Temperature Free Surface Mold h= oo, Matched Molds
Temperature
Mold Free Surface Water Spray
Mold
Free Surface
Mold
Free Surface
Figure 5.9 The effect of various free-surface cooling techniques on time-dependent temperature profiles of thermoformed part cooling against a metal mold
contact heat transfer, then blown from the heater directly onto the mold surface. There is an extensive discussion of transient heat transfer to thin sheet in Chapter 3. This lumped-parameter analysis is directly applicable to the cooling of thin sheet in ambient air. The dimensionless temperature, Y, is given as: (5.23)
where T1 is the initial sheet temperature, Tair is the air temperature, 6 is time, a is thermal diffusivity, k is thermal conductivity, h is convection heat transfer coefficient between the sheet and the ambient air, and L is the sheet thickness. Note that the cooling time, 0 is proportional to the sheet thickness to the first power. In contrast, for conduction-controlled heat transfer, the cooling time is proportional to the square of sheet thickness. The lumped parameter cooling time curves for various film thicknesses are compared with experimental data in Fig. 5.10. Since nothing is known about the experimental processing conditions or sheet material parameters, the curves are fit at L = 0.15 cm or 0.060 in by selecting values for the convection
Time, s
Calculated h = 10 Rtu/ft2h°F Ambient Air Forced Air
Water Spray Figure 5.10 Effect of sheet thickness on cooling time for con vection-controlled thin sheet. Solid lines are calculated. Dashed lines are experimental
Sheet Thickness, ft
heat transfer coefficient, h. The shapes of these convection-controlled curves agree better with the data than do the conduction-controlled curves. Transient Heat Removal From the Sheet The energy in the sheet is removed by conduction to the mold and free surfaces. The transient one-dimensional conduction heat transfer equation, Equation 3.4, applies: (5.24)
subject to the following boundary conditions: (5.25)
(5.26) (5.27) Equation 5.25 is the heat flux from the free sheet surface to the ambient air, with hConv a s the convection heat transfer coefficient, Table 3.2. T1 is the initial sheet temperature at the time of contact with the mold surface. If draw-down onto the sheet surface is very rapid, T1(X) is represented by the equilibration temperature profile discussed in Section 3.13. As a first approximation, T1(X) = T1, an average sheet temperature. Two limiting conditions bound the solution of this equation and its attendant boundary conditions. Quiescent Ambient Air When heat transfer to air is very small relative to the rate of energy conducted to the mold, h->0, the free surface is approximated by an insulated surface. This is usually the case for natural convection of heat to quiescent air. Figure 5.11 is used
T Mold, Conduction
Dimensionless Temperature
T
o
Free Surface, Convection T
o
Biot Number, hL/k
Dimensionless Time, Fourier Number Figure 5.11 Time-dependent average sheet temperature as a function of the rate of heat loss from the free surface. Dimensionless temperature, Y = (T — T0V(Tj — T0) where Tj is the initial sheet temperature and T 0 is the mold surface temperature and ambient air temperature. Biot number, Bi = hL/k, where h is the convection heat transfer coefficient and k is polymer thermal conductivity. Fourier number, Fo = a0/L2 where a is the thermal diffusivity, 9 is time and L is sheet thickness
to obtain the dimensionless time, Fo = a9/L 2 , with the dimensionless temperature, Y, given as: ( T - Tmold) CTi-T mold ) where T1 is the average sheet temperature. Since h conv = O, Bi = hL/k, the Biot number is zero. L is the actual thickness of the sheet. This is illustrated in Example 5.7.
Example 5.7 Cooling Time for Heavy-Gage PS Sheet—I A polystyrene sheet 0.438 in or 1.11 cm thick initially at 375°F or 191°C is cooled by pressing it against a mold at 75° F or 24° C. Determine the time required to cool the sheet to an average temperature of 175°F or 79° C. PS thermal conductivity is 0.073 Btu I ft -h-°F or 0.0003 cal/g • s 0C. PS density is 65.5 Ib /ft3 or 1.05 g/cm3. PS specific heat is 0.5 Btu jib • 0F= 0.5 cal/g • 0C. The free surface is exposed only to ambient air. Assume Zz00 = O.
The dimensionless average temperature, Y is given as: Y =
(175-75) (375-75) = °- 3 3 3
From Fig. 5.11, the Fourier number at this value of Y for Bi = O is Fo = 0.345. The polymer thermal diffusivity is given as: a=— = p-cp
5.7x 1 0 - 4 — = 2.2 x 10~3 ^ s h
The cycle time is given as: r/fl
1
F o = j - 2 = 5.7 XlO" 4 - ^
5
- 6[S] = 0.345
or 8 = 746 s. This is shown as the top line of Table 5.5. Moving Ambient Air Figure 5.11 is also used to approximate the relative effect of air movement on the cooling time, so long as T a i r « T mold . Now the dimensionless temperature, Y, is given as: v —
~
mold
)
(T — Tair)
(T,-T m o l d r(T,-T a i r )
p 2y)
-
Note that as Bi increases, through increase in the value for the convection heat transfer coefficient, the cooling time drops rapidly. When Bi = oo, the dimensionless time to reach the same dimensionless temperature drops to one-fourth that for the quiescent case (Bi = 0). This directly supports the discussion in Chapter 3 that the value of L should be half the actual sheet thickness when energy interchange is symmetric across the sheet. Example 5.8 illustrates the effect of heat transfer coefficient value on cooling time. Example 5.8 Cooling Time for Heavy-Gage Polystyrene Sheet—II Using the data from Example 5.7, determine the reduction in cooling time if the following free surface coolants are used: a) Ambient air with a heat transfer coefficient of h = 1 Btu/ft2 -h'°F
or 5.68 W/m2 • 0 C,
b) Forced air with a heat transfer coefficient of h=10
Btu/ft2 -h
0
F or 57 W/m2 • 0 C, and
c) Water mist with a heat transfer coefficient of h = 100 Btu/ft2 -h-°F
or 570 W/m2 • 0 C.
For each case, the Biot number Bi = hL/k. 1 Btu 0.438 1 ft • h •0 F Ac a)Bl= F l ^ - I ^ f t ' 0 ^ - B t u - = 0-5 .
The value of Fo for Y = 0.333 and Bi = 0.5 from Fig. 5.11 is Fo = 0.256 or 0 = 554 s. This is about 26% reduction in cycle time from the insulated example, Bi = 0 of Example 5.7. b) Bi = 5. The value of Fo from Fig. 5.11 is 0.123 and the cycle time 9 = 266 s. This is a 64% reduction in cycle time. c) Bi = 50. The value of Fo from Fig. 5.11 for Bi = oo is 0.086. The best cycle time possible is 0 = 187 s. This is a 75% reduction in cycle time from the insulated example. These values are tabulated in Table 5.5. The effect of altering free surface cooling conditions is seen in Fig. 5.12 [12]. The nature of the polymer and the details about the processing conditions are unknown. For L = 0.15 cm or 0.060 in sheet, water spray reduces the cooling time by about 60%. For thicker sheet, L = 0.45 cm or 0.180 in, water spray reduces the cooling time by about 65%. As expected, the cooling time increases with increasing sheet thickness. As expected, the effect is most obvious with ambient air cooling. On the other hand, if conduction heat transfer through the plastic sheet controls the cooling time, the effect of sheet thickness is easily determined. At any given average sheet temperature, the dimensionless time, Fo, is a simple function of the Biot number: Fo = f(Bi) (Y
fixed)
(5.30)
Ambient Air
Time, s
Forced Air
Water Spray Calculated
Sheet Thickness, ft
Figure 5.12 The effect of various cooling techniques on cooling time as function of sheet thickness, theory from Fig. 5.11. Experimental data from [12]
Table 5.5 Calculated Cooling Times for Polystyrene Sheet (Combined Convection/Conduction Heat Transfer) Type of free surface cooling
Convection heat transfer coefficient (W/m 2 • 0C)
Thin-gage sheet
Heavy-gage sheet
L - 0 . 1 1 1 c m - 0 . 0 4 3 8 in
L = 1.11 cm = 0.438 in
Biot no.
Biot no.
(Btu/ft2 • h • 0 F) Fourier no.
Cycle time
Fourier no.
(S)
Insulated Ambient air Forced air Water spray Direct contact or matched die
0 5.7 57 570
0 1 10 100
0 0.05 0.5 5.0
OO
OO
OO
0.345 0.323 0.256 0.123 0.086
7.46 6.98 5.54 2.66 1.87
Cycle time (S)
0 0.5 5.0 50 OO
0.345 0.256 0.123 0.086 0.086
746 554 266 187 187
Initial sheet temperature, T1 = 190.60C or 375°F Mold ambient temperature, T 0 = 23.90C or 75°F Final average temperature, T a = 79.4°C or 175°F Thermal conductivity = 0.0003 cal/gm • s • 0 C or 0.073 Btu/ft • h • 0 F Thermal diffusivity = 0.00057 cm2/s or 0.0022 ft2/h From these values, the following are found: Y = 0.333 Bi = hL/k Fo = oc9/L2 = 0.0863[l + 3 exp( - 0.667 Bi0-667)]
As seen in Fig. 5.11, the approximate form for Equation 5.30 is: Fo = Fo00[I + p exp(-aBia)]
(5.31)
Fo00 is the value of Fo when Bi = oo, the limiting case where both sides of the sheet contact solid surfaces. When Bi = 0, Fo = 4Fo00. Since Fo = oc9/L2, the cooling time 9 is proportional to the square of the sheet thickness for both limiting cases. It is apparent then, that when conduction from the plastic sheet controls heat transfer, doubling the sheet thickness always increases the cooling time by a factor of four. See also Table 5.5 where Equation 5.31 is used to compare cycle times for various free surface cooling modes. As seen in Fig. 5.13, actual cooling times show a relationship that is more linear with thickness. The observed values are substantially higher than the values obtained from Fig. 5.12. This indicates that, at least in this case, the experimental sheet is not being cooled in a conduction-controlled environment. Again, the exact conditions used to obtain the experimental data of Fig. 5.13 are unknown. Cooling on Nonmetallic Molds For metal molds, the time-dependent conduction resistance through the mold during the heat removal process from the sheet is usually negligible. Heavy-walled, non-
Ambient Air
Tjme, s
Forced Air
Water Spray
Sheet Thickness, in
Figure 5.13 Measured sheet thickness-dependent cooling times for various cooling techniques. Figure adapted from [23]
metallic molds alternately store and liberate heat during each forming cycle. An estimate of the rate at which heat penetrates the mold is obtained by integrating the time-dependent heat conduction equation, as discussed below. As with energy input to plastic sheet, Chapter 3, there are two limiting conditions that are important. If the energy transfer is constant heat flux and the mold is considered as a semi-infinite slab of thermal diffusivity, oc, the depth of penetration of energy, 5, is approximately: (Constant Heat Flux)
6 = v/6oc6
(5.32)
2
The penetration dimensionless time, Fo = aO/L = 1/6 [13]. If the surface is raised instantaneously to a constant temperature, the depth of penetration of energy, 5, is approximately: (Constant Surface Temperature)
5 = ^/24ae
(5.33)
2
and the penetration dimensionless time, Fo = a0/L = 1/24. In thermoforming, the actual condition is closer to the constant flux approximation. If D is the effective thickness of the mold, then the time for the heat to be felt at the coolant interface is: D2 A D2 2^<0<6^ ^34> Example 5.9 illustrates how the type of mold material dictates the penetration time of heat into the mold. For many thermoforming operations where actively cooled nonmetallic molds are used, the coolant probably would not see all the energy removed from the sheet until after the sheet had been removed from the mold. The mold, in effect, is storing the sheet thermal energy during the cooling cycle, then transferring it to the coolant after the cycle. The heat is also being convected away from the mold surface during the times when no sheet contacts the mold surface, as shown in Fig. 5.14. The approximate increase in mold temperature during the cooling cycle and the approximate time required to return the mold to within 2% of its initial temperature are illustrated in Example 5.10. For all practical cases where low-conductivity molds made of wood, plaster, fiberglass and even certain metal-filled epoxies are used, the average mold temperature continues to increase in value during the forming process
Mold in Contact With Plastic Mold
Plastic
Mold Cooling in Ambient Air
Figure 5.14 Schematic thermoforming mold temperature profiles when mold is in contact with hot polymer [top] and with ambient air [bottom]
Mod l
Ambient Air
until the energy added during the cooling portion of the cycle just equals that extracted during the entire cycle time. From Equation 5.2, the amount of heat added per unit area of the mold for a given cycle is: (5.35)
Example 5.9 Transient Heat Penetration into Molds Consider two molds, a prototype plaster mold with a relative thickness D = 2 cm or 5.1 cm, and a production aluminum mold with a relative thickness D = 0.2 in or 0.51 cm. Determine the elapsed time for a heat pulse to travel to the reverse side of each of these mold materials. The thermal diffusivity for aluminum is 0.49 Cm2Is= 1.9ft2/h and for plaster is 3Ox 10~4 cm2/s or 11.6 x 10~3 ft2/h.
From Equation 5.34, the penetration time is bracketed by D2/c • a, where c = 24 for constant surface temperature and c = 6 for constant heat flux. For aluminum, D2/oc = 0.0816 s. For plaster, D2/oc = 1333 s. Thus the penetration time for aluminum is: 0.0034 s<9<0.0136 s The penetration time for plaster is: 55.5 s < 0 < 2 2 2 s For aluminum, it is apparent that energy transfer is almost immediate, within milliseconds. For plaster, there is a substantial lag in energy transfer.
Example 5.10 Approximate Increases in Cycle Time for Prototype Molds Consider the case where a prototype plaster mold heats during contact with the formed sheet. If the initial mold temperature is 75°F or 24°C and the final mold temperature is 125°F or 52°C, estimate the average sheet temperature at 746 s (see Example 5.7) for an insulated free surface. Then estimate the time required to cool the sheet to an average temperature of 175°F or 79°C. Then determine the approximate time required to cool the mold back to its initial temperature.
The correct approach to this problem is to solve the transient heat conduction equations for the cooling sheet and the heating mold, as done in Section 5.6. The bounds on the answer are obtained by assuming an initial mold temperature of 125°F or 52°C. At Fo = 0.345 and Bi = 0, Y = 0.333. Y =
(T-T 0 ) (T-125) O W J = (375- 125) = 0 ' 3 3 3 Tave = 2080F = 98°C
In other words, the average sheet temperature is somewhere between 175°F or 79°C as determined with an isothermal mold and 2080F or 98°C as determined by an artificially high mold temperature of 125°F or 52°C. The time needed to attain an average sheet temperature of 175°F or 79°C is obtained as follows:
For Bi = 0, Fo = 0.53 from Fig. 5.11. Therefore 0 = 1145 s. The actual time is somewhere between 746 s for 75°F or 52°C mold temperature and 1145 s for 125°F or 52°C mold temperature. The increase of more than 50% in cycle time is a strong indication of the importance of maintaining constant mold surface temperature. Figure 5.11 is used to determine the cooling rate of the prototype mold. Consider cooling the mold to within 2% of its initial temperature. That is Tmold,final = 76°For24°C. Now:
For Bi = 0, Fo = 1.4. The cooling time is given as: I - *
For plaster, oc = 30 x 10~4 cm2/s and D = 2 cm. Therefore the cooling time is given as 0 = 1870 s. It is apparent that temperatures in prototype molds increase with the number of parts molded.
where tavg is the average sheet thickness, for this illustration. T1 is the initial sheet temperature, T f is the final sheet temperature and T* is the time-average sheet temperature, such as TJ = (T1 + T avg )/2. This amount of heat is to be removed in the cooling time, 0C. There are N forming cycles in the total time 6T. The total amount of heat to be removed from the sheet in the time 0 T is thus given as: QtOtHi = N - P C p - ^ ( T 1 - T f )
(5.36)
The heat convected away by the cooled air in contact with the sheet in the time 9 T is: A O
= h (T*- T )
Vconv
lx
airV A a
A
air/
COQl
(5 37) \~>.J>i)
A
The time when no sheet contacts the mold surface is given as (1 — 6COOI/6T)- During this time, energy is being transferred from the mold surface to the cooling air: /1 A \ Qconv = h a i r (T m o l d a v g — T a i r )
Ux
(5.38)
That absorbed by the mold is given as: Qmold = Qavg - Q c o n v
(5-39)
The amount of heat transferred to the coolant during the entire cooling portion of the cycle is: Qcooi ~ h c o o l (T m o l d avg — T c o o l )
(5.40)
The overall heat balance is then given as: ^cool
^coolv A mold,avg
A
cool/
= N • pc p • U 8 (T 1 - Tf) - h air (T* - T air ) % ^ - h air (T mold , avg - T air ) ° ~ 9 c o o l )
(5.41)
Ux Ux As is apparent, T m o l d a v g is the only unknown temperature. Example 5.11 illustrates the relative temperature increase for cyclic cooling on a plaster mold. As expected, average equilibrium mold temperature values increase with decreased time between forming steps and decrease with higher coolant flow rates, lower coolant temperatures and more efficient convection cooling at the free surface. A more exact analysis is presented below when all aspects of transient heat removal from plastic sheet are incorporated in a general computer program in the next section. Example 5.11 Equilibrium Mold Temperature Make a steady-state heat balance on a plaster mold to determine its equilibrium mold temperature. The mold is cooling a 0.060 in or 1.5 mm PSpart in 20 s. There is a 20 s delay for part removal, insertion and draw-down of the next part. The initial average sheet temperature is 375°F or 1900C. The final average sheet temperature is 175°F or 79°C. The initial mold temperature is 75°F or 24°C. The PS specific heat is 0.45cal/g •0C or 0.45Btujib • 0 F. The PS density is 1.05g/cm3
Next Page or 65.5 Ib I ft3. The convection heat transfer coefficient to forced air is hair = 28.4 W/m2 • 0C or 5 Btu/ft2 • h • 0F. The air temperature is 75°F or 24°C. The heat transfer coefficient to the coolant is hcool = 284 W/m2 • 0C or 50 Btu/ft2 • h • 0F. The coolant temperature is 75°F or 24°C.
All the values for Equation 5.41 are known except the equilibrium mold temperature, T mold avg. The first term on the right is: N • rcp • tavg(Tx - Tf) = 90 • 65.5 • 0.45 • ~
• (375 - 175) = 2650
J ^
This is the heat that must be removed from the sheet. The second term on the right is the amount of heat convected from the sheet to the air. Here 0 cool /0 T = 0.5. The average sheet temperature is T avg = 375 — 175 = 275°F. h a i r (T a v g -T a i r )-0.5 = 5 0 0 ^ The average heat loss from the uncovered mold is given as the third part of the right side of Equation 5.41: hair(Tmold,avg - Tair)(l - 0.5) = 5 • 0.5 • (T mokUvg - 75) And the average heat loss to the coolant is given as the term on the left in Equation 5.41: hcool ' ( l m o l d , a v g
^ cool)
=
^
' V ^ mold,avg
'^)
The mold temperature is then obtained from: (50 + 2.5) • (T mokUvg - 75) = 2650 - 500 = 2150
J ^
OrT m o l d , a v g =116°For46.6°C.
5.6
Transient Heat Transfer During Sheet Cooling on the Mold Surface—Computer Models
As shown in Fig. 5.1, the convective and conductive elements discussed above represent resistances to heat removal from the sheet. Time-dependent sheet temperature is determined by simultaneously solving the transient heat conduction equations for both the formed plastic sheet and the mold1: (5.42) (5.43) 1
The general transient one-dimensional heat conduction equation was described in detail in Chapter 3.
Previous Page or 65.5 Ib I ft3. The convection heat transfer coefficient to forced air is hair = 28.4 W/m2 • 0C or 5 Btu/ft2 • h • 0F. The air temperature is 75°F or 24°C. The heat transfer coefficient to the coolant is hcool = 284 W/m2 • 0C or 50 Btu/ft2 • h • 0F. The coolant temperature is 75°F or 24°C.
All the values for Equation 5.41 are known except the equilibrium mold temperature, T mold avg. The first term on the right is: N • rcp • tavg(Tx - Tf) = 90 • 65.5 • 0.45 • ~
• (375 - 175) = 2650
J ^
This is the heat that must be removed from the sheet. The second term on the right is the amount of heat convected from the sheet to the air. Here 0 cool /0 T = 0.5. The average sheet temperature is T avg = 375 — 175 = 275°F. h a i r (T a v g -T a i r )-0.5 = 5 0 0 ^ The average heat loss from the uncovered mold is given as the third part of the right side of Equation 5.41: hair(Tmold,avg - Tair)(l - 0.5) = 5 • 0.5 • (T mokUvg - 75) And the average heat loss to the coolant is given as the term on the left in Equation 5.41: hcool ' ( l m o l d , a v g
^ cool)
=
^
' V ^ mold,avg
'^)
The mold temperature is then obtained from: (50 + 2.5) • (T mokUvg - 75) = 2650 - 500 = 2150
J ^
OrT m o l d , a v g =116°For46.6°C.
5.6
Transient Heat Transfer During Sheet Cooling on the Mold Surface—Computer Models
As shown in Fig. 5.1, the convective and conductive elements discussed above represent resistances to heat removal from the sheet. Time-dependent sheet temperature is determined by simultaneously solving the transient heat conduction equations for both the formed plastic sheet and the mold1: (5.42) (5.43) 1
The general transient one-dimensional heat conduction equation was described in detail in Chapter 3.
where p, c p and k are the density, heat capacity and thermal conductivity values and " p " and "m" are for polymer and mold, respectively. Thermal diffusivity, oc is defined as k/p • cp. The boundary conditions needed to solve these equations are: (5.44) (5.45) (5.46) (5.47) (5.48) The first two equations represent convection conditions at the free surface and the mold/coolant interface, respectively. The third set of three equations represents the heat conduction across the interfacial air trapped between the plastic sheet and the mold surface. The last two equations represent the initial sheet and mold temperatures, respectively. The solution to these equations uses finite difference [14,15]. The explicit method uses a time step defined as: At = Fo • Ax2/oc
(5.49)
where Fo is the Fourier number. For mathematical stability, Fo <\x- Once the time step is determined, the temperatures at t + At are obtained from: (5.50) (5.51) (5.52) (5.53) Bi is the Biot number, given as:
The proper value of hw, the effective convective heat transfer coefficient for the coolant, must include the film heat transfer coefficient for the coolant, the shape factor discussed in Section 5.4 and any fouling factor. The time-dependent temperature profile depends on relative material and geometric values of the plastic sheet and the mold. Figure 5.15 gives one example of the coupled temperature profiles with no interstitial air layer, that is T11 = T12 = T1. Table 5.6 is a parametric study of some of the parameters. In this study, it is apparent in the first block of data that the total cooling time is strongly affected by mold materials from aluminum to plaster. As expected, the effect of coolant methods on 1
Since there are two Fourier numbers, one for the plastic and one for the mold, stability is achieved by selecting the smaller time step that satisfies the Fo < \ criterion.
Coolant
Mold
Increasing Mod l Thermal Conductivity Temperature
Plastic
Coolant
Temperature
Increasing Convection Heat Transfer
Mold Plastic
Figure 5.15 Schematic temperature profiles through coolant, mold and polymer with increasing mold thermal conductivity [top] and increasing coolant convection heat transfer [bottom]
cooling time is less important for prototype materials such as plaster than for production materials such as aluminum. The effect of mold thickness for production mold materials such as aluminum is essentially nil. In all conduction heat transfer models, such as that used to produce Fig. 5.12, the unaccomplished temperature change, Y, is shown to be proportional to the Fourier number of the polymer, Fo = oc9/L2, where a is the polymer thermal diffusivity, 6 is time and L is the thickness of the polymer sheet. If the average sheet temperature at removal from the mold surface is fixed, the unaccomplished temperature change, Y, is fixed and so is the Fourier number. The time required to cool the sheet to that temperature should then be proportional to the square of the sheet thickness: ecooi = (Fofixed/a)-L2
(5.54)
Doubling the sheet thickness should increase the cooling time by a factor of four. This concept is confounded in practice by the presence of the mold and the attendant transient heat conduction to the coolant. Figure 5.16 shows that the effective cooling time of a polymeric sheet in contact with a mold having finite thermal conductivity is not in proportion to the square of the sheet thickness, but rather to a powder somewhat less than 21. The heat conduction square law, Equation 5.54, is therefore conservative. 1
For the example shown, 0 is proportional to L17.
Table 5.6 Parametric Study of Cooling of Polystyrene Sheet to an Average Temperature of 1500F Against a Mold of Various Materials Mold material
Coolant type
Surface cooling
Plastic thickness (in)
Mold thickness (in)
Time to cool (S)
Interface temperature* (0F)
Surface temperature* (0F)
Aluminum Aluminum
Water Water
Forced air Natural air
0.100 0.100
0.500 0.500
19.4 26.4
77.7 77.1
171.1 187.6
Steel Cu/bronze Zn alloy Al-epoxy Maple
Oil Oil Oil Oil Oil
Natural Natural Natural Natural Natural
air air air air air
0.100 0.100 0.100 0.100 0.100
0.500 0.500 0.500 0.500 0.500
28.3 28.8 28.5 45.5 236.4
86.2 85.6 88.1 117.6 149.5
182.3 183.5 182.2 162.8 146.9
Plaster Plaster Plaster
Oil None None
Natural air Natural air None
0.100 0.100 0.100
0.500 0.500 0.500
116.9 116.9 200.0
144.1 144.4 145.0
149.2 149.3 152.6
Aluminum Aluminum Aluminum Aluminum
Water Water Water Water
None Natural air Forced air Water spray
0.100 0.100 0.100 0.100
0.500 0.500 0.500 0.500
29.7 26.4 19.4 7.4
76.8 77.1 77.7 78.1
192.4 187.6 171.1 78.5
Aluminum Aluminum Aluminum Aluminum
Water Water Water Water
Forced Forced Forced Forced
air air air air
0.100 0.100 0.100 0.100
0.500 1.000 2.000 4.000
19.4 19.2 19.1 19.5
77.7 77.1 76.1 76.1
171.1 171.3 170.9 167.8
Aluminum Aluminum Aluminum Aluminum
Water Water Water Water
Forced Forced Forced Forced
air air air air
0.050 0.100 0.200 0.400
1.000 1.000 1.000 1.000
5.7 19.2 61.1 190.5
76.5 77.1 75.2 72.6
180.7 171.3 156.1 135.2
* When average sheet temperature <150°F
Free Surface Temperature, 0F or Time, s
Free Surface Temperature,°F
Time, s
Sheet Thickness, in Figure 5.16 Calculated sheet thickness-dependent cooling time and free surface temperature—parametric study
Interfacial Air The actual thickness of the interstitial air layer between the polymer sheet and the mold is unknown. Arithmetically, Equation 5.44 is used with two interfacial temperatures, T11 being the polymer surface temperature at the polymer/air interface and T12 being the mold surface temperature at the air/mold interface. With some manipulation, these interfacial temperatures are related to the interior plastic and mold temperatures, Tp and Tm, respectively. (5.55) (5.56) (5.57) (5.58) (5.59)
Table 5.7 Parametric Study of Cooling of Polystyrene Sheet to an Average Temperature of 1500F Against an Aluminum Mold Using Forced Air and Water as Coolants With an Air Interstitial Layer (Plastic sheet thickness = 0.100 in) (Mold thickness = 1.00 in) Time to cool
(0F)
Plastic/air interfacial temperature (0F)
171.2 170.4 165.8 162.1 158.8 153.8 149.4 147.2
77.1 78.2 86.9 94.9 101.2 110.7 120.5 124.9
19.2 19.5 21.9 24.2 26.5 30.8 36.3 39.7
Interfacial air layer thickness (in)
Surface temperature
0 0.0001 0.0010 0.0020 0.0030 0.0050 0.0080 0.0100
(S)
Cooling Time, s
The numerical solution to the coupled transient heat transfer equations proceeds as before, using standard finite difference equations. Table 5.7 shows the results of one parametric study. As redone in Fig. 5.17 for this specific study, the overall cycle time
Air lnnerlayer Thickness, in Figure 5.17 The effect of trapped air gap thickness on cooling time—parametric study
increases with interstitial layer thickness in a power-law fashion. Example 5.12 shows another way in which this arithmetic can be used in thermoforming. Example 5.12 Finding Air Bubbles Can infrared scanning detect an air bubble in an opaque plastic sheet while it is in contact with the mold surface?
Consider the database used in the parametric study of Table 5.7. Assume the gap between the plastic and the mold in the air bubble is 0.005 in, Fig. 5.18. The bulk of the plastic, in intimate contact with the mold surface, reaches an average sheet temperature of 1500F in 19.2 s. At that time, the free sheet surface temperature is 1710F. From the computer model at 19.2 s, the average temperature in the plastic over the air bubble is 185°F, the temperature of the polymer/air bubble interface is 128°F and the surface temperature of the plastic over the air bubble is 1910F. The 2O0F temperature difference in plastic free surface temperature should be easily detected with a standard infrared scanning device.
5.7
Shrinkage
As with all materials, plastics increase in specific volume or decrease in density with increasing temperature1. The specific volume of any polymer changes in slope with temperature at the glass transition temperature (Fig. 5.19). The specific volume of a crystalline polymer shows a distinct discontinuity in slope during melting. The
1
Volumetric change at thermodynamic equilibrium, Ve, the result of increased molecular motion, such as rotation and reptation, is related to the coefficient of thermal expansion, COE, in the following way. Volumetric change is a function of temperature and pressure, according to: (5.60) Rearranging: (5.61) (5.62) where k is the volume expansivity or coefficient of thermal expansion, k = COE, with units of temperature"1, and P is the isothermal or bulk compressibility, with units of pressure"1. Thermal expansion is usually restricted to dimensional changes of the polymer over a temperature range in which the polymer has no thermodynamic transitions. Typical values for coefficients of thermal expansion of many polymers and some mold materials are given in Table 5.8.
Air Bubble or ,,Lake"
Sheet Air Gap Mold Figure 5.18 Schematic of air bubble or lake in molded part
volumetric change in the polymer during cooling from the forming temperature to room temperature is called "shrinkage". All polymers shrink when cooled, regardless of the process. Shrinkage occurs in thermoforming when the hot polymer sheet is cooled against a rigid mold. There are two general types of shrinkage: •
Unconstrained shrinkage, sometimes called isotropic shrinkage. The formed part decreases uniformly in dimension to the densities shown in Fig. 5.19. The final part is said to be in thermodynamic equilibrium. • Constrained shrinkage. The formed part is constrained from shrinking in at least one direction. The final part density may not achieve the thermodynamically equilibrated value until some time after the part has been removed from the mold and trimmed from its web.
Unconstrained Shrinkage Crystalline polymers heated above their melt temperatures typically have greater unconstrained shrinkage values than amorphous polymer, as seen in Fig. 5.19 and Table 5.9 [16]. This figure shows the difference in volumetric change between an amorphous and a crystalline polypropylene. The volumetric change is converted to isotropic linear dimensional change as follows. Volumetric shrinkage, Sv is defined as [17]: (5.63)
Table 5.8 Coefficients of Thermal Expansion For Plastics [ASTM D 696] Material
ABS ABS/PVC ABS/PC 20% GR ABS POM acetal copolymer Cast PMMA Extruded PMMA Ethyl cellulose Cellulose acetate Cellulose butyrate Cellulose propionate PCTFE PVDF PTFE Polyamide 6 (PA 6) Polyamide 66 (PA 66) Polybutylene Polycarbonate Polybutylene terephthalate Polyethylene terephthalate PETG Polyetherimide LDPE HDPE Polyimide Polymethyl pentene mPPO PPS PP homopolymer PP copolymer PS—unmodified FR PS—rubberized SAN SMA Thermoplastic polyurethane Polysulfone Polyether sulfone Thermoplastic elastomer PVC-rigid PVC-flexible
Thermal expansion (solid) CF)"1
(0C)-1
60-130 50-90 70 20 60-85 50-90 50-90 100-200 80-180 110-170 80-120 35-70 70-140 70-120 80 80 125-150 70 60-95 65 50-70 50-55 100-220 60-110 45-55 65 40-70 25-50 80-100 70-95 50-80 45 65-70 80 100-200 55 55 85-190 70 70-250
35-70 30-50 40 10 35-45 30-50 30-90 55-110 45-100 60-95 45-65 20-40 40-80 40-65 45 45 70-85 40 35-55 35 30-40 30 55-120 35-60 25-30 35 20-40 15-30 45-55 40-55 30-45 25 35-40 45 55-110 30 30 50-105 40 40-140
Specific Volume, cm 3 /g
Amorphous PP
Crystalline PP
Temperature,0C Figure 5.19 Temperature-dependent specific volume of amorphous and crystalline polypropylene, PP homopolymer [16]. Figure used with permission of copyright owner
where Vm and Vf are the specific volumes of the polymer at room temperature and the forming temperature, respectively. Linear shrinkage, S1, is given as: (5.64) When the cube root is expanded in series form, the linear shrinkage is approximated as: S1« -^ + higher order terms
(5.65)
Shrinkage values are usually given as ranges. The actual values depend on the temperature difference between forming temperature and room temperature. Table 5.9 gives representative shrinkage ranges for thermoformed polymers. The recommended shrinkage values are used when actual experience with shrinkage of a specific polymer is unknown. The following processing aspects influence the extent of shrinkage [18]: •
Part Design. Draft on both female and male surfaces influence the extent of constraint on the sheet as it cools. This is discussed below and again in the
Table 5.9 Shrinkage Values for Thermoformable Polymers Polymer
Shrinkage range (%)
Recommended shrinkage (%)
ABS-Medium impact ABS-Heat resistant ABS-Flame retarded Cellulose acetate Cellulose butyrate Cellulose propionate Ethylene vinyl acetate (20%) FEP fluoropolymer PTFE fluoropolymer Polycarbonate
0.6-0.9 0.5-0.8 0.5-0.8 0.4-0.9 0.3-0.9 0.3-0.9 0.3-0.8 1.5-4.5 5.0-10.0 0.5-0.7
0.7 0.7 0.7 0.5 0.4 0.5 0.6 3.0 7.0 0.6
Polyetherimide PEEK Polyethersulfone LDPE HDPE
0.6-0.8 0.8-1.0 0.6-0.8 1.5-4.5 2.0-4.5
0.7 0.8 0.7 3.0 2.5
PMMA mPPO PP HIPS PS
0.2-0.8 0.5-0.7 1.0-2.5 0.5-0.8 0.5-0.7
0.6 0.7 2.0 0.6 0.6
0.7-0.9 0.5-1.0 10.0-15.0 2.0-3.5 0.1-0.5
0.8 0.8 12.0 3.0 0.3
0.5-2.5 0.1-0.5 0.5-0.9 0.3-0.5 0.4-0.8
1.5 0.3 0.7 0.5 0.7
0.2-0.4 0.3-0.6 10.0-18.0 0.4-0.8
0.4 0.5 12.0 0.7
Polysulfone Thermoplastic urethane Flexible PVC Flexible PVC (filled) Rigid PVC PVDC Rubberized styrene (Kraton) SMA SAN K-Resin PBT Amorphous PET Crystallized PET XT Polymer
• • •
chapter on mold design. Male elements such as posts, bosses, partitions and gussets in female molds also influence shrinkage. Part Wall Thickness Uniformity. Thin sections cool more rapidly than heavy sections and as a result differential shrinkage will result when part wall thicknesses are not very uniform. Mold Temperature. A 100C or 18°F difference in mold surface temperature may change shrinkage values by as much as 0.1%. Depth of Draw. Deeply drawn parts are usually characterized by nonuniform wall thickness, part regions that are formed at lower temperatures than others, and
Specific Volume
Rapid Cooling Rate
Slow Cooling Rate Mobile State
Solid State
Temperature Figure 5.20 The schematic effect of cooling rate on specific volume of an amorphous polymer
•
regions that have contacted lower temperature plugs. All these aspects influence local shrinkage. Initial Sheet Forming Temperature. Lower forming temperatures result in lower shrinkage.
Constrained Shrinkage Applied stresses inhibit shrinkage. When the plastic sheet is constrained against the mold surface by part design, mold temperature or applied force, complete isotropic shrinkage may be inhibited. Even if mold design and processing conditions are ideal, differential shrinkage may result due to differences in part wall thickness. When the stresses holding the sheet against the mold surface are removed, shrinkage continues. As noted, volumetric change is temperature dependent. Rapid cooling of the plastic sheet forces the polymer into a thermodynamically non-equilibrium state since there is insufficient time for molecular relaxation before the molecular mobility is inhibited. Consider the temperature-dependent volumetric change schematic of Fig. 5.20. The specific volume of the polymer is written as: (5.66)
Specific Volume, cm 3 /g
V
e
v-v e
V1
Time Figure 5.21 Characteristic time-dependent change in specific volume of an amorphous polymer to a step change in environmental temperature [19]. Figure used with permission of copyright owner. V1 is the initial volume. Ve is the final volume of the polymer
where T is temperature and 9 is time. The differential form for the volume is: (5.67) The temperature-dependent volumetric change is given as: (5.68) where r = dT/d6, the rate of cooling. Consider a time-dependent change in specific volume in response to a step change in environmental temperature for an amorphous polymer such as polystyrene (Fig. 5.21) [19]. The initial change in specific volume is given as V1 and the time-dependent change is: (5.69) where Ve is the equilibrium value of the specific volume and x is the isothermal rate constant. If the constant pressure temperature-dependent equilibrium volume is written as: Ve = aT + b (5.70) the rate of change of actual volume with temperature is given as: (5.71) Equation 5.71 shows that the maximum amount of shrinkage owing to a step change in sheet temperature for an amorphous polymer is a function of the isothermal rate constant, x, and the degree of quench, r. The isothermal rate constant, x, is related to material relaxation once applied stresses are removed. Stress relaxation time, X9
at the glass transition temperature, Tg, for most polymers is about 1000 s [20]. The stress relaxation time, X, usually increases exponentially with increasing temperature: X = A exp(AE/RT)
(5.72)
where A is a pre-exponential constant and AE is the energy of activation. Values for AE are predicted for amorphous and some crystalline polymers for temperatures above Tg [21]. Extrapolation to most crystalline polymers and to temperatures below Tg is unwarranted. The isothermal rate constant, T, mirrors the stress relaxation time constant, X: T = K e- c/T
(5.73)
1
where K has the units of time" and C has the units of temperature. The solution to Equation 5.71 with Equation 5.73 substituted for x is not available in closed form. For intense quenching, r-> — oo. Thus: g-> x
(5.74)
That is, the final specific volume change simply equals the initial instantaneous volume change. When r->0, V = Ve. Figure 5.22 shows the effect of quenching on the final specific volume of polystyrene. Example 5.13 illustrates the time-dependency of specific volume as determined through stress relaxation. As a practical example, the effect of mold temperature on HDPE shrinkage is seen in Table 5.10 [22]. Example 5.13 Temperature-Dependent Stress Relaxation Consider a polymer with AE « 40 kcal/g mol • K. Its glass transition temperature Tg= WO0C= 2100F. Determine the stress relaxation time at T= 800C= 176°F relative to that at the glass transition temperature.
Taking the logarithm of Equation 5.72 yields: AF In(X) = InA +
-
For the two temperatures: in (X100) - in (X80) ~
( ^ 3 " 3^3) ~ (2-681 - 2.833) = -3.058 X80 = 21.3 times that of X100 As noted for most polymers, XT « 1000 s. As a result, the approximate relaxation time for PS at 800C is§5.9 h. About 70% to 80% of the dimensional change due to shrinkage occurs as the sheet cools from the forming temperature to the set temperature or the heat distortion temperature at 455 kPa or 66 lbf/in2 [23]. Stabilization to final dimension may take several hours, however. Strain recovery is one of the major causes of the
Specific Volume, cm 3 /g
Temperature, 0K Figure 5.22 Temperature-dependent specific volume of amorphous polystyrene, PS. r is the rate of quenching. Figure used with permission of copyright owner
Table 5.10 Effect of Mold Temperature on HDPE Shrinkage Drawn into a H:D = 1 Symmetric Mold [22] Mold temperature (0C)
Shrinkage (%)
40 65 75 90
1.8 1.9 1.9 2.4
long times needed to achieve stable part dimensions. Uneven strain recovery caused by nonuniform orientation in the trim area, as an example, is the major cause of long-term part distortion and warping [18]. In difficult cases, 24 h annealing at temperatures approaching mold temperature or maximum part use temperature prior to trimming can reduce warping.
Shrinkage can cause serious part removal problems when forming onto male molds. Draft angles are estimated from: 0draft = tan" 1 (2 x shrinkage fraction)
(5.75)
Example 5.14 shows the difference in recommended draft angles for amorphous and crystalline polymers [24]. For amorphous plastics, draft angles can be as small as \ degree to 1 degree. For crystalline polymers, it should be greater than 2 degree to 3 degrees. Female portions of molds require no draft if smooth and \ degree if textured. Draft angles are also discussed in Chapter 6 on mold design. Example 5.14 Draft Angles for Amorphous and Crystalline Polymers A mold designed for PS has recently been used to run PC. Are the draft angles correct? Can this mold be used to run POM, acetal? POM has a recommended - shrinkage value of 3.0%.
From Table 5.9, the recommended shrinkage values for both PS and PC are 0.6%. Therefore if the draft angles for PS were initially correct, they are correct for PC. To estimate draft angles for POM, consider Equation 5.75: 9draft = tan"1 (2 x shrinkage fraction) For PS and PC, the recommended draft angle is: 0draft = tan- 1 (2 x 0.006) = 0.7 degrees For POM: 6draft = tan- 1 (2 x 0.03) = 3.4 degrees The original draft angles are too small for POM.
5.8
Trimming
There are many acceptable ways of efficiently separating formed parts from the surrounding plastic. Thin-gage parts are usually trimmed automatically. Very heavygage parts are trimmed manually. Medium-gage and heavy-gage parts are usually fixtured and trimmed manually or with computer-aided robots. Routers, water-jets and lasers are used for automatic trimming. As discussed below, the cutting surface must be fed at a fixed rate in a plane - perpendicular to the cutting direction. Prototype parts are usually trimmed manually with routers and bandsaws. Very thin parts can be trimmed with a paper cutter or hand scissors. Typical trimming devices are shown in schematic in Fig. 5.23. The trimming devices include: •
Manual knives, including Bread knives for low-density foams,
•
• •
•
Linoleum knives or knives with recurving blades, Knives with replaceable blades, Routers, such as Hand-held, high-speed routers at 20,000 RPM with carbide router tips, Table-mounted fixed-position routers, Multi-axis routers, Band saws, Circular saws, including Stationary saws, Hand-held, small diameter saws, Saws with toothless blades for foams, Abrasive wheels,
Toothed Saw or Router
Die Cut, Prototype
Bandsaw Nibble Cut
Hot Wire
Shear Cut
Hot Gas Jet Abrasive Wheel Water Jet In-MoId Die Cut
Laser Figure 5.23 Schematic examples of various trimming methods
•
• • • • •
Sharp-edged compression blades, including Steel-rule dies, Ground forged dies, Machined dies, Guillotines, including One-sided linear shear, Two-sided linear shear, Flames, Lasers, Water jets, and So on.
Trimming Heavy-Gage Parts Heavy-gage parts are usually removed from the molds with the web attached, then placed on trimming fixtures and trimmed with manual or computer-aided trimming devices. For prototype parts and a few hundred parts, hand operated routers, saws and bandsaws are commonly used. For parts having a planar trim path, simple compression or dinking presses are used (Fig. 5.24). The press consists of a steel rule die mounted in a wooden frame and mounted to the movable top platen and a ductile cutting surface mounted to the stationary bottom platen. The part and web is registered against stops on the bottom platen cutting surface and the press is closed pneumatically, mechanically or hydromechanically. For production runs, steel rule dies are mounted in rigid steel or aluminum frames (Fig. 5.25). The trim is removed by compression. Specifications for the steel rule die are given below. For very heavy-gage plastic where the trim surface is
Upper Platen Hold-Down Screw Shim Steel Rule Die Formed Part UHMWPE Pad Lower Platen Figure 5.24 Schematic of steel rule die prototype trim or dink station
Trim Die Platen
Bracket Adjusting Screw
Steel Rule Die
Figure 5.25 Characteristic steel rule die mounting assembly
piecewise linear, a standard sheet guillotine is used. Forged and machined dies are also growing in popularity. For longer production runs, computer-driven multi-axis routers and saws are used. Figure 5.26 shows a typical five-axis table used to drive a multiple router head. When using a multi-axis trimmer, the part to be trimmed is fastened tightly against a fixture using clips or vacuum. The cut is initially programmed by leading the router head manually around the fixture. The computer
Figure 5.26 Multiple-axis computer-driven router trimmer. Figure used with permission of Thermwood Corporation
learns the correct path in this manner. Minor changes in the cutting path are usually incorporated in this first-pass program in order to fine tune the trim path. For heavy-gage parts, trimming can also involve other post-molding operations such as: • • • • • • • •
Drilling, Slotting, Grooving, Ultrasonic welding, Solvent welding or other forms of gluing, Ultrasonic insertion of fasteners, Grinding or milling local wall thickness to tolerance, and So on.
Trimming Thin-Gage Parts Typically, many parts are simultaneously formed on roll-fed presses. Thin-gage, roll-fed parts are typically trimmed either: • •
After forming but while the sheet and web are still on the mold, usually referred to as "trim in place", or After the sheet and web are stripped from the mold, in a separate in-line mechanical or hydromechanical press.
These trimming systems are quite different and represent a major early decision when choosing a thermoforming line. Trim-in-place punch-and-die systems are usually considered as part of the mold design (Fig. 5.27). If the parts are completely punched from the web, methods must be used to remove the parts from the mold region as quickly and thoroughly as possible. Common methods are vacuum suction, mechanical part removal and mold rotation [25]. For vacuum suction, a vacuum tube is used for each cavity. The parts adhering to the tubes are shuttled from the press to a drop box. The drop box feeds an orienting and stacking device. In mold rotation, the mold containing the parts drops free of the web plane, then rotates to dump the parts into the drop box (Fig. 5.28). Frequently, air assist blows the parts free of the cavity. Frequently, the trim die is tabbed so that a small portion of the part remains attached to the web. As a result, the parts are not quite separated from the web in the mold. However, once the tabbed part-web structure is free of the mold, air or mechanical assists punch the parts from the web. The primary concerns with on-mold trimming are: • •
Incomplete separation of all parts from the web. The parts that are still attached to the web as it exits the mold area may foul downstream machinery or web wind-up equipment. In addition, these good parts are not saleable, Parts that remain in some mold cavities after the removal process, due to undercuts, poor mechanical or vacuum picking, or static charge between the part and the mold cavity,
Die As Isolator
Steel Rule Die Plug Mold
Sheet
Die As Trim Sheet
Steel Rule Die Plug Mold
Figure 5.27 Trim-in-place or in-situ trim die. As shown, trimming is by compression
• •
Parts that accidentally drop back into the cavity plane after picking, and Dust and microflbers that remain on the mold surface. This detritus is usually transferred to as-molded parts. Punch-and-die design and tabbing are discussed in detail below. In most thin-gage forming operations, the web and formed part sheet is removed from the mold to an in-line trimming press. Usually the sheet is held in a vertical plane while being trimmed. As a result, the sheet is brought from the horizontal position to the vertical position by means of a hump-back or camel-back arch (Fig. 5.29). The hump-back trimming press allows the punched out parts to be collected on horizontal tables, thus simplifying the counting and bagging process. The die used in in-line trimming can be steel rule die, but is usually machined or forged. Again, punch and die design is discussed in detail below. Technically, punch and die trimming uses the shear mechanism of cutting, as described below.
5.9
Mechanics of Cutting
There are five general mechanisms of cutting (Fig. 5.30) [26]. They are: • •
In-plane uniaxial compression or die-cutting, Mode III antiplane pure shear or nibbling and shear cutting,
B: Trimming Step
A: Forming Step
Trim Die
Hot Sheet Mold
Web Formed Parts Rotating Mold
Collection Bin
D: Part Removal
C: Mold and Web Separation
Figure 5.28 In-mold trimming with part removal by mold rotation
Formed Parts
Web
Registry Cam Formed Parts Trim Die Cam Trim Punch
Figure 5.29 Camel-back or hump-back in-line roll-fed former trimming press with cam-operated punch-and-die trimmer. Figure redrawn from [27]
• • •
Abrasion or abrasive cutting, grinding, riling, buffing and water jet cutting, Brittle tensile fracture or routering, drilling and sawing, and Thermal or hot knife, hot wire and laser cutting.
Compression
Shear
Thermal
Abrasion
Chip or Fracture Cutting
Figure 5.30 Five characteristic cutting mechanisms. Figure redrawn from [26]
Mechanical compression and shear cutting dominate the trimming industry. The characteristics of some of these mechanisms are detailed below. The Trim Region Typically, the trim region is relatively well-defined as the linear edge where the part ends. In certain cases, the region is demarked in the forming process as a trim channel (Fig. 5.31). The accuracy of trimming to tolerance depends on several elements: • • •
Local polymer shrinkage at the trim line, Whether the polymer is crystalline or amorphous, Whether the polymer continues to shrink for some time after forming but before trimming, • Whether the polymer is tough or brittle at the trim temperature, • The tightness of the fixture to the formed part, • The allowable variation in part temperature at the trim station, • The presence of registry or locating cones, • The trim die temperature and its variation with time, • The thickness and thickness variation of the part at the trim line, • The allowable variation in local part wall thickness,
Trim Die
Trim Die
Trim Channel 0.003 to 0.005 in
Figure 5.31 Compression (left) and shear or pinch trimming (right) configurations
• • •
The increase in trim die temperature from the temperature at which the die gaps were set, The strength of the die clamping frames, and The amount of flexure in the die during cutting.
Registering the Trim Site Trim registers or locators are usually designed into the mold. These are cones or truncated pyramidal structures, as shown in schematic in Fig. 5.32. For heavy-gage sheet, risers or indentations are used by the operator to positively position the sheet against the trim fixture prior to trimming. For thin-gage sheet, the locators catch indexing lugs ahead of the in-line trim die. For thin-gage sheet, peripheral locators are located on the four corners of the multicavity mold and interstitial locators are
3 to 10 Times Local Sheet Thickness Pyramidal
Conical
Figure 5.32 Various shapes for sheet registry on punch station
Cubical
located on at least a few of the web regions between cavities. The indexing lugs on the trim press are usually adjusted to ensure full engagement of all locators on the sheet surface prior to start-up and then once or twice a shift as the various elements of the forming and trimming presses warm to equilibrium. During long production runs, periodic examination of locators after contact with trimming lugs may indicate if long-term forming problems are developing. The actual number of trim locators is not as important as the shape. Typically, the locator riser should have substantial draft of at least 15 degrees. Truncated cones are frequently used. Truncated boxes, wedges and pyramids are used, albeit with very generous vertical side radii, where trimming tolerance is critical and where the polymer may move locally between the forming and trimming stations. The Nature of the Cut The toughness of the polymer at the time of trimming dictates the nature of the fracture, as discussed below. The polymer toughness is best demonstrated by the polymer resistance to applied compression stress, as delivered by a toothless trim die (Fig. 5.33). As seen, for tough, ductile or hot polymers such as HDPE, PC and FPVC, the cutting blade forces the polymer to essentially flow away from the blade tip. The tip of the cut is therefore just ahead of the blade tip. For brittle polymers such as PS, APET and PMMA, the crack propagates very quickly from the initial point of blade tip insertion. For rubber-modified polymers such as HIPS and ABS, the crack propagation is arrested by the rubber particles. Microscopic examination of Trim Die Soft, Hot Polymer
Force Plastic Distance Trim Die
Force
Hard, Cold, Brittle Polymer
Plastic Distance Trim Die
Hard, Cold, Tough Polymer Force
Plastic Distance
Figure 5.33 Characteristic polymer response to trim die penetration
Meandering Crack
Multiple Cracks
Figure 5.34 Characteristic problems in trimming of brittle polymers
the trim surface of rubber-modified polymers shows fragments of rubber and holes where the rubber particles have been torn from the crack surface. Since the crack propagates very rapidly during compression cutting of brittle polymers, the crack path can meander (Fig. 5.34). Multiple cracks can occur as the cutting blade passes through the cutting zone. These cracks generate discrete particles, which are typically called trim dust. Microscopic examination of these particles reveals chunky, sharp-edged particles of 1 to 50 (xm in dimension. The high surface area of these high-surface energy particles implies high static attraction to surrounding ungrounded surfaces, such as the plastic parts and web structure. Although PS has the most tenacious trim dust, adhering trim dust is a problem with PMMA, APET, CPET, PC and other brittle and tough-brittle polymers. In addition to the production of micron-sized particles, edge microcracks are also formed perpendicular to the cutting plane during trimming of brittle plastics. These microcracks produce near-serrated edges under 30-power optical
Figure 5.35 Optical microphotograph of compression cut of polystyrene, PS
micrography (Fig. 5.35). In addition to yielding an undesirable rough lip, these microcracks are sources for crack propagation or splitting into the part. For certain ductile polymers such as PP, HDPE and CPET under certain cutting conditions, microfibers are formed. These microfibers are usually called angel hair or fuzz, are typically 50 to 150 um in cross-sectional dimension and can be 50 mm long. Although there is no consensus as to the primary cause of microfibers [27,28], they usually occur when trimming fiber-forming or crystalline polymers. Some of the conditions that are thought to minimize microfibers include: • • • • • •
Reducing the polymer temperature prior to trimming, Resharpening the cutting blade, Using a single-sided honed blade with a hardened tip, Increasing the rate of travel of the blade into the sheet, Ensuring that the cutter blade fully contacts the cutting anvil for steel rule dies, Ensuring that the steel rule die does not move out of plane during its travel through the sheet, • Reducing the gap between the punch and die for in-line trimming, • Ensuring that the blade engages the sheet at all places on the trim line simultaneously, and • Ensuring that the only mode of cutting is compression cutting. The dulled cutting tip is probably the most common cause of microfiber generation. Like cutter dust, microfibers are tenacious, particularly on PP and CPET. Since food containers are the primary products of these polymers, microfibers are unacceptable both from an appearance viewpoint, as they resemble human hair, and a health viewpoint, since these polymers are not approved as "food additives" [29].
Fracture Mechanics Trimming is semi-controlled fracture mechanics. The purpose of the trimming process is to separate one piece of plastic into at least two pieces. Mechanical chipping such as drilling, abrasive sanding, multi-tooth cutting and routering, results in many granular pieces of plastic, in addition to the desired part and the web. Ideally, compression and shear cutting with toothless blades should result only in the desired part and the web. Unfortunately, such is not the case. The toughness of the polymer at the time of trimming dictates the nature of the fracture, as discussed above. The mechanics of multi-tooth and toothless cutting are relatively well known. Kobayashi [30] considers all mechanical cutting as controlled tensile fracture of the plastic. This section develops the mechanics of fracture as it pertains to trimming.
Mechanical Chipping As a first step to understanding trimming parameters, examine the interaction of a single cutting-edge tool with the polymer (Fig. 5.36). A single cutting-edge tool is
Cutting Tool
Polymer
Figure 5.36 Orthogonal single-edge cutting geometry [30]. Figure used with permission of copyright owner
used in machining, turning and shaping but not in trimming of thermoformed parts. But the cutting actions of tools having multiple edges, such as saws, drills, routers and mills represent the sum of cutting actions of many single-edged tools. The physical factors affecting cutting actions on plastics are summarized in Table 5.11. Tool geometry factors are more complex for multiple-edged tools. The nature of the Table 5.11 Factors Affecting Cutting Characteristics of Plastics1 X = Major effect x = Minor effect Factor
Effect Chip formation
Tool design: Tool geometry*: Rake angle Relief angle Point radius Tool material Machining conditions: Depth of cut** Cutting speed Feeding speed Ambient work Temperature: Cooling system
Cut surface roughness
Tool wear
Heat generated
X
x
X X X
X
X
X
X
X
X
X
X
Gumming, burning
X X X X X X X
1 Adapted from [26], with permission of the author * For single-edged cutting tools. Tool geometry effects are more complicated for multiple-edged cutting tools ** Tooth depth of cut
chip formed in cutting is used as a guide cutting tool selection, and as an indication of how cutting is proceeding (Table 5.12). For example, PS chips in multiple-edge saw cutting should be discrete and separate easily, with no evidence of softening, gumming, or threadlines.
Multiple-Edged Tool or Toothed Saw Performance Kobayashi [26] presents extensive experimental results for plastics performance when cut with single-edge tools. A cutting force balance is shown in Fig. 5.36. When the perpendicular cutting-force component F t is zero, the cutting tool obtains the maximum cut surface accuracy. The cutting tool rake angle at this condition is known as the critical rake angle. All tools should have cutting angles equal to or greater than this value. The optimum cutting conditions for nearly all polymers should produce continuous chips of uniform thickness. If the cutting depth or tooth depth is too large, discontinuous chips are produced and the cutting surface has many microcracks. If the cutting depth is too small, the plastic will heat from friction and may burn or gum the cutting tool. Multiple-edged tool performance is determined by comparing the tooth depth of cut and the cutting speeds with single-edged tool performance. For a circular saw (Fig. 5.37), the tooth depth of cut, g, is: g=V
-
^
(5.76)
where U is the peripheral speed of the blade [m/min], U = TTDN, D is its outside diameter [m], D = 2R, N is the blade speed [RPM], v is the cut-off speed or the work feed rate [m/min], and p is the tooth spacing [mm]. The angle § is given as: • = co,-'^>
(5.77)
where h is the cut-off height or the distance between the saw centerline and the bottom of the plastic sheet [m], and b is the sheet thickness [m]. Example 5.15 illustrates these relationships.
Figure 5.37 Toothed saw trimming geometry [30]. Figure used with permission of copyright owner
Table 5.12 Classification of Plastic Machining Chips1 Classification
Nature of chip
Continuousflow
Continuous
Continuousshear
Continuous
Discontinuous simple shear
Discontinuous
Discontinuouscomplex
Discontinuous
Discontinuouscrack
Discontinuous
Discontinuouscomplex (shear with cracks)
Discontinuous
Thicknessto-cut depth
>1
>1
Cutting force fluctuation
Surface roughness
Nature of deformation
Material type
Cutting speed
Typical plastics
Comments on cause
Small
Small
Elastic
High elongation, rubber-like
Slow
PE, PTFE, FEP, PP
High elastic deformation
Small
Irregular, shear marks
Plastic
Irregular
Plastic
Moderate
Brittle
Irregular
Very irregular, wavy
Elastic
Very large
Hackle marks
Brittle, elastic fracture
Very large
Gouges
Brittle fracture
Large
PMMA High, PMMA, PS
Brittle sticky
>1 Irregular Chips
PS, ABS
Medium Brittle
Irregular
1
Mediumhigh
Adapted from [26], with permission of author
Brittle
Slippage continuously by shear stress Plastic fracture by simple shear shear Plastic fracture by shear with compressive and/or tensile stress
PMMA, PS
Elastic fracture, brittle fracture
High modulus, Low-elongation
Plastic fracture by shear with compressive and/or tensile stress
High Brittle High
Example 5.15 Cutting with a Saw Consider a D = 15.2 cm or 6 in diameter saw having four teeth per in. The blade revolves at 1000 RPM. The sheet is 0.100 in or 0.254 cm thick. The cut-off height is 2 in or 5.1 cm. A minimum tooth depth, g, is selected to be 0.004 in or 0.1 mm to minimize gumming or burning. Determine the maximum feed rate.
From Equation 5.76: v
_
u-g
p sin (j) p is the tooth spacing or 1/4 (teeth/in) = 0.25 in or 0.637 cm. The peripheral speed of the blade, U = TCDN. For this example: U = Ti • 15.2 cm
— = 47,750 cm/min mm
The angle is given from Equation 5.77 as: . *=
l C0S
(h-b/2) - D / ^ = C0S
1
(5.1-0.254/2) 15.2/2
(j) = 49 degrees Therefore: 47,750 • 0.01 cm2/min , . v= — — = 990 cm/mm =16.5 cm/s = 6.5 m/s 0.637 cm • 0.756 This is the maximum feed rate of this stock into the saw.
Note that the feed rate is proportional to blade speed and diameter and inversely proportional to tooth spacing. Thermal damage to the plastic is minimized by: • • • • •
Wide tooth spacing, Coarse toothed blades, Small blades, Low speed blades, and High feed rates.
However wide tooth spacing causes relatively rough cut edges with many brittle polymers such as PS, ABS, SAN, PMMA, and RPVC. Hollow-ground blades with no tooth set and wide-kerf carbide blades yield smooth cut edges. Spring-set and swag-set teeth also produce quality cut edges (Fig. 5.38). Abrasive Cut-Off Wheel Abrasive wheels with 30- to 200-grit surfaces produce relatively smooth cut surfaces at high cut-off rates with about one-half to one-third the heat generated by toothed
Carbide Tip
Hollow Ground
Spring-Set
Swaged
Tangential Cutting Force, Ft , kgf
Figure 5.38 Typical saw tooth designs
36 Grit Silicon Carbide Abrasive Hollow-Ground Tooth Saw, No Set 36 Grit Aluminum Oxide Abrasive
Hollow-Ground Tooth Saw, Spring-Set
Feed Rate, v, mm/min Figure 5.39 Comparison of abrasive disk and toothed saw trimming forces as function of polymer feed rate [30]. Figure used with permission of copyright owner
saws [26]. Typical abrasives include aluminum oxide or alumina, silicon carbide, tungsten carbide and diamond. Diamond abrasive wheels are the most expensive but last longest. Abrasives are held together with thermosetting binders such as phenolics, ureas and epoxies. Cutting forces are usually higher for abrasive wheels than for toothed wheels at the same feed rate (Fig. 5.39). Abrasive wheel cut surface roughness is usually smaller (Table 5.13). Finer grit wheels produce smoother surfaces but at reduced cut-off rates (Table 5.14). The machinability of a plastic, r\, is written as [26]: (5 78)
^V^s{
-
3
where V1n is the volume of polymer cut per unit time [mm /min], Vw is the amount of tool wear per unit time [mm3/min], HP is power consumption [kg • m/min], and Sf is the cut surface roughness [urn]. For properly selected cutting wheels, the amount of tool wear is essentially negligible, and machinability is redefined as:
Table 5.13 Cutting-Off Operation1 Peripheral speed 2500 m/min Polymer
Surface roughess (urn)
SAN ABS PA-610 (a nylon) PC
Abrasive wheel
Circular saw
A
B
C
D
32 28 34 8
23 16 16 6
8 10 6 5
200 200 36 25
1
After [26], with permission of author Key: A: 36 Grit silicon carbide, resinoid—medium grade B: 36 Grit aluminum oxide, resinoid—medium grade C: Saw, hollow-ground, zero-set teeth, 300 mm, diameter, 2 mm thick, 2.3 teeth/cm or 5.8 teeth/in, 0° rake-angle, 60° relief angle D: Saw same as C except 0.2 mm set to teeth
Table 5.14 Finishing Operations Sanding Belt Surface Roughness1 Silicon carbride sanding belt 2000 m/min, 0.5 kg/cm 2 applied force, 20 min Polymer
Surface roughness (um) 60 Grit 240 Grit
Amount removed (g) 60 Grit 240 Grit
PMMA RPVC PC
36 39 41
295 360 235
1
2 2 2
28 8 9
Removal rate (mg/s) 60 Grit 240 Grit 246 300 196
23.3 6.7 7.5
Adapted from [26], with permission of author
(5.79)
For cutting wheels: (5.80)
where b is the sheet thickness, B is the wheel thickness and F t is the tangential component of the cutting force. The ratio of efficiencies of abrasive and toothed wheels operating at the same feed rates and peripheral speeds is written as: (5.81)
Abrasive wheels are typically 2 to 5 times thicker than toothed wheels. Both produce about the same surface roughness on the cut edge at the same cut-off speeds (Table 5.13). The cut-off forces for abrasive wheels are about 2 to 5 times those for toothed wheels. Therefore:
Although the cut-off efficiencies of abrasive and toothed wheels are about the same, the cost of operating abrasive wheels is about 5 to 10% that of toothed wheels. When loaded, abrasive wheels are redressed with a gum block or a wire brush. Toothed wheels require resharpening and tooth resetting.
Toothless or Shear and Compression Cutting Saw cutting depends on brittle tensile fracture of the plastic under the force of the tooth. In solids, Young's modulus, E, is the proportionality between pure elastic tensile stress and strain: G =E - e
(5.83)
When a solid is sheared, the proportionality between pure shear stress and strain is the modulus of rigidity or shear modulus, G: O5 = G • es
(5.84)
The bulk modulus, B, is the ratio of hydrostatic pressure to solid volume change per unit volume. Solid compressibility is the reciprocal of the bulk modulus. These moduli are related through Poisson's ratio, v, the ratio of unit width change to unit length change [31]: E = 2G • (1 + v) = 3B • (1 - 2 • v)
(5.85)
Poisson's ratio, v = 0.5 for a material with constant volume under stress. For most plastics, 0 . 3 < v < 0 . 4 . Table 5.15 gives representative values for Poisson's ratio. A value of v = 0.35 is used if none is available for a given polymer. At this value, E/G = 2.7 and E/B = 0.9. Thus the expected resistance to shearing forces is only about 40% of the resistance to stretching or tensile forces. When this is applied to traditional thermoform trimming operations, shear cutting should require lower specific energy than, say, saw cutting.
Fracture Mechanics in Trimming Fracture mechanics is the study of crack propagation in plastics under stress. There are three general types of fracture, as shown in Fig. 5.40 [32,52]. Mode I is a tensile mode where fracture surfaces are spread apart by the stress. Mode II is a shear mode, where stress forces the fracture surfaces to slide perpendicular to the advancing crack. Mode III is a tearing mode, where the fracture surfaces are forced apart
Table 5.15 Poisson's Ratio for Several Thermoformable Polymers [50] Polymer
Poisson's ratio
LDPE HDPE PP PIB PS
0.49 0.47 0.43 0.47 0.38
Rigid PVC PCTFE PTFE PMMA mPPO
0.42 0.44 0.46 0.40 0.41
PPS PET PBT PA 66 PA 6
0.42 0.43 0.44 0.46 0.44
PC Polysulfone Polyimide
0.42 0.42 0.42
by the stress in the direction parallel to the crack [32]. Shear cutting is considered as Mode III, antiplane shear. This fracture mode is also found in torsion of notched rods. Mode I fracture, cleavage or tensile-opening, dominates classical fracture analysis since it is the most common form of material failure and since it is the easiest to study in the laboratory. If the plastic is not held tightly, Mode III crack propagation control is difficult to maintain. The advancing crack tends to meander uncontrollably, and secondly, tangent cracks can form. The amount of force required to propagate a crack in any mode and the rate at which a stable crack is propagated can only be estimated from the extensive studies of Mode I failures. The amount of energy needed to initiate a crack in any polymer is substantially less than its theoretical cohesive strength. Cracks begin at flaws or defects in the polymer. They propagate when the decrease in elastic strain energy equals or exceeds the energy needed to create a new crack surface. When a tensile specimen with a small horizontal crack, a in length, is stressed, it is in plane stress. The stress needed to propagate that crack is: (5.86) where E is Young's modulus and G* is the fracture energy: (5.87)
Mode I, Tensile Fracture
Mode II, In-Plane Shear or Sliding Fracture
Mode III, Anti-Plane Shear or Tearing Fracture
Figure 5.40 Characteristic fracture modes [32]. Redrawn Figure used with permission of PrenticeHall Publications, Inc.
where P is the plastic work done during yielding and y is the surface energy of the polymer. In Equation 5.86, Kc is the fracture toughness. The stress needed to initiate a crack is frequently far greater than that needed to sustain crack propagation [33]. For PMMA for example, the ratio of stress levels is about 1000. For vulcanized natural rubber, it is about 325. The plastic deformation stretching energy is usually much greater than the surface energy. For ductile plastics such as PTFE, PP, PET and TPO, P » y. Even for very brittle plastics such as PS and PMMA, P > 2 • y. Example 5.16 illustrates these relative values. One measure of the fracture toughness of a polymer is the area under its tensile stress-strain curve. If the area is large, the polymer is tough. Polymers that show great plastic flow after yielding, such as HDPE, PP and PET, have high fracture toughness. If the area under the tensile stress-strain curve is small, as with PS and PMMA, the polymer is brittle. The stress level that produces fracture is analogous to the crack tip stress intensity level that produces sustained fracture. As noted in the second part of Equation 5.86, fracture toughness or stress intensity factor, Kc is written as: (5.88) Characteristically, the stress intensity factor is written as: (5.89)
Example 5.16 Fracture Energies for Ductile and Brittle Polymers Consider vulcanized rubber and PMMA as typical of ductile and brittle polymers, respectively. Determine the relative ratio of yielding work to surface energy of each of these polymers. The plastic work during yielding of PMMA is P = 0.185 ft-lbf/in2 = 0.211 kJ/m 2 . The surface energy for PMMA is about y = 0.039 kJ/m 2 = 0.0342 ft-lbf/in2. The fracture energy is given as: G* = 2(P + Y) = 2(0.211 + 0.039) = 0.5 kJ/m2 = 0.44 ft-lbf/in2 The ratio of plastic work to surface energy, P/y = 0.211/0.039 = 5.4. This is a strong indication of a very brittle polymer. The plastic work for vulcanized rubber, P, is unknown. However, the fracture energy, G* = 13 kJ/m 2 = 11.4 ft-lbf/in2 and the surface energy for vulcanized rubber is about y = 0.012 kJ/m 2 = 0.010 ft-lbf/in2. The calculated value of plastic work is: P = ^ - - Y = y - 0.012 = 6.49 kJ/m2 = 5.67 ft-lbf/in2 Thus the ratio of plastic work to surface energy, P/y « 6.49/0.012 = 567. This is a strong indication of a very ductile polymer. The coefficient C depends on the geometry of the crack and the surface being fractured. One example of C is given in Fig. 5.41 [32], for an edge crack of length a in a sheet of width W under uniaxial tension. For unreinforced polymers, values for Kc range from about 0.5 to 10. Typical values for Kc for a few polymers are given in Table 5.16. The fracture stress given in Equation 5.88 is written symbolically as:
Stress Intensity Factor
a =
Reduced Crack Width, a/W
Material Parameter : Geometric Parameter
^_ (5.90)
Figure 5.41 Geometric parameters for stress concentration factor for mode I, tensile fracture [32]. Redrawn Figure used with permission of Prentice-Hall Publications, Inc.
Table 5.16 Stress Intensity Factors for Some Plastics and Other Materials1 Values in parentheses obtained from K c — ^JE • G* Materials
Young's modulus, E (GPa)
(1000 lbf/in2)
Vulcanized rubber Polyethylene PS HIPS PMMA
0.001 0.15 3.0 2.1 2.5
21.8 435 305 363
Epoxy Rubber-modified epoxy FRP Glass Wood Aluminum
2.8 2.4
406 348
7 70 2.1 69
0.145
1,015 10,150 305 10,000
Fracture energy, G*
Stress intensity factor, K
(kJ/m2)
(ft-lb/in2)
(MN/m3/2)
(1000 lb/in3/2)
13
11.4
( 0.114)
( 2.05)
20* 0.4 15.8* 0.5
17.5 0.35 13.8 0.48
( 1.73) 1.1) ( 5.76) 1.1
( 31.2) 19.8 (104) 19.8
0.1 2
0.087 1.75
0.5 2.2
9.0 39.8
7 0.007 0.12 20
6.12 0.0061 0.105 17.5
7 0.7 0.5 37
126 12.6 9.0 666
1 Adapted from [33], with permission of copyright holder * J-Contour Integral. See [33: p. 82]
In the tensile Mode I, an infinite stress is needed to initiate a crack of zero length. Once the crack is propagating, the stress diminishes rapidly. The rate of crack propagation is also important. For fatigue failure where the load is applied in cyclic fashion, the following relationship is used: ^
= A f -AK»
(5.91)
where N is the number of cycles, AK is the stress intensity factor range, AK = Kmax — Kmm, and m and Af are polymer material properties [33]. Some values for Af and m are given in Table 5.17. AK is proportional to Kc, the fracture toughness. For many polymers [33,34], 0.5 < [AK/KJ < 0.67. Cyclic crack propagation rate is used only as a guide to determine crack speed in Mode I tensile fracture. Cyclic fatigue crack growth occurs at substantially lower stress levels than those needed to sustain crack growth in continuous loading. In turn, this guideline can be used only as an estimate of the shear stress needed to control crack propagation in Mode III antiplane shear fracture. As noted, Mode III fracture is the apparent mode occurring during shear cutting of plastics such as guillotining, diagonal brake cutting, nibbling and paper cutting. An appropriate relationship for the rate of crack propagation, a = da/d9 is: da a = — = P • am • ocm/2 d(3
(5.92)
where a is the shear stress and (3 includes geometric factors and material constants. If the crack length ahead of the shear is to remain stable, or a is to be constant, the
Table 5.17 Crack Propagation Parameters da/dN = Af • AKm da/dN units are mm/cycle AK units are MN/m 3/2 Af units are [MN/m 1 / 2 ]- m Note: For crystalline polymers, the general relationship is: da/dN = A* • (AK/E) 7 where 0.5 < A* < 3 (AK/E) units are m 1/2 Polymer
Af x 1000
m
Range of AK
PS PMMA PES HDPE PC
2.65 99 1.5 0.35 0.118
3.73 10.0 9.5 5.22 4.81
0.5 0.4 0.6 1.0 1.0
to to to to to
1.2 1.0 1.2 2.5 3.0
6.2 2.2 3.63 3.2
1.0 0.5 1.5 1.5
to to to to
3.0 1.0 8.0 8.0
mPPO RPVC PA 66 PVF
0.0365 0.164 0.00728 0.0087
rate of shear is approximately proportional to the applied force to the mth power. For RPVC in Table 5.17, m = 2.2 and the shear rate should increase about four times when the applied load is doubled. On the other hand, for PMMA, m = 10 and the shear rate should increase about four times with only a 15% increase in applied load. Compression cutting occurs when the steel rule die is pressed perpendicularly into plastic sheet that is resting on an unyielding surface. Load compression follows the true material stress-strain curve. A modification of compression molding that employs uniaxial plane-strain compression is used to determine stress-strain curves for polymers that neck or fracture easily [35]. Compression cutting is particularly useful when the polymer yields in compression but fractures brittlely in tension or shear. RPVC, PC and PMMA are typical polymers that lend themselves well to compression cutting. Compression yield stresses are usually higher than tensile or shear yield stresses (Table 5.18). Thus more force per unit cutting area is required to die cut a plastic than to shear cut it. Comparison of typical stress-deformation curves, Fig. 5.42 [35], shows that the area under the compression curve continues to increase with increasing strain. As a result, crack propagation in compression is more stable for polymers that are brittle or neck badly. Compression cutting is the preferred method for cutting LDPE and should be considered for trimming PET, PA or nylon, POM or acetal, low-density foams and thin-gage OPS and PMMA. For a very brittle polymer being trimmed with a very sharp, wide die, a perpendicular crack is created ahead of the blade. The crack can propagate as a Mode I fracture, as shown in schematic in Fig. 5.43. The crack can be uncontrollable with an irregular reverse side cut surface, microcracking and crazing. The stress required to cut through the material is given in terms of the stress intensity factor,
Table 5.18 Yield Stresses and Cutting Shear Stresses Polymer
Tensile yield stress (MPa)
(10001bf/in2)
HDPE LDPE PP PET PC
28 10 34
4 1.5 5
62
9
RPVC PS HIPS ABS mPPO
41
6
21 34 48
3 5 7
PA 66* CA CAB CAP PMMA
55
8
POM**
10 * Dry nylon 69 ** Polyoxymethylene, acetal homopolymer
Compressive stress (yield) (MPa)
(10001bf/in2)
Flexure stress (yield) (MPa)
(10001bf/in2)
20
3
41 83 86
6 12 12.5
45 98 94
6.5 14 13.5
69 83
10 12
41 76
6 11
77 77 35 35 84
11 11 5 5 12
103
15
17 6 5 4 13 14
21 83
12
119 42 35 28 91
110
16
98
Sharp knife cutting stress (MPa)
(10001bf/in2)
91-126 110
13-18 15.8
60 45-50
8.6 6.4-7.1
Stress
Uniaxial Compression
Uniaxial Tension
Tension on a Notched Specimen
Figure 5.42 Stress-strain curves for various types of fracture in a notch-sensitive ductile polymer [35]. Figure used with permission of John Wiley & Sons, Inc.
Deformation
Trim Die
Polymer
Figure 5.43 Characteristic mode I fracture with wedge effect of trim die into brittle polymer sheet
Equation 5.89, and is frequently much less than the compression yield strength. One way of partially controlling crack propagation in very brittle polymers such as PS and PMMA is to place a very slightly resilient mat between the plastic sheet and the table. Very hard rubber or heavy-gage UHMWPE works well. If the plastic or rubber is too soft, the plastic may bind the cutting blade and chipping, splitting and uncontrolled fracture may be aggravated. Typically the force required to cut through a polymer sheet is proportional to the cut length and the sheet thickness to some power a, Force a (cut length) x (sheet thickness)a
(5.93)
Since the crack proceeds the cutting blade tip, the force required to cut through a brittle polymer may be only weakly dependent on sheet thickness. For a ductile polymer and a blunt die, the deformation stress is obtained directly from the stress-strain curve. Since most polymers strain harden to some extent in
Trim Die
Polymer
Shear Anvil Pinch Gap Figure 5.44 Characteristic combined shear and compression punch- and die-cutting of tough or ductile polymer
compression, the force required to cut through a tough polymer increases with the depth of cut [36] and a « 1: Force oc (cut length) x (sheet thickness)1
(5.94)
For ductile polymers, a combination shear and compression die cut is used (Fig. 5.44). With this type of cut, the lower force of a shear cut is combined with the stable crack propagation at increasing stress-strain of a compression cut. Heavy-gage plasticized PVC or FPVC, HDPE and PP are cut in this way. Combination shear cutting forces for several cutter blade designs are shown in Figs. 5.45 and 5.46 [37] for RPVC and PS, respectively. It is apparent that cutter force is proportional to sheet thickness, or a = 1 in Equation 5.93. Cutting forces for dull knives at 200C or 680F are measurably higher for polymers that yield, such as PVC, as seen in Table 5.19. These values compare well with blanking force guidelines for thin-gage sheet (Table 5.20) [38]. Values for effective shear stress or cutting force per unit thickness and cutter length are about the same as compressive yield stress values in Table 5.18. Cutting forces at 600C or 1400F are about 10% lower than those at 200C or 68°F. Nibbling Nibbling is a cyclic trimming process. An estimate of nibbling force is made from Mode I tensile fracture crack propagation. Example 5.17 illustrates this. As noted earlier, the force required to initiate a crack is as much as 1000 times greater than that needed to sustain it. Nibbling is a process requiring crack initiation at each stroke. Further additional force is required to overcome friction between the nibbler
Force, 100 kgf
Dulled Cutter
Cutter Design 4 Cutter Design 3 Sandwich Cutter
RPVC
Thickness, mm
Figure 5.45 Experimental sheet thickness-dependent shear cutting force for rigid polyvinyl chloride, RPVC, for several trim dies [37]
Table 5.19 Shear Cutting Forces Data from Figs. 5.45 and 5.46 [37] Blade length = 10 in or 250 mm Sheet thickness = 0.039 in or 1 mm Polymer
Blade design
Cutting stress
Total force (kgf)
(Ib)
(MPa)
(10001bf/in2)
PVC
#3 #4 Sandwich Dull*
2600 2710 3100 3900
5720 5960 6820 8580
104 108 124 156
15.1 15.8 18.0 22.6
PS
#3 #4 Sandwich Dull**
2680 2680 2680 2900
5900 5900 5900 6380
107 107 107 116
15.5 15.5 15.5 16.8
* Exhibits a "zero thickness" resistance of 1360 kgf or 2990 lbf, or an equivalent shear stress of 54 MPa or 7900 lbf/in2 ** Exhibits a "zero thickness" resistance of 460 kgf or 1000 lbf, or an equivalent shear stress of 18 MPa or 2700 lbf/in2. In addition, the force-thickness curve is nonlinear
Dulled Cutter Sandwich Cutter
Force, 100 kgf
Cutter Design 4 Cutter Design 3
PS Figure 5.46 Experimental sheet thickness-dependent shear cutting force for polystyrene, PS, for several trim dies [37]
Thickness, mm
Table 5.20 Blanking Force Guidelines for 0.25 mm or 0.010 in Sheet [38] Nature of polymer
Type of polymer
Force
Total force in 10 in or 25 cm
(kgf/cm)
(lbf/in)
(kgf)
(lbf)
Soft
Polyolefins, cellulosics
27
150
680
1500
Medium
Flexible PVC
46
250
1140
2500
Hard, Tough
OPS, PET, PS PMMA, RPVC
91
500
2280
5000
blade and the plastic and to push the cut-off plastic piece from the kerf. As with compression cutters, a good first approximation of the value of the cutting-off shear stress is the yield strength value of the plastic (Table 5.18). Example 5.17 Nibbling Force for PMMA Thin-gage PMMA sheet, 0.025 in or 0.1 cm thick, is to be cut in one cycle. Determine the force needed to sustain a crack. For PMMA, Af= 0.1 (MN/m1/2)~m and m = 10.
From Equation 5.91, the stress intensity factor range is obtained: AK = (da/dN)1/m-Af-1/m Now da/dN>0.1 cm. Assume da/dN=l. Then AK =1.26 MN/m1/2. If AK = 0.5 Kc, the critical stress intensity factor for crack propagation and C = 2, the tensile stress needed to sustain the crack is given as: a = ^ • V ^ = 1-26 V*-0.001 =
Qm
M N / m 2 = 1Q 3
^
2
This is the tensile stress needed to propagate the crack. The tensile yield stress of PMMA is about 45 MN/m2 or 8500 lbf/in2. Since nibble-cutting should require about the same expenditure of force as compression-shear cutting, the apparent force needed to sustain a crack in PMMA is only about 0.1% of the total force needed to cut the plastic. Brittleness, Orientation and Trimming Temperature Many brittle plastics exhibit uncontrolled fracture, secondary crack propagation, reverse-side chipping, crazing and splitting when compression or shear cut. Brittle fracture occurs when the brittle strength of the polymer is less than its yield strength. The brittle strength of a polymer below its glass transition temperature, Tg, is weakly dependent on temperature over a wide range of temperature, 1000C or more. On the other hand, polymer yield stress is essentially a linearly decreasing function of temperature (Table 5.21) [35]. As the polymer temperature increases, the probability of fracture at stresses below the yield stress decreases. The problems associated with brittle fracture trimming diminish as well. At elevated temperatures approaching Tg, the polymer is ductile and high-speed cutting-ofT techniques that depend on brittle fracture crack propagation such as routering and sawing, become inefficient. Table 5.21 Temperature Effect on Yield Stress For Various Polymers1 Polymer
Linear region
Temperature coefficient of yield stress (0F)
(0C) PMMA PTFE PE* RPVC PP
50 -250 -60 -80 -40
PA 66 APET PC
-100 to 60 - 2 0 to 60 - 4 0 to 120
to to to to to
100 -140 20 60 20
122 -420 -76 -112 -40
to to to to to
212 -220 68 140 68
-150 to 140 - 4 to 140 - 4 0 to 250
3 Adapted from [35], with permission of copyright owner * Chlorinated polyethylene
(MPa/°C)
(lbf/in2 - 0F)
0.97 0.85 0.82 0.80 0.74
78.2 68.5 66.1 64.5 59.6
0.74 0.49 0.32
59.6 39.5 25.8
Next Page
Thermoformed shapes frequently have high degrees of orientation in the trim areas. Part shape can enhance nonuniform orientation. Cutting relieves local stresses. Although this aids crack propagation to some degree, particularly in shear cutting, it can also cause: • • • •
Nonuniform part dimensions, Binding of the cutting tools, Part warping, and Part distortion.
Secondary fracture effects such as crazing can result. Uncontrolled crack propagation can proceed in the orientation direction rather than in the desired cut path, or the crack can meander. This results in splitting and splintering, dust and angel hair. Highly nonuniformly oriented parts of brittle polymers are frequently formed on hot molds and then the parts with the trim attached are partially annealed prior to trimming. The trim is then cut away while the parts are still warm. Heavy-gage amorphous polymers such as RPVC and ABS and easily oriented crystalline polymers such as PA 66 and PP benefit by this trimming approach. As a general rule for all polymers, dust and angel hair problems and part warpage and distortion may be minimized by increasing the part temperature at the time of trimming. Increasing trim die temperature is usually ineffective. Part of the difficulty in trimming with hot dies is in conduction heat transfer from the heating source to the cutting tip. The die is envisioned as a metal fin. The effectiveness of conduction heat transfer to fins decreases rapidly with the length-to-thickness ratio of the fin [39]. This is due primarily to convection heat transfer to the cool ambient air:
where mL is given as: mL = / ^ L
(5.96)
where h is the convection heat transfer coefficient between the heated trim die and the ambient air (Table 5.4), k is the thermal conductivity of the trim die steel, L is the distance between the heater and the cutting tip and t is the thickness of the trim die. As is apparent in Fig. 5.47 [40], the energy efficiency of heated dies decreases rapidly with L/t ratio, for both rectangular and tapered dies. In words, since heated dies are very inefficient heat transfer devices, it is usually difficult to maintain cutting tips at the proper temperature.
5.10 Steel Rule Die As noted, the steel rule die is the most common method of cutting prototype sheet having thickness less than about 0.100 in or 2.5 mm. Steel rule dies are most effective
Previous Page
Thermoformed shapes frequently have high degrees of orientation in the trim areas. Part shape can enhance nonuniform orientation. Cutting relieves local stresses. Although this aids crack propagation to some degree, particularly in shear cutting, it can also cause: • • • •
Nonuniform part dimensions, Binding of the cutting tools, Part warping, and Part distortion.
Secondary fracture effects such as crazing can result. Uncontrolled crack propagation can proceed in the orientation direction rather than in the desired cut path, or the crack can meander. This results in splitting and splintering, dust and angel hair. Highly nonuniformly oriented parts of brittle polymers are frequently formed on hot molds and then the parts with the trim attached are partially annealed prior to trimming. The trim is then cut away while the parts are still warm. Heavy-gage amorphous polymers such as RPVC and ABS and easily oriented crystalline polymers such as PA 66 and PP benefit by this trimming approach. As a general rule for all polymers, dust and angel hair problems and part warpage and distortion may be minimized by increasing the part temperature at the time of trimming. Increasing trim die temperature is usually ineffective. Part of the difficulty in trimming with hot dies is in conduction heat transfer from the heating source to the cutting tip. The die is envisioned as a metal fin. The effectiveness of conduction heat transfer to fins decreases rapidly with the length-to-thickness ratio of the fin [39]. This is due primarily to convection heat transfer to the cool ambient air:
where mL is given as: mL = / ^ L
(5.96)
where h is the convection heat transfer coefficient between the heated trim die and the ambient air (Table 5.4), k is the thermal conductivity of the trim die steel, L is the distance between the heater and the cutting tip and t is the thickness of the trim die. As is apparent in Fig. 5.47 [40], the energy efficiency of heated dies decreases rapidly with L/t ratio, for both rectangular and tapered dies. In words, since heated dies are very inefficient heat transfer devices, it is usually difficult to maintain cutting tips at the proper temperature.
5.10 Steel Rule Die As noted, the steel rule die is the most common method of cutting prototype sheet having thickness less than about 0.100 in or 2.5 mm. Steel rule dies are most effective
Fin Efficiency, % Characteristic Fin Length, Lf2(h/kAm)1/2 Figure 5.47 Heat transfer efficiency for heated dies with rec tangular and triangular cross-sections. L is the length of the die from the heating source and A is its cross-sectional area. Redrawn from [40]
if the sheet thickness at the point of trimming is less than about 0.025 in or 0.64 mm. Typically, the steel used in thermoforming trim dies is A2D2. Depending on the method of hardening, this steel has a hardness of 48 to 52 Rc. It is considered a hard steel. The steel hardness range depends on the particular application, the polymer and the ease of sharpening the die: •
Steels with 45 to 48 Rc hardness are considered maleable or peenable. They are easily bent and sharpened and are easily dulled by cutting against compression plates having equal hardness. • Steels with 48 to 52 Rc hardness hold excellent edge but are not normally honed. They form the base stock for advanced hardening techniques. Steels with this hardness dull when cutting toughened polymers. • Steels with 52 to 56 Rc hardness are considered hardened steels. They hold excellent edge even when single- and double-honed, as described below. If they are chipped or dulled, they are difficult to resharpen but can be honed. • Steels with 56 Rc and higher hardness are usually produced by locally hardening lower Rockwell steels. Dies with 60 Rc hardness are used to trim filled, reinforced, and composite thermoformed parts. Although there are many ways of hardening steel, steel rule dies are usually hardened by: • •
Case hardening, Induction hardening,
• •
Shot peening, particularly the cut edge, and Cubic boron nitriding.
Nitriding yields the hardest cut edge. Typically, nitrided dies are rarely resharpened at the thermoforming press. Steel rule dies are usually 1 in or 25 mm to 2 in or 50 mm in depth. The die thickness depends on the sheet thickness, its toughness and the depth of draw of the part. Although dies are standardized in the following thicknesses: • • •
Thin-gage die with 0.028 in or 0.71 mm thickness, Medium-gage die with 0.042 in or 1.07 mm thickness, and Heavy-gage die with 0.056 in or 1.42 mm thickness,
steel rule dies are fabricated from sheet steel of any thickness if necessary. The die steel is available in strip form or in continuous roll. The cutting edge shape is ground in one of several configurations shown in Fig. 5.48. The single-sided cutting edge is most common, since it is inexpensive to grind and to resharpen. The double-sided cutting edge is recommended if the die is quite long, since the forces are centered directly over the fracture zone. The double-sided cutting edge is more difficult to align for trim line accuracy than the single-sided cutting edge. Honed cutting edges are used when a very sharp, very hard cutting edge is needed. These edges tend to feather and nick easily however. Recently, there has been interest in the single-sided double bevel cutting edge, which requires less frequent sharpening than the single bevel cutting edge.
Double Bevel
Single Hone
Single Bevel
Double Hone
Figure 5.48 Characteristic cutting edges on trim dies
Double Angle
Blunt Nose
Trim Knife
Rubber Particles
Brittle
Rubberized
Polymer
Dull Knife
Feathered Edge
Figure 5.49 Generation of dust and angel hair from various trim die cutting edges
Resharpening In time, all steel rule dies dull. The edge either flattens from repeated contact with the compression plate or the edge rolls or feathers (Fig. 5.49). As noted, blunt dies require greater force to penetrate the plastic than sharp dies. Blunt dies are considered to be the primary source of dust, microcracks, crazing and angel hair. With the possible exception of nitrided dies and dies having hardness values in excess of 56 Rc, all dies can be resharpened. Usually the die must be removed from the trim press for resharpening. There are several ways to resharpen the dies: •
Stropping, or smoothing the cutting edge with a leather strap. Stropping is most effective when the cutting edge shows a very light feather. The technique removes very little if any steel, typically < 0.0005 in or <12 |im. In fact, stropping is recommended prior to installing a newly ground die. • Honing, or smoothing the cutting edge with a ceramic or Arizona stone. Honing removes up to 0.0015 in or 40 jLim steel from the edge. The die can probably be placed in the trim press without additional shimming to compensate for metal loss. • Peening or 200 grit glass sphere blasting. This is most effective with mediumhardened dies where microscopic nicks have occurred in the cutting edge. Again, only about 0.002 in or 50 jim are removed. These dies should be shimmed before reinitiating trimming. • Chemical etching. Again, this is effective with medium-hardened dies. Although the chemical etch can remove substantial amounts of metal, usually less than 0.005 in or 125 jim of metal are removed. These dies should be shimmed before reinitiating trimming. • Grinding. This is effective with hardened dies. Usually less than 0.010 in or 250 jim metal is removed. If more than this must be removed owing to nicks or breaks in the die cutting edge, the die is usually scrapped.
Figure 5.50 Characteristic steel rule die mounting configuration that allows for adjustments after resharpening. Redrawn from [41]
There are two general ways of fabricating a trim die. If the die has relatively few bends, it is fabricated of one or two strips of die steel, with all radiuses carefully bent such that the die lays flat to within \ degree. Bend radiuses for thin-gage die steel should not be less than 1/8 in or 3.2 mm. The desired radius is 1/4 in or 6.4 mm. If the required trim line is very complex, the die is constructed of many strips of die steel, with the intersections being welded and hand ground. As noted, for simple parts and prototype parts trimmed on a manual compression press, the trim die is mounted in a simple wood framework. For production presses, the trim die has adjusting slots drilled at 1 in or 25 mm spaces about 0.5 in or 12 mm above the cutting edge. This allows the die to be mounted in a metal bracket that acts to reinforce the blade and allow blade adjustment (Fig. 5.50) [41]. The trim die bracket is usually aluminum. Tabbing and Notching In many cases with thin-gage roll-fed forming, there are many parts formed simultaneously. As noted in Section 5.7, if these parts are completely separated from the web, the many parts must be collected, oriented and stacked. In certain instances, depending on the gage of the sheet, the brittleness and tear resistance of the polymer and the specific part design, the parts are only partially punched from the sheet. The die is tabbed or notched so that the parts remain with the web until manually removed. Figure 5.51 shows two examples of tabbing dies. The frequency and dimension of tabs remain an art form dictated in part by the notch sensitivity of the plastics and
Figure 5.51 Characteristic die cutting edge configurations. The notched blade is used for tabbing
its resistance to tear. One measure of tear resistance is obtained from ASTM D 1004, known as the Graves tear initiation test or from ASTM D 1922, known as the Elmendorf tear test. Although these tests are designed for ranking the tear resistance of films (Table 5.22) [42], the results are useful in ranking the tab strength of thermoformed sheet. As is apparent, the tear strengths of polyolefins and flexible PVC are substantially greater than that of PS. As a result, the lengths of the tear tabs for polyolefins need to be substantially shorter than those for PS. If the tear tab is too long, part removal from the web will be inhibited and the torn edge may be unsightly.
5.11 Punch and Die Trimming Figure 5.52 [43] shows a typical punch and die arrangement. Punch and die trimming is common for in-mold and in-line trimming of thin-gage roll-fed formed parts. The key to successful punch and die trimming lies in the accuracy with which the punch is aligned with the die. As discussed earlier, the tolerance between the punch and the die is critical to the minimization of dust, angel hair and microcracks (Fig. 5.45). The gap width is usually set with feeler gages at about 0.0015 in or 37.5 jim when the set is cold. The gap width when the cutting surfaces are hot and at steady temperature should not exceed 0.001 in or 25 jim. The punch is harder than the die, with the punch steel being hardened to 60 Rc to 65 Rc. The punch is usually ground after
Table 5.22 Tear Strength of Films [42] (ASTM D1004 Graves initiation tear strength, all films 0.001 in or 25 (am thick) Tear strength
Polymer
Cellulosic (Cellophane) Cellulose acetate Low density polyethylene Copolymer polyethylene High-density polyethylene Unoriented polypropylene Oriented polypropylene PA 6 Polycarbonate Ionomer APET Polyimide FPVC Polystyrene PVDC (Saran)
(gf/mil)
(mN/m)
0.8-3.9 1.6-3.9 8 7 20 25 4-6 7.8-20 7.8-9.5 5.9-9.8 10-60 3.1 24-39 2 3.9-39
0.3-1.5 0.6-1.5 3.1 2.7 7.7 9.7 1.5-2.3 3.0-7.8 3.0-3.7 2.3-3.8 3.9-23.2 1.2 9.3-15 0.78 1.5-15
being hardened. The die steel hardness is about 45 Rc to 50 Rc. As a result, the die wears in and the punch wears out. The cut surfaces of the web and part are good indicators of die misalignment or wear:
Punch Trim
Die Lip Formed Part
Die Figure 5.52 Schematic of punch-and-die arrangement yielding a pinch-type compression cut
• • • •
If the plastic is soft or warm, the cut edge may appear smeared or feathered, If the plastic is a fiber former, the cut edge may show microfibers at 30-power magnification, If the plastic is ductile or ductile-brittle, the cut edge may appear lacy, and If the plastic is brittle, the cut edge may appear jagged with many microcracks at 30-power magnification.
For accurate compression-shear cutting, it is necessary for the cutting edge of the die to mate with the punch simultaneously everywhere. Frequently, an intense light is shone behind the die as the punch advances. The point of peripheral extinguishment should occur simultaneously everywhere. Punches and dies wear and the gap width increases. To regap, the die lips are usually shot- or grit-peened. The punch and the newly peened die are slowly brought together and any interference is pressed out by the press action [44]. If the punch shows erosion or microscopic galling, the punch edge is also stropped. Although punch and die sets are designed to mate in a planar fashion, there are occasions when this is not desirable. For example, when very heavy sheet is being
Die
Double Shear Punch
Die
Single Shear Punch Figure 5.53 Punch geometries that yield a pinch-type shearing cut
Die
Hollow-Ground Punch Figure 5.54 Hollow-ground punch that yields a combination of compression and shear cutting
trimmed in place on the forming press, the punch is altered to a single shearing punch (Fig. 5.53). The shearing action reduces the load on the hydraulic system driving the punch. If the sheet is not tightly held during shearing, it may move and the trim line may move away from the desired line. To minimize this effect, the punch is altered to a double-shearing punch (Fig. 5.53). The initial punch penetration at two points acts to stabilize the sheet against lateral movement. Shear and compression cutting is sometimes combined when the punch is dished or hollowed (Fig. 5.54). Forged and Machined Dies Steel rule dies are not normally used for sheet with thickness greater than 0.050 in or 1.3 mm in the trim area and for parts deeper than about \\ in or 38 mm. Machinable tool steel such as P7 or H20 is used to manufacture heavy duty dies. These dies are first oil or air annealed, then sharpened. For tough polymers, the dies are hardened to about 50 Rc. These dies are assembled into easily aligned fixtures and are nearly always removed for resharpening. Although forged and machined dies are more expensive than steel rule dies, they are the dies of choice for tough, filled or reinforced polymers formed into heavy-gage parts. The causes of dust and angel hair with forged dies are similar to those with steel rule dies. Similarly, forged dies wear, chip and dull in ways similar to steel rule dies. Chipped dies are rewelded and worn dies are resharpened rather than discarded [45].
5.12 Drilling Drilling, slotting and grooving are mechanical operations similar to trimming. These operations are frequently done while the thermoformed shape is still held in the
D A B
Figure 5.55 Two-tooth twist drill geometry [26]. Figure used with permission of author
trimming fixture. Plastics are quite difficult to drill without some damage to the surrounding area. Friction between the drill flutes and the drilled hole heats and expands the plastic inward, burning it or gumming the drill. Continuous chips from polyphenylene sulfide or PPS, PC and other high performance plastics can spiral around the drill, binding and stalling it. With olefins, thermal distortion at the hole inlet can cone the hole. For PMMA, PS and SAN, the hole exit can be chipped as the drill tip breaks through. Nevertheless, most plastics are drilled with conventional two-tooth twist drills (Fig. 5.55) [26]. Single-edged tool cutting guidelines are used for drilling. The depth of cut per drill tooth, d, is given as: d = - • sin - = —— sin (5.97) n 2 nN 2 where n is the number of teeth on the drill (usually two), N is the rotational drill speed [RPM], v is the axial feed rate [mm/min], and 0 is the point tooth angle [deg]. The drill feed speed, s = v/n [mm/rev]. A large depth of cut produces cut surface fracture and fracture around the hole as the drill exits. A small depth of cut enhances friction and can result in gumming and hole distortion. Example 5.18 illustrates the manner in which Equation 5.97 is applied to the drilling of PMMA. Example 5.18 Drilling PMMA Experimentally, the drill feed rate, vg, below which PMMA will gum the drill is given as: vg = 25x 10~6 N2 [mm/mm] where N is the rotational drill speed, [RPM]. At high drill feed rate, vc, PMMA will crack, producing hackle marks in the drilled hole. Experimentally:
vc = 0.28N-20
x 10~6 N2 [mm/min]
Determine the acceptable drill feed rate range for N = 2000 RPM, 4000 RPM and 6000 RPM. At N = 2000, the drill feed rate range from Equation 5.97 is given as: 100 [mm/min] < v < 480 [mm/min] At N = 4000, the range is: 400 [mm/min] < v < 800 [mm/min] At N = 6000, the range is: 900 [mm/min] < v < 960 [mm/min] Above N = 6000 RPM, there is no acceptable value for v.
Table 5.23 Effect of Drill Geometry on Drilling Conditions in Plastics1 Drill parameter
Drilling condition
Point angle Rake angle Relief angle Helix angle Shape of flutes
Rotational drill speed Drill feeding speed Work temperature Cooling provisions Nature of the hole
1
Adapted from [26], with permission of author
Drilling conditions for many plastics are given in Tables 5.23 and 5.24. For many polymers, high elastic deformation and recovery can wear drill, gum drill surfaces and distort the drilled hole. The drills for plastics such as PS, RPVC, and PC should be air- or liquid-cooled. An air jet on the drill shank during drilling of most plastics is beneficial [46]. Water is sometimes used for PS and RPVC. Rapeseed oil produces optimum cooling for PC. Nylons or polyamides must be moisture-controlled or drilled hole dimensions will change. In crystalline and tough, amorphous polymers such as HDPE, PP, and high-rubber content ABS, nonuniform biaxial orientation in the plastic may cause the hole to become elliptical. Excess friction during drilling aids in this distortion. In highly elastic plastics such as HDPE, UHMWPE and PTFE, the drilled holes are always smaller than the drill. Tapered, highly polished, widely-spaced flutes on the drill are desired. Further, for tough, highly elastic polymers or for critical hole dimensions, holes should first be drilled undersized. Then the hole should be enlarged to the desired diameter.
Table 5.24 Drilling Conditions for Plastics1 Polymer
Point angle (deg)
Helix angle (deg)
Lip relief angle (deg)
Rake angle (deg)
Feeding speed (mm/rev)
Drill speed (rpm)2
PE 70-90
10-20
9-15
0
0.18-0.25
0
6
NA
»0.3
2000
Wet pref.
Extralarge flutes
12-20
NA
»0.05
2000
Water/ oil
Polished
NA
60-90
40-50
12-15
0
ABS-low rubber
70-90
10-20
9-15
0
ABS-med. rubber
70-90
10-20
9-15
0
ABS-high rubber
70-90
10-20
9-15
0
70-90
10-20
9-15
0
70-90
10-20
9-15
0
*
9-15
*
0 (dry) 0.025-0.4 (wet) 0.025-0.4 0.05-0.4 0.05-0.4 0.2-0.4
500
500-2000
0.1-0.4
500-2000
PTFE
High plasticity
Inlet hole poorer than exit hole
Wide, highly polished
8+
Easy to gum. Inlet holes can cone at low feed rates
Polished
4
Can gum at inlet
Polished
4
Can gum at inlet
Polished
5
Wet perf.
Polished
5
More elastic than ABS. Hole smaller than drill
Deep, highly polished
1
Dry OK
Very high elasticity, hole always smaller than drill
Polished
3
Carbide drills preferred
NA
500-1000 NA
0.025-0.1
Comments
Some gummy inner surfaces. Extract drill frequently
500-1000 NA
500
Degree of difficulty in drilling3
3
4000 Wet only 500-2000
SAN
PA 6
3 point drill pref.
NA
PS
70-90
Dry OK
»27
PMMA 55-140
Flute condition
2000-4000
RPVC »120
Wet/dry
Dry OK
PA 66
70-90
*
9-15
*
0.2-0.4
500-1000 Dry OK
Special drill useful
3
Dimensions can change if not properly dried
PA 610
70-90
*
9-15
*
0.2-0.4
500-4000 Dry OK
Special drill useful
3
Pull drill out frequently in deep holes
PC
70-90
10-20
9-15
0.05-0.2
500
NA
2
Some gumming, chips very tough, can blind drill. Rapeseed oil
Wide, highly polished
2
Some exit cracks at low drill speeds
NA
1
High elasticity gumming at low speeds
Correct Wet/ Oil
POM (Acetal)
60-90
PP
*
NA
10-15
NA
0.05-0.4
500-4000 Dry OK
*
*
*
0.2-0.4
500-4000 Dry OK
1
Adapted from [26], with permission of author On 8.1 mm diameter drill 3 0 = Easy. 9 = Very difficult * Conventional twist drill angles 2
5.13 Other Cutting Techniques Nearly every way of separating one portion of a material from another has been attempted with plastics. Some of the more successful methods include: • • • •
Hot wire cutting or thermal cutting, Laser beam cutting, in essence an advanced form of thermal cutting, Water jet cutting, and Flame or thermal cutting.
Thermal Cutting Most plastics can be trimmed thermally by simply locally melting the plastic. The cutter can be a hot wire or blade, requiring direct contact of a hot solid with the plastic at the trim point. Or it can be non-contact trimming with hot air, a combustion flame or a thermal laser. In addition to being energy inefficient, hot jet cutting torches are difficult to maintain. Typical problems include: • • • • • • • • • •
Cut surface scorching, Local degradation or discoloration at the parting line, Kerf width variability, Hot gas temperature variability, Polymer slag spatter, Slag deposition and dripping, Slag threadlines, Local polymer ignition, including drips, Potentially noxious gas generation from combustion, and Obnoxious smoke, particularly from fire-retarded styrenics.
When the cutting shape does not need to be precise and the polymer is easily melted, direct contact flame cutting works well. For example, it is used to produce drain holes in polyolefin disposable plant trays in an in-line process. In laser cutting, the polymer is vaporized by the intense focused energy beam. Laser cutting is slower than hot gas cutting but is more accurate and cleaner. A typical cutting rate for a 5OW laser through 0.500 in or 12.7 mm PMMA is about 1 ft/min or 300 mm/min. In contact melting, the heated wire is typically only a few degrees above the polymer melt or flow temperature [47,48]. Wires are electrically heated, rheostatically controlled, and PTFE-coated nichrome resistant. Heated blades are frequently resistance tapes or plates adhered to steel saw blades. The plastic melting rate per unit width of heating surface, rh [kg/m • s or lb/ft • h], is given in terms of a convective heat transfer coefficient, hp, for flowing plastic melt. Approximate values of hp = 200 W/m2 •0C, 0.00475 cal/cm2 • s •0C or 35 Btu/ft2 • h •0 F are reported. The melting rate is: (5.98)
where c p is the polymer heat capacity and D is the heated wire diameter. For a heated blade, TtD -• L*, the width of the heated blade. Nu is the Nusselt number, the ratio of conduction to convection heat transfer: Nu = ^
(5.99)
where h is a convection heat transfer coefficient, L is a characteristic fluid film thickness and k is the thermal conductivity of the polymer. Pe is the Peclet number, the product of two other dimensionless groups. Pe = Re Pr, where Re is the Reynolds number, a ratio of inertial to viscous forces, and Pr is the Prandtl number, a ratio of thermal to viscous resistance: Pr = ^
(5.100)
where JI is the polymer Newtonian viscosity. The ratio, Nu/Pe, occurs frequently in heat transfer to flowing fluids. For melting polymers, the ratio is a function of two material parameters:
§?*f(B) 0 2 6
(5.101)
where A is a fluid film parameter having a range of 0 . 5 < A < 3 for crystalline polymers and B is a solid parameter having a range of 0.1 < B < 1 for crystalline polymers [47]. Example 5.19 illustrates how these relationships are used to predict cutting rates for HDPE. Example 5.19 Trimming HDPE With a Heated Wire Consider trimming 0.250 in or 6.35 mm thick HDPE using a 0.030 in or 0.76 mm diameter nichrome wire. Determine the maximum trimming speed. For this example, A = 3 and B =0.1 in Equation 5.101. The specific heat of HDPE is 1.0 BtuIIb -0F or LOcal/g - 0 C. The appropriate values for Nu/Pe needed in Equation 5.98 are obtained from Equation 5.101:
^ = | (B)0-6 = I (0.1) 06 = 0.167 The melting rate, m, is obtained from Equation 5.101: • 71D • t - hp n -6.35 -0.076 -0.00475 -0.167 m=— • (Nu/Pe) = — = 0.00060 g/s 2 - cp 2*1 where h p = 0.00475 cal/cm2 • s • 0 C. The melting rate of 0.6 mg/s or 0.001 lb/h is the maximum cutting speed. The volume rate of plastic melted is given as:
The projected cutting surface is:
As a result, the maximum cutting rate, v, is:
A is a melt shielding parameter, the ratio of melt sensible heat to latent heat of fusion. B is the equivalent ratio for the solid phase. For high latent heat crystalline polymers, a substantial fraction of heat is carried away by the melt. A and B are small and the ratio, Nu/Pe, is relatively large. As a result, the cutting rate can be high. For polymers with low latent heats, the ratio, Nu/Pe, is small and the cutting rate is low. The Griffin melting model [48] is truly not applicable to amorphous polymers since they have no latent heats. Increasing the hot wire temperature increases the relative values of A and B. This effectively decreases the melting rate, since some cutting energy must now be used to heat the polymer to a higher temperature. As noted, the cutting rate is inversely proportional to the sheet thickness.
Water Jet Cutting Water jet cutting and abrasive water jet cutting are new techniques developed for trimming high-modulus, low elongation to break polymers. The techniques have found greatest application in trimming composite thermoplastic and thermosetting structures. The typical water jet uses ultra-filtered water that is delivered to the cutting jet at pressures up to 690 MPa or 100,000 lbf/in2. Typical water jet pressures are about 345 MPa or 50,000 lbf/in2. The water is directed through a sapphire orifice having a diameter of about 0.5 to 2.5 mm or 0.020 to 0.100 in. The jet velocity near-sonic is about 1000 m/s or 3300 ft/s. For tough polymers and composites, abrasive garnet grit of 100 to 500 jim diameter is added to the water stream at about 5% (volume). A schematic of an abrasive water jet cutting head is shown in Fig. 5.56 [49]. Water jet cutting works well when polymers have yield stresses of 80 MPa or 12,000 lbf/in2 or less. For polymers with higher yield stresses or for composites, abrasive water jet cutting is recommended. The kerf produced is typically about 5% wider than the diameter of the jet at jet entrance to the sheet. It is recommended that the jet-to-sheet distance be no more than 5 mm or 0.200 in. Water jet cutting has several advantages over thermal cutting: • • •
The process is dustless, The process does not generate noxious gases, The jet can be stopped or slowed without any damage to the part being cut and without widening of the cutting kerf,
Figure 5.56 Water jet cutting device for thermoformed composites and laminates
• •
The cutting process can be started at any point on the part, and The cutting process is essentially isothermal and low temperature.
There are several disadvantages to water jet and abrasive water jet cutting: • • • •
There is substantial noise owing to air coupling at the impingement point, The jet nozzle tip wears rapidly when abrasives are used, Abrasives are relatively expensive and not easily recovered, Water cleanliness is extremely important. Fouled water will result in erratic cutting, • At high feed rates, the water jet can be diverted by irregularities in the polymer or variations in polymer thickness or when very heavy-gage ductile plastics are cut. This causes the kerf to meander, and • The kerf tends to be wider at the entrance to the piece. This is particularly noticeable with heavy-gage ductile plastics such as HDPE and when abrasives are used. Table 5.25 gives some cutting speeds for abrasive and nonabrasive water jets.
Table 5.25 Water Jet Cutting Speeds for Polymers and Composites [49] Material class
Thickness (mm)
Cutting speed (in)
Water Jet at 360 MPa or 52,000 Ibf I in2 and 20 HP 0.250 Polyurethane, "1 6.4 0.500 Polyethylene, I 12.7 1.000 Rubber (30+ | 25.4 Durometer) J Rubber (30 — 1 Durometer), Paper, fabric, > Corrugated cardboard J EPS, foam rubber,"! Foam PUR, Y Balsa wood J
0.13 0.38 0.81 1.6 3.2 6.4 1.6 12.7 25.4
(m/min) 6 3 1
(in/min) 225 100 40
0.005 0.015 0.032 0.063 0.125 0.250
15 8 8 8 8 8
600 + 300 + 300 + 300 + 300 + 300 +
0.063 0.500 1.000
15 12 7
600 + 450 275
Abrasive Jet at 240 MPa or 35,000 Ibf\in2, 150 jum Garnet and 20HP 1.60 0.125 3.2 Epoxy-graphite,! 0.75 0.250 6.4 Epoxy-aramid, > 0.46 0.500 12.7 Polyester-glass J 0.30 0.750 19.1 0.13 1.000 25.4
63 30 18 12 5
5.14 Trimming—A Summary The selection of a trimming technique depends primarily on the stress-strain nature of the polymer at its trimming temperature. However many processing elements influence the choice including: • • • • • • • • • • • •
The The The The The The The The The The The The
gage of the sheet, part size, overall draw ratio, nonplanar nature of the trim line, complexity of the trim line, acceptable level of cut surface roughness, required dimensional tolerance, economically required speed of trimming, extent of fixturing or hold down, number of secondary or ancillary piercing steps required, skill of the operator or pressman, availability of the desired trim equipment,
Table 5.26 Suitability of Trimming Techniques (Heavy-gage in parentheses) O = Unsuitable 9 = Preferred, best Trim category Type of polymer
Typical polymer
Die cut
Shear cut
Nibble cut
Router
Circular saw
Abrasive wheel
Band saw
Hot wire
Hot gas jet
Water Jet
Grit blast
Laser cut
Very brittle
PS, PMMA, SAN
9(0)
6(2)
4(4)
0(4)
2(6)
2(9)
3(4)
6(7)
4(6)
5(2)
8(8)
7(8)
Brittle
ABS, RPVC CA, CPET, CAB
9(0)
7(2)
5(4)
2(5)
3(7)
4(9)
3(4)
4(7)
5(4)
6(2)
8(8)
7(8)
Tough
mPPO, CAP, PPS, PA 6, PA 66, PET OPS
5(2)
9(6)
6(8)
3(8)
5(9)
5(7)
4(7)
3(8)
7(6)
5(2)
8(2)
7(8)
8(2)
9(8)
7(8)
5(3)
7(6)
7(5)
2(3)
2(8)
3(6)
3(5)
0(0)
7(9)
Ductile, rubbery
LDPE, PP, HDPE, FPVC, TPE, TPO, PTFE, FEP
Table 5.27 Trim Quality—Thin Gage1 Process
Trimming type
Tooling type Pressure/vacuum Parts per shift Quality A = highest Scrap rate
Time for delivery of tooling—weeks
Manual/Steel rule Manual/Steel rule In-line/Steel rule Off-line/Punch & die Roll-fed/Contact heat Trim-in-place Roll-fed Trim-in-place
Epoxy Aluminum Aluminum Aluminum
Vacuum Pressure Both Both
Lowest Medium High Highest
D D C B
High Low Low Low
3-4 5-6 5-6 12-15
Aluminum Aluminum
Pressure Pressure
Medium Low
B A
Low Low
5-6 15-20
Process type
Setup time
Tooling cost/ Skill required cavity
Machine cost
Per Part cost
Number formed Comments parts per shift— comparative
Roll-fed/Cut sheet Epoxy tool Roll-fed/Cut sheet Aluminum Roll-fed/In-line Trim Roll-fed/OfT-line Punch & die
Lowest
Lowest
Lowest
Lowest
Highest
Low
Low
Low
Low
Medium
Medium
Medium
High
High
Low
Medium
Roll-fed/Cut sheet Roll-fed/Cut sheet Roll-fed Roll-fed
Form-trim-inplace— Contact heat Form-trim-inplace— Oven heat 1
800
Manual die cut
High
4000
Manual die cut
Medium
Low
4000
High
High
Lowest
8000
Medium
Low
Medium
Low
5000
Highest
Medium
Highest
Low
8000
Adapted from [51], with permission of copyright owner
Large number of cavities, maximum number of parts Female, nonplugged molds Fewer cavities, fewer formed parts
• •
The availability of resharpening methods, Among others.
As noted, not all trimming devices are suitable for all types of plastics in all thicknesses. For example, automatic programmed laser cutting is clean and accurate but is impractical for trimming thin-gage roll-fed APET. Die cutting is quicker, cheaper and can be installed as part of the in-mold forming process and therefore becomes the trimming process of choice. Some techniques such as abrasive grit cutting are dusty and work best on high modulus, brittle polymers. Abrasive and toothed wheel cutting and routering generate dust. Heavy-gage parts of PMMA, ABS and PS should be sprayed with an antistat prior to trimming to minimize the almost-impossible-to-remove cutter dust. The rank of trimming techniques in Table 5.26 is meant only as a guideline, in terms of matching the intrinsic natures of the cuts and the material stress-strain behavior. Economics and availability may dictate a less-than-optimum choice for trimming. Table 5.27 illustrates some of the economic considerations needed for thin-gage trimming [51].
5.15 References 1. D.Q. Kern, Process Heat Transfer, McGraw-Hill Book Co., New York (1950), Table 12 of Appendix, p. 845. 2. M.R. Kamal and S. Kenig, "The Injection Molding of Thermoplastics. Part II: Experimental Test of the Model", Polym. Eng. ScL, 12 (1972), pp. 302-308. 3. M.K. Liao and CS. Li, "Investigation of Thermal Conduction Between Mold and Melt During Injection Molding Process", SPE ANTEC Tech. Papers 40 (1994), pp. 501-505. 4. B.O. Rhee, CA. Hieber and K.K. Wang, "Experimental Investigation of Thermal Contact Resistance in Injection Molding", SPE ANTEC Tech. Papers 40 (1994), pp. 496-500. 5. J. Schneider, "Conduction", in W.M. Rohsenow and J.P. Hartnett, Eds., Handbook of Heat Transfer, McGraw-Hill Book Co., New York (1973), Section 3, pp. 3-14 to 3-16. 6. J.L. Throne, Plastics Process Engineering, Marcel Dekker, Inc., New York (1979), Figure 10.5-6A, p. 518. 7. S.W. Churchill, Viscous Flows: The Practical Use of Theory, Butterworths, Boston (1988), pp. 12-13. 8. R.B. Bird, W.E. Stewart and E.N. Lightfoot, Transport Phenomena, John Wiley & Sons, Inc., New York (1960), pp. 401-404. 9. CP. Kothandaraman and S. Subramanyan, Heat and Mass Transfer Data Book, 3rd Ed., John Wiley & Sons, Inc., New York (1977), pp. 13-16. 10. F. Kreith, Principles of Heat Transfer, 2nd Ed., International Textbook Company, Scranton PA (1965), Appendix IL 11. J.P. Holman, Heat Transfer, 4th Edition, McGraw-Hill Book Co., New York (1976), p. 207. 12. W.K. McConnell, Jr., Handout, SPE Industrial Thermoforming Symposium and Workshop, Arlington TX, 12-14 March 1985. 13. T.R. Goodman, "Application of Integral Methods to Transient Nonlinear Heat Transfer", in T.F. Irvine, Jr., and J.P. Hartnett, Eds., Advances in Heat Transfer, Vol. 1, Academic Press, New York (1964), p. 54, p. 59. 14. D.R. Croft and D.G. Lilley, Heat Transfer Calculations Using Finite Difference Equations, Applied Science Publishers, London (1977).
15. G.M. Dusinberre, Heat-Transfer Calculations by Finite Differences, International Textbook Co., Scranton PA (1961). 16. P.C. Powell, Engineering with Polymers, Chapman & Hall Ltd., London (1983), pp. 254-257. 17. R. C. Progelhof and J. L. Throne, Polymer Engineering Principles: Properties, Processes, Tests for Design, Hanser Publishers, New York (1993), p. 342. 18. G. Gruenwald, Thermoforming: A Plastics Processing Guide, Technomic Publishing Co., Inc., Lancaster PA (1987), pp. 34-36. 19. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, Tests for Design, Hanser Publishers, New York (1993), Figure 4.34. 20. G.L.F. Ehlers, "Thermal Stability", in E. Baer, Ed., Engineering Design for Plastics, Reinhold, New York (1964), p. 402. 21. Z. Tadmor and C G . Gogos, Principles of Polymer Processing, John Wiley & Sons, New York (1979), p. 163. 22. D. Burgess, "Vacuum Forming of High-Density Polythene", British Plast., 32 (1959), pp. 195-6, 223. 23. W.K. McConnell, Jr., "Thermoforming Plastic Sheet and Film", from Tool and Manufacturing Engineers Handbook, Vol. 2., 4th Ed., Part of handout at SPE Industrial Thermoforming Symposium and Workshop, Arlington TX, 12-14 March 1985. 24. G. Beall, Glenn BealVs Design Guide II for Pressure Formed Plastic Parts, Arrem Plastics Inc., Addison IL (1985), pp. 11-12. 25. J.H. Schut, "Make Way for Lots of Firsts", Plast. World, 52:6 (Jun 1994), pp. 57-61. 26. A. Kobayashi, Machining of Plastics, McGraw-Hill Book Co., New York (1967), Chapter 1, "Fundamental Considerations". 27. J. Florian, Practical Thermoforming: Principles and Applications, Marcel Dekker, Inc., New York (1987), pp. 112-113. 28. G. Gruenwald, Thermoforming: A Plastics Processing Guide, Technomic Publishing Co., Inc., Lancaster PA (1987), p. 57. 29. J. Florian, Practical Thermoforming: Principles and Applications, Marcel Dekker, Inc., New York (1987), p. 112. 30. A. Kobayashi, Machining of Plastics, McGraw-Hill Book Co., New York (1967), p. 32. 31. L.E. Nielsen, Mechanical Properties of Polymers, Reinhold, New York (1962), p. 6. 32. R. W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, John Wiley & Sons, New York (1976), p. 262. 33. AJ. Kinloch and R J . Young, Fracture Behaviour of Polymers, Applied Science Publishers, London (1983), p. 87. 34. R.W. Hertzberg and J.A. Manson, Fatigue of Engineering Plastics, Academic Press, New York (1980), p. 136. 35. P.I. Vincent, "Fracture—Short-Term Phenomena", in N.M. Bikales, Ed., Mechanical Properties of Polymers, Wiley-Interscience, New York (1971), p. 125. 36. J. Florian, Practical Thermoforming: Principles and Applications, Marcel Dekker, Inc., New York (1987), pp. 103-106. 37. H. Voigt, Lehrgang fur Thermoformung, Paul Kief el Thermoformmaschinen GmbH, Freilassing, Germany, undated, p. 1.4.2. 38. G. Gruenwald, Thermoforming: A Plastics Processing Guide, Technomic Publishing Co., Inc., Lancaster PA (1987), p. 59. 39. J.P. Holman, Heat Transfer, 4th Edition, McGraw-Hill Book Company, New York (1976), pp. 38-39. 40. J.P. Holman, Heat Transfer, 4th Edition, McGraw-Hill Book Company, New York (1976), p. 40. 41. J. Florian, Practical Thermoforming: Principles and Applications, Marcel Dekker, Inc., New York (1987), pp. 106-112. 42. M. Bakker, Ed., The Wiley Encyclopedia of Packaging Technology, John Wiley & Sons, New York (1986). 43. J. Florian, Practical Thermoforming: Principles and Applications, Marcel Dekker, Inc., New York (1987), Figure 31-1.
44. J. Florian, Practical Thermofowning: Principles and Applications, Marcel Dekker, Inc., New York (1987), p. 116. 45. J. Florian, Practical Thermoforming: Principles and Applications, Marcel Dekker, Inc., New York (1987), p. 114. 46. J. Frados, Ed., Plastics Engineering Handbook, 4th Ed., Van Nostrand Reinhold, New York (1976), p. 701. 47. O.M. Griffin, "Thermal Transport in the Contract Melting of Solids", Polym. Eng. Sci., 12 (1972), pp. 265-271. 48. J.L, Throne, Plastics Process Engineering, Marcel Dekker, Inc., New York (1979), p. 824. 49. J. Korican, "Water-Jet and Abrasive Water-Jet Cutting", in CA. Dostal, Ed., Composites, Volume 1, Engineered Materials Handbook, ASM International, Metals Park OH, 1987, pp. 673-675. 50. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, Tests for Design, Hanser Publishers, New York (1993), p. 551. 51. S.R. Rosen, "Trimming Basics", paper presented at SPE Thermoforming Conference, Midland MI (Sept. 1992). 52. R.M. Caddell, Deformation and Fracture of Solids, Prentice-Hall, New York (1980), p. 209.
6 Thermoforming Molds 6.1 6.2
Introduction Prototype Molds Wood Fiberboard Plaster Plastic White Metal Nickel 6.3 Production Molds Aluminum Steel Other Metals 6.4 Mold Coolant Channels Mold Channel Flow Expansion Contraction Sharp-Edged Orifice 6.5 Vent Holes Sizing Vacuum Systems—Steady State Sizing Vacuum Systems—Dynamic Solenoid Valve Flow Resistance Vent Hole Resistance to Flow Vent Hole Diameter Other Types of Vents Vent Hole Placement 6.6 Surface Treatments Surface Texture 6.7 Plug Design Considerations Plug Materials Wood Plugs Plastic Plugs Metal Plugs Plug Design Concepts 6.8 Sheet Clamping 6.9 Sag Bands and Sheet Supports 6.10 Other Aspects of Mold Design Undercuts Encapsulation Moving Elements Stripper Plates/Bars Mold Releases Web Breakers, Catchers and Chasers Moats, Dams and Double Steps Chamfers and Radii Prestretching Restraints 6.11 Efficient Use of Sheet Heavy-Gage Sheet Thin-Gage Sheet 6.12 References
6.1
Introduction
The thermoforming mold can be as simple as a smoothed block of wood over which a heated sheet is draped. Many production molds may be as complicated as injection molds and may include: • • • • • • •
Moving elements, Articulated plugs, Sophisticated means for isolating sheet over multicavities, Means for ejecting formed sheet from mold cavities, In-mold trimming of formed sheet, Means for retrieving trimmed parts, and Down-stream filling and sealing means.
Selection of suitable mold materials depends to a great degree on the severity and length of service. If only a few parts are to be made and the hot plastic sheet is deformed at relatively low temperatures with vacuum alone, wood, plaster or reinforced or filled thermosetting resin is usually used as a mold material. On the other hand, if thousands of parts are needed and high temperatures and pressures are needed to achieve final part design criteria, durable mold materials such as aluminum and even steel are used. Regardless of the materials used, every mold must meet specific criteria and must therefore have certain features: • • • • • • •
Provisions are needed for clamping the sheet against the mold surface, Vent or vacuum holes are needed in those areas into which the sheet is drawn last, The mold surface should be relatively nonadhesive during sheet contact and static-free after the sheet is removed, The mold surface must be sufficiently hard to retain its shape and texture for the lifetime of the part, The mold must not change in dimensions during fabrication through thermal expansion, The mold must not change in dimensions during storage through moisture absorption, and The mold material should be relatively free from chemical and moisture attack to minimize: Swelling, Cracking, Rusting, Corrosion, and Patina development.
Appropriate mold material selection depends on economic considerations as well. Some of these are: • •
Initial cost of the material, Ease of fabrication,
• • • • • • • • •
Ease of repair, Ease of maintenance, Ease of serviceability, Quick-change suitability, Requirements for safe storage, Mold weight, Availability of mold materials, Shop personnel familiarity with the material, and Material toughness against accidental abuse while in use and in storage.
Some of these intrinsic factors frequently rule out an otherwise acceptable mold material [I]. In this chapter, prototype and production mold materials are discussed. Design of coolant flow channels and vacuum holes are then described. Some design features regarding surface treatment and surface texture are detailed. Plug design is described. Clamping methods, sheet supports, rapid mold change concepts and some aspects of break-away molds are discussed.
6.2
Prototype Molds
Strictly speaking, prototype molds are designed to produce a few parts. These parts may be used to demonstrate part design concepts that are to be subsequently either production thermoformed or injection or blow molded. The parts may be used for product testing and prototype assembly schemes. Frequently, however, prototype molds are used to produce tens to hundreds of parts in a classical production run. Some of the many heavy-gage sheet applications that are made exclusively on prototype molds include: • • • • • • • • • •
Indoor and outdoor signs, Point-of-purchase displays, Horticultural pool shells, Swimming pools, Spas, Plant containers, Custom dunnage, Bathtubs, Equipment housings, and Medical furniture.
Wood, plaster, glass fiber-reinforced plastic, filled epoxy and zinc and white metal alloys are materials commonly used for prototype molds. Each has many advantages and some serious limitations. A review of each follows.
Table 6.1 Finishing Qualities of Selected Hardwoods Used in Prototype Thermoform Molds [2] Wood
Planing
Shaping
Drilling
Sanding
Resistance to splitting
Ash Hickory Hard maple Red oak Walnut White oak Mahogany
C C E A D D C
E H C H G G F
A A A A A A A
C B G B G G E
C D E C E E F
A = 90-100 C = 70-79 E = 50-59 G = 30-39 J = 10-19 B = 80-89 D = 60-69 F =40-49 H = 20-29 K = 0-9
Wood Hardwoods are used for prototype and short production runs. The wood must be thoroughly kiln-dried before shaping to minimize stress relief in the form of warping, cracking and checking during fabrication, forming and storage. Properties of typical hardwoods used in thermoforming are shown in Tables 6.1 and 6.2 [2]. Woods such Table 6.2 Minimum Mechanical Properties of Selected Hardwoods Used in Prototype Thermoform Molds [2] Property
Unit
Wood type Shagbark hickory
Sugar maple
Pinoak red oak
White oak
Walnut
40 640 1.57 10.8 23.7 1.67 4580 31.6
35 560 1.55 10.7 13.3 0.94 4020 27.7
36 580 1.32 9.10 14.0 0.99 3680 25.4
37 600 1.25 8.62 11.6 0.82 3560 24.5
32 510 1.42 9.79 14.6 1.03 4300 29.6
670 4.62 5.96
840 5.79 5.45
640 4.41 6.28
720 4.96 5.11
670 4.62 5.31
490 3.38 8.78
38 0.97
74 1.88
40 1.02
48 1.22
42 1.02
37 0.94
White ash Density Flexural modulus Work to maximum load Maximum crushing strength parallel to grain Fiber stress at proportional limit Parallel-toperpendicular compression ratio Impact bending height to complete failure
lb/ft3 34 kg/m3 550 x 106 lbf/in2 1.44 GPa 9.93 in-lbf/in3 16.6 cm-kg/cm3 1.17 lbf/in2 3990 MPa 27.5 lbf/in2 MPa
in m
as walnut or pecan are oily. The exuding oil may interfere with adhesives during fabrication and may be undesirable during forming. Wood such as balsa, boxwood and certain second-growth pines are too soft for mold materials. Repeated forming pressure crushes the cell structure, producing poor surfaces and loss of dimension. Conventional woodworking techniques are used to fabricate the molds. Wood sections are usually assembled with fluted dowels and resorcinol, hot melt or epoxy adhesives. Hot melt adhesives allow faster assembly but yield weaker joints than other adhesives. Standard wood-filling techniques are used to remove surface defects during mod fabrication. Vent holes are usually drilled through the primary surface first, then enlarged by drilling from the back of the mold. Final sanding to 200 grit is usually sufficient for most low-pressure forming techniques. It is very important that the assembled wood be carefully and thoroughly dried prior to finishing. During forming, the rapid, cyclical heating from contact with the hot plastic will pull moisture from the wood. If the wood is not thoroughly dried, the wood can crack or check. Wood grain is characterized by alternating hard and soft bands. Occasionally, the softer portions preferentially shrink. This leads to an unacceptable texture that is transferred to the formed shape. After thorough drying, the surface may need to be sealed with temperature-resistant enamel or varnish1. Recently, epoxy enamels and varnishes have been developed that protect wood surfaces for hundreds of cycles without refinishing. For low-temperature forming of polymers such as cellulose acetate, flexible PVC and PS foam, polyurethane varnishes work satisfactorily. If mold release is needed, paraffin wax, carnuba wax, Treewax, Vaseline or a light coating of white grease is used. For food contact and medical parts, vegetable oil spray is used. Wood is also used as a component in molds made of more permanent materials. For example, since wood is rapidly and easily shaped, temporary plugs, web catchers and web breakers can be formed during early mold shake-down trials to determine optimum material distribution. Owing to the high compression strength and low density of end-grain woods such as oak and walnut, these are used for permanent plugs in many production runs. Fiberboard Fiberboard is produced by mixing wood fibers with thermosetting resins such as urea or phenolic, then pressing the mass into sheets at elevated temperature to crosslink the resin. The sheet product so produced is typically 0.125 to 3 in or 3.2 to 75 mm in thickness and is available in at least three grades:
1
It may not always be necessary or desirable to seal the wood surface. As an example, the mold is not usually sealed when it is used to produce parts of slightly different designs. When a wood that is not thoroughly dried is sealed, then cyclically heated, the moisture diffusing to the surface will crack or blister the sealant. Excessive blistering leads to unacceptable surface texture in the formed shape. Sometimes it is more feasible economically to rebuild the mold than to strip the sealant from the surface.
Low-density fiberboard, with a density range of 0.1 to 0.4 g/cm3 or 6 to 25 lb/ft3. This product is used in construction as moderately good insulation sheathing. One brand is known in the US as Cellotextm, • Medium-density fiberboard, with a density range of 0.5 to 0.7 g/cm3 or 30 to 45 lb/ft3. This product is relatively new and is produced by radio-frequency curing of the thermosetting resin. It finds use in the thermoforming industry as a mold material, as described below. One brand is known in the US as Moldboardtm [45], and • High-density fiberboard, with a density range of 0.8 to 1.3 g/cm3 or 50 to 90 lb/ft3. This product is used in construction as grainless dense paneling. One brand is known in the US as Masonitetm. •
Physical properties of medium-density fiberboard used as a mold material are given in Table 6.3 [44]. Pressure is not very high during fabrication of this density fiberboard. As a result, the board is somewhat porous. This allows vacuum to be drawn everywhere through the mold surface, as shown in schematic in Fig. 6.1. The fiberboard is worked using conventional woodworking saws and shapers. Overheating the cutting surface will result in gum deposit on the cutting surface, however. The porosity of the fiberboard is not exceptional. As a result, fiberboard molds work best for relatively shallow-draw male parts. Although primary surfaces are usually semi-gloss or matte, there are no vent hole nibs or nipples. Plaster Most commercial molding plasters are not strong or tough enough to be used for prototype molds. The properties of the few that are strong enough are given in Table 6.4 [3-5]. Plasters are inorganic calcicious materials that hydrolytically react and
Table 6.3 Medium-Density Pressed Fiber Board for Prototype Tooling [44] Property
Density Internal bond Modulus of rupture Modulus of elasticity Linear expansion from 50% to 90% RH at room temperature Moisture content Thickness tolerance Length/width tolerance Corner to corner tolerance
Unit
Thickness 3/16 to 5/16 in
3/8 to 7/8 in
1 to \\ in
lb/ft3 lbf/in2 lbf/in2 lbf/in2 %
50 125 5,500 500,000 40
48 110 4,500 450,000 30
47 90 4,000 400,000 30
% Wt
5 to 7 ±0.005 ±0.0625 ±0.0156
5 to 7 ±0.005 ±0.0625 ±0.0156
6 to 8 ±0.005 ±0.0625 ±0.0156
in in in/ft
Air
Porous Mold
Air
Vacuum Hole
Vacuum Hole
Vacuum Box
Vacuum Line to Surge Tank Figure 6.1 Schematic of mold, vacuum holes, vacuum box and corrugated line to surge tank. Mold material here is porous fiberboard through which air will pass
Table 6.4 Molding Plasters [3,4] Commercial
Pattern shop hydrocal (Hydrocal A-Il) Industrial white Hydrocal Ultracal 30 Densite K5 Super X Hydro-Stone
(PPh)
Setting time (min)
Dry compressive strength (MPa) Obr/in2)
US Gypsum
54-56
20-25
22.1
3,200
US Gypsum
40-43
20-30
37.9
5,500
US Gypsum Georgia Pacific US Gypsum
35-38 27-34
25-35 15-20
50.3 65.5
7,300 9,500
21-23
17-20
96.5
14,000
Source
Water ratio
harden when mixed with water. Molds are formed by casting the newly prepared water-plaster mixture against a part pattern. Since the hydrolytic reaction is exothermic to 1000C or 2000F or so, the pattern should not be fragile. Typically, pattern surfaces are coated with a release agent such as a water soluble polyvinyl alcohol or PVOH. Soaps such as Murphy's oil soap are also used1. Vents are designed in by placing release-agent-coated wires perpendicular to the pattern surfaces prior to casting. For very thick molds made in multiple pours, soda straws are placed over the wires after the first pour. This allows the wire to be easily extracted later and also provides for a modicum of "back-drafting". For very thick molds made in a single pour, release-agent-coated tapered pins should always be used. 1
Murphy's oil soap is available in leather goods stores and laundry and cleaning areas of grocery stores. It is used primarily to clean porous surfaces such as wood and leather. To use it as a water-soluble release agent, coat the pattern with a generously thick coat and allow it to dry thoroughly. Add a second coat to those areas that are not at least semi-glossy.
A very hard void-free surface on the mold is achieved by "splatting" a thin layer of relatively high water content plaster slurry against the pattern. This thin layer is allowed to harden before further casting continues. This technique is adapted from that used by artisans working in fine plaster art [3]. To ensure adequate dispersion, the plaster must be very carefully mixed into the water. Once the plaster and water are thoroughly mixed, the mass is vibrated for several seconds to dislodge large air bubbles. Sisal, straw and glass fibers are excellent reinforcing fibers for plaster1. To ensure adequate wet-out and adhesion, the organic fibers are soaked in water for several minutes before being mixed into the water-plaster mixture. Typically, fiber reinforcement levels are 10% to 20% (vol). The mixture becomes harsh with higher reinforcement levels and air bubbles and voids are easily entrapped. Additional water reduces the strength of the plaster matrix. Typically, 35 parts water per hundred parts of plaster is a useful starting recipe [4]. Cure against the pattern usually takes about 30 min, although slower reacting plasters and those with fibers or fillers need as much as 1 h to reach demolding or green strength given in Table 6.4. While casting the primary mold, the moldmaker usually pours a simple test mold. This test mold is used to judge the level of exotherm and the degree of cure. After the pattern has been removed and the vent wires pulled, the mold is set aside in a dry, warm area for several days. This time is needed to develop the final properties and to stabilize the water content. The mold can crack if it is used before being thoroughly dried. The mold surface is then finished with open grit paper. Epoxy floor varnish is used if a smoother surface is needed. However, plaster molds are usually used for expediency and a fine surface is of secondary concern. Plaster molds are surprisingly durable. They can withstand cyclic forming temperatures of most commercial plastics quite well. They are quite heavy however. The molds should never be subjected to flexural loading since failure is catastrophic. Plaster breaks are repaired with epoxy, as are spalled surfaces. Auto body putty also works well. However, broken molds are rarely repaired and so patterns are usually preserved to produce a new mold. Glass- and polymer-fiber reinforced plasters and cementitious products such as water-curing hydraulic cement are also prototype mold materials, but material costs are up to 5 times those of conventional molding plasters. Plastic Great advances have been made in the last few years in formulating thermosetting plastic resins for thermoforming mold. In particular, plastic molds are economically preferred for: • •
Heavy-gage sheet forming, Part forming where heat buildup on the mold surface is intermittent,
1
Other fibers are used to reinforce plaster. As an example, polypropylene and polyethylene fibers are used to produce impact-resistant construction grade plaster board. Normally, these fibers are too expensive to be used for prototype thermoforming tooling.
• •
• •
Parts where the mold does not need to be heated to facilitate forming, Very large surface area parts such as, Outdoor signs, Camper tops, Outdoor swimming pools, Drape and low-pressure vacuum forming, and Prototype forming for less than 100 parts.
For applications where mold surface temperatures do not exceed 600C or 1400F and where drape and vacuum forming are used, epoxy and unsaturated polyester resin or UPE are materials of choice. These resins are usually combined with various forms of glass fibers. The exact manner of mold fabrication depends on the mold shop, but the general procedure usually followed is described below. Since thermosetting resins usually cure most efficiently at relatively high temperatures of 1000C to 125°C or 2000F to 2600F, the pattern must be thoroughly dried before beginning mold fabrication. Plaster and wood patterns should be thoroughly air oven dried at 500C or 1200F for at least 24 h [5]. The pattern surfaces are then sealed with at least two coats of air-sprayed thinned automotive lacquer or industrial polyurethane or PUR. The hard surfaces are then waxed twice with a hard paste wax such as carnuba or Treewax. The surfaces are power-buffed after each wax application. PVC plastisol is recommended as a release agent [5]. If the patterns are thoroughly dried, aqueous polyvinyl alcohol or PVOH can also be used. These release agents should be air-sprayed to ensure uniform coverage. Two coats are recommended. Generally, epoxy and UPE molds are fabricated in similar ways, although UPE mold construction is more complex and requires more steps. For glass fiber-reinforced UPE or GR-UPE molds, a 0.3 to 0.4 mm or 0.010 to 0.015 in layer of special resin known as gel-coat is first sprayed against the prepared pattern. A typical gel-coat recipe is given in Table 6.5. This layer is allowed to air-cure, either at room temperature or under infrared lamps, until tacky. An optional second layer can then be applied. The surface should then be carefully inspected for bubbles or other defects. Care at this point can obviate expensive surface repairs later on. A layer of very fine glass fabric known as C-veil is then placed against the gel-coat. A thin layer of UPE laminating resin is sprayed over the fabric and gently squeegeed into it1. Once the C-veil layer has cured to a tacky state, the first layers of reinforcing glass are laid. The glass fabric normally used is a plain weave of about 4 to 10 threads per cm or 10 to 25 threads per in [tpi]. The fabric weight is about 500 g/m2 or 20 oz/yd2. Plain weave is used because: • • • •
It It It It
has good strength in both directions, can be easily oriented and shifted to fit tight curves, has an open weave to minimize air entrapment, and is an expensive fabric structure.
1
An alternate method involves dipping the C-veil in catalyzed resin and applying the wetted fabric to the gel-coated surface. Since the wet fabric is quite weak and the resin drains readily from it, this approach is quite messy and consumes more resin than spraying. However, it leads to far fewer dry pockets between the gel-coat and C-veil.
Table 6.5 Typical Recipe for Unsaturated Polyester Resin Gel-Coat for Prototype Thermoforming Molds Resin recipe
Molar ratio
Isophthalic acid Maleic anhydride Neopentyl glycol, glycol excess, 2%
1 1 2.04
Acid number « 18 Hydroxyl number « 30 Gel time % 5 min Peak exotherm « 225°C or 4370F Formulation (polystyrene in polyester at 40 wt %)
Parts by weight
Polyester, as above TiO2 pigment Styrene diluent Fumed silica Cobalt octoate promoter Methyl ethyl ketone peroxide catalyst
48 20 32 1.5 0.3 to 0.6 0.2 to 0.3
Clear casting properties on 0.32 cm or 0.125 in thick sample Flexural strength Flexural modulus Elongation Tensile strength Heat distortion temperature
145 MPa 3.9 GPa 1.9% 65.5 MPa 112°C
21,000 lbf/in2 570,000 lbf/in2 9,500 lbf/in2 234°F
Strips are cut 50 mm by 500 mm or 2 in by 20 in, hand-dipped in catalyzed resin and hand-applied to critical high-stress areas of the mold such as corners and rim. The strips are then hand-rolled to express air and ensure intimate contact with the C-veil layer. Usually the resin bath is catalyzed for a 1 h gel time1. The moldmaker needs to know approximately how much resin can be applied in that time. A typical resin recipe is given in Table 6.6. Since UPE resins exotherm when curing, the thickness of the built-up layer of uncured resin on the mold must be restricted to about 6 mm or 0.25 in. Excessive thickness will cause the resin to crack during curing. Thicker mold sections are fabricated by building atop the mostly cured mold substrate. Once the critical stress areas on the mold have been constructed, reinforcing elements such as thoroughly dried, untreated wood or plaster are added. Scrap fully cured GR-UPE pieces are also used. These are held in place with resin and resin-wetted woven glass fabric. Automotive body putty, a filled UPE product, can also be pressed into irregular areas. These materials are then cured in place. The rest of the mold surface area is then built, either by hand dipping squares of fabric in catalyzed resin and hand applying, or by applying dry fabric to the surface and 1
The gel time is that time when the resin becomes stringy and jelly-like. Beyond the gel time, no further manipulation such as rolling or expressing, is possible.
Table 6.6 Typical Recipe for Unsaturated Polyester Resin With Fiberglass Mat Reinforcing for Prototype Thermoforming Molds Resin recipe
Molar ratio
Isophthalic acid Maleic anhydride Propylene glycol
1 1 2.2
Acid number « 8 Hydroxyl number « 45-50 Gel time « 8 - 1 2 min Peak exotherm « 225°C or 437°F Formulation (polystyrene in polyester at 40 wt %) [recipe depends on wet-out method, type of fabrication—hand layup, spray-up, etc.]
Parts by weight
Polyester, as above TiO2 pigment Styrene diluent Cobalt octoate promoter Methyl ethyl ketone peroxide catalyst
42 28 30 0.3 0.15 to 0.3
Total physical properties of fiberglass-reinforced polyester Flexural strength Flexural modulus Elongation Tensile strength Heat distortion temperature
138 MPa 7.0 GPa 1.0% 82.8 MPa 1900C
20,000 lbf/in2 1,000,000 lbf/in2 12,000 lbf/in2 375°F
squeegeeing resin into it. These layers are then cured to tackiness. Once the entire pattern surface has been covered with at least one layer of nearly-cured fabric and resin, additional layers are added in rapid succession. Wet fabric does not stick well to vertical surfaces. As a result, the mold orientation during fabrication usually dictates the total mold construction time. After a solid reinforced layer is built over the entire mold surface to 3 mm or 0.125 in or so, chopped glass and reactive resin is sprayed onto it. Since the sprayed material resembles wet hay, it must be carefully rolled to express air. Rolling is done with special spaced-disk rollers. The reason for restricting spray-up techniques to supporting roles for hand lay-up is that spray-up laminates have only about 70% to 80% of the flexural strength and modulus of hand lay-up laminates [5]. The spray-up technique is much less labor intensive than hand lay-up and so mold costs are reduced by using it in a supporting role. Once the minimum mold thickness of about 6 mm or 0.25 in is reached, the inner mold structure is constructed. The moldmaker must keep in mind that molds built this way are very large. Even the low pressures used in vacuum forming generate substantial forces that can crush or buckle an unreinforced plastic mold. A standard inner structure is an egg-crate of 2 to 2.5 cm or 0.75 to 1 in thick exterior plywood or laminated wood having 10 to 15 cm or 4
Figure 6.2 Egg-crate cradle that fits into male mold
to 6 in openings. For a male mold, the egg-crate is shaped to fit inside the formed mold structure (Fig. 6.2). For a female mold, the egg-crate is fashioned into a cradle to support the flat sides and bottom of the mold (Fig. 6.3). The plywood is held in place with reactive resin and glass fiber tape or automotive body putty. The plywood core allows for easy access to vent holes. For additional reinforcement, aluminum or phenolic-impregnated paper honeycomb sheet up to 5 cm or 2 in thick is used. This is just laid into the wet resin against the mold back and held in place until the resin cures. PVC, aluminum or GR-UPE pipe is also used for reinforcing. Pipe sections are joined to each other and to the mold back with resin-wet fabric strips and held until the resin sets. The rim of a very
Figure 6.3 Egg-crate cradle into which female mold fits
Figure 6.4 Pipe reinforcement in castable reinforced resin mold
large mold is commonly reinforced in this manner (Fig. 6.4). If the mold must withstand large buckling forces although not necessarily large pressures, lightweight organic cement can be cast against the mold back. Recently, many cements have been developed where a low density aggregate such as slag or Perlite expanded material is mixed with 5 to 10% (wt) UPE or epoxy resin as a binder, then troweled in place. Expanded polystyrene or EPS beads can be mixed with low viscosity epoxy resin as a low-density backing agent1. It is necessary to ensure adequate vent hole placement and access before the mold back is sealed in several cm or inches of cement. Once the mold construction is complete, it must be cured thoroughly, preferably at room temperature. Curing normally takes 24 to 48 h, although more time may be required if some areas are quite thick. To ensure a hard, thorough cure, the mold and pattern is placed in a warm air oven at 500C or 1200F for an additional 24 to 48 h. It is difficult to cure UPE in thin cross-sections to a tack-free state at room temperature, however. Oxygen inhibits reactivity on exposed surfaces. One way around this is to spray a thin layer of air-drying, film-forming PVOH solution on the exposed curing UPE surface. Once the UPE is fully cured, the resulting thin film is then stripped from the mold. If the pattern has been properly prepared, it should release easily from the mold. UPEs and epoxies shrink on curing. If sufficient taper has not been provided on female molds and female portions of male molds, the mold and pattern can become locked together. Even with adequate pattern preparation, considerable manpower and time may be required to release very large molds from patterns. Mold release is best accomplished with combinations of air, water and weight. The entire assembly is suspended slightly above the shop floor with the heavier element nearest the floor. Air and water from separate sources are forced between the edges of the mold and the pattern at the interface. In desperate cases, the pattern must be destroyed to free the mold. The mold surface is then adequately cleaned, waxed and buffed prior to use. Even though plastic molds can last for hundreds of cycles, surface deterioration can begin 1
EPS cannot be used with unsaturated polyester resin, since UPE contains styrene monomer, a solvent for EPS.
in a very few cycles. The most common problem is pinholing, due to collapse of small bubbles trapped in and behind the gel-coat during fabrication. Some dimples and dents are caused by problems in applying the release coat to the pattern. Delamination and blistering are also problems. Usually surface repairs are straightforward. The defect area is sanded or ground down to good material. A patch of catalyzed resin containing a filler such as fumed silica is then troweled into the defect. Cure is by infrared lamp. The region is then finished by feathering into the surrounding good mold material. A cave-in, break-out or development of star cracks during forming require heroic repair efforts. Growing numbers of these usually indicate that the mold was improperly reinforced. Fabrication of a new mold is preferred over attempted repair. Although this section has focused on UPE mold fabrication, epoxy molds are fabricated in a similar fashion [5]. Most epoxies are mineral- or aluminum-powder filled [6]. The extent of shrinkage varies with the filler content. There is very little exotherm generated with the higher loaded epoxies. Glass fabric is used with epoxies in a manner similar to that with UPE. Some molding epoxies have very high viscosities, however, and substantial effort is required to thoroughly wet out the glass fabric. Water lines are easily cast in place in molds made using either UPE or epoxy. GR-UPE is economically preferred for very large molds and water lines can be PVC pipe or aluminum electrical conduit. Epoxy is more expensive than GR-UPE and so is used for small molds where water lines are aluminum or copper tubing. Filled thermosetting polyurethanes are now available for prototype tooling [46]. The PUR systems are typically two-part 1:1 mixtures. Most of the systems are heavily loaded, typically with calcium carbonate or other inorganics. By varying the catalyst concentration, prepared recipes have been developed that allow pot life times of a few minutes to several hours. Table 6.7 gives properties of some typical prototype PURs. Two other approaches for producing prototype molds are being developed. The first uses the concepts of rapid prototyping, detailed in Section 7.3. Rapid prototyping or RP is the generic term used to describe several methods for producing prototype parts [47]. The process uses the mold shape as the computer-generated image. Stereolithography or SLA has been used to produce small prototype molds from UV-curable polyurethane. The cured SLA sheet was back-filled with aluminumfilled epoxy for rigidity [48]. Syntactic foams are also being used to produce prototype tools. The computer-generated mold image is fed to a multi-axis trimming station, Chapter 5. The syntactic foam is then machined into the prototype mold. Both techniques provide rapid turn-around times. These allow the designer to evaluate specific part details and to make necessary changes in a very short time. SLA and syntactic foam molds are not expected to produce more than a few parts. Recently, aerospace applications have included thermoforming of high temperature polymers1. The typical GR-UPE and GR-epoxy molds described above are restricted to about 600C or 1400F use temperature. Higher temperature epoxies are 1
Composite thermoforming is covered in detail in Chapter 9 on advanced thermoforming techniques.
fet7] sPl°P\[ uwojouiiaqx adijojojj JOJ opsBfj §ui[oox auBqjajnifoj jo sapjadojj //9 ajqcx Property
Gel time Demolding time Specific gravity Hardness Shrinkage Compressive strength Flexural strength Flexural modulus Tensile strength Tensile modulus Izod impact strength Heat deflection temperature @ 66 lb f /in 2 @ 264 lb f /in 2 Mixed viscosity Volumetric yield
Unit
Reprotm Identifier Fast
10
83
Slow
Light
min @ 770F min g/cm3 Shore D % lbf/in2 lbf/in2 x 1000 lb f /in 2 lbf/in2 x 1000 lbf/in2 ft-lbf/in
4-5 15-30 1.90 83-85 0.05 6,470 5,140 939 3,130 941 0.31
5-6 30-60 1.90 83-85 0.04 6,470 5,140 939 3,130 941 0.31
6-7 60-90 1.90 83-85 0.02 6,470 5,140 939 3,130 941 0.31
14-16 180-240 1.90 83-85 0.01 6,470 5,140 939 3,130 941 0.31
6-8 90-120 0.90 68 0.05 3,980 2,620 347 1,530 350 0.15
0
57 55 1,100 16
57 55 1,100 16
57 55 1,100 16
57 55 1,100 16
56 48 1,500 30
C C cp in3/lb 0
used to produce molds with use temperatures to 1500C or 3000F. Molds of these materials require much high curing temperatures and much greater care in pattern making and preparation. One manufacturer [7] recommends graphite cloth with aerospace-grade epoxy for fabricating molds that see sheet temperatures of 2000C or 3900F or more. These molds are used to form reactive reinforced resin sheet at low temperatures with curing of the formed sheet against the heated mold at temperatures of 2000C or 3900F. These sophisticated molds include aluminum or copper pipe so that hot oil can be used as a coolant. A mold life of 500 parts is claimed.
White Metal The metal welding industry relies on the establishment of an intensely hot arc that is drawn between electrically isolated metal surfaces energized with high amperage, low voltage DC power. The arc causes most common metals to melt. When high velocity air is blown into the arc, the molten metal breaks into very fine drops. The molten drops can be transported by the air for short distances before cooling below their fusion temperature. One system, the TAFA system, is shown in Fig. 6.5 [8,50]. The TAFA system establishes the electrical arc between metal wires that are fed in a controlled fashion into the spray zone. By accurate control of the metal wire speed, a uniformly fine metal spray issues. The spray is used to coat a surface. Although most metals can be sprayed, zinc and zinc-alloy metals offer good balances of: • • • • • •
Flexibility in spraying, Relatively low molten metal temperatures, thus preserving pattern surfaces, Small drop sizes, Good densification and low porosity, Good hardness in the metal mold, and Good strength in the metal mold.
Typically, zinc has a spraying temperature of 4100C or 7700F and is dispensed at 5 kg/h or 10 lb/h at a power level of 50 to 150A, 20 V, 2 kW. A typical surface hardness is 70 Rb. Other physical properties are given in Table 6.8 [8]. The spraying process begins by securely fastening the pattern, if small, to a turntable and then coating it and the table edges with aqueous PVOH release agent. Once the pattern is secured and dry, the metal spray unit is activated and an arc established1. The spraying rhythm is similar to paint spraying. The objective is to build up a uniform coat over the entire surface. It is necessary to begin spraying at the edges of the pattern. This ties the edges of the metal layer tightly to the edges of the turntable. If this is not done correctly, the air carrier can infiltrate a loose edge, lift the thin metal layer, and catastrophically tear it from the pattern. The process
1
Care must be taken at this point. If the release coating is not dry, the hot metal will cause steam bubbles in the finished mold surface. If the metal is focused too long against one portion of the PVOH-coated mold, the PVOH may degrade and pits will form in the finished mold surface.
Figure 6.5 Rendering of tafa metal spray technique for thermoform mold fabrication. Photo by permission of TAFA Metallisation, Dow (Concord) NH
must then be restarted beginning with pattern preparation. It is recommended that spraying be done in a well-ventilated hood and the operator should wear a breathing helmet. The pattern can be made of temperature sensitive materials such as plastic, foam or paper. However, care must be taken to prevent concentrated hot metal spraying in a small area. If the pattern is small and spraying is continuous, the interfacial temperature between the pattern and the mold can easily exceed 1000C or
Table 6.8 Properties of Sprayed Zinc [8] Hardness Tensile strength Melting point Temperature on contact with pattern Density, % theoretical Shrinkage Cost Weight Melting power Spray droplet size
70 Rc 128 MPa 4100C 2400C
18,500 lbf/in2 7700F 6500F
92 to 95% 0.1 to 0.2% $102/m2 24.3 kg/m2 0.44 kW/kg 50 to 150 ^m
$9.50/ft2 5.0 lb/ft2 0.2 kW/lb
2100F. Temperatures to 2000C or 3900F have been measured. Typically, spraying continues until a uniform layer of metal of at least 1.5 mm or 0.060 in has been deposited. Reinforcing structures, copper water lines, and other features are then placed on the molded shell and these are encapsulated by spraying additional metal (Fig. 6.6). For greater metal rigidity in stress areas such as edges, corners, and deep recesses, the zinc layer is built to 6 mm or 0.25 in or more. To complete the mold fabrication, epoxy cements are cast behind the metal skin. If the mold needs to be a good heat sink, metal-filled epoxies of the types described above are used. These typically have continuous use temperatures to 1200C or 2500F. Note that certain epoxy formulations depolymerize at local temperatures of 2000C or 3900F or more. Although spray metal molds have been used in production for vacuum forming for years without appreciable wear, pressure forming dramatically shortens mold life.
TAFA Spray Head Molten Metal Droplets Mold
Pipe
Pattern
Figure 6.6 Schematic of metal coolant line or metal pipe rein forcement for spray-up white metal mold
When molding sheet molding compound or SMC for example, pressures to 1.5 MPa or 200 lbf/in2 and temperatures to 1200C or 2500F are common. For SMC, mold life is reduced to 100 pieces or so. The primary mode of failure is surface flaking or spalling. In SMC applications, chrome surface diffusion plating is used to harden the zinc surface. The chrome surface is 0.08 to 0.188 or 0.003 to 0.007 in thick and its hardness is 55 to 65 Rc. This treatment increases the cost and delivery time of the mold and should be used only when spray molds are used in pressure thermoforming.
Nickel Nickel molds are also used for prototype thermoforming. A thin electroformed nickel surface is reinforced with sprayed zinc metal, cast white metal or cast aluminum- or nickel-filled epoxy. The nickel used is a very pure electroplating grade of 99.95% with a trace of cobalt. The pattern surface must be conductive. For wood, plaster, ceramic and plastic patterns, a coating of PUR varnish is sprayed over the pattern surface. While the varnish is still tacky, a very fine coating of powdered graphite is air-blown onto it. The PUR is then cured, either at room temperature or in a free convection oven at 500C or 1200F. The pattern is then immersed in a cold plating bath. Nickel is laid against the surface at 4 jim/h until a uniform layer of about 1.5 mm or 0.060 in thick has been deposited over the entire pattern surface. The pattern and nickel layer assembly is then removed from the bath. The dried surface is then backed with sprayed white metal or cast epoxy. Alternately, the pattern and nickel assembly is immersed in a second plating bath where copper is added to a thickness of 10 mm or 0.400 in thick or so. Hot plating techniques lay nickel against the pattern surface at the rate of 10 to 20 um/h, but may produce a coarse-grained porous surface. Normally this surface is dull and matte. It cannot be polished to semi-gloss. But the surface is quite satisfactory for production of non-appearance low-pressure thermoformed parts. Nickel produced by hot plating has about 50% of the toughness of cold plated electroformed nickel. It also costs about 50% of the cost of cold plated electroformed nickel. Recently, a vapor deposition technique has been developed that achieves dry nickel vapor deposition of 0.25 mm/h or 0.010 in/h. Thicknesses of 1 mm or 0.040 in to 25 mm or 1-in are possible without secondary backing. Surface hardness of 40 to 42 Rc with Class A and texture finishes are possible [9].
6.3
Production Molds
Roll-fed sheet forming economics dictate high production rates and long mold life. For this reason, metals yielding low maintenance, good surface hardness, reasonably low cost and low wear are selected. Aluminum has been the choice for many years for the following reasons:
• • • • • • •
Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum Aluminum
molds wear well, has outstanding heat transfer characteristics, is relatively lightweight, is easy to machine, is easy to cast, is moderate in cost, and has excellent strength-to-weight ratio.
Of these, low cost, ease of fabrication and lightweight are most important. Aluminum molds do not appreciably increase the inertial factor of mechanically acting forming presses. More details are given below. Many newer forming processes involve increased pressures, temperatures and stresses. Processes such as: • • • • • •
High speed forming, Matched die forming, In-mold punch-and-die trimming and cutting, Pressure forming, Heated mold forming for crystallizing polyethylene terephthalate (CPET), and Composite sheet forming,
are challenging the ability of aluminum to meet long-term high-production requirements. Steels that are normally used in injection molding are sometimes used in severe conditions in thermoforming. Molds for these high-demand applications may be quite expensive. The expense is justified only on the basis of faithfulness and accuracy over millions of cycles and other features, such as sliding action or in-mold punch-and-die trimming and only if these features cannot be achieved in any other mold material. Aluminum As noted, aluminum is the material of choice for nearly all thermoforming molds. It is easily fabricated, it has a very high thermal conductivity so sensible heat from the formed plastic sheet is rapidly removed and it is a lightweight, tough metal. Thermoforming molds can be made of either machined plate or cast metal. Typically, molds are fabricated from plates of either 2024-T4 or 6061-T651, aircraft grade. Table 6.9 gives the chemical analysis of these aluminums. Typical machined aluminum is 130 Brinnell. Since tool steel hardness is as high at 300 Brinnell, care must be taken during mold changing and alignment with steel members to avoid marring, gouging and dinging the softer aluminum. Aluminum also has a relatively high thermal expansion coefficient of 19XlO - 6 0 C" 1 when compared with steel at 11 x 10^ 60 C" 1 . Care must be taken to minimize abnormal stress and potential buckling or bowing when heating large tightly clamped molds. Molten aluminum is cast at 550 to 6000C or 1000 to 11000F against ceramic, dried and fired gypsum plaster or foundry sand patterns. Usually atmospheric casting is used to produce prototype of short production-run molds. Atmospheric or foundry casting yields molds that may have surface porosity and nonuniform surface hardness. Porosity
Table 6.9 Chemical Analysis of Machined Aluminum 2024-T4 or 6061-T651 Cu Mg Mn Si Fe Ni Ti Zn
1 to 2% 0.5 to 1% 0.5% 4 to 8% 1% [maximum] T% trace trace
can be a problem when pressure forming or if drilled coolant lines pass close to the mold surface. A uniformly high finish is very difficult with foundry cast molds. Pressure casting produces a much denser mold with much more uniform surface hardness, albeit at a higher cost. Patterns must be rugged enough to withstand the thermal shock of molten metal and 7 MPa or 1000 lbf/in2. Fired ceramic patterns are recommended. A casting ceramic of ethyl silicate and quartz powder can be fused into patterns that will withstand pressure casting conditions [10]. Steel The most severe service of any thermoforming process cannot match, say, typical mold temperatures, pressures, erosiveness, or number of required parts of a standard injection molding using filled or reinforced thermoplastics. As a result, thermoforming molds do not need to be constructed of the same tool steel as that specified for injection molds. However, mold shops that specialize in injection molds are accustomed to working in specific types of steels. They will therefore frequently quote jobs in these materials. Prehardened steels such as AISI P20 are recommended for large molds and molds with low demands on wear resistance. P20 is more difficult to machine and polish than, say, S7 or Hl3 steels. Since the last two must be air-hardened after machining, the mold shop does not risk mold dimensional change or distortion with P20. The chemical analyses of Hl3 and P20 are given in Table 6.10. H13 hardness is 30 to 36 Rc. Sophisticated techniques have been developed for machining and hobbing molds and for hardening steel surfaces. Although these heroic methods are not really needed for the thermoforming mold itself, hardened steel is used for mold elements such as: • • • • • •
Slides, Collapsing cores, Rails, Guides, Platen frames, Sheet clamps,
Table 6.10 Chemical Analysis of Tool Steels Oil-hardened P20 tool steel
Air-hardened Pl3 tool steel
• • •
C Cr Mo V
0.35% 5.0% 1.5% 1.0%
C Cr Mo
0.35% 1.25% 0.4%
Hardness
50 to 54 Rc
Hardness
30 to 36 Rc
Hold-downs, Pins, and Pin-chains.
Similarly, investment casting of molten steel against ceramic patterns is also not needed [H]. Other Metals In injection molding, beryllium/copper and Kirksite are frequently used for prototype tooling [11,12]. Typically, molds of these materials yield more parts than aluminum, sprayed metal and plastic molds. Steel molds yield more parts than all other materials (Table 6.11). Low-pressure thermoforming molds see much less severe service than injection molds. As a result, these exotic materials are rarely used. Nevertheless, the service guides given in Table 6.11 hold for low-pressure forming molds as well, with mold lifetimes extended by a factor of at least 10. The mold
Table 6.11 Guide to Tooling Materials [12] Material
Epoxy Sprayed metal Kirksite Beryllium/copper Aluminum Cast Machined Steel 1 2
Delivery time, (weeks) 2 2 4 4
to to to to
4 4 20 12
3 to 8 12 to 20 12 to 26
Number of parts, x 1000 Injection mold 0.1 0.05 100 500 50 100 1,000
Repairs1
Changes, texture
Surface2 finish
3 3 1 2
No No Yes Yes
C/D C/D B A/B
2 2 1
Yes Yes Yes
A/B B/C A
Thermoform 0.1 to 10 0.1 1,000 1,000 200 1,000 10,000
1 = Easy, 3 = Difficult A = Diamond, B = Buff polish, C = 400-600 Grit, D = 350-400 Grit
lifetimes for high-pressure pressure forming and composite forming at elevated temperatures are much closer to those for injection molding.
6.4
Mold Coolant Channels
Many prototype molds and all production molds are actively cooled. Recommended mold temperatures are given in Table 2.5. In production molds, the coolant lines are usually gun-bore drilled in a manner similar to those drilled in injection molds [13]. There are many ways of embedding coolant lines in prototype molds, as noted above. Plastic, aluminum or copper pipe is cast in place in spray-up GR-UPE molds and cast epoxy molds. Copper or aluminum tubing is fastened in place in spray-up white metal and electroformed nickel molds. The location, diameter and number of coolant lines depends on the size and complexity of the mold, and the heat removal potential of the mold material. The determination of heat removal rates is given below. It is recommended that a mold with a properly designed coolant channel pattern should exhibit no more than 3°C or 5°F temperature variation across its surface at steady-state production and that the coolant temperature increase is no more than 3°C or 5°F from inlet to outlet [14]. It is apparent from Table 2.5 that for most commodity polymers, the coolant of choice is hot water. Figure 6.7 shows a simple closed circulating system for treated water as a coolant in thermoforming. To cool polycarbonate, polysulfone and other engineering polymers, the water coolant system must be pressurized to 0.4 MPa or 50 lbf/in2 or more. Hot oil is recomManifold
Mold
Manifold
Coolant
Chiled Water Circulating Pump Shell-and-Tube Heat Exchanger Figure 6.7 Mold coolant plumbing schematic
mended for filled and fiber-reinforced engineering polymers and for higher temperature polymers. Mold Channel Flow Figure 6.7 shows an example of a closed circuit coolant system for a thermoform mold assembly. Pressure losses in complex plumbing systems such as that shown in Fig. 6.7 are best analyzed in terms of Darcy-Weisbach "head losses" for each of the various elements in the system [15]. For simple flow in a constant-area pipe, the head loss is given as:
where L/D is the pipe length-to-diameter ratio, v is the average fluid velocity, gc is an appropriate conversion factor, and f is the friction coefficient. The value of f depends on the nature of fluid flow in the pipe. There are three types of fluid flow that can occur in mold channel flow. These are identified in terms of the fluid Reynolds number, defined as: Dv • p Re, Reynolds number = (6.2) where D is the pipe diameter, v is the average fluid velocity, p is the fluid density, and |i is the fluid viscosity. Re is dimensionless and the other variables are in appropriate units. The fluid is called laminar when Re ^ 2000. The friction factor for laminar flow is given as:
The fluid is in transition when 2000 < Re < 10,000 or so. And the fluid is considered to be turbulent when Re > 10,000. For transition and turbulent flow, the friction factor is given in terms of a relative pipe wall roughness factor, e/D [16,17]. An approximate correlation for e/D < 0.04 and Re > 10,000 is [18,19]: f=a + b R e - c (6.4) where a = 0.094 [e/D]° 225 + 0.53 [e/D] b = 88 [e/D]044 c =1.62 [e/D]0134 For flow through non-constant area elements, the head loss equation is written as: h= K|-
(6.5)
An appropriate value for K, the head loss coefficient, is needed for each flow area change. These are summarized as follows:
Expansion For flow from a small diameter pipe, D1, to a large diameter pipe, D2, K is obtained from: * - [ . - ( D 7
When the pipe discharges into a reservoir, K = I . Contraction For flow from a large diameter pipe to a small diameter pipe, the head loss coefficient is given as:
K = (I-lJ
(6.7)
where c, the contraction coefficient, is a function of the area ratio of the pipes (Fig. 6.8). Note that c asymptotically approaches c = 0.61. This value is frequently used when the exact area ratios are unknown, such as flow through pinched tubing. Sharp-Edged Orifice
Contraction Coefficient, c
On occasion, short constrictions are used to control fluid flow. Approximate values for K for valves, elbows, tees and other constrictions are given in Table 6.12 [20,21]. In certain instances, quick-disconnects and other devices that allow for rapid
Asymptote
Area Ratio, A1 /A 2 Figure 6.8 Head loss contraction coefficient for coolant flow
Table 6.12 Head Loss Coefficients for Various Plumbing Fittings [20,21] Type of constriction
K, Head loss coefficient
Elbow Tee 180° bend Globe valve fully open Check valve fully open Gate valve fully open Gate valve 3/4 open Gate valve 1/2 open Gate valve 1/4 open Diaphragm or butterfly Diaphragm or butterfly Diaphragm or butterfly Diaphragm or butterfly
0.9 1.8 2.2 10.0 2.5 0.19 1.15 5.6 24.0 2.3 2.4 4.3 21.0
valve valve valve valve
fully open 3/4 open 1/2 open 1/4 open
disassembly are employed. These devices can be considered as sharp-edged orifices and the head loss coefficients obtained from: K = (l-l)
(6.8)
where co is obtained from Fig. 6.8, it is advisable to use a single velocity when making head loss calculations for complex systems. The complex system head loss equation would appear as:
In certain cases, as with multiple flow channels in a conventional mold, head losses in the manifolded section should be calculated separately. Example 6.1 is an analysis for water as the coolant. Example 6.2 shows the effect of using oil as the coolant. In Section 5.5, heat transfer between the sheet, its ambient air environment and the coolant medium was considered in detail. As noted, heat transfer efficiency is highest when coolant flow is turbulent, that is, when Re > 10,000 or so. This is usually the case for most dedicated water coolant recirculating systems. High Reynolds number is achieved through high fluid velocity, small pipe dimension, and low fluid viscosity. Turbulent flow is best achieved by high volumetric flow rates although it is apparent from the head loss equation, Equation 6.9, that pressure drop increases roughly in proportion to the square of fluid velocity. Increasing coolant viscosity reduces coolant effectiveness. Thus, reducing coolant temperature, changing from water to brine, water-ethylene glycol, or water-glycerine, and changing to oil usually results in increased pressure drop and a reduction in heat transfer efficiency.
Example 6.1 Water as a Coolant Consider the mold coolant system of Fig. 6.7 using water with the following dimensions: Waterline diameter = i | in Water line length (total)= 100ft Water temperature = 700F Water kinematic viscosity= 1.06x 10~5ft2js Water density = 62.4 Ib/ft3 Fluid velocity in 1\ in water line is 4.1 ft Is. Pipe and mold roughness ratio, e/D = 6x 10~5. The friction factor\ f determined from empirical Equation 6.4, to be: f= 0.01058+ 1.221 Re-044 Plumbing to the mold includes: 6 elbows 1 fully open gate valve Ij open gate valve 1 expansion into a 2\ in manifold 1 contraction from a 2\ in manifold Consider pressure loss through manifold negligible. Mold conditions include: Coolant diameter = 3/4 in Coolant length = 10 ft 4 parallel coolant lines in mold Plumbing in mold includes: 6 90° turns or elbows 1 expansion into 2j in manifold 1 contraction into 2\ in manifold 2 quick disconnects considered to be orifices Determine pressure drop through plumbing complex. Flow in Ij in waterline Reynolds number, Re = Dvp/ji = 50,000. Flow is turbulent. Friction factor, f= 0.021. Head Head Head Head Total
loss coefficient, fL/D = 16.83 loss for 6 elbows, 6 x 0.9 = 5.4 loss for valves = 5.79 loss for expansion, contraction = 1.5 head loss 29.52
Total pressure drop in \\ in waterline: v2 P = 29.52 — x p = 3.31 lbf/in2 2gc Flow in mold channels With 4 parallel lines, velocity in mold channels same as that in \\ waterline from pump. However, Re decreases: Reynolds number, Re = Dvp/ji = 25,000. Flow is turbulent. Friction factor, f = 0.0248. Head Head Head Head Total
loss coefficient, fL/D = 3.96 loss for 6 elbows, 6 x 0.9 = 5.4 loss for 2 sets of orifices = 3.374 loss for expansion, contraction = 1.5 head loss 10.27
Total pressure drop in 3/4 in mold coolant channel: P =10.27 ^ - x p =1.59 lbf/in2 Thus the total pressure drop for the plumbing system of Fig. 6.7 is given as: P total = 3.31 +1.59 = 4.9 lbf/in2 Pumping rate: Q=
v 1 | p 2 _|_ = 225gal/m . n
Example 6.2 Oil as a Coolant Consider the mold coolant system of Fig. 6.7 using oil with the following dimensions: Oil coolant line diameter — Ij in Oil coolant line length (total)= 100ft Oil temperature = 1500F Oil kinematic viscosity1 = 1.3 x 10~4 ft2/s Oil density = 54.5 Ib/ft3 Fluid velocity in Ij in oil coolant line is 4.1 ft Is. Pipe and mold roughness ratio, e/D = 6 x IO~5. The friction factor, f is determined from empirical Equation 6.4, to be: / = 0.01058+ 1.221 Re-044 1
Equivalent to SAE 10 oil
Plumbing to the mold includes: 6 elbows 1 fully open gate valve 1 open gate valve 1 expansion into a 2\ in manifold I contraction from a 2-$ in manifold Consider pressure loss through manifold negligible. Mold conditions include: Coolant diameter = 3/4 in Coolant length = 10 ft 4 parallel coolant lines in mold Plumbing in mold includes: 6 90 turns or elbows 1 expansion into 2j in manifold 1 contraction into 2\ in manifold 2 quick disconnects considered to be orifices Determine pressure drop through plumbing complex. Flow in l\ in oil coolant line
Reynolds number, Re = Dvp/ja = 3850. Flow is in transition. Friction factor, f= 0.0429. Head Head Head Head Total
loss coefficient, fL/D = 34.31 loss for 6 elbows, 6 x 0.9 = 5.4 loss for valves = 5.79 loss for expansion, contraction = 1.5 head loss 47.00
Total pressure drop in \\ in oil coolant line: v2 p = 47.00 — XD = 4.60 lbf/in2 2gc Flow in mold channels
With four parallel lines, velocity in mold channels is same as that in \\ oil coolant line from pump. However, Re decreases: Reynolds number, Re = Dvp/}i = 1925. Flow is laminar. Friction factor, f= 0.0333. Head Head Head Head Total
loss coefficient, fL/D = 5.33 loss for 6 elbows, 6 x 0.9 = 5.4 loss for 2 sets of orifices = 3.374 loss for expansion, contraction = 1.5 head loss 15.60
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Total pressure drop in 3/4 in mold coolant channel: P =15.60 ^- x p=1.52 1bf/in2 Thus the total oil coolant pressure drop for the plumbing system of Fig. 6.7 is given as: Ptotai = 4.60+1.52 = 6.12 lbf/in2
6.5
Vent Holes
As the hot plastic sheet is drawn into the mold, the trapped air must be evacuated. Small holes are drilled into the mold surface in the regions where the last portion of the drawing sheet contacts the mold. The number and diameter of these vent or vacuum holes is determined prior to mold design. If the vent hole diameter is too large, hot plastic is drawn into it, producing an unsightly bump, nipple or nib on the finished part. If the nib is excessive, the sheet can rupture. If too few holes are provided or if the vent area is too small, the rate of draw-down will be controlled by the rate of air flowing from the cavity. If the rate is very slow, the sheet may cool so much during draw-down that it can no longer be stretched into the corners and full mold shape replication is not achieved. Vent hole design is coupled to vacuum system design. Figure 6.9 shows a schematic of a typical thermoformer vacuum system. The basic system consists of: •
Vacuum pump, capable of achieving 28 to 28.5 in mercury (28 in Hg to 28.5 in Hg) vacuum,
Mold Cavity
Vacuum Hole Back-Drill Vacuum Channel
Vacuum Box
Vacuum Gauge
Vacuum Line
Shut-Off Valve
Vacuum Pump Surge Tank
Figure 6.9 Typical plumbing between mold cavity and vacuum pump
Previous Page
Total pressure drop in 3/4 in mold coolant channel: P =15.60 ^- x p=1.52 1bf/in2 Thus the total oil coolant pressure drop for the plumbing system of Fig. 6.7 is given as: Ptotai = 4.60+1.52 = 6.12 lbf/in2
6.5
Vent Holes
As the hot plastic sheet is drawn into the mold, the trapped air must be evacuated. Small holes are drilled into the mold surface in the regions where the last portion of the drawing sheet contacts the mold. The number and diameter of these vent or vacuum holes is determined prior to mold design. If the vent hole diameter is too large, hot plastic is drawn into it, producing an unsightly bump, nipple or nib on the finished part. If the nib is excessive, the sheet can rupture. If too few holes are provided or if the vent area is too small, the rate of draw-down will be controlled by the rate of air flowing from the cavity. If the rate is very slow, the sheet may cool so much during draw-down that it can no longer be stretched into the corners and full mold shape replication is not achieved. Vent hole design is coupled to vacuum system design. Figure 6.9 shows a schematic of a typical thermoformer vacuum system. The basic system consists of: •
Vacuum pump, capable of achieving 28 to 28.5 in mercury (28 in Hg to 28.5 in Hg) vacuum,
Mold Cavity
Vacuum Hole Back-Drill Vacuum Channel
Vacuum Box
Vacuum Gauge
Vacuum Line
Shut-Off Valve
Vacuum Pump Surge Tank
Figure 6.9 Typical plumbing between mold cavity and vacuum pump
•
Vacuum surge tank, typically having 6 to 20 times the volume of the combined mold cavity volumes, • A solenoid-actuated shut-off valve, • A flow control valve, • Large-diameter plumbing between the surge tank and the vacuum box, • A vacuum box or chamber fixed between the mold platens, • A mold or molds containing: Vacuum or vent holes, and Vacuum slots or drilled holes between the vent holesand the vacuum box, and • A mold cavity or mold cavities. As discussed in Chapter 1, two types of vacuum systems are currently used. For very large installations with many thermoforming machines and other uses for evacuated air such as vacuum-routering, a central vacuum system is used. Very large diameter (4 in minimum with 6 in typical) vacuum lines are plumbed to each application. This is shown in schematic in Fig. 6.10. For small installations, each thermoforming machine is equipped with a dedicated vacuum system. This is shown in schematic in Fig. 1.23 for a shuttle press1.
Surge Tank
Vacuum Pump
Vacuum Box
Shut-Off Valve
Figure 6.10 Central vacuum system schematic
1
Even though a central vacuum system is preferred for a multiple former shop, it is important to reserve at least one, dedicated, working vacuum pump and surge tank for emergencies or for auxiliary evacuation for deep cavity jobs.
Table 6.13 Gas-Law Constant Numerical value
Units
1.987 1.987 82.06 0.08205 10.731 0.7302
cal/g-mol-K Btu/lb-mol • 0 R cm3 • atm/g-mol • K liter • atm/g-mol • K ft3 • lbf/rn3 • lb-mol • 0R ft3 • atm/lb-mol • 0R
Sizing Vacuum Systems—Steady State Low pressure air is compressible. As a result, the arithmetic needed to size vacuum lines and vent holes depends on compressible fluid flow. For all intents, air can be considered as an ideal gas. The ideal gas equation is: PV = nRT
(6.10)
where P is pressure, V is volume, T is absolute temperature, n is a function of the molecular weight of the gas, and R is the gas constant (Table 6.13). For most cases, air flow can be considered as isothermal. That is, the gas does not change in temperature as it flows through various constrictions in the piping system. In this case, the relationship between gas pressure and volume is given as: P 0 -V 0 = P 1 -V 1
(6.11)
where P is pressure (absolute), V is volume and " o " and " 1 " represent the various states of the air. Example 6.3 illustrates how this expression is used to size the surge tank. Typically, the minimum volume of any vacuum system, including the piping and vacuum box, should be 6 to 20 times that of the mold cavity.
Example 6.3 Surge Tank Volume Determine the surge tank volume, Vs, needed to evacuate a mold of Vmft3 volume initially at Pm pressure (absolute). The minimum desired pressure on the hot sheet against the mold is to be Pmin. The vacuum pump is capable of achieving Pv pressure (absolute) and the air temperature is constant. The working equation is: Y-P v
s
x
+
v ~
Y v
. p _ (Y _|_ y \ . p . m
x
m
V
v
s ~
v
m)
x
mm
Consider the case where: Pv = 28 in Hg = 0.94 lbf/in2 (absolute) p min = 24 in Hg = 2.9 lbf/in2 (absolute)
P m = 14.7 Ib2/in2 (absolute) = atmospheric pressure (14.7- 2.9) s m m (2.9-0.94) In other words, the vacuum surge system, including all the piping and the vacuum box, should be at least six times the volume of the mold cavity. Consider the case where blow air is used to prestretch the thermoformed sheet. For this case, P m is greater th,an atmospheric pressure. The typical prestretching pressure for 10% talc-filled polypropylene from Table 6.13 is 8 to 10 lbf/in2. Repeat the above calculation, using P m = 24.7 lbf/in2 to determine the minimum vacuum surge system volume. .(24.7-2.9) Vs
V1n
( 2 9
_
0 9 4 )
11-1 V m
Typically, vacuum tank volumes range from six to 20 times the expected cavity volume.
Sizing Vacuum Systems—Dynamic The above discussion does not consider the time required to evacuate a mold cavity. The fundamentals of compressible fluid flow are given elsewhere [22,23]. As a first approximation, air flow in thermoforming vacuum systems can be considered as isothermal. Correctly, gas flow is adiabatic for high velocities through constrictions. That is, the pressure-volume relationship is: PoVJ = P1VI
(6.12)
where y = 1.4 for air. The speed of an adiabatic compression wave moving through stagnant air is given as: c2 =
Y• P
1
— (6.13) P where p is the density of the gas. c is usually called the velocity of sound. As shown in Example 6.4, the velocity of sound at 70 0 F and atmospheric pressure is about 1100 ft/s. The Mach number, Ma, is the ratio of gas velocity to sonic velocity: Ma = c
(6.14)
Example 6.4 The Velocity of Sound in Air Determine the velocity of sound at one atmosphere and 700F and at 0.05 atmospheres and 700F.
The velocity of sound, c, at 14.7 lbf/in2 is: c =1078 ft/s p = 0.05 • 0.082 = 0.0041 lbm/ft3 The velocity of sound, c, at 0.74 lbf/in2 is: c = 241 ft/s Gas velocities equal to the velocity of sound are sonic and those less than the velocity of sound are subsonic. Usually, air flow in vacuum systems is always subsonic. However, sonic conditions can exist at the vent hole inlet, as discussed below. If the fluid velocity is low in certain portions of the vacuum system, that region can be considered as incompressible and traditional incompressible fluid mechanics can be used. If the velocity is high—that is, if the Mach number is on the order of 0.3 or more—the flow must be considered compressible. Sonic flow is established so long as the absolute pressure differential across the vent hole is less than 0.53. For incompressible air flow in vacuum systems, as detailed in Section 6.4, an appropriate pressure drop-flow rate relationship is written in "head loss" terms:
where f is the friction factor, L is the pipe length, D is the pipe diameter, V is average air velocity, gc is a unit correction term, and K is the effective resistance through a specific constriction (Table 6.12). The pressure drop, dPi9 through the ith segment of the vacuum system is given as: dPi
=
V
PM^811
(616)
where h{ is the head loss through the ith segment and pi5inean is the average or geometric mean air density through that segment. The total pressure drop is then: CiPtOtHi = Z d P 1
(6.17)
Another less accurate method is to obtain an effective pressure drop, given as: dP = h t o t a l -p m e a n
(6.18)
Note that p mean is an appropriate mean value of the density of the air. It can be the simple geometric mean of the density of the inlet and exit gas stream or the average of the densities of the air at every segment. Considering air as an incompressible gas in order to determine pressure drop is satisfactory for all the piping with the exceptions of: • •
Flow through solenoid valves, and Flow through vent holes.
Orifice Coefficient, c
A0ZA1
Pipe Reynolds Number, Re Figure 6.11 Flow rate-dependent orifice coefficient for compressible air in vacuum systems. Reynolds number, Re = Dv • p/|i where D is pipe diameter, v is air velocity, p is air density and [i is air viscosity
Solenoid Valve Flow Resistance Solenoid valves act to isolate the surge tank-vacuum pump system from the vacuum box-mold system. Although vacuum system solenoid valves are designed to offer minimum resistance to the flowing air, their shapes are such that the pressure loss is best considered as the result of compressible flow through a sharp-edged orifice. Figure 6.11 gives the orifice coefficient for incompressible flow. The pressure dropflow rate equation is written as: in = C 0 YA 0 ^dP) 1 / 2
(6.19)
where rh is the mass flow rate, co is the orifice coefficient, A 0 is the minimum area of the orifice, A 0 = 7iDo/4, P1 is the density of air in the pipe ahead of the orifice and dP is the pressure drop across the orifice. The compressibility correction factor, Y of Fig. 6.12, is dependent on the pressure drop across the orifice and the diameter ratio of the orifice and pipe. Example 6.5 illustrates the use of this equation. Example 6.5 Compressible Air Pressure Drop Across Solenoid-Orifice Air at 5 Iby/'in2 (absolute) pressure and 700F flows at 1 lbm\s through a 2-in diameter pipe. A solenoid valve, acting as an orifice, has an internal constriction, A0/A1 = 0.5. What is the pressure drop across the valve? p (14.7 & 700F) = 0.082 l b j f t 3
Re > 100,000 From Fig. 6.11, C(AJA1 = 0.5) = 0.69 D J D 1 =0.707 Equation 6.19 is used to obtain the result: rh = C0YA0 (2P1ClP)1/2 The air density at 5 lbf/in2 is: p = 0.0812 • (-^~\
= 0.0276 lb/ft3
Since Y is a function of pressure drop, initially assume Y = 0.9 (P 2 /Pi = I)Solving for AP: 4 I2 144
[
0.695-1.0-4,J 2-0.0276-32.3-= ° - 5 3 1 b f / m 2 P 2 = 5 - 0 . 5 2 = 4.48 lbf/in2. P2ZP1 = 0.89. The value for Y is then iterated using this value of P2ZP1. When Y = 0.96, AP = 0.57 and P 2 = 5.43 lbf/in2.
Expansion Factor, Y
Orifice-Flange Taps or Vena-Contracta Taps
Venturi
Pressure Ratio Figure 6.12 Expansion factor for vacuum system compressible air flowing through orifices and Venturis
Vent Hole Resistance to Flow When the solenoid is actuated to open the valve, the compression shock wave propagates from the valve upstream to the vent holes. Since the vent holes offer very high flow resistance, sonic velocity may be established at the entrances to the vent
holes. If this is the case, the maximum rate of evacuation of the mold cavity is calculated from: rhmax = NAV • c • p
(6.20)
where A v is the area of the vent hole, N is the number of vent holes, c is the sonic velocity and p is the density. If the evacuation time of a mold cavity having volume v m is t, and the diameter of a given vent hole is D, the air velocity is:
v =
(6 21)
- 'Wm
-
If the velocity of air through the hole is sonic, the number of vent holes of diameter D is given as: N=
— (6 27) K } c(;rD 2 /4)t Example 6.6 illustrates the relationship between rate of cavity evacuation and the absolute minimum number of vent holes. The analysis above assumes that the vent hole has essentially zero length. As expected, the pressure drop increases with increasing vent hole length. The effect of vent hole length is determined from compressible "head loss" calculations. In essence, the friction factor is determined in standard fashion, as outlined earlier in this chapter. The head loss factor, fL/D, is calculated and the reductions in velocity and pressure are determined from Table 6.14. Example 6.7 illustrates the way in which this is determined.
Example 6.6 Vent Hole Sizing and Evacuation Rate What is the absolute minimum number of vent holes needed to evacuate a I ft3 mold cavity in 10 si D = 1/32-in. Individual vent hole area, A = TID 2 /4 = 0.000767 in2 Mass flow rate = 1 ft3/10 s = 0.1 ft3/s. Sonic velocity = 1000 ft/s Mass flow rate, a single vent =
— = 0.00533 ft3/s
Total minimum number of vents, N = 0.1/0.00533 = 18.8 « 20
Example 6.7 Effect of Vent Hole Length on Pressure Drop and Air Velocity Consider the case where 700F air is exhausting at sonic velocity through a 0.0313-in diameter vent hole. Determine the pressure drop and velocity reduction for vent hole lengths of 0.125 in and 0.250 in. Consider the drilled hole to be smooth-bored. The kinematic viscosity of air is 2.15 x 10~4ft2/s.
The Reynolds number is given as:
From the Moody friction factor-Reynolds Number diagram, Fig. 6.13 (see Streeter, pp. 288-289), f = 0.029. Thus: fL/D = 0.029 • 0.125/0.0313 = 0.116 Interpolating from Table 6.14, v/c = 0.789 and P/P c = 1.365. At the exit of the vent hole, the velocity is 1000 x 0.789 = 789 ft/s. And the pressure is 14.7/1.365 = 10.77 psi. For L = 0.250 in, fL/D = 0.232. Interpolating from Table 6.14, v/c = 0.694 and P/P c = 1.519. At the exit of the longer vent hole, the velocity is 694 ft/s and the pressure is 9.69 psi.
Table 6.14 Effect of Vent Hole Length on Pressure Drop fL/D
V/c
P/Pc
0 0.0033 0.0145 0.0363 0.0723 0.1273 0.2081 0.3246 0.4908
1 0.958 0.915 0.870 0.825 0.779 0.732 0.684 0.635
1 1.061 1.129 1.205 1.289 1.385 1.493 1.618 1.783
Note that the Reynolds number through a vent hole is relatively small, even though the air velocity is sonic. This is due to the very small vent hole diameter. The volumetric flow rate through the piping between the vent holes and the vacuum surge tank is determined from: (6.23) where N is the number of vent holes and c is sonic velocity. As a first approximation, the air velocity everywhere else is given as: (6.24) Thus the Reynolds number in any pipe of diameter D p is related, on first approximation, to the sonic velocity Reynolds number:
(6.25) Example 6.8 explores the relative values of these variables. Example 6.8 Relative Velocities and Reynolds Numbers in Vacuum Pipe Flow Assume the air velocity through a 0.0313-in diameter vent hole is 1000 ft Js1. There are 100 vent holes. Calculate the volumetric flow rate, the Reynolds number through the vent hole, and the Reynolds number through the 2-in diameter pipe to the vacuum surge tank.
Volumetric flow rate = If the volumetric flow rate is constant, the Reynolds number in the 2-in diameter pipe is given as:
If the density is constant, the velocity in the 2-in diameter pipe is given as:
1
This assumes that the vent hole length is negligible. If it is not, it is necessary to reduce this value to the proper one as shown in Example 6.7.
It is apparent from the examples for flow through the solenoid valve and the vent holes that such constrictions can severely restrict the rate at which air is exhausted from the mold cavity. Before summarizing the evacuation flow characteristics, consider the replacement of traditional hard piping for vacuum lines with corrugated flexible tubing. Corrugations act as localized expansions and contractions along the entire length of the tubing. The worst case scenario is obtained by multiplying the orifice head loss coefficient K by the number of corrugations in the tubing length. The best case scenario assumes that the pipe has great roughness. As seen in Fig. 6.13, the friction factor approaches a constant value at relatively low Reynolds numbers for very rough pipe. For a pipe of e/D = 0.05, for example, the friction factor approximates 0.072 for Re > 30,000 or so. Computation of flow rate-pressure drop through the vacuum system requires trial-and-error. The following protocol will enable rapid iteration: 1. Assume the air pressure in the mold cavity to be atmospheric. 2. Assume sonic velocity at the inlet to the vent holes.
Complete Turbulence, Rough Pipe
e/D=0.05
Friction Factor, f
Transition
e/D=0.000001
Reynolds Number, Re Figure 6.13 Flow rate-dependent friction factor for flow in a pipe. e/D is measure of roughness, Reynolds number, Re = Dv • p/ji where D is pipe diameter, v is fluid velocity, p is fluid density and u is fluid viscosity
3. 4. 5. 6. 7.
Determine the velocity, density, and pressure at the exit of the vent holes. Calculate the Reynolds number for air flow in the vent hole. Estimate the practical number of vent holes to be used1. If a solenoid valve is used, estimate the pressure loss from the orifice equation. Using the "head loss" approach, calculate the total head losses for the piping, elbows, vacuum box, back-drilled region on the mold, expansion loss into the surge tank and the pressure loss across the solenoid. 8. Add to this the pressure loss across the vent hole. 9. If the calculated pressure loss is greater than that determined from the available pressure differential between the surge tank and atmosphere, the assumed flow rate is too great. In other words, there is too much resistance to flow for the chosen velocity. Since the controlling factor is the assumption of sonic flow at the inlet to the vent hole, it is necessary to reduce this velocity to a value below the velocity of sound. Estimate this velocity by multiplying the ratio of available to calculated pressure drops by the velocity of sound. Continue to iterate until there is reasonable agreement on pressure drop values. 10. If the calculated pressure loss is less than that determined from the available pressure differential between the surge tank and atmosphere, the assumed flow 1
This number is usually 3 to 5 times greater than the minimum number of vent holes calculated. One method is to assume that the Reynolds number in the vacuum pipe equals that in the vent hole. From this, the number of vent holes can be estimated.
rate is too small. Unfortunately, the greatest flow rate that can be assumed is sonic flow. This means that the cavity volume could be evacuated even faster than the current mold design allows. One way of increasing evacuation rate is to increase the number of vent holes. Another is to increase the diameter of the vent holes. Both of these options can lead to part design problems, as detailed later. Example 6.9 illustrates a portion of this iterative procedure. Example 6.9 Pressure Drop Through Vacuum System Consider the mold vent hole and vacuum line assembly outlined in Examples 6.7 and 6.8, with the vent hole length of 0.250 in, the vacuum line being 2-in smooth bored pipe 100ft in length and having eight elbows, two tees, one solenoid valve and one check valve and one globe valve. Assume that air flow through the vacuum box represents 10 equivalent ft of smooth bored pipe, and that there are two flow expansions and two flow contractions. Use a mean air density between the surge tank and the vent hole outlet. Assume the flow to be isothermal, for the most part. Density of air at the exit of the vent hole is directly proportional to the pressure at that point. P vent exit
Patmospheric v^exit/ *atm/
Pventexh = 0.082 • (1/1.519) = 0.054 lb m /ft 3
The pressure in the surge tank is assumed to be 0.05 atmospheres (absolute). The density at 70 0 F is therefore: Psurge = 0.082 • (0.05/1) = 0.004 lbm/ft3 The mean density is: Pmean = Vpsurge ' Pvent exit = 0.015 lb m /ft 3
Assume the Reynolds number in the 2-in pipe = 18,900. From Fig. 6.13 for smooth-bored pipe, f =0.0251. So: fL/D = 0.0251 • (100 + 10) • 12/2 = 15.67 The head losses from the rest of the system, with the exception of the vent hole and solenoid losses, include: 2 2 8 2 1 1
expansions x 1.0 = contractions x 0.5 = elbows x 0.9 = tees x 1.8= check valve = globe valve =
2.0 1.0 5.4 3.6 2.5 1O1O 24.5
Thus the total head loss value is given as: Ktotai= 15.67 + 24.5 = 40.2 The velocity through the 2-in pipe is given as 24.5 ft/s:
The total head loss, htotal is then given as: htotal = 40.2 -(v2/2gc) = 374.7 ft The pressure drop is then: AP = htotal • p mean = 374.7 • 0.015/144 = 0.04 lbf/in2 The pressure drop through the solenoid is given in Example 6.5 as AP = 0.57 lbf/in2 and that through the vent holes in Example 6.7 as AP = 5.01 lbf/in2. Thus the total pressure drop is: Pressure drop through vent holes = Pressure drop through solenoid= Pressure drop through piping = Total pressure drop =
5.01 0.57 0.04 5.62 lbf/in2
Since the calculated pressure drop is less than the maximum available pressure drop (1 — 0.05) • 14.7 lbf/in2 = 14.0 lbf/in2, the rate of evacuation is restricted by sonic velocity at the vent holes. Increased evacuation is possible by increasing the number of vent holes or increasing the vent hole diameter.
Vent Hole Diameter Mold vent hole diameter depends on several factors, including the modulus of the hot plastic sheet, the sheet thickness over the hole and the allowable draw depth into the vent hole. The maximum deflection 8, of a sheet of thickness h and modulus E into a hole diameter d is given as [24]:
where the maximum deflection is proportional to h, with oc as the proportionality or acceptable nib or nipple height, q is the applied pressure, and v is Poisson's ratio (Table 5.15). For many plastics, 0.35 < v < 0.5. If v = 0.5:
« = 0.516-|-(|y
(6.27)
The maximum nib or nipple height is usually specified by the user or the designer. This establishes an upper limit for a = 5/h. Rearranging Equation 6.27:
This is shown in Fig. 6.14. As discussed in Chapter 4, the secant modulus or (|>(T) is about 100 lbf/in2 or 0.7 MPa for vacuum forming where the pressure is about 15 lbf/in2 or 0.1 MPa. Thus the E/q is 7. A typical range for E/q is 2 < E/q < 10. A good range for d/h in Equation 6.28 is: 1 . 4 a 1 / 4 < £ < 2 . 1 oc1/4 n
(6.29)
Hole Diameter to Local Sheet Thickness Ratio, d/t
Characteristic Sheet Modulus, dE/q Figure 6.14 Specific vent hole design parameter, d/t, as function of modulus-to-pressure ratio, E/q, and relative nib height, a. This is for initial draw-down into vent hold
Example 6.10 further explores this relationship. If the nib or nipple height is restricted to no more than the sheet thickness, the vent hole diameter must be less than 2.1 times the sheet thickness. This value is compared with Gruenwald's rule [25]: "... vacuum hole sizes smaller than the (local) material thickness will not become visible..."
That is, holes where d/h < 1 yield acceptable nib heights. Example 6.11 tests the sensitivity of Equation 6.28 as regards local sheet thickness and sheet temperature. As illustrated, locally thin sheet produces a much greater effect on nib or nipple size than does locally hot sheet. It is recommended that the vent hole diameter be based on the first common drill size below the calculated value. The vent holes should be drilled perpendicular to the plane of the mold. The backs of the vent holes must be enlarged by machining vacuum channels or drilling large holes on the reverse side or back of the mold (Fig. 6.15). Since the objective is to reduce flow resistance through the long vent hole, the counterboring, "back-drilling" or "back-drafting" should be taken within 0.5 in or 13 mm of the mold surface or closer if possible. This counterboring must be done carefully to minimize locally weakening the mold in the Example 6.10 Relative Nipple Height Determine the maximum vent hole diameter for 0.040 in PS sheet drawn 4:1 against the vent hole area. Assume E/q < 10. Consider the maximum nipple height to be equal to the local sheet thickness.
From Equation 6.29, d/h < 2.1 oc1/4 for E/q < 10. At 4:1 draw ratio, the local sheet thickness is 0.010 in. The maximum nipple height is 0.010, with a = 1. The hole diameter must be less than 2.1 • h or dmax = 0.0210 in.
vent hole region. Drilling too closely or milling a channel that is too wide invites long-term metal fatigue and possible local collapse [26]. Experienced mold-makers avoid drilling too few vent holes of diameters that are too large. If the vent hole diameters are too large, objectionable nibs or nipples result, even though the volume of entrapped air is exhausted in a reasonable time. Large diameter vent holes force the fabricator to lower sheet temperature. If stretching forces are limited or the sheet is particularly stiff, poor part replication results.
Example 6.11 The Relative Sensitivity of Nipple Height to Process Parameters Consider polymers having the following temperature-dependent elastic moduli:
Determine the relative effects on nipple height on: ± 10% change in pressure, ±10% change in sheet thickness, and ±20° C change in sheet temperature for PMMA where 1/0 = 200C'1 and PE where 1/0 = 850C'1.
Equation 6.28 is differentiated as follows:
Now dd/d = 0. The expression for dE is:
Therefore:
For PMMA:
The sheet temperature affects the PMMA nipple height the most. For PE:
I The sheet thickness variation affects the PE nipple height the most.
Vent Hole
Mold Thickness
Vent Hole
L
d. L
Mold
Vacuum Slot or Vacuum Box
D Vacuum Slot or Vacuum Box Back-Drill or Back-Draft
Figure 6.15 Characteristic geometric factors for vacuum or vent hole without back-drilling (left) and with back-drilling (right)
Occasionally a mold that is functional for one polymer yields unacceptable nipple or nib heights with another. Peening the vent hole area will reduce the vent hole size, albeit at the risk of deglossing the mold in that area1. Note that Equation 6.28 is also acceptable for determining vent hole size for pressure forming. As discussed in Chapter 9, pressure forming pressures are typically four to six times greater than vacuum forming pressure. As a result, the lower inequality in Equation 6.29 is operative. A properly dimensioned vent hole for vacuum forming would yield a relative nib or nipple height that is four times greater with pressure forming. One saving aspect is that pressure forming sheet temperatures are usually somewhat lower than equivalent vacuum forming temperatures. Cooler sheet implies higher elastic modulus and shorter nibs or nipples.
Vacuum Slot
Vacuum Slot
Vacuum Slot
Vacuum Channel or Vacuum Box Figure 6.16 Vacuum or vent slots for two-piece female mold (left) and one-piece female mold (right) 1
Plugging and redrilling the hole is always an option.
Figure 6.17 Vacuum or vent slots for male mold
Other Types of Vents Slot vents are used when linear protruding elements occur inside a female mold (Fig. 6.16) or along the bottom rim of a male mold (Fig. 6.17). Slots are end-milled or cut with a wire EDM along the two-dimensional corner. Exit vents are then drilled from the reverse side. The width of the slot vent is determined in a manner similar to that for round holes. From Fig. 6.18, let d be the slot width. The maximum deflection, 5, is given as [27]: (6.30) Rearranging: (6.31) Since this equation is of the same form as Equation 6.28 for a circular hole, Fig. 6.14 is used for slot vents if: (6.32)
y d
Figure 6.18 Vacuum or vent hole geometric factors
Table 6.15 Porous Metal Product Manufacturers (Specialties in parentheses) Allied Sinterings, Inc. (small parts) 29 Briar Ridge Rd. Danbury CT 06810 203-743-7502 Arrow Pneumatics, Inc. (bronze) 500 Oakwood Rd. Lake Zurich IL 60047 708-438-9100 Astro Met, Inc. (stainless steel, powder metallurgy) 9974 Springfield Pike Cincinati OH 45215 Atlantic Sintered Metals (powder metallurgy) 12 Cushing Dr. Wrentham MA 02993 508-384-3100 Helsel, Inc. (stainless steel) State Rd. 60 W. r K°n K Txr ym™ Campbellsburg IN 47108 813-755-4501 . f Mott Metallurgical Corp. (stainless steel) Farmington Industrial Park 84 Spring Lane Farmington CT 06032-3159 203-677-7311
National Sintered Alloys, Inc. (parts, powder metallurgy) 10 Heritage Park P.O. Box 332 Clinton CT 06413 203 669 8653 Newmet Krebsoge, Inc. (stainless steel, bronze, titanium) P.O. Box 68 Terryville CT 06786 800-426 0977 8 °° 4 2 6 °977 Pacific Sintered Metals, Inc. (bronze, stainless ^ 0 Permaflow? Inc at the same address] 14002 s
Ayalon
^ 1 CA 310-715 9800
Los
p T I T e c h n o l o ies 950 R a n c h o
Blyd
^
6 1
Inc
^onejo
Blyd
Newbury Park CA 91320 OQQ ^Q, Q^g1 SSI Technologies, Inc. (stainless steel, bronze) ^^32 Palmer Dr Janesville WI 53566 608-755-1900 The Wakefield Corp. (stainless steel, bronze) 35 Foundry St. Wakefield MA 01880 800-548-9253
For the same allowable depth of draw into the vent, slot vent widths need to be only 83% of circular vent diameter. For a given dimension, slot vents have two to four times greater venting area. Reverse side exit holes must be large enough to allow unrestricted air flow from the cavity. And slot vent width must be small enough to minimize part undercutting into the vent or the formation of an unsightly line. Porous metal plugs are used in flat areas in place of multiple vent holes. Sintered powders of bronze, brass or stainless steel of about 50% open area are commercially available (Table 6.15). These plugs are machined to fit an existing vent hole region or can be custom ordered to meet a specific design. A hole large enough to vent the area, usually 6.4 mm or 0.250 in or more, and deep enough to accommodate the plug, usually 6.4 mm or 0.250 in or more, is drilled in the primary mold surface (Fig. 6.19).
Porous Plug Mold
Vacuum Box Figure 6.19 One method of fastening porous plug in mold cavity for evacuation
Exit holes are then drilled from the reverse side to facilitate venting. Another approach is to use a tapered hole and a tapered plug that is inserted from the reverse side and held in place with a simple spring ring or screw (Fig. 6.20). The effective porous metal venting area width is as much as ten times greater than the venting area from clustered vent holes. Nipples cannot form when porous vent plugs are used. However, the open areas or pores in the plugs tend to fill with detritus, particularly if in-mold trimming is used. Other sources of detritus include sander and router dust, atmospheric dust and contamination on the incoming sheet. Venting efficiency gradually decreases with time, necessitating periodic plug replacement. Fine stainless steel, nickel and brass welded wire screen is also commercially available. Open area for ^100 mesh screen is usually 35% to 65%. Screen must be supported to minimize bending under sheet draw-down forces. Screen may also leave an undesirable pattern on the part. The poppet valve is usually mechanically operated and is used in injection molding to break the suction between a part and the mold surface on flat, large-area parts. The poppet valve can be used in this fashion for parts thermoformed onto male molds. In venting, poppet valve is used to rapidly exhaust cavity air in large-volume deep-draw female molds (Fig. 6.21). The evacuating poppet value is spring loaded and is normally open. It is closed either on a clock timer or by the sheet draw-down force. Example 6.12 illustrates the high evacuating efficiency of a poppet valve.
Porous Plug Mold
Vacuum Box Figure 6.20 One method of fastening porous plug in mold cavity for evacuation
Poppet Valve Open Poppet Valve Closed
Mold Spring Vacuum Channel
Vacuum Channel
Spring
Figure 6.21 Spring-loaded poppet valve for evacuating large-volume or deep female mold cavities
Example 6.12 Poppet Valve in Mold Evacuation A 6-in diameter x 8-in deep female mold cavity is currently being evacuated in LOs through 18 vent holes, each 1/16-in in diameter. Determine the maximum evacuation rate if the number of vent holes is doubled. Then compare this with the evacuation rate if a 3-in diameter poppet valve with an open gap of 0.020 in is installed in the cavity bottom. The cavity volume is 7iD2L/4 = 226.2 in3. The current volumetric evacuation rate is 226.2 in3/1.0 s = 226.3 in3/s. The area of current vacuum holes is: N
' ^ = 18 • 0.7854 • (0.0625)2 = 0.0552 in2
The current air flow is 226.2/0.0552 = 4096 in/s = 341 ft/s or subsonic flow. If the number of holes doubles and the air flow remains the same, the cavity is evacuated in 1.0/2 = 0.5 s. The vent area of the open gap of 0.020 in on the poppet valve is 7idp • 0.020 = 0.1885 in2. The total vent area is then 0.0552 + 0.1885 = 0.2437 in2. If the air flow remains the same, the cavity is evacuated in 1.0(0.0552/0.2437) = 0.23 s.
Vent Hole Placement It is apparent that there must be venting in areas where the plastic last contacts the mold surface. These areas are usually two- and three-dimensional corners. There is substantial verification that adequate parts can be made by vacuum forming into a five-sided female mold having venting only in the four three-dimensional corners.
Vent Holes on Flat Surface
Figure 6.22 Vent hole location on flat or planar mold surface for both male and female molds
The wall thickness prediction programs of Chapter 7 are most useful in defining where other potential late evacuation regions are. Other areas where vent holes are desirable include: •
Flat, large-area horizontal surfaces on both male and female molds (Fig. 6.22). The sheet usually touches the mold surface here first. Subsequent shrinkage can tightly lock the sheet to the surface. The vent holes are used primarily to blow the cool sheet from the mold surface. • Vertical walls and vertical two-dimensional corners, in particular (Fig. 6.23). These vents serve primarily to lock the sheet against the mold surface during stretching. These vents are particularly important for low coefficient of friction polymers such as polypropylene, polyamide and PTFE. • In and around lettering, bosses, ribs, and corrugations. Since it is not always apparent how the plastic will form around and into these details, venting must be adequate and vent holes regularly spaced (Fig. 6.24). • In the rim regions for female molds, particularly when dams or moats are used (Fig. 6.25). These help lock the sheet against the mold and minimize the amount of web area sheet drawn over the rim and into the mold cavity. Vent Holes on Vertical 2D Corner
Vent Holes to Minimize Slip
Figure 6.23 Vent hole location on vertical two-dimensional female mold surfaces
Boss Raised Letter With Insert Vent Hole
Rib
Vent Hole
Mold
Figure 6.24 Vent hole location around bosses, raised sections and ribs Dam
Vent Hole
Shelf
Moat/Dam
Vent Hole
Vent Hole
Mold
Mold Mold
Figure 6.25 Venting around moat (left), moat/dam (center), and shelf rims (right) for female molds
• •
Along the double step for male molds (Fig. 6.26). These help lock the sheet against the mold before most of the forming occurs. This locking effect minimizes air bleed under the sheet during the final stages of draw-down. Along two- and three-dimensional corners on male molds (Fig. 6.27).
Although usually not necessary, vent holes are regularly spaced along horizontal two-dimensional corners on female molds (Fig. 6.28). These regularly spaced holes
Sealing Off
Mold
Figure 6.26 Two-step hold-down for male mold, showing seal-off effect on right
Mold
2D Corner Vents
2D Corner Vents Sealing Vents
Figure 6.27 Vent hole locations on two-dimensional vertical and horizontal male mold surfaces and sealing locations
are used in place of vent holes clustered in three-dimensional corners. Functionally, they do not perform as well as clustered vent holes but are more esthetically pleasing.
6.6
Surface Treatments
Unlike injection molds, thermoform molds rarely require intermittent topical applications of mold release in areas where the formed shape is particularly difficult to release from the mold surface. There are several reasons for this:
Mold Side
Vent Holes on Horizontal 2D Corners Mold Bottom
Figure 6.28 Uniformly spaced vent hole locations on horizontal two-dimensional corners in female mold
• •
The pressures used in thermoforming are modest, The plastic is a rubbery solid rather than a sticky fluid and so polymer adhesion is minimal1, • The plastic shape is usually quite flexible when stripped from the mold and so vacuum pockets usually do not form, and • The mold surfaces are usually vented in precisely thoseareas where sticking might occur. Surface treatments on thermoform molds are used for other reasons. When biaxially stretched, hot sheet contacts a cold high energy surface such as metal mold and stretching ceases. Walls of simple vacuum-formed female parts thin with draw depth as described in Chapters 4 and 7. In order to avoid excessive draw-down, or to effect preferential draw-down into a specific region, permanent surface treatments are used. Baked-on surface treatments of low-friction materials such as PTFE and FEP are common. These treatments produce surfaces that are essentially integral parts of the mold surface. In certain mold designs, the sheet must not slide against the surface. Olefins tend to alternately slip and stick when vacuum formed. This causes visible ridges in the part surface. These are sometimes wrongly attributed to plug mark-off. Roughening the mold surface does little to prevent sliding and may aggravate the problem. Roughening may actually reduce contact area as shown in schematic in Fig. 6.29. A better alternative is to treat the surface with a high frictional coefficient substance such as a curable polyurethane, polybutadiene or silicone rubber. Also additional forming pressure is used to minimize sliding. The relationship between frictional force Fs and normal force F n is: (6.33)
Sheet Mold Asperities Sheet
Mold Figure 6.29 Aspects of mold surface texture replication by thermoformed sheet. Matte surface at top, rough textured surface at bottom
1
There are exceptions to this, of course. Parts can stick if the polymer contains an adduct that blooms to the surface and/or becomes tacky, if there are sufficient undercuts or if the mold is very hot.
W z
N
D Figure 6.30 Geometric factors for extensional drawdown v. sliding of sheet into female mold
where c is the kinetic frictional coefficient and takes the experimental range of 0.67 to 1.0. Larger values of a indicate that the deformation of contact area of the plastic is determined by its viscoelastic properties. Values of c are in the range of 0.1 to 0.25 for typical smooth-surface metal molds and most solid plastics [49]. To better understand the surface effect on forming, consider a simple example of draw-down of a sheet of initial thickness to and tensile strength T into a cylindrical female mold of diameter D with a differential pressure P. As shown in Fig. 6.30, the sheet has already contacted the cylinder to a depth Z and has thinned to a thickness h. The normal force holding the sheet against the surface is: F n = P • TiDZ
(6.34)
The second part of the term on the right is the contact area of the sheet on the mold. If the sheet is to slide on the mold rather than stick to the mold, it must be pulled with a force greater than this. This is written as: F s > c • F n = c • P n • (7iDZ)n
(6.35)
The force required to draw the sheet is the polymer tensile strength times the cross-sectional area, A: F s = T • A = T • TiDh
(6.36)
Note that the cross-sectional area is at the point where the sheet last contacts the mold surface. If the force needed to slide the sheet exceeds that needed to draw it, the sheet will tend to draw. This is written as: F s > F d -• c • (PTiDZf > T • TiDh
(6.37)
Consider the example where oc = 1: (6.38) or: (6.39)
If the force needed to draw the sheet exceeds that needed to slide it, the sheet will slide. Thus:
z<
%
(6-4°)
Example 6.13 illustrates how much sliding occurs before the sheet actually sticks to the mold surface. It is apparent from Equation 6.39 that if the sheet is to stick to the mold rather than slide, c must be as large as possible. Increasing the applied pressure and reducing sheet temperature, an action that increases the tensile strength, reduces the depth at which the sheet stops sliding. Example 6.13 Sliding Sheet into Mold Cavity Hot PP sheet is easily marked when it slides against cool metal. The amount of marking on a drink cup must be restricted to no more than 0.25 in below the rim. Determine the extent of mark-off for local 0.020 in sheet if the sheet tensile strength is 150 lbf/in2 or 1 MPa and the applied pressure is 40 lbf/in2 or 0.276 MPa. The coefficient of friction, c= 0.25.
The appropriate equation is Equation 6.39: 7-ht For the data given: _ Z
0.020-150 = 1X25^40- = ° - 3 m
The mark-off will be seen below the \-in line. To reduce the extent of mark-off, the coefficient of friction needs to be increased to at least 0.30. A slight roughening of the region just below the rim will minimize the extent of mark-off. Note that for straight vacuum forming, Pmax = 15 lbf/in2 and the coefficient of friction must be at least 0.80 to minimize the extent of mark-off.
Surface Texture The primary factors influencing replication of mold surface texture by hot rubbery plastic sheet are applied pressure and sheet temperature. Very high surface replication is intrinsic to compression and injection molding processes where applied pressures are normally on the order of 10 MPa or 1,450 lbf/in2. In low pressure structural foam molding [28,29], pressures are on the order of 2 MPa or 290 lbf/in2 and so finer mold surface details, measured in microns or urn, are not accurately replicated. Typically, these absences are seen as loss in sharpness of detail in product code lettering and boss and rib edges. Parts are therefore designed with larger edge radii and lettering. For low pressure molding, the relationship between applied
Smooth
Surface Roughness, ^m
Matte
lbf/in2
AJr Pressure, bar Figure 6.31 Experimental relationship between applied air pressure and extent of texture on formed sheet. Redrawn from [51] and used with permission of Society of Plastics Engineers, Inc.
pressure and molded part surface texture is shown in Fig. 6.31 [51]. This relationship is applicable to pressure forming, as well. In traditional vacuum thermoforming, the ability to replicate the mold is further reduced by the normally lower applied pressure and the less pliable nature of the polymer1. The inability to faithfully reproduce fine mold detail must be recognized during early design. Furthermore, part appearance depends primarily on the sheet surface quality prior to contact with the mold. Excessive mold surface preparation cannot differentially improve low pressure thermoformed part surface appearance [30]. The analysis used to determine the height of nibs or nipples in vent holes is applicable to determination of the maximum depth of texture. Consider Fig. 6.32, a slight reworking of Fig. 6.18. Let d be the relative width of the lettering, grain or texture in the mold. The maximum depth of sheet penetration into this texture, 5, is given as Equation 6.26, as cited before [27]:
1
Recall that the amorphous polymer in thermoforming is in a rubbery elastic state. Crystalline polymer is usually liquid but is formed only a few degrees above its melting temperature range and so is an elastic liquid. Mobility of thermoformable polymers at their forming temperatures is limited to mild chain extension and chain segment rotation. As a result, the thermoforming polymeric sheet cannot orient into fine mold details in the manner characteristic of injection molding or compression molding polymeric fluids.
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d Sheet
Mold Figure 6.32 Geometric factors for draw-down onto textured mold surface
where q is the applied pressure, h is the local sheet thickness, and E is the modulus of the sheet at the time of forming into the texture. The depth of penetration is considered to be a measure of sheet replication of the mold surface. Note that for a given texture, d is constant and the replication is proportional to the applied pressure. Doubling the pressure doubles the ability of the sheet to replicate the mold. Further, replication is strongly dependent on the local sheet modulus. Since the modulus is highly temperature-dependent, decreasing local sheet temperature a few degrees results in dramatic loss in replication. Probably the most important aspect of Equation 6.41, however, is the strong relationship between replication and local sheet thickness. Note that small changes in local sheet thickness yield dramatic changes in replication. For example, a 10% change in sheet thickness results in a 30% change in the value for 5. Equation 6.41 is rearranged to relate minimum applied pressure to the geometric parameters, as: qmm = 46E(T)^
(6.42)
For a given texture, 5 and d are fixed. For a given sheet thickness, h, the local sheet thickness is predictable within reason, according to Chapter 7 arithmetic. For given process parameters, E(T) is known. As a result, Equation 6.42 yields the minimum pressure needed to achieve mold replication. Pressures in excess of this minimum value ensure replication despite variation in local sheet thickness or temperature. Example 6.14 illustrates this. Example 6.14 Mold Texture Replication The texture in a Euro grain-textured mold is 0.001 in deep and the minimum span is 0.005 in. Determine the pressure needed to force 0.030 in thick FPVC into this texture of the polymer modulus is 100 lbf/in2 or 0.69 MPa.
The operative equation is Equation 6.42:
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6.7
Plug Design Considerations
Mechanical pushers or plugs were first developed for heavy-gage, cut-sheet forming. They are now used extensively in thin-gage, roll-fed forming as well. As detailed in Chapter 7, the role of the plug is to aid in polymer redistribution. Plugs are made of many materials. On large, simple forming presses, plugs are usually wood. In many cases, they are manually advanced along greased channels or hand-cranked along rack-and-pinion channels. On most automated heavy-gage operations and for all thin-gage operations, the plugs are automatically advanced and retracted according to very specific sequences. Mechanical toggle, hydromechanical action and pneumatic action are the common mechanisms used to activate automatic plug travel. The choice of plug mechanism depends on the linear travel distance of the plug, the surface area of the plug and the gage and toughness of the polymer being pushed. Very large plugs require auxiliary guide rods to maintain planar travel. Air pressure actuated cylinders are easy to maintain and are relatively inexpensive. As a result, they are commonly used for relatively simple pushing operations. There are five general characteristics to plugs: • • • • •
Plug material, Plug temperature, Plug shape, Plug rate of travel, and Relative time of plug contact with sheet surface.
The first two are considered in this section. The last three are discussed in Chapter 7.
Plug Materials The choice of plug materials is somewhat dictated by: • • • • •
Whether the operation is prototype or production, Whether the plug design is fixed or is still being modified, Whether the polymeric sheet is marked by certain plug materials, Whether the plug needs to be active, and The gage of the sheet and the sheet temperature.
There are two general categories of plugs. Plug materials such as plastics (syntactic foams, nylon or PA, epoxy, PTFE) and wood are thermally passive. That is, the final plug temperature is determined by the relative contact time the plug has with the hot sheet. Plug materials such as aluminum are active. That is, positive temperature control of the plug surface is achieved with coolant fluid flow. Table 6.16 gives typical property values for several plug materials.
Table 6.16 Comparative Properties of Non-Metallic Plug Materials Plug material
Density (g/cm3)
(lb/ft3)
Compressive strength (lbf/in2) (MPa)
Wood—sugar maple Wood—oak Wood—black walnut Syntactic foam PA 66 PTFE Epoxy—unfoamed
0.55 0.60 0.55 0.50 1.15 2.20 1.90
34 37 34 31 72 135 120
10 7 7 45 80 12 45
1,500 1,000 1,000 6,500 12,000 1,700 6,500
Service temperature (0F) (0C) 150 135 150 175 200 120 150
300 275 300 350 400 250 300
Thermal conductivity (Btu/ft • h • 0F) (cal/cm - S - 0 C ) 0.00037 0.00041 0.00079 0.00025 0.00024 0.0006 0.0010
0.09 0.10 0.19 0.06 0.058 0.145 0.242
Wood Plugs The easiest and in many aspects the best plug material is hardwood. Typically, end-grain maple, ash and walnut make excellent, easily fabricated plugs. Oak and mahogany are also used. As with wood for molds, wood for plugs needs to be kiln-dried to minimize checking and cracking. Wood plugs are usually sanded to 320 grit or more to minimize plug mark-off1. Polyurethane and epoxy coatings are also used. If the mark-off is attributed to the sheet being chilled by the colder plug, blanket or pool table felt is used to cover and insulate the plug end. Wood plugs are commonly used with HDPE and styrenics such as ABS and HIPS. Plastic Plugs There are several types of plastic plugs. Nylon 66 or PA 66, mineral-filled epoxies and PTFE such as Teflontm have been used for many years. Solid plastic plugs have exceptional compressive strength and excellent high temperature capability. These polymers have higher thermal conductivities than wood or syntactic foams, discussed below. As a result, plug mark-off can be more serious. And these polymers are heavier than wood or syntactic foams. As a result, the plug supports need to be more robust. Solid polymeric plugs are used for PVC and polyolefins. PTFE is usually recommended for PP. Syntactic foam is quite popular. These foams are made by incorporating sintered or foamed microspheres of fly-ash or phenolic into a polyurethane or phenolic resin matrix. The matrix, too, may be foamed. These foams are normally available from the foam supplier as plank, slab-stock or block in density ranges of 0.2 g/cm3 to 0.8 g/cm3 or 12 lb/ft3 to 50 lb/ft3. Casting grade foams have recently become available as well. Table 6.17 lists typical properties for one of these syntactic foams. Syntactics are used for styrenics such as HIPS and ABS, amorphous PET and PVC. In certain cases, syntactic surfaces are coated. Polyurethane coating is used for amorphous PET. Epoxy enamel or PTFE-impregnated epoxy enamel is used for amorphous PET and POM or polyacetal. Metal Plugs Machined aluminum is used whenever the plug surface temperature must be carefully controlled, as with oriented polystyrene or OPS and crystallizing PET or CPET. If the plug temperature is to be heated, electric cartridge heaters are inserted 1
Plug mark-off or chill mark is a line or region on a part that exhibits slightly different texture than the region next to it. In some cases, there is a distinct change in the part wall thickness at this point. There are two known reasons for mark-off. One is that the plug actively removes heat from the sheet in contact with it. Once the sheet is free of the plug, the colder sheet region does not stretch as much as the hotter region and so a demarcation is evident. A second reason is that hot sheet in contact with a solid surface tends to replicate the solid surface texture, whereas hot sheet that is free does not. This difference in texture can be quite apparent.
Table 6.17 Typical Properties for Thermoforming Syntactic Plug Material [Syntac 350-W. R. Grace Co.] Coefficient of thermal expansion Thermal conductivity Specific heat Shear strength Service temperature Compressive strength
17 x K)- 6 0 C" 1
10 x 10" 6 0 F " 1
0.06 Btu/ft • h • 0 F 0.30 Btu/lb • 0 F 3000 lbf/in2 3500F 6500 lbf/in2
0.0010 W/cm • 0 C 0.30 cal/g • 0C 21 MPa 175°C 45 MPa
Pusher
Thermal Break
Cartridge Heater
Metal Plug
Removeable Tip
Figure 6.33 Schematic of electrically heated metal plug
into predrilled holes in the plug tip (Fig. 6.33). The leads are passed up the shaft of the plug to the region where the plug is attached to the cylinder rod. Usually a thermal break such as PA 66 or nylon is placed between the heated plug tip and the main body of the plug to minimize heat conduction to the body and the pushing mechanism (Fig. 6.33). Liquid coolant is used if the plug temperature is expected or predicted to rise above the acceptable maximum value during sustained production. It is difficult to adequately control plug temperature with liquid coolant. Large diameter coolant lines remove cross-sectional area from the plug and could weaken it. The plug tip may be designed with circular milled grooves so that the coolant floods
Baffle
Tempered Water
Figure 6.34 Schematic of hot water heated metal plug similar to injection mold bubbler
the back of the tip (Fig. 6.34) [31], in much the same fashion as for actively cooled injection mold cores [32]. The coolant lines exiting the plug top must be flexible enough to allow for adequate plug travel. For a large aluminum plug, copper rods are embedded in the plug tip. The free ends of the copper rods are cooled with liquid coolant or are finned and cooled with directed air jets. Heat pipes are effective for small diameter plugs [33]. The heat pipe is a hollow metal tube, usually stainless steel. The tube contains a fine metallic mesh. It is evacuated and partially filled with an ultrapure fluid such as methanol or ethanol. One end of the tube is placed in a heated zone and the other in a suitable coolant. The fluid in the heated end of the tube evaporates. The vapor diffuses to the cooled end where it condenses. The fine mesh draws the condensed fluid to the heated end by capillary action (Fig. 6.35). At steady temperature input, these devices are many times more efficient than solid copper rods. The decision to actively heat or cool a plug must be made early in the mold design. If the plug is very cold, the sheet will surely freeze to it. As detailed in Chapter 7, drawing always occurs between the point where the plug and the sheet separate and the sheet and the mold rim meet. Usually, no drawing occurs on the plug surface during pushing. If the plug is very cold, very little drawing occurs after the sheet has been stripped from the plug by the stretching forces. In extreme cases, the sheet will shrink onto the plug during stretching. If the plug is very hot, the sheet may tear at
Heat Pipe
Radiator Fins Evaporation Zone
Pusher
MeOH
Thermal Break
Fine Wire Mesh as Wick Condensation Zone
Metal Plug Body
Figure 6.35 Section of thermal pin heated metal plug
the point where the plug enters the sheet. Actively controlled plug temperatures are usually between the sheet forming temperature and the mold surface temperature. For most amorphous plastics, the most effective plug temperatures are 20 to 300F or 10 to 15°C below the surface temperature of the sheet as it exits the oven. Example 6.15 illustrates the relative effect plug temperature has on formability of sheet [52]. Example 6.15 Effect of Plug Temperature on Sheet Properties A 0.120-in thick PS sheet at 375°F is stretched with an aluminum plug at 3000F. The plug is in contact with the sheet for 36 s. Determine the average sheet temperature and the relative sheet modulus when it releases from the plug. The thermal diffusivity of PS is 2.2 x 10~3 ft2/h. The exponential coefficient for PS modulus is 500C'1.
Fig. 6.36 gives the time-dependent average temperature of the sheet. The unaccomplished temperature change is given as: Y
_
375-T 375 - 300
The dimensionless time, Fo, is:
Fo = 0.22. From Fig. 6.36, Y = 0.15. Therefore the average sheet temperature is: T = 375 - 0.15 • (375 - 300) = 363.8°F The effect on modulus is given as: -^363.S _
-e
(375 - 363.8)/50 _ 1
9c
- I.ZD
Dimensionless Temperature
The modulus of the sheet just released from the plug is 25% greater than the sheet that has not touched the plug.
Dimensionless Time, Fourier Number Figure 6.36 Dimensionless temperature loss from sheet when contacting sold plug. Dimensionless temperature, Y = (T0 - T)/(TO - Tp) where T0 is the initial sheet temperature and T p is the plug temperature. Fourier number, Fo = a9/L2, where a is sheet thermal diffusivity, 0 is time, and L is sheet thickness
Plug Design Concepts As detailed earlier, the purpose of a plug is to influence final part wall thickness. Plug shape has the greatest influence on final part wall thickness. A flat or blunt-nose plug (Fig. 6.37), allows maximum sheet drawing in the annulus between the plug and the rim, while fixing the sheet thickness in contact with the plug bottom. A part made with this type of plug will have a heavy bottom and thin sidewalls. And there will be a ridge or sharp wall thickness demarcation between the freely stretched portion and the plugged portion of the sheet. Blunt-nose plugs are also used where sheet must be brought in from the rim region or where the sheet is billow-stretched prior to plugging.
Flat- or Blunt-Nosed Plug
Bullet or Bull-Nose Plug
Plug
Plug
Mold
Mold
Figure 6.37 Two plug tip shapes
Ring Plug
Figure 6.38 Ring plug for forming over male projections in female mold
Initially, only a small amount of the sheet contacts the tip of a bullet- or bull-nosed plug (Fig. 6.37). More and more sheet contacts the plug surface as the plug penetrates the sheet. Differential sheet stretching continues as the plug advances and so there is no sharp demarcation between the plugged sheet and stretched sheet. Ring-type or wire-frame plugs are used when a large portion of the bottom of the sheet must remain pliable and formable. Wire-frame plugs are used when the sheet must replicate a mold texture or lettering or a logo or when the sheet must stretch over a male portion of the female mold (Fig. 6.38). Wire-frame assisted stretching is similar to that for the blunt-nose plug. Once the plug has fully advanced, the sheet is stripped away from the plug by applied pressure. The disk in the middle is then stretched into the mold cavity. The wall thickness in the vicinity of the polymer that contacted the wire frame is usually quite irregular. Plugs are used in pressure forming as well. The shaft holding the plug is pressuresealed with O-rings. If the internal pressure is quite high, on the order of 1 MPa or 145 lbf/in2 or so, special labyrinth seals or hard, nonextrudable O-rings are used.
Mold Undercut
Cantilevered or Articulated Plug Action
Figure 6.39 Example of articulated plug motion Table 6.18 Application Areas for Various Plug Types Plug type
Application
Blunt-nosed, flat bottom
Maximum drawing from rim, where rim material must be drawn into cavity, shallow draw parts. Very deep draws, where thinning of sidewall is critical, where wall thickness uniformity is important, where polymer chills rapidly. Where bottom detail is required, where sheet must stretch over male portion in female mold. Where sheet must be tucked under in deep undercut, where local wall thickness is increased from local thicker sheet.
Tapered, bulletor bull-nosed Wire-frame, can Articulated
On certain occasions, articulated plugs are required. The simplest of these plugs operates on a cam (Fig. 6.39). As the plug shaft advances, the plug head moves down, then out. These articulated plugs are used with deep undercuts, Table 6.18. More complex articulation is needed if polymer must be stretched from the bottom of the sheet to the corners. As an example, a tulip-like device enters the sheet in its closed form (Fig. 6.40a). As plug advances, the vanes or sections of the device expand outward from the axis (Fig. 6.40b). When the plug and its sections are fully extended, the sheet is stripped from the mold (Fig. 6.40c). The plug sections collapse as the plug withdraws. Owing to the complexity of this plug design, plug cooling is usually not possible. A variation to this, called "cuspation", was patented and saw limited commercialization in deep-drawn, parallel-walled cans in the 1980s [34,35].
Dilation Cam Forming Blades
Sheet Rib Forming Begins
Blade Dilation Forms Rib
Part Cools Against Cavity Wall
Thinned Bottom
Vacuum On
Figure 6.40 Schematic of Hitek cuspation-dilation forming, showing stretching sequence [34]
Peripheral HoldDown or Clamp
Clamp Frame
Sheet
Mold Figure 6.41 Schematic showing mold sealing cavity, followed by peripheral clamping
6.8
Sheet Clamping
As discussed in Chapter 1, the sheet clamp has several functions. Holding the sheet rigidly during draw-down is one of its most important functions. For cut-sheet forming, the sheet is clamped everywhere along its perimeter. During forming, the mold pushes into the hot sheet past the plane of the clamp prior to initiation of mechanical plugging or forming pressure (Fig. 6.41) [36]. This effectively seals the hot sheet against the mold surface. A secondary sheet clamp is used for some tough
Grid or Cavity Isolation Clamp
Edge Clamp
Sheet
Pin-Chain
Mold Figure 6.42 Schematic of individual cavity isolation or grid in combination with peripheral clamping
polymers such as ABS and PC. The secondary or perimeter clamp presses the sheet against the mold surface after the mold has passed the clamp plane (Fig. 6.41). This ensures a positive sheet seal against the mold surface. For prestretching with a vacuum or draw box, the edge of the vacuum box acts as the secondary sheet clamp as the mold enters the billow. In pressure forming, the edge of the pressure bell serves as the secondary sheet clamp. For roll-fed forming, the sheet is only held along two edges. If secondary sheet clamping is not used during multicavity mold travel and forming, the sheet is pulled into the leading and trailing edges of the mold. The result is nonuniform part weight, warping and distortion. The full perimeter clamp is the most common secondary sheet clamp (Fig. 6.42). This clamp engages the sheet just prior to the time the mold touches the sheet and before the mold has reached its final position. The clamp resides above the sheet for forming presses where the mold is situated below the sheet. Individual cavity clamps, cages or grids are used for products that have stringent wall thickness requirements. Individual cavity clamping ensures that polymer from one cavity region will not be preferentially pulled into another. The cavity clamp framework is also positioned above the sheet for forming presses where the mold is situated below the sheet. The cavity clamp framework may also contain the perimeter clamp or it may be on a separate framework and may be sequenced to engage the sheet after the mold has reached its final position but before the plugs and vacuum sequences have begun. In certain cases, the cavity clamp may provide other functions, for example: •
The clamp may contain steel rule dies for trimming. The dies may partially cut through the polymer during the initial phase of the clamp. The die then acts as the clamp. When the part is formed and cool, the die resumes its travel, cutting through the sheet as a trim-in-place die (Fig. 6.43) [36]. • The clamp may contain a forming ring that compresses the rim region. This is called "coining" and is used whenever the formed part must have a molded-to-tolerance rim thickness. Deli container rims are sometimes coined. Coining may also
Plug Advance
Trim Die Fully Deployed
Trim Die Partially Deployed Sheet
Mold Vacuum On Figure 6.43 (Left) Example of in-mold trim die acting as cavity isolator followed by (right) trimming after forming
be used if the container rim must be rolled to provide rim stiffness, as discussed below. The force required to coin a Hp is a function of the compressive strength of the polymer at its instant temperature. Consider a polymer with the following temperature-dependent compressive stress-strain relationship: a c = C(T)-e n
(6.43)
where a c is the applied compressive stress, being the compressive force per unit area of the lip, C(T) is the temperature-dependent compressive modulus of the polymer, is the compressive strain, with 0 < e < 1, and n is an empirical shape factor for the stress-strain relationship. The amount of force required to compress the polymer in the lip a specific amount is given as: F = GC • 2TCRW = C(T) • 2TIRW • en
(6.44)
where R is the radius of the lip and w is its width. Example 6.16 illustrates the application of this expression to the forming of a cup lip. Example 6.16 Coining Force for PP Lid Consider a 4-in diameter PP deli cup having a lip width of 0.100 in. Determine the force required to coin the Hp from a thickness of 0.055 in to 0.050 in. The value for C(T) is 800 Iby i'in2 and the compressive stress-strain relationship for PP is Hookean, or n = 1. If 24 cups are coined simultaneously, what is the force the mold must resist.
The force is given by Equation 6.44 as:
For 24 cups, the mold resistance is:
•
The clamp may combine with an ejection ring on the cavity to allow separation of the part from the trim. The formed part is held momentarily stationary between the ring and the clamp while the mold moves away and the trim is pulled downward. Then the clamp retracts, leaving the part on the ejection ring. The trim moves once the part and ring assembly have cleared the trim plane.
6.9 Sag Bands and Sheet Supports Sheet sag is one of the most vexing problems in thermoforming. All polymers sag to some degree when heated. Certain polymers are quite weak when heated to forming temperatures1. As a class, crystalline polymers are more problematic than amorphous ones. HDPE, PP and PA or nylon sag greatly when heated. Certain amorphous polymers such as cellulose acetate and toughened FPVC sag when heated to their upper forming temperatures. Sheet supports or sag bands are used in roll-fed forming to minimize catastrophic drooping during the final stages of heating. There are two common types of sheet supports. Stationary PTFE-coated hollow rods are placed parallel to the rails in the last section of the oven. PTFE-coated steel wires are also used. These wires may be stationary but are sometimes driven at the speed of the chain rail. Sag bands sometimes extend into the mold area and beyond. Provision for them must be included in the overall mold design layout. The presence of sag band slots in the mold structure can seriously restrict the arrangement of parts of unequal size in family mold designs. Early consideration must be given to their presence if forming of sagging polymers is ever to be considered. Sheet supports are not used in heavy-gage forming with single cavity molds. Pneumatic lifting methods are preferred.
6.10 Other Aspects of Mold Design Often, seemingly impossible designs are achieved through thoughtful, mature mold design. Mold designs that are impossible with high pressure applied against sticky fluids such as injection molding are quite feasible with thermoforming. This is because thermoforming is a process that uses only modest pressure applied against a rubbery solid sheet. So long as a portion of the sheet remains rubbery, in theory it can be stretched. As a result, secondary in-mold forming steps are frequently used. One technique moves male plugs against the sheet that is already formed in a female mold. This technique allows bosses and ribs to be formed of polymer having a thickness different from that of the main surface [37]. 1
Sag is also discussed in some detail in Chapter 5.
Mold
Mold
Hinged Flipper for Undercut
Pin-Hinged Flipper for Undercut
Figure 6.44 Two examples of flipper design for shallow or thin undercuts
Undercuts Molds, particularly large prototype molds, can be made in sections that move in different directions. In this way, parts with severe undercuts are fabricated. For some severe undercuts, the trapped mold section is built like an interlocking wooden puzzle. A key section is removed first to allow the remaining segments to unlock and fall free. These sections are then reassembled and the key section reinserted to lock the segments in place for the next forming operation. This is not an uncommon technique on prototype tooling, but it requires great ingenuity by the mold designer. Flippers and hinged sections are used in automated molds. Figure 6.44 shows an example of a flipper or pin-held rotating section. Figure 6.45 shows examples of single- and double-hinged sections. The double-hinged section is used when the section to be swung away is very thick and would interfere with sheet extraction if only attached with a single hinge. For some prototype parts, the undercut is so severe that even these approaches are infeasible. If alternate methods such as post-forming assembly are also infeasible, forming around a disposable mold section is possible. A very soft grade of plaster is used. It is shaped and hardened in the traditional way described above. It is held in the mold with alignment pins as the sheet is formed around it. The disposable section is then adequately softened with very hot water and removed in chunks. In order to minimize gas trapping and part distortion around the disposable insert, its surface is covered with a single thin layer of cheesecloth, held in place with tape or daubs of
Double Hinged Flipper for Deep Undercuts
Mold
Pivot
Air Cylinder Swing-Out Section for Large Undercut
Mold Figure 6.45 (Top) For deep undercuts, double-hinged flipper is used; (bottom) for large undercuts, pneumatic swing-out mold wall segment is used
water-thinned plaster. Sculptor's wax has also been used as a disposable insert when forming lower temperature polymers such as LDPE and FPVC [3]. Encapsulation In certain special cases, the insert becomes part of the product. Usually inserts are restricted to captured stiffening agents such as rods and angles. One thermoformed industrial single-deck shipping pallet has tfye rim reinforced and stiffened with hollow aluminum conduit. In sequential twin-sheet thermoforming, reinforcing elements of wood or metal pipe or channel are often used. Forming around this superstructure is surprisingly straight-forward. Care must be taken to allow for the nearly ten-fold difference in coefficients of thermal expansion between the plastic and the aluminum. If the sheet is pulled too tightly around the tubing or if the tubing is too rigid, the plastic will crack on cooling or during low temperature usage. A car-top sign formed on a male mold uses encapsulated gussets on the two-dimensional vertical corners.
These gussets eliminate the traditional webbing problem with male molds and also help reinforce the corners of the part. Moving Elements Many injection molding devices are successfully used in thermoforming [38]. These include: •
Collapsing cores. As noted above, expanding cores can be used as plugs for special stretching cases. Tulip collapsing cores are used in injection molding with undercuts such as large diameter molded-in internal threads. • Unscrewing devices are used in injection molding when complete molded-in internal threads are needed. The best application for these devices is in pressure forming. • Cammed sections. As with injection molding, cammed sections move away from the molded part with the mold action. One application is full perimeter undercut on a female mold (Fig. 6.46) [39]. • Slides. There are many slide designs [40]. Most are used to remove parts with undercuts. One example is the formation of a hinge in a five-sided box (Fig. 6.47). Another is the formation of an isolated undercut for a recessed door handle. In Sliding Core Closed
Sliding Core Open
Mold Superstructure
Core
Mold Mold Action Figure 6.46 For complex undercuts, (left) sliding cores are actuated by (right) mold motion
Hn i ged Lid - Open Position
Slip-Coated Formn i g Rod Figure 6.47 (Left) For pin hinges, mold around forming rod; (right) for nested hinge lid, mold both pieces around forming rods
certain cases, slides are used to stretch plastic into an undercut during forming, much like a plug. Many of these techniques work best when the mold pressure is greater than one atmosphere. The standard material for these devices is machined aluminum. The temperature of long, thin cams, slides and unscrewing devices is difficult to control. Poor temperature control leads to mold mark-off and sheet adhesion to the devices. Stripper Plates/Bars In most cases, part design is simple enough and draft angles large enough to allow the part to simply fall or be easily plucked from the mold. For cut-sheet parts, the trim serves as the region against which force is applied to free the formed sheet from the mold. Mechanical part removal is necessary if: • • • • • • • • • • •
The mold surface is deeply textured, The mold is a male mold, The mold temperature is low and the mold is male, The mold is a shallow five-sided box, The mold bottom is quite flat and the mold is smooth, There are male portions to the female mold, The mold is very hot and the polymer is crystalline, The polymer shrinks greatly during cooling, The polymer is crystalline and is processed in its melt phase, The polymer has very low shrink, the mold is female and the draft angle is very small, There are substantial incidental undercuts,
Mold
Air Blow-Off
Vacuum Break Poppet Valve Action
Figure 6.48 Vacuum break, air blow-off and poppet valve opening for part release from mold
•
The polymer is very rigid, is heavy gage and there are deliberate or incidental undercuts, • The mold is used to form polymers that out-gas corrosives that attack or pit the mold surface, and • The mold is old and/or its surface has not been well-protected. Very rigid parts are difficult to remove from molds with slight incidental undercuts or tool damage. Very soft polymers such as LDPE, TPEs, PP and FPVC are difficult to remove from very smooth molds. It is apparent that adequate draft, proper surface texture, and diligent mold surface maintenance are vital to ensuring a stick-free surface. Nevertheless, there are occasions when positive methods for ejecting a part or parts from mold cavities are necessary. For heavy-gage sheet, a poppet or ejector valve located at the bottom of the mold aids in breaking the vacuum between the sheet and the mold surface (Fig. 6.48). The poppet is used in combination with air blow-back through the vent holes. For multicavity thin-gage thermoforming, ejector rings are used. For a female molded part, a perimeter ejector ring is used directly under the part lip (Fig. 6.49). The ejector ring is driven by ejector pins that pass through the mold to an ejector plate. The ring is actuated by mold action. Ring recovery is either through springs or stops during mold motion [41]. If there are many cavities and substantial trim area, large diameter ejector pins are placed between the cavities on the trim. These advance and touch the trim shortly after the ejector rings deploy.
Mold Releases Ejection is sometimes aided by mold releases. There are two common types of mold releases:
Air Actuated Stripper Ring or Plate
Mold
Vacuum Break Figure 6.49 Air-actuated stripper ring or plate in combination with air blow-off for part release from mold
•
Temporary mold releases. Usually available in 12 oz or 400 g aerosol containers, these mold releases are used when only a few parts are needed, when evaluating a new polymer or during production start-up. Although silicones are ideal mold releases, they must be used with caution. Silicones interfere with decorating, sealing, painting and labeling. Even though silicones might be acceptable for one product, they are typically atomized and the spray may contaminate other areas of the plant where other surface-sensitive products are being manufactured. Most aerosols are CFC- and HCFC-free today. If the formed part is to contain food, FDA approved mold releases are needed. Vegetable oil spray is an effective, FDA-approved temporary mold release. • Permanent mold releases. PTFE and FEP-derived coatings are used with aluminum molds and plug assists. These coatings are applied by powder spraying onto a suitably prepared metal surface. Usually, fluoropolymer coatings last 100,000 or more cycles. The primary mode of failure is uneven wear. Delamination or peeling is a sign of improper metal surface preparation. Cuts and slices are signs of improper mold protection during storage and set-up. Florian [42] notes that: "The extra cost of Teflon (sic) coating becomes a luxury only when it is completely unnecessary."
Web Breakers, Catchers and Chasers
Webs are formed when the hot stretched plastic surface area in a local region is greater than the surface area of the mold in that region. Even though the plastic is considered to be an elastic rubbery solid, as the sheet is drawn toward the mold surface, certain sections of the sheet touch other sections before they touch the mold surface. When hot plastic touches hot plastic, the forces required to pull them apart are far greater than the force needed to stretch surrounding plastic against the mold surface. As a result, a web is formed (Fig. 6.50). In many cases, the mold design is such that the web cannot be completely eliminated. This is most common in female parts that have
Male Mold
Web Web
Web Catcher
Figure 6.50 Web formation and web catcher for male forming
male projections. Multiple plug assists, pre-blown bubbles, prestretching restraints and articulated plug assists are sometimes used to minimize web formation. If the web forms near the rim of the part, web catchers are used. These are simple outriggers, posts or stanchions positioned beyond the rim of the part (Fig. 6.50). The stretching sheet catches on these posts. The web is formed at the bases of these posts and away from the part rim. Web breakers are usually incorporated in mold designs by experience. For simple prototype molds, wood is used. For production molds, aluminum is used. There is no technology available to design web catcher dimensions. Moats, Dams and Double Steps A moat or dam is used to seal the sheet against the lip region of a female mold. A double step serves the same function for a male mold. A moat is a groove or indentation outside the lip region (Fig. 6.51). These devices provide an early seal of the sheet to the mold surface, thus minimizing air leak. They also are used to minimize the amount of sheet drawn into the mold cavity from the rim region. The minimum moat width should be five times the local sheet thickness. A moat width of ten times the local sheet thickness is recommended. The moat depth should be at least equal to the local sheet thickness and a depth of twice the local sheet thickness is recommended. For polymers that have low coefficients of friction such as polyolefins
Moat
Figure 6.51 Design parameters for moat
Figure 6.52 Design parameters for dam
Sealing Steps
Dam
Mold
Figure 6.53 Double-step design for male mold to minimize air leak
or fluoropolymers, and for heavy-gage sheet, a dam is more effective (Fig. 6.52). The minimum height of the dam should be twice the local sheet thickness. The width is less important than the height. Sharp-edged dams are quite effective with heavy-gage sheet. Male molds are difficult to seal against air leakage. The double step (Fig. 6.53) is frequently used. The draping sheet bridges the edges of the two steps before vacuum is applied. The ideal design has the sheet touching the edges at 45 degrees or TI/4 radians at this time. The plastic between the two edges forms the seal once vacuum is applied. The exact spacing and height of these steps depends on the depth of draw of the mold and the amount of plastic between the edge of the mold and the clamp. For tall molds, the steps need to be high and narrow. For shallow molds or where there is substantial web, the steps need to be low and wide. Molds are sometimes built with a single step. Once the press and sheet dimensions are confirmed, the second step is added as a separate plate attached to the vacuum box. Chamfers and Radii Designers have always used two-dimensional and three-dimensional radii for corner configurations in thermoformed parts. As shown in Chapter 7, the relative drawdown into a two-dimensional corner radius is given as:
Radius R Chamfer
Mold
Figure 6.54 Geometric factors for chamfers and radiuses
(6.45)
where t is the local thickness at radius r and to is the thickness at radius ro. The relative draw-down into a three-dimensional corner radius is given as: (6.46) To get crisp corners, small radii are needed. For two-dimensional corners, the local sheet thickness is reduced about 21% when the corner radius is reduced by 50%. For three-dimensional corners, the local sheet thickness is reduced by 50% for the same radius reduction. Since the thinnest section of the part is the weakest under load, sharp radii dramatically weaken the part. This is true whether the part is a thin-walled deli container or a heavy-gage spa. Recently, designers have rediscovered the chamfer as a way of maintaining corner thickness and stiffness (Fig. 6.54). The chamfer is typically 45 degrees or TT/4 radians to the bottom or top rim or lip. It is easy to show that the plastic in the twodimensional chamfer is TT/2 =1.57 times that in the equivalent radius. As a result, the stiffness of the chamfer corner is about three times that of the radius corner1.
1
The stiffness of the chamfer also depends on the folding strength of the line where the chamfer intersects the side wall and the bottom. The polymer thickness along this line is less than that in the rest of the chamfer, as shown in Chapter 7. Furthermore, the mechanism of bending of the chamfer as a plate differs from the mechanism of bending of a radius [43] and so the relative stiffnesses really cannot be compared.
Restraining Bar Restraining Bar Motion Into Bubble Air Prestretching
Sheet
Edge Clamp Male Mold
Mold
Mold Action
Figure 6.55 Restraining bar to provide two bubbles for double compartment male part
Prestretching Restraints On occasion, air inflation is used to form a bubble into which a compartmented mold is plunged (Fig. 6.55). A severe web will be formed if the mold is plunged directly into the bubble. To overcome this, a restraint is lowered into one side of the bubble as the mold enters the other. The restraint acts to push the web to the edges of the forming sheet, beyond the perimeter of the part. This technique is used to form heavy-gage refrigerator liners, two-basin lavatories, and outdoor signs.
6.11 Efficient Use of Sheet The economics of thermoforming turn on the efficient use of extruded sheet. As discussed in detail in Chapter 8, excessive incorporation of regrind can lead to: • Multiplying extrusion costs, • Polymer deterioration owing to multiple extrusion and forming, • Processing problems with lowered polymer hot strength, and • Customer concerns about loss in mechanical properties or appearance, among other problems. The efficient use of sheet depends on using the smallest sheet dimension to produce the part. Heavy-Gage Sheet Usually in heavy-gage forming, only one part is made at a time. The part geometry dictates the absolute minimum sheet dimension (Fig. 6.56). The following dimensions must be added to these dimensions:
Part
Trim Region
Lip Region Moat/Dam Clamp Frame
Mold Clearance
Figure 6.56 Various elements that make up sheet usage in forming molded part
• • •
Any lip or rim area needed for the functioning of the part, Any trim area including trim tolerance, Any moats, dams or steps needed to seal the sheet against the mold surface prior to forming, • Any additional sheet dimensions needed to ensure adequate pre-blowing1, • Additional sheet dimensions needed to allow the mold to clear the edge of the clamp frame without substantial tensile or shearing effects on the sheet in the clamp, and • Sufficient dimension to allow the sheet to be adequately clamped in the clamp frame2. These are shown in Fig. 6.56. Example 6.17 gives an illustration. Typically, heavygage trim is 20% to 40% of the total sheet surface area. Example 6.17 Efficient Sheet Use for Heavy-Gage Sheet A rectangular part, 48 in x 40 in, with 2 in corner lip radiuses is to be formed from 0.250 in sheet. The Hp must have 0.5 in width for trimming. A dam requires another 0.5 in width. The mold mounting frame extends an additional 3 in in all directions beyond the dam dimension. A 1 in clearance between the mold mounting frame and the clamp frame is required to minimize sheet pullout during mold travel. The clamp frame is 1.5 in wide. Determine the minimum sheet dimension and the amount of trim. 1
2
These dimensions are important since the sheet at the clamp frame is uniaxially oriented whereas that in the center of the sheet is biaxially oriented. Sufficient distance between the clamp frame and the lip of the part must be provided if the polymer has known splitting tendencies. Although some clamp frames are designed to hold sheet with as little as 0.5 in or 12 mm of sheet in the clamp frame (Fig. 6.57), this requires that the sheet must be absolutely square to the clamp frame. Since sheet dimensions are usually not that accurate, a good rule of thumb is to allow a minimum of 1 in or 25 mm beyond the outer mold dimensions on all edges.
The amount of plastic that extends from the part surface in each direction by the amount: 0.5 + 0.5 + 3 + 1 + 1.5 = 6.5 in Thus the sheet dimensions are: 40 + 6.5 x 2 = 53 in by 48 + 6.5 x 2 = 61 in The sheet dimensions are 53 x 61 x 0.25 in. The sheet area is 53 x 61 = 3233 in2. The plastic that is trimmed off the corner radii is given as: (4-Ti)-R 2 = 3.4 in2 The plastic part surface area is then 40 x 48 — 3.4 = 1916.6 in2. The amount of trim is therefore:
Underbite Sheet Clamp Clamp Sheet
Ca l mp Clamp
Knurled Surface Sheet
Ca l mp Friction Sheet Clamp Clamp Ca l mp
Sheet Pins Spaced 1 in or 25 mm Apart
Figure 6.57 Three ways to clamp sheet in heavygage forming
Pin Puncture Sheet Clamp
Thin-Gage Sheet Usually roll-fed forming has a higher trim fraction than heavy-gage forming. There are several reasons for this: • •
Part dimensions are smaller relative to lip area, Many parts are round or oval,
Triangular Pitch Figure 6.58 Triangular pitch part and mold layout
•
The head and tail of the sheet on the mold surface are undamped, requiring perimeter in-mold clamping area, • Individual cavity clamps are used for plug assisted parts, and • The relative amount of plastic outside the mold frame is large.
In an effort to efficiently use sheet surface, part layout on mold surfaces can be creative, particularly with circular or oval parts. Equilateral and other triangular pitches yield the greatest number of parts per unit area (Fig. 6.58). However, most mold builders prefer rectangular pitch (Fig. 6.59). Rectangular pitch mold designs are preferred because: • • •
The molds fit well on rectangular mold bases, Coolant channels are easier to lay out, and Rectangular pattern provides more satisfactory modular designs.
Example 6.18 illustrates trim fraction for three pitch designs. For circular parts formed in rectangular sheet, the trim percentage ranges from 40% to 75% or more. More on this important subject is found in Chapter 7.
Rectangular Pitch
Figure 6.59 Rectangular pitch part and mold layout
Example 6.18 Efficient Use of Sheet—Thin-Gage Consider the forming of 2-in diameter drink cups. The required Hp and moat region is 0.5 in, half of which remains with the cup. The space between cavities must be at least an additional 0.5 in to accommodate individual cavity clamps. The mold must clear the former rails by at least 1 in. And 0.5 in sheet space is needed in the pin rail to ensure adequate clamping. Determine the minimum sheet width if the maximum mold base is 34 in wide by 46 in long. Determine the number of cavities if the molds are placed on rectangular pitch. Rework the arithmetic for molds on triangular pitch and triangular pitch when cavity perimeters abut. Consider the rectangular pitch first. The outer effective diameter of each cavity is given as: 2 in + 2 x 0.5 in (lip and moat) + 2 x (0.5/2) in (clamp) = 3.5 in For the 34 in wide mold, 34/3.5 = 9.7 cavities are possible on a rectangular pitch. For 9 cavities: 9 x 3.5 + 0.5 (cavity clamp) = 32 in For the 46 in wide mold, 46/3.5 =13.1 cavities are possible. For 13 cavities: 13 x 3.5 + 0.5 (cavity clamp) = 46 in The minimum sheet width is then: 32 + 2 x 1 (clearance) + 2 x 0.5 (pin-chain) = 35 in. The total number of parts produced on the 32 x 46 mold are: 9 x 13 = 117 per shot. The amount of plastic in each cup is given as: 7
^- = | (2 + 2 • 0.5/2)2 = 4.91 in2
The amount of plastic as product: 4.91 x 117 = 574 in2 The total surface area used to form these parts: 35 x 46 = 1610 in2 Thus the trim total percentage is given as: l t i m = 1 0 0 - ( 1 6 1 1 ° - 5 7 4 ) = 64o/, 1610 For equilateral triangular pitch, the triangle must inscribe a circle of 2r = 3.5 in diameter (Fig. 6.60). The base of the triangle, b, is given as:
r = 1.75 in
Figure 6.60 Geometric factors on triangular pitch
2b = 6.06 in
The distance from the apex to the center of the circle, c, is given as:
The total height of the triangle, h = r + c = 3r. The area of the triangle is:
The base of the triangle, 2b = 617'y/3 = 3.464r. For 2r - 3.5 in, 2b = 6.06 in. For the maximum mold length of 46 in, there are places for 7.6 triangle bases or 7 complete triangles. Between each triangle is another triangle on apex. With proper adjustment, one triangle on apex can be fit at one end or the other of the triangle bases. Therefore 13 complete triangles fit within the 46 in mold length. The height of the row of triangles is 5.25 in. For the 34 in wide mold, 6.5 parallel rows are possible, or 6 integer rows. As a result, for triangular pitch molds, 6 x 13 = 78 molds are possible. Again, the area for a single cup is 4.91 in2. For 78 cavities: 4.91 x 78 = 383 in2 The total surface area used to form these parts: 35 x 46 =1610 in2 Thus the trim total percentage is given as: Trim= 100 • ( 1 6 1 1 ° - 3 8 3 ) ^ 76Q/O 1610 This triangular pitch is less efficient than the previous rectangular pitch. A more efficient equilateral triangular pitch mold layout follows. If the outer perimeters of the molds touch (Fig. 6.61), there are 13 cavities in odd rows and 12 cavities in even rows. The relationship between the width of the mold, W, and the number of rows, N, is given as: W = (N - 1) • h + 2r
where h = ^ 3 • r/3. For W = 34 in and r = 3.5/2 in, N is 11.1 rows, or 11 integer rows. With six odd rows and five even rows, there are 6 x 13 + 5 x 12= 138 cavities. Since the surface area of a single cavity is 4.91 in2, the total surface area for molded parts is: 4.91 x 138 = 677.6 in2 The total surface area used to form these parts: 35 x 46 =1610 in2 Thus the trim total percentage is given as: Trim=
!00-^^1=58% 1610
6.12 References 1. L. Sors, Plastic Mould Engineering, Pergamon, London (1967), p. 108. 2. Anon., Wood Handbook: Wood as an Engineering Material, Forest Products Lab., Madison WI, USDA Agriculture Handbook #72 (Aug 1974). 3. R.M. Miller, Figure Sculpture in Wax and Plaster, Watson-Guptill, New York (1971), p. 11. 4. C. Chaney and S. Skee, Plaster Mold and Mold Making, Van Nostrand Reinhold, New York (1974), pp. 114-120. 5. W.P. Benjamin, Plastic Tooling, McGraw-Hill Book Co., New York (1972), p. 20. 6. Rentm epoxies available from Ciba-Geigy Corp., Polymers Division, Seven Skyline Dr., Hawthorne NY 10532-2189, 914-785-2000. 7. Anon., "Toolrite Composite Tooling Materials System", Fiberite Corp., 501 W. Third St., Winona MN 55987, undated. 8. M.E. Thorp, "Progress Report: Sprayed Metal Faced Plastic Tooling", 35th Annual conference, RP/C, New Orleans LA (4 Feb 1980). 9. Nickel Tooling Technology, Highway 12, P.O. Box 399, Midland Ontario Canada L4R 4Ll (June 1994). 10. J. Worbye, "Steels for Molds", SPE ANTEC Tech. Papers, 30 (1984), pp. 948-951. 11. J.L. Throne, Plastics Process Engineering, Marcel Dekker, New York (1979), p. 530. 12. D.A. Schrage, "Prototype Molds: Getting Out of Them What You Need", Plast. Mach. Equip., 13: 6 (Jun 1984), p. 35. 13. R.G.W. Pye, Injection Mould Design: A Design Manual for the Thermoplastics Industry, 2nd Ed., George Godwin, London (1978), pp. 155-185. 14. H.R. Osmers, "Mold Cooling Concepts", Handout in W.K. McConnell, Jr., SPE Industrial Thermoforming Symposium and Workshop, Arlington TX (12-14 March 1985). 15. V.L. Streeter, Fluid Mechanics. 5th Ed., McGraw-Hill Book Co., New York (1971), p. 277. 16. V.L. Streeter, Fluid Mechanics. 5th Ed., McGraw-Hill Book Co., New York (1971), Figure 5.32, pp. 288-289. 17. O.W. Eshbach (late) and M. Souders, Eds., Handbook of Engineering Fundamentals, 3rd Ed., John Wiley & Sons, New York (1975), p. 618. 18. D.T. Wood, "An Explicit Friction Factor Relationship", Civil Eng., 36: 12 (Dec 1966), pp. 60-61. 19. V.L. Streeter, Fluid Mechanics. 5th Ed., McGraw-Hill Book Co., New York (1971), p. 292. 20. V.L. Streeter, Fluid Mechanics. 5th Ed., McGraw-Hill Book Co., New York (1971), p. 297.
21. O.W. Eshbach (late) and M. Souders, Eds., Handbook of Engineering Fundamentals, 3rd Ed., John Wiley & Sons, New York (1975), p. 622. 22. A.H. Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow, 2 VoIs, The Ronald Press Co., New York (1953). 23. V.L. Streeter, Fluid Mechanics. 5th Ed., McGraw-Hill Book Co., New York (1971), Chapter 6, "Compressible Flow". 24. R J . Roark and W.C. Young, Formulas for Stress and Strain, 5th Ed., McGraw-Hill Book Co., New York (1975), p. 363. 25. G. Gruenwald, Thermoforming: A Plastics Processing Guide, Technomic Publishing Co., Lancaster PA (1987), p. 38. 26. G. Gruenwald, Thermoforming: A Plastics Processing Guide, Technomic Publishing Co., Lancaster PA (1987), pp. 39-40. 27. R J . Roark and W.C. Young, Formulas for Stress and Strain, 5th Ed., McGraw-Hill Book Co., New York (1975), p. 97. 28. J.L. Throne, "Principles of Thermoplastic Structural Foam Molding", in N.P. Suh and N.H. Sung, Eds., Science and Technology of Polymer Processing, MIT Press, Cambridge MA (1979), p. 77. 29. J.L. Throne, Thermoplastic Foams, Chapman & Hall, New York (1995), Chapter 7, "Skins and Surfaces on Foams". 30. Anon., "Thermoforming Lustran ABS, Lustrex Polystyrene, and Cadon Engineering Thermoplastics", Monsanto Bulletin #6547, undated. 31. R.G.W. Pye, Injection Mould Design, 2nd Ed., G. Godwin, London (1978), p. 180. 32. R.G.W. Pye, Injection Mould Design, 2nd Ed., G. Godwin, London (1978), p. 174. 33. Heat pipes designed for the plastics industry are available from Noren Products, Inc., 1010 O'Brien Dr., Menlo Park CA 94025, 415-322-9500. 34. A Brockschmidt, "Thermoforming Barrier Containers: How It's Different", Plastics World, 42:9 (Sep 1984), pp. 67-71. 35. J.L. Throne, "Thermoforming—A Look Forward", SPE ANTEC Tech. Papers, 29 (1983), pp. 464-465. 36. This technology is once again being promoted as an effective way of clamping and trimming very thin-gage sheet by Paul Kiefel Thermoformmaschinen GmbH, IndustriestraBe 17-19, Postfach 16 60, 83395 Freilassing Germany. 37. W.K. McConnell, Jr., SPE Industrial Thermoforming Symposium and Workshop, Arlington TX (12-14 March 1985). 38. R.G.W. Pye, Injection Mould Design, 2nd Ed., G. Godwin, London (1978). 39. R.G.W. Pye, Injection Mould Design, 2nd Ed., G. Godwin, London (1978), p. 210. 40. R.G.W. Pye, Injection Mould Design, 2nd Ed., G. Godwin, London (1978), Chapter 9, "Side Cores and Side Cavities". 41. R.G.W. Pye, Injection Mould Design, 2nd Ed., G. Godwin, London (1978), Chapter 3, "Ejection". 42. J. Florian, Practical Thermoforming: Principles and Applications, Marcel Dekker, Inc., New York (1987), p. 308. 43. A.C. Peterson, Applied Engineering Mechanics: Strength of Materials, 2nd Ed., Allyn and Bacon., Boston (1982). 44. Fiberboard is available from Al Grosskopf, Alpine Plywood, Inc., 12210 W. Silver Spring Rd., Milwaukee WI, 414-462-5450. 45. PVI Mold Boardtm is available from Plasti-Vac Inc., 214 Dalton Ave., Box 5543, Charlotte NC 28225, 704-334-4728. 46. Reprotm PUR systems available from Freeman Mfg. & Supply Co., 1246 W. 70th St., Cleveland OH 44102-2097. 47. M. Burns, Automated Fabrication: Improving Productivity in Manufacturing, PTR Prentice Hall, Englewood Cliffs NJ (1993), particularly Chapter 3. 48. D.S. Cummings, "Utilizing Stereolithography to Produce a Rapid Prototype Thermoforming Mold", SPE ANTEC Tech. Papers, 40 (1994), pp. 3550-3554.
49. H. Chang and R.A. Daane, "Coefficient of Friction for Solid Polymers in Various Forms", SPE ANTEC Tech. Papers, 20 (1974), pp. 335-. 50. One sprayed metal system is offered by TAFA Metallisation, Inc., Dow Rd., P.O. Box 1157, Bow (Concord) NH 03301. 51. S. Semerdjiev, Introduction to Structural Foams, Society of Plastics Engineers, Brookfield Center CT 06804 (1982), p. 52. 52. PJ. Schneider, "Conduction", Chapter 3 in W.R. Rohsenow and J.P. Hartnett, Handbook of Heat Transfer, McGraw-Hill Book Co., New York (1973), Figure 33, pp. 3-60.
7 Parts Design 7.1 Introduction 7.2 Elements of Parts Design Material Testing and Its Relevance to Part Performance Philosophy of Parts Design Minimizing the Amount of Sheet to be Reground Rules for Part Layout on Heavy-Gage Rules for Multiple Part Layout on Thin-Gage Economics of Buying Sheet of Specific Size 7.3 Prototyping as a Justification for Thermoforming 7.4 Draw Ratio Areal Draw Ratio Linear Draw Ratio H:D Rim and Lip Sheet for Female Cavities Draw Ratio Usage—A Rationale Mechanical Assists—Some Design Features Preblowing or Inflation—Comments Plug Assist—Comments 7.5 Computer-Aided Design in Thermoforming 7.6 Wall Thickness Prediction—A Justification Geometric Element Analysis or GEA Finite Element Analysis General Comments on Plug Design Plug Assist Analysis Plug Design—Geometric Element Analysis Plug Design—Finite Element Analysis 7.7 Regrind Material Property Deterioration on Regrind Property Value Loss—Experiment and Protocol Cascading 100% Regrind 7.8 General Guidelines for Part Design General Tips Process Tips Mold Tips Prestretch Tips Part Design Tips Rim and Edge Designs Design—A Comment 7.9 References Appendix 7.1 Draw Ratios for Truncated Cone Appendix 7.11 Mechanical Property Loss in Regrind
7.1
Introduction
It is apparent that there are many variations on the basic sheet stretching process and that there are many potential polymers from which to choose. As a result, design of thermoformed parts must of necessity follow careful protocol. In this chapter, the philosophy of parts design forms the basis for the specific details on parts design. Prototyping is usually the first step in any molding program. It rarely succeeds without problems and these problems frequently reveal potential problems in production processing. Many typical processing problems and courses of action are highlighted in the trouble-shooting section and some general do's and dont's are presented. There are several ways of defining draw ratio. Areal and linear draw ratios and depths of draw are defined for several simple geometries. Rim draw down is also arithmetically accounted for. Draw ratios are gross and imperfect measures of the amount of stretching a sheet must endure in order to replicate the mold and produce a perfect part. As will be seen, polymer is stretched least just below the mold rim and most as the sheet is drawn into three-dimensional corners. Polymer sheet must have sufficient elongation at the drawing temperature and applied pressure or it will either split or fail to replicate the mold. Overall draw ratios fail to accurately predict potential stretching of the sheet to ultimate elongation. Differential draw ratios yield more relevant information. Accurate prediction of local wall thickness yields the most useful information. Part wall thickness is a function of the depth of draw and the geometry of the part. The arithmetic is presented for conical and other simple shapes. Frequently the sheet is prestretched by inflation or with plug assist. The obvious reason is polymer sheet material redistribution or material reallocation. Advanced finite element methods are being developed for wall thickness prediction of more complex shapes. Designers are beginning to use computer-assisted software programs for their toughest thermoforming designs. As with other chapters, this chapter's material progresses from descriptive to technically advanced concepts. Regardless of the degree of technology needed to achieve adequate designs on today's parts, the designer should take comfort in knowing that the technical support for the tough designs of the future is at hand.
7.2
Elements of Parts Design
The ultimate objective of polymer processing is the fabrication of a product that must meet certain nominal performance requirements. There are many concerns that must be met in the manufacture of any product. Three important ones are: • • •
Will the finished part meet all required and specified design criteria? Can the part be produced at the minimum cost for the projected market size? What are the consequences if the part fails to meet minimum requirements?
The last concern is important today. Plastics parts fail in use for several fundamental reasons. The most common is customer "misuse", in that the device is used in a way that is beyond the designer's original intent. It is impossible to design against all levels of stupidity. However, safety factors and sources of inherent product weakness must always be considered in critical parts design. Whenever possible, parts should always be designed to fail safely when used beyond design conditions. The polymers selected for the product must have certain inherent characteristics such as: • • • •
Stiffness, Toughness, Environmental resistance, and/or Optical/electrical properties.
When the polymer is transformed from pellets to product, certain other characteristics are imposed, such as: • • •
Dimensional changes, Color, or Internal stresses.
Assembly or initial use may impose other characteristics, such as: • • • •
Differential expansion, Color shift or mismatch, Loss in gloss, or Abrasion or scuffing.
The ultimate use of the product imposes other parameters, such as: • • • •
Environment, Periodic or aperiodic loading, Time under load, and/or Temperature.
All polymers have a myriad of inherent properties, only a few of which are important in the performance of a specific product. For products assembled of sub-products, subsets or basic elements, each of the subsets places specific mechanical and/or chemical demands on the polymer used. The property set required by the assembled product must be a "mean" of the properties of the subsets. The polymer material properties needed to delineate the performance criteria are ascertained only when the subset demands are clearly identified. A proper design approach establishes a formal design check list. Typical items for such a check list include: • • • •
Environmental conditions, both nominal and extreme, Materials specifications, Part mechanical behavior and tolerance under environmental conditions, and Dimensional tolerances.
Table 7.1 lists some additional items that require identification and definition. From this master list, secondary check lists are written, Tables 7.2 through 7.7.
Table 7.1 First-Level Design Elements for Thermoformed Parts, See [80,81] For Additional Information, Additional Detail Given in Noted Tables •
•
•
•
Field of application—Table 7.2 Food packaging Materials handling Disposable Permanent Part function—Table 7.3 Decorative Protective Container (liquid, solid) Structural Environment—Table 7.4 Temperature Nature (corrosive, liquid solid) Nature of load (static, cyclical) Appearance—Table 7.5 Surface quality (Class A) Nonappearance Trim line appearance
• •
•
•
•
Cost—Table 7.6 Balanced against material requirements Number of parts required Competitive processes—Table 7.6, Chapter 10 Injection molding Blow molding Rotational molding Part design limitations—Table 7.7 Strength Load characteristics Potential abuse Government regulations Standards (FDA, FM, EPA) Biodegradability Fire retardancy Interaction with other elements—Table 7.3 Assembly requirements Metal-to-plastic concerns
Table 7.2 Check List for Thermoform Parts Design: Application •
•
General field Packaging Leisure Transportation Military Medical Sub-category, such as packaging Food Disposable Storage Cook-in Barrier Animal feed
•
Cosmetics Pharmaceuticals Chemicals Electronics Display items And so on Part life Permanent, such as swimming pool Part of a permanent assembly, such as computer housing Limited life, such as celery boxes Disposable, such as blister packs and unit servings
Material Testing and Its Relevance to Part Performance Once the designer has selected appropriate polymer candidates for the proposed product, he/she must verify that the product will perform in accordance with the desired and necessary design criteria. In other words, the designer must test his/her selection. The most obvious test specimen is the part itself. However, if the part is still conceptual or is too large or too small, alternate testing data are needed. Usually polymers are selected on the basis of resin producers' design and material data sheets. The designer must select properties from these sources with great caution:
Table 7.3 Check List for Thermoform Parts Design: Part Function •
•
•
Container Single-use Continuous Solids Liquids (corrosive nature) Convenience Protective Shipping Food packaging Blister pack Decorative Architectural Interior decoration Cosmetic
•
•
Structural Total load bearing Temporary support Compression load function (foams) Interaction with other elements Stand-alone Covering, edge contact/interlocking only Elements assembled into formed shapes Formed shape incorporated into others Plastic/plastic assembly Plastic/nonplastic assembly
Table 7.4 Check List for Thermoform Parts Design: Environmental Conditions • • • • • • •
Use temperature range Design temperature range (maximum and minimum) Extreme temperature range (maximum and minimum) Limitation on part shape deformation (under expected load, at use temperature) Extreme chemical environment (under load, at temperature) UV environment (outdoor, fluorescent) Nature of load Static (expected and maximum) Vibrational or periodic (expected and maximum) Interface with user (casual, continuous, leisurely, in crisis situation)
•
Table 7.5 Check List for Thermoform Parts Design: Appearance • •
• •
Quality Class-A (automotive) Plating substrate Optical Aircraft Automotive/RV Furniture Cosmetics Blister pack Food containers Medical containers
•
• •
Decorative Deckled Textured Painting substrate Replication of letters, logos, symbols Nonappearance Trim line appearance Secondary finishing Buffing Location of trim line
First, the test data should accurately represent polymer properties. Then, there should be a unique set of relationships between material properties and measured parameters.
Table 7.6 Check List for Thermoform Parts Design: Cost and Competitive Processes • •
•
• •
•
•
Target part cost Materials cost Quality of extrusion Level of regrind Property requirements (price, property, performance) Quantity of material needed (price break) Prototype cost Tooling Parts fabrication Performance evaluation Allowable cost of fabrication, tooling Tooling quality Run length Tolerance Cycle times Maintenance Alternate/competitive process cost Injection molding Rotational molding Stamping from hot sheet Blow molding Metals/ceramics (non-polymer) processing
And finally, there needs to be a causal relationship between measured properties and polymer performance.
Two criteria of test acceptability are proposed [1-3]: Criterion I: The mechanical state must be definable in physical terms.
The physical state can be dimension, applied load, applied stress, strain, rate-ofstrain, dimensional change, color change and/or temperature. Criterion II: The mechanical state must be definable in causal mathematical terms.
The stress-strain data should be capable of being fitted with an Ogden or Rivlin model, for example. Or the sheet dimensions should be predicted from coefficient of expansion data. With acceptance of standard testing routines by such organizing bodies as ISO, DIN, and ASTM, proper protocol for performing a specific procedure is clarified. These tests are referred to as performance tests. Care must be taken in assuming that the results from these tests can be directly applied to the perform ance of a given product. It has been noted that [4]: "The ASTM tests for plastics were designed as quick, easy, reproducible tests to provide a rough comparison among similar materials—but principally for material quality control, not for material performance. Thus, these test data should be regarded only as material specifications for purchasing and quality control, not as indications of performance under long-time real-life conditions...9'
Table 7.7 Check List for Thermoform Parts Design: Part Design Limitations • •
• • •
•
Intrinsic polymer material properties At nominal use conditions At extreme conditions Process/polymer interactions Draw ratio Strength of thinned material Strain-induced brittleness Recycle property loss Allowable corner/lip design Allowable part tolerance, dimensional variation, draft angle Part appearance Warp, racking Optical distortion Draw lines, stretch marks Trim edge appearance Mold detail replication (texture, letters) Interaction with non-plastics Nature of interference Slip-fit Adhesive Mechanical assembly Interference Snap-over Undercut Detent Strain under temperature extremes Strain during, after assembly
Most ASTM tests yield non-design properties for polymers. They do not meet the criteria of test acceptability and as a result they are not useful in determining the in-use performance of most polymer parts. In addition, the designer must realize that the effects of the process must also be included in any performance analysis of the product under its environmental influence. This is in addition to testing the polymer. If the test data are to bear any relationship to product performance in actual use, the test specimen must include the appropriate effects of the process1. Philosophy of Parts Design Regardless of the nature and depth of prior experiences of the designer, the mold maker, the thermoformer or the customer, no plastics fabrication should be at1
Furthermore, the designer must guard against using statistics to verify that the data are significant. The collection of more and more data usually does not contribute to bridging the gulf between test specimen properties and the final performance of the product made of the polymer [5].
Needed Product Design Criteria Polymer Selection
Sheet Quality Specification
Mold Material Selection
Process Parameter Selection
ComputerAided Solids Modeling
Rapid Prototyping Mold Design Manufacture
Process Selection
Thermoformed Wall Thickness Calculation
Stress Analysis
Production Part Testing, Qualification Figure 7.1 Computer-aided engineering flow chart for thermoforming
tempted without strict, formal written protocol on parts design. All parties must clearly understand the project objective and ancillary part performance standards. Guidelines must be carefully written and agreed on, in writing, by all principals. This should be done with all principals present, just prior to issuance of purchase orders for materials, molds and forming time. Processes, applications and materials continue to grow in sophistication. As a result, the parts designer is destined to play an increasingly important role as project coordinator. It is incumbent on him/her to ensure correct protocol, particularly in this increasingly litigious era. Figure 7.1 [6] shows a particularly useful scheme when computer-aided mold design, part design and structural analysis are available. Once the overall design concepts are well understood by all parties, initial part designs, material specifications, process elements as identified in Chapter 1, and cycle parameters can be estimated. These should be kept quite preliminary and should focus on general fitting of proper materials and process elements to the application. The objective of this portion of the effort is to make an early test of concept feasibility. At this point, no prototype should have been authorized. Designers should be working from quality sketches or computer renderings. Not every potential application results in a thermoformed part. Some reasons for not selecting thermoforming include: • • • • •
The application may require polymers that are not successfully extruded into sheet, The candidate polymer is not successfully drawn to the requisite depth, The forces required to stretch the candidate polymer may exceed the available process equipment capability, The part may be too large for available equipment, The part may be too small for available equipment,
• • • • • • • • •
The customer may need too few parts to make thermoforming economical, The customer may need too many parts, The design may waste too much material, The web material may be unprocessable as regrind, resulting in prohibitive material and processing costs, The design may require structural polymers that are not normally thermoformed, The design may require highly reinforced polymers or highly filled polymers that are difficult to thermoform or beyond the thermoformer's ability, The tolerances and draft angles may require exotic mold designs for thermoforming, The design may require parts with uniform wall thicknesses, or Competitive processes may be more economic1.
Once it is apparent to all that thermoforming offers a technically feasible, economically viable process to make a part of a polymer needed to meet the application constraints, the sketched out process may be ready for prototyping. Prototyping is discussed in the section that follows. Certain emerging technologies, such as stereolithography and LOM, have altered the way in which prototypes are developed. Not all these new techniques are directly applicable to thermoforming, however. In certain instances, prototyping is not necessary and the design is ready for fine tuning. Techniques for determining part wall thickness are described in detail below. In general, fine tuning should focus on optimizing material distribution across the part to achieve the greatest local part strength at the lowest material usage. And every fine tuning should concentrate on minimizing web. Minimizing the Amount of Sheet to be Reground The amount of plastic to be trimmed as non-product begins by minimizing trim and web area through intelligent mold design and careful sheet size selection2. Proper part design minimizes unnecessary trim, particularly in rim area for thin-gage multiple part forming. Usually the fraction of regrind generated is a function of several components of the thermoforming process: • •
1 2
Conservative part designs usually generate less out-of-specification parts than exotic designs. Exotic, multi-step, and/or relatively new processes usually produce more trim for regrind than that from some one-step processes such as vacuum or drape forming. Competitive process design and economics are discussed in Chapter 10. In an earlier book by this author [92], and in other books and encyclopedic chapters on thermoforming, the term "scrap" was used to categorize that portion of the sheet of plastic that is not the desired product. In fact, the economics of thermoforming dictate that the non-product portion of the sheet must be recovered, reground, and reextruded into sheet for subsequent thermoforming. For thermoformers, the term "scrap" is in fact this non-product portion of the sheet. However, in general, the term connotes a wasteful process. Therefore, the industry has agreed to the terms "trim" or "web" to denote the non-product portion of the sheet.
• •
•
Polymers that are drawn close to their extensional limit will usually cause higher regrind levels. Process equipment that is not in good operating condition or that has inadequate or inferior automatic cycle control generates more off-specification parts than equipment that is automated and maintained well. Workers who are not fully trained in the nuances of: the requisite forming process, the trimming process, the polymers of choice, and/or the specific design details, typically generate higher-than-anticipated quantities of regrind.
Rules for Part Layout on Heavy-Gage Usually only one part is made from a section of cut sheet for heavy-gage. If the contribution of plastic from the rim is negligible, as shown in Fig. 7.2, the plastic that makes up the part comes from the sheet clamped against the rim. Consider a simple five-sided box of dimensions A x B x C deep to be formed from a sheet having dimensions A x B x h o thick. The average sheet wall thickness, h, is given as: ho
AxB + 2-AxC + 2-BxC
K
'
J
As shown shortly, the average wall thickness has little value. The reciprocal of the wall thickness ratio is the overall areal draw ratio, R a : (7.2)
C
A B L1
L2 h
Figure 7.2 Part, rim and edge material layout for heavy-gage thermoforming
If the initial sheet dimension is A + 2L1 x B + 2L 2 where L1 and L2 are the respective distances from the rims of the part to the cut edges of the sheet, the amount of trim, T, is given as: T = (A + 2L1) x (B + L2) - A x B
(7.3)
Example 7.1 illustrates how the fraction of trim is determined for heavy-gage sheet. For many parts, plastic in the rim region is deliberately drawn into the mold cavity. The effect is to increase the average sheet .thickness and reduce the fraction of trim. Even though the purpose of sheet prestretching is to increase the sheet wall thickness uniformity, it also increases the average sheet thickness and reduces the fraction of trim. It is apparent that trim is minimized by minimizing the distance from the mold rim to the edge of the sheet. However, as discussed in detail in Chapter 6, the sheet must be clamped sufficiently well to prevent extrusion and pull-out during stretching. Certainly, trim is minimized by forming rectangular parts from rectangular sheets. Examples 7.2 and 7.3 illustrate how the shape of a part affects the amount of trim. Example 7.1 Trim Fraction for a Heavy-Gage Part If the distance from the mold rim to the edge of the sheet must be at least 2 in, determine the amount of trim generated for a five-sided box, 17.3 x 38.7 x 12.4 in deep. Then determine the amount of trim if the sheet is most economically purchased as 24 x 48 in blanks. The sheet dimensions are: (17.3 + 2 • 2) x (38.7 + 2 • 2) = 909.51 in2 The surface area of the box is given as 17.3 • 38.7 = 669.51 in2. The amount of trim is: '
= 0.26 or 26% of the initial sheet.
For the 24 x 48 sheet, its area is 1152 in2. The amount of trim is: ~
— = 0.42 or 42% of the initial sheet.
Example 7.2 Trim Fraction for an Oval Heavy-Gage Part If the distance from the mold rim to the edge of the sheet must be at least 2 in, determine the amount of trim generated for an oval box, 17.3 x 38.7 x 12.4 in deep. Then determine the amount of trim if the sheet is most economically purchased as 24 x 48 in blanks. The sheet dimensions are: (17.3 + 2 • 2) x (38.7 + 2 • 2) = 909.51 in2 The surface area of an oval or elliptical box is given as:
where a and b are the major and minor axes of the ellipse. For the example: A = 71(17.3 -38.7)/4 = 525.83 in2 The amount of trim is: :
—
— = 0.42 or 42% of the initial sheet.
For the 24 x 48 sheet, its area is 1152 in2. The amount of trim is: ~~
= 0.54 or 54% of the initial sheet.
Example 7.3 Trim Fraction for a Circular Heavy-Gage Part If the distance from the mold rim to the edge of the sheet must be at least 2 in, determine the amount of trim generated for two cylinders, 17.3 in diameter x 12.4 in deep. Then determine the amount of trim if the sheet is most economically purchased as 24 x 48 in blanks. The sheet dimensions are: (17.3 + 2 • 2) x (38.7 + 2 • 2) = 909.51 in2 The surface area of the cylinder is: A = 7id2/4 where d is the diameter of the cylinder. For the example: A = 7r(17.3)2/4 = 235.06in2 Since there are two cylinders, the total area is 470.12 in2.The amount of trim is: 909 51 — 470 12 ' ' = 0.48 or 48% of the initial sheet. For the 24 x 48 sheet, its area is 1152 in2. The amount of trim is: 1152
" ~ 4 7 0 - 1 2 = 0.59 or 59% of the initial sheet.
Rules for Multiple Part Layout on Thin-Gage In thin-gage forming, the web between the multiple cavities contributes a great amount of recyclable trim. For rectangular parts, the layout is simply a multiple of that used for heavy-gage. Cavity spacing depends on a number of factors: • •
The rim design and width of the individual cavity, The required width of the sheet clamp or cavity isolator,
• •
•
The required wall thickness of the mold, The mechanics of connecting individual mold elements, such as: Coolant lines, Air blow-off lines, Vacuum lines, and/or Sliding and moving core interactions, and Stripper or ejector plate width requirements.
The area of sheet used for an individual rectangular cavity, for example, is written as: (7.4)
where L1 n and L 2n represent the half-distances between the cavities. The total sheet area is the sum of the individual areas plus that portion of the sheet between the outermost row of cavities plus the allowable half-distances and the edge of the sheet: (7.5) For cylindrical parts, such as cups or plates, there are two layout methods (Fig. 7.3). The square pitch is more common than the equilateral triangular pitch, since the molds are all square and mold assembly is easy. The square pitch layout generates more trim than the triangular pitch, however, as illustrated in Example 7.4. The added bother and expense of triangular pitch molds might be tolerated if the amount of trim is important to the economic success of the product, as might be the case with medical products. Example 7.4 Triangular and Rectangular Pitches for Molding Drink Cups 3-in diameter drink cups are to be molded 6-wide and 48-up. The polymer selected is known to sag extensively even at moderate sheet widths. Determine the minimum sheet width for rectangular pitch if a I-in spacing is needed between each cavity and if the mold edge-to-sheet edge is 2 in. Determine the extent of trim for each.
Using the square pitch of Fig. 7.3, the rectangular mold dimensions are 24 x 32 in. The sheet width is 24 + 22 = 28 in. For the triangular pitch of Fig. 7.3, the diagonal is the sum of the mold cavity diameters and the intercavity spacing, 6 • 3 + 5 • 1 = 23 in. The vertical is given as: y = r sin 9 = 23 • 0.866 = 19.9 in « 20 in The mold width is an addition \ + \ in, for a total of 21 in and the sheet width is 21 + 2 • 2 = 25 in. Molds on the rectangular pitch require a sheet
that is 3 in or 12% wider than molds on a triangular pitch. The triangular pitch mold shape is a parallelogram, with the overall mold length being 32 + 23 • cos 0 = 43.5 in. Even though the square pitch mold base is wider than the triangular pitch mold base, it is square and the individual cavities are also square. Right angles are much easier to fabricate than equilateral angles. If the mold-to-edge distance on the free sheet edge is also 2 in, the total sheet area for each shot is 28 x (32 + 2 • 2) = 1008 in 2 . The area used to produce the required 48 drink cups is 48 • TT32/4 = 339.3 in 2 . The trim amount is: Trim =
1008-339.3 —— = 0.66 or 66% of the total sheet.
lUuo
For the triangular pitch sheet, the parallelogram area is 25 x (32 + 2 • 2) = 900 in2. The trim amount is: Trim =
~
= 0.62 or 62% of the total sheet.
The difference in trim amount between the two pitch layouts is small in this case and would be significant only if the trim could not be recycled.
Square Pitch
Figure 7.3 Square and triangular parts and mold cavity layouts
Triangular Pitch
Economics of Buying Sheet of Specific Size Usually sheet extruders produce sheet product to custom dimensions. As a result, the designer, processor and mold builder agree to the minimum acceptable sheet dimensions and the extruder then supplies sheet to that specification. There are some instances where a less expensive sheet of a ready-made size is available. For example:
Reprocessing Regrind Drying R Extrusion and Thermoforming
M
V
Figure 7.4 Simple steady-state reprocessing loop
•
The extruder may have an inventory of sheet in standard widths, lengths and gages, • A resin supplier may be sampling the thermoforming industry with a new polymer product, • The extruder may have sheet left from an earlier production run, or • The thermoformer may have sheet left from an earlier production run. As discussed later in this chapter, on regrind, there are material property penalties attached to regrinding and re-extruding trim. There are also economic penalties. The economic penalty decreases with increasing extruder throughput but nevertheless is never a negligible cost to the product. The economics of recycle are obtained in the following fashion. Consider a recycle stream as shown in Fig. 7.4 [7]. Assume that the polymer material costs M units, is used at 100%, and that the process is 100% efficient. The cost of the salable fabricated part, F, is: F= M+ C (7.6) where C is the unit conversion cost. For thermoforming, the conversion cost is the sum of extrusion and thermoforming unit costs. Now assume that a fraction, Y, of the fabricated product is trim. If the trim value is zero, the unit cost of the salable fabricated product must be increased to account for the loss in efficiency:
F=M±^
(7 . 7 )
V 1-Y Note that the processing cost is included since it logically costs the same to produce unsalable parts and non-product trim as it does to produce quality parts. Now assume that the trim has a value S on the open market. When the trim is sold, the processing cost is reduced by an amount YS. With no recycle and virgin polymer, the final unit cost is:
(7.8)
If the polymer material is 100% virgin, its cost M = V, the cost of the virgin polymer. If a mixture of two materials is used as the feed, the material cost, M, is linearly proportional to the cost of the individual materials: M = ( I - Y ) V + YR
(7.9)
where Y is the amount of second source used and R is the value of the second source. Now let the trim, with a value, S, be reprocessed at a cost X. This reprocessing cost may include grinding, drying, and/or re-extrusion into pellets, but does not include extrusion and thermoforming costs, C. The cost of the repurchased trim is S H- X. Let this be the second source: R = S+ X
(7.10)
M = (I - Y ) V + Y(S+ X)
(7.11)
The polymer material cost is now:
And the unit fabrication cost, F, is: F =
^ C - Y S
= V +
C
^
(7]2)
The first term on the right is just the cost of virgin polymer. The second term includes the cost of conversion and the cost of reprocessing the trim. It is apparent that if there is no trim, Y = O and the production cost is just V + C. As the extent of trim increases, the unit cost increases. As expected, as the trim content approaches unity, Y->1 and the production costs approach infinity, F->oo. Example 7.5 illustrates this. To determine the effect of using a standard size sheet and tolerating greater trim, consider Equation 7.12 for two cases: Fcustom = V + ^ + ^
(7.13)
Fstd = V + ^ ± ^
(7.14)
Yc is the fraction of regrind generated from the custom sheet, and Vc is the cost of the sheet. Similarly, Ys is the regrind from the standard sheet and Vs is the cost of that sheet. Accordingly, Yc < Ys and all other things are equal, F custom is greater than ^standard- Example 7.6 illustrates this. Example 7.5 Economics of Reusing Trim—I It costs $0.20/Ib to extrude ABS and SOAOjib to thermoform and trim it. It costs SO.05 jib to regrind it. Virgin ABS costs S 1.00/Ib and the market value of clean reground ABS trim is SOAOjIb. If the thermoforming process generates 40% trim, determine the unit product cost with and without recycling the trim.
The unit cost for salable formed parts is given from:
For the first case, the trim is sold after grinding. As a result, M = V, C = 0.1 + 0.2, V = 1.00, Y = 0.4, S = 0.4 - 0.051. From Equation 7.8: _ M + C - YS
T^Y the value for F is $1.93/lb. For the second case, the unit cost with recycling is given from the same equation, written as, P = V+
^
It is assumed that R = S + X. Therefore F = $1.53/lb. The savings on using regrind is $0.40/lb of salable parts. 1
Note that the market value of ABS requires regrinding at X = $0.05/lb.
Example 7.6 Economics of Reusing Trim—II Consider the economic information of Example 7.5. Compare these results with advantages of purchasing ABS sheet at SO. 18/Ib even though 45% of it must be recycled. Reconsider if the sheet extrusion cost is SO. 10jib, but 55% must be recycled.
From the information in Example 7.5, F custom = $1.53/lb for recycled trim. For standard sheet, C = 0.1+0.18, V=LOO, Y = 0.45, X = 0.05. F std is given from Equation 7.14 as $1.55/lb. Products made of custom sheet are a couple of pennies per pound cheaper than those made from standard sheet. For the second case, C = 0.1 + 0.1 and Y = 0.55 and Fstd is $1.51/lb. In this case, standard sheet leads to a cheaper product.
7.3
Prototyping as a Justification for Thermoforming
In the plastics industry, prototype parts are produced primarily to check part design and appearance. Frequently, thermoforming is used to produce prototype parts for other processes such as injection molding, rotational molding and blow molding. Prototype thermoformed parts are used when: • Materials are relatively unproven, • One aspect of the design is particularly critical, or • The part is to fit with other components. Prototyping can serve as an important early warning to future processing problems, such as: • • •
Narrow processing windows, Badly sagging sheet, or Sheet orientation problems.
It is frequently used to identify possible post-forming problems, such as:
• • • •
Warping and distortion, Trimming problems, Long-term dimensional change, particularly with ABS, CPET and certain olefins, and Assembly problems.
Mold designs can be evaluated and trimming fixtures developed and refined during prototyping. And of course, prototype thermoformed parts are excellent visual aids when promoting a new concept or application. The field of rapid prototyping or "RP" has grown dramatically in the last few years. The objective of RP is to produce a part for customer approval in a very short time. All concepts begin with computer modeling of the designer's idea. The three-dimensional model is then sliced into electronically thin wafers, each of which is stored as a separate file. These files are then exported to an appropriate device that "reassembles" them into a solid three-dimensional object. Some of the assembly techniques include: •
Stereolithography or SLA, where a ultraviolet beam is directed against a polymer syrup that reacts when exposed to UV. The beam is controlled by the computer that simply reads the outline of the electronic wafer file. After each computer file "slice" is completed, the reacted polymer is lowered by the thickness of the wafer, and the process repeats. The final shape takes about 24 h to complete. The reacted syrup structure is jelly-like as it emerges from the unreacted syrup bath. The structure is then drained of unreacted resin and thoroughly cured in a convection oven. Large parts are formed by electronically slicing the original designer's concept into quadrants, individually reaction-forming the quadrants, then gluing the quadrants together after curing. The wall thickness is typically greater than about 0.010 in. • Polymer powder fusion, where a thermal laser beam is directed against fusible polymer powder such as nylon or polyethylene. Again the beam is controlled by the computer. After each pass, the fused powder in the bed is lowered by the thickness of the wafer, fresh powder is layered on the surface, and the process repeats. The final shape has a sand casting-like surface and can be friable or fragile. Wall thickness is greater than about 0.015 in. • Layered sheet molding, where a thermal laser beam is directed against a film of polymer such as polyethylene, nylon or PET. The polymer film has a heat-sensitive coating on the reverse side. Before laser cutting, it is stretched over the last shape cut. Again the beam is controlled by the computer. After the laser has completed cutting the sheet, the cut film is pressed with a heated platen or iron against the stack of previously cut film, thus fusing it to the stack. The laminate is indexed downward by the thickness of the film, which should be the exact thickness of the electronic wafer. The final plastic shape has minutely stepped edges but otherwise appears identical to the designer's concept. Wall thickness is greater than about 0.015 in but thinner walls are contemplated. • Layered paper molding, where a thermal laser beam is directed against a sheet of SBS paperboard. The paperboard is usually about 0.010 in thick and usually has
a heat-sensitive adhesive on the reverse side. Some work is underway to use paperboard with pressure-sensitive adhesive. The final paper shape has faint stepped edges and is heavier than the plastic models. This technique is reported to be very fast, with models being produced in half to one-third the time of plastic models. Wall thickness is greater than about 0.020 in. • Water-cut paper molding, where a water jet instead of a laser beam is used to cut the paperboard. It is said that this technique generates no odor, smoke or dust and a very smooth surface is obtained on the final shape. It is slower than the laser cutter and has about the same wall thickness restrictions. • A very recent development uses a desktop technique similar to ink-jet printing, where 0.0025 in diameter polymer droplets are dispensed according to the scanned image. The technique uses a second plotter head to dispense wax in areas where undercuts and removable support structures occur. The wax and plastic are finished with a horizontal milling cutter. All elements are microcomputer or PC driven [8]. No lay-down speeds or minimum wall thicknesses are available. Four of these techniques are shown in Fig. 7.5 [9]. When early versions of these techniques were introduced a decade ago, the units cost in excess of US$200,000, the operation was dusty or messy, and the parts were restricted to no more than 20 in on a side by the sizes of the chemical tanks. The equipment for some of the newer techniques now costs less than US$100,000 and parts of 40 in on a side have been fabricated. When "cut-and-paste" techniques are fully developed, part sizes appear to be unlimited [10]. In addition to making prototypes, RP technology is beginning to be used to make prototype thermoforming molds [H]. RP allows the molder or mold maker to make changes in mold details such as texture, polymer shrinkage and boss and rib locations quite rapidly. This is an important addition to getting a functional product to the marketplace quickly.
7.4
Draw Ratio
Draw ratio1 is a common measure of thermoformability. There are at least three accepted ways of representing draw ratio: • • •
Areal draw ratio, Ra, Linear draw ratio, RL, and H:d or H.D.
In addition, reduced thickness or thickness ratio, (t/to), is also used. Some of this was introduced in an earlier section. The draw ratio concept is usually given more importance than it deserves. For example, areal draw ratio is usually considered to be a measure of the biaxial orientation of the sheet. However, it is an artificial concept, since it yields an average sheet thickness. No thermoforming process yields 1
Draw ratio is also called "depth of draw" or "extent of draw".
Laser Sintering
Stereolithography Scanning Mirror
Scanning Mirror Laser
Laser
Powder Supply/Roller
Lift Device Formed Object
Formed Object
UV Curable Polymer
Loose Powder
Directed Light Fabrication Turning Mirror Laser Laser Focusing Z-Stage
Powder Feed
Laminated Object Manufacturing (LOM) Scanning Mirror Laser Laser Cuts and Welds y Foil, Paper, or Plastic
Formed Object Formed Object X-Y Stage Figure 7.5 Four examples of automated fabrication of rapid prototyping, used in thermoforming for the production of prototype molds and for plugs
a uniform wall thickness part, however. No form for the draw ratio uniquely defines the events of biaxial and/or uniaxial stretching [12]. And no draw ratio describes the local extent of elongation at every point across the part surface. Nevertheless, since the draw ratio concept is so pervasive, certain definitions and rules are in order. Areal Draw Ratio Regardless of the stretching process used to produce the formed shape, initial sheet of plastic with an area A0 and thickness to is stretched to provide a part having a surface area A and an average thickness ta. Since the plastic volume is constant: (7.15)
d
R D=(1+n)d
s
Figure 7.6 Geometric factors for draw-down into parallelwalled cylinder with rim material contribution
The simplest measure of stretch is the areal draw ratio, Ra = A/A0. Ra is also the reciprocal thickness ratio, Ra = (Vt0)"1. The areal draw ratio is a measure of the biaxial orientation of the sheet. The areal draw ratio of a parallel-sided cylindrical female part, Fig. 7.6, for example is: (7.16)
where s is the part and d is its diameter. Sometimes, a reduced areal draw ratio, R* = Ra — 1, is used [12]. The areal draw ratio is known by other names: • • • •
Stretch ratio [64], Stretching ratio [13], Stretch factor [65], or Areal elongation [66].
d/2
s/2
Figure 7.7 Geometric factors for draw-down into parallel-walled cylinder with male segment
Table 7.8 Areal Draw Ratios for Regular Shapes Shape
Figure
Area
Areal draw ratio, Ra
Hemisphere
2TTR2
2
Right cylinder
TTR2 + 27tRh
1 + (2h/R)
Right cone
7cR(R2 + h2)1/2
[l+(h/R) 2 ] 1/2
Truncated cone
Tir2 +
(r/R)2 +
R = Major radius
7i(R + r)-[(R-r) 2 + h2]1/2
(1 + r/R) • [(I - r/R)2 + (h/R)2]1/2
r = Minor radius Square, a = side
5a
5
Right rectangle a x b x h1
2ah + 2bh + 2ab
2 0 + h / b + h/a)2]1/2
Wedge a xbxh
2h + 2b[h2 + (a/2)2]1/2
(h/b) + [l+(2h/a)2]1/2
Right pyramid a xb xh
(ab/2)[l+(2h/b)2]1/2 + (ab/2)[l + (2h/a)2]1/2
(l/2)[l+(2h/b)2]1/2 + (l/2)[l+(2h/a) 2 ] 1/2
Truncated right pyramid a x b x h and a x b
l/2(ab-ab)[l+(2h/b) 2 ] 1/2 + l/2(ab-ab)[l+(2h/a) 2 ] 1/2 + ab
1/2[1 - (ab/ab)][l + (2h/b)2]1/2 + 1/2[1 - (ab/ab)][l + (2h/b)2]1/2 + (ab/ab)
1
h is the perpendicular height for the right rectangle, wedge, right pyramid and the truncated right pyramid
Areal draw ratios for other simple geometries are given in Table 7.8. Areal draw ratios for complex shapes are obtained by combination, as seen in Examples 7.7 and 7.8. The average areal draw ratio is also insensitive to local drawing. Figure 7.8 compares the average areal draw ratio of a rounded bottom cylinder with a corner radius, r = a • d with a square bottom cylinder, r = 0. The area of the rounded bottom cylinder is:
(7.17)
Example 7.7 Areal Draw Ratios for Cylindrical Parts—I Consider a female straight-walled cylinder of diameter d and height s, with a solid center rod of diameter d\2 and height s/2 in its center, Fig. 7.7. Determine the overall areal draw ratio. Then replace the solid center rod with a hollow cylinder of the same dimensions but zero wall thickness. The wall area of the outer cylinder is: Awaii = 7tds
The area of the bottom outer cylinder is: Abottom = Ud2IA - rc(d/2)2/4 = 37id2/16 The wall area of the inner cylinder is: Awall = 7i(d/2)s The area of the top of the inner cylinder is: Atop = 7r(d/2)2/4 = d2/16 The total area of the two cylinders is: Tid2
37ids A
I
The area of the initial disk is: AO = 7id2/4
:
Therefore the areal draw ratio is:
For the hollow cylinder, the area of the sides is [inside and outside of the short cylinder]: ASide = 2 x 7ids/2 = 7ids
The area of the bottom is: A b o t t o m = 7i(d/2) 2 /4
The total area of the double cylinder is: A total = 27ids + 7id2/4
And the areal draw ratio is:
Example 7.8 Draw Ratios for Cylindrical Parts—II Using the information from Example 7.7, determine the draw ratio for the hollow inner cylinder only. Compare the overall draw ratio value with this local draw ratio value for s = d. If the inner surface of the inner cylinder of Fig. 7.7 is drawn only from the disk of material formerly on the top of the cylinder, the areal draw ratio for this is:
But this material has already been drawn. The material touching the inner cylinder rim has been drawn into a hemisphere of area, A hemi = nd2/2. The draw ratio of a hemisphere is: R
a hemi
'
=7td2/2 = 2 7id 2 /4
Therefore the average draw ratio of the polymer forming the inside of the inner cylinder is the product of draw ratios: Rmner = R a -R a , hemi = 2 - ( 4 s / d + l ) If s = d, then Rinner = 10. From Example 7.7, the overall draw ratio for the hollow inner cylinder is:
The areal draw ratio is: (7.18) As seen in Example 7.9, average areal draw ratios for bottom-radiused cylinders are not much less than that for a cylinder with a zero corner radius. Yet for the square bottom cylinder, the last polymer sheet drawn into the sharp corner must be infinitely elongated. This is even more apparent when the linear draw ratio is used. Example 7.9 Areal Draw Ratio of Round-Cornered Cylinder If the round-cornered can of Fig. 7.8 has a radius r = d/8, determine the areal draw ratio relative to a square bottomed can. What is it for r = d/2, a hemispherical bottom? If s = d, determine the absolute values. From Equation 7.18:
For r = d/8: For a hemispherical bottom, r = d/2: If s = d:
Linear Draw Ratio The linear draw ratio, RL, is the ratio of the length of a line projected onto a part surface to its length on the unformed sheet (Fig. 7.9). Note that it is possible to define several linear draw ratios for unsymmetric parts. Traditionally the largest
r*=d/8
Figure 7.8 Draw-down into (top) sharp-cornered cylinder and (bottom) radiused cylinder. Corner radius, r' = d/8, where d is cylinder diameter
Figure 7.9 Geometric factors for linear draw-down into irregular shape. R L , = ABCD/AOD. R L 2 = A'B'C'D'/AOD
value of RL is used. RL reflects uniaxial stress-strain behavior of a polymer. For example, the linear draw ratio for the parallel-sided cylinder of Fig. 7.6 is:
RL is also called the depth of draw ratio [12]. A reduced linear draw ratio is sometimes used. It is written as RJ = RL — 1. Except in simple geometric cases, there is no relationship between the areal draw ratio and any of the linear draw ratios. As with areal draw ratio, RL is an artificial concept, since the local draw down usually differs substantially from the average value. Example 7.10 illustrates linear draw ratios for the straight-walled cylinder of Fig. 7.6. Example 7.10 Linear Draw Ratios for the Cylindrical Shapes of Examples 7.7 and 7.8 Consider the straight walled cylinder of Fig. 7.7 with solid and hollow inner cylinders. Determine the linear draw ratios for these.
The linear draw ratio for the solid cylinder is the ratio of the line scribed on the surface of the cylinder to that scribed on the disk.
Line, L0
Area, A0
D
Area, Ad
H
Line, Ld
Areal Draw Ratio
Linear Draw Ratio
H:D
a)
b)
C)
Figure 7.10 Geometric factor comparison for (a) areal draw ratio, R a , (b) linear draw ratio, R L , and (c) H:D or H:d
H:D Another form of linear draw ratio is the ratio of depth of draw to mold opening at the rim. It is written H:D or H:d [13]. Except for simple shapes, it too is difficult to define unambiguously. For a simple parallel-side cylindrical part of Fig. 7.6, the relationship between H:D and RL is: R L =1 + 2(H:D)
(7.20)
Figure 7.10 shows all three draw ratios for a straight-sided cylinder. The draw ratio relationships are given in Fig. 7.11. The three draw ratios for draw-down into a two-dimensional corner are compared in the following way1. Figure 7.12 shows a three-dimensional view and an end-on view of the two-dimensional corner. The initial area of the sheet at radius R is TTRL/2. Its volume is V = 7iRLt/2 where t 1
The approach used here is Geometric Element Analysis, or GEA. That is, the sheet is assumed to be an infinitely extensible membrane having a thickness much less than its surface area. The arithmetic assumes no causal relationship between the amount of force required to stretch the membrane and the extent of stretching. Furthermore, there are no physical limits such as elongation at break to prevent the sheet from stretching any desired amount. GEA is discussed in more detail in Section 7.6.
Draw Ratio
RA (Areal) R L(Linear)
H:D
Figure 7.11 Comparison of areal draw ratio, linear draw ratio and H:D for parallel-sided female cylinder as a function of extent of draw
Side Dimension Disk Dimension
Figure 7.12 Draw into two-dimensional corner, two views
is the sheet thickness. The volume of polymer sheet on the wall after a differential draw is 2L(5R)(t — 5t/2). That remaining in the stretched sheet not in contact with the wall is (TIL/2)(R - 8R(t - 8t). The material balance yields: (7.21)
This is rearranged and 5R5t is assumed to be less than either 5R or St: (7.22)
This is integrated to yield: (7.23)
where to is the sheet thickness when R = R0. This is the instant thickness of the sheet at the instant radius, R. The average thickness does not depend on the radius at all. The areal draw ratio is: (7.24)
The linear draw ratio is: L
_ final line length _ "" initial line length "
2R (TCR/2)
_4 " n
(
*
}
And H:D is: initial line length ri:u
=
TTR/2
rr—-;—:—
=
•=
n = —•=
(I
.Ib)
inscribed circle gap ( v /2R/2) Jl Note that the reciprocal average thickness ratio, the areal draw ratio and the linear draw ratio all agree. From Equation 7.23, it is apparent that the sheet thickness approaches zero as the radius approaches zero. This demonstrates the general problem with the global draw ratio concept. Example 7.11 considers progressive drawing into this corner to illustrate this point. Example 7.11 Differential Drawing into a Two-Dimensional Corner Consider progressive draw-down into a two-dimensional corner, Fig. 7.13. The initial sheet length is nR/2. At r = nR, the sheet length is nr/2 + 2(R — r). The linear draw ratio is: 4 RL = n + -
(1-n)
71
Determine the average linear draw ratio when n= 1 and n = 0. Then consider a progressive draw where the distance to the corner is halved in each draw. Compare the draw ratios. The average linear draw ratio for n = 1 is R L = 1. When n = 0, R L = 4/TC, as expected. Consider drawing the sheet from r = R/2 (n = \) to r = R/4 (n = \). Now:
RU1 = i + £=1.137 R L 2 = 1 + - = 1.205 4
Tl
Consider drawing the free surface from r = R/4 to r = R/8. Now:
R
-4+^=I-239
The free portion of the sheet in this step has been drawn: R L1 R L 2 R L 3 = 1.698 In fact for the Mth draw step, the local draw ratio is:
The first term approaches 2 as M approaches oo. The second term approaches M as M approaches oo. In other words, R L o o = oo. Thus the last infinitesimal amount of sheet is drawn to an infinitely small thickness, even though the average linear draw ratio, R L = 4/TT.
!
R
R/8 R/4
Figure 7.13 Progressive draw-down into two-dimensional corner
R/2
Rim and Lip Sheet for Female Cavities The volume of polymer found in formed parts is usually greater than that in the material free of the mold surface prior to forming [14-16,74]. In some cases, sheet is deliberately pulled over the edge and into the female mold cavity in order to aid in wall thickness distribution. In other cases, the design of the part restricts the use of a moat or moat and dam combination. The plastic on the flat lip therefore tends to be drawn into the female mold cavity. The amount of plastic drawn into the mold varies from 15% to 35% or so, depending on the lip geometry. Additional sheet can be supplied by billow pre-stretching or it can be drawn from the Hp or rim region into the mold cavity during draw-down (Fig. 7.14). To account for the excess material, it is recommended that the calculated areal draw ratio values include 50% of the sheet surface area between the lip and the clamping ring [17]. Consider forming a parallel-sided cylinder d
nd Fb
FD'
F
D
Figure 7.14 Schematic of rim area coordinates, comparing stretching force, F d , and sliding force, F s . F'd is the component of the stretching force in the sliding force direction
of depth s and diameter d, clamped at diameter D = (1 + n)d, as shown in Fig. 7.14. The areal draw ratio with no rim material is given as Equation 7.16: (7.16) If all the rim material is included in the draw ratio: (7.27) If only a fraction, g, of the rim material is included: (7.28) or: (7.29) If D = (1 + n)d, this expression is written as: (7.30) Example 7.12 illustrates how the draw ratio is affected by the rim material. Figure 7.15 illustrates this where n is the rim fraction of polymer drawn into the female cavity. For the experimental observations of 15% to 35% greater volume, n = 0.07 to 0.16 on a circular cavity. Example 7.12 Effect of Rim Material on Draw Ratio Consider a parallel-sided cylindrical part where s = d and D = 1.2d. Determine the effect of rim material if 100% is involved in draw-down and if 50% is involved in draw down. Equation 7.30 is the proper equation:
When g = 1, R a , nm = 3.78. When g = 0, R a , nm = 5. When g = 0.5, R a , nm = 4.28. A more formal analysis examines the relationship between the forces required to stretch the sheet and those needed to slide it along the mold surface. A simple force balance illustrates this. The stretching force, F d , is written as: F d = x-A'
(7.31)
where x is the tensile strength of the sheet at the forming temperature and A' is the sheet cross-sectional area at the edge of the cavity (Fig. 7.14). The sliding force, F s , is written as: (7.32)
(RA-1)/(4s/d)
g=0 Fraction of Rm i Material Included in Draw-Down
Rim Fraction of Diameter, n Figure 7.15 Effect of rim material contribution on areal draw ratio, g = fraction of rim material included in draw-down
where N is the normal force, P is the pressure applied to the free-to-deform rim material and A is the contact area between the clamp and the rim. C is the kinetic coefficient of friction between the polymer and the mold surface [67,68]. The experimental value of a is 0.67 to 1 [69]. The force required to slide the sheet along the rim is vectored perpendicularly to the draw axis. The deformation force, F d , is initially vectored in the sliding force direction, but as the sheet draws, FJ, the component of F d in the horizontal or F s direction, diminishes rapidly. FJ = 0 when the sheet touches the wall of the parallel-sided female cylinder mold, as an example. FJ is given as: (7.33)
where P is the sheet angle to the horizontal and ho is the initial sheet thickness. If the rim is clamped at D = (1 -f n)d, the force needed to slide this area of the sheet, Fs, is: (7.34)
The sheet stops sliding when FJ < Fs. Since P is the amount of pressure that is holding the sheet against the rim, this equation is solved for P: (7.35) For the special case where a = 1: (7.36)
The amount of pressure required to keep the sheet from sliding is proportional to the tensile strength of the polymer, its initial thickness and the diameter of the cavity. It is inversely proportional to the coefficient of friction and to the amount of plastic on the rim, n. Example 7.13 illustrates this relationship. If the mold is a parallel-sided cylinder, the sheet stops sliding and begins stretching before the sheet contacts the wall. If the mold is a cone with an angle less than 74.4°, contact occurs first. Example 7.13 Sliding and Stretching Forces Given a 0.030 in thick sheet of plastic having a hot tensile strength of tau = 0.7MPa= 100 Ibf I in2, determine the angle fi where the stretching forces exceed the sliding forces for a 2-in drink cup. The coefficient of friction is 0.25, a= 1 and n = 0.2.
The operative expression is Equation 7.36:
If the maximum applied pressure is 14.7 lbf/in2, then the angle is: P = cos-1 (14.7/54.55) = cos"1 0.269 = 74.4° In other words, the sheet slides on the surface until that portion that is in the mold cavity reaches an angle of 74.4° with the horizontal. For billow prestretching, the dimensions of the expanding sheet differ from the mold dimensions. An appropriate factor must be included in the rim-included draw ratio definitions to account for this type of prestretching. Example 7.14 illustrates this. Prestretching is also considered in the text below. Example 7.14 Areal Draw Ratio With and Without Prestretching Determine the areal draw ratio of a straight-sided cylinder with and without prestretching. For prestretching, the bubble diameter D = (1 + n)d, where d is the diameter of the cylinder. Determine the proper equation for a bubble height from y = 0 to y = D/2.
The areal draw ratio of a straight-sided cylinder without prestretching is given by Equation 7.16:
The area of a spherical zone or cap is given as:
When y = 0, the area is a disk:
When y = D/2, the area is a hemisphere:
The areal draw ratio is given as:
where the initial surface area is the area of the cap. This equation is rewritten as:
The last bracketed term represents the effect of pre-blowing on the draw ratio. If n = 0 and y = d/2, or the bubble is a hemisphere, Ra,prebiow = R a/2.
Draw Ratio Usage—A Rationale Average draw ratios are used primarily to screen candidate polymers. For example, CAB, PS, PETG and HDPE can be pre-blown into bubbles that are greater than hemispherical [17]. Usually, PVC, PMMA and PC cannot. Low-density PS foam cannot be drawn greater than about H:D = 1:1 [18] unless coated with an unfoamed capsheet. Crosslinked polyethylene foam cannot be drawn greater than about H:D = 0.6:1 to 0.8:1 [19]. Practical temperature-dependent H:D draw ratios for several polymers and several initial sheet thickness for simple vacuum forming into a parallel-sided female mold are shown in Fig. 7.16. Mechanical Assists—Some Design Features The wall thickness analyses that follow concentration on the geometric prediction of part wall thickness during simple female forming. Many forming processes described in Chapter 1 depend on prestretching to improve material distribution. Inflation and plug assist are two common prestretching'methods. Preblowing or Inflation—Comments Figure 7.17 shows experimental draw down for sheet into the bottom corner of a truncated cone [20]. The sheet thickness ratio, h/ho is experimentally shown to be
Areal Draw Ratio, R A
H:d Local Thickness, um
Temperature,0C
Figure 7.16 Temperature-dependent areal draw ratio and H:D for tapered cylindrical female mold for several polymers: 1. 0.4 mm LDPE; 2. 0.5 mm HDPE; 3. 0.4 mm PP; 4. 0.3 mm HIPS; 5. 0.25 mm OPS; 6. 0.5 mm ABS; 7. 0.3 mm RPVC; 8. 0.3 mm FPVC; 9. 0.5 mm PVC copolymer; 10. 0.3 mm cellulose acetate; 11. 0.2 mm PC; 12. 0.3 mm PMMA; 13. 0.5 mm CAB; 14. 0.5 mm CAP; 15. 0.5 mm Hostalit Z; 16. 0.5 mm PS foam. Figure used with permission of Carl Hanser Verlag
PS PVB
Areal Draw Ratio, RA
Figure 7.17 Experimental sheet thickness as function of areal draw ratio for draw-down into truncated cone bottom cylinder. PS = polystyrene, PVB = polyvinyl butyral. Figure redrawn from [20] and used with permisssion of copyright owner
inversely proportional to the square of the areal draw ratio. Inflation is a method of prestretching sheet (Fig. 7.18). For inflation of an unformed sheet, experiments show that the sheet thickness away from the rim region is a function only of the inflation height, y (Fig. 7.19) [15]. For very large inflation ratios, exceeding hemispherical, the sheet thickness is constant only in the polar region [17]. An analytical solution to the
a
to
Figure 7.18 Geometric factors for bubble inflation
Reduced Sheet Thickness, t/t o
t
Experimental Data
Theory
1+(<5/a)2 Figure 7.19 Experimental and theoretical inflated bubble thickness [15]. Solid circles are polymethyl methacrylate, PMMA. Pluses are polystyrene, PS. Solid line is best fit of data. Dashed line is theory. Figure redrawn and used with permisssion of Ellis Harwood, Ltd., copyright owner
nonlinear clamped-edge plate deformation problem is also available [21]. If the polymer in the cap is assumed to have a uniform overall thickness [22]: (7.37)
For purely elastic sheet [15,17], the relationship between inflation height, y, and inflation pressure, P, is: (7.38)
where E is the modulus obtained from the polymer elastic stress-strain equation, G = E. As seen in Fig. 7.19 for HIPS and PMMA, there is a distinct offset in the thickness ratio relationship to y/a. An approximate relationship is: (7.39) The offset is the result of the sheet in the rim area being substantially thicker than the average. The extent of inflation is determined by the amount of prestretching desired to achieve the desired wall thickness uniformity and on the ability of the polymer to inflate without bursting, as discussed in Chapter 4. Typical prestretching air pressure values for several polymers are given in Table 7.9. If the inflated cap is to be snapped into a female mold, the cap surface should not touch the mold bottom on
Table 7.9 Typical Prestretching Air Pressure Polymer
PS PS—foam ABS HIPS CA PMMA PMMA/PVC PC FEP PET HDPE LDPE PP 10% talc—PP 20% talc—PP PSO2 RPVC FPVC PVC-foam
Pressure range above atmospheric
Temperature range (0C)
(0F)
(kPa)
(lbf/in2)
135-150
275-300
140-150 135-150 140-155 160-180 155-170 175-190
280-300 275-300 280-310 325-360 310-340 350-375
135-160 130-150 125-145 150-165 150-165 150-190 215-250 115-140 115-140
275-300 270-300 260-290 300-330 300-330 300-380 420-480 240-280 240-280
14-28 NR 10-28 14-28 7-21 48-70 35-48 41-70 NR 14-28 7-21 7-21 7-14 55-70 55-70 41-55 10-21 7-21 NR
2-4 NR 1.5-4 2-4 1-3 7-10 5-7 6-10 NR 2-4 1-3 1-3 1-2 8-10 8-10 6-8 1.5-3 1-3 NR
NR = Not recommended
eversion (Fig. 7.20). As a starting point for predicting draw-down, the sheet thickness can be considered as uniform everywhere. In a more advanced program, the thicker material near the rim can be considered, through application of the approximate relationship above, Equation 7.38. Preinflation is used with a male mold to minimize the amount of plastic on the surface that first contacts the sheet. A balance on the extent of preblowing bubble height must be struck. If the bubble is blown too large, webs are formed on the outside three-dimensional corners. If the bubble is too small, the corners of the mold can tear the sheet as the mold is inserted. Bubbles do not always tend toward hemispherical. Flat-topped and rectangular bubbles are formed with proper temperature programming. Although the amount of trial-and-error effort needed to achieve
Figure 7.20 Bubble eversion schematic
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non-symmetrical bubbles is great, the reward is the ability to form splitty or weak polymers into parts with excellent wall thickness distribution. Plug Assist—Comments Plugs are used to mechanically prestretch sheet in applications where a product would otherwise be only marginally acceptable. The plug redistributes polymer along the part wall. Wall thickness distribution with simple vacuum forming into a near-parallel sided cylindrical mold with H:D = 1:3 or Ra = 2.33 and RL = 1.67 is shown in Fig. 7.21 for several polymers. In Fig. 7.22, the effect of plug assist for 0.016 in. or 0.4 cm MIPS into a cylindrical cup at H:D = 1:3 and H.D = 1:1, or Ra = 5 and RL = 3, acts to distribute polymer from the side and bottom of the part to the traditionally thinner corner. The plug usually moves along the center axis of a female mold (Fig. 7.23). The plug design parameters include: • • • • •
The The The The The
7,5
shape of the plug tip, plug penetration depth relative to the cavity depth, plug diameter relative to the cavity diameter, plug surface temperature, and coefficient of friction between the plug surface and the stretching sheet.
Computer-Aided Design in Thermoforming
There are many reasons for computerizing the entire forming process. Some of these are:
Figure 7.21 Wall thickness distribution for several polymers under typical vacuum forming conditions. H:D= 1:3. polymers are: 1. PP; 2. PVC formed at low temperature; 3. LDPE; 4. HIPS; 5. PVC formed at high temperature; 6. PVC copolymer; 7. Cellulose acetate; 8. PC. Figure redrawn from [91] and used with permission of Carl Hanser Verlag
UMDA
Local Thickness, \\m
B
A
D
M
Location
U
B
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non-symmetrical bubbles is great, the reward is the ability to form splitty or weak polymers into parts with excellent wall thickness distribution. Plug Assist—Comments Plugs are used to mechanically prestretch sheet in applications where a product would otherwise be only marginally acceptable. The plug redistributes polymer along the part wall. Wall thickness distribution with simple vacuum forming into a near-parallel sided cylindrical mold with H:D = 1:3 or Ra = 2.33 and RL = 1.67 is shown in Fig. 7.21 for several polymers. In Fig. 7.22, the effect of plug assist for 0.016 in. or 0.4 cm MIPS into a cylindrical cup at H:D = 1:3 and H.D = 1:1, or Ra = 5 and RL = 3, acts to distribute polymer from the side and bottom of the part to the traditionally thinner corner. The plug usually moves along the center axis of a female mold (Fig. 7.23). The plug design parameters include: • • • • •
The The The The The
7,5
shape of the plug tip, plug penetration depth relative to the cavity depth, plug diameter relative to the cavity diameter, plug surface temperature, and coefficient of friction between the plug surface and the stretching sheet.
Computer-Aided Design in Thermoforming
There are many reasons for computerizing the entire forming process. Some of these are:
Figure 7.21 Wall thickness distribution for several polymers under typical vacuum forming conditions. H:D= 1:3. polymers are: 1. PP; 2. PVC formed at low temperature; 3. LDPE; 4. HIPS; 5. PVC formed at high temperature; 6. PVC copolymer; 7. Cellulose acetate; 8. PC. Figure redrawn from [91] and used with permission of Carl Hanser Verlag
UMDA
Local Thickness, \\m
B
A
D
M
Location
U
B
Vacuum With Pu l g Asssi t Vacuum Onyl
Local Thickness, urn
Local Thickness, um
1:3
1:1
Vacuum Wtih Pu l g Assist Vacuum Onyl
Location Location Figure 7.22 Effect of plug assist on wall thickness distribution for 0.4 mm or 0.016 in MIPS for H:D = 1:3 and H:D = 1:1. Dashed line, vacuum only. Solid line, vacuum with plug assist. Figure redrawn from [73] and used with permission of Paul Kiefel GmbH
Figure 7.23 Geometric factors for blunt-nose plug assist penetration
•
Production of sheet from pellets or powders is a process expense that most other technologies do not incur. The added extrusion costs range upward from $0.15/lb or US$0.33/kg. • Most thermoforming operations convert only 50% to 75% of the ready-to-beformed sheet into formed products. The rest—web, edge, cutouts, trim, selvage—must be reprocessed at additional costs with some loss in properties. In some cases such as medical products, web material cannot be used. • Despite technical advances in processing equipment, thermoforming is an energy intensive process. As a result, processing costs are usually higher than those in other converting industries. • The nature of the thermoforming process is biaxial deformation and thinning of a rubbery elastic sheet. Thus, the average part thickness is substantially less than the initial sheet thickness. • As a first approximation, plastic sheet draws only when free of the solid surface. This leads to parts of nonuniform wall thickness. In one-step natural drawing—
Stress Concentration Factor Corner Radius to Local Sheet Thickness Ratio Figure 7.24 Stress concentration factor as function of radius per unit local sheet thickness
vacuum forming, pressure forming or drape forming—parts are thinner in twodimensional corners and thinnest in three-dimensional corners. • The nature of the forming process dictates that the plastic in the thinnest areas is stretched the most. This material is therefore closest to its ultimate strength. Part performance under load therefore depends on the method of stretching the sheet and on the thinnest section under load. The stress in a formed corner is strongly dependent on the radius to local wall thickness ratio. As seen in Fig. 7.24, the stress concentration factor exceeds 2 when R/t < 1/4. A strong corner design has R/t > 3/4. • Conversely, many regions of the formed part are relatively unoriented, are weaker or thicker than desired, and thus are wasteful of expensive polymer. • Computer-aided engineering or CAE of the thermoforming process encompasses many of the following: • •
Control of sheet temperature prior to forming, The application of the applied forming forces to include necessary sequencing of pressure to allow inflation and/or plug assist prestretching, and • Proper sheet cooling techniques to ensure optimum overall cycle time or optimum energy efficiency. • Computer-aided part design or CAD, is only one facet of CAE. It depends on material allocation or distribution. For a given processing history and a given mold configuration, a specific element of the unformed sheet will always transform into a specific element on the formed part (Fig. 7.25). The controllable CAE parameters such as: • • • • •
Local sheet temperature, Applied pressure Relative pre-inflation parameters, Relative plug parameters, and Stretching sequence,
Figure 7.25 Concept of polymer sheet allocation. Translation of [A,B,C] points on flat sheet to [A',B',C] points on inflated bubble
• • • •
•
only differentially alter the relative location, differential area and thickness of that element. The easiest approach to material allocation is to assume large-scale isothermal biaxial stretching of an isotropic rubbery elastic sheet. This assumption allows two-dimensional finite-element analysis to be used to determine wall thickness for one-step formed shapes. With proper selection of the initial deformation mesh, prestretching can be added as a preliminary step. As a further simplifying assumption, the material allocation algorithm includes a non-slip condition. Only the sheet free of a solid surface will stretch under applied force. Two further aspects of free surface stretching can be included in model-building. A material balance shows that the volume of free sheet that continues to stretch is simply the difference between the initial volume of material in the unformed sheet and that already deposited on the mold wall. And the free material thickness tends to be uniform across its surface at any time during the stretching process. Computer-assisted thermoforming may be of greatest value when multi-layer rigid barrier containers become economically viable. Thermoforming will then meet a specific product need as the packaging industry, in particular, moves toward products requiring precise wall thickness control.
7.6
Wall Thickness Prediction—A Justification
By its very nature of the stretching and forming process called thermoforming, the product so produced has wall thicknesses that are not uniform. Stretching nearly always occurs only in the plastic sheet that is free of the wall. The last area of the mold to be covered by sheet is usually the thinnest. Traditionally, the thinnest walls of female parts are in the bottom three-dimensional corners. The thinnest walls on male parts can be in the outside three-dimensional corners or in the inside three-
h Uniform Load b L
Figure 7.26 Uniform flexural loading of simply-supported beam
dimensional corners. Prestretching devices aid in polymer material redistribution but in general, thermoformed parts have nonuniform wall thicknesses. For some thermoformed products, structural integrity is a secondary function. For many applications, however, the formed part must withstand mechanical loads. Consider two examples of mechanical loading: •
One-dimensional flexural loading of a simple beam (Fig. 7.26). The product might be a thin-gage fast-food container or a heavy-gage spa. The appropriate causal relationship between uniform load, w, and maximum deflection, ymax, is:
where L is the span, E is the modulus of the polymer and I is the moment of inertia. I is given as: I = bh3/12 (7.41) where b is the beam width and h is its thickness. Combining these equations: 60(wL)L3 ymax K } 384-Ebh3 Note that the extent of deflection of the beam is inversely proportional to the cube of its thickness. If the beam thickness or if the thermoformed sheet thickness varies by 10%, the extent of deflection varies by 33%. •
One-dimensional buckling of a plate (Fig. 7.27). The product might be a thin-gage disposable drink cup or the side of a heavy-gage formed equipment cabinet. The appropriate causal relationship is the Euler buckling equation:
where F is the buckling load, E is the polymer modulus, L is the effective length of the column and I is the moment of inertia, as before. Again, substituting the moment of inertia yields:
Force
L b
h
Figure 7.27 Uniform compressive loading and buckling of uniform-walled plate
(7.44)
•
Again a 10% variation in the column thickness or the thickness of the thermoformed sheet results in a 33% variation in the ability of the product to support a buckling load.
As noted above, prestretching enables material redistribution, with the objective being an increase in part wall thickness in load bearing regions. Consider the benefits for material redistribution. If the design wall thickness is currently adequate to support the design loads, material redistribution will allow sheet thickness downgaging. Consider the following: • •
Reduction in sheet thickness results in reduction in purchased cost of sheet. Reduction in sheet thickness results in more rapid and more uniform heating, resulting in lower cycle times and higher productivity. • More uniformity in sheet heating can result in fewer surface problems such as scorching, ofT-gassing, or blistering. • Reduction in sheet thickness may result in less sag since the weight of the sheet is reduced. • Reduction in sheet thickness results in lowered forces required to stretch the sheet. • Lowered forming forces may allow for deeper draws, faster forming, more surface texture. • With lowered forming forces, the sheet does not need to be heated as much, meaning that further cycle time reduction is possible. • Reduction in sheet thickness results in shorter cooling time on the mold. • Reduction in sheet thickness may result in reduced trimming costs and efforts, in that dies may not need to be resharpened as frequently and trimming defects such as splits may not be as prevalent. • Product shipping costs may be reduced since the parts weigh less.
There are two approaches to part wall thickness prediction. The first, a geometric method, has been used extensively in blow molding as well as thermoforming in Germany, Poland, Russia and Japan for more than a quarter century [26,55-57,7583,85,87-90]. The method follows a protocol for the stretching of an infinitely extensible membrane over a surface of known geometry. No polymer properties are needed and since the method is manual, no computer is needed. The technique is called Geometric Element Analysis or GEA. The second method is based on Finite Element Analysis or FEA. It stretches a mesh-like membrane over a surface of known geometry. A causal stress-strain relationship is needed to predict the relative forces generated by the stretching. The method depends on forming a nodal network of elements and the simultaneous solution of the stress-strain equations at each of these elements. A relatively large-capacity computer is needed.
Geometric Element Analysis or GEA The simplest illustration of GEA is draw-down of a sheet into a conical mold, as shown in Fig. 7.28. At time 0, a sheet of initial thickness, to, has been drawn into the cone of angle (3 to a depth, 1I1. The sheet is in contact with the mold surface for d/2
hi
h
Figure 7.28 Geometry and coordinates for progressive draw-down into female conical mold
a diagonal distance or slant height, s. That portion of the sheet not in contact with the mold forms a spherical cap of radius, R. The plastic sheet in the cap has a uniform thickness, t. The cap area is: (7.45) At time 0 + d0, a differential amount of material from the edge of the cap has been deposited on the cone surface. The cap material has been differentially stretched so that it is differentially thinner. A material balance [20] gives: (7.46) R is written in terms of h, s and P as: (7.47) and dR = — ds/tan (3. The differential material balance is written as: (7.48) This is integrated to yield: (7.49) where t* is the sheet thickness when s = 0. The sheet does not initially touch the cone side as it sags into the cavity. It touches when A o t o = A cap t* at s = 0: (7.50) Since h = (d/2) tan (3, the sheet thickness ratio is given in terms of the initial sheet thickness as: (7.51) Example 7.15 shows that for P = 60°, the sheet thickness decreases linearly with distance down the cone side. At the 60° cone tip, s = d, and t/t o = 0. Appendix 7.1 gives expressions for areal draw ratio as a function of draw-down. This thickness equation for a cone has been experimentally verified for many amorphous polymers [14,20,23,86]. Example 7.15 Slant Height Wall Thickness for 60° Cone Determine the expression for wall thickness for thermoforming into a 60° cone.
From Equation 7.49, for cos 60° = \ , sec 60° = 2, t* = 3/4, and:
The wall thickness for a 60° cone is linear with slant angle.
B
A
C
d
L
D
8
E
G
Figure 7.29 Various geometric shapes that have been analyzed using geometric analysis: (A) Full cone; (B) deep truncated cone; (C) shallow truncated cone; (D) triangle or wedge-shaped channel; (E) prism; (F) deep truncated wedge; (G) shallow truncated wedge
Note that this derivation depends solely on part geometry. No material properties are required. Initial sheet thickness and material temperature can only affect the depth of draw and not material distribution. Thickness equations for other shapes such as those shown in Fig. 7.29 are also available and are tabulated elsewhere [20,24,25]. For even the simplest three-dimensional shapes such as truncated wedges, these equations are very complex and a computer is needed to rapidly obtain meaningful functional relationships. A more functional approach, GEA, segments the mold geometry into very simple geometric elements, calculates the relative thickness reduction in those elements, then combines the results for an overall view of the local thickness. GEA assumes that any thermoform mold can be described by combinations of simple shapes. Differential material balances on these simple shapes result in simple equations. The first step is sectioning. The mold is envisioned to be divided into sections. Each section is idealized as one of five forming shapes, discussed below. The sheet thickness at each of these sections is calculated and the calculated local sheet thickness is the product of the thicknesses of each shape used to arrive at that point [26]. The application of each of these shapes is the design protocol.
Three-Dimensional Corner a)
c)
b)
Rectangular Channel t/t o = exp [-2X/TTR 0 ]
Two-Dimensional Corner t/to = (R/Ro) 0273 t/to = R/Ro d)
e)
Wedge-Shaped Channel t/to =(R/Ro) K Fukase One-Side Laydown
Dimensionless Thickness, t/to
One-Side Laydown e=45°
f)
Angle, G0 Figure 7.30 Five elements of geometric analysis: (a) Two-dimensional corner; (b) three-dimensional corner; (c) rectangular channel; (d) wedge-shaped channel; (e) one-side laydown; (f) relative thickness for one-side laydown
1. The two-dimensional corner (Fig. 7.30A). The thickness ratio is given as: (7.52) where t o is the thickness of the quarter-circle of radius R 0 . 2. The three-dimensional corner (Fig. 7.30B). The thickness ratio is given as: (7.53) Again to is the thickness of the sphere octant of radius R 0 . Note that the 3D corners thin at a much greater rate than 2D corners1. 3. Parallel walls (Fig. 7.30C). The rubbery sheet touches both walls at the same initial point. It freely expands as a two-dimensional semi-circle between the walls, with X being the distance down the walls and R 0 is the half-distance between the walls. The thickness ratio is given as: (7.54) 4. Converging walls or the wedge (Fig. 7.30D). The rubbery sheet expands freely as a two-dimensional arc of a circle. The thickness ratio is given as: (7.55)
Example 7.16 Chamfers and Radiused Corners f Compare the material thicknesses of a 2D corner of radius R and an equivalent I corner with 45° chamfers.
The length of an arc forming a corner of radius R is given as:
j The length of a chamfered corner, Fig. 7.31, is:
I The relative thickness ratio is given as: I Since stiffness is proportional to the cube of thickness, the chamfered corner is 1.113 = 1.37 or 37% stiffer than the radiused corner. 1
Note that other corner shapes are stiffer than sections of circles or spheres. Example 7.16 shows that a 45° chamfer yields a corner that is considerably stiffer than the equivalent 2D corner.
R
L
R
L
Figure 7.31 Geometric factors for (left) two-dimensional radius and (right) chamfer
where K is given as: (7.56) When O = TI/2, the walls intersect at right angles, and K = 0.273. The equation agrees with that for 2D corners, Equation 7.52. When 9 > TT/2, the results are useful for prediction of draw-down into a two-dimensional corner with substantial draft. Example 7.17 illustrates this. Example 7.17 Prediction of the Effect of Draft Angle on Wall Thickness Consider a right angle corner where R/R0 = 0.1. Determine the thickness Then consider the case where the corner has a 10° draft.
ratio.
From Equation 7.52, the thickness ratio for a right angle 2D corner is: t/to = (O.I)0273 = 0.533 From Equation 7.55, for 0 = 100°, K = 0.202. Therefore the thickness ratio for a 2D corner with 10° draft is: t/to = (0.I)0-202 = 0.628 If stiffness is a design criterion, the corner with draft is (0.628/0.533)3 = 1.636 or more than 64% stiffer than that without draft. 5. One-side lay-down (Fig. 7.30E). This was first used in blow molding [26]. The concept is somewhat difficult to comprehend. Basically, one edge of the sheet pivots against a mold point while the other edge lays onto the mold surface. It is considered here only in two dimensions. It always represents an intermediate step. As soon as the sheet touches all intersecting walls at the same relative angle, the design criterion shifts to one of the other four cases. In the case of right-angle two-dimensional intersecting walls, this occurs when the angle 0 = 45° or TC/4. The
initial angle, 9, that the sheet forms with the pivot point is usually greater than 45O1. The thickness ratio is given as: (7.57)
Figure 7.30F gives a plot of thickness ratio as a function of 6 with 9O as a parameter. In addition to the five basic elements given above, some ancillary expressions are valuable. In order to apply the sectioning method, it is necessary to determine a priori whether the freely expanding sheet touches the sides of the mold before or after it touches the bottom of the mold. A shallow mold is defined as one in which [27]: (7.58) where L is the shortest side of the mold and is the angle of the mold at the rim (Fig. 7.32) [28]. For a mold with right angle sides, P = 90 and the mold is shallow if H < L/2. For a long shallow mold, where the length, L, is much greater than the width, W, the uniform thickness of the sheet at the point of its contact with the bottom is given as: (7.59) where to is the initial sheet thickness and L is the length of the longer side. For a shorter mold, it is recommended that the thickness ratio be calculated from Equation 7.59 first for L = L', then L = W and that the product be considered the thickness ratio: (7.60) For a deep mold, the sheet contacts the mold walls before it contacts the bottom. As a result, the sheet deformation and thinning is calculated from parallel walls or the wedge arithmetic. L R
H X
Figure 7.32 Geometric factors for shallow rectangular mold [28] 1
For forming into a recess or undercut, O0 can be less than 45°. Care must be taken in laying out the segment to ensure that the proper pivot point is chosen.
Figure 7.33 Sequential factors for geometric analysis of shallow rectangular mold [29]
The protocol for a shallow mold (Fig. 7.33) [29] is as follows: •
Calculate the thickness ratio for the sheet as it just touches the bottom of the mold. • Identify lines A-A', B-B', C-C, and D-D' as being H units from the projected zero radius two-dimensional corners of the mold. • Identify lines E-E' and F-F' as being lines that bisect lines C-C, D-D' and A-A', B-B', respectively, as shown in Fig. 7.34. • The bottom wall thicknesses at E-E' and F-F' are determined by applying one-side lay-down arithmetic.
Figure 7.34 Top view of geometric analysis factors of shallow rectangular mold of Figs. 7.32 and 7.33
• • • •
The bottom thicknesses at points G are now determined by multiplying the thicknesses at E by those at F. The wall thicknesses in the 2D corners at E, E', F, F' and G are determined from the 2D corner Equation 7.50. The thickness in the 3D corners H is obtained from Equation 7.53. Make certain that the value used for to in this equation is the value obtained for G, above. Finally, calculate the 2D vertical wall thickness from the 2D corner, Equation 7.52.
Since the GEA method does not involve forces, the model is applicable to thin-gage and heavy-gage, alike [30,31]. Accuracies within 20% of measured thickness are expected. Typically, accuracy in horizontal 2D and 3D corners is within 10%. Vertical 2D corner measured values usually show the most variation with the arithmetic with errors of 30% common [32]. Figure 7.35 shows a comparison of measured and GEA-calculated wall thicknesses for a shallow mold. The GEA method is also applicable to plug assist, as detailed below. Finite Element Analysis As noted, even though there are arithmetic equations for some relatively simple geometries, it is necessary to solve them with some form of electronic computer. Approximate thickness values for complex mold geometries are obtained by assuming that the actual shape of the mold surface is approximated by a simple geometry or series of geometries. Finite element analysis or FEA is a practical scheme for determining the wall thickness of well-behaved stretched elastic membranes. The general scheme is to overlay the surface to be stressed with a grid or network (Fig. 7.36). The grid pattern is triangular or quadrangular. Depending on the sophistication of the computer model, the elements are two-dimensional (2D) with X and Y coordinates but no thickness, or they are three-dimensional (3D), with X and Y coordinates and a finite thickness. The three-dimensional elements are sometimes layered through the thickness. It is thought that 3D elements are necessary when there may be heavy-gage sheet bending resistance over sharp edges or when shear is expected [33]. For most applications, 2D or thin membrane elements are acceptable. The elements are connected via nodes. The connected elements form a discrete surface or mesh that replicates the actual continuous surface (Fig. 7.36). Since a finite number of elements are used to describe an infinite number of points on the sheet surface, the analysis is usually called /inite element analysis, or FEA. When forces are applied to the simulated surface, the elements distort, with the extent of distortion determined by balancing the forces and moments at each intersection or node. The relationship between applied force and resulting strain is called the constitutive equation of state of the material. Many hundreds or thousands of elements are needed to faithfully simulate structure response to applied load. Since many equations are needed for each node and three or four nodes are on each element, thousands of equations must be solved simultaneously to affect a solution. As a result the artificial computer time step must be very small to minimize error
Figure 7.35 Geometric factors for draw-down into 19x 11 x 6 i n deep deli pan mold. Initial sheet thickness was 0.145 in. Three wall thickness values obtained at various locations: Location
Measured thickness (in)
Measured circles (in)
GEA calculated (in)
FEA calculated (in)
Comments
A B C D E F G H
0.080 0.043 0.050 0.045 0.069 0.048 0.070 0.021
0.085 0.045 0.089 0.054 0.066 0.047 0.071 0.038
0.074 0.053 0.067 0.051 0.062 0.049 0.042 0.015
0.070 0.050 0.070 0.050 0.060 0.050 0.040 0.020
Short—midwall Short—2D corner Long—midwall Long—2D corner Bottom center Bottom 45° Vert 2D midwall 3D corner
generation during iteration. The simulation of a structure response to applied load requires extensive computer capacity, thousands of equations and many time steps. Despite these caveats, FEA is a given, accepted way of determining how a conceptual part will respond to applied load. FEA has been used for many years for structural analysis. As a result, the methodology is well-established [31]. When FEA is extended to thermoforming, difficulties arise. The very large deformation experienced by the sheet, or equivalently, by the replicating elements, leads to rapid error generation and eventual instability in the surface contour. For the large scale deformations encountered in thermoforming, the area of a given element may increase ten-fold or more. If that element is deforming into a sharp corner in the mold, for example, its final size must
Node
Force
Force Node Node Force
Figure 7.36 Geometric factors and methodology for finite element analysis, FEA
be as small as possible to replicate the actual forming process. This means its initial size must obviously be even smaller, and simple constitutive equations must be replaced with more complex hyperelastic equations as discussed in Chapter 4. Consider the deformation of a triangular element. The location of the element at computer time is given by the [X19Y15Z1] coordinates of each of three nodes. The nodes can rotate, translate and separate under force. At computer time 6 + dG, there are new coordinates [X29Y25Z2], and there are nine coefficients describing the linear deformation of the element. For each iteration, the forces acting to deform the element are in equilibrium. Internal forces represent the sheet response to the applied forces. If W is the internal energy function and u is the displacement coordinate, the internal force for the ith element is: (7.61) The external force for the ith element is the pressure, p, acting perpendicularly to the surface in the normal direction, n: (7.62) For the entire surface of the sheet, an equilibrium force balance is: (7-63) where the summation is over all N elements. This set of equations are nonlinear in both geometrical and physical structure. The stress-strain constitutive equations of state discussed in Chapter 4 are used to determine the appropriate values for the internal force terms. In one computer model [34], the equations are solved using a standard Newton-Raphson iterative method [35]. In another, the Galerkin weighted residuals method is found to be the most efficient in finding appropriate values [36]. Iteration is performed in a given computer time step until the change in geometric
position for each node is less than some very small fraction of the sheet dimension. The nodal positions for each element are scanned to determine if any element has a node on or outside the mold [X,Y,Z] plane. If so, that node is fixed against the mold surface, thus restricting the movement of the remaining nodes on that element. When all three nodes are against the mold surface, the element is immobilized. Computation ends when all the nodes are immobile or when the maximum allowable pressure is reached and the elements can no longer deform. Computational time is strongly dependent on the number of elements. Typically, up to ten iterations are needed for each d8 computer time step. Doubling the number of elements usually more than doubles the real time required to achieve a given d0 computer time step. The key to successful FEA application to thermoformed parts having complex shapes is the proper initial selection of the sizes of elements across the mesh. Three approaches are used in current FEA programs: •
Initial specification of element sizes, without recourse to altering their sizes throughout the computation. This approach is quite successful if a standard protocol is followed. A coarse mesh is assumed for the first pass. Examination of the computer results reveals the regions showing great element areal increase. The mesh for a second pass is then constructed, with those specific regions having finer mesh. Additional passes may be required, each having finer meshes in critical areas. • An adaptive mesh generator where, during computation, elements are split when their area increases beyond some proscribed limit. • An adaptive mesh generator where, during the later stages of computation, elements inside critical regions such as corners or edges are remeshed automatically. Regardless of the technique used, instability is still the major problem of commercial programs. Instability manifests itself as: • • • •
Localized elements that increase very rapidly in area in very few computer time steps, Elements that interfere with other elements that are affixed to solid surfaces, Neighboring elements that try to occupy the same spatial areas, and Elements that are fixed to solid surfaces at computer time but are freed from the surfaces at computer time 0 + d0, such as with elements against plug assists.
Unfortunately, instability problems manifest themselves near the end of a computation time that may have lasted several hours. Figure 7.37 shows the initial chosen mesh for simple vacuum forming up into a five-sided box with an insert. Figure 7.38 shows the extended mesh at the time the computation was terminated by an instability caused by elements trying to occupy the same space. However, the scheme clearly demonstrates the formation of a web at each insert corner. Figure 7.39 shows the local sheet thickness at the mid-plane in the YZ-direction. Figure 7.40 shows the forming sequence for forming over a five-sided male mold and Fig. 7.41 shows the thickness contours for the sheet having attained its final shape1. The actual practice 1
These FEA programs use hyperelastic models such as the Ogden or Mooney-Rivlin model discussed in Chapter 4. As a result, mathematically, forming is instantaneous. The intervals shown are therefore computed forming intervals, not real time intervals.
OJf
zmm
EXIT
Figure 7.37 FEA-gridded sheet positioned over female mold, shown as dotted line. T-FormCad Program, Hamilton ON Canada
Thickness
txl
Figure 7.38 FEA sheet stretched into mold, showing corner element "buckling" and element "webbing"
Thickness [run] Thickness [mm!
Arc length Cmm]
Arc length Emm]
Figure 7.39 FEA-calculated local sheet thickness through the lengthwise and widthwise center of Fig. 7.38
of folding of plastic against outside three-dimensional corners is tricky, with webs frequently formed. Figure 7.42 demonstrates a wrinkle that is in many respects the FEA equivalent of a web. An extensive effort is underway to verify FEA models. For example, the Treloar experiment in which the inflation pressure passes through a maximum as a rubber
Figure 7.40 FEA computer-time plot of sheet formation over male five-sided box. PITA program by A.C. Technology, Ithaca NY. [32]. Used with permission of Society of Plastics Engineers, Inc.
sheet is inflated [37], is considered a true test of the stability of the simulation arithmetic. Figure 7.43 compares the Treloar data with an FEA program using neo-Hookean stress-strain elasticity and a special limit point algorithm [38]. Figure 7.35 shows a comparison of GEA and FEA results with experimental data. Although FEA should yield more accurate wall thickness results than GEA, it is apparent that the two analytical models agree more with each other than with the experimental data. Figure 7.44 shows a comparison of experimental wall thickness measurements for several polymers with an FEA model. Even though the polymers have forming temperatures more than 1000C apart, the experimental data agree better with each other than with the computer values [70]. Since these polymers have widely diverse stress-strain curves at their forming temperatures, the implication is that geometry dominates local wall thickness distribution, not polymer properties. General Comments on Plug Design A substantial effort is needed to properly shape plugs. Generally, plug shape for symmetrical products such as cups begins as either a blunt-nosed tapered cylinder or as a truncated cone with generous edge radii (Fig. 7.45). Usually, the design is material-safe. Plug material is then removed on a trial-and-error basis, depending on the location and intensity of the plug mark. For unsymmetric parts, plug design is trial-and-error from the beginning. Regardless of the initial shape of the plug, the final plug will have generous corner radii and domed rather than flat surfaces. Plug
FEA Simulation
Measured on Formed Part Figure 7.41 Comparison of calculated and experimental wall thickness distribution for male fivesided box. See Fig. 7.40
Figure 7.42 Finite element analysis, FEA of corner of sheet draped over male mold. Figure redrawn from [32]
Dimensionless Force, F(ro/2ho), kg/cm2
Neo-Hookean With Clamped Ends
Neo-Hookean With Simply Supported Ends Treloar's Data
Extensional Ratio Figure 7.43 Internal check on computer results—comparison with inflation of rubber sheet, solid circles [37]
Thickness, cm
Cut Line
Computer-Generated FEA PC/PBT PC PEI
Distance Along Cut Line, cm Figure 7.44 Comparison of local thermoformed wall thicknesses of several polymers with general electric PITA finite element analysis, FEA [70]
Figure 7.45 Plug geometries for symmetrical products. (Left) Truncated cone with generous radius and (right) blunt-nosed cylinder
functions are discussed in detail in Chapter 4. For a female mold, the plug usually moves along the center axis of the mold. For a male mold, the plug moves along a line that bisects a corner (Fig. 7.46). For a male portion of a female mold, the plug may be hollow. For a boss, the plug may be a ring (Fig. 7.47). Plugs can be articulated to allow plastic sheet to be tucked under a lip or moved out of vertical plane to minimize a web on the female portion of a male mold. Consider a prototypical flat symmetrical plug of Fig. 7.23, with radius b and penetration depth 5, stretching a sheet of radius a. The sheet thickness ratio is: (7.64) where r is the sheet radius, b < r < a [22]. The sheet thickness on the plug surface is to. At values of 5/a greater than about 0.4, the thickness ratio from b to a is about equal to the radius ratio, b/a, as shown in Example 7.18. The initial volume of plastic is V = 7ia2to. The sheet is distributed unstretched over the top of the plug and is
Plug Action Line Plug Action Line
Figure 7.46 Examples of off-axis plug motion for male molds
Ring Plug
Boss
Figure 7.47 Ring plug for stretching sheet over bosses
stretched in a truncated cone between the plug edge and the mold rim. The volume of plastic on the plug surface is V p = 7ib2to. The polymer volume in the stretched sheet is: (7.65) This is approximated as: (7.66) Since V = V p + Vs, the average thickness ratio is given as: (7.67) As seen in Example 7.18, the average value is very close to the calculated value for 5/a > 0.5 or so. The approximation fails as b/a decreases in value. Nevertheless, this simple computation can save extensive computer time if only approximate wall thicknesses are needed.
Example 7.18 Wall Thickness of Polymer Stretched with a Flat Plug The thickness ratio of the plastic stretched between the edge of a flat plug and the rim of the mold is given by Equation 7.64. Determine the thickness ratio for S \a— 1.0 and S/a = 0.2 for b/a = 0.8. Compare with the appropriate r/a value. Then calculate the average sheet thickness ratio from Equation 7.66. Finally, compare the results for SJa=I and b/a= 0.4. Equation 7.64 for this example for 5/a = 1 is:
r[ 1+ CiirW)T 1/2=[1+2a08(a/r)2rl/2 For r / a = 1, t/t o = 0.218. For r/a = 0.9, t/t o = 0.197. For r/a = 0.8, t/t o = 0.176. The average sheet thickness ratio is given from Equation 7.67 as: W = i _ ^ = 0.200 to 1 The average value is quite close to the calculated one. Equation 7.64 for this example for 8/a = 0.2 is:
^[^(rln^) 2 ]" 1 ^^ 0 - 8 0 3 ^ 2 1 " 1 7 2 For r / a = 1, t/t o = 0.745. For r/a = 0.9, t/t o = 0.709. For r/a = 0.8, t/t o = 0.666. The average sheet thickness ratio is given from Equation 7.67 as:
^
=
!^ =1 .oo
to 0.2 The average value is not accurate for this case. Equation 7.64 for this example for 8/a = 1 and b/a = 0.4 is:
r[ i + (r-biA4)T 1 / 2 = [ i + u 9 i ( a / r ) 2 i " i / 2 For r / a = l , t/t o = 0.676. For r/a = 0.7, t/t o = 0.540. For r/a = 0.4, t/t o = 0.344. The average sheet thickness ratio is given from Equation 7.67 as: ^ to
=1 ^
= 0.600
1
The average value is not accurate in this case. The plug tip shape aids in stretching the sheet, as discussed in Chapter 4. The effect of plug surface curvature is approximated by using an effective value of b, the plug radius. Consider a spherical plug tip (Fig. 7.48), of radius b, penetrating a sheet
Locus of Tangent Points Defining Effective Plug Radius
Plug Depth
Figure 7.48 Spherical nose plug assist, showing locus of sheet tangent to plug during penetration
of radius a. Let b' be the effective plug radius. When the plug tip just touches the sheet, b' = 0. When the plug has penetrated to a depth 5 = b, the sheet touches it at b'/a = (b/a)2. And when it has penetrated to a depth 5 = 2a, the effective reduced radius is b'/a = 1 — cos 2a, where oc = tan" 1 (b/a). If the sheet does not slide on the plug, a conservative estimate of the sheet thickness at any plug depth, 5/a, is obtained by using the effective radius, b'/a, in Equation 7.64. As expected, drawdown at the same value of 5/a is less with a spherical plug than with a blunt one.
Plug Assist Analysis The force required to stretch the sheet to a given penetration depth 5 with the flat plug is given for large values of 5 as [22]:
where E(T) is the temperature-dependent neo-Hookean modulus discussed in Chapter 4. For the large strain model, the force is directly proportional to the penetration depth and the initial sheet thickness. Example 7.19 illustrates this. A similar relationship is used for the bull-nosed plug, except that b is replaced with b', the effective plug radius. Example 7.19 Linear Force for Shallow Plugging A 1 in diameter dosage cup of 0.050-in sheet is to be stretched to a depth of 0.2 in using a flat plug of 0.8-in diameter. Determine the force if the neo-Hookean modulus of the plastic is 80 lbf/in2. From equation 7.68: _ 27i5E(T)ho _ 2n • 0.2 • 80 • 0.05 ~ ln(a/b) ~ ln(l/0.8) "
f>
Since the area of the plug is the plug is:
TT(0.8) 2 /4
= 0.5 in2, the pressure needed to push
The extent of sheet stretching over a plug tip is estimated from the force balance used for rim material draw-down. To obtain an appropriate thickness ratio relationship for stretching over a curved plug tip, a differential force balance is integrated over the length of plug travel. The force holding the sheet against the plug increases with increasing penetration. The component of tensile force stretching or sliding the sheet on the plug tip decreases with increasing plug penetration. Thus, any biaxial extension of the sheet in contact with the plug probably occurs just as the plug penetrates the sheet. In practice, stretching of the free sheet dominates throughout the plug motion. As stretching continues, the stretching becomes nonlinear. The sheet is extended in a "plane strain" fashion. That is, the view of the sheet from the vertical shows no relative effect of the plug (Fig. 7.49), even though stretching is extreme [39,40,72]. The plane strain relationship between force and extension for the Mooney-Rivlin constitutive equation is given as: (ft __ iy/2{l
_ x-2)
=
(F/27r)(2C01 + 2C10)ho
(7.69)
where F is the force applied to the plug to stretch the sheet and r is the radius position, a < r < b (Fig. 7.50) [41]. The predicted force-deflection profile for a conventional rubbery sheet is compared with the experimental profile and with the linear version of Equation 7.69 in Fig. 7.51 [42]. As is apparent, the linear force-deflection profile representing the large strain solution overestimates the initial extent of deflection and underestimates the later extent of deflection. Figure 7.52 compares the analytical model, the FEA model and the experimental data [43].
Clamp
Circle
Circle
Clamp
Ellipse Ellipse Plug Sheet Moving Downward
Sheet Continuing Downward
Figure 7.49 Schematic showing how distorted element appears undistorted when viewed from above
Force, F
Deflection, D
Plug Diameter, b
Cavity Diameter, a
Figure 7.50 Plane strain stretching geometric factors
Load, kg
Natural Rubber Data
Wiliams' Linear Model
Plane Strain Model
Deflection, cm Figure 7.51 Experimental and theoretical load-deflection values for plug assisted plane strain stretching of natural rubber sheet. Solid circles are natural rubber data
Plug Force, N
Natural Rubber Data
Plane Strain Model
FEA-I FEA-II
Deflection, cm Figure 7.52 Comparison of experimental and theoretical load-deflection curves for plug assisted plane strain stretching of natural rubber sheet. Solid circles are natural rubber data. FEA models are described in [49]
Plug Design—Geometric Element Analysis The GEA protocol discussed earlier holds for plug assist as well [44]. The stretching protocol is shown in a series of steps in Fig. 7.53. Plug assist is useful for the stretching of elastic membranes so long as the angle the sheet makes with the horizontal exceeds TT/4 or 45° (Fig. 7.53A). When the plug reaches its maximum, the sheet is stripped from the plug, as shown in Fig. 7.53B. The GEA element in Fig. 7.53A and 7.53B is one-side lay-down. Once the sheet is horizontally tangent with the plug face, it is stripped from it (Fig. 7.53C, 7.53E1 or 7.53E2). If the plug is near the bottom of the mold, the sheet simply lays onto the mold surface without stretching. This is the most probable case. If the sheet is not near the bottom of the mold, the sheet continues to stretch in a semicircular or hemispherical fashion until it touches the mold bottom. Once the sheet is on the mold bottom, stretching takes place by one-side lay-down until the angle between the vertical and horizontal sections of the sheet reaches n/4 or 45°. After that, the sheet is stretched according to the 2D protocol discussed above. Figures 7.54, 7.55, and 7.56 show the relative effects of cavity depth on reduced thickness as a function of the relative depth of the plug. In all cases, b/a = 0.7 but the relative plug depth, 8/a varies. As is apparent, as the plug depth increases, the 2D corner thickness increases to a maximum value and the bottom thickness also increases. The reason for the latter effect is that the sheet in contact with the plug simply is laid down onto the bottom without substantial
A
E1
E2
B F
C
G
D Figure 7.53 Sequence of stripping sheet from plug and laying sheet onto mold surface: A = End of plug travel; B = sheet laying onto vertical mold surface; C = sheet releases from plug when F = 45°; D = sheet shape at instant of release from plug; E1 = sheet laydown for deep plug, shallow cavity; E2 = sheet laydown for shallow plug, deep cavity; F = sheet contacts mold bottom; G = sheet draws into mold corner
Thickness Ratio, t/to
Side And Botom
2D Corner Plug-Assist Draw-Down, XO/RQ = 0.33
Plug Depth Figure 7.54 Computed plug depth-dependent sheet thickness at side, bottom and two-dimensional corner for X o /R o = 0.33
Plug-Assist Draw-Down, Xo/Ro = 1.0
Thickness Ratio, t/t o
Side Bottom
2D Corner
Plug Depth Figure 7.55 Computed plug depth-dependent sheet thickness at side, bottom and two-dimensional corner for X o /R o = 1.0
Thickness Ratio, t/t o
Side
Bottom
2D Corner Plug-Assist Draw-Down, Xo/Ro = 1.5
Plug Depth Figure 7.56 Computed plug depth-dependent sheet thickness at side, bottom and two-dimensional corner for X 0 /R 0 = 1.5
stretching. The closer the plug comes to the cavity bottom, the less stretching occurs before the sheet contacts the cavity bottom. Plug Design—Finite Element Analysis One of the earliest tests for FEA models was the prestretching of the sheet with a plug. As noted, mechanical stretching of a membrane is plane strain deformation. All elements on the sheet surface appear undistorted when viewed in the stretching direction, regardless of the extent of deformation. This is seen for circular plug stretching a thin rubber membrane in Fig. 7.57. FEA yields accurate plane strain simulation of a barrel-shaped plug penetrating a rectangular sheet in top and side views (Fig. 7.58). The sheet grid shows distortion only along the vertical edges of the plug. Viscoelasticity is most significant in plug stretching in the region where the plug edge touches the sheet [46,85]. As noted in Chapter 4, the classic K-BKZ viscoelastic model is used [47]. As with the Ogden stress-strain model, the K-BKZ model theoretically has an infinite number of coefficients. As seen in Fig. 7.59 [46], three coefficients do not fit the strain-rate dependent curves very well. However, more constants result in extended computational times and potential instabilities [46].
Figure 7.57 Photo showing plug-assist plane strain stretching. Top view (top) shows limited distortion of circles. Side view (bottom) shows substantial distortion of circles
If the sheet is to be freely stretched between the plug tip and the mold rim, the pressure on each side of the sheet must be the same (Fig. 7.60a). If the cavity pressure is allowed to build (Fig. 7.60b), the sheet is forced against the plug sides. The formed part will be thin in the rim area. If the cavity pressure is low, the sheet is forced against the mold sides (Fig. 7.60c). This reduces the effectiveness of the plug and results in parts that are thin in corners. Control of sheet position becomes much more difficult as b/a approaches unity. A tapered plug stretching sheet into a mold having the same sidewall taper helps overcome this lack of control (Fig. 7.6Od).
Top V i e w TJticJcwess VAI
CUT
mm
EKIT
Side
View
Figure 7.58 Top and side views of finite element analysis, FEA solution of sheet stretched over shaped plug. FEA program is T-FormCad from McMaster University
From practical considerations [44,68,84], polymers are elastic liquids. For GEA and FEA running without the K-BKZ option, the sheet is treated as a rubbery elastic membrane. As a result, when the sheet is stripped from the plug, the instantaneous response of the sheet, prior to any additional stretching, is to elastically recover to a uniform sheet thickness in the free portion of the sheet. The sheet that adheres to the mold surface during the plugging phase is assumed to keep its local thickness
Stress, MPa
K-BKZ Model
Experimental Data
Extensional Ratio Figure 7.59 Stress-strain comparison of K-BKZ viscoelastic model with experimental data at two temperatures. Redrawn from [46]
throughout the rest of the stretching sequence. As a result, the ideal elastic sheet response produces a part wall thickness discontinuity at the point of elastic recovery (Fig. 7.61a) [48]. This discontinuity usually occurs on the side wall of the part and
b)
a)
Balanced Differential Pressure
Higher Cavity Pressure d)
C)
Lower Cavity Pressure
Tapered Plug
Figure 7.60 Schematic effect of differential pressure on draw-down during plug penetration
"Elastic" Bump or Plug Mark
Uniform Thickness a) Purely Elastic Sheet Response
"Viscous" Bump or Plug Mark b) Purely Viscous Sheet Response Figure 7.61 Schematic local wall thickness as sheet leaves plug, (a) Purely elastic response and (b) purely viscous response
is usually called a plug mark or chill mark. On the other hand, if the sheet is considered to respond in an ideally viscous way, no free sheet thickness recovery can occur. As a result, the ideally viscous sheet yields a part wall thickness discontinuity at the point where the sheet was attached to the plug surface (Fig. 7.61b). This discontinuity should occur on the bottom of the part. FEA computer simulation using the K-BKZ viscoelastic model shows how the sheet thickness changes as the sheet is stripped from the plug (Fig. 7.62) [49]. From examination of many plugassisted thermoformed parts, ridges are occasionally seen on the side walls of parts. Bottom ridges are rarely seen. This is a strong indication that the sheet recovers more elastically than viscously as it is stripped from the plug. In general, a blunt plug with generously rounded edges, essentially a compromise between a flat plug and a hemispherical one, is the best basic design (Fig. 7.63). The plug is usually kept warm, to within 200C or 400F, of the set temperature of the plastic or is insulated to minimize conduction heat loss, as discussed in Chapter 6 on plug materials. Heated plugs are needed whenever the polymer in contact with the plug must be drawn further in subsequent forming steps.
Next Page
Sheet Height
Pressure Box
Maxm i um Plug Height
FEA-Computed Sheet Thickness
Clamp Edge
Plug Center
Clamp Edge
Sheet Diameter Figure 7.62 FEA computer simulation of sheet wall thickness during and after plugging, using K-BKZ viscoelastic model. Redrawn from [49]
Locus of Tangent Points Defining Effective Plug Radius
R=b/2 R=b/4 b
a
Figure 7.63 Schematic of blunt plug with generous corner radii
7.7
Regrind
Regrind is an economic necessity in all but the most mission-oriented thermoformed product. The polymer is exposed to shearing and heating throughout the extrusion, thermoforming and regrinding process. The way in which the trim from the forming
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Sheet Height
Pressure Box
Maxm i um Plug Height
FEA-Computed Sheet Thickness
Clamp Edge
Plug Center
Clamp Edge
Sheet Diameter Figure 7.62 FEA computer simulation of sheet wall thickness during and after plugging, using K-BKZ viscoelastic model. Redrawn from [49]
Locus of Tangent Points Defining Effective Plug Radius
R=b/2 R=b/4 b
a
Figure 7.63 Schematic of blunt plug with generous corner radii
7.7
Regrind
Regrind is an economic necessity in all but the most mission-oriented thermoformed product. The polymer is exposed to shearing and heating throughout the extrusion, thermoforming and regrinding process. The way in which the trim from the forming
process is recovered, reground, stored, dried, and re-extruded is quite important to the success of a forming program. Material Property Deterioration on Regrind A large portion of the thermoformed sheet is web or trim. The efficient recovery and reuse of trim is essential to the economic viability of the process. For roll-fed sheet, rectangular shapes yield up to 25% trim. For small, round shapes, about 50% trim is expected. In cut sheet thermoforming, sheet-stock of standard dimension may be more economical than sheet cut to special size. But the use of standard dimension sheet-stock may lead to high percentages of trim. Even if trim can be totally recycled with minimum loss in material properties, the cost of regrinding, drying, and reextruding must be carefully considered in the process economics. This is discussed earlier in this chapter. The action of heat and shear in grinding, extrusion and to some extent, thermoforming, can thermomechanically degrade most polymers. The typical mechanical effect is chain breaking. This results in loss of ultimate tensile strength, elongation at break, toughness or the area under the stress-strain curve, and impact strength. With some polymers such as RPVC or PP and other polyolefins, oxidative degradation occurs. This results in yellowing and odor generation. Polymers with extensive plasticizer packages become brittle owing to deterioration or loss of effectiveness of the packages. Flexible polyvinyl chloride or FPVC is a classic example. Polymers with fire retardants and UV stabilizers are particularly sensitive to the high time-temperature environments common in multiple recyclings. Regrinds of moisture-sensitive polymers must be carefully dried to minimize dehydrolysis. Condensation polymers such as PET, PA and PC are classic candidates. In glass-fiber reinforced polymers, fiber length is quickly reduced by mechanical grinding and shear in extrusion. Usually, thermomechanical deterioration is not catastrophic. Small changes in observed physical properties usually do not cause dramatic changes in processing conditions. And final part performance is not substantially lowered. Nevertheless, the mechanical properties of a polymer that has been reground and recycled many times should be lower than those of the virgin polymer. As an example, CPET was dried, extruded, reground, dried, and mixed 50:50 with dried virgin PET and reextruded. The effect of reprocessing on mechanical properties is shown in Table 7.10. Note the loss in intrinsic viscosity or deterioration in molecular weight, and an indication of loss in elongation at break, ultimate tensile strength and Spencer impact. These property values losses are small and are usually not considered detrimental to the final part performance. For thermoforming to be a viable technology, web, edge trim, beginning and ends of roll-stock and unacceptable formed parts must be recycled into new sheet. Regrinding, drying, re-extruding and re-thermoforming are mechanical and thermal environments that may cause loss in important polymer characteristics such as: • •
Molecular weight, Impact strength,
Table 7.10 Effect of Regrind Material on Room Temperature Polyethylene Terephthalate Mechanical Properties ( + Standard Deviation) Property
Run 1 virgin
Run 2 50% virgin
Run 3 50% virgin
Intrinsic viscosity
0.83
0.68
0.68
Secant modulus MD x 103 lbf/in2 TD x 103 lbf/in2
2.59 (±0.075) 2.375 (±0.135)
2.44 (±0.06) 2.07 (±0.098)
2.45 (±0.06) 2.36 (±0.167)
Percent elongation at yield MD TD
10.0 (±2.9) 10.2 (±1.1)
10.0 (±0.7) 10.0 (±0.7)
9.8 (±0.8) 9.7 (±1.2)
Tensile strength, yield MD x 103 lbf/in2 TD x 103 lbf/in2
5.0 (±0.39) 4.6 (±0.15)
4.9 (±0.20) 4.6 (±0.23)
5.1 (±0.16) 4.6 (±0.54)
Tensile strength, break MD x 103lbf/in2 TD x 103lbf/in2
8.3 (±0.61) 7.8 (±0.39)
7.9 (±1.90) 7.1 (±0.58)
7.0 (±2.30) 4.7 (±1.08)
Spencer impact, 1000 g
2.8 (±0.65)*
2.3 (±1.03)
2.4 (±0.91)
• Two of 5 specimens did not break at 6400 g
• • • • • • • •
Elongation at break, Tensile and flexural strengths, Tensile and flexural moduli, Fire retardancy, Ultraviolet resistance, Fibrous or particulate coupling agent effectiveness, Pigment color, and Fiber length.
Theoretically, in a closed loop process, a small amount of polymer is reground and reprocessed many times. The arithmetic needed to predict the effect of regrind property loss on final part performance depends on: •
The way in which the specific property deteriorates with time at processing temperature, and • The way in which the specific property of the regrind and that of the virgin polymer are melded. The simplest form of closed-system reprocessing is shown in Fig. 7.64a [50]. The black box represents the effect of extrusion and forming processes. The effect of the regrinding process is ignored. Figure 7.64b includes the effect of the regrinding process on property deterioration. Figure 7.64c considers reprocessing of extruded but unthermoformed sheet and again ignores the regrinding process. As is apparent, more complex schemes can be considered.
a)
b)
c)
Figure 7.64 Closed-loop steady-state reprocessing or recycling of trim, (a) Represents effect of extrusion and thermoforming and ignores effect of regrinding. (b) Represents extrusion and thermoforming and includes effect of regrinding. (c) Represents separate effects of extrusion and thermoforming, with separate recycle streams being added to virgin
Single-pass property value loss data are relatively easy to generate [51-53,73]. Algorithms are used to relate single-pass property value loss data to steady-state property value loss. There are two general types of laws of mixtures: •
The linear law of mixtures for which the important property of a combined polymer stream is additive: A = yB + (1 - y)C
•
(7.70)
where A is the property of the mixed stream, B is the property of polymer B, C is that of polymer C, and y is the weight fraction of B in the mixed stream. The logarithmic law of mixtures for which the logarithm of the important property of a combined polymer stream is additive: In A = y In B + (1 - y) In C
(7.71)
This is also written as: A=ByC
l y
(7.72)
In addition, there are several models to describe the way in which the polymer loses its important property. Three such models are: •
The proportional property loss is given as: D = X-M
(7.73)
Table 7.11 Typical Polymer Properties and Their Proposed Recycle Algorithmic Interactions [7]* Material property
Linear loss Tensile strength Flexural strength Tensile modulus Flexural modulus Elongation at break Impact strength Impact strength (foams) Ductility (toughness) Fire retardancy UV stability Oxidative resistance Molecular weight Intrinsic viscosity Melt viscosity
Logarithmic law of mixtures
Linear law of mixtures Declining loss
Power-law loss
Offset loss
Linear loss
Power-law loss
Offset loss
X X X X X X
X
x X X
X
X
X
X
X
x
X
X
X
X
X
• In many cases, experimental data are too few and so the proper method is frequently inconclusive. Furthermore, property loss may be so small that more than one algorithm may seem to fit. If so, the simplest algorithm should always be used
•
where M is the property before processing, D is the property after processing and X is a proportionality. The power-law property loss is given as: D = X • Ma
(7.74)
where a is an exponent, usually less than 1. •
The offset property loss is given as: D= M-Z
(7.75)
where Z is a fixed amount of property. Table 7.11 compares typical polymer properties and corresponding proposed algorithmic recycle types. The derivation for the linear property value loss-linear mixture case is given in Appendix 7.II. The resulting equation is: M00 X ( I - Y ) (7 76) M^I^XY" where M00 is the steady-state mixed property value, M0 is the property value of the virgin polymer, X is the fraction of property value retained by the polymer after a single pass through the processing equipment, and Y is the weight fraction of the recycled polymer in the mixed stream. The value of X is determined by standard
100% regrind/recycle studies. As noted in Appendix 7.II, if X = 0.9 and Y = 0.5, the specific property of the mixed polymer after three cycles is 83.5% of that of the virgin polymer and after an infinite number of cycles or steady state, the mixed polymer property is 81.8%.
Property Value Loss—Experiment and Protocol There are several studies on material property deterioration with regrind [51-54]. Nearly all studies use conventional injection molding machines and focus on determining mechanical properties of 100% regrind after several passes. Standard processing conditions such as temperature and shear rate profiles and residence times are usually not given. As a result, extrapolation of these data to the thermoforming process is tenuous at best. Tables 7.12 and 7.13 give experimental and calculated values for multiple passes of 100% regrind high-impact polystyrene (HIPS) and ABS. Tables 7.14 and 7.15 give experimental and calculated values for the effect of regrind level on the second pass properties of HIPS and ABS. The agreement is relatively good, considering the scatter in the data and the assumption of simple laws of mixture and property loss. Mechanical shear at melt condition seems to be the primary way in which polymer properties deteriorate mechanically. Mechanical grinding is a secondary way. Long residence time at melt condi tion in the extruder is the primary way in which polymers thermally deteriorate. Heating in the thermoforming oven is a secondary effect. As a result, an appropriate protocol for regrind studies of thermoformed web or trim should focus on extrusion rather than injection molding. One protocol follows:
Table 7.12 Comparison of Experimental and Calculated Impact Strengths and Elongations at Break for High-Impact Polystyrene [54] Property
Unit
Number of passes 0
1
2
3
4
5
6
Impact resistance Measured Calculated1
kJ/m2 kJ/m2
18.7
17.0 17.0
15.0 15.4
14.0 14.0
15.0 12.7
13.0 11.5
12.0 10.4
Notched impact strength Measured Calculated2
kJ/m2 kJ/m2
6.3
5.4 5.2
4.1 4.3
3.3 3.6
4.0 3.0
2.5 2.5
2.1 2.1
Elongation at break Measured Calculated3
% %
12.7
10.3 10.3
7.9 8.9
8.0 8.1
7.6 7.6
7.1 7.4
7.2 7.2
1 2 3
Model used is: M pN = XN • M0 where X = 0.833 Model used is: M pN = XN • M 0 where X = 0.907 Model used is: M pN = XN • M0 + B • (1 - XN)/(1 - X) where B = (1 - X) • Masymp and X = 0.576, M asymp = 7.0 and B = 2.97
• Select a production extruder commonly used to produce thermoformable sheet. • Establish the appropriate extrusion conditions to produce sheet at commercial rate. • After steady state, obtain sufficient sheet for both the regrind study and the thermoforming study. Label this as "First Pass". This should be several hundred pounds or kg. Table 7.13 Comparison of Experimental and Calculated Impact Strengths and Elongations at Break for ABS [54] Property
Unit
Number of passes 0
1
2
3
4
5
6
Impact resistance Measured Calculated1
kJ/m2 kJ/m2
72.9
49.0 49.0
33.0 32.9
18.0 22.0
15.0 14.9
10.0 10.0
6.1 6.7
Notched impact strength Measured Calculated2
kJ/m2 kJ/m2
39.3
25.0 25.0
13.0 15.9
10.5 10.1
7.6 6.4
4.1 4.1
2.3 2.6
Elongation at break Measured Calculated3
% %
96.4
24.0 24.0
10.4 10.9
8.6 8.5
8.9 8.1
8.0 8.0
7.7 8.0
1 2 3
Model used is: M pN = XN • M 0 where X = 0.672 Model used is: M pN = XN • M 0 where X = 0.636 Model used is: M pN = XN • M 0 + B • (1 - XN)/(1 - X) where B = (1 - X) • M asymp and X = 0.181, Masymp = 8.0 and B = 6.55
Table 7.14 Effect of Regrind Level on Second Pass Impact Strength and Elongation at Break for High-Impact Polystyrene [54] Property
Unit
Regrind level (fraction) 0
0.05
0.10
0.15
0.25
0.50
Impact resistance Measured Calculated1
kJ/m2 kJ/m2
17.5 17.5
17.0 16.9
16.0 16.8
16.0 16.7
15.5 16.5
16.1
Notched impact strength Measured Calculated2
kJ/m2 kJ/m2
5.4 5.2
5.2 5.1
5.3 5.1
4.7 5.0
4.7 4.9
4.7
Elongation at break Measured Calculated3
% %
10.3 10.3
10.4 10.1
9.3 10.0
9.2 9.8
8.0 9.5
8.7
1 2 3
The model is: Mp2 - [X(I - Y)(I + XY) + (XY)2]MO where X = 0.907 and M 0 = 18.7 The model is: Mp2 = [X(I - Y)(I + XY) + (XY)2]MO where X = 0.833 and M 0 = 6.2 The model is: Mp2 = [X(I - Y)(I + XY) + (XY)2JM0 + B where X = 0.576, B = 2.97 and M 0 = 12.7
Table 7.15 Effect of Regrind Level on Second Pass Impact Strength and Elongation at Break for ABS [54] Property
Unit
Regrind level (fraction) 0
0.05
0.10
0.15
0.25
0.50
Impact resistance Measured Calculated1
kJ/m2 kJ/m2
49.0 49.0
48.5 48.2
48.5 47.4
39.5 46.6
45.5 45.0
41.0
Notched impact strength Measured Calculated2
kJ/m2 kJ/m2
26.5 25.0
21.0 24.5
14.4 24.1
12.2 23.6
12.2 22.7
20.4
Elongation at break Measured Calculated3
% %
24.0 24.0
26.4 23.3
20.9 22.6
19.9 21.9
15.6 20.4
16.9
1 2 3
•
The model is: M p 2 - [X(I - Y)(I + XY) + (XY) 2 JM 0 where X = 0.672 and M 0 = 72.9 The model is: M p 2 = [X(I - Y)(I + XY) + (XY) 2 JM 0 where X - 0.636 and M 0 = 39.3 The model is: M p 2 = [X(I - Y)(I + XY) + (XY) 2 JM 0 + B where X = 0.181, B = 6.55 and M 0 = 96.4
Regrind a sizable quantity of "First Pass" and extrude it at 100% to produce "Second Pass". Again save a quantity of this sheet for thermoforming study and regrind the rest. • Continue regrinding and reextruding for N passes where N is at least 3 and preferably 5. • Injection mold the various regrind passes to obtain samples for mechanical property evaluation. At the same time, injection mold virgin polymer to obtain samples for mechanical properties. • Test all samples according to the proper ASTM, DIN or ISO protocol. • From the injection molding data, determine the relative influence of the injection molding process on the material properties. This effect is important since each regrind step is subjected to injection molding after the extrusion process history and so this effect must be extracted from the experimental data. • Curve-fit the data to determine the appropriate mathematical models for the 100% regrind study. In particular, appropriate values are sought for M0, the virgin mechanical property, and X, the fraction of property retained after each pass through the extruder. Offset and asymptotic values and other ancillary values are determined at this point also. • Next, reestablish the extrusion processing conditions on 100% virgin. • If there is substantial property loss between the virgin polymer and "First Pass" regrind, dry-blend this regrind with virgin at 50:50 ratio. If the property loss is not significant until the Nth 100% regrind pass, dry-blend this regrind with virgin at 50:50 ratio. The objective here is to determine what law of mixtures is appropriate—linear or logarithmic. • Again injection mold the necessary test samples, and again back out the effect of injection molding on the property loss to establish the relative experimental effect
• • •
•
•
of regrind on appropriate mechanical properties. Then determine what law of mixtures is appropriate for each mechanical property. Return to the extruder and reestablish the processing conditions on 100% virgin. Dry-blend virgin and "First Pass" at 50:50 and run to steady-state. Collect it as "50:50 First Pass" and regrind this and dry-blend it with virgin at 50:50 to produce "50:50 Second Pass". Continue the above for N passes. Again injection mold each of these "50:50" passes, again test according to ASTM of DIN protocol, and again extract the effect of injection molding from the data. The purpose of this is to verify that the combined property loss model and the law of mixtures model predict the steady-state or infinite recycle physical properties. Note that this protocol includes a grinding step for each pass. The effect of grinding on the mechanical properties is usually much smaller than the effect of extrusion. However, if there is concern about mechanical damage induced by grinding, test samples can be pressed from extruded sheet. If there is concern about the thermal effects of thermoforming, the sheet saved from each pass can be thermoformed conventionally, then reground in the manner outlined for the extrusion/regrind protocol. In many cases, thermoforming may affect only one or two properties, such as color or fire retardancy. As a result, the testing level is substantially reduced.
Note that the protocol has several pivotal keys: • • •
It must be carried out on commercial equipment, to ensure that the thermal and shear histories are comparable to that expected in commercial thermoforming operations, Care must be taken to extract the effect of injection molding test samples from the data, and Regrind level must be at a level typical of thermoforming operations. The 50:50 ratio is chosen for this reason.
Many thermoformed products must meet performance criteria based on polymer material properties. The obvious purpose for this apparently elaborate protocol is to ensure that the polymer in the products being thermoformed has not deteriorated unduly during the regrinding and re-extrusion process. Example 7.20 illustrates how to obtain the necessary values for the arithmetical models. Example 7.20 Determination of Long-Term Physical Properties From Regrind Data The table below gives measured properties of 100% regrind and 50% regrind (in regular face type). Determine the method of predicting the effect of regrind level on physical properties. 100% Regrind (Extrusion) Number of passes Property value
0 1.00
1 0.90
2 0.81
3 0.73
4 0.66
5 0.59
6 0.53
OO
0
Mixed Regrind/Virgin (First Pass) Regrind level Property value
0 0.9
25% 0.88
50% 0.86
Mixed Regrind/Virgin (Second Pass) Regrind level Property value
0 0.9
25% 0.87
50% 0.86
Mixed Regrind/Virgin (oo Pass or Steady State) Regrind level Property value
0 0.9
25% 0.87
50% 0.82
From the 100% regrind data, or X = 0.900. The values for the 4th and higher regrinds are calculated and given in bold face in the table. Note that this predicts that the physical property goes to zero after an infinite number of 100% regrind cycles. The equation for Y fraction of recycle in virgin polymer is:
The calculated values are given in bold face in the tables for first pass, second pass and infinite pass or steady-state virgin/regrind ratio.
Cascading 100% Regrind The concept of cascading 100% regrind is growing in acceptance. As shown in Fig. 7.65, the process begins with 100% virgin sheet. (1 — Y) fraction of this sheet is converted into quality parts. The Y fraction of web, trim and other recyclable nonproduct sheet is reground and re-extruded as 100% regrind into new sheet. (1 — Y) of the reground sheet produces acceptable parts and the Y fraction of that is reground and recycled. After N passes, only YN fraction of the original virgin polymer remains. This is considered sufficiently small to be discarded. The philosophy behind cascading 100% regrind focuses on the following points: •
With closed-loop recycling, contamination simply goes around and around. As a result, it can accumulate to a level where the entire sheet is contaminated. This does not happen with the cascading process, where unacceptably contaminated regrind is simply discarded. • Even for relatively large recycle fractions, only a few cascades are needed before the economics favor discarding rather than re-extrusion.
Virgin (1-Y) Product Y(Trim) (1-Y)Y
Process
2
Y 2
(1-Y)Y Y3
(1-Y)YN YN
Figure 7.65 Cascade reprocessing or recycling of trim
•
Usually physical properties do not deteriorate dramatically, even with five or six trips through the process equipment. This is particularly true with polyolefins, especially polyethylenes.
The linear property loss algorithm for cascading 100% regrind is quite simple: (7.77) where N is the cascade number. The fraction of good parts is given as: (7.78) The term approaches unity as N-»oo. Example 7.21 compares cascading 100% regrind property loss with steady-state recycling. Cascading 100% regrind is feasible when the polymer property loss approaches an asymptote, so long as the asymptotic value yields a part with an acceptable property.
Example 7.21 Steady-State and Cascading Regrind In the current process, the polymer loses 10% of its tensile strength on one pass through the extrusion and thermoforming process. The trim loses no tensile strength on regrind and drying. If trim and off-spec parts comprise 40% of the extruded sheet surface, determine the steady-state tensile strength required in the virgin sheet. Then consider the cascade recycle scheme, where the trim and off-spec parts are discarded after three recycles. Assume the tensile strength properties are linearly additive.
The appropriate steady-state equation is:
According to the information, X = 0.9, Y = 0.4. As a result, M 0 = 1.185 • M 00 . In other words, the virgin polymer must have a tensile strength 19% greater than the design specifications. Theoretically 100% of the polymer is converted to good parts in a steady-state scenario. For the cascade scheme, the tensile strength of the acceptable parts must meet the design criterion after three passes through the processing equipment. The appropriate cascade equation is:
where N is the cascade number. For X = 0.9, M 0 = 1.372 • M 0 0 . In other words, the virgin polymer must have an initial tensile strength 37% greater than the design specifications. For the cascade process, the fraction of good parts for the three-pass scenario is:
or 93.6% of the initial amount of polymer is converted to good sheets. The remaining 6.4%o of the polymer is discarded.
7.8
General Guidelines for Part Design
If the part design has been thoroughly reviewed by all principals, improper mold design or unsuitable polymer choice should not be a cause of unacceptable parts. Unfortunately, in real life, improper mold design, part design, and poor choice of polymer still remain the major causes of product failure in the market place. For novel designs or experimental processes, extensive development and prototyping should be done far in advance of production manufacturing. Again, if everyone has reviewed all details and signed off on their portion of the program, few processing problems should be attributed to improper part design or other aspects of the thermoforming process. In addition to guidelines and steps to correct processing problems, certain do's and don'ts are sufficiently general to be considered as guidelines to thermoforming. In many cases, the items in the list that follows are helpful to the designers. However, designs that violate some of these can also be successful.
General Tips • •
Pressure forming is most economical for 5000 to 20,000 parts 1 . Pressure forming competes with injection molding at about one-fourth the mold cost and one-fourth to one-half the lead time.
1
Pressure forming details are given in Chapter 9 on advanced thermoforming techniques.
d Rod Heaters h
Sheet Figure 7.66 Rod heater spacing relative heater-to-sheet spacing
• •
Silicone is recommended when slip-sliding sheet from the rim to the mold cavity or as a topical lubricant on plugs. However, silicone cannot be used on a given application if it is not allowed in other parts of the plant. Sprayed vegetable oil is an effective FDA-approved temporary lubricant for certain parts. However, the oil breaks down after some time and so must be wiped from the molds on a regular basis.
Process Tips • • • • • • • • • • • 1 2
Most common plastics are formed in a temperature range of 200 to 4000F or 100 to 2000C. Sheet thicker than about 0.400 in or 10 mm is best heated in forced convection air ovens. Sheet thinner than about 0.010 in or 0.25 mm is best heated by direct contact hot plate. For rod heaters, the horizontal distance between heater elements should be less than the vertical distance between the element plane and the sheet (Fig. 7.66). The extent of sheet sag during heating is a useful and sometimes the only way of determining material formability. Filled or reinforced sheet rarely sags during heating. Short fiber-reinforced sheet "lofts" or grows in thickness when heated. As a result, a bladder is sometimes used to recompress the sheet during forming1. A cap-sheet will also minimize fiber prominence but at an increased cost. Low-density foam sheet increases in thickness as it is heated, due to internal gas pressure2. This results in a relatively poor free surface finish. In vacuum forming, the surge tank volume should be 6 to 20 times the free cavity volume. In vacuum forming, the vacuum should always be greater than 500 mm Hg or 20 in Hg and 710 to 725 mm Hg or 28 to 28.5 in Hg is standard. The faster the vacuum is applied, the better the draw-down becomes, to a point [84]. Other information is given in Chapter 9 on advanced thermoforming techniques. Other information is found in Chapter 9 on advanced thermoforming techniques.
• • • • • • • •
• • • • • • • • •
Excessive draw-down rate leads to excessive webbing. Slow vacuum draw-down requires hot molds for mold replication. Chatter lines on the formed part are due to variation in draw-down and hot sheet. The vacuum system should be carefully monitored. If small amounts of air are used for prestretching, the air does not need to be heated. If an excess of blowing air is used, it should be preheated to within 200F or 100C of the sheet temperature to minimize premature chilling of the sheet. This is particularly true with sequential twin-sheet forming. Woven stainless steel window screen is an effective temporary screen for pattern heating. Welded stainless steel wire is the desired permanent screen for pattern heating. Aluminum window screen can be used for pattern heating of a few parts but it usually oxidizes and falls apart quite quickly. Since it is easier to cut and is less expensive and more readily available than stainless steel, aluminum window screen is frequently used when developing new pattern heating profiles. Once the final shape is determined, the aluminum screen is used as a pattern for the more permanent stainless steel screen. If the formed shape is for an optical application, the hot sheet should not touch a cold surface during forming. In pressure forming, the mold and the pressure box should be mechanically or hydraulically locked together during forming. Bayonet locking, V-groove locking and overlap joints are typical ways of positively positioning pressure box and mold during pressure forming. A flexible silicone or neoprene gasket is usually required for adequate seal. Although air pressures to 500 lbf/in2 or 3.4 MPa have been used to pressure form composites, current practice uses 50 to 100 lbf/in2 or 0.34 to 0.7 MPa air pressure. Snap-back forming should actuate when the bubble top intersects a photocell beam. Matched die molding is needed when the sheet is normally too stiff at forming temperature to be easily vacuum drawn. Typical polymer states are PS foam, CPET, HDPE, PP, and short-fiber and mineral filled polymers. Typical matched die molding clamping pressures are 50 to 100 lbf/in2 or 0.34 to 0.7 MPa. Matched die molding is used if details are needed on both sides of the part or if the part design requires abrupt changes in wall thickness or direction. Coining or local matched die molding is used if details or dimensional tolerance is only needed in a small section of the part (Fig. 7.67).
Mold Tips • •
Owing to their high shrinkage values, crystalline polymers usually require moats in female cavities to prevent air leakage during forming (Fig. 7.68). The hotter the mold, the greater the final shape shrinkage becomes.
Sheet
Coining Plug
Mold
Figure 7.67 Coining or localized compression molding
Moat
Dam
Sheet
Mold
Figure 7.68 Moat and dam female mold configuration for polyolefins and other crystalline polymers
• • • • •
•
1
The colder the mold, the more nonuniform the wall thickness becomes for simple vacuum forming (Figure 7.69) [55]. The colder the mold, the more apparent chill marks become. Male molds are less expensive to make but require greater draft angles than female molds. Vacuum hole diameter should be less than the local sheet thickness to prevent nibbing. Vacuum holes should be bunched in two-dimensional and three-dimensional corners but are usually spaced along the part corners for appearance reasons. As a result, far more vacuum holes are used than are needed to evacuate the mold cavity. Typical vent hole spacing is about 1 in or 25 mm (Fig. 7.70). For twin-sheet forming, edge blow pins can be put in place just as the two sheets meet. Surface or puncture blow pins, on the other hand, need to be pneumatically or mechanically driven through the sheet as it contacts the mold surface1.
More information about twin-sheet thermoforming is given in Chapter 9 on advanced thermoforming techniques.
Sidewall Length, cm
Mold Temperature =700C
Side Wall Thickness, cm Figure 7.69 Effect of mold temperature on wall and corner thickness uniformity for simple vacuum forming [55]
Prestretch Tips • • •
Metal plug temperatures should be within 15 to 300F or 10 to 200C of the sheet temperatures to minimize plug marks on the sheet. Syntactic foam and plastic-surfaced plugs are not heated. Plugs with good surface slip reduce but do not eliminate the need for close temperature control.
1 inch or 25 mm Vent Holes
Figure 7.70 Classic vent hole spacing on heavy-gage two-dimensional horizontal corners
Plug Action
Positive Textured Surface Mold Vent
Figure 7.71 Plug forming against the positive, textured surface on male molding
• •
Plugs can be used on textured appearance surfaces (Fig. 7.71). A typical initial prestretch depth equals half the narrowest unformed sheet dimension. Thus for a 100 in x 200 in rectangle, 50 in is a beginning good prestretch depth (Fig. 7.72). • If the prestretch bubble is unstable when blown with air pressure, substitute a vacuum prestretch box. • In snap-back forming, an optimum bubble height is 2/3 the draw ratio or H:D = 2:3 (Fig. 7.73).
Plug
H/2 Sheet
Mold
Figure 7.72 Recommended starting plug depth for symmetric parts
H
D/2
d = 2D/3
Bubble Sheet
Mold
H
Figure 7.73 Recommended starting bubble height for symmetric parts
Part Design Tips •
Specification on part thickness should be on the thinnest allowable wall thickness needed for mechanical performance. • If mold features need to be optically or visually read, their dimensions must be at least three times the local sheet thickness (Fig. 7.74). • Female molds produce parts with thick rims and thin bottoms. • Male molds produce parts with thick bottoms and thin rims. • Typical female draft angles are 0° to 2°, with an average of about \° to 1° (Fig. 7.75). • Typical male draft angles are 1° to 5°, with the average of about 4° (Fig. 7.76). • As with injection molding, draft angles must be increased to compensate for texturing on perpendicular parts. Typically, 1° of draft per 0.2 thousandths depth of texture is acceptable. • For textured details to be sharp in traditional vacuum forming, their depth should be greater than the local sheet thickness (Fig. 7.77). • A wide variety of textures and patterns are now possible with pressure forming. However, common aesthetic sense must prevail when placing different textures and patterns on the same part. Sheet h H>3h Figure 7.74 Recommended relative mold dimensions for readable features
Mold
0 to 2 Minimum Mold
Figure 7.75 Draft angle range for female molds
Mold
1 to 5° Minimum
Figure 7.76 Draft angle range for male molds
No Detail
H>h h
No Sharp Corners Figure 7.77 Traditional vacuum forming into mold details
•
• • • • • •
For fine texture detail with vacuum forming, textured sheet is used. Care must be taken in reducing thickness by more than 30%, particularly in corners, as the texture washes easily. Forming is usually done at the minimum possible forming temperature. Any draft is better than no draft at all. The largest amount of draft that fits within the constraints of the part requirements should be specified. Deep undercuts should have generous corner radii. Otherwise the part corner will be very thin (Fig. 7.78). Parts with undercuts should be stripped from the mold with strippers pushing uniformly against the part rim (Fig. 7.79). Deep undercuts require actuation for part removal even for very ductile or soft polymers. Otherwise extensive scuffing or tearing may occur. Both external and internal threads can be molded in with twin-sheet thermoforming (Fig. 7.80).
Very Thin Corner
Figure 7.78 Draw into undercuts more successful if radii are generous Ejector Plate Sliding Core
Figure 7.79 Undercuts stripped by (left) ejector plate or (right) sliding core
• • • • • •
Partial internal threads are possible by secondary action with single-sheet thermoforming (Fig. 7.81). Typical part shrinkage for amorphous polymers is on the order of 0.5% for male molds and 1% for female molds. Typical part shrinkage for crystalline polymers is on the order of 2% for male molds and 2% to 3% for female molds. 50% to 75% of part shrinkage occurs before the part temperature has fallen to its heat distortion value. For simple vacuum forming, an easy to form radius is 4 times thickness of the starting sheet (Fig. 7.82a). For simple vacuum forming, the minimum recommended radius of any twodimensional or three-dimensional corner is equal to the thickness of the starting sheet (Fig. 7.82b).
Top Mold Trim Line a)
Bottom Mold
Top Mold Trim Line
b) Internal Thread Automatically or Manually Unsceewed Bottom Mold Figure 7.80 Twin-sheet forming of male thread (a) and female thread over unscrewing mandrel (b)
Trim Line
Sheet
Mold
Unscrewing Threaded Core
Figure 7.81 Molding over unscrewing core, then trimming for bung
a)
b)
Figure 7.82 Recommended easy-to-form relative radius (a) and minimum relative radius (b)
• • •
Pressure forming allows outside corner radius of 0.015 in for most polymers. Higher sheet temperature is required for smaller radii corners (Fig. 7.83) [56]. Chill marks are usually an indication of rapid thickness change. They are caused by slow vacuum, a cold mold, or an inherent yielding of the polymer at the forming temperature. • Lakes or shiny spots on parts indicate inadequate vacuum or air trapped between the sheet and a highly polished mold. • The extent to which a plastic sheet is stretched is a strong function of its hot strength. However, areal draw ratios are usually less than 5, linear draw ratios are less than 3 and H:D ratios are less than 1. • When notch-sensitive plastics such as PA or nylon, PMMA and PS are drawn into sharp corners, the parts may fail because of the inherent brittleness of the polymer. • Parts with acute angles or angles of less than 90° can be notch-sensitive regardless of the polymer. • Polarized filters aid in detecting highly stressed regions in transparent PS, PC, PET and PMMA parts. • The diameters of solvent-welded bosses should be proportional to the sizes of the metal inserts to minimize torsion cracking during component assembly (Fig. 7.84). • Dimensional tolerances are rarely specified on free or non-tool surfaces. • To attain local accuracy in sheet thickness, a heavier gage sheet should be formed and the local area routered to the correct thickness (Fig. 7.85). • Typical dimensional tolerances are 1% on small parts and 0.2% on large parts.
H:D = 1:2
Corner Radius, cm
,OPS
r
RPVC CA
FPVC SAN PVAQ
S-B
CAP PET Copolymer
CAB
Sheet Temperature,0C Figure 7.83 Temperature-dependent corner radius for several polymers for H:D = 1:2 draw ratio female part, redrawn from [56]
Figure 7.84 Recommended relative solvent- or thermally-welded boss dimensions
•
Sheet thickness tolerance is about 5% on medium and heavy gage sheet. This tolerance should be doubled and added to the dimensional tolerance for inside dimensions on parts formed in female molds. • Stiffening ribs, corrugations, flutes and multiple cones are typical ways of stiffening thermoformed parts. • Increase stiffness on large surface area parts by adding a slight dome, of 0.15 in/in, adding concentric ribs, or adding radial ribs (Fig. 7.86).
* > design
Sheet Mold
Design
Figure 7.85 Routering high tolerance areas in heavy-gage sheet Reinforcing Rings
0.15 in/in
Ribs
Figure 7.86 Using doming, reinforcing rings and/or radial ribs to minimize optical distortion, eversion in thermoformed disks
h
A > 3h/2
Figure 7.87 Recommended rib height and spacing to minimize distortion in flat parts. Redrawn from [57,58]
Trim Line
Figure 7.88 Method of forming slots or vents by machining away rib tops Dam Vacuum Loss Ridge Polyethylene Sheet
Polyethylene Sheet
Mold Figure 7.89 Vacuum loss ridge formed on crystalline polymers Finish Surface
Trim Line
Figure 7.90 Method of forming non-view slots or vents by machining away rib tops
• • • • • • •
Distances between multiple male ribs or corrugations should be greater than D = 1.5 • H where H is the height of the rib (Fig. 7.87) [57,58]. The guideline above holds also for rows of slots, where the top portion of the rib is removed by routering (Fig. 7.88). An unexpected ridge at the rim of a polyolefin female part is an indication of air leakage during cooling (Fig. 7.89). Shrinkage of fiber-reinforced parts is less important than dimensional changes due to "spring-back" or elastic recovery once the applied forces are removed. Non-view slots require side-core action and pressure to achieve detail in the acute angled areas (Fig. 7.90). Non-view slots in a female part are best designed with the inside of the slot facing up (Fig. 7.91). This accommodates the natural drape of the sheet. Whenever possible, slots on vertical sides of female parts should run parallel to the rim rather than vertical (Fig. 7.91). This minimizes differential distortion between ribs and the splittiness of the uniaxially oriented polymer in vertical walls.
Forming Direction
Ventilation Slots
Figure 7.91 Recommended orientation of horizontal non-view slots relative to forming direction
•
Although some progress has been made in properly indexing the side core extension during stretching to better stretch sheet in the slot region, fully extended side cores are nearly always used.
Rim and Edge Designs There are usually fundamental differences in the functions of the edges of heavy-gage and thin-gage parts. For heavy-gage parts, the edge left by trimming of both in-plane and contoured parts is frequently acceptable for the particular application. If the part edge is not assembled or inserted into other parts, further finishing such as sanding or flame polishing may be needed to achieve the desired appearance edge1. If thermoformed parts are to be adhesively bonded, appropriate traps for the adhesive bead are formed into the part edges (Fig. 7.92) [59]. As with all thermoformed parts, appropriate draft angles and shrinkage factors must be applied to ensure adequate seal with the minimum amount of adhesive used. The classic example of rim treatment of thin-gage parts is the rolled rim (Fig. 7.93). Although rim rolling is a standard method of reinforcing the rim region of a round thin-gage part such as a cup or a tub, rim rolling is used on occasion for oval, 1
The design of the edge of a twin-sheet formed part is covered in detail in Chapter 9 on advanced thermoforming techniques.
Adhesive Trap
Adhesive Traps
Figure 7.92 Formed-in adhesive traps for assembling, twin-sheet forming
elliptical or oblong parts with generous corner radii. The standard method of rim rolling is shown in schematic in Fig. 7.94. Typically, a heated air jet is directed against the spinning part while the part is held against a simple edge forming fixture. The process is continuous at about 5,000 to 10,000 cups/h. Although there appears to be no science in determining the dimensions of a rim in rim roll design, some guidelines can be established. The bending strength of a round rim is compared with the bending strength of the flat sheet of plastic needed to form the rim in the following way: The deflection, ymax, of a simply supported beam of width b and length L loaded in the center is given as: (7.79) where I is the moment of inertia, P is the applied load and E is the polymer modulus. This equation is applicable to both the flat sheet and the rolled rim for slight bending loads. Therefore the ratio of deflections is given as: (7.80) For the flat sheet, the moment of inertia is: (7.81) For the rolled rim, the moment of inertia is: (7.82)
Circular Rolled Lip
Flat Rolled Lip Figure 7.93 Two types of rolled rims beginning with formed flat
Rod Heaters Formed Cup Inventory
Articulated Rim Rolling Tool Timing Screw
Figure 7.94 Schematic of rim rolling with timing screw feed and articulated rim rolling tool
where r is the radius of the roll. But 2nr = b. Therefore Equation 7.80 is written as: (7.83)
Equation 7.83 shows that so long as b > 3.85 • t, the deflection of a rolled rim is always less than the deflection of a flat rim. To put it another way, the rolled rim is stiffer than the equivalent flat rim. Example 7.22 also shows a similar effect for the folded rim of Fig. 7.93. Capillarity in rolled rims is a problem when the product is used as a drink cup. Since the rim is usually not sealed, liquid wicks into the roll tube. Capillary action then forces the liquid up the roll tube, with the result being that the rim "leaks", or acts as the thermoforming equivalent of a "dribble glass". Capillary action depends on the surface tension of the liquid, a, the wettability of the liquid with the wall, the radius of the tube, r, and the density of the liquid, p. The appropriate expression is: (7.84)
Example 7.22 Rim Stiffness Determine the relative stiffness of a rolled rim if the sheet thickness is 0.030 in and the flat rim width is 1.5 in. What is the roll radius when the flat rim width is 0.75 in? What effect does this have on stiffness of the rolled rim? Then determine the stiffness if the flat rim is simply folded.
From Equation 7.83:
From the data given, t = 0.03, b = 1.5, and the roll radius is 0.24 in. The deflection ratio is 0.00263. Or the rolled rim is nearly 400 times stiffer than the flat rim. For the narrower rim, where b = 0.75 in, the roll radius is 0.120 in and the deflection ratio is 0.0105 or the rolled rim is about 100 times stiffer than the flat rim. The deflection ratio for the double thick, half-width rim is:
For the flat sheet, the moment of inertia is: For the double-flat, the moment of inertia is: Therefore the deflection ratio is:
The double flat has only 25% the deflection as the original flat, but the double flat is still nearly 100 times more flexible than the roll.
where y is the liquid height, 0 is the contact angle between the liquid and the tube wall, and g is gravitational constant. For pure water the surface tension is 60 dyn/cm. For other drinkables such as beer or soda, the surface tension is about 30 dyn/cm. The contact angle for water with glass is 0° and for water with paraffin is 107°. For contact angles less than 90°, the interfacial meniscus is positive and liquid rises in the tube. For contact angles greater than 90°, the interfacial meniscus is negative and the capillary liquid level is below the bulk liquid level. For polymers such as PS and PET, the contact angle is on the order of 0° and the cos 0 ^ 1 . For polymers such as PP and PE, the contact angle may be as high as 90°. For these, cos 0 ^ 0 and there is no capillarity. This implies that the leaking effect is maximum with PS and PET and is minimized with olefins. Example 7.23 illustrates the relationship between rim roll radius and capillary height. Example 7.23 The Leaking Rim Roll Using the information from Example 7.22, determine the height of the capillary, assuming it is closed along the rolled side. Assume the contact angle is 0° and the surface tension is 30 dyn/cm. The liquid is water. If the distance from the lowest point of the rim to the edge of a person's Hp is 0.25 in, will either of the two rim dimensions leak? At what radius will the rim begin to leak?
The operative equation is:
For the data given: For r = 0.24 in = 0.61 cm, y = 0.1 cm = 0.040 in. For r = 0.12 in = 0.305 cm, y = 0.2 cm = 0.080 in. Neither of these values is greater than 0.25 in, so neither will leak. Using y = 0.25 in = 0.635 cm, the minimum radius for a non-leaking rim is r = 0.096 cm = 0.04 in. Design—A Comment There are many sources for plastic part design information [60-63]. The emphasis above is on fundamental design tools. Full understanding of these tools is not always required to design thermoformed parts. However, these tools are being used to meet increasingly stringent design standards. Beall [60] notes that overall final piece part inaccuracies today are caused by: • • • •
Tooling-associated inaccuracies, Sheet-to-sheet and run-to-run variations, Female versus male tooling, Piece part geometry,
• • •
Specifics of the vendors' manufacturing processes, Operator skill and training, and Tooling maintenance procedures.
He further recommends that the customer carefully select "... a vendor with proven capabilities to meet the designer's tolerance requirements." The tools described above should enable all par ties to better minimize final part inaccuracies.
1.9
References
1. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, and Tests for Design, Hanser Publishers, Munich (1993), p. 504. 2. M. Mooney, Symposium on Consistency, American Society for Testing and Materials, Philadelphia (29 Jun 1937), pp. 9-12. 3. S. Turner, Mechanical Testing of Plastics, 2nd Ed., George Godwin, London (1983), p. 187. 4. C.Chastain, 4Tn Designing With Plastics, How Much Should You Trust ASTM Test Data?", Machine Design, 42\ 2 (23 Jan 1975), p. 108. 5. S. Turner, Mechanical Testing of Plastics, 2nd Ed., George Godwin, London (1983), p. 181. 6. J.L. Throne, "Computer-Aided Engineering for Thermoforming—The Latest Improvements and What's Coming Next", SPI Conference Proceedings, National Plastics Exposition (7 Jun 1994). 7. J.L. Throne, "Effect of Recycle on Properties and Profits: Algorithms", Adv. Polym. Tech., 7 (1987), pp. 347-360. 8. Additional information available from Sanders Prototype Inc, Wilton NH. 9. J.L. Throne, "Computer Aided Engineering for Thermoforming—The Latest Improvements and What's Coming Next", 7 June 1994, NPE '94 Conference Proceedings, Vol. I. 10. M. Burns, Automated Fabrication: Improving Productivity in Manufacturing, Prentice Hall, Enlewood Cliffs NJ (1993). 11. D.S. Cummings, "Utilizing Stereolithography to Produce a Rapid Prototype Thermoforming Mold", SPE ANTEC Tech. Papers, 40 (1994), pp. 3550-3554. 12. L.R. Schmidt and J.F. Carley, "Biaxial Stretching of Heat Softened Plastic Sheets Using an Inflation Technique", Int. J. Eng. ScL, 13 (1975), pp. 563-578. 13. H. Voigt, "Lehrgang fur Thermoformung", Paul Kiefel Thermo formmaschinen GmbH, IndustriestraBe 17-19, Postfach 16 60, D-8228 Freilassing Germany, undated, p. 3.4.1. 14. N. Rosenzweig, M. Narkis and Z. Tadmor, "Wall Thickness Distribution in Thermoforming", Polym. Eng. Sci., 19 (1979), pp. 946-951. 15. M.O. Lai and D.L. Holt, "The Extensional Flow of Poly(methyl Methacrylate) and HighImpact Polystyrene at Thermoforming Temperatures", J. Appl. Polym. Sci., 19 (1975), pp. 1209-1220. 16. D. Gruenwald, Thermoforming: A Plastics Processing Guide, Technomic Publishing Co., Inc., Lancaster PA (1987), p. 57. 17. L.R. Schmidt, "Biaxial Stretching of Heat-Softened Plastic Sheets", Ph.D. Dissertation, Univ. Colorado, Boulder CO (1972), p. 129. 18. CJ. Benning, Plastic Foams, Vol. 1, Wiley-Interscience, New York (1969), p. 86. 19. Anon., "Volara Vacuum Forming Guide", Voltek, Division of Sekisui America Corp., Lawrence MA (Jan 1984). 20. R J . Crawford and S.K.L. Lui, "Prediction of Wall Thickness Distribution in Thermoformed Mouldings", Euro. Polym. J., 18 (1982), pp. 699-705. 21. S. Timoshenko and J.N. Goodier, Theory of Elasticity, 3rd Ed., McGraw-Hill Book Co., New York (1968), p. 207.
22. J.G. Williams, Stress Analysis of Polymers, 2nd Ed., Ellis Harwood Ltd/Halsted Press, London (1980), p. 240. 23. J.L. Throne, Thermo forming, Carl Hanser Verlag, Munich (1987), Table 7.11, p. 201. 24. N. Rosenzweig, "Wall Thickness Distribution in Thermoforming", SPE ANTEC Tech. Papers, 29 (1983), pp. 478-482. 25. J.L. Throne, Thermoforming, 1st Ed., Carl Hanser Verlag, Munich (1987), Table 7.12, pp. 204-205. 26. H. Fukase, "Prediction of Wall Thickness Distribution in Blow Molded Articles", I.H.I. Engineering Review, 75:1 (Jan 1975). An English language copy of this paper is available from Hisahiko Fukase, Researcher, Machinery Department, Ishikawajima-Harima Heavy Industries Co., Ltd., Research Institute, 1, Shinnakaharamachi, Isogoku, Yokohama Japan. 27. J.L. Throne, "New Concepts in Thermforming", Polym.-Plast. Techn. Eng., 30 (1991), pp. 761-808. 28. J.L. Throne, "Guidelines for Thermoforming Part Wall Thickness", Polym.-Plast. Techn. Eng., 30 (1991), pp. 685-700, Figure 3. 29. J.L. Throne, "Guidelines for Thermoforming Part Wall Thickness", Polym.-Plast. Techn. Eng., 30 (1991), pp. 685-700, Figure 4. 30. J.L. Throne, "Guidelines for Thermoforming Part Wall Thickness", Polym.-Plast. Techn. Eng., 30 (1991), pp. 685-700, Figure 6. 31. J.L. Throne, "Computer-Aided Engineering for Thermoforming—The Latest Improvements and What's Coming Next", SPI Conference Proceedings, National Plastics Exposition (7 Jun 1994), Figure 5. 32. H.G. DeLorenzi and H.F. Nied, "Finite Element Simulation of Thermoforming and Blow Molding", Chapter 5, in A.I. Isayev., Ed., Modeling of Polymer Processing, Hanser Verlag, Munich (1991). 33. W.N. Song, F.A. Mirza, and J. Vlachopoulos, "Finite Element Analysis of Inflation of an Axisymmetric Sheet of Finite Thickness", J. RheoL, 25 (1991), pp. 93-102. 34. K. Kouba and J. Vlachopoulos, "T-FORMCAD: A Finite Element Software Package for Thermoforming and Blow Molding", Accuform Co., Ltd., and CAPPA-D, Dept. Chem. Eng., McMaster University, Hamilton ON, Canada (1993). 35. W. Song, "Large Deformation Finite Element Analysis for Polymer Forming Processes", Ph.D. Dissertation, McMaster University, Hamilton, Ontario CAN (1993). 36. K.H. Huebner, The Finite Element Method for Engineers, John Wiley & Sons, New York (1980), p. 6. 37. L.R.G. Treloar, "Stress-Strain Data for Vulcanized Rubber Under Various Types of Deformation", Trans. Faraday Soc, 40 (1944), pp. 59-70. 38. L.R.G. Treloar, "Strains in an Inflated Rubber Sheet, and the Mechanism of Bursting", Trans. Inst. Rubber Ind., 19 (1944), pp. 201-212. 39. J.L. Throne, "Modeling Plug-Assist Thermoforming", Adv. Polym. Tech., 9 (1989), pp. 309320. 40. J.G. Williams and H. Ford, "Stress-Strain Relationships for Some Unreinforced Plastics", J. Mech. Engrg. Sci., 6 (1964), pp. 405-417. 41. J.L. Throne, "Some Design Guidelines for Plug Assists", SPE ANTEC Tech. Papers, 39 (1993), Figure 3, pp. 182-190. 42. J.L. Throne, "Some Design Guidelines for Plug Assists", SPE ANTEC Tech. Papers, 39 (1993), Figure 4, pp. 182-190. 43. W. Song, "Large Deformation Finite Element Analysis for Polymer Forming Processes", Ph.D. Dissertation, McMaster University, Hamilton, ON Canada (1993), Figure 6.9. 44. J.L. Throne, "Plug-Assist Thermoforming—A New Design Protocol for Rectangular Parts", Polym.-Plast. Techn. Eng., 30 (1991), pp. 685-701. 45. J.L. Throne, "Some Design Guidelines for Plug Assists", SPE ANTEC Tech. Papers, 39 (1993), Figure 5, pp. 182-190. 46. K. Kouba, O. Bartos, and J. Vlachopoulos, "Computer Simulation of Thermoforming in Complex Shapes", Polym. Eng. Sci., 32 (1992), pp. 699-704.
47. R.L Tanner, Engineering Rheology, Clarendon Press, Oxford (1985), pp. 202-207. 48. J.L. Throne, "Plug-Assist Thermoforming—A New Design Protocol for Rectangular Parts", Polym.-Plast. Tech., Eng., 30 (1991), pp. 685-701. 49. W. Song, "Large Deformation Finite Element Analysis for Polymer Forming Processes", Ph.D. Dissertation, McMaster University, Hamilton, ON Canada (1993), Figure 6.16. 50. J.L. Throne, "Effect of Recycle on Properties and Profits: Algorithms", Adv. Proc. Tech., 7 (1987), pp. 347-360. 51. J.W. Shea, E.D. Nelson and R.R. Cammons, "The Effect of Recycling on the Properties of Injection Molded Polycarbonate", SPE ANTEC Tech. Papers, 21 (1975), pp. 614-617. 52. S.B. Driscoll, "Thermoplastic Resin Regrind Study", SPE ANTEC Tech. Papers, 23 (1977), pp. 536-538. 53. P. Basile, C. Jolicoeur and H.P. Schreiber, "Polymer Reprocessing: Properties of PolyethylenePolyvinyl Chloride Mixtures", SPE ANTEC Tech. Papers, 2(5(1980), pp. 475-477. 54. M. Heneczkowski, "Weather Resistance of PS After Multiple Processing", Kunststoffe, 83 (1993), pp. 473-475. 55. M.A. Sheryshev, LV. Zhoyolev and K.A. Salazkin, "Calculation of Wall Thickness of Articles Produced by Negative Vacuum Forming", Soviet Plastics, 7 (1969), Figure 2, pp. 30-34. 56. W.A. Nietzert, "Die Thermoformung von Kunststoff-Folien", Plastverarbeiter, 27: 5 (1976), Figure 17, pp. 244-249. 57. H. Oelze, "Verformen von PVC-Hartfolien", Kunststoffe, 47(1957), Figure 17, pp. 9-14. 58. G.L. Beall, TFl (Thermoforming Software), IDES, Inc., Laramie WY, 1990. 59. Anon., "Structural Adhesives for the Transportation Industry Worldwide", ITW Adhesive Systems, Farmington MI, Bulletin TGl (Jan 1993). 60. G.L. Beall, "Solving the Plastic Product Design and Development Puzzle", Seminar, University of Wisconsin-Milwaukee, Milwaukee (18-22 Apr 1994). 61. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, and Tests for Design, Hanser Pub Ushers, Munich (1993), Section 6.1. 62. R.A. Malloy, Plastic Part Design for Injection Molding, Hanser Publishers, Munich (1994). 63. B.S. Benjamin, Structural Design with Plastics, 2nd Ed., Van Nostrand Reinhold Co., New York (1982). 64. Crawford and Lui [20] call areal draw ratio "stretching ratio" or "stretch ratio". 65. W.L. Gheen, "Computer Aids to Thermoforming: Stretch Factor and Average Formed Thickness", SPE ANTEC Tech. Papers, 30 (1984), pp. 748-749. 66. L.R. Schmidt and J.F. Carley, "Biaxial Stretching of Heat-Softened Plastic Sheets: Experiments and Results", Polym. Eng. Sci., 15 (1975), pp. 51-62, especially footnote, p. 60. 67. A Kobayashi, Machining of Plastics, McGraw-Hill Book Co., New York (1967), p. 44, Table 2.1. 68. A.S. Lodge and H.G. Howell, "Nonlinear Elastic Properties of Molten Plastics", Nonlinear Elasticity, Symp. Proc. Phys. Soc, 76B (1974). 69. H. Chang and R. A. Daane, "Coefficients of Friction for Solid Polymers in Various Forms", SPE ANTEC Tech. Papers, 20 (1974), pp. 335-. 70. G.A. Taylor, "Finite Element Simulation of Thermoforming - Experiments and Analyses", SPE ANTEC Tech. Papers, 35 (1989), pp. 435-437, Figure 5. 71. C M . Campbell, "Designing for Thermoforming", Materials Presented, Distributed at SPE Thermoforming Symposium & Workshop, Arlington TX (20 Mar 1984). 72. J.L. Throne, "Some Design Guidelines for Plug Assists", SPE ANTEC Tech. Papers, 39 (1993), pp. 182-190. 73. H. Voigt, "Lehrgang fur Thermoformung", Paul Kiefel GmBH, 8228 Freilassing, Industriestrae 19 (Undated), p. 3.4.1. .pa 74. M.O. Lai and D.L. Holt, "Thickness Variation in the Thermoforming of Poly(methyl Methacrylate) and High-Impact Polystyrene Sheets", J. Appl. Polym. Sci., 19 (1975), pp. 1805-1814. 75. A.M. Voskresenskii, Ya.C. Neiman and Y.V. Nikitin, "Kinetics of Cooling a Deformable Sheet Thermoplastic Blank During Vacuum Forming", Plast. Massy (Feb 1975), pp. 27-28. 76. M. A. Vilyaf, CL. Moskovskii, Y. V. Nikitin, and V.I. Bichgalter, "Calculation of the Nonuniformity of Thickness of Cylindrical Vacuum Pneumatic Formed Products", Plast. Massy (May 1976), pp. 34-36.
77. Y.V. Nikitin and T.G. Shlyakhova, "Evaluation of the Moldability of Sheets Made of ImpactResistant Polystyrene", Plast. Massy (Jan 1979), p. 55. 78. Y.V. Nikitin, T.G. Shlyakhova and H.M. Efremova, "Thermomechanical Analysis of Sheets Made of High-Impact Polystyrene", Plast. Massy (May 1982), pp. 42-43. 79. Y.V. Nikitin and T.G. Shlyakhova, "Effect of Properties of Impact-Resistant Polystyrene Sheets and Their Draw Ratio on the Properties of Thermoformed Parts", Plast. Massy (May 1983), pp. 32-39. 80. Y.V. Nikitin, T.G. Shlyakhova and E.A. Belova, "Effect of Cooling on Residual Stresses in Thermoformed Parts", Plast. Massy (Aug 1983), pp. 27-28. 81. Y.V. Nikitin, T.G. Shlyakhova and P.B. Chudinov, "Effect of the Properties of Sheet and Their Uniaxial Drawing Ratios on the Properties of Thermoformed Parts", Plast. Massy (Sep 1984), pp. 24-26. 82. Y.V. Nikitin, T.G. Shlyakhova, T.A. Burdeinaya and V.V. Scherbak, "Effects of the Stress State on Impact-Resistant PS Sheets and the Rate of Their Drawing on the Properties of Thermoformed Products", Plast. Massy (Aug 1986), pp. 30-32. 83. M.A. Scheryschew and LK. Gawrilow, "Vakuumformung von Form teilen aus Kautschukmischungen", Plast. Kautschuk, 25:2 (Feb 1978), pp. 95-98. 84. A.R. Ragab and S.A. Khorshied, "A Simplified Model for Prediction of Processing Time in Pressure Thermoforming", Plast. Rubber Proc. Appl., 6(1986), pp. 21-27. 85. C.J.S. Petrie and K. Ito, "Prediction of Wall Thickness of Blow Moulded Containers", Plast. Rubber: Proc, 5 (1980), pp. 68-72. 86. J.L. Throne and M. Kmetz, "Computer-Aided Design in Thermoforming", Plast. Eng., 45:9 (Sep 1989), pp. 35-38. 87. H. Fukase, A. Iwaaki, and T. Kunio, "A Method of Calculating the Wall Thickness Distribution in Blow Molded Articles", SPE ANTEC Tech. Papers, 24 (1978), pp. 650-652. 88. W.A. Neitzert and H J . Schmidt, "Die Thermoformung von Kinststoff-Foilen", Plastverarbeiter 77(1966), pp. 493-498. 89. W.A. Neitzert and H J . Schmidt, "Die Thermoformung von Kunststoff-Folien", Plastverarbeiter 7^ (1967), pp. 316-322. 90. W.A. Neitzert and H J . Schmidt, "Die Thermoformung von Kunststoff-Folien", Plastverarbeiter 7^ (1967), pp. 537-541. 91. A. Hoger, Warmformen von Kunststoffen, Carl Hanser Verlag, Munich (1971), p. 61. 92. J.L. Throne, Thermoforming, Carl Hanser Verlag, Munich (1986).
Appendix 7.1 Draw Ratios for Truncated Cone As shown in Fig. 7.95, a sheet that is partially drawn into a cone of slant height s, depth h and diameter d and cone angle p is divided into the frustum of a cone and a spherical cap. R = d/2, the cone radius at the rim. If r is the indeterminate radius at the bottom of the frustum, the frustum area is: (7.1.1) Ji1 is related to h by: (7.1.2) and h = R tan (3. The area of the spherical cap is: (7.1.3)
R=d/2
hi h
H
Figure 7.95 Geometric factors for draw-down into full right cone of angle
But
So: (7.1.4)
Now r = a cos P and 5 = a(l — sin p). Thus: (7.1.5) The total area, in terms of r, is: (7.1.6) Areal Draw Ratio The areal draw ratio is: (7.1.7) For full draw-down into P = 60° cone, Ra = 2. The relationship between r and H, the depth of the formed part, H < h, is: (7.1.8) The areal draw ratio, in terms of measured depth of draw, H:D, is: (7.1.9)
For a 60° cone: (7.1.10) Linear Draw Ratio The slant height s down the cone frustum is given as: (7.1.11) (7.1.12) The distance across the cap is: (7.1.13) where oc is the base half-angle in radian, oc = TC/2 — P'. In terms of r: (7.1.14) The linear draw ratio, RL, is: (7.1.15) (7.1.16) For P = 60° cone: (7.1.17) RL = 2 for full draw, r = R. In terms of measured depth of draw, H:D, RL is: (7.1.18) For 60° cone: (7.1.19)
Appendix 7.11 Mechanical Property Loss in Regrind Consider the simple regrind scheme in Fig. 7.96. The following assumptions are made: • • • •
After each processing step, the mechanical property is X times that of the polymer property before processing. For each unit of polymer processed, Y units are reground. A composite mechanical property is obtained from the properties of the virgin polymer and the regrind according to a linear law of mixtures. As a result, 0 < X < 1 and 0 < Y < 1.
Process
Figure 7.96 Schematic of steady-state recycle loop, including extrusion and thermoforming effects but ignoring regrind effects
The following definitions hold: • • • •
Mo is the mechanical property of the virgin polymer. Mr is the mechanical property of the regrind. Mm is the mechanical property of the mixture. Mp is the mechanical property of the process polymer system.
For the first pass, there is no regrind. thus: (7.II.1) For the second pass: (7.II.2) But: (7.II.3) And: (7.II.4) Therefore: (7.II.5) For the third pass: (7.II.6) But: (7.II.7) And: (7.II.8) Therefore: (7.II.9) For the Nth pass: (7.II.10) But: (7.II.11)
Therefore, for the Nth pass: (7.II.12) For an infinite number of cycles, N - * oo: Since (XY)
(7.II.13)
And: (7.II.14) For X = 0.9, Y = 0.5: After After After After After After
1 pass, 2 passes, 3 passes, 8 passes, 20 passes, oo passes,
Mp1ZMo = 0.9 Mp 2 /Mo = 0.855 Mp 3 /Mo = 0.835 Mp 8 /Mo = 0.8185 Mp20/Mo = 0.8182 Mp/Mo = 0.8182
Thus, after three cycles, in this example, accuracy is within 2% of the limiting vales, which is usually well within experimental standard deviation.
8 Producing Sheet and Film 8.1
Introduction
8.2
Forming Thin Films
8.3
Forming Sheet Single-Screw Extrusion Filtering the Polymer Flow Improvement Devices Pressure and Temperature in Extruder Sheet Die Concepts Gage Thickness Monitoring and Control Twin-Screw Extrusion
8.4
Roll Stacks
8.5
Sheet Trimming
8.6
Take-Off and Take-Up Rolls
8.7
Residence Time and Residence Time Distribution Through Extruder and Die
8.8
Drying
8.9
Producing Biaxially Oriented Sheet
8.10 Multilayer Sheet Formation Coextrusion Lamination 8.11 Sheet Quality and Quality Control Sheet Dimension Orientation Sheet Squareness and Flatness Moisture Sheet Appearance Annoyance Factors Lamination Quality 8.12 References
8.1
Introduction
To produce their final products, injection molders, extruders and blow molders begin with polymer resin in the form of pellets or powders. Thermoformers produce their final products from sheet or film purchased from a converter or the processor who converts the polymer resin. The production of the sheet or film by extrusion or one of a handful of allied processes that impart shear and heat to the polymer resin adds economic and physical property penalties to the process. In addition, a substantial portion of the sheet or film is not formed into product and that portion must be returned to the converter for additional reprocessing. While the details of the conversion process are not of paramount importance to the thermoformer, the quality of the sheet or film is. The emphasis in this chapter, then, is on an understanding of those aspects of the conversion process that most affect the performance of the sheet as it passes through the thermoforming process: • Thermal history, • Shear history, • Residence time in the conversion equipment, • Techniques in drying, • Aspects of the chill roll, such as: Roll diameter, Roll temperature, and Roll texture, • Bank buildup, • Machine direction and cross-machine direction orientation, • Methods of orienting sheet, • Effect of processing on polymer morphology, • Desirable molecular weight for extrusion v. that for thermoforming, • Sheet gage measurement and control, • Identification and sourcing of surface defects, • And so on. As a result, this chapter presents a general overview of the conversion process, with primary focus on single-screw extrusion through a sheeting die, the most common method of producing thermoformable sheet. The technical aspects of extrusion are given elsewhere1. 1
There are many sources of technical information on extrusion and extruder screw design. Some of these are: P.N. Richardson, Introduction to Extrusion, Society of Plastics Engineers, Greenwich CT (1974). J.L. White, Twin Screw Extrusion: Technology find Principles, Hanser Publishers, Munich (1991). R T . Fenner, Extruder Screw Design: Solutions to Polymer Melt Flow in Extrusion Equipment, Including Wire-Coating Dies, Iliffe Books, London (1970). S. Levy and J.F. Carley, Plastics Extrusion Technology Handbook, 2nd Ed., Industrial Press, Inc., New York (1989). W. Michaeli, Extrusion Dies: Design and Engineering Computations, Hanser Publishers, Munich (1984). C. Rauwendaal, Polymer Extrusion, Hanser Publishers, Munich (1986). F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988). N.M. Bikales, Ed., Extrusion and Other Plastics Operations, Wiley-Interscience, New York (1971).
Table 8.1 General Extruded Film and Sheet Types [1] Film/sheet type
Thickness range (um) (mils)
Flat film Cast sheet Thermoformable film Thermoformable sheet Thermoformable sheet Oriented films Uniaxial Biaxial
0.4-6 4-16 4-16 16-100 100-300
10-150 100-400 100-400 400-2500 2500-7500
1.2-24 1.2-100
30-600 30-2500
8.2
Film/sheet widths (mm) (in) 48-126 32-88 18-64 24-56 40-80
1200-3200 800-2200 450-1600 600-1400 1000-2000
24-72 16-60
600-1800 400-1500
Forming Thin Films
Thermoformable sheet is usually considered to be thin-gage when its thickness is less than 60 mils, 0.060 in or 1500 um and to be heavy-gage when its thickness is greater than 120 mils, 0.120 in or 3000 jim. When the sheet thickness is less than 10 mils, 0.010 in or 250 |im, it is considered to be a film. Table 8.1 gives a general summary of sheet characteristics [I]. Most films are thin enough to have some flexibility and are produced by extruding the polymer melt through an annular ring, then inflating and stretching the tube to achieve thinness and to introduce biaxial orientation and toughness. The configuration of a typical blown film tower is shown in Fig. 8.1 [2]. This equipment is primarily used for polyethylenes. Polypropylene, polystyrene and polyamide films are usually extruded through a slot die onto chill rolls. This type of extrusion is discussed in detail below. Flexible and rigid polyvinyl chlorides and certain types of ABS are usually calendered. The various elements that make up the desired compound are usually blended in ribbon blenders, then mixed or fluxed in batch mixers such as sigma or Henschel mixers. The mixed or fluxed batch is then discharged to a two-roll mill or a short barrel extruder. The milled product is then fed to a continuously turning calender (Fig. 8.2) [3]. Figure 8.3 shows a schematic of a typical polyvinyl chloride calendering operation [4]. Flexible polyvinyl chloride is usually calender-coated against release paper. The release paper is then rolled together with the polymer sheet and is continuously stripped from the polymer sheet as the sheet enters the thermoforming machine. Thermoplastic polyurethane is extruded from pellets into the nip of the two-roll mill of Fig. 8.2 and is also calender-coated onto release paper. Calendered sheet is usually available in the thickness range of 2 to 50 mils, 0.002 to 0.050 in or 50 to 1250 um. Of course, calendering or the production of continuous uniform thickness sheet is only one of the ways in which the milled product can be treated. Pelletizing is the most common use of the milled product. Calendering usually yields a lower-cost sheet than extrusion. In addition, the physical properties of thermally sensitive polymers such as polyvinyl chloride are not compromised.
Reheat Box
Nip Rolls
Double Bubble
Collapsing Frame Blown Film Bubble
Frost Line External Air Ring Extruder
Windup Roll Stack Die Ring Blown Film Die Internal Air Inlet
Figure 8.1 Typical blown film tower with optional double bubble stretching section [2]
Regrind is difficult to accommodate in calendering, and dirt, gels and contamination can be a problem. Films are also produced by solution casting. Any polymer that can be solvated or dissolved in a carrier can be cast into film. Typically, polymers that cannot be extruded or melt processed are solution cast into films. Examples include polyimides, polyazoles and latexes. Solution casting is usually a manual batch process although
Two-Roll Mill
Two-Roll Mill
"L" Calender Roll Stack
Inverted "L" Calender Roll Stack
Figure 8.2 Two calendering roll stack configurations. Redrawn from [3] and used with permission of copyright owner
Two-Roll Mill
"F"1 Calender Roll Stack "Z" Calender Roll Stack
Two-Roll Mill
Figure 8.3 Two calendering roll stack configurations. Redrawn from [4] and used with permission of copyright owner
latex casting has been automated. With proper care, the resulting films are quite uniform in thickness and properties. Films having thicknesses of 1 mil, 0.001 in or 25 um or less are common. Solvent cast films are usually quite expensive. Residual solvent can be a serious problem during reheating of the film in the forming operation. Thin films are also needed when coextruded sheet is required. In this case, the polymer is melt-extruded with a secondary extruder into a special multilayer die. This is discussed below.
The criteria for judging the quality of thin films are the same as those for heavier gage sheet. These are discussed below. With thin films, there is a greater concern about gels, fish-eyes and other occlusions in the sheet simply because the dimensions of these defects may be equal to or greater than the thickness of the film.
83
Forming Sheet
As noted, calendering is used to produce thin-gage sheet to 50 mils, 0.050 in or 1250 jim in thickness. Its use is usually restricted to polymers that require fluxing or masticating and those that are thermally sensitive. Polyvinyl chloride is the dominant polymer produced as calendered sheet. High molecular weight polymethyl methacrylate is sought for clarity and chemical resistance in pools, spas, shower stalls, and most glazing applications. It is produced by cell casting [5]. Generally, methyl methacrylate monomer with its hydroquinone inhibitor removed is mixed with benzoyl peroxide catalyst and heated to 90-950C. The catalyzed syrup is cast between two highly polished plates separated by flexible polyvinyl chloride or polyvinyl alcohol gaskets. The plates are held against the gaskets with carefully calibrated spring-loaded clips since the polymer increases in density or decreases in volume as its molecular weight increases. Temperature is maintained at 400C early in the polymerization but gradually raised to 95-97°C after several hours to allow the polymerization to proceed to completion. The sheet is then cooled to below 400C, removed from the plates and annealed for up to 2 hours at 1400C to minimize internal stresses. Although the original batch process is still used to produce sheets with special sizes and thicknesses or acrylics that are lightly crosslinked, the continuous cell-cast process dominates the production of most commercial glazing acrylic sheets. The continuous process uses a monomer/polymer syrup containing up to 20% highmolecular weight polymer. Although the abrasion and chemical resistances are thought to be somewhat inferior to the batch cell-cast product, this product is substantially less expensive. Continuous cell-cast acrylic can also be crosslinked to improve impact strength. With proper temperature control, lower molecular weight polymethyl methacrylate pellets and granules are extruded into sheets using conventional single-screw extruders. Such products have lowered abrasion, impact and scratch resistances and may not have the surface quality and clarity of higher molecular weight acrylics. And extrusion-grade acrylics are usually not crosslinked. Extrusion through a slot die is the primary method of producing sheet of thicknesses from 10 mils, 0.010 in or 250 urn to 500 mils, 0.500 in or 12 mm or more. Table 8.2 lists the scope of continuous screw extrusion techniques. Plasticating single-screw extruders and twin-screw extruders dominate production of sheet for thermoforming. Of the rest, two-stage and tandem extruders are used to produce foam sheet. This is covered in some detail in Chapter 9 on forming foam sheet.
Table 8.2 Types of Continuous Screw Extruders Single-screw extruders
Multi-screw extruders
Melt fed or plasticating Single stage Multi-stage Plastic Rubber
Twin screw Gear pump Planetary gear Multi-screw (>2)
Single-Screw Extrusion Figure 8.4 is a cut-away schematic of a conventional single-screw extruder. The basic elements are: • • • • • •
Constant diameter flighted screw, Constant bore barrel, Zoned heater bands, Keyed bearing block, Feed hopper, Venting ports,
Hopper Barrel
Gear Box Heater Band
DC Motor
Figure 8.4 Schematic of single-screw extruder for thermoplastics
Screw
Table 8.3 Typical Compression Ratios Single-Screw Extruders
• • •
Polymer
Compression ratio
Regrind polyethylene fluff Polyethylene powder Regrind polystyrene foam Other amorphous powders Polypropylene pellets PVC pellets Polystyrene pellets ABS pellets Crystalline PET pellets Polyamide (nylon) pellets
4.5:1 4.0:1 4.0:1 3.5:1 3.0:1 2.5:1 2.5:1 2.5:1 2.0:1 1.5:1
Electric motor, Power coupling between motor and flighted screw, and Temperature and speed controls.
The most common screw is single-flighted. The screw serves to advance the polymer from the hopper to the die end, compressing, melting and increasing the pressure on it as it advances. The screw root increases along the screw, compressing and pressing the polymer against the heated barrel inner wall. The amount of compression is the compression ratio. Table 8.3 gives typical compression ratios for some polymers. The function of the screw is intellectually divided into three segments (Fig. 8.5) [6]: •
Solids conveying, where the plastic pellets or powder is augered from the hopper into the barrel. Energy transfer to the polymer is minimal. Friction between the semi-solid polymer and the barrel and screw surfaces dominates. Typically the screw root dimension does not change in this zone.
Transition Section
Feed Section
Shank
Channel Depth
Metering Section
Screw Diameter
Screw Tip
Key Hub
Pitch Screw Flight Helix Angle Screw Root
Screw Flight
Channel Width
Figure 8.5 Schematic of screw for single-screw extruder with identification of various screw elements. Redrawn from [6] and used with permission of copyright owner
Molten Polymer Film
Melt Pool
Solid Polymer Granular Bed
Barrel
Screw
Figure 8.6 Schematic of the interrelationship of solid and melt polymer and screw and barrel in the plastication region for single-screw extruder [7]
• •
Plasticating or melting, where the compressed cake melts against the barrel surface and the melt is continuously conveyed into a pool at the front of the trailing flight (Fig. 8.6) [7]. In this zone, the screw root dimension linearly increases. Melt pumping, where the molten polymer is homogenized and compressed to build pressure necessary to flow through the extrusion sheet die. In this zone, the screw root dimension remains constant.
These extruders are usually described in terms of screw diameter and the screw length-to-diameter ratio, L/D. In the US, screw diameters are given in inches as 1, \\, 2, 2\, 3|, A\, 6, 8, 10, 12 and so on. In Europe and other metric areas, screw diameters are given in mm as 20, 25, 30, 35, 40, 50, 60, 90, 120, 150 and so on. L/D ratios are as low as 12:1 to 16:1 for rubber and thermoplastic elastomeric polymers to 20:1 to 36:1 for most commercial extruders to 48:1 for certain olefinic extruders. 24:1 and 30:1 extruders make up the bulk of sheet extrusion capability in the US while most European extruders are typically 30:1 to 36:1. Increased L/D allows for improved solids conveying and melt homogenization but increases the residence time and shear history on the polymer melt. Table 8.4 gives an overview of the capacities of extruders of various diameters [8]. Extruder throughput rates are also dependent on the type of polymer, as seen in Table 8.5 [9]. These rates represent extruder capacity when the flow rate through the die is not controlling. This is the case for most heavy-gage sheet extrusion. For thin-gage sheet extrusion, on the other hand, extruder throughput rates may be reduced by flow resistance through the die, as seen in Table 8.6 for the extrusion of 15 to 80 mil, 0.015 to 0.080 in or 400 to 2000 urn flat sheet of certain polymers [10]. Example 8.1 shows the relative output for a given extruder screw diameter.
Table 8.4 Typical Extruder Capacities [8] Extruder size (in)
4i 6 8
Average power (HP)
(mm) 38 64 89 114 152 203
10-15 20-30 40-75 80-125 150-225 300-500
Barrel heater (kW)
Output (lb/h)
(kg/h)
50-75 120-160 250-400 400-700 800-1200 1500-2000
23-74 54-73 113-181 181-318 363-544 680-907
7.5 21 45 75 140 225
Example 8.1 Extrusion Capacity Your thermoforming operation requires 40 in x 52 in x 0.060 in ABS sheet. Determine the number of 100 sheet pallets that can be produced from a 4-in extruder. Compare the output with the maximum output of that extruder. Determine the weight of each pallet.
From Table 8.6, the 4^-in extruder with a sheeting die can produce 1320 to 1430 lb/h ABS. The specific gravity of ABS is 1.05 g/cm3 = 65.5 lb/ft3. Thus the volumetric output is 20 to 22 ft3/h. The volume of each sheet is 124.8 in3 = 0.072 ft3. Therefore the extruder will produce 275 to 300 sheets per hour or 2.75 to 3 pallets per hour. The plastic on each pallet weighs 470 Ib. According to Table 8.5, a 4^-in extruder can plasticate 1170 to 1430 lb/h. Therefore, the extruder with a sheeting die is running at maximum capacity. Many single-screw extruders have venting ports or vents at some location along the barrel. Some polymers contain small amounts of volatiles. These are removed prior to the sheeting die to eliminate foaming and to minimize microbubbles, pits and pores in the finished sheet. Venting screws usually have a decompression or let-down region just ahead of the vent, as seen in Fig. 8.7 [H]. Vented or devolatilizing extruders usually have L/Ds of 30:1 or more. Although vents can be plugged and the extruder run unvented, the screw is usually not optimum and so the polymer may be subjected to higher than normal shear and residence time at melt temperature. Vented extruders should not be used to dewater polymers. Polymers having high moisture level potentials should be thoroughly dried prior to being charged to the extruder. Filtering the Polymer A filter screen is usually placed between the end of the extruder and the die to catch contaminants, unmelted polymer and some gel particles. The generic screen is a plate with regularly spaced holes. Screens with different sized holes are usually grouped together to form a screen pack. A typical screen pack might have several 100 mesh
Table 8.5 Extruder Output Rates for Several Polymers [9] Screw diameter (mm) (in)
LLDPE (lb/h)
64 89 114 130 152 203
275-340 550-650 900-1100 1150-1400 1600-1950 2840-3475
5.12 6 8
Screw diameter (mm) (in) 64 89 114 130 152 203
5.12 6 8
(kg/h)
Throughput HDPE (lb/h) (kg/h)
PP (lb/h)
(kg/h)
FPVC (lb/h)
(kg/h)
210-260 420-510 695-850 900-1100 1225-1500 2200-2675
330-425 650-800 1080-1320 1390-1700 1920-2350 3400-4170
360-440 700-865 1170-1430 1510-1840 2080-2540 3700-4500
160-200 320-390 530-650 685-835 945-1150 1680-2050
415-510 815-1000 1350-1650 1740-2125 2400-2930 4260-5200
190-230 370-450 610-750 790-965 1090-1330 1940-2370
(kg/h)
PMMA (lb/h)
(kg/h)
PC (lb/h)
(kg/h)
225-280 440-550 725-900 935-1170 1290-1615 2300-2870
415-510 815-1000 1350-1650 1740-2125 2400-2930 4260-5200
190-230 370-450 610-750 790-965 1090-1330 1940-2370
285-350 560-680 925-1125 1200-1450 1650-2000 2900-3500
130-160 250-310 420-510 550-660 750-900 1325-1600
(kg/h)
LDPE (lb/h)
125-155 250-300 400-500 525-650 725-890 1290-1580
475-575 925-1125 1530-1870 1975-2400 2700-3300 4800-5900
(kg/h)
ABS (lb/h)
(kg/h)
360-440 700-865 1170-1430 1510-1840 2080-2540 3700-4500
160-220 320-390 530-650 685-835 945-1150 1680-2050
150-195 300-360 490-600 630-775 870-1065 1550-1895
Throughput RPVC (lb/h) 220-270 435-530 720-880 925-1135 1280-1560
100-120 195-240 325-400 420-515 580-710
I HIPS (lb/h) 490-615 965-1200 1600-2000 2060-2580 2840-3550 5050-6320
Table 8.6 Polymer-Dependent Extruder Throughput Rates [10] 0.4 to 20 mm sheet thickness Screw diameter (mm) (in)
Screw L/D
75 90 105 120 150
30-36 30-36 30-36 30-36 30-36
4 6
PP (lb/h) 400-440 570-640 700-770 1050-1210 1430-1650
(kg/h)
HIPS (lb/h)
Throughput ABS (lb/h) (kg/h)
(kg/h)
PET (lb/h)
(kg/h)
180-200 260-290 320-350 480-550 650-750
660-700 990-1100 1320-1430 1650-1870 2400-2650
300-320 450-500 600-650 750-850 1100-1200
220-250 360-400 450-480 600-650 850-900
260-310 400-480 530-620 700-790 1060-1200
120-140 180-220 240-280 320-360 480-540
480-550 790-880 990-1060 1320-1430 1870-2000
Constant Taper
Constant Taper Screw Feed
Metering
Transition
Mixing/Metering Screw Feed
Transition
Metering
Decompression
Transition
Metering
Two-Stage Vented or Gas Injection Screw Figure 8.7 Schematics of various screw configurations for single-screw extruders. Figure redrawn from [11] and used with permission of copyright owner
screens placed against several 50 mesh screens. The screen pack is then placed against a breaker plate. Screens can be plates with drilled holes, welded wire mesh, woven wire cloth or porous sintered metal. Filter screens are used throughout the sheet extrusion industry and are especially important when running large percentages of regrind, particularly if the polymer is an intrinsic gel former such as polyethylene terephthalate, polyamide, low-density polyethylene, polypropylene and rigid polyvinyl chloride. Pigmented polymers can also cause substantial filtering problems, particularly in regrind. Pressure drop across the filter screen must be continually monitored to determine when the screen has clogged and needs to be replaced. Continuous screen changers are expensive but useful if the polymer is heavily contaminated.
Flow Improvement Devices In recent years, there has been great progress in improved plastication and homogenization of the polymer melt, primarily through improved screw design and motor drive and thermal feedback controls. Some typical plasticating and mixing screw sections are shown in Fig. 8.8 [12]. Surging, the bane of quality sheet production, has been greatly reduced. Gear pumps and static mixers are used to further improve melt quality prior to the die. Figure 8.9 is a schematic of an extruder having these features. Static mixers are dissipative devices that improve laminar mixing by separating the melt stream into many layers, reorienting the layers and then
Mixing Pin Screw
Double-Wave Screw
UC or Maddock Mixing Screw Tip
Barrier Screw
Barr Screw
Parallel Interrupted Flight Screw Figure 8.8 Schematics of various mixing sections for single-screw extruders. Figure redrawn from [12] and used with permission of copyright owner Screw
Barrel
Extruder
Static Mixer
Ring Barrier Screw Gear Pump
Die
Figure 8.9 Schematic of extruder/static mixer/melt pump/die configuration
recombining the layers in a different order. There are more than 30 types of static mixers [13]. The mixing section of a Kenics mixer is shown in Fig. 8.10 [14]. Improved homogenization or mixing efficiency must be weighed against increased shear history and pressure loss through these devices. Today, static mixers are used when the screw design is not optimum for the polymer, when the melt pumping zone on the screw is too short or when the overall extruder L/D is too short. The relative effectiveness of many of these devices is reviewed elsewhere [15-18]. Gear pumps or melt pumps are characterized as "closely intermeshing counterrotating twin screw extruder(s)" [19]. Details are shown in Fig. 8.11 [20]. One gear is driven. It drives the other. The polymer melt is engaged by the gear teeth and forced
Figure 8.10 Kenics static mixer element configuration. Redrawn from [14] and used with permission of copyright owner
Figure 8.11 Two views of gear or melt pump showing intermeshing gear rotation relative to flow direction [20]
against the pump wall. The remeshing of the gear teeth forces the polymer from the pump. Gear pumps were originally employed to counteract surging and secondary flow effects from screw flights. Today they are used primarily to boost melt pressure prior to the die. Owing to leakage between the gear teeth and pump wall and between the edge of the gears and the pump wall, the pumps are not positive displacement pumps. Although the typical volumetric efficiency is 90% or so, low viscosity melts and high pressure drops can reduce efficiencies to 50% or less [20]. Gear pumps are high shear devices. As a result, it is not unusual to see melt temperature increases of 100C or more as the polymer passes through the gear pump. These pumps are not recommended for thermally sensitive polymers such as polyethylene terephthalate and rigid polyvinyl chloride. Pressure and Temperature in an Extruder The stated purpose of an extruder is to plasticate or melt the polymer and to deliver the conditioned, homogeneous polymer melt at a constant flow rate. The majority of
pressure buildup occurs in the melt pumping zone. The melt is advanced by drag flow and retarded by pressure flow. Drag flow is the result of the relative motion between the screw and the barrel. Pressure flow is a measure of the viscous resistance to the flow. A simple pressure drop-flow rate relationship for a purely viscous Newtonian fluid is: (8.1) where W is the width of the flow channel or the right-angle distance between flights, H is the depth of the flow channel or the distance between the screw root and the barrel and is the Newtonian viscosity. V2 = TiDN cos <|), where D is the screw diameter, N is the speed of the screw, rev/min, and 4> is the screw helix angle. 17.65° is the helix angle for a single-flighted screw. gz = AP/L, the pressure drop along the flow channel, and L is the length of the flow channel. F d and F p are correction factors that account for screw curvature, leakage and other dissipative effects and are usually less than unity. Equation 8.1 can be written simply as: (8.2) This is the extruder performance characteristic equation. Simply stated, melt-pump controlled extruder output is directly related to extruder speed and is diminished by high exit pressure and polymer viscosity. Similar relationships are available for power-law fluids [22]. The extruder performance characteristic is shown in Fig. 8.12 [23]. This will be coupled with the die performance characteristic later. Viscous dissipation or frictional heating of the polymer is always of concern. The maximum temperature increase is determined by assuming that all the power used to build pressure in the polymer is converted to heat [24]. The power is given as: (8.3)
If the dissipation is adiabatic or without loss to the environment, the increase in bulk melt temperature, AT, is given as: (8.4)
This represents the maximum amount of viscous dissipation anticipated on extrusion. Example 8.2 shows the typical heat buildup order of magnitude of polymer melts. Example 8.2 Heat Buildup in ABS Determine the heat buildup in ABS and HDPE if the melt pressure differential is 4000 lbflin2 [27.6 MPa]. For ABS, p = 65.5 Ib/ft3 and cp = 0.4. For HDPE, p = 60 Ib/ft3 and cp = 0.98.
The temperature increase is given from Equation 8.4. For ABS:
AT = 28°F for ABS Using the same equation:
Volumetric Flow Rate
AT=13°Ffor HDPE
Operating Point Pressure Drop Figure 8.12 Interrelationship between flow rate-pressure drop characteristics of extrusion die and flow rate-pressure drop characteristics of single-screw extruder. Adapted from [23]
Sheet Die Concepts All the pressure created by the extruder is dissipated in the sheet die. The most common sheeting die has a rectangular slot outlet. Annular dies are used for foams and blown film. Figure 8.13 shows two views of one type of flat sheet die with attendant nomenclature [25]. Figure 8.14 shows an annular die for the production of polystyrene foam [26]. The objective of the slot die is to efficiently and uniformly spread the melt from the cylindrical cross-section inlet to the rectangular slot outlet. Figure 8.15 shows several flow channel shapes for slot dies [27]. The coathanger die is most common in the US. Figure 8.16 is an example of a small coathanger die for producing 440 lb/h or 220 kg/h nominal 0.100 in or 2.5 mm thick polystyrene sheet [28]. The land height is constant at 0.100 in or 2.5 mm. As is apparent, the majority of the pressure loss is in the land. The pressure drop expression for a viscous-only Newtonian fluid is: (8.5)
Manifold Choke Bar
Land
Manifold
Extruder Flexible Lip
Extrudate
Lip
Adjustable Lip Land
Die Body
Choke Bar Figure 8.13 Characteristics of one type of flat sheet die. Adapted from [25]
Screen Plate
Mandrel
Flow Channel
Die
Spider Legs
Figure 8.14 Characteristics of an annular sheet die used in low-density foam production. Two methods of holding mandrel in place are shown. Redrawn from [26] and used with permission of copyright owner
1
T" Die 1
Fishtail Die
"T" Die 2
Coathanger Die
Land Length, cm
Figure 8.15 Four types of flat sheet dies. Redrawn from [27] and used with permission of copyright owner
Pressure, bar
Die Width, cm
Figure 8.16 Characteristics of a specific type of manifold/land die for sheet production. Redrawn from [28] and used with permission of copyright owner
where is the Newtonian viscosity, L is the length of the channel, V is the flow rate, B is the channel width and H is the channel depth. Since the pressure drop is equal everywhere along the die, L = yo. Example 8.3 illustrates the capacity of a slot die. Example 8.3 Capacity of a Slot Die Determine the flow rate through a die land with the following dimensions: B — 50 in, H=OJOO in, yo = 20 in. The polymer is PMMA with a melt viscosity of 1000 Pa - s and the melt pressure is 30 MPa at 2000C. How many 64 in long sheets are produced per hour?
In consistent unit s, B = 127 cm, H = 0.254 cm, yo = 50.8 cm. From Equation 8.5, the flow rate is given as:
The cross-section area of the die is B x H = 32.3 cm2. The velocity is: 64-in long sheets per hour
Equation 8.5 is written symbolically as: (8.6) This is the die performance characteristic equation, showing that the Newtonian flow rate through a slot die (or any other shaped die, for that matter) is directly proportional to the available pressure and inversely proportional to the melt viscosity. The die performance characteristic is shown in schematic in Fig. 8.12. Example 8.4 illustrates the interrelationship between the extruder characteristics and the die characteristics. The maximum temperature increase due to viscous dissipation is also obtained from these equations as: (8.7)
Increased screw speed and viscosity yield increased viscous dissipation, as is expected and observed. Example 8.4 Matching the Die to the Extruder The flow rate from an extruder must match the flow rate from the die. Consider an extruder to be melt pump controlled. For a Newtonian fluid, show that the flow rate is independent of pressure and that the maximum pressure is directly proportional to the screw speed.
Solve Equation 8.6 for pressure drop:
where C represents geometric parameters. Substitute this into Equation 8.2:
where A and B represent geometric parameters. Solving for Q:
Note that the flow rate is independent of viscosity as well as pressure. To determine the maximum pressure, substitute this expression into the equation for pressure drop, above:
The maximum pressure is directly proportional to the polymer viscosity and screw speed. It is apparent that actual matching can be considerably more complex than the examples just cited. Most polymers are non-Newtonian. The melt pumping portion of the extrusion process does not always dominate. In certain cases, pressure buildup during plastication is important. Screw design can involve depressurization zones as in the venting area and the overall pressure drop-flow rate relationship will be altered [29]. Figure 8.17 shows some of these effects [30]. Although computer feedback control of screw speed and barrel temperature and modern screw design have eliminated much of the extruder-induced processing problems, the die operating conditions can introduce some problems. A coupling between a periodic 4.5°C temperature fluctuation in the die and a periodic 4.5% variation in sheet thickness is seen in Fig. 8.18 [31]. Gage Thickness Monitoring and Control For thin-gage sheet to 30 mils, 0.030 in or 750 |im or so, in thickness, beta and gamma gages are used to measure sheet thickness. The reading is then fed back to control bolts that differentially open or close the die gap at specific places along the die length. Heated bolts are commonly used in this application (Fig. 8.19) [32]. For heavy-gage sheet, sheet thickness can be measured using beta or gamma devices, but manual micrometer measuring of the cut sheet is common, particularly on short runs. Die gap control is done by manually adjusting the die bolts.
Volumetric Flow Rate
Deep Channel
Large Die Opening
Die Characteristics Shallow Channel
Small Die Opening
Screw Characteristics
Pressure Drop
Time, min
Figure 8.17 Comparison of die and extruder characteristics for manifold/land dies and single-screw extruders. Adapted from [30]
Temperature Fluctuation, °C
Thickness Variation, jjm
Figure 8.18 One example of interrelationship between process parameter, temperature, and product quality, sheet thickness variation. Redrawn from [31] and used with permission of copyright owner
Flexible Lip Adjustment Choke Bar Adjustment
Adjustment Heater
Figure 8.19 Sheet die with thermal bolt sheet thickness control. Redrawn from [32] and used with permission of copyright owner
Twin-Screw Extrusion Two styles of twin screws are commercial. Figure 8.20 shows parallel constant diameter screws and conical screws [33,34]. Parallel screw machines dominate. There are four major ways in which the two screws interact as shown in Table 8.7 [35,36]. In addition, the non-interacting screws can have tangential contact or can be separated by a gap. These variations are shown in Fig. 8.21 [35]. Twin-screw machines usually have modular screws. That is, the screws are custom constructed of several types of elements such as mixing elements, kneading elements, forward pumping and backward pumping screw elements, lefthanded and righthanded elements and so on. Twin-screw extruders excel in their abilities to customize the way in which the polymer is plasticated and pumped. With proper selection of the various elements, twin-screw extruders provide superior mixing, excellent heat transfer, large melting capacity, excellent devolatilization capability, unique ability to allow for down-extruder addition of fillers, reinforcements, fire retardants and other adducts, low shear history and hence minimal heat generation, and/or accurate stock temperature control1. Further, the feed rate to twin-screw 1
Note that not all these attributes can be achieved in a single screw configuration. For example, twin-screw extruders are used extensively for compounding, where adequate mixing usually involves high shearing and hence heat generation.
Table 8.7 Twin-Screw Arrangements [35,36] Corotating intermeshing
Werner & Pfleiderer LMP Windsor Berstorff Betol Mitsubishi Heavy Industries Kobe Steel IKG Colombo
Corotating non-intermeshing
No equipment
Counterrotating intermeshing
Leistritz Krupp Anger Japan Steel Works
Counterrotating non-intermeshing
Werner & Pfleiderer Baker Perkins Farrel Corp. Welding Engineers Japan Steel Works Kobe Steel
Metering
Compression Precompression Preheating
Gas-Melt Mixing
Feed
Figure 8.20 Characteristics of parallel intermeshing twin screws (top) and conical intermeshing (bottom) twin screws. Redrawn from [33,34] and used with permission of copyright owner
Co-Rotating
Counter-Rotating
Separated
Tangential
lntermeshing
Fully
Partially
Fully
Partially
Figure 8.21 Characteristics of several twin screw configurations. Redrawn from [35] and used with permission of copyright owner
extruders is decoupled from the screw speed. Twin-screw extruders are typically starve- and meter-fed. The extruder screw speed can be changed to affect the mixing characteristics with no effect on flow rate. The primary applications for twin-screw extrusion are in compounding, devolatilizing, polymerizing and molecular weight appreciating or "finishing". Compounding includes addition of adducts such as brighteners, ultraviolet and thermal stabilizers, fire retardants, as well as fillers, dry and liquid pigments, solid and liquid foaming agents, and short and long glass fibers. Certain thermally sensitive polymers such as most polyvinyl chlorides and certain acetates and polyamides do best when extruded using twin-screw extruders. Despite major theoretical efforts to explain flow behavior in twin-screw extruders [37,38], the many available elements and machine configurations confounds the prediction of screw geometry when polymer properties, expected shear and heat histories, and processing conditions are known. Likewise, processing conditions and shear and heat histories cannot now be predicted from given screw geometries and polymer properties.
If the twin-screw extruder is used simply as a method of solids conveying, plasticating and pumping polymer melt, typical extruder lengths can be shorter than those of single-screw extruders, that is, 18:1 to 24:1. If the twin-screw extruder is also used to add plasticizer, for example, to polyvinyl chloride, or calcium carbonate to polypropylene, the extruder needs to be longer. Multipurpose twin-screw extruders are typically 24:1 to 30:1. If the twin-screw extruder is used for several functions, such as blending colorant masterbatches and mixing plasticizers into polyvinyl chloride for example, a shorter extruder can be used if its extrudate is fed to the throat of a short-barreled single-screw extruder to build pressure in the compound melt. The twin-screw extruder is usually mounted directly against the sheeting die, with only a filter screen and breaker plate between.
8.4
Roll Stacks
The sheet extrudate is usually laid against a cold polished metal surface to quench it prior to rolling or guillotining. Commercially, sheet cooling occurs continuously against polished rolls. The rolls are called polish rolls or chill rolls and the assemblage is called a roll stack or chill roll stack. Several roll stack configurations are shown in Fig. 8.22 [39,40]. The most common roll stack in the US is the vertical same-size three roll stack with sheet moving either in the down direction if the rolls are relatively small or in the up direction of the rolls are large. Classically, the extrudate is laid directly onto the polish roll as close to the nip as the die can be placed (Fig. 8.23) [41]. The extruder speed and the roll speed should be matched to minimize any bank, bead or pencil. The rolls serve several functions: •
Shaping. The extrudate may not be uniform in thickness and the extrudate edges or "beads" may be dogbone in shape. The rolls aid in making the sheet more uniform. • Cooling and rigidifying the sheet. In order for the sheet to retain its shape it must be cooled substantially below its amorphous glass transition temperature or its crystalline melting temperature. The rolls remove the heat by conduction to the coolant circulating within the rolls. • Producing a uniform sheet temperature and therefore flat sheets. Sheet curling and other nonplanar effects can be caused by improper cooling that results in an unsymmetrical temperature profile through the sheet. • Gage thickness control. Although nearly all the gage thickness control should be done by setting die gap, some thickness control can be achieved in the nip between the polishing roll and the pressure roll. • Surface texture. The most common roll stack uses highly chrome-polished rolls to provide a smooth, glossy texture to the sheet. However, where the application warrants, the polish roll is replaced with a textured roll. Textures can range from semi-gloss, "haircell" or matte, to leather- and wood-grain.
Die
Die
Die Die
Air Knife
Die Die
Die
Die
Die
Figure 8.22 Several roll-stack configurations. Adapted from [39,40]
•
Machine-direction orientation. In certain cases, such as with oriented polystyrene, machine-direction orientation is needed. By differentially varying the speeds of the various rolls, some orientation can be added. If substantial orientation is needed, standard orienting equipment is used1.
Residual orientation in both machine-direction and cross-direction can dramatically affect thermoformability of polymer sheet. As a result, differential roll speeds and "banking" or using the nip between the polish roll and the pressure roll to spread the extrudate are not recommended for the production of thermoformable sheet. Figure 8.24 shows a typical temperature profile through an 80 mil, 0.080 in or 2 mm 1
See Section 8.9 for information on biaxial orientation.
Pressure Profile
Melt Bank, Pool, or Bead Nip Region
Velocity Profile From Die
Figure 8.23 Velocity profile of polymer melt in nip region of roll stack. Redrawn from [41] and used with permission of copyright owner
Sheet Center RoIM
Sheet Temperature,0C
Die Melt From Die
Roll 3 Roll 2
Roll 2 Air
Air Gap
Bank
Roll 3
Air
Sheet Surface Temperature
Sheet Distance, cm Figure 8.24 Time- or distance-dependent sheet temperature during cooling of 80 mil polystyrene, PS on down-roll chill stack, insert. Redrawn from [42] and used with permission of copyright owner
Roll 2
Roll 3
Air
Roll 2
Roll 3
Air
Temoerature, 0C
Roll 3 RoIM
RoIM
Roll 3 Roll 2 Crystallization
1
R2
Roll 2 Crystallization
T T
R3
Sheet Distance, cm
R2
T
R3
Sheet Distance, cm
Figure 8.25 Two examples of sheet temperature profile for PP extrusion onto chill roll stacks. Roll stack configurations shown in inserts
polystyrene sheet in contact with a chill roll stack [42]. Banking is particularly critical for certain polymers such as PP and PET. An additional analysis is given for the cooling of CPET in Chapter 9. For polymers that cool rapidly or crystallize slowly, care must be taken to size the chill roll diameter to the sheet thickness and the rate of extrusion. Figure 8.25 shows the effect of chill roll configuration on the time-dependent temperature of PP sheet [43]. The cooling rate can change the degree of crystallization of PP. For example, if the chill roll temperature is changed from 1000C to 400C, the cooling rate of 1.5 mm or 0.060 in thick PP initially at 2300C changes from l°C/s to 10°C/s. This changes the room-temperature density from 0.905 to 0.891 g/cm3 and the degree of crystallization from 50% to 37% [43]. Changing the morphological characteristics of a polymer such as polypropylene can also change the size of the spherulites, thereby changing the polymer impact strength and haze level. More important to thermoformers, changes in crystallization level and spherulite size may dramatically alter the polymer sag characteristics [44] and therefore the forming window1. The effect of chill roll residence time is even more important with very slowly crystallizing polyethylene terephthalate.
8.5
Sheet Trimming
Two general types of trimming are used in extrusion of thermoformable sheet. Gross sheet width control in the machine direction is usually carried out with die deckles. These are steel bars that are either clamped to the die edges or are fitted into the die 1
An extended discussion on the problems and desirable properties of polypropylene in thermoforming is given in Chapter 9.
land when the die halves are assembled (Fig. 8.26). Since deckles are usually not carefully machined and heated, melt usually pools behind them. Long residence times at melt temperatures can lead to thermal degradation in even the most heatinsensitive polymers. Some polymers such as rigid polyvinyl chloride and polyethylene terephthalate can suffer substantial thermal damage even at short times, so deckling is not recommended for anything but short production runs. For thingage sheet, sheet is trimmed to width with fixed industrial razor blades (Fig. 8.27) [45]. For heavier gage sheet of rigid polymers such as HIPS, RPVC, ABS, PC and PMMA, razor blades are used to score the warm sheet and the edge trim is manually broken off after guillotining or saw cutting. If the sheet is very thick, the edges are band-saw or circular-saw cut just ahead of the guillotine. Cross-sheet cutting in thin-gage sheet is done at the take-up roll with a flying razor blade or knife. Heavier gage sheet that is pallet stacked is cut either with a mechanical or hydromechanical shear known as a guillotine. To achieve a square edged cut, these shears sit at an angle to the machine direction. Circular and band saws are used to cut very heavy sheet. While hot wires are used on occasion, the cutting rate is usually too slow for very heavy-gage sheet. Dust and polymer slivers are common nuisances in mechanical cutting and fumes and odor are problems with hot wires.
8.6
Take-Off and Take-Up Rolls
Thin-gage sheet is usually delivered to the thermoformer in large-diameter rolls. Some polymers such as polypropylene and certain types of low-density polyethylene have inherent blocking or high cohesion tendencies. This causes the layers of sheet on a roll to stick together, sometimes so tenaciously that the sheet cannot be stripped from the roll without substantial force. Antiblocking agents such as silica and/or fatty acid slip agents such as oleamide are usually added to the polymer if this is a known problem. Since slip agents usually "bloom" to the sheet surface, care must be taken to ensure that their presence does not compromise the function of the end product. For example, the agents must be FDA-approved for food packaging and must not interfere with printing inks or adhesives if the product is to be printed, labeled or sealed to another surface. Winding tension is always critical in take-off systems. Two winding schemes are currently used (Fig. 8.28) [46]. Most polymers can be wound by driving the roll. Some polymers, such as olefins and flexible PVC, require surface winding. The length of sheet on a roll, L, is obtained from: (8.8)
where D is the diameter of the roll, d is the diameter of the core and s is the sheet thickness. The number of plies on a roll, n, is given as: -
2
^
Inside Corner Deckle Sheeting Die
Extruder Extruded Sheet
Outside Corner Deckle
Sheeting Die Extruded Sheet Extruder
Center Deckle
Extruded Sheet
Figure 8.26 Deckle bars for flat sheet extrusion. Top shows inside and outside deckles. Bottom shows splitter deckle
Edge Trim Knife
Blade
Figure 8.27 Industrial razor blade edge or selvage trimming. Redrawn from [45] and used with permission of copyright owner
Main Roll Under Low Tension Nip Roll
Tension Roll
Nip Roll
Idler Roll
Take-up Roll Under Tension Figure 8.28 Two winding schemes. Redrawn from [46] and used with permission of copyright owner
Example 8.5 illustrates the way in which these equations can be used. Information on tension measurement and control is found elsewhere [47]. Example 8.5 Number of Parts from a Roll of PVC Flexible PVC is thermoformed into instrument panel skins for the automotive industry. The 0.060 in (1500 m) thick sheet is available on rolls. The thermoformer take-off roll stack is capable of handling 1000 Ib rolls on 6 in diameter cores. The thermoform mold uses a 46 x 84 in sheet. What is the diameter of the roll and the number of parts that can be formed from the roll, assuming 100% utilization. The PVC density is 1.4 gjcm3.
Next Page
The weight of sheet per foot of length is:
The length of 1000 Ib of sheet is:
The diameter of the roll is given as:
Each part requires 84/12 = 7 ft of sheet. Therefore: Number of parts per roll = 85 + The number of plies on the roll is:
8.7
Residence Time and Residence Time Distribution Through Extruder and Die
Residing at melt temperature for extended time can be detrimental to the mechanical properties of many polymers, including ABS, RPVC, mPPO, PP and PET. Since a substantial portion of the sheet supplied to thermoformers must be recycled, an understanding of the residence time and residence time distribution in the extrusion process is particularly important. If the extrusion process could be considered as a plug flow process, the residence time would be simply the length of the flow channel, z, divided by the flow velocity, v: tPiug = z/v
(8.10)
For the journey through the extruder, the velocity would be the volumetric flow rate divided by the cross-section of the channel formed by the screw root, barrel and flights. The length would be the unwrapped length of the screw flight, z = L/sin 4>. If <\> = 17.65° for a single-flighted screw, z == 3.3 L. The mean residence time is obtained by dividing the volume of the extruder occupied by polymer, V*, by the volumetric flow rate, v: tmean = V*/V
(8.11)
When the extruder is completely full of polymer, tplug = t mean . Example 8.6 illustrates these two residence times.
Previous Page
The weight of sheet per foot of length is:
The length of 1000 Ib of sheet is:
The diameter of the roll is given as:
Each part requires 84/12 = 7 ft of sheet. Therefore: Number of parts per roll = 85 + The number of plies on the roll is:
8.7
Residence Time and Residence Time Distribution Through Extruder and Die
Residing at melt temperature for extended time can be detrimental to the mechanical properties of many polymers, including ABS, RPVC, mPPO, PP and PET. Since a substantial portion of the sheet supplied to thermoformers must be recycled, an understanding of the residence time and residence time distribution in the extrusion process is particularly important. If the extrusion process could be considered as a plug flow process, the residence time would be simply the length of the flow channel, z, divided by the flow velocity, v: tPiug = z/v
(8.10)
For the journey through the extruder, the velocity would be the volumetric flow rate divided by the cross-section of the channel formed by the screw root, barrel and flights. The length would be the unwrapped length of the screw flight, z = L/sin 4>. If <\> = 17.65° for a single-flighted screw, z == 3.3 L. The mean residence time is obtained by dividing the volume of the extruder occupied by polymer, V*, by the volumetric flow rate, v: tmean = V*/V
(8.11)
When the extruder is completely full of polymer, tplug = t mean . Example 8.6 illustrates these two residence times.
Example 8.6 Plug Flow and Mean Residence Times of a Single-Flighted Screw Determine the plug flow residence time and the mean residence time of a single flighted 4-in diameter, 24:1 extruder having a melt pumping channel depth of 0.400 in. The extruder is pumping 1.2 specific gravity PVC at 800 Ib/h. Assume zero flight width. Owing to solids conveying, 40% of the channel length is only half-full. How much plastic remains in the extruder for times longer than 2 mean residence times? Three mean residence times? The channel width is given as [48]:
The channel cross-section is then:
The volumetric flow rate is:
The velocity is then:
The channel length is:
And the plug flow residence time is: minutes The plastic volume in the channel is given as: For a volumetric flow rate of 5.13 in3/s, the mean residence time is: minutes According to Fig. 8.29 [49], about 4.6% or 0.046 x 649.8 = 30 in3 reside in the extruder for at least two mean residence times or 4.2 minutes. 1.3% or about 8.5 in3 reside in the extruder for more than three mean residence times or 6.3 minutes. The cumulative residence time distribution, CRTD, is given as: (8.12) From theory, the minimum residence time is given as: (8.13)
Residence Time Age Distribution
Dimensionless Time Figure 8.29 Residence time age distribution through a single-screw extruder. Redrawn from [49] without experimental data and used with permission of copyright owner
where |i is the Newtonian viscosity, z is the down-channel length, AP is the pressure drop and R is the hydraulic radius of the channel. As expected, residence time increases with extruder L/D and viscosity and decreases with pressure drop and channel geometry. The experimental CRTD for a single-screw extruder is shown in Fig. 8.29 [49]. Twin-screw extruders show similar CRTD shapes. Note that for the single-screw extruder of Fig. 8.29, more than 1% of the polymer remains in the extruder for more than three times the mean residence time. See Example 8.6 for additional information. The mean residence time in a standard sheeting die is obtained from an expression similar to that for the extruder [50]: W d 1 6 = BHy0/V
(8.14)
The cumulative residence time distribution in a simple flow channel such as an extruder die can be estimated from equation 8.12. Example 8.7 details the calculation of mean residence time and residence time distribution in a slot die.
Example 8.7 Mean Residence Time in a Slot Die Determine the mean residence time and the fraction of polymer residing in the slot die described in Example 8.3 after 2 and 3 mean residence times.
From Equation 8.14: From Equation 8.12: For t = 2tmean die, CRTD = 0.75, or 25% of the polymer remains in the die longer than 32 s. For t = 3tmean5 die, CRTD = 0.89, or 11% of the polymer remains in the die longer than 48 s.
8.8
Drying
Nearly all solid surfaces adsorb moisture under certain conditions. Virgin polymers are sold to the extruder as pellets, powders, granules or chips. All these shapes have very large surface to volume ratios. Polymers transported from cold warehouses or silos to warm extrusion rooms can adsorb large quantities of water that must be removed before feeding to the extruder hopper. Example 8.8 gives an example of the thickness of water film as a function of moisture pickup. Typical water film thicknesses are around 1 jim. For polymers that are not hydroscopic such as most polyolefins and many PVC formulations, simply exposing the pellets to warm air is sufficient to evaporate surface moisture. A hopper dryer using warmed recirculated air will suffice. Many polymers absorb as well as adsorb moisture. The moisture does not just reside on the pellet surface but diffuses into the pellet volume. Polymers that hydrogen bond well, such as polyamides and polycarbonate, polymers that have great sensitivity to water when molten, such as polyamides, PET, PBT and cellulosics, and most filled and reinforced polymers require extensive drying. Table 8.8 gives normal moisture contents and moisture contents required to provide bubble-free extruded sheet without substantial property deterioration. For amorphous polymers not listed in the table, select a drying temperature of (Tg — 20)°C and a drying time of 2-4 h. Figure 8.30 [54] shows the relationship between moisture absorption and relative humidity for several polymers. The long drying times at elevated temperatures are required in order to reverse the moisture diffusion process. For these difficult-to-dry polymers, hopper dryers are usually inadequate. Recirculating dryers are used with the air dehumidified to — 400C dewpoint by contact with refrigerated metal coils, silica gel or molecular sieve beads (Fig. 8.31) [52]. Figure 8.32 [55] shows the interrelationship of PET equilibrium moisture content, drying temperature and the dewpoint of the recirculating air. Note that to achieve a 0.02% moisture content, the
Table 8.8 Drying Conditions for Various Thermoplastic Drying times are for polymer pellets. These drying times can also be used for sheet. The drying times are then per mm (0.040 in) of sheet thickness. Two drying temperatures and two drying times are listed for some polymers. With the exception of PET, these are recommendations from differing sources [51-53]. Polymer
Glass transition temperature (0C)
Equilibrium Required moisture moisture content content for at 100% RH extrusion (%) ' (%)
Maximum drying temperature (0C)
Typical drying time (h)
PA 6 PA 66 PET* PS/HIPS ABS CA CAB PBT PMMA PC PPO RPVC
50 50 70 100 100 100 100 70 100 150 105 70
1.0-3.0 1.0-2.8 0.1-0.2 0.2-0.6 0.2-0.6 2.0-2.5 1.0-1.5 0.1-0.3 0.6-1.0 0.15-0.3 0.08-0.2 0.04-0.3
50, 75 50, 80 65,160 80 80, 90 60, 90 70, 90 160 80, 95 150 120 70
3-4, 2 3-4, 2 3-4,4 2 2 3, 1.5 3, 2 4 3, 2 4 4 2
<0.08 <0.03 <0.005 <0.02 <0.02 <0.05 <0.05 <0.02 <0.05 <0.05 <0.02 <0.02
* Lower drying temperature for amorphous PET. Higher value for crystallized PET
air must have a dewpoint of less than - 2 0 0 C at 1600C. A very long time is required to achieve this moisture level, however. Careful monitoring of the air dewpoint is required to maintain good efficiencies. Most recirculating beds require periodic regeneration and careful maintenance. Example 8.8 Moisture Pick-up on Pellet Cube Consider an ABS cube 0.060 in on a side. Determine its surface-to-volume ratio and the thickness of absorbed water for 1% (wt) moisture pickup. The specific gravity of ABS is 1.05. The The The The
volume of the cube is V = L 3 = 216 x 10~ 6 in3 area of the cube is A = 6L2 = 2.16 x 10~ 2 in2 area-to-volume ratio is A/V = 6/L = 100 weight of a single pellet is:
The weight of water is 0.01 x W = 8.19x 10~ 8 Ib and the volume is:
The film thickness is:
Moisture Content, wt %
30% Glass PA
PA, Nylon
ABS
PET
30% Glass PET Relative Humidity, % Figure 8.30 Room temperature relative humidity-dependent equilibrium moisture content for several thermoplastics. Redrawn from [54] and used with permission of copyright owner
Polymer Feed
Dryer Absorption Canisters
Figure 8.31 Canister dessicant dryer and hopper configuration for extrusion. Adapted from [52] and used with permission of copyright owner
Relative Humidity, %
Dewpoint, C
Drying Temperature,0C Figure 8.32 Interrelationship. between equilibrium relative humidity, air dewpoint and drying temperature for polyethylene terephthalate, PET. Redrawn from [55] and used with permission of copyright owner
8,9
Producing Biaxially Oriented Sheet
Thin-gage oriented polystyrene or OPS, biaxially oriented polypropylene or BOPP, and polyethylene or BOPE, are frequently thermoformed into cake domes, transparent lids and deep drawn containers. Polystyrene impact strength and clarity is dramatically improved by orientation. A dramatic reduction in haze is apparent with oriented polyethylene and polypropylene films. Films to 10 mils, 0.010 in or 250 urn, are usually biaxially oriented by inflating the extrudate from an annular die. Heavier gage sheet requires secondary or post-extrusion orientation. Tentering is the most common biaxial stretching method (Fig. 8.33) [56]. In certain cases, the extrudate sheet is stretched in the machine direction while still hot on heated bridle rolls running at differential speeds, then cooled and stretched in the cross-machine direction. Figure 8.34 [57] shows a typical clip or clamp used in the cross-machine stretcher. Polystyrene sheet is frequently supplied to the tenter as a cold roll. The sheet is then reheated in an infrared oven to 500C or so above its glass transition temperature prior to sequential machine-direction and cross-direction stretching. For
Temperature, 0C Figure 8.33 Schematic of tenter frame process for producing biaxially oriented sheet and film. Adapted from [56] and used with permission of copyright owner
Clip
Clip
Sheet Thickness Edge Thickness
Usable Width Figure 8.34 Schematic of tenter clips for TD sheet stretching. Redrawn from [57] and used with permission of copyright owner
crystalline polymers such as polypropylene, machine-direction stretching occurs at temperatures just below melt temperature and cross-direction stretching occurs at or just above melt temperature. Table 8.9 gives representative property values for oriented thin films and sheet [58,59]. Birefringence is one way of determining the degree of orientation in transparent sheet goods [60]. Transparent polymers have three indices of refraction along the three primary axes. When the polymer is preferentially oriented, the index of refraction in that direction changes. The change
Table 8.9 Comparative Properties of Unoriented and Oriented Polymer Films and Sheets Property—Sheet [53]
Polymethyl methacrylate
Polystyrene Unoriented
Biaxially oriented
Unoriented
Biaxially oriented
Tensile strength (MPa) Elongation at break (%) Impact strength
34.5-62 1-3.6 0.25-0.5
48-82.7 8-18 >3
51.7-69 5-10 4
55-75.8 25-50 15
Property—25 um, 1 mil or 0.001 in film [58]
Polystyrene
PET
Polyamide
PP homopolymer
Biaxially oriented
Biaxially oriented
Biaxially oriented
Unoriented
Biaxially oriented Two-stage
Areal stretch ratio Tensile strength—MD (MPa) Tensile strength—TD (MPa) Elongation at break—MD (%) Elongation at break—TD (%) Puncture resistance (N) Low-temperature resistance (0C)
10:1 70 70 10 10
6.5:1 200 220 130 110
18:1 300 300 70 70
50 40 430 540 23 0
10:1 140 270 140 40 200 -50
Simultaneous 10:1 200 200 80 80 -50
in any pair of indices is birefringence in that direction. Polystyrene has an exceptionally high level of birefringence. Polyethylene terephthalate and polyvinyl chloride show moderate birefringence. Polymethyl methacrylate and polycarbonate have weak levels of birefringence and polyethylene and polypropylene show essentially no birefringence. Figure 8.35 shows typical in-direction and cross-direction tensile strength values compared with birefringence values for 0.100 in thick or 2.54 mm injection molded polystyrene [61]. Similar comparisons have been made for elongation at break and impact strength. Birefringence can be easily observed using low-cost polarizing filters placed 90° to one another. The classic effect is very narrow bands of color for high stress regions and wide bands elsewhere1. Biaxially oriented sheet shows high stress regions at the points where the clips held the sheet during cross-machine stretching. A very high level of birefringence at those points is an indication that the sheet may have been stretched at too low a temperature.
8.10 Multilayer Sheet Formation Multilayer sheet is used in extremely thin gage of 1.5 mil, 0.0015 in or 37.5 Jim polyamide for speaker cones and computer touch screens to 50 mils, 0.050 in or 1250 jim, for CPET single serving dinner trays to 500 mils, 0.500 in or 12.5 mm, PVC/PMMA for pools and spas. Interfacial adhesion is paramount in multilayer sheet. Polymeric systems in which adducts are slightly different from layer to layer usually bond well when both sheets are hot. Examples include TiO2 -pigmented PET/regrind PET, TiO2-pigmented PP/CaCO3-filled PP, and virgin ABS/regrind ABS. Some polymers such as PVC and PMMA, nylon and ionomer, and PVC and ABS have excellent adhesion characteristics. When both are very hot, adhesion is very good. Other polymer combinations, such as HDPE/PP, PVC/PS, PP/EVOH/PS, and HDPE/ PVDC/PS have poor adhesive characteristics. As a result, these layers are bonded together using a "tie layer" or a ductile hot melt adhesive such as polyethylene, ethylene vinyl acetate, ethylene, methylene and other acrylic acids or certain amino-acid polymers. Multilayer structure selection is discussed elsewhere [63,64]. Table 8.10 gives a cross-list of pairs of traditional polymers and their adhesive characteristics [65]. 1
Birefringence can be explained in the following way. The oriented polymer molecules separate polarized light into one component that is parallel to the direction of molecular travel and one that is perpendicular. One portion of the light ray travels slightly faster than the other. The retardation will cancel a particular wavelength from the white-light spectrum leaving a combination of the remaining colors. No orientation yields black and high orientation is green. Birefringence is given as: ^
~
(815)
where Ar] is the difference in indices of refraction or the birefringence, X is the wavelength of light, = 5500 A for white light, R is the level of retardation, and D is the thickness of the film or sheet. R is determined by counting the number of orders and assigning fractional values to various colors. For example, black = 0, yellow = 0.3, red = 0.6 and green =1.0 [62].
Tensile Strength, 1000 lbf/in2
Flow Direction
Transverse Direction
Birefringement, 104 Figure 8.35 MD and TD tensile strength characteristics of injection molded polystyrene, PS as functions of measured birefringence. Adapted from [61] and shown without experimental data
Coextrusion While coextrusion is not normal for multilayer structures of dissimilar polymers, it is common for multilayer structures of similar polymers. As an example, for some refrigerator liner applications, an ABS gloss layer is coextruded with a core layer containing regrind. An overview of a typical multilayer extrusion system is shown in Fig. 8.36 [66]. The way in which the various melt streams are combined is key to quality coextrusion. Figure 8.37 shows an example of flow streams combined in the extrusion die block [67]. Figure 8.38 shows an example of flow streams combined in a feedblock [68]. Geometry restricts the number of streams to three. The multiple layered stream from the feedblock is then fed to a single manifold die. Dow has shown that it is possible to produce a melt stream of as many as 500 layers using their feedblock concept. Either die concept requires very careful design and superior pressure and temperature control for specific polymers to minimize serious flow instabilities, nonuniform inner-layer thickness, sheet distortion and curling and local inner-layer bleed-through.
Table 8.10 Adhesion Between Pairs of Polymers [65] Polymers
ABS
CA
EVA
ABS CA EVA PA 66 PC HDPE LDPE PMMA PP mPPO PS iPS PBT RPVC FPVC SAN
G G
G G P
P G
G P P G P P P G G F G
G G G
PA 66
G P P P
PC
HDPE
LDPE
PMMA
PP
G
P
P
G
P
G P
G P
G G P F
G G P G
P P G P
P P
P F
P
P
G G G
P F
G F G
G = good to excellent adhesion F = fair adhesion—depends on processing conditions P = poor or no adhesion
PS
iPS
PBT
RPVC
FPVC
SAN
P
P
G
G
F
P
G
F
P
P F
G P
G
P
G
mPPO
F G P G P P P
P P G G G
P F P G G G
G G P
P G G G
P G P
G
P P
P P P G
G P P P
P P
P P
G G G
G G G
G G
Secondary Extruder
Secondary Extruder Sheeting Die
Primary Extruder Manifold Die-Block
Cap Sheet Extruder
Figure 8.36 Top view schematic of coextrusion equipment and die block. Redrawn from [66] and used with permission of copyright owner
Two general types of multilayer flows are considered in die design: •
Symmetric flow, where the polymer 1 stream is evenly divided by the polymer 2 stream (Fig. 8.39) [69]. For this case, the pressure drop-flow rate relationships focus on the shear layer between the two streams. Flow characteristics such as viscous dissipation and temperature distribution through the sheet are symmetric and standard pressure drop-flow rate relationships can be used, with proper adjustment [70]. Depending on the relative viscosities and flow rates, symmetric flows can rapidly become unsymmetric, with the inner layer migrating toward the wall and folding the outer layer inward.
Adjustable Trim 1
Adjustable Die Lip Polymer 1
Polymer 2
Adjustable Trim 2
Figure 8.37 Cross-section schematic of multi-flow die block. Adapted from [67] and used with permission of copyright owner Selector Plug
Flow Divider
Single Flow Die-Block
Distribution Pins Cloeren Multi-Flow Adapter Figure 8.38 Cross-section schematic of Cloeren multilayer feed block. Redrawn from [68] and used with permission of copyright owner
Polymer 1 Velocity Profile Polymer 2 Shear Stress Profile
Polymer 1
Figure 8.39 Symmetric flow of two polymers, with polymer 2 between two layers of polymer 1
•
Asymmetric flow, where polymer 1 and polymer 2 streams flow side by side (Fig. 8.40) [71]. Asymmetric heating and viscous dissipation are expected and pressure drop-flow rate relationships must be altered. The developing polymer temperature profile across the melt for dissimilar viscosities and flow rates as a function of distance downstream is shown in Fig. 8.41 [72]. An example of the effect mismatched viscosity is seen in Fig. 8.42 for unfilled and TiO2-filled polyethylene [73,74].
Lamination Lamination is the adhering of an already-extruded sheet to an extrudate. Laminations are frequently used if tie layers are involved or if the extrudate cannot tolerate hot melt coextrusion. As an example of the former, a tie layer is melt coated to solid polypropylene sheet and this is laminated to polyvinylidene chloride extrudate to form barrier sheet. As an example of the latter, cooled polystyrene foam sheet is laminated to a semi-molten polystyrene "cap sheet" in a nip roll to improve the foam sheet cut resistance [75]. Other commercial laminations include solid acrylic (PMMA) sheet laminated to rigid PVC or ABS sheet for spas and PVDC film + tie layer laminated to HIPS for refrigerator liners. Two examples of lamination are shown in Fig. 8.43 [76]. On the left is a lamination process where a reheated solid sheet is laminated to
Velocity Profile
Shear Stress Profile
Polymer 1 Polymer 2
Figure 8.40 Asymmetric flow of two polymers, with polymer 1 and polymer 2 side-by-side. Adapted from [71]
Polymer 2
Melt Temperature,0C
Melt Temperature, 0C
Polymer 1
Lower Wall Normalized Channel Height
Upper Wall Lower Wall
Polymer 2 Polymer 1
Normalized Channel Height
Upper Wall
Figure 8.41 Examples of developing temperature profiles for asymmetric flow of two polymers. Left figure shows equal volumetric flow of polymers 1 and 2. Right figure shows unequal volumetric flow. Redrawn from [45] and used with permission of copyright owner
1.0
1.56
3.35
Figure 8.42 Effect of mismatched viscosities of polymer melts on shape of extrudate. Shaded area is unfilled polyethylene. Open area is TiO2-filled polyethylene. Marginal number is viscosity ratio at extrusion temperature. Adapted from [74]
Laminating Sheet
Cap-Sheet Extruder Die
Extruder
Extruder Die
Roll Stack
Sheeting Die
Roll Stack
Figure 8.43 Schematics of (left) solid lamination, and (right) hot melt extrusion lamination. Redrawn from [76] and used with permission of copyright owner
the extrudate and on the right is a lamination process where the laminating cap-sheet is extruded directly onto the primary extrudate. Lamination is frequently used even if the selected polymer combinations have excellent adhesion. Coextrusion feedblocks and die blocks are expensive to design and fabricate and take inordinate time to perfect, and changes in the final product design
Table 8.11 Major US Sheet Extruders* [77] Sheet extruder
1993 sales, $M
Percent sheet
AtoHaas North America, Inc., Philadelphia PA Spartech Plastics, Clayton MI Primex Plastics, Corp., Richmond Ind. O'Sullivan Corp., Winchester VA Cyro Industries, Mount Arlington NJ Uniroyal Technology Corp., Sarasota FL Gundle Lining Systems, Inc., Houston TX HPG-International, Inc., Somerset NJ Packaging Corp. of America, Northbrook IL SLT North America, Inc., Conroe TX
205 175 159 127 125 99 83 81 80 80
100 95 100 90 100 100 100 90 100 100
Plaskolite Inc., Columbus OH Fabri-Kal Corp., Kalamazoo MI Aristech Chemical Corp., Acrylic Sheet Unit, Florence KY Pawnee Extrusions, Wichita KA Sheffield Plastics, Inc., Sheffield MA
71 70 59 50 50
100 100 100 100 100
Preferred Plastic Sheet, Greenville OH Vinyl Plastics, Inc., Sheboygan WI New Hampshire Plastics, Inc., Manchester NH Portage Industries Corp., Portage WI Lustro Plastics Co., Evanston IL
49 43 30 29 22
100 91 100 100 40
Wellman Extrusion, Ripon WI Allen Extruders, Inc., Holland MI Goex Corp., Janesville WI Kleerdex Co., Mt. Laurel NJ Witt Plastics Inc., Greenville OH
21 19 19 19 18
100 100 100 100 100
Pace Industries, Inc., Reedsburg WI Trio Products, Inc., Elyria OH Bixby International Corp., Newburyport MA Ex-Tech Plastics Inc., Richmond IL Farber Plastics, Inc., Oceanside NY
15 15 14 5.5 5.1
100 100 100 100 100
Plastics Slip Sheets (US) Inc., Denver CO Repete Plastics Inc., Geneva IL Superior Plastics Extrusion Co., Inc., West Boylston MA Mitech Corp., Twinsburg OH Envirosafe Products, Inc., Staten Island NY
3.5 3.2 2.8 2.5 2
100 100 100 100 100
Abulco Plastics Industries, Inc., Hazleton PA Coon Manufacturing Inc., Spickard MO
1.5 1.5
100 100
* Not all sheet manufacturers listed are solely custom sheet extruders
are quite restricted. On the other hand, lamination allows for very rapid changes in polymer combinations, including alternate tie layers and extrudate thicknesses, at relatively low total cost. For long production runs, multilayer extrusion is cost effective. For development work, prototyping, and short runs, laminating is desired. Table 8.11 gives a list of major US custom extruders [77].
8.11 Sheet Quality and Quality Control There are many adages and old saws that pertain to quality and the importance of quality control, from serenely subjective: "Beauty is in the eye of the beholder"
to positively threatening: "Pay me now or pay me later".
The thermoformer must always realize that he is a value-added part of the economic chain from wellhead to refinery to polymerization to compounding to extrusion to forming to assembly to use. He is his sheet supplier's customer and as such, he needs to conduct business in much the same way as his customer deals with him. The thermoformer knows how to conduct business with his customer. Regardless of the nature and depth of prior experiences of the parts designer, the mold maker, the thermoformer, the customer or the ultimate end user, no plastics fabrication should be attempted without strict, formal written protocol on parts design. All these parties must clearly understand the project objectives and any ancillary part performance standards. Guidelines are usually carefully written and agreed on, in writing, by all principals. This should always be done with all principals present, just prior to the issuance of purchase orders for materials, molds and forming times. Processes, applications and materials continue to grow in sophistication. As a result, the thermoformer, his engineer, or his designer is destined to play an increasingly important role as project coordinator. It is incumbent on him to ensure correct protocol, particularly in this increasingly litigious era. In this section, the interface between the thermoformer and the extruder is addressed. Later on, the other aspects of good business are discussed. It is always good business to maximize profit. Business management teaches many ways of doing this. Thermoformers have an additional variable that most plastic processors lack—reuse of non-product. Careful management of nonproduct or web can yield substantial economic benefits but can also be the primary source of severe processing and quality control problems. Some classical definitions are: Virgin. Virgin means "unprocessed". By strict definition, virgin resin is that supplied to the extruder by the resin supplier. Virgin sheet, therefore, is that sheet made only from virgin resin. This excludes all other materials, such as factory regrind of virgin sheet, regrind returns from a specific source or multiple sources and so on. The purchase order for virgin sheet should state: "Virgin sheet to include no trim, regrind or other adulterants..."
If the thermoformer agrees to accept factory regrind of virgin sheet, the purchase order specifications should state so, in terms such as: "Virgin sheet to include no more than 10% factory edge trim, selvage and ends of virgin sheet extruded on this job on this extruder..."
Care must be taken here to ensure that the customer will accept this product. Medical and biomedical applications are usually very specific as to the exact composition of the polymer. Virgin + Regrind. This specification can be misused unless carefully defined by the thermoformer. Regrind can come from many sources. For example: Extrusion factory regrind. This implies that regrind is from any extruder in the factory from any operation, including but not restricted to your job. Regrind from thermoformer. This implies that regrind is supplied to extruder by you, as regrind. It can come from any source within your plant, at any time. You have the responsibility for knowing what you have supplied to the extruder for regrind. Any-source regrind. This implies that the extruder selects the regrind, without any input from you. Typically the specific amount of regrind should be part of the purchase order, such as: "The extruder shall use only virgin polymer blended with 30% ± 5% regrind sent to the extruder from the thermoformer and identified by barcode ..." Note that the specification does not state " . . . up to 35%.." as recommended in older specifications. The variability in properties from 0% or all virgin to 35% regrind can sometimes be deleterious to both the extruder and the thermoformer. Regrind Only. Frequently, the thermoformer may be using a sheet that contains 20% regrind, yet may be producing 40% web. The accumulation of regrind needs to be worked off. If a particular product can tolerate 100% regrind, the thermoformer should contract with the extruder to run a carefully controlled order of regrind only. Both parties must understand that this is a separate and distinct job from those that precede or follow. The specification should read something like: "Extruder shall produce sheet from regrind only, identified from the thermoformer as having barcode numbers , , and , The extruder and thermoformer agree to this special order, which shall be clearly marked on all rolls/pallets as REGRIND ONLY..."
Table 8.12 gives an annotated list of various purchasing specifications that the thermoformer as the customer must review with the extruder as the sheet supplier [78]. Obviously not all these specifications apply to every occasion. And not all are the sole responsibility of the extruder or the thermoformer. Some specifications, such as texture and color, are imposed by the customer or end-user of the thermoformed product. Some, such as impact strength and tensile strength, are imposed by the intrinsic performance requirements of the product. Some, such as gage tolerance and orientation, are critical to the way in which the polymer performs in specific thermoforming equipment. Some, such as melt index, intrinsic viscosity, molecular weight, water absorption, coefficient of thermal expansion, coefficient of friction, and abrasion, are intrinsic to the polymer selected for the application. Some, such as weatherability and fire retardancy, may be a function of the base polymer or its
Table 8.12 Sheet and Film Purchasing Specification Check List1 Specification Degree of orientation Required Allowed Sheet sag characteristics
Certifier/Tester (X = Major, x = Minor) Thermoformer Both Extruder X X X
Use of regrind, trim, selvage Dimensional tolerances Gage tolerance
X
Width and length tolerances Sheet flatness tolerance Impact strength Drop ball, dart, Izod
X X
Material consideration but extrusion characteristics may need to be considered too.
X
X
X
Moisture level
X
Foreign matter Agglomeration (type, frequency) Contamination (type, frequency)
X
x
Sheet-to-sheet accuracy to require extruder input also.
X
Again, extruder input important.
X
X
Gel count
X
X
Decision as to who will run test and what test is required must be clearly decided a priori. Specific drying methods must be spelled out for certain materials.
X
X X
Finish of surface required embossing
Comments
X
X
Smoothness
X
Gloss
X
Extruder input important particularly for short runs, materials that burn or degrade easily, or polymers with fugitive processing aids, fillers, fire retardants and so on. Again agreement required for polymers that crosslink easily, transparent sheet, film, oriented film. Depth of texture,finishthe primary control of the extruder. Surface quality the realm of the extruder but certain polymers, regrind difficult to control re: surface quality. As above.
Pits
X
Dimples Waves Air Entrapment
X X X
Bumps Optics
X
X
X X
Mechanical properties Tensile strength, compressive strength, hardness, elongation, yield strength, elastic modulus, coefficient of linear expansion, thermal conductivity, abrasion resistance, weatherability, water absorption, coefficient of friction, electrical properties. Heat deflection temperature at 66 lb f /in 2 at 164 lb f /in 2 Effect of melt index, melt flow, intrinsic viscosity on formability Hot tensile modulus at forming temperature Elongation at forming temperature Tear resistance at room temperature at forming temperature Foam compression set Foam density Closed cell count - foam
X
X
X X X X X X X X X
Good quality product can only be made from good quality sheet. As above. Quality extrusion should yield minimum waves. Quality extrusion should yield sheet with no air-caused defects. Quality extrusion should yield flat sheet. If optics are important, both thermoformer and extruder need to define quality sheet, re: color, transparency, defects, residual stresses, surface marks, and so on. If mechanical properties are critical, thermoformer must specify what tests are to be run, at what frequency, how the data are to be reported, and who will pay for it.
Extruder could run these tests but probably should run by the thermoformer as measure of formability. Only the thermoformer can determine this effect. Extruder cannot be expected to qualify sheet on this specification. As above. Extruder can run this test if necessary. Extruder should not be expected to run this test. Extruder can run this test if necessary. Extruder can run this test if necessary. Extruder probably should not be expected to run this test. (Continued)
Table 8.12 (Continued) Specification
Certifier/Tester (X = Major, x = Minor) Extruder Both Thermoformer
Pigment distribution Filler condition
X
X X
Fire retardant condition
X
X
Odor
X
Laminate properties Moisture (WVTR) Oxygen permeability
X
Packaging Core size Roll diameter Skid weight Single or double polyethylene wrap Drying compound
X
1
Adapted from [78]
Comments Need to determine what tests to run first. Conditions include particle size, size distribution, drying conditions. Conditions include method of addition (masterbatch, concentrate, dry blend) and perhaps method of determining effectiveness after extrusion, forming. Certain polymers have obnoxious odors. Tests for odor may need to be defined. If water, oxygen barrier is critical, tests need to be defined and carried out for proper certification. In certain conditions, film thickness, pinhole number need to b£ measured at extruder for qualification. Sheet surface quality, mechanical properties can be compromised if packaging is not adequate.
additive package. Other specifications, such as gel count or specks, may be a combination of specifications and realistic expectations. This is particularly true if substantial regrind is required in the final sheet. In all cases, before a specification can be agreed to, everyone must agree to: • • • • • • • •
A specific protocol or way of testing for the desired physical characteristic, The specific group who will carry out the test, The frequency of testing required to meet the specification, A realistic bound or standard deviation for the test, An appropriate way of reporting the test results, The cost of the individual test, The financial and temporal penalty for not meeting the specification, and The way in which this cost is to be distributed among the various elements (polymer supplier, extruder, thermoformer, customer, end-user).
Some specifications such as dimensional tolerance, orientation, moisture, coextrusion structure and sheet appearance are considered generic. These are discussed in additional detail below.
Sheet Dimension When plastic sheet is stretched, it becomes thinner. A sheet that is already thin yields parts that can be substantially thinner than desired. Thick sheet, on the other hand, yields parts that are over-designed and thus more costly than expected. Although significant improvements have been made in recent years in controlling the thickness of extruded sheet, some tolerance must still be given. The extruder and thermoformer usually compromise on overall sheet thickness or gage. It appears that with today's technology, sheet thickness variation can be held to less than 5% on sheet thinner than 3 mm or 0.120 in. On thicker sheet, tolerance can be held to within 0.2 mm or 0.005 in. Edge-to-edge uniformity is also important. Sheet thickness variation across the sheet width can be held to within 2% of the nominal sheet thickness dimension.
Orientation As noted above, sheet can become preferentially oriented in the machine direction during extrusion. This is usually not a serious problem in roll fed thermoforming processes since the sheet being heated and formed is essentially infinite in the machine direction. Cross-machine direction or TD orientation can be the result of using a narrow die to extrude a wide sheet. In roll fed thermoforming, relaxation of excessively high TD residual stress can cause the sheet to pull free of the pins on the pin-chain. In cut-sheet thermoforming, on the other hand, both types of direction orientation can be serious problems. If the orientation in the sheet is excessive, the residual strain in the clamped sheet can be so great that the sheet can be physically pulled from the clamp frame during heating.
A simple oven test is used as a quality control method [79]. Either 250 mm x 50 mm or 10 in x 2 in strips or 250 mm x 250 mm or 10 in x 10 in squares are cut from as-received sheet. It is recommended that these strips be cut in a fixed pattern every time the test is run. Preferably, strips should be cut from both edges and the center of the sheet. These strips are placed on a metal plate that has been coated with a bake-on mold release such as silicone, polytetrafluoroethylene, or FEP, or with a fine layer of powdered talc. A wooden pizza paddle can be used in an emergency. The plate is placed in the radiant heating zone of the thermoformer for a time typical of the heating time needed during thermoforming. The samples are cooled and measured to determine the degree of orientation1. The degree of orientation is the change in sample dimension in a given direction divided by the initial dimension of the sample. Example 8.9 illustrates MD x TD orientation. Example 8.9 Extruded Cut Sheet Orientation and Squareness An order has been placed for 0.125 in x 40 in x 40 in ABS sheet with a 2% diagonal squareness, a 2% thickness tolerance, a 2% diagonal flatness and no more than 8% MD and 4% TD orientation. Determine the allowable dimensions of a 10 in x 2 in test strip after heating and the allowable dimensions on the extruded sheet. Do these dimensions meet the squareness criterion of 90° ±\°?
If the 10-in direction of the test strip is in the machine direction or MD, the ranges on after-heating test strip dimensions are 9.2 to 10.8 in (MD) by 1.92 to 2.08 in (TD). Note that if the test strip shrinks to the limit in both MD and TD directions, the sheet thickness increases 13% to 0.142 in. The diagonal flatness based on 40 x Jl = 56.57 dimension is 1.13 in. If the free sheet corner is raised by less than this value when the other three are clamped to a flat table, the sheet passes the requirement. The cut sheet diagonal dimension is 40 x -Jl = 56.57 in. The allowable squareness factor is 1.13 in. This means that the maximum difference in cross diagonal dimensions are 57.13 to 56.00 in. The sheet is a parallelogram, as shown in Fig. 8.44. Consider the short diagonal. The edge in the right angle shown is: x = ^/(562 - 402) = 39.192 in The base in the small triangle is therefore 40 — 39.192 = 0.808 in. The angle is tan" 1 e = tan~1(40/0.808) = 88.84°. This angle is substantially less than the minimum recommended value of 89.75°. Uniformity and consistency in orientation are important. Sheet-fed frames can be adjusted for a given unequal biaxial orientation. Wide variation in orientation can 1
If the sheet exhibits an excessive amount of curl, the technique can be altered. Place the extruded sheet between two friction-free thin aluminum plates that have been shimmed apart with metal stock at least 20% thicker than the polymer sheet. Place the sandwich structure in a conventional convection oven for several minutes. The exact time in the oven depends on the sheet thickness. Keep the sheet between the aluminum plates until thoroughly cooled [18].
Figure 8.44 Geometry of cut sheet for Example 8.9
lead to sheet pull-out or excessive sheet sagging. The former is important with high melt-strength polymers such as ABS and PC. The latter is important with low melt-strength polymers such as LDPE and PP. It is recommended that orientation uniformity be controlled to within 5%. The shape of the heated strip can also give information about the internal stresses in the sheet. As noted in Chapters 3 and 5, plastics heat and cool quite slowly when compared with other materials. In sheets thicker than 5 mm or 0.200 in, heating relieves or anneals the cooling stresses. This results in a very slight increase in sheet thickness and a measurable necking-in or bowing-out all along the sheet edge. Excessive sample edge curl is also an indicator of nonuniform residual stress through the sheet. Poor processing skills such as low processing temperature, excessive extrusion throughput rate, poor melt homogenization by the screw, high nip roll pressure or excessive roll stack cooling can lead to heated sheet edge deformation. Sheet Squareness and Flatness Cut sheet overall dimension is also of concern. Thick-gage sheet is frequently cut to within 3 mm or 0.125 in in the length and width dimensions. This minimizes web held in the clamping frames. Out-of-square sheet frequently cannot be clamped. One quality sheet extruder recommends cross-diagonal dimensions to within 5%. Another recommends that corners be at right angles to within ± J ° o r 89|° to 90|°. Example 8.10 shows the importance of sheet tolerance and squareness when buying sheet to fit. Sheet bowing and warping can cause clamping problems. The flatness of the sheet is determined by clamping three corners of the cut sample on a flat surface and measuring the height of the fourth corner above the surface plane. Out-of-flatness of 2% based on the diagonal dimension of the sheet can probably be tolerated. Very thick sheet may need to be oven-annealed prior to forming in order to flatten the sheet enough to close and tighten the clamp frame. Example 8.10 Minimum Sheet Dimension The clamp frame on a cut-sheet shuttle machine will clamp on a ^-in sheet width. If the clamp frame is exactly 90° square, determine the minimum sheet dimension needed to clamp a within-tolerance sheet over a 40-in square mold. Commercial sheet tolerance is ± 0.125in in all dimensions and the corner angle tolerance is 90°±L4°.
If the sheet is cut to exactly right angles and to exact dimensions, it needs to be 40 + 2 ^ = 41 in on a side. For a trim tolerance of +0.125 in, the minimum right angle sheet must be 41 + | = 41.125 in on a side. For a non-right angle sheet, the sheet dimension must be increased by: 2x41.125 • tan 0.25° = 0.359 in The overall minimum in-tolerance sheet dimension should be at least 41.48 in on a side or just less than \\ in greater than the mold dimension. Moisture The importance of drying polymers thoroughly before extrusion has been discussed above. Many plastics such as polycarbonate, polymethyl methacrylate, polyethylene terephthalate and ABS are hygroscopic. The extent to which a given polymer absorbs water depends on the nature of the polymer and the time that the sheet has been exposed to the environment. As noted, there are two forms of water attachment. Adsorption is surface water only. Adsorption is usually the direct result of high humidity and cold surface temperature. Water absorption is a diffusion process. The water molecules move from the moist environment, humid air, into and through the entangled polymer molecules that make up the dry polymer sheet. The rate of diffusion depends on the concentration driving force, being the amount of water in the air, and the nature of the polymer. Some polymers such as polyamide and PET have strong affinities to water, through hydrogen bonding along the polymer backbone. As a result, these polymers absorb water readily and to a relatively high level. It is thought that the water molecules cluster in the void regions between molecular chains. When wet sheet is rapidly heated, as in thermoforming, these microscopic clusters expand to produce microvoids. Additional water molecules diffuse to these voids to produce visible bubbles. In mild cases, an otherwise transparent sheet appears hazy. In extreme cases, that sheet appears translucent, opaque white or blistered. Typically, the sheet producer should stack moisture-sensitive cut sheet directly onto polyethylene film that is then sealed around the stack. Polyethylene film is an excellent moisture barrier film. Moisture-sensitive thin-gage roll-stock should be sealed in a similar fashion. Quality control samples should be taken by the thermoformer at the time of shipment receipt. A visual inspection for moisture can be made at the time the degree-of-orientation test is being made. The inspection should be made again prior to forming. In order to ensure dry sheet, polymer suppliers recommend that specific moisture-sensitive polymers be thoroughly dried immediately prior to thermoforming. Table 8.8 gives some guidelines for the drying temperatures and times of several types of polymers. The drying times are per mm or 0.040 in of sheet thickness.
Sheet Appearance As detailed above, most applications require specifications on various aspects of sheet surface quality or appearance. Since requirements vary from application to application, no general set of criteria can be established. General sheet appearance can be categorized as follows: Linear Surface Marks. Die lines and polish roll or calender roll marks are usually linear lines in the sheet direction. Some of these surface defects are minor and can disappear when the sheet is heated. Most die lines can be quite noticeable however. Since they occur when the sheet is hot and being formed, they usually cannot be annealed out. Wavy linear lines appear in some polymers such as PET and PVC if the material is extruded at an excessively high extrusion melt temperature or if insufficient back pressure is applied to the die lips during extrusion. Wavy lines can be attributed to the downstream image of the tip of the rotating screw. These effects are not seen when gear melt pumps, static mixers or screen packs are in place. Irregular Surface Marks. Other marks seen on the sheet can be categorized as irregular marks. Marks that have exact periodicity are directly attributed to the roll stack. These can be as simple as detritus on the roll itself or as complicated as a plugged waterline or bad bearing in a chill roll. Teardrop- or disk-shaped dents are usually entrained air at the roll stack, indicating that the air knife is not functioning properly. Chatter or ribbon marks on one side of the sheet can be attributed to an unstable bank on that side of the roll. The source of microscopic web, nerviness or tracks can be rapid chilling of the extrudate prior to contacting the nip roll or very low level hesitation in the polish roll. Small splits in the edge bead indicate that the extruder die or deckle is too narrow for the sheet width being extruded. Holes, Pits and Lumps. These are discrete, isolated, random occurrences in the sheet which do not disappear when the sheet is heated. On the contrary, these defects can lead to sheet splitting during forming. As a result their frequency must be carefully monitored. There are at least three major sources of these defects contaminated virgin polymer, contaminated or thermally damaged regrind, and moisture in the extruder feed. Of these, contaminated or thermally damaged regrind is usually considered to be the primary problem. Two other sources of contamination are specks and gels. Specks are usually the result of dead zones in the polymer flow stream from the plastication section to the die lip. There are many sources of specks including inadequate purging, thermally sensitive polymer, improperly compounded pigment, mechanically unstable additive package, poor die design, poorly streamlined deckle and choke bars, poorly tapered breaker plate and airborne contamination at the die face or around the hopper area. As expected, specks are most obvious in transparent and white sheet. Thermally sensitive polymers can degrade during reprocessing with the result being the formation of gels. Off-spec virgin resin can contain gel particles. Gel particles are usually resinous, thermally crosslinked polymer that cannot be adequately remelted. Gel particles are a prominent source of defects in polymers
such as HDPE, PP, PET and PVC. Gels are most obvious in transparent or hazy sheet. Color Quality. Advanced color computer matching techniques have minimized the obvious problems in obtaining good color matching. However, it is incumbent on the thermoformer to make certain that batch to batch color uniformity is met. The pigments used to produce colors in thermoformable sheet must be permanent and must not change in tint during typical thermoforming, regrinding and re-extrusion operations. Color intensity across the sheet must always be uniform. In highly oriented thin-gage sheet and film such as oriented PS (OPS), light and dark regions can be produced if the orientation is not uniform. Some tinting dyes used in certain polymers such as PET lose their effectiveness during thermoform heating. As a result, transparent PET can yellow. PVC is highly sensitive to surface temperature and can also yellow. The PET regrind can be re-tinted whereas the PVC discoloration is intrinsic to the polymer and is therefore very difficult to hide. Obviously the problem is apparent with transparent polymers, pure white and dark colors. Surface Appearance. Gloss and embossing-retention represent the extremes in sheet surface appearance. The degree of gloss can be regulated to some degree by the surface temperature of the finishing rolls and to some degree by the extrudate temperature and the temperature and speed of the first roll the extrudate contacts. Usually the free surface of any extrudate has higher gloss than the contact surface. Polymers such as ABS, mPPO and HIPS usually yield intrinsically semi-glossy sheet owing to their two-phase nature. In some cases, the base polymer will not yield the necessary gloss and so must be laminated or melt coated with a polymer specifically designed to yield a high gloss surface. High gloss can be obtained by high melt extrusion temperature, slow extrusion speed and high polish roll temperature. On the other hand, embossed design details are best retained when the sheet temperature is low, the embossing roll is cold and the polymer has very low elastic memory. The last point was discussed in Chapter 4 and is quite important to retention of the embossing details in the formed product. For example, if the pattern is embossed into a polymer that has excellent memory retention, that pattern will be lost when the sheet is reheated prior to forming. Thus the quality of the image retention from the embossing roll is less important than the technically proper selection of polymer to be embossed.
Annoyance Factors In addition to the litany of quality factors given above and in Table 8.12, there are always nuisance factors that must be considered a priori. Many polymers such as PS, ABS, and PET have very high surface energies when extruded. Static charge buildup can yield uncomfortable and annoying shocks. It is a major reason for tenacious dust and dirt accumulation on sheet which can lead to rejected product. Static charge can also be the source for ignition when using a hydrocarbon foaming agent. Some charge effect can be minimized through antistatic processing aids.
Copper wool bleed-off bands and ionized air jets are also used to minimize static charge1. Eliminating trim or cutter dust from the heating and forming area can help as well. Minor blocking, or the sticking of one ply to another on roll-fed sheet, can be a minor problem. The drag or stick effect can affect the way in which the sheet is fed to the pin chain. The tugging can elongate the pin rail holes allowing the sheet to differentially move during forming. If the sheet plies can only be separated with heroic effort, the severely blocked sheet must be scrapped and the reasons for the blocking investigated. Typical solutions include proper control of extruded sheet tension during take-up, addition of a blooming agent or external lubricant such as a stearate to minimize incidental adhesion and reduction in sheet temperature at the time of take-up. Aged sheet containing an antiblock agent usually shows more blocking tendency than fresh sheet, simply because the antiblock diffuses from the interface between the plies back into the polymer sheet. High temperature sheet storage will usually exacerbate blocking. Torpedoing or core extrusion can be a nuisance as well. Here the core slowly extrudes from the roll of sheet ultimately making the roll unusable. Typical reasons for torpedoing include excessive antiblocking agent, nonuniform gage, with one side of the sheet slightly thicker than the other, nonuniform winding tension and a winding station take-up axis that is not parallel to the sheet delivery system.
Lamination Quality As noted, multilayer sheet and film are used in many ways. UV-barrier films are applied over PS and ABS substrates so that the formed parts can be used outside for signs, pools and camper tops. 0.2 mm, 8 mil or 0.008 in, cap-sheets of PS are applied to one or both sides of low-density PS foam to increase depth of draw and to dramatically improve product stiffness and cut resistance. In order to process crystallizing PET or CPET to proper stiffness without causing brittleness, two layers of PET are coextruded. One layer contains a crystallizing agent and the other may contain an impact modifier2. In addition to standard material property monitoring and control of each layer, care must be taken to monitor laminate thickness, adhesion, and thickness distribution across the sheet. A common monitoring device is the ultrasonic gage. This device is particularly effective if the velocities of sound in the laminated layers are substantially different. Of course, thickness can be determined by simply sectioning the sheet and optically measuring the thicknesses of the various layers. Warping and cupping during heating of multilayer sheet can be quite 1
2
For many high-appearance applications, the sheet surface must be protected from scuffing and dust while in transit from the extruder to the thermoformer. Thin LDPE film is used between the layers of both cut sheet and roll-fed sheet. For cut sheet, once the sheet is installed in the clamp frame, the film is manually stripped and segregated for recycling. For roll-fed sheet, the layer is continually stripped as the sheet enters the pin-chain end of the former. The added expense of this protective layer ensures that the sheet will be free from detritus and scuffs prior to thermoforming. It does not guarantee that the formed part will have the same attributes. See Chapter 9 for more details on thermoforming CPET.
severe if the thermal expansion coefficients of the various layers are not carefully matched, if the laminate thicknesses are not carefully controlled, or if dissimilar polymers are used on opposite sides of the laminate centerline. The oven test used for measuring the degree of orientation can be used as a screening test for laminate curl and delamination potential. Another important concern to the thermoformer is interlayer delamination during heating and forming. Delamination can appear as swarms of bubbles or blisters in the formed part. In the extreme, two layers can separate completely. This can occur as the formed part cools or during plug-assisted stretching. The primary cause for process delamination is inadequate adhesion during the sheet fabrication process. This may be caused by low interfacial temperature, inadequate compressive forces or short residence time under pressure. However, some of the following causes of delamination have been observed: • • • • • • •
Excessive or uncontrolled heating during thermoforming can severely reduce the interfacial adhesion forces, A transparent surface layer can allow radiant energy to penetrate to the interface, resulting in a loss of adhesion, A mismatch in thermal expansion coefficients of polymers in different layers can cause one layer to separate from another, A wet layer can evolve moisture at the inner layer, Fugitive processing aids can evolve gas at the inner layer, Air may be trapped between the layers due to inadequate nipping, and So on.
As a result, the cause of delamination is not always apparent on first examination.
8.12 References 1. H. Bongaerts, "Flat Film Extrusion Using Chill-Roll Casting", Chapter 6 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), p. 164. 2. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, and Tests for Design, Hanser Publishers, Munich (1993), Figure 5.8, p. 411. 3. M.L. Berins, Ed., Plastics Engineering Handbook of the Society of the Plastics Industry, Inc., 5th Ed., Van Nostrand Reinhold, New York (1991), Figure 5.13, p. 443. 4. M.L. Berins, Ed., Plastics Engineering Handbook of the Society of the Plastics Industry, Inc., 5th Ed., Van Nostrand Reinhold, New York (1991), Figure 5.15, p. 444. 5. J.A. Brydson, Plastics Materials, 4th Ed., Butterworth Scientific, London (1982), pp. 366-367. 6. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, and Tests for Design, Hanser Publishers, Munich (1993), Figure 5.4. 7. J.L. Throne, Plastics Process Engineering, Marcel Dekker, Inc., New York (1979), Figure 8.3-1. p. 404. 8. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, and Tests for Design, Hanser Publishers, Munich (1993), Table 5.8. 9. D.V. Rosato and D.V. Rosato, Blow Molding Handbook: Technology, Performance, Markets, Economics, The Complete Blow Molding Operation, Hanser Publishers, Munich (1989), Table 1.4, p. 14.
10. H. Bongaerts, "Flat Film Extrusion Using Chill-Roll Casting", Chapter 6 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), Table 9. 11. D.V. Rosato and D.V. Rosato, Blow Molding Handbook: Technology, Performance, Markets, Economics, The Complete Blow Molding Operation, Hanser Publishers, Munich (1989), p. 11. 12. D.V. Rosato and D.V. Rosato, Blow Molding Handbook: Technology, Performance, Markets, Economics, The Complete Blow Molding Operation, Hanser Publishers, Munich (1989), Figure 1.5. 13. C. Rauwendaal, Polymer Extrusion, Hanser Publishers, Munich (1986), pp. 330-332. 14. C. Rauwendaal, Polymer Extrusion, Hanser Publishers, Munich (1986), Figure 7-49a. 15. C. Rauwendaal, Polymer Extrusion, Hanser Publishers, Munich (1986), Section 7.7.2, "Static Mixing Devices". 16. S.K. Skoblar, "Why All the Fuss About Motionless Mixing?", Plast. Tech., 20: 11 (Oct 1974), pp. 37-43. 17. G. Smoluk, "How to Stretch Your Additive Dollar: Motionless Mixing", Plast. World, 36: 5 (May 1978), pp. 40-43. 18. G. Gruenwald, Thermoforming: A Plastics Processing Guide, Technomic Publishing Co., Inc., Lancaster PA (1987), p. 95. 19. C. Rauwendaal, Polymer Extrusion, Hanser Publishers, Munich (1986), p. 33. 20. S. Levy and J.F. Carley, Plastics Extrusion Technology Handbook, 2nd Ed., Industrial Press, Inc., New York (1989), Fig. 2-39, p. 73. 21. S. Levy and J.F. Carley, Plastics Extrusion Technology Handbook, 2nd Ed., Industrial Press, Inc., New York (1989), pp. 81-83. 22. C. Rauwendaal, Polymer Extrusion, Hanser Publishers, Munich (1986), pp. 267-270. 23. S. Levy and J.F. Carley, Plastics Extrusion Technology Handbook, 2nd Ed., Industrial Press, Inc., New York (1989), Fig. 2-10, p. 41. 24. C. Rauwendaal, Polymer Extrusion, Hanser Publishers, Munich (1986), p. 311. 25. W. Michaeli, Extrusion Dies: Design and Engineering Computations, Hanser Publishers, Munich (1984), Figuress 5.28 and 5.29. 26. J.L. Throne, Thermoplastic Foams, Sherwood Publishers, Hinckley OH (1996), Chapter 10. 27. W. Michaeli, Extrusion Dies: Design and Engineering Computations, Hanser Publishers, Munich (1984), Figure 5.31. 28. W. Michaeli, Extrusion Dies: Design and Engineering Computations, Hanser Publishers, Munich (1984), Figures 5.42 and 5.43. 29. C. Rauwendaal, Polymer Extrusion, Hanser Publishers, Munich (1986), p. 401. 30. S. Levy and J.F. Carley, Plastics Extrusion Technology Handbook, 2nd Ed., Industrial Press, Inc., New York (1989), Figure 2-11, p. 42. 31. W. Michaeli, Extrusion Dies: Design and Engineering Computations, Hanser Publishers, Munich (1984), Figure 5.51, p. 206. 32. W. Michaeli, Extrusion Dies: Design and Engineering Computations, Hanser Publishers, Munich (1984), Figure 5.53, p. 208. 33. S. Levy and J.F. Carley, Plastics Extrusion Technology Handbook, 2nd Ed., Industrial Press, Inc., New York (1989), p. 56. 34. J.L. Throne, Thermoplastic Foams, Sherwood Publishers, Hinckley OH (1996), Section 5.3, "Twin-Screw Extrusion". 35. J.L. White, Twin Screw Extrusion: Technology and Principles, Hanser Publishers, Munich (1991), Figure 1.4-1, p. 10. 36. C. Rauwendaal, Polymer Extrusion, Hanser Publishers, Munich (1986), Table 2-2, p. 31. 37. J.L. White, Twin Screw Extrusion: Technology and Principles, Hanser Publishers, Munich (1991), Chapter 8, "Mechanisms and Modeling of Intermeshing Counter-Rotating Twin Screw Extruders". 38. C. Rauwendaal, Polymer Extrusion, Hanser Publishers, Munich (1986), Section 10.3, "Intermeshing Co-Rotating Extruders". 39. H. Bongaerts, "Flat Film Extrusion Using Chill-Roll Casting", Chapter 6 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), p. 172.
40. H. Breuer, "Production of Films and Sheets by the Roll-Stack Process", Chapter 7 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), p. 211. 41. H. Breuer, "Production of Films and Sheets by the Roll-Stack Process", Chapter 7 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), Figure 5, p. 208. 42. H. Breuer, "Production of Films and Sheets by the Roll-Stack Process", Chapter 7 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), Figure 15, p. 220. 43. H. Bongaerts, "Flat Film Extrusion Using Chill-Roll Casting", Chapter 6 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), p. 152. 44. K.E. McHugh and K. Ogale, "High Melt Strength Polypropylene for Melt Phase Thermoforming", SPE ANTEC Tech. Papers, 36 (1990), pp. 452-454. 45. H. Bongaerts, "Flat Film Extrusion Using Chill-Roll Casting", Chapter 6 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), p. 146. 46. H. Bongaerts, "Flat Film Extrusion Using Chill-Roll Casting", Chapter 6 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), p. 153. 47. H. Bongaerts, "Flat Film Extrusion Using Chill-Roll Casting", Chapter 6 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), pp. 154-155. 48. R J . Crawford, Plastics Engineering, 2nd Ed., Pergamon Press, London (1987), p. 162. 49. C. Rauwendaal, Polymer Extrusion, Hanser Publishers, Munich (1986), Figure 11-17, p. 528. 50. W. Michaeli, Extrusion Dies: Design and Engineering Computations, Hanser Publishers, Munich (1984), p. 193. 51. H. Bongaerts, "Flat Film Extrusion Using Chill-Roll Casting", Chapter 6 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), p. 173. 52. W. Miicke, "Feeding of Extruders", Chapter 20 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), Figure 30, p. 660. 53. J.L. Throne, Thermo forming, Carl Hanser Verlag, Munich (1987), p. 223, Table 8.2. 54. W. Miicke, "Feeding of Extruders", Chapter 20 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), p. 657. 55. W. Miicke, "Feeding of Extruders", Chapter 20 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), Figure 26, p. 658. 56. F. Hensen, "Manufacture of Oriented Films" Chapter 8 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), Figure 4, p. 265. 57. F. Hensen, "Manufacture of Oriented Films" Chapter 8 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), Figure 17, p. 278. 58. F. Hensen, "Manufacture of Oriented Films" Chapter 8 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), p. 262. 59. R.D. Deanin, Polymer Structure, Properties and Applications, Cahners Books, Boston (1972), Table 5-12, p. 266. 60. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, and Tests for Design, Hanser Publishers, Munich (1993), Figure 5.34, pp. 445-450. 61. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles: Properties, Processes, and Tests for Design, Hanser Publishers, Munich (1993), Figure 5.34, p. 448. 62. J.L. Throne, Plastics Process Engineering, Marcel Dekker, Inc., New York (1979), p. 536. 63. E.L. Martin, "Multilayer Flexible Packaging", in M. Bakker, Ed., The Wiley Encyclopedia of Packaging Technology, John Wiley & Sons, New York (1986), pp. 451-464. 64. L.D. Storr, "Thermoform/Fill/Seal", in M. Bakker, Ed., The Wiley Encyclopedia of Packaging Technology, John Wiley & Sons, New York (1986), pp. 664-668. 65. F.A. Shutov, IntegraljStructural Polymer Foams: Technology, Properties and Applications, Springer-Verlag, Berlin (1986), Table 7.1, p. 83. 66. F.R. Nissel, "Coextrusion Machinery, Flat", in M. Bakker, Ed., The Wiley Encyclopedia of Packaging Technology, John Wiley & Sons, New York (1986), Figure 1, p. 194. 67. C. Rauwendaal, Polymer Extrusion, Hanser Publishers, Munich (1986), Figure 9-18, p. 455. 68. F.R. Nissel, "Coextrusion Machinery, Flat", in M. Bakker, Ed., The Wiley Encyclopedia of Packaging Technology, John Wiley & Sons, New York (1986), Figure 4, p. 195. 69. W. Michaeli, Extrusion Dies: Design and Engineering Computations, Hanser Publishers, Munich (1984), Figure 6.10.
70. W. Michaeli, Extrusion Dies: Design and Engineering Computations, Hanser Publishers, Munich (1984), pp. 275-288. 71. W. Michaeli, Extrusion Dies: Design and Engineering Computations, Hanser Publishers, Munich (1984), Figure 6.11. 72. W. Michaeli, Extrusion Dies: Design and Engineering Computations, Hanser Publishers, Munich (1984), Figure 6.16. 73. N. Minagawa and J.L. White, "Coextrusion of Unfilled and TiO2-Filled Polyethylene: Influence of Viscosity and Die Cross Section on Interface Shape", Polym. Eng. Sci., 15(1975), p. 825-830. 74. S. Levy and J.F. Carley, Plastics Extrusion Technology Handbook, 2nd Ed., Industrial Press, Inc., New York (1989), Figure 7-7, p. 232. 75. J.L. Throne, Thermoplastic Foams, Sherwood Publishers, Hinckley OH (1996), Chapter 7, "Skins and Surfaces on Foams". 76. H. Breuer, "Production of Films and Sheets by the Roll-Stack Process", Chapter 7 in F. Hensen, Ed., Plastics Extrusion Technology, Hanser Publishers, Munich (1988), Figure 30, p. 237. 77. D. Loepp, "Special Report-Processor Rankings: Film and Sheet Manufacturing", Plast. News, 6: 29 (19 Sep 1994), pp. 13-31. 78. W.K. McConnell, Jr., "The Seven Fundamentals of Thermoforming", Plast. Eng., 46: 12 (Dec 1990), pp. 31-34. 79. A typical standard is "Procurement and Supply Form SP-IOl", Chrysler Corporation, P.O. Box 2866, Detroit MI 48288.
9 Newer Thermoforming Technologies 9.1 Introduction 9.2 Thermoforming Crystallizing Polyethylene Terephthalate PET Crystallinity CPET Patents Characterizing Polyethylene Terephthalate The Effect of Temperature on Crystallization During Sheet Extrusion Cooling CPET on Chill Rolls Heating CPET in Roll-Fed Thermoformers Forming the Sheet Cooling the Formed Part Trimming Parts from Web Troubleshooting CPET Forming 9.3 Pressure Forming Thin Gage Heavy Gage 9.4 Forming Filled and Reinforced Polymers 9.5 Laminated Sheet Thermoforming Heating Multilayer Sheet Forming Multilayer Sheet 9.6 Twin-Sheet Thermoforming Simultaneous Twin-Sheet Forming Sequential Twin-Sheet Forming Seal Area—Adhesion Seal Area—Compressive Force Seal Area—Design 9.7 Polypropylene Thermoforming Sag Test Modified Polypropylenes 9.8 Thermoforming Foam Sheet Cell Architecture—Actual v. Ideal Radiant Energy Transmission Internal Cell Gas Pressure Forming Window for Foam The Forming Equipment 9.9 Other Forming Technologies Interdigitation Sealed Air Cushion/Dunnage 9.10 References
9.1
Introduction
It has been observed that there have been more advances in certain aspects of thermoforming in the last few years than in the previous five decades [I]. The many reasons for this were detailed in Chapter 1. Certainly new business opportunities have led to substantial improvements in heating and forming methods. In many cases, new products have required dramatic modifications in processing techniques. This chapter focuses on some of the newer processing techniques, such as: • •
•
•
•
•
•
Crystallizing polyethylene terephthalate (CPET) forming, developed for higher temperature microwavable food container applications, Pressure forming of both thin-gage and heavy-gage sheet. The former technology was developed for markets needing the properties of polypropylene. The latter was developed to compete with injection molding in electronic cabinetry. Both areas have been rapidly broadened recently. Laminate or multilayer thermoforming. Heavy-gage multilayer parts are used in pools, spas and outdoor structures. Thin-gage multilayer parts are used as barrier containers for foodstuffs and medicine and Pharmaceuticals. Twin-sheet forming, demonstrated decades ago but only recently developed as markets for hollow flat panels have evolved. As noted below, there are many ways of producing thermoformed hollow structures. Forming of filled and reinforced polymers. This includes filled commodity polymers such as talc-filled PP and high-performance composites such as carbon-fiber reinforced PEEK. Low-density foam thermoforming. Although this established market is more than 500 MIb (225 Mkg), there has been relatively few studies to determine the ways in which foams heat and stretch. This is now changing with the development of markets for polyolefin foams, higher temperature styrenic foams, PET foams and certain high-performance fire-retardant foams. Forming low-melt strength crystalline polymers, as epitomized by polypropylene. Polypropylene market development has always been inhibited by the poor melt strength of traditional homopolymer. Recent developments in high melt strength polymers and copolymers hold promise for both thin-gage and heavy-gage sheet.
And as with any evolving technology, there are newer technologies that are not quite market-ready. Some of these are outlined here as well.
9.2
Thermoforming Crystallizing Polyethylene Terephthalate
In the early 1970s, microwave technology had developed to the point where small microwave ovens were being used to reheat prepared foods in institutions and restaurants. Traditional unit serving containers were of aluminum. The industry sought a container that was "dual-ovenable", that is, a container made of an
inexpensive polymer that would be transparent to microwave energy and also capable of withstanding 2000C or 4000F convection oven temperatures. Crystalline polyamide~66 or nylon 66 and polyethylene terephthalate or PET were the logical choices. PET was chosen primarily on price and stiffness at 2000C. PET is a condensation polymer of ethylene glycol and terephthalic acid: X HOCH2-CH2-OH + X HOC-(|>-COH — 4OC-(|)-CO-CH2-CH2}X + X H2O
(9.1)
The useful polymer molecular weight range is about 20,000 to 40,000. The primary applications for PET are in films and fibers. In 1993, about 2,700 MIb or 1.2 Mkg PET was consumed in the US. Of this, approximately 170 MIb or 0.075 Mkg was converted into sheet for packaging. Of this, approximately 60 MIb or 0.027 Mkg was converted into crystallized PET, or CPET dual-ovenable packaging [2]. CPET applications have expanded from the ubiquitous "TV dinner tray" to bakery containers and bacon crispers [46]. The competition to CPET is PET-coated paperboard, BMC-thermoset polyester resin, talc-filled PP (in some instances), and styrene-maleic anhydride or SMA. PET Crystallinity PET is one of a family of condensation polymers that are characterized as slowly crystallizing, semi-crystalline polymers having glass transition temperatures above room temperature and melt temperatures in excess of 1500C. Table 9.1 gives a list of many polymers that meet these criteria [3,4]. PET was one of the first polymers to be exploited in polymer-specific processing schemes. Polymer-specific processes are those that have been invented specifically to circumvent the inherent processing weaknesses in the polymer that prevent it from being run in conventional processing equipment. The best example of polymer-specific processing is the development of stretch-blow molding for PET. Since PET has relatively poor melt strength, it cannot
Table 9.1 Transition Temperatures of Semicrystalline Polymers [3,4] Polymer
Glass transition temperature (0C)
Crystalline melting temperature (0C)
Crystallization rate at 300C below melt temperature (um/min)
Polyoxymethylene (POM) (Polyacetal) Nylon 610 (PA 610) Nylon 6 (PA 6) Nylon 66 (PA 66) Polyethylene terephthalate (PET) Polyphenylene sulfide (PPS) Polyetheretherketone (PEEK)
-50
180
400
40 50 50 70
225 225 265 265
— 150 1200 10
90 140
285 335
— —
be parison-blow molded with any degree of success. The high gas barrier properties of highly oriented PET provided sufficient incentive to develop an entirely new process, just for PET [5,45]. The high crystalline temperatures of the polymers in Table 9.1 have always intrigued designers and processors. Two characteristics have inhibited commercial realization of high temperature polymer performance. The rates of crystallization of most of these polymers are low when compared with polyethylene. And the practical ultimate extents of crystallization, that is crystallinity at an infinite time, X00, are also low. Most crystalline-tendency polymers show crystallinity levels of 40 to 90% [6]. With some polymers such as polycarbonate and polyvinyl chloride, the crystallization rate at processing temperature is so low that the polymer is amorphous for all intents. With other polymers such as nylon 6, PA 6 or polycaprolactam and PET, the crystallization rate is sufficiently low enough that the polymer can be readily quenched to an amorphous state. For PET, for example, thermoformers refer to amorphous PET as "APET". With carefully controlled temperatures, nylon 6 can be crystallized to 80% or more. On the other hand, even with carefully controlled temperatures, unadulterated PET usually cannot be crystallized beyond about 40%. For most semicrystalline polymers, the large noncrystalline or amorphous regions surrounding the crystallites are quite rubbery at temperatures substantially above the glass transition temperature but below the crystalline melting temperature. As a result, the semicrystalline sheet or shape in this temperature range is usually quite tough but not stiff. HDPE at room temperature range is a classic example. CPET at 2000C is another. These characteristics limit processing and performance of neat, unfilled or unreinforced polymers. In the past two decades, there have been many attempts to develop a high temperature PET food container. PET exhibits a very great density change with crystallinity, about 0.0012 g/cm3 or about 0.09% increase with each 1% increase in crystallinity. As a result, when PET is injection molded into a very hot mold and crystallized in situ, the mold part is under very high residual stress and is very brittle. If PET is injection molded into a very cold mold, the resulting part is usually amorphous. If this part is crystallized without fixturing, the internal stresses and reduction in part volume lead to excessive shrinkage and warpage. In the 1970s, it was found that PET crystallization rate could be altered with nucleants and other adducts. As a result, relatively heavy gage—to 60 mil, 0.060 in or 1.5 mm—PET sheet could be extruded without substantial crystallinity, typically < 3%. Since the glass transition temperature is 700C, the sheet is typically transparent and brittle-tough at room conditions. This sheet could be heated to a condition where the crystallization rate became significant. If the rapidly crystallizing sheet was then formed against a heated mold, crystallization could be continued until the formed sheet was sufficiently crystalline, typically about 20%, to withstand 2000C or 4000F air for up to 60 min. This development, commonly called CPET thermoforming, was commercialized in the mid-1980s and paralleled the other PET polymer-specific process of stretchblow molding. The formed part was unique in that it could sustain continuous use temperatures far in excess of the maximum forming temperature without excessive distortion. This is in contrast to conventional thermoforming, where the locked-in forming stresses relieve at use temperatures 20 to 500C below the highest forming temperature.
CPET Patents Since its discovery in the 1920s, polyethylene terephthalate has become one of the most important and one of the most studied polymers. Early on, PET was found to crystallize relatively slowly to a relatively low level. This is used to advantage in the production of high-tenacity fibers, since it allows an added degree of control of the molecular orientation during spinning. In turn, this allows for orientation-induced or strain-induced crystallization as well as thermally-induced crystallization. As noted above, amorphous PET sheet is brittle-tough at room temperature. Thermoforming applications for unoriented sheet include food, drug and medical packaging. APET is considered as a recyclable replacement for unmodified PS and RPVC for many applications. Uniaxially oriented PET is used as recording and photographic film tape base. Blown films are biaxially oriented, have high levels of orientation-induced crystallization and exhibit improved gas barrier properties. The stretch-blow molding process utilizes biaxial orientation to achieve high barrier levels for CO2 and is commercially one of the most successful polymer-specific processes developed. Keep in mind, then, that there are two ways of achieving crystallinity in PET and other polymers. Orientation-induced crystallization is common in biaxially oriented structures. Thermally-induced crystallization is used to produce high-temperature thermoformed containers. Fine inorganic powders are known to alter the thermally-induced rate of crystallization of PET [7]. Incompatible organic polymers such as polyethylene and polypropylene are also used to change the neat PET crystallizing rates [8-11]. In 1976, McTaggart patented a multistep method of producing a thermoformed crystalline PET part beginning with a PET containing 2 to 16% (wt) poly-4-methylpentene-1 and 1% (wt) TiO2 [12]. He taught forming on a cold mold and then fixturing and heating the formed part to crystallize the PET. He thought that the olefin retarded high levels of crystallinity and therefore the product was tougher and less brittle. In 1978, Dempsey et al patented a single step forming method that used up to 0.5% (wt) talc as a nucleant [13]. The sheet was rapidly heated using radiant heaters with surface temperatures up to 14000F or 7600C until the sheet had reached a crystallinity level of 3 to 10%, in approximately 10 s for 30 mil, 0.030 in or 0.75 mm thick sheet. It was then rapidly transferred to a mold having a temperature of 280 to 2900F or 138 to 143°C and held there until the sheet had achieved 25 to 30% crystallinity, approximately 10 s for 30 mil, 0.030 in or 0.75 mm sheet. In 1984, Gartland et al [14,15] found that olefins also acted as nucleants and so inorganic nucleants were not needed. They heated the 0.85 to 1.0 IV, 15 mil, 0.015 in or 0.38 mm sheet to 135 to 1500C until the crystalline level reached 10%, then held it against a heated mold for 5 to 7 s, or until the sheet had reached 20 to 35% crystallinity. They recommended against forming sheet thicker than 40 mils, 0.040 in or 1.0 mm. Characterizing Polyethylene Terephthalate As detailed below, intrinsic viscosity or IV is a measure of the molecular weight of PET. The IVs for PETs used for tire cord, certain films and many heavy fiber-form-
ing applications are typically in the 0.62 to 0.68 IV range. The IV range for bottle-grade, thin film and some fine fiber-forming PET applications is typically 0.78 to 0.85. PETs with IVs in the range of 0.9 to 1.0 are used in thermoforming, blown films and fine fibers. PETs with IVs in excess of 1.0 are usually very difficult to produce. These PETs are sought for high-tenacity fibers, injection blow molding and foams. Although low-IV PETs were used in the early CPET work, it was evident that higher molecular weight PETs gave improved crystallization rate control and tougher final products. With higher molecular weight, there are indications of finer spherulites and earlier secondary crystallization, leading to slower crystallization rates throughout the forming process and during the long-time, high-temperature use of the final product. Thus the final product has lower crystallinity, less brittleness and greater ductility at the end of the oven cycle. The recommended solvents for PET IV measurements are usually combinations of either phenol and tetrachloroethane or trifluoroacetic acid and methylene chloride. The relationships between inherent viscosity, [r|], intrinsic viscosity, IV, and numberaverage molecular weight, Mn, for various solvents are given in Table 9.2, as are other relationships, such as IV to inherent viscosity and zero-shear melt viscosity to IV [16]. Since melt viscosity is easier and faster to determine in quality control laboratories than is solution viscosity, the last correlation is commercially important. Intrinsic viscosity is not equal to inherent viscosity. At 1.0 IV, the error is about 7.4%. At 0.7 IV, the error is just less than 5%. The error in using these terms interchangeably is about 10% in the value of the number-average molecular weight at 1.0 IV and somewhat less at lower values of IV. As noted below, PET crystallization rate is maximum at about 175°C. However, the rate is so rapid at this temperature that laboratory measurements of isothermal crystallization rate, half-time for crystallization and induction time cannot be accuTable 9.2 PET Viscosity Relationships [16] Solvents (3O0C) 3 pts trifluoroacetic acid 1 pt methylene chloride (DuPont) 1 pt phenol 1 pt tetrachloroethane (3M) 60 pts phenol 40 pts tetrachloroethane (Goodyear) Other correlations Goodyear Zero-shear viscosity 1
Relationship1 [T\] = 2.45 x 10~3 (Mn)0-587 [rj] = 7.55 x 10~4 (M n ) 0685 [r\] = 7.50 x 10~4 (M n ) 068 [r|] = 0.5 • e(0 5 IV - !> + 0.75 • IV Ti0(poise) = 0.033 • (IV)502 • exp[15(kcal/mol)/R(T + 273)]
M = Inherent viscosity, IV = Intrinsic viscosity, Mn = Number-average molecular weight.
In (Induction Time, min)
Nucleant Concentration, wt % Figure 9.1 Effect of SiO2 nucleant concentration on isothermal induction time for polyethylene terephthalate, PET. Adapted from [17]
rately determined. As a result, these data are usually obtained at 1400C foramorphous PET initially at room temperature and at 2000C for amorphous PET initially at melt temperature. Many nucleants are used to promote crystallization in high-IV PETs. Figure 9.1 shows the effect of SiO2 concentration on the isothermal induction time of 1.0 IV PET [17]. The data can be described by: tx = ti,o eac
(9.2)
where t; is the induction time, ti>o is the induction time extrapolated to zero nucleant concentration, c is the nucleant concentration in (wt %), and a is the scale factor. This equation is thought to be reasonably accurate for inorganic nucleant concentrations up to 1% or so. The value for ti>o for inorganic nucleants is about 5 to 10 times less than the actual measured induction time for unadulterated PET. Thus inorganic nucleants in low concentrations act to accelerate the beginning of nucleation. Organic nucleants, on the other hand, show much less influence on induction time, as seen in Table 9.3 for LLDPE nucleant in [r|] = 1.04 PET [14]. The equation describing organic nucleant effect at isothermal conditions is: I1 = U l + b e — ]
(9.3)
where a and b are empirically determined constants for the specific organic nucleant. In addition, nucleants act to accelerate the rate of nucleation. One measure of the rate of nucleation is the half-time of nucleation. This is defined as the time needed to achieve 50% of the final level of crystallinity, as determined by isothermal differential scanning calorimetry or dilatometry [18]. As seen in Table 9.3, the half-time, t1/2, for LLDPE in PET decreases with increasing concentration in a fashion similar to that for induction time. Thus Equation 9.3 can be used for both induction time and half-time, if the proper values for a and b are determined. The relative effect of molecular weight on these empirical equations is unknown.
Table 9.3 1400C Isothermal Crystallization Rate Data for LLDPE-Nucleated PET, [r\] = 1.04 [14] Nucleant concentration
0% 1% 2% 3% 10%
Induction time, t;
(S)
Half-time, t1/2 Experimental (s)
Calculated (s)
26.5 20.8 18.5 17.6 17.0
22 15* 11.5 10.5 12
22.4 15.0 12.1 10.9 10.0
Experimental (s)
Calculated
26.5 22 18.5* 17.0 17.6
* Correlation points
As stated above, PET never achieves 100% crystallinity. The experimental upper limit for nitrogen-crystallized PET appears to be about 50 to 60% [19]. The degree of crystallinity at infinite time, X00, is a function of the isothermal crystallization temperature (Fig. 9.2) [20], A functional relationship for X00(T) to temperatures of 2000C or so is: X00(T) = OA[I - e - c < T - d ) ]
(9.4)
where again c and d are experimentally determined coefficients. This expression implies that the highest crystallinity level that can be achieved is 40% and that it is independent of the level of diluent. There is sufficient evidence to indicate that diluents such as LLDPE in PET change the induction time and the rate of crystallization but do not appreciably change the final level of crystallinity. The room temperature density for amorphous PET is 1.335 g/cm3. The extrapolated room temperature density for 100% crystalline PET is 1.455 g/cm3. The law of mixtures is used to obtain densities at various levels of crystallinity [21]:
I =*+ ^ P Pc Pa
(9.5)
where X is the crystalline fraction and pc, pa, and p are the densities of the crystalline, amorphous and partially crystalline polymers. A linear relationship is sometimes used [13]: p = XPc + ( l - X ) P a
(9.6)
Although this is not technically correct, it is accurate to within 1% of the law of mixtures to crystallization levels of 40% or so and it is much simpler to use than Equation 9.5. The relatively slow crystallizing nature of PET and its commercial importance has made PET the polymer of choice for technical studies of crystallization kinetics. The traditional method of observing and measuring crystallization is to watch crystallites grow on an isothermal hot stage of an optical microscope. Again, amorphous room temperature PET film is heated to 1700C or PET melt is cooled to 2000C for examination. The observer records the time when the first crystallites appear as the
Density, g/cm3
Temperature, 0C Figure 9.2 Temperature-dependent density of crystallized polyethylene terephthalate, PET, at ten crystallization half-times. Redrawn from [20]
induction time, and the time when crystallization has reached half its final value, X(t) = X00, as the half-time. The isothermal crystallization process has been described by the Avrami equation [22-24]: X(t) = X00[I -exp(k(T)tn] (9.7) where k(T), the isothermal Avrami function, is strongly dependent on temperature and n, the Avrami coefficient, is a function of the molecular nature of the crystallizing process. This equation is considered applicable only so long as the crystallites are growing unhindered. This is referred to as the primary crystallization region. In this region, the Avrami coefficient value for PET has a range of 3.0 to 3.5. The Avrami coefficient is a characteristic of the nature of the crystallization and its value does not appear to be influenced by nucleants. The Avrami function, k(T), is directly related to the half-time of crystallization and the value of the Avrami coefficient: (9.8)
Crystallization Half-Time, t1/2, min
Arnite A200,1.0 IV Goodyear 5041,1.0 IV Goodyear VFR 3801, 0.6 IV Goodyear 5041, 0.3% Talc Goodyear 5041,0.6% Talc
Crystallization Temperature, °C Figure 9.3 Crystallization half-times for various types of polyethylene terephthalate, PET
As shown in Fig. 9.3 [25], the crystallization half-time appears to be symmetric around a specific temperature, the temperature of maximum crystallization rate, T max . One rule of thumb relates this temperature to the glass transition temperature and crystalline melting temperature as: TJLx = KTSeIt + !?)
(9.9)
where the asterisk means absolute temperature. Another rule of thumb gives: T*ax = 0.8T*eit
(9.10)
For PET, T melt = 265°C and T g = 700C. These equations yield T m a x =168°C and 157°C, respectively. From isothermal half-time determinations, it appears that T m a x =175°C, experimentally, although values of 165°C to 1900C have been reported. It appears that T max is about 100C higher when the polymer is cooled from the melt than when it is heated from room temperature. The shape of the half-time crystallization curve appears to be a Gaussian distribution that is symmetric about T max and is given as [26]: ti/2(T) = t1/2(Tmax) • exp [4 In 2 (T - Tmax)2/D2]
(9.11)
When T = T max , t1/2 = t1/2 min . D is the half-width of the distribution function. For PET, D = 32°C. The characteristic crystallization data for PET are given in Table 9.4. Figure 9.3 shows the relative effect of PET IV on the isothermal half-time of crystallization [27].
Table 9.4 Characteristic Isothermal Crystallization Kinetic Data on PET Parameter
Data range
Recommended value
Avrami coefficient, r| TmeIt (0C) T g (0C) Tmax,cooling (0C) Tmax,heating (°Q T 1/2 , min (s)[1.0IV] D (0C)
3.0-3.5 252-265 67-70 174-190 158-165 30-60 8-32
3.55 255 68 175 162 35 32
Note that the earliest method of studying crystallization kinetics was the isothermal hot plate, a constant temperature environment. Newer techniques such as the differential scanning calorimeter (DSC) and the differential thermal analyzer (DTA) can examine polymer characteristics in a nonisothermal environment. And of course, the thermoforming process is quite nonisothermal. Although there have been many studies to relate nonisothermal test environments to the isothermal Avrami kinetics discussed above, most require reinterpretation of the initial Avrami assumptions. Ziabicki proposed a simple, empirical model [28]: K(T) = K(Tmax) • exp [1 - f(T - Tmax)]
(9.12)
where K(T)= l/t1/2(T) and K(Tmax) = l/t1/2.min. The rate of crystallization is then given as:
=(1 X)K(T)
£(£> -
^
This model is similar to the differentiated form for the Avrami equation if n = 1, contains no discrete induction time and so is frequently faulted. It has been noted, however, that "...nonisothermal crystallization kinetics are too complex for meaningful conclusions concerning mechanism and energetics of the nucleation process to be deduced..." [27]. The lack of an identifiable induction time in the nonisothermal process is of concern to others [26,28,30]. In one effort in which crystallization is considered akin to chemical reaction, the nonisothermal crystallization rate equation is replaced with a reaction rate equation in which the reaction rate constant replaces the Avrami-type constant. The nonisothermal induction time is considered a material function, and is given as: X1 = ^0- exp (T/To) (9.14) where ti>o and T0 are considered material properties that are obtained through standard DSC characterization. For most rapidly heating or cooling processes such as blown film or thermoforming, the relative effect of nucleants on induction time can probably be ignored as a first approximation. And the overall effect of induction time can probably be folded into the general crystallization kinetics equation as a portion of the half-time value.
The Effect of Temperature on Crystallization During Sheet Extrusion The general characteristics of extrusion and chill roll cooling were summarized in Chapter 8. Extrusion of PET requires an understanding of the interaction of sheet cooling and crystallization kinetics. This translates into proper chill roll size and careful roll stack temperature control for a given sheet thickness, nucleant concentration and IV value. There are two general approaches to heat transfer in relatively thin-gage sheet. The first is called the "distributed parameter system" or DP, where the time-dependent temperature is assumed to vary throughout the thickness of the sheet [29]. The second is called the "lumped parameter system" or LP, where time-dependent temperature is assumed to be uniform throughout the thickness of the sheet. For the distributed parameter or DP system, the operative equation is the one-dimensional transient heat conduction equation [31]: (9.15) where T is the local temperature, x is distance into the sheet and 6 is time. For a material, such as water or steel that exhibits a phase change at a very specific temperature, this equation is applied to each side of the liquidus-solidus interface. At the interface, the two equations are coupled through two boundary conditions. One states that the liquid and solid temperatures at the interface are equal and the second states that interfacial energy transfer must include the latent heat of fusion for the material. Methods of solution are given elsewhere [32-34]. Since most polymers exhibit phase change over a substantial temperature range, Equation 9.15 can be applied over the entire structure so long as it is modified to include a heat generation term: (9.16) where q', the heat generation term, is given as: (9.17) where p is the density and AH is the enthalpy of crystallization in Btu/lb or cal/g. As will be seen below, the boundary conditions include convection and radiation at the free surface and balanced heat flux and temperature at some internal plane for sheets heated or cooled on both sides. There are many ways of solving Equation 9.16 with appropriate boundary conditions. The standard method uses finite difference equations or FDE, the simplest version of which is the explicit or backward-time form. The equations in the x-direction or spatial gradient and 9-direction or temporal gradient are: (9.18)
(9.19) The heat generation term becomes: (9.20) These equations are combined to yield the forward FDE:
(9.21) The stability of this equation is given by: (9.22) The time step can be quite small, as seen in Example 9.1. Example 9.1 Time Step for Explicit FDE for Thin-Gage PET Consider 0.040-in thick PET sheet with a thermal diffusivity of 0.001 in2/s. If the heating time for this PET is 30 s and the sheet is heated from both sides, determine the time step and number of iterations needed if Ax = 0.002 in.
The time step is given as: AG < (0.002)2/2 • 0.001 = 0.002 s Therefore 30/0.002= 15,000 steps are required. There are three general types of boundary conditions to be considered here. The first is a conduction boundary condition such as direct contact of the extruded sheet against the chill roll. This boundary condition is given as: (9.23) where T0 is the surface temperature of the chill roll, for example. The second is a convection boundary condition such as contact of the extrudate with the cooler environment. This boundary condition is written as: (9.24) where Tsurf is the surface temperature of the polymer, Ta is the air temperature and h is a proportionality constant called the "heat transfer coefficient". The third is a radiation boundary condition such as the radiant heating of the sheet during thermoforming. The boundary condition in this case is given as: (9.25)
where T£ is the absolute radiant heater temperature and Tfurf is the absolute sheet surface temperature. Each of these equations can be developed into FDE forms [32,33]. Additional details are given in Chapter 3. For very thin sheet, the temperature across the sheet thickness is uniform and a lumped parameter or LP, time-dependent energy balance is used. For combined convection and radiation: (9.26) where Asl and A s 2 are the surface areas for convection and radiation, respectively, and V is the volume of the sheet. Consider the simple case where the sheet is cooled or heated uniformly on both sides. Then Asl = As2 = A, and V = AL where L is the sheet thickness. Then the equation is written as: (9.27) If Fo = a • d9/L 2 , the differential Fourier number, Bi = hL/k, the Biot number and R" = F*L/k, a radiation term, then the equation is written as: (9.28) One way1 of defining a radiation heat transfer coefficient, h r is: (9.29) As a result, the Biot number is redefined as Bic + r = (h -h h r )L/k and Equation 9.29 is written as: (9.30) Note that Bic + r can be positive if the air temperature is greater than the sheet temperature and negative if the sheet temperature is greater than the air temperature. This equation can be solved analytically to yield: (9.31) This represents a first-order response to a step change in environmental conditions. The first-order time constant is given as: (9.32) As is apparent, the time constant is larger-and the plastic sheet cools or heats more slowly for thick sheet or low values of heat transfer coefficient. Other examples are given in Chapter 3.
1
See Chapter 3 for another way of defining an effective heattransfer coefficient.
Hopper/Dryer
Down-Roll Chilled Stack Extruder
Figure 9.4 Sheet extruder schematic for 60 mil, 0.060 in or 1.5 mm amorphous nucleated polyethylene terephthalate, PET
Cooling CPET on Chill Rolls Even though PET is extruded in a melt condition and quenched as quickly as possible, crystallizing PET sheet for thermoforming applications is rarely absolutely amorphous. Several conditions contribute to this. The sheet has a finite thickness, low thermal conductivity and thermal diffusivity, and is usually cooled one side at a time. Even though the PET is doped with nucleants to enhance crystallization rate during the heating phase of thermoforming, they act to enhance crystallization rate during quenching of the extruded sheet. Consider a simple three-roll down-stack (Fig. 9.4) [34]. Although the Figure shows a bead or bank between the caliper roll and the first chill roll or polish roll, this bead must be maintained as small as possible. Flow in the nip between the first two rolls, the complex nature of flow in the bank, and the nature of viscoelastic swell of polymer as it exits the pressure zone of the nip are quite complex and are addressed elsewhere [35-37]. The heat transfer analysis of the crystallizing, cooling sheet has been carried out recently [38]. Typical assumptions are: • • • • • •
Flat velocity profile through the sheet, Constant chill roll temperature, Sheet thin when compared with roll diameter, Heat loss to the environment is accounted for with a single heat transfer coefficient, Differential bead thickness relative to sheet thickness can be easily accounted for, and The sheet does not move relative to the roll surface.
The easiest way of visualizing the cooling of CPET sheet is by unwrapping the sheet from the roll surfaces, as shown in Fig. 9.5 [39]. This schematic also shows the
Ambient
Roll #1 Sheet Thickness
Extrudate
Roll #3 Ambient
Ambient Roll #2
Time
Sheet Temperature Profile
Figure 9.5 Time-dependent temperature profile for extruded 60 mil, 0.060 in or 1.5 mm amorphous nucleated polyethylene terephthalate, PET [39]
expected time-dependent temperature profiles through the sheet. Note that sheet thickness, roll diameter and take-off speed will alter these temperature profiles. The base case is given in Table 9.5 for one example. As seen, the sheet thickness is 60 mil, 0.060 in or 1.5 mm, being extruded at 30-in or 760 mm at 1000 lb/h or 450 kg/h onto 36-in or 915 mm diameter chill rolls that are at 500C surface temperature. The ambient air heat transfer coefficient is assumed to be 5 Btu/ft2 • h • 0 F 1 . The nonTable 9.5 Crystallizing PET on Chill Roll Stack Basic Design Information [40] Initial polymer melt temperature Roll 1 surface temperature Roll 2 surface temperature Roll 3 surface temperature Contact time on roll 1 Contact time on roll 2, total Contact time on roll 3 Ambient air temperature Ambient air heat transfer coefficient Initial sheet thickness, extruded Sheet thickness on rolls 2 and 3 Polymer IV Nucleant concentration Minimum half-time of crystallization Temperature at minimum half-time
285°C 200C 5O0C 500C 2s 15 s 20 s 30 s 5 Btu/ft • h • 0 F 0.120 in 0.060 in 0.9 1.0% 35 s 176°C
The following data are for computation of temperature profile Number of elements Finite difference time step 1
8 0.1 s
See Section 5.4 for other information on convection heat transfer coefficients.
Temperature, 0C Crystallinity Level, % Figure 9.6 Computed time-dependent temperature and crystallinity level profiles for 60 mil, 0.060 in or 1.5 mm amorphous nucleated polyethylene terephthalate, PET on chill roll stack
isothermal crystallization kinetics are assumed to be Ziabickian for 0.9 IV and 1.0% inorganic nucleation. Figure 9.6 (top) shows the temperature profile through the sheet beginning with the bead at the back and moving forward to the sheet exiting the second chill roll [41]. Figure 9.6 (bottom) shows the crystallinity through the sheet for the temperature profiles of Fig. 9.6 (top). As is apparent from the arithmetic and as is clearly observed in actual practice, the crystallinity level of the surface of the sheet in immediate contact with the first chill roll shows essentially no crystallinity, while the surface that does not contact the chill roll for some time shows the highest level of crystallinity, 12% in this case. This is used to advantage in coextruded PET sheet where the low-IV layer containing the nucleant is extruded against the first chill roll and the high-IV layer containing no nucleant is exposed first to ambient air. An important insight into laboratory simulation of the quenching process is gathered from this example. The thermal gradient at one-fourth the distance into the
Crystallinity Level, %
275 0C
300 0 C
Sheet Thickness Figure 9.7 Parametric study of chill roll parameter effect on 30 mil, 0.030 in or 0.76 mm nucleated polyethylene terephthalate, PET for two intrinsic viscosities [IV]. (Top) 275°C PET melt temperature. (Bottom) 3000C PET melt temperature. Solid lines are 1% [wt] nucleant level. Broken lines are 0% nucleant level. Adapted from [42]
sheet from the initially free surface is as much as 30°C/s through the crystallizing region above 1200C or so. The final sheet crystallinity at this point is only 3%. Free surface cooling at this condition is only about 10°C/s and so yields a sheet having more than 11% crystallinity. In order to determine crystallization kinetics using differential scanning calorimetry, the DSC must be able to cool at rates of 10°C/s or less to rates of 30°C/s or more. The effects of polymer molecular weight and nucleant concentration on the final crystallinity levels of 30 mil, 0.030 in or 0.76 mm sheet extruded at two temperatures are shown in Fig. 9.7 [42]. As expected, lower IV PET crystallizes to a higher level than higher IV PET and nucleated PET crystallizes to a higher level than unnucleated PET. It is further apparent that the reduction in maximum crystallinity level between this 30 mil sheet and the 60 mil sheet of Fig. 9.6 is the result of sheet thickness.
Heating CPET in Roll-Fed Thermoformers Thermoforming equipment used for CPET forming is similar to but not identical to equipment used for APET, PVC or PS. Specific details of the equipment are discussed later. The general concepts of thermoforming, detailed in Chapters 3 and 4, applied to CPET forming, are considered here. Recall that crystallization is highly time- and temperature-dependent. Thus, the key to forming CPET parts beginning with nearly amorphous crystallizing PET sheet is to raise the sheet temperature to the forming range before substantial crystallization can occur. If the sheet is thin enough, rapid heating is controlled by the heater temperature. For relatively thick CPET sheet, care must be taken to prevent overheating and scorching the sheet surface before the sheet centerline is in the forming temperature range. Typically, residence time of the sheet in the oven should be about 2 to 5 times the residence time of the sheet on the heated mold. For example, if the residence time on the mold is 5 to 10 s, the residence time in the oven should be in the range of 10 to 50 s. Longer residence times in the oven imply low heater temperatures or exiting sheet having very high crystallinity levels. The exiting sheet surface temperature should be between 1200C and 1600C and the overall sheet crystallization level should be 3% to 12%. If the sheet crystallinity is too low, the sheet might stick and locally tear on the hot mold. If the sheet crystallinity is too high, the sheet stiffness may prevent complete draw-down into the mold or may require excessive forming pressure. As with most organics, PET absorbs at 3.5 um wavelength or a peak monochromatic temperature of about 6000C. There is also an absorption peak at about 5.9 um or about 2300C. For one type of oven [43], the effects of radiant heater temperature and residence time on the average sheet temperature and level of crystallinity are shown for a 0.9 IV, 60 mil, 0.060 in or 1.5 mm thick sheet with 1% inorganic nucleant using the lumped parameter heat transfer and a Ziabickian crystalline kinetic model (Fig. 9.8). As is apparent, crystallization levels are low if the radiant heater temperatures are low. It is also interesting to note that the crystallinity level plateaus if the heating rate is too high. A comparison of the distributed parameter method using FDE and the lumped parameter method using Equation 9.32 for 60 mil, 0.060 in or 1.5 mm 0.9 IV PET with 1% inorganic nucleant is shown in Fig. 9.9 [44]. Note the good agreement between the average temperature and average crystallinity level predicted by the DP and the value from LP. Forming the Sheet The sheet that is presented to the mold should have an average temperature of 1200C to 1600C, about 3% to 12% crystallinity and should be rapidly crystallizing. For transparent PET, the sheet is exhibiting whitening as it is transported into the mold/platen area. The sheet may also be tightening between the chain rails. Excessive crystallization may result in the sheet tearing out of the pins. The mold temperature should be 1500C to 1900C or within a few degrees of Tmax, the temperature for maximum crystallization rate. The exact mold temperature will depend on:
Temperature,0C
Crystallinity Level, %
Base Case
Base Case
Oven Time, s Oven Time, s Figure 9.8 Parametric effect of radiant heater temperature for 60 mil, 0.060 in or 1.5 mm nucleated polyethylene terephthalate, PET, using lumped parameter model. (Left) Time-dependent sheet temperature with radiant heater temperature as parameter. (Right) Time-dependent crystallinity level at same conditions
Distributed Parameter Surface Average Centerline
Crystallinity Level, %
Temperature,0C
Lumped Parameter, Base Case Lumped Parameter, Base Case Distributed Parameter Surface Average Centerline
Oven Time, s Oven Time, s Figure 9.9 Comparison of lumped parameter model and distributed parameter model for 60 mil, 0.060 in or 1.5 mm amorphous nucleated polyethylene terephthalate, PET with radiant heater temperature of 4000C [see Fig. 9.8]. (Left) Time-dependent temperature profile through sheet. (Right) Time-dependent crystallinity level through sheet at same conditions
• • • • • • • • •
The temperature and crystallization level of the sheet, The sheet thickness, The IV of the polymer, The depth of draw, The amount of detail required in the molded part, The role of plug assist, The orientation of the mold (male or female), Whether pressure is used, and if so, The available pressure for forming.
Typically, CPET parts are formed into an up mold. That is, the female mold is mounted above the sheet with plugs advancing from below the sheet. Actively heated aluminum plugs are recommended, with the plug surfaces nylon- or teflon-coated if plug mark-off is a problem. For pressure forming, the pressure box is advanced against the sheet from below. In cases where very thin sheet is being formed into relatively large surface area parts, a cavity isolator or clamping-off grid carries the sagging sheet upward against multiple cavity molds. Keep in mind that as the PET crystallizes, it is rapidly increasing in density. This is manifested as dramatic shrinkage in sheet dimension. Much of this is taking place while the sheet is against the hot mold. As a result, the forming pressure must be sufficient to keep the sheet pressed tightly against the mold surface throughout the crystallizing portion of the cycle. Air pressure of at least 50 lbf/in2 or 0.34 MPa is recommended, with the pressure being maintained throughout the molding time. The machine sequence must allow for cavity venting prior to separating the pressure box from the mold base. The instant the sheet surface touches the hot mold, it attains the mold surface temperature. As with nearly all thermoform molding operations, the sheet surface that is free of the mold surface can interchange energy only with quiescent air. The rate of conduction heating is proportional to the square of the sheet thickness. As a result, the thinnest sections of the sheet, such as the three-dimensional corners, heat much more rapidly than the thickest sections, such as the lip or rim region or the bottom of shallow draw containers. Even though this effect is somewhat tempered by the fact that the thick sections touch the mold first and the thin sections touch last, the crystallization levels in the thin sections are usually substantially greater than those in thick sections. Since excessive crystallization yields brittleness in thermallyinduced crystalline PET, thin three-dimensional corners are more likely to fail under impact than the thicker rim areas. As noted, residence times of 5 to 10 s on hot molds are typical for 30 to 60 mil, 0.030 to 0.060 in or 0.76 to 1.5 mm sheet. Cooling the Formed Part When the part has been formed and the crystallinity level of the sheet reaches about 20% to 25%, the sheet is stripped from the mold. The hot sheet is then exposed to ambient conditions and the web cools to room temperature or until the parts are ready to be trimmed from the web. The sheet continues to crystallize during cooling. As a result, traditional quenching means such as forced air or water spray mist are
Temperature,0C
Equilibration Oven Mold Cool
Crystallinity Level, %
Time, s
Time, s Figure 9.10 Distributed parameter parametric effect of environmental conditions on time-dependent temperature, top, and crystallinity level, bottom, For 40 mil, 0.040 in or 1.0 mm nucleated polyethylene terephthalate, PET. A: Sheet surface temperature during heating for base case. B: Sheet surface temperature during heating with 50% greater air convection heat transfer. C: Centerline temperature for base case. D: Free surface temperature when thermoforming into 1400C mold rather than 175°C base case mold temperature
not recommended. In some machines, a cooling table is provided, This allows the web to cool very slowly and allows the thicker sections of the molded parts to continue to crystallize while the thinner sections usually cease crystallizing relatively quickly. In some machines, a second mold is used to retain the formed part dimension during cooling. In this machine, the second mold temperature is carefully monitored. If it is too high, crystallinity continues and the final part becomes brittle. If it is too low, the formed part has low' crystallinity and it will distort at elevated use temperatures. Figure 9.10 [45,46] shows several temperature profiles for 40 mil, 0.040 or 1 mm sheet, beginning with 0% crystallinity and ending with about 20% crystallinity. As is apparent, the sheet first contacts the mold with a crystallinity level of about 5% to 7% and exits the mold with a crystallinity level of about 15%. Crystallinity continues throughout the cooling portion of the process until the formed part reaches a final value of about 20%. The crystallinity level of the free
surface is about 3% to 5% below that for the part surface that had contacted the 1400C mold surface.
Trimming Parts from Web Trimming technology is discussed in detail in Chapter 5. Trimming CPET parts from web offers additional challenges. Since PET exhibits a significant increase in density with crystallinity level, trim die dimensional tolerances are difficult to predict. Since the parts continue to crystallize after release from the mold, trim-in-place is not practical. Spacing between formed parts, trim guides and registration nubs can change, depending on the crystallinity level of the polymer in the web between parts. Furthermore, uneven crystallinity level between webs can cause the structure to warp into a non-flat configuration, leading to feeding problems in the trim press. Greater daylight between platens on hump-back trim presses is required and spring-loaded guide rods are sometimes used to help center the sheet prior to trimming. Conical or deep-drawn wedge-shaped registration nubs and individual cavity locators are recommended. Room temperature CPET at about 20% crystallinity level is ductile-tough. Therefore, substantial force is needed to trim parts from web. Furthermore, since PET is a fiber-forming polymer, fibers are frequently formed during the trimming. Fibers, also called angel hair or fuzz, are most prevalent when trim dies are dull or blunt. As a result, very sharp trim dies are required and dies must be meticulously honed or sharpened on an hourly or shift basis. To minimize fiber forming, compression cutting is preferred over shear cutting. Even though CPET at elevated temperature is much easier to trim, continuing crystallization and attendant warpage makes elevated temperature trimming difficult, if not impractical. Heated dies can be effective if the sheet is more than 40 mil, 0.040 in or 1 mm thick and if the initial cutting rate is slow.
Troubleshooting CPET Forming Traditional troubleshooting guidelines of Chapter 10 apply to thermoforming CPET. Additional guidelines are given in Table 9.6. Other extrusion guidelines are given in Chapter 8.
9.3
Pressure Forming
As noted in Chapter 1, in the 1870s, some of the first semi-synthetic plastics were skived into thin sheets that were then steam heated and pressed into detailed molds to produce items such as baby rattles and jewelry cases. Modern-day pressure
Table 9.6 Troubleshooting Guide for CPET Thermoforming Problem
Probable cause
Suggested course of action
Excessive outgassing of sheet during heating
Fugitive adducts in polymer
Remove volatile adducts Rapidly heat sheet only in last zone of oven Change to HDPE, PP nucleants
Organic nucleants such as LLDPE, LDPE in polymer
Sheet splits, pulls from rails
Moisture
Check moisture level in PET sheet before forming Use in-line predryer
Sheet crystallizing in oven
Shield rails from heaters Water-cool rails Reduce amount of nucleant Use parallel rails Use rounded pins Increase (slightly) pin diameter Reduce last zone oven temperature Reduce time in oven Increase transfer rate to mold
Diverging rails Pin shape causing notch sensitivity Sheet crystallizing between oven and mold
Sheet tears during forming
Sheet too hot Crystallinity level too low
PET IV too low
Plug advancing too quickly, too early Incorrect plug shape
Sheet sticks to mold
Mold surface too hot Polymer contains adduct that is diffusing to the sheet surface
Reduce sheet temperature Hold sheet in oven longer Delay applying plug/pressure assist Increase next-to-last zone oven temperature Increase molecular weight of virgin PET Reduce amount of regrind Thoroughly dry PET, PET rolls Delay plug advance Slow initial plug advance rate Redo plug shape, rounding all radii Reduce plug dimension
Reduce Reduce Change duct Reduce
mold temperature sheet temperature to higher temperature adadduct concentration (Continued)
Table 9.6 (Continued) Problem
Webbing
Oily plate-out on mold, plug
Excessive part distortion
Nipples on formed part
Probable cause
Suggested course of action
Draft angle too low
Increase draft angle on male mold elements
Excessive sheet sag
Reduce sheet temperature Thermoform into up mold Increase crystallinity at molding time Add web catchers at corners
Low molecular weight
Increase PET molecular weight Check PET sheet IV Check moisture content of PET sheet Reduce regrind amount
Mold cavities too close
Increase land between cavities Create artificial dam to catch web
Pattern heating profile wrong
Change pattern heating to reduce temperature in center of sheet
Fugitive adducts in polymer
Check for waxes, internal lubricants, colorants and remove
Organic nucleants such as LLDPE, LDPE in polymer
Chemically analyze for olefin Reduce olefin concentration Change to HDPE, PP nucleant
Part crystallizing after molding
Increase mold temperature Increase time in contact with mold
Crystallization too high
Reduce nucleant concentration Reduce residence time on mold Decrease (or increase) mold temperature Increase molecular weight
Part releasing from mold prematurely
Increase cavity pressure during forming Reduce crystallization rate
Nonuniform wall thickness
Change plug shape Change pattern heating profile
Sheet too hot
Reduce sheet temperature
Mold too hot
Reduce mold temperature Increase sheet crystallinity prior to touching mold by delaying oven transfer
Table 9.6 (Continued) Problem
Transparent areas/bands
Blotchy or shiny/dull areas on part
Probable cause
Suggested course of action
Excessive pressure
Reduce pressure Delay pressure boost until sheet has cooled slightly
Vacuum holes too large
Plug/redrill vacuum holes
Sheet not touching mold locally
Add vacuum holes Increase air pressure Check mold draft angle
Excessive sheet sag at molding temperature
Reduce sheet temperature locally Employ sag bands
Sheet temporarily folding
Check sheet transfer rate for nonuniformity Reduce sheet temperature
Poor mold heat transfer
Check channel flow for blockage
Mold surface temperature nonuniform
Check mold temperature with IR monitor Check flow paths through mold Check all fluid lines
Sheet temperature nonuniform
Readjust heating pattern Check for excessive sag away from top heaters
Poor regrind mixing
Measure IV of sheet in blotchy areas Add backpressure to extrusion process
Poor vacuum
Check all vacuum holes for plugging Increase vacuum in critical areas Check vacuum at mold cavity Make certain air pressure is adequate for sheet temperature, mold temperature, and crystallinity level
Poor air pressure
Microscopic surface bubbles in parts
Mold surface too smooth
Roughen mold surface locally
Moisture
Thoroughly dry PET before extruding Store PET rolls in silica gel/PE wrap Employ preheater to pre-dry sheet
Fugitive adducts in PET
Replace with stable adducts If accompanied by mold plate-out, replace low melting olefin nucleant with higher melting one (Continued)
Table 9.6 (Continued) Problem
Probable cause
Suggested course of action
Poor bottom logo definition
Crystallinity too high
Increase Increase Increase Increase
Mold too cold
Increase mold temperature
Excessive regrind
Reduce regrind amount
Overheating
Reduce temperature Reduce regrind amount Increase thermal stabilizer package
Crystallinity level too high
Reduce time on mold Cool finished parts more rapidly Reduce nucleant level Increase molecular weight
Yellowing
Parts splitting during trimming
Fuzz or angel hair on parts
sheet temperature forming rate number of vacuum holes air pressure
Edges have sharp radii
Increase radii
Excessive orientation at edges
Use moats, dams Use cavity isolators to minimize sheet pull-down into cavity
Excessive thickness differential between edges and mold flats
Use more generous radii
Dull trim dies
Sharpen trim dies on regular schedule Change to hardened dies, selfsharpening dies
Shear cutting
Compression cutting
forming began in earnest in the late-1970s when designs in electronic cabinets, automotive interiors and other consumer products moved away from generouslyrounded contours and relatively smooth surfaces toward crisp, sharp corners and distinct textures such as pebble finish, wood grain and simulated leather [47,48]. In traditional vacuum forming, crisp texture and sharp radii can only be achieved with very hot sheet and heated molds. In the discussion on vacuum hole size, a clear relationship was developed between the amount of plastic drawn into a depression and (P/E), the ratio of applied pressure to temperature-dependent modulus: (9.33)
where D is the characteristic lateral dimension of the depression, oc is the characteristic depth of the depression, a is a geometric constant with a value between 1 and 2, and t is the local sheet thickness. D is usually very small and a is very large for most surface textures. A temperature-dependent material parameter, 4>(T), essentially the temperature-dependent secant tensile modulus, was defined in Chapter 4 to characterize the polymer resistance to applied pressure. As noted in Table 4.8, the value of (J)(T) should be less than about 10 times the applied pressure value in order to achieve draw-down. For vacuum forming, the differential pressure never exceeds 14.7 lbf/in2 or 0.1 MPa and is usually about 10 lbf/in2 or 0.07 MPa. As a result, for vacuum forming, cj>(T) is usually less than about 147 lbf/in2 or 1 MPa. To get crisp detail, P/E or P/(|)(T) must be as large as possible. And as details become finer, P/E or P/c()(T) must increase. It is therefore apparent that applied pressure must be increased if increased surface detail cannot be achieved by further increasing sheet temperature. Vacuum forming is truly pressure forming with the differential pressure on the sheet being 1 atmosphere, 14.7 lbf/in2 or 0.1 MPa or less. Pressure forming as understood today is the application of additional pneumatic or air pressure, with pressures to 100 lbf/in2 or 0.7 MPa common and pressures to 200 lbf/in2 or 1.4 MPa used for reinforced and highly filled polymers and certain difficult-to-form neat polymers such as polycarbonate. Safety is of paramount importance when pressure forming. When the pneumatic pressure exceeds about 100 lbf/in2 or 0.7 MPa, special attention must be paid to the machinery and controls. The platen clamping system needs to be sufficiently robust to withstand the air pressure. The mold must be capable of tolerating high pressures without distortion, metal fatigue, surface microcracking or catastrophic collapse. Bolsters or support posts are needed throughout the vacuum box. The pressure box, and in some instances the mold and pressure box combination, may need certification as unfired pressure vessels. The method of closing and clamping the pressure box against the mold and the method of gasketing against the air pressure must be carefully reviewed with regard to safety. Safeguards for venting the pressure box prior to opening the mold must be in place and regularly inspected. If it is determined that pneumatic pressure in excess of 100 lbf/in2 or 0.7 MPa is required to thermoform the hot sheet to the desired level of detail, a careful cost, engineering and safety comparison of pressure forming on special machines, matched die molding, and sheet stamping or compression molding is warranted [49-53].
Thin Gage Pressure forming is used with thin-gage and heavy-gage sheet. In the 1970s, pressure was used to form 30 mil, 0.030 in or 0.76 mm polypropylene homopolymer below its melt temperature [54]. The technique is called "solid phase pressure forming" or SSPF (Fig. 9.11) [55]. The melt viscosity of homopolymer polypropylene at its melt forming temperature is about one-tenth that of polystyrene at its forming temperature. As a result, this type of polypropylene exhibited excessive sag and was considered unformable. The apparent viscosity of this polypropylene about 1600C or about 2° to 5°C below its melt temperature was about 100 times that of polystyrene.
Polypropylene Sheet Heated to 1600C
0.4 to 0.7 MPa Air Applied at End of Plug Travel
Figure 9.11 Schematic of plug-assisted pressure forming of polypropylene, PP, also called solidphase pressure forming or SSPF
In order to form this polypropylene at this temperature in the solid phase, the sheet required plug assist and air pressure of 80 to 100 lbf/in2 or 0.55 to 0.7 MPa. The characteristic stress-strain curves for homopolymer polypropylene to 1600C are given in Fig. 9.12 [56]. Note that this polypropylene shows relatively little strain-rate hardening at 1600C. In the past decade or so, improvements to polypropylene melt strength have enabled thermoformers to melt form polypropylene in much the same way as low-density polyethylene. Improvements include copolymer polypropylene, high molecular-weight polypropylene and high crystallinity polypropylene [57-59]. The nature of polypropylene forming is discussed in more detail below. The development of crystallizing polyethylene terephthalate (CPET) thermoforming has also required applied pressure during the forming and crystallizing step. As noted above, air pressure helps prevent the formed part from shrinking away from the mold as it crystallizes. Pressures to 100 lbf/in2 or 0.7 MPa are used in CPET forming. Recently, pressure has been used during plug-assisted deep draw forming of APET or amorphous polyethylene terephthalate into thin-wall drink cups. The combination of pressure and controlled plug rate is used to minimize necking or banding1 in the side wall and rim region of axisymmetric parts such as cups. 1
Necking is an obvious change in the thickness of the part wall, usually in a band perpendicular to the axis of the part. As discussed in the section on stress-strain-rate of strain behavior of polymers, necking is the result of localized drawing during forming. Necking is a temperaturedependent material property and so is distinguished from chill marks or mold marks that are related to localized drawing on the mold surface, and plug marks that are related to the region where the cooler plug touches the hot sheet.
Strain, MPa
Elongational Ratio Figure 9.12 Temperature-dependent tensile stress-strain curves for polypropylene, PP, homopolymer. Redrawn from [56] and used with permission of copyright owner
Heavy Gage Pressure formed heavy-gage products were first produced in 1959 [50]. Heavy-gage pressure forming focuses on surface texture and contour crispness. Pressure forming is sometimes used to compensate for extraordinarily long pre-stretching time. For example, when the product requires deep forming onto a male mold, the sheet is usually stretched first into a bubble either by inflation or by stretching into a vacuum box. Then the mold is immersed in the stretched sheet. In order to achieve good bubble stability, most polymers must be relatively cool during inflation. This is also true if the mold also acts as a plug to stretch the sheet during initial contact. A pressure box or bell is placed over the mold near the end of or just after the mold immersion. Pressure is then used to press the cool sheet against the mold in two- and three-dimensional corners. Pressure is used with female molds for the following reasons:
Vacuum Forming
Corners Incompletely Formed
Pressure Forming
Corners Completely Formed
Figure 9.13 Pressure forming (right) yields details on female portions of the mold surface that have greater sharpness than those produced by vacuum forming (left)
• The part requires crisp texture and sharp corners, • There must be a sharp demarcation between textured and non-textured surface areas, • The draw is deep, • A cool plug or a very large surface area plug is used, • The sheet does not have good hot strength, and/or • The modulus is very temperature-dependent, requiring that the sheet be formed very rapidly [60]. Typical air pressures are 20 to 50 lbf/in2 or 0.14 to 0.34 MPa. Corner radii to 0.005 in or 0.13 mm have been pressure formed from PMMA and polycarbonate into transparent fresnel lenses and light fixtures [61]. This is shown schematically in Fig. 9.13 [62], Texture surface dimensions of 100 microinches, 0.0001 in or 2.5 urn and depths to 0.010 in or 0.25 mm with ABS have been achieved using pressures to 100 lbf/in2 or 0.7 MPa. Draft angles of 1° plus 1° per mil, 0.001 in or 25 urn of texture depth are recommended for vertical sides of female molds and 5° plus 1° per mil, 0.001 in or 25 urn of texture depth for vertical sides of male molds are recommended [61]. Forming tolerances for cast aluminum molds of +0.020 in or ±0.5 mm for the first 12 in or 305 mm of mold length and an additional ±0.001 in per inch of length or ±0.001 mm per mm beyond are expected. For machined aluminum molds, forming tolerances of ±0.001 in per inch or ±0.001 mm per mm are expected [63]. For ribs and louvers, the height of the rib and the distance between ribs should be equal. Some additional design information is given in Table 9.7. In addition to the safety and engineering aspects of pneumatic pressure, molds must be sufficiently robust to withstand forces of at least twice that expected. Water lines, for example, must be sufficiently far from the mold surface to prevent mold collapse into them. The high pressure that is sought to press plastic into highly
Next Page Table 9.7 Recommended Radius Dimensions for Pressure Thermoformed Equipment Cabinet Applications [63]
Depth of draw
Radius
(in)
(mm)
(in)
(mm)
0-3 3-6 6-12 >12
0-76 76-152 152-305 >305
> 0.030 0.030-0.090 0.090-0.125 >0.125
>0.76 0.76-2.3 2.3-3.2 >3.2
detailed textures also forces plastic into vent holes, machining marks, scratches, ejector pins and rings and other elements on the mold surface. Molds are usually cast or machined aluminum. Sprayed metal/epoxy molds are used for very short runs of less than 100 parts at reasonably low pressures, less than 50 lbf/in2 or 0.34 MPa. For production runs of less than about 10,000, large-part, heavy-gage pressure forming is economically competitive with injection molding, reaction injection molding and foam injection molding [64]. Pressure forming is also combined with other processing elements to achieve unique products [65-67]. For example, the pressure box can contain hydraulic or pneumatic elements that allow secondary stamping or coining on the still-hot free surface of the sheet. In this way, part numbers or other identification codes can be placed in non-appearance portions of the part. These elements can also press inserts into the hot free surface of the sheet.
9.4
Forming Filled and Reinforced Polymers
Fillers are usually inorganic particulates such as talc, calcium carbonate or chalk, mineral wool, glass or quartz powder, graphite, carbon black and metal oxides. Most fillers are spherical or platy. Some such as asbestos and TiO2 are acicular or fiberlike. Long fibers and continuous fibers provide substantial reinforcement to the polymer. Figure 9.14 [68] shows the various types of textile glass fiber products. Carbon, organic fibers such as polyaramides and polyamides, silicon carbide and boron fibers are also used to reinforce thermoplastics. The characteristic effects of fibers and reinforcements on polymer properties are illustrated in Table 9.8 [69]. Fillers and fibers are usually added to improve polymer stiffness. They can dramatically change the polymer load-bearing characteristics as shown for polystyrene in Fig. 9.15 [70]. As is apparent, below the polymer glass transition temperature, polymer stiffness increases with increasing filler loading. Although there appears to be a slight increase in polymer stiffness with filler loading at Tg, the shapes of
Previous Page Table 9.7 Recommended Radius Dimensions for Pressure Thermoformed Equipment Cabinet Applications [63]
Depth of draw
Radius
(in)
(mm)
(in)
(mm)
0-3 3-6 6-12 >12
0-76 76-152 152-305 >305
> 0.030 0.030-0.090 0.090-0.125 >0.125
>0.76 0.76-2.3 2.3-3.2 >3.2
detailed textures also forces plastic into vent holes, machining marks, scratches, ejector pins and rings and other elements on the mold surface. Molds are usually cast or machined aluminum. Sprayed metal/epoxy molds are used for very short runs of less than 100 parts at reasonably low pressures, less than 50 lbf/in2 or 0.34 MPa. For production runs of less than about 10,000, large-part, heavy-gage pressure forming is economically competitive with injection molding, reaction injection molding and foam injection molding [64]. Pressure forming is also combined with other processing elements to achieve unique products [65-67]. For example, the pressure box can contain hydraulic or pneumatic elements that allow secondary stamping or coining on the still-hot free surface of the sheet. In this way, part numbers or other identification codes can be placed in non-appearance portions of the part. These elements can also press inserts into the hot free surface of the sheet.
9.4
Forming Filled and Reinforced Polymers
Fillers are usually inorganic particulates such as talc, calcium carbonate or chalk, mineral wool, glass or quartz powder, graphite, carbon black and metal oxides. Most fillers are spherical or platy. Some such as asbestos and TiO2 are acicular or fiberlike. Long fibers and continuous fibers provide substantial reinforcement to the polymer. Figure 9.14 [68] shows the various types of textile glass fiber products. Carbon, organic fibers such as polyaramides and polyamides, silicon carbide and boron fibers are also used to reinforce thermoplastics. The characteristic effects of fibers and reinforcements on polymer properties are illustrated in Table 9.8 [69]. Fillers and fibers are usually added to improve polymer stiffness. They can dramatically change the polymer load-bearing characteristics as shown for polystyrene in Fig. 9.15 [70]. As is apparent, below the polymer glass transition temperature, polymer stiffness increases with increasing filler loading. Although there appears to be a slight increase in polymer stiffness with filler loading at Tg, the shapes of
Glass Filament
Glass Strand Single Glass Filament Yarn
Glass Roving
Chopped Glass Strand
Milled Glass Fiber
Folded or Cabled Filament Yarn
Multiple Wound Glass Filament Yarn
Woven Glass Roving Fabric Woven Glass Textile Glass Mat Figure 9.14 Various types of fibrous products used in thermoplastics [68]
60% Mica 40% Mica 60% Asbestos
Shear Modulus, GPa
40% Asbestos 20% Mica
20% Asbestos 20% CaCO 3
Neat PS
Temperature,°C
Figure 9.15 Effect of fillers and fibers on temperature-dependent shear modulus of polystyrene, PS. Redrawn from [70]
Table 9.8 Effect of Fillers and Reinforcements on Polymer Properties [69] Key tofillersand fibers A = Glass fibers B = Asbestos C = Wollastonite D = Carbon fibers E == Whiskers
F = Synthetic fibers G = Cellulose H = Mica I = Talc
Polymer property Price reduction Extrusion rate Tensile strength Compressive strength Elastic modulus Impact strength Reduced thermal expansion Reduced shrinkage Heat conductivity Heat resistance Electrical conductivity Electrical resistance Chemical resistance Abrasion performance Abrasion in equipment
J = Graphite K = Sand or quartz powder L = Silica M = Kaolin or clay
Fibrousfillersand reinforcements B A C D E
- +
G
Platelet-like types I H J
+
+ -
+ +
+ +
+
+ +
+ +
++
+ + + +
+ 0
0
0
0
0
+ +
+ +
+ +
+ + +
+ +
+ +
++ + +
0 0
+ + = Strong effect + = Mild effect 0 = No effect — = Negative effect —t- or H— = Variable effect
+ - +
+
4-
+
Q
+
+ +
p
O
++ +
+
+
+
+ +
N
0
++
++
Spherical fillers M L K
++
+ +
++ +
F
N = Glass spheres O = Calcium carbonate P = Metal oxides Q = Carbon black
+ + 0
0
0
the curves are quite similar. Increased forming pressure is needed to overcome the increased stiffness at temperatures just above the glass transition temperature. Filled thermoplastics are usually clamped solidly during forming. Under tensile load, randomly oriented short fibers, whether natural such as asbestos and TiO2, or prepared from continuous glass and mineral wool, behave much like particulate fillers. The thermoforming biaxial stretching mechanism acts to separate the short fibers and filler particles. If the fiber concentration is relatively low, less than 20% wt or so, there is little initial entanglement in the extruded sheet. As a result, fiber resistance does not add greatly to the tensile resistance of the matrix or polymer around the fiber during the forming portion of the process. If continuous fibers are used or if the discontinuous fiber concentration is increased to 40% wt or more, the composite becomes greatly resistant to tensile loading. Consider continuous uniaxial fiber reinforcement of a polymer matrix. The stress-strain equation in the fiber direction is given as: (9.34) where a is the applied stress, <|)f is the volume fraction of fiber, af is the stress on the fiber and a m is the stress on the matrix or polymer. If both the fiber and polymer are Hookean, or have linear stress-strain curves, this equation is written as: (9.35) where Ef and Em are the moduli and ef and em are the elongations of the fiber and matrix, respectively. The composite modulus is: (9.36) where Ec is the modulus of the composite. For most reinforcing fibers at matrix thermoforming temperatures, E f » Em. For reasonable values of cj)f, this equation is approximated as: (9.37) It has been noted that the "...polymer matrix is ... simply acting as a glue..." [71]. As noted above, good formability depends on the value of applied pressure being at least one-tenth the value of the sheet modulus. As a result, as the fiber concentration increases, the applied pressure must increase in proportion. For randomly placed continuous fibers, the following moduli apply: (9.38) (9.39) where Ec is the value obtained from Equation 9.37.
Pressure Forming Clamp Frame
Air Pressure Oven
Oven Laminate Mold
Vacuum
Heating
Forming Matched Die Forming
Clamp Frame Oven
Oven
Plug Laminate
Cavity
Heating
Forming
Figure 9.16 Illustrations of (top) pressure forming and (bottom) matched die molding of reinforced or stiffened laminate or composite. Redrawn from [72,73]
Continuous fibers are considered to be inextensible. As a result, thermoforming focuses on slip forming or changing the shape of the sheet without substantially increasing its surface area (Fig. 9.16) [72,73]. Products are restricted to shallow draws and very simple shapes. Example 9.2 clearly illustrates this. It is now believed that the standard method of deformation is interply slip, much like the way in which individual playing cards slide over one another in a bending mode. The proliferation of technical developments dealing with shaping continuous fiber-reinforced highperformance thermoplastics attests to the growing economic importance of this area [74-88].
Example 9.2 Approximation of Pressure Required to Thermoform Reinforced Sheet Consider that an unreinforced polymer is vacuum formed with 10 Ibf•/'in2 or 0.07MPa. The polymer modulus at the forming temperature is 100 lbf/in2 or 0.7MPa. The polymer is random-in-plane reinforced with glass having a modulus of 100,000 MPa. Determine the approximate pressure required to stretch jform the sheet containing 10% (vol) continuous glass fibers and 10% (vol) discontinuous glass fibers with na — 2. Can this sheet be thermoformed?
For vacuum forming, the modulus-to-pressure ratio, E/P=10. The onedimensional modulus of the continuous fiber composite is: Ec = 0.1 • 100,000 MPa = 10,000 MPa For two-dimensional mat, the modulus is: E2D c = 0.375 • 10,000 = 3,750 MPa The pressure required to stretch and deform this sheet is then: Pc « 0.1 • 3750 = 375 MPa = 54,000 lbf/in2 For discontinuous fiber, From Fig. 9.17, r\ «0.2. As a result, the pressure required to stretch and deform the continuous fiber-reinforced sheet is: Pd = 0.2 -P c = 10,900 lbf/in2 It is apparent that this sheet must be compression molded or slip formed.
For long, discontinuous fibers, Equation 9.36 is modified to account for the stress concentrations at the fiber tips: Ec,d = T v c ^ - E f + ( l - ^ ) - E m
(9.40)
where r| is a correction factor that depends on the product, na, where n is a function of the ratio of polymer to fiber moduli and of the ratio of interfiber spacing to fiber diameter, and a is the fiber aspect ratio or length-to-diameter ratio. The value of rj is extremely dependent on the value of na as seen in Fig. 9.17 [89]. Typically n is on the order of 0.1 to 0.4 and a should be greater than 50. Equations 9.36 and 9.37 are used for random two- and three-dimensional structures, with Ec being replaced with Ec d. Discontinuous fiber reinforced thermoplastics are also frequently slip formed as shown in Fig. 1.19. Matched metal molds are usually used with applied pressures to 200 lbf/in2 or 1.38 MPa (Fig. 9.18) [90]. If pressure forming is used, a flexible membrane or diaphragm is placed over the sheet prior to forming to provide an air seal at the pressure box edges (Fig. 9.19) [91,92]. Straight diaphragm forming is also used in an autoclave, with the superplastic aluminum membrane being inflated with differential air pressure (Fig. 9.20) [93]. In addition to the increased stiffness of the polymer at the forming temperature, other practical forming problems include:
Fiber Length Correction Factor
na Figure 9.17 The effect of fiber length, given as na, on the reinforcing effect or fiber length correction factor, for fiber reinforcement of thermoplastics [89]
Platen
Insulation Mold
Laminate
Heaters Clamp Ring Mold
Platen
Figure 9.18 Matched die forming of high-performance composite. Redrawn from [90]
•
"Lofting" during heating. The fiber network is flattened into the polymer matrix during the fabrication of the composite sheet. This locks in fiber stresses. When the sheet is reheated, the stresses relieve and the composite grows in thickness and
Platen
Forming Pressure Inlet
Insulation
Radiant Heater
Laminate
Diaphragm
Vacuum Mold
Heaters
Air Outlet Steel Cylinder
Platen Figure 9.19 Pressure forming of high-performance composite. Redrawn from [91]
Superplastic Aluminum Radiant Heaters Pressure Chamber
Vacuum Manifold
Composite
Movable Mold Differential Pressure Prestretching
Mold Motion
Pressure Forming
Figure 9.20 Plug-assisted pressure forming of high-performance composite. Redrawn from [93]
increases in porosity. Lofting is a serious problem with all but the shortest fibers. Acicular fillers such as TiO2 and platy fillers such as talc exhibit mild lofting as well. In the mildest case of lofting, the free surface of the sheet shows "fiber prominence". In severe cases, the formed surface shows fiber prominence and the free surface is bristled. • Moderate to severe trimming difficulties. Most fiber-reinforced composites cannot be trimmed with steel rule dies. The method of trimming depends on the type of fiber and the toughness of the matrix. Typically, for filled and short-fiber reinforced composites where the polymer matrix has a relatively low elastic modulus, such as talc-filled polypropylene, forged steel dies are used. For high-performance composites such as carbon-fiber reinforced PEEK, diamondcoated toothed saws and routers are used [94]. Diamond-coated abrasive wheels are usually used to finish the cut surfaces. The major problems are delamination of the matrix from the fibers, shedding, and the formation of splinters. Internal delamination results in stress concentration at edges and cut-outs, which in turn results in premature failure. To minimize heat build-up on saws and drills, wateror air-cooling the cutting area is strongly recommended. Despite precautions, splintering remains a major processing problem with high-performance composites.
9.5
Laminated Sheet Thermoforming
There are many applications for thermoformed laminated products. Heavy-gage applications include PMMA/ABS and PMMA/PVC for pools, spas, soaking tubs and shower stalls, and cap-sheet acrylic on ABS or HIPS for exterior products. Thin-gage applications include rigid barrier containers of PS/EVOH/PP and PS/ PVDC/PE. The heating and forming philosophies of multilayer sheet rely entirely on the heating and forming philosophies of monolithic sheet. There are some important exceptions that are documented here. Heating Multilayer Sheet Heating the multilayer structure is the primary focus of the few studies of thermoforming conditions [95-98]. If all the layers are infrared-opaque, the sheet behavior is similar to the behavior of a monolithic sheet. Radiant and convective energy is absorbed on the sheet surface and conducted through the various layers. The arithmetic of Section 3.15 is used for each layer. For the ith layer: (9.41) The boundary conditions at the sheet surface and centerline remain as before. In addition, there are interlayer boundary conditions:
Temperature
Increasing Time
"""initial
Surface
Centerline Sheet Thickness
Figure 9.21 Sheet thickness- and time-dependent temperature profile through XYXY-type laminate. Variation in thermal conductivity and/or thermal diffusivity causes differential change in temperature from broken lines to solid lines
(9.42) (9.43)
For N layers, the N heat conduction equations are simultaneously solved to yield the temperature profile through the laminate. Figure 9.21 shows a typical temperature profile for a constant heat flux input to the sheet surface [99]. In addition to the infrared-opaque sheet, there are several other variations: • A multilayer sheet where a semitransparent layer is in the interior of the laminate. One example is PS/PVDC/PP where EVA is the tie-layer between the plies. For this example, the heating profile is essentially the same as that for infraredopaque sheet [98]. • A multilayer sheet where an outside layer is semitransparent. An example is the PMMA cap-sheet on ABS for outdoor applications. The energy transmitted to the inner layer is wavelength-dependent. Beer's law is frequently used to describe the extent of energy absorption by the semitransparent layer: I(x,X) = I 0 e ~ a №
(9.44)
where I 0 is the energy intensity on the sheet surface (x = 0) and OL(X) is the wavelength-dependent absorptivity, Chapter 2. If the surface layer is physically thick or has a large absorption value, essentially all the incident energy is absorbed before reaching the interface. The arithmetic becomes considerably more complex if the surface layer is physically or radiantly thin [95]. The interface between the first two layers acts to reflect a portion of the incident energy back
Temperature
Opaque
Figure 9.22 Effect of internal reradiation on temperature profile through transparent-opaque-transparent laminate
Transparent Opaque
No Reradiation lnterfacial Reradiation
Surface
Centerline Sheet Thickness
through the first layer, and the analysis requires an integral technique known as the "two-flux method" [100]. Figure 9.21 is a schematic of the relative effect of internal reradiation on the thickness-dependent temperature profile [101]. For heavy-gage sheet where a thin layer is used as a protective layer, the reradiation effect is small enough to ignore. The effect usually cannot be ignored for roll-fed multilayer sheet. However, another simplification is possible. Figures 9.23 and
Transmission, %
PVDC (First)-EVA-PS
Wavelength, jum Figure 9.23 Infrared transmission through PVDC-EVA-PS laminate with PVDC as first layer
Transmission, %
PS (First)-EVA-PVDC
Wavelength, pm Figure 9.24 Infrared transmission through PS-EVA-PVDC laminate with PS as first layer
9.24 are infrared absorption spectra of PS-EVA-PVDC [102]. The first figure shows PVDC first and the second shows PS first. As is apparent, the through-ply absorption spectra are essentially the same. From Fig. 9.25 [103], it is apparent that Beer's law, Equation 9.44, will yield the extent of wavelength-dependent volumetric absorption, regardless of which ply is the first surface to receive infrared radiation. This means that when analyzing the heating characteristics of thin-gage
Transmission, %
PS-Reflective IR
Wavelength, pm Figure 9.25 Thickness-dependent reflective infrared transmission through polystyrene, PS
multilayer structures, as a first approximation, they can be treated as simple monolithic polymers albeit with unique sets of energy absorption characteristics. Forming Multilayer Sheet The polymers that make up a multilayer sheet usually have quite different temperature-dependent stress-strain curves. The objective is to determine the appropriate forming temperature range for the laminate. Obviously, the polymers in all layers must be at or above their individual minimum forming temperatures, as given by Table 2.5. And, no polymer should be above its maximum forming temperature. The forming window for a laminate is usually narrower than that for any of its individual layers (Fig. 9.26). It is apparent that the breadth of the forming window is also important in the way in which the laminate is heated. If one of the layers is very thick, the formability of that layer will dominate that of the other layers. As a first approximation, then, the formability characteristics of the dominant polymer dictate the forming parameters of the laminate. If no layer dominates the strength of the laminate at the forming temperature, the laminate resistance to applied load is obtained from the rule of equivalent moduli. That is, the ratio of local stresses at a given strain is: ^ =^
(9.45)
where <J{ is the stress and E1 is the modulus in the ith beam and cro is the stress and E0 is the modulus in a reference beam. For simple beam bending (Fig. 9.27) [104], the effective widths of the beam sections change in inverse proportion to their moduli: (9.46)
Temperature
Polymer 1 Polymer 2 Surface Centerline Time Figure 9.26 Schematic of time-dependent temperature profile through two-ply laminate where the ply forming windows overlap
Equivalent Stiffness Figure 9.27 Equivalent stiffness concept for three-ply laminate. (Left) Actual thicknesses of laminate. (Right) Effective thicknesses when plies vary in modulus
As a result, the deflection of a simple beam, 5, under uniform load is given as: (9.47)
where wo is the weight per unit length, L is the span of the beam, and I* is the sum of the moments of inertia of the various elements that make up the effective beam structure of Fig. 9.27. This analysis is appropriate so long as the neutral axis remains in the beam structure. Once the entire beam is in tension, the appropriate property is the composite tensile strength. The amount of force required to stretch the laminate, Flam, is simply the sum of the forces required to stretch the individual layers to the same extent. This is given as: (9.48)
where T1 is the tensile strength of the ith layer and A1 is its cross sectional area. For a constant-width laminate, A1 is proportional to the thickness of the ith layer. Example 9.3 illustrates this.
Example 9.3 Strength and Deflection of Laminates Currently, 0.400-in thick PMMA sheet is being thermoformed into a female mold for a spa. At the lowest forming, temperature, the 1.05 g/cm3 PMMA sheet has a modulus of 1000 lbf/in2. A portion of the PMMA sheet is to be replaced with fire retardant PVC at 1.4 g/cm3. The PVC chosen has a modulus of 500 Ibf I in2 at the forming temperature. Use Equations 9.46 and 9.47 to determine the effect of polymer replacement on sheet sag for a 10-in wide section having an 18-in span. For the first case, assume that 50% of the PMMA is replaced with PVC. In the second case, assume that 75% is replaced with PVC.
The moment of inertia of the monolithic P M M A sheet is given as 1 : bh 3
10 x 0.43
IPMMA = - j y =
j2—
. = 0 0533
'
3
m
where b is the width of the sheet and h is its thickness, 0.400 in. The unit weight of the sheet is given as: wo =
1.05x62.4x0.4x10 . . . —— = 0.152 Ib per inch of span 172o
The deflection is given as: 5woL* 5x0.152x18* ° P M M A ~ 384EI ~ 384 x 1000 x 0.0533 ~
J>W
For the replacement where the modulus is 50% of that being replaced:
b' = b(f)-0.5b As a result, the beam is replaced with a T-beam, with the top section 10 in wide and 0.2 in thick and the lower section 5 in wide and 0.2 in thick. The moment of inertia of this T-beam is determined by first obtaining the distance from the top surface of the T-beam of the centroid: yda 5x0.2x0.1+5x0.4x0.2 n i ^ . iJL y = 0.1667 in y = -— = A 5 x 0.2 + 5 x 0.4
The combined moment of inertia for the two elements of the T-beam about the top surface is: Ix =
5xOy
+
5xa£
= ai20in4
The moment of inertia about the centroid is then given as: Icentroxd = Ix - AY2 = 0.120 - (5 x 0.2 + 5 x 0.4) x 0.16672 = 0.0366 in4 The new weight per inch of span is given as: wo =
/1.05+ 1.4\ \
Z
x
62.4x0.4x10 A 1 ^ 1 U . , —— = 0.177 Ib per inch off span
J
1/Zo
The new deflection is: 0.177 x 0.5 x 184 *PMMA + PVC -
3 8 4 x
10Q0 x
Q Q 3 6 6
£
^
- 0-014
A
. in
This is nearly 70% increase in deflection. 1
Again note that the neutral axis is outside the dimensions of the part. Correctly, this equation does not yield the correct answers in this case. However, the relative effects are considered to be about right.
For the 25-75 PMMA-PVC, the following obtains: y = 0.17 in, Icentroid = 0.1083 - 2.5 x 0.172 = 0.0361 in4 / 3 x l . 4 + 1 . 0 5 \ 62.4x0.4x10 TU wo = I Ix -— = 0.190 Ib per inch of span \ T1 J 1 / Zo and 5pMMA + 3PVC = 7.20 in or an increase in deflection of nearly 85% from the monolithic PMMA. For this case, note that 25% of the increase in deflection is due to the increased weight of the sheet when PVC is substituted for PMMA. The rest is the result of the lower PVC modulus.
Wall thickness variation in the formed laminate is independent of the make-up of the laminate of or the strength of adhesion between the layers [103]. Figure 9.28 illustrates the draw-down of components of a PVDC-EVA-PS multilayer into a 60° cone. As is apparent, the wall thickness along the cone is essentially independent of the nature of the laminate. For the analyses above, the plies are considered to be firmly laminated. That is, the forces required to bend and stretch a laminate are substantially less than the forces required to delaminate the plies. Three general cases are: •
•
•
Interlayer sliding without interlayer shear. This is equivalent to thermoforming a set of stacked cards with the coefficient of friction between the cards being zero. Each layer or ply is considered as isolated from the others. The amount of force required to thermoform each layer is given by the temperature-dependent stressstrain characteristics of that polymer. The total force required to form the laminate is therefore the sum of the forces required to form the individual layers. If one of the layers is prone to forming pinholes or ruptures beyond a given strain level, it will also do so in the laminate. The draw ratio of each layer is identical to the draw ratio of the laminate. No interlayer sliding or shear. In this case, the laminate is behaving as a monolayer. Regardless of the difficulty in the draw, the interfacial adhesion is far greater than the interfacial shear. Interlayer shear without interlayer sliding. In this case, the bending forces create shearing stresses that vary from zero at the neutral axis to maximum at the outer fiber stress. The local shearing stress, x, is given as:
where V is the vertical shear on the beam, I is the moment of inertia of the beam, A is the area of the section between the horizontal plane where the stress is to be determined and the bottom or top surface of the beam, y is the distance from the centroid of the area to the neutral axis of the beam and b is the width of the
PVDC x 10
Thickness, in
PS+ i +PVDC (| Te PS,,
PS1
Cone-Side Distance, mm Figure 9.28 Measured wall thickness for draw-down of several elements of laminate into 60-degree cone [103]
beam.1 Example 9.4 illustrates the method of calculating the local shearing stress. If the local shearing stress exceeds the interlayer shear strength of the laminate at any point, the plies may delaminate. As an example, when a laminate having a very thin protective outer layer is stretched over a male mold, the delaminated thin layer can tear at concave 3D corners and compressively buckle at convex corners.
1
Again, this expression is strictly valid only when the neutral axis remains within the physical dimensions of the beam.
Example 9.4 Interply Shear Strength Consider a 9 in wide, 0.400-in laminated beam having a 0.050-in cap-sheet being stretched with 15 Ib vertical shear. The adhesive strength of the interface is 1200 IbfI in2. Determine whether the laminate will delaminate.
Equation 9.49 gives the interfacial shear strength for this laminate. The moment of inertia is given as I = bh3/12: Va _12.vy t_12. y = (0.400 - 0.050)/2 = 0.1875 in. V = 15 Ib. Therefore the shear strength is:
the interply shear strength exceeds the adhesive strength and the plies may delaminate. Differences in thermal expansion coefficients between the plies will acerbate the delamination problem, as well [97].
9.6
Twin-Sheet Thermoforming
Twin-sheet thermoforming is the process of producing an initially hollow container beginning with two sheets of plastic [105-107]. Rotational molding, blow molding, thermoforming double-walled extruded sheet and seam welding two thermoformed sheets are some of the many competitive ways of making an initially hollow container. For many products such as garage doors, equipment cabinet sides, marine dock floats, components for voting booths, gurneys, food serving carts, refrigeration and freezer doors, cargo compartment doors, transit and mass seating, truck bedliners, pallets and tote boxes, the containers are in reality hollow flat panels that can be foam filled for added stiffness or thermal insulation1. Foam reaction injection molding, rotational molding, laminated honeycomb, gas-assisted injection molding and foam injection molding of thermoplastics produce competitive products. Table 9.9 gives a comparison of competitive ways of fabricating rigid flat panels [109]. There are two general ways of producing two-sided or double-walled structures. Sequential thermoforming produces one formed surface after the other, with assembly taking place either on the forming press or in a secondary fixture removed from
1
Although nearly all of the twin-sheet applications are currently in heavy gage sheet, it is reported that the earliest twin-sheet thermoformed products were ping-pong balls, in 1935 [108].
Table 9.9 Comparison of Several Process for the Fabrication of a Rigid Flat Panel [109] Item
Thermoplastic structural foam [low-pressure]
Rotational molding
Twin-sheet thermoforming
Industrial blow molding
Gas-injection molding
Resin form
Pellets
Powder
Sheet
Pellets
Pellets
Availability of polymers
Excellent
Fair
Good
Limited
Excellent
Polymer cost
Standard
Price includes grinding
Price includes sheet extrusion
Above average
Standard
Breadth of polymers
All
Restrictedolefin dominated
Amorphous polymers preferred
Restricted - olefin dominated
Most
Nonproduct produced per shot
<5%
5%
30-50%
30%
<5%
Nonproduct reuse
Immediate
No thermally sensitive polymers
Must be reextruded
No thermally sensitive polymers
Immediate
Color
Colored pellets or masterbatch1
Colored sheet
Colored pellets or masterbatch
Colored pellets or masterbatch
Controllable but color can change
Difficult to impossible
Moderate
Dry blend
Processibility of thermally sensitive polymers
Moderate
Melt viscosity control
Moderate
Easy flow polymers
Requires good hot strength
Requires excellent melt strength
Moderate
Variety of mold materials
Aluminum of steel
Sheet metal, aluminum, steel
Wood, plaster aluminum
Aluminum
Steel but aluminum ok
Very difficult
(Continued)
Table 9.9 (Continued) Item
Thermoplastic structural foam [low-pressure]
Rotational molding
Twin-sheet thermoforming
Industrial blow molding
Gas-injection molding
Cost of molds
Moderate
Low
Low to moderate
Moderate
Moderate to high
Mold maker reliability, quality
Good
Poor to good
Fair
Fair to good
Good
Mold closure
Butt
Tongue/groove
Butt, tongue/groove
Butt
Butt
Method of holding mold closed
Platen hydraulics
Mechanical toggle
Pneumatic, hydraulic
Hydraulic
Platen hydraulic
Thermal cycle
Moderate to long
Long
Long
Moderate to long
Moderate to short
Major trial/ error problems
Part density, minimum cooling time, blowing agent cone.
Ratio of arm speeds, warpage
3D corner thickness, thickness, parting line integrity
Pinchoff, wall uniformity
Gas injection rate, time
Cooling method
Mold core
Water spray
Mold, one-side
Mold core, one-side
Mold core
Part release
Ejector pins
Manual
Manual
Manual, air
Ejector pins
Operating pressure
Relatively low
Low
Low
Moderate
Moderate to moderately high
Operating temperature
Polymer melt temperature
Above polymer melt temperature
Below polymer melt temperature
Polymer melt temperature
Polymer melt temperature
Life of molds
Moderate to high
Low to high
Low to high
High
Moderate to high
Controlling part of cycle
Cooling
Heating
Heating2
Cooling
Cooling
Skill of operator
High
Low
Moderate
High
High
Man/machine interaction
Moderate
Very high
High
Moderate
Moderate
Filling method
Automatic hopper load
Manual
Manual to semi-automatic
Automatic hopper load
Automatic hopper load
Part removal method
Automatic to manual3
Manual
Manual
Automatic to manual3
Automatic to manual3
Part wall uniformity
Good to excellent
Fair to good
Fair to good
Good
"Skin" thickness Uniformity
Fair
Fair to good
Fair to good
Fair
Parting line
Weld line/ tackoff
Parting line, blow pin hole
Gate region
Molding characteristics requiring attention
Gate region
Fair Fair
"Skin" thickness control
Poor
Fair to poor
Fair to good
Fair to good
Fair
Method of skin thickness control
Injection rate, blowing agent concentration
Ratio of arm speeds
Temperature, mechanical assists
Parison programming
Gas injection rate, time
Method of increasing part stiffness
Part design Ribs, bosses
Foam filling
Tackoff, foam filling
Tackoff, foam filling
Mold design Ribs, bosses
Inserts
Feasible
Special design only
Post-molding inserts only
Feasible
Feasible
Polymer orientation
Low to moderate4
Unoriented
Highly biaxial
Biaxial and uniaxial
Biaxial and uniaxial
Stress retention
Low to moderate4
Little
High
Moderate to high
High (Continued)
Table 9.9 (Continued) Item
Thermoplastic structural foam [low-pressure]
Rotational molding
Twin-sheet thermoforming
Industrial blow molding
Gas-injection molding
Method of controlling warpage, distortion Primary mechanical part failure Surface finishtypical Processing problems that causes poor surface Part cost 1,000 10,000 100,000 1,000,000 Production of small parts (brush handle) Production of very large parts (pallets)
Cooling, fixturing, mold temperature
Internal air during cooling
High mold temperature
Internal air pressure, mold temperature
Time in cooling, fixturing
Weldline, low density region
Low tensile strength, poor fusion
Thin corners, poor weld at parting line Good to excellent
Thin corners, poor weld at parting line
Thin skins
1 2 3 4
Poor
Fair
Excellent
Excellent
Pock marks
Poor replication of mold surface
Air bubbles
Very high High Moderate Moderate/low
Low/very low Moderate High Very high
Moderate Moderate Moderate/high High/very high
High/very high Moderate Moderate Moderate/low
Very high High Moderate Moderate/low
Excellent
Impractical
Impractical
Probable
Good
Very expensive
Excellent
Excellent
Good, expensive
Very expensive
Swirls, bubbles
Owing to swirl pattern, color matching is very difficult, particularly with dark colors For single heater shuttle, heating dominates. For dual heater shuttle, forming and cooling dominate Depends on the part size and weight Orientation increases substantially with decreasing part wall thickness and relative flow length
Break-through
the forming press. Simultaneous thermoforming produces both surfaces at the same time, with assembly taking place within the forming press. Simultaneous Twin-Sheet Forming Two general approaches are used here. The first, primarily for heavy-gage parts, employs two thermoforming machines that interact at the assembly station (Fig. 9.29) [HO]. Either shuttle or rotary presses are used. The loading and unloading sequence for a dual shuttle press is more difficult than that for rotary presses owing to the complexity of the twin-sheet mold and assembly machinery. The objective is to simultaneously heat and form the two sheets in separate machines, then move the formed, hot sides in their molds into an assembly press to produce the double-walled part. The second technique uses a single thermoforming machine, with the two sheets clamped in a single frame although separated with spacers (Fig. 9.30). The clamping frame is equipped with air nozzles and air is injected between the sheets to keep them separated throughout the heating and forming process. A single robust forming press is used. During forming, the mold cavities are evacuated and additional warm air may be injected through hypodermic needles that pierce the sheet. Air pressures to 50 lbf/in2 or 0.34 MPa are typical. Other mold characteristics are described in Chapter 6 on mold design. Although simultaneous thin-gage twin-sheet thermoforming is technically feasible, it has few major commercial successes. Blow molding dominates the thin-wall hollow container applications and single-ply thermoformed low-density foam dominates the flat panel and tray applications.
Platen Oven Oven
Top Sheet
Platen Bottom Sheet
Figure 9.29 Schematic of dual shuttle machine for simultaneous or sequential twin-sheet forming
Oven Clamp Frame
Air
Top Sheet
Bottom Sheet Oven
Figure 9.30 Schematic of simultaneous twin-sheet forming using a single clamp frame
Sequential Twin-Sheet Forming This technique is reserved for heavy-gage forming. There are several ways of producing two-sided structures using sequential thermoforming. The simplest uses a single forming press. The press can be either a shuttle press or a rotary press. The objective is to install the mold for the first side and to form a quantity. This mold is then replaced with the mold for the second side and a quantity of the second side is formed. The two sides are then assembled away from the press by solvent or thermal welding. This technique is shown in schematic in Fig. 9.31. A more automated but more complicated method also employs a single press but has the two female molds installed in the press at the same time. The first sheet is heated and Shuttle Press Adhesive or Thermal Bonding
Inventory
Shuttle Press Figure 9.31 Schematic of twin-sheet production where mating parts are inventoried prior to fabrication
Oven
Oven Mold
Oven
Mold
Oven
Oven First Sheet Forming Oven
Second Sheet Forming
Thermal Forming Seams
Figure 9.32 Sequential twin-sheet forming schematic
formed into the first mold, in the down position, for example. The second sheet is heated and formed into the second mold, in the up position. The press then closes to form the double-walled product. So long as the region to be welded on the first sheet is kept hot, no secondary welding is required. This is shown in schematic in Fig. 9.32. If one or both of the molds are male molds, the formed sheet is usually transferred from the male mold to a holding frame prior to forming the double-walled product. Sequential twin-sheet thermoforming also uses the two-machine twin-sheet forming concept (Fig. 9.29). For sequential forming, the first sheet is heated and formed several seconds to a minute ahead of the second one. Usually the most difficult draw is done first. The delay allows for inspection of the formed part as well as for
Table 9.10 Adhesion Temperature [170] Polymer
T m , Melt temperature (0C)
T g , Glass transition temperature (0C)
T t , Tack temperature (0C)
Low-density polyethylene
120 + 1
—
115 + 5
High-density polyethylene
130 + 2
—
130 + 5
General-purpose polystyrene
—
105
110 + 5
Medium-impact polystyrene
—
105
110 ± 5
ABS
—
105
125 + 5
Polymethyl methacrylate Polycarbonate
—
105
105 + 5
—
155
160 + 5
Obtained by blowing —35 mesh polymer powder against a linear temperature melting point apparatus held in the vertical position
insertion of reinforcing elements or insulating pads, as examples. In reality, most two-machine forming operations that begin as simultaneous forming usually operate as sequential forming. Some increase in the speed of forming and in the efficiency of welding, the seam is achieved by using a four-station rotary with two ovens. The first sheet is rotated to the second oven and the second is immediately rotated to the first. When the first sheet is hot, it is rotated to the forming station and formed. The second sheet remains in the second oven until the first is formed. It is then rotated to the forming station for forming and mating with the first. Quartz or rapid response ceramic ovens are required for this form of twin-sheet forming. Table 9.11 compares the advantages and disadvantages of these twin-sheet forming techniques. Seal Area—Adhesion Successful twin-sheet forming depends on the success of the peripheral seal or weld between the two sheets. The seal must be 100% liquid-tight if the hollow cavity is to be subsequently filled with polyurethane foam. In simultaneous forming, the mating surfaces of the two separately formed sheet are usually quite hot and adhesion is usually not a significant problem. In sequential forming, on the other hand, the first sheet formed is cooling while the second sheet is being formed. In certain cases the time delay between the formation of the first sheet and the mating is so long that good adhesion is not possible. Auxiliary heaters are then required. Usually high-intensity quartz tube heaters are indexed into the mold cavity over the first sheet just prior to moving the molds together. To achieve good adhesion, both sheet surfaces
Table 9.11 Advantages and Disadvantages of Various Types of Twin-Sheet Thermoforming Method
Advantage
Disadvantage
Simultaneous two-machine (Fig. 9.29)
Very high productivity. Both sheet free surfaces very hot, so welds very good.
Sequential two-machine (Fig. 9.29)
High productivity. Insert reinforcement possible. Plug assist possible only if assembly station separate from forming stations. Good productivity. Capital cost less than two-machine. Pressure-formed surface textures possible.
Sheet thicknesses need to be similar. Imperfection in one sheet requires scrapping entire formed part. Difficult to insert reinforcing elements. Capital intensive compared with other sequential methods.
Simultaneous one-machine (Fig. 9.30)
Sequential one-machine, one mold at a time (Fig. 9.31)
Sequential one-machine, two molds at a time (Fig. 9.32)
Sheet of different thicknesses, colors possible. Very low capital, mold cost. Ideal for prototyping. Reinforcement insert easy. Solvent, thermal welding possible. Can be done on conventional thermoforming machine. Plug-assist possible. More automated than one-machine, one-mold.
Load/unload difficult with shuttle press. Long cycle times since each sheet heated only on one side. Careful air control to keep sheets from touching when hot. Sheet thicknesses need to be similar or identical. No means of inserting reinforcements. Special purpose machines with very heavy clamps needed for pressure forming. High manual labor, particularly in assembly area. Plastics must be thermal or solvent weldable. Welds may not be as strong as with other techniques.
First sheet weld area must be kept hot. Welds may not be as strong as with other techniques. More robust press required. Plug-assist very difficult, even with assists that shuttle into and out of press.
must be above the glass transition temperature of the polymer. The desired temperature is the "tack" temperature or the temperature where the polymer begins to feel sticky. Tack temperatures for several polymers are given in Table 9.10 [170]. Typically the tack temperature is just above the melt temperature of a crystalline polymer and about 00C to 200C above the glass transition temperature of an amorphous polymer. It is always better to err on the side of high polymer temperatures in the seal area. In addition to sufficiently high polymer temperature, the seal region must be free of contaminants such- as: • • • • •
External lubricants and waxes, Low-molecular weight carriers for pigments, Antistatic agents, Processing aids, particularly stearates and titanates, and Dispersing agents.
Seal Area—Compressive Force Care must be taken to ensure proper registry without shear during the mating of the two surfaces. Because the seal area is usually not planar, the mating halves must seat uniformly along the seal line. Otherwise, uniform seal compression is impossible. For very large molds or for mold halves operating at different temperatures, the difference in thermal expansion between the mold halves may cause the mating to be out of registry. This is particularly important if one or both sheets are relatively thin. The seal is simply a thermal weld. In structural blow molding [111], the parison halves are compressed to half their total thickness. The same level of compression is recommended for twin-sheet thermoforming. Owing to mold-to-mold tolerances, typical compression levels are 25% to 50% of the total sheet thickness. Consider a simple butt-weld (Fig. 9.33). Consider squeezing the polymer at a constant squeezing rate [112]: (9.50) where ho is the initial double-sheet thickness. The rate of compression is: (9.51) where a is the squeezing rate constant. The squeezing force, F, is given as: (9.52) where r| is the Newtonian viscosity and V is the volume of the seal area. The initial force, F 0 is obtained when h = ho. The final thickness, hf, is given as: (9.53) And the final force is given as: (9.54)
Extrudate
Clamping Area
Figure 9.33 Characteristics of squeezing at twin-sheet mating seal
Because the seal area is assumed to have a constant volume, the spreading width, X, is simply given as: Xf = Xo/p
(9.55)
Figure 9.34 shows the force ratio, Ff/Fo and the spreading width, Xf/Xo, as functions of the compression, hf/ho. Note that the force required to compress the seal area to 50% is 32 times that required to just mate the surfaces. This force must come from the clamping system on the press. The mating tolerance along the seal area should be no more than 25% of the total sheet thickness in the seal. In quality molds, the seal areas are constructed separately from the mold body. This allows fine tuning and adjustments of the seal areas with shims. It also allows the seal area to be constructed of hardened steel for better wear resistance. In addition to traditional guide pins, secondary guides and lockups are sometimes used to provide the necessary close tolerances. Increasing press clamping force usually does not solve any seal area tolerance problem and can result in damaging the mold or the press. Seal Area—Design In addition to sheet temperature and clamping forces, the design of the seal area is important. Figure 9.35 shows several sea! area schemes. The most common are the butt-weld, the channel and the vee seal. No vent holes are provided in the seal area. The seal area should be designed with some relief on both sides of the seal. In blow molding, this is known as a gutter-dam design. This allows the compressed plastic to shear-flow from the compression zone at right angles to the seal. Blow pins are usually required in all twin-sheet molds, regardless of whether fabricated simultaneously or sequentially. For heavy-gage sheet, the blow pins are
Force or Squeezing Ratio
Force Ratio, Ft /F0
Squeezing Ratio, Xt /X0
Compression Amount, ht /h o Figure 9.34 Compression level-dependent squeezing or force ratio. See Fig. 9.33
typically 3/16-in to 1/4-in in outside diameter, with 1/8-in inside diameter. Hypodermic needles are sometimes used if blowing through a finished surface is required. Typically blow pins are used in pairs, with one acting as the exhaust pin. With appropriate air line valving, the exhaust pin can also act as a blow pin, if needed. It is recommended that one blow pin be used for every 1 ft3 or 0.03 m3 of internal volume in the part. The actual number of blow pins depends on the extent of internal constrictions in the part. The objective of the blow air is to keep the sheets separated. As seen in Table 7.9, the required level of air pressure is very low. Air flow is important as a means of supplemental cooling of the free sheet surfaces. Blow pins are either fixed in the mold surface or driven through the formed sheet just after the part half has been formed. Air cylinders are usually adequate to push the pin through the sheet. Functional blow pins require the plastic to seal the internal air pressure around the blow pin itself. Peripheral blow pins are usually mechanically extended into place just before the two sheets are brought together. The seal area must be designed to accommodate and pinch off the sheet around the blow pin.
Vee
Butt
Overbite EII-Up
Under bite
Angle 2
Angle 1
Snap-Finger
Ell-Down
Hinge-Pin
Pipe Slide-Lock
Channel Molded-in Angle
Molded-in Stiffener Figure 9.35 Examples of seal area methods
Figure 9.36 Examples of internal tack-off or kiss-off configurations. Lower example shows rightangle tack-offs
Twin sheet designs frequently include "kiss-offs" or "tack-offs" (Fig. 9.36) [113]. These tack-offs greatly improve the stiffness of the hollow shape. Unlike structural blow molding, thermoforming tack-offs do not usually mark or strike through to the exterior sheet surface. This is because the sheet is rubbery rather than fluid at the tacking temperature. The molding protocol depends on the mold characteristics [114] . If one portion of the mold is predominantly male, it should be placed on the top platen to take advantage of sheet sag. If one portion is predominantly female, it should be placed on the bottom platen, again to take advantage of sheet sag. The first sheet is usually formed into the bottom mold. This allows the clamp to release the sheet without having the sheet experience substantial distortion or warpage. The bottom mold is then run hotter to ensure minimum distortion and warpage1.
9.7
Polypropylene Thermoforming
Polypropylene epitomizes the best and worst aspects of thermoformable crystalline polymers. For decades, polypropylene has been considered an inexpensive commodity polymer. It has the highest melt temperature of all commodity polyolefins and its 1
Note, however, that if the bottom mold temperature is substantially higher than the upper mold temperature, the sheet will shrink more on the bottom mold. This may change the nature of the sheet in the seal area.
good chemical resistance makes it attractive for autoclavable and microwavable containers. Owing to its relatively high crystallinity level, unpigmented and unfilled PP is usually translucent or "contact transparent". The size of the crystallite determines the level of haze or translucency. Crystallites having dimensions 0.1 um to 10 jim affect visible light transmission as haze. Polypropylene has a relatively narrow melting point range of 160° to 165°C. As seen in Fig. 9.37 [55], the apparent viscosity of homopolymer polypropylene changes by a factor of 1000 or more in this melting point range. As is apparent, PP is a solid below its melt temperature and the temperature-dependent strain or elongational response to applied stress is appropriate (Fig. 9.12) [115]. PP is a liquid above its melt temperature and the temperature-dependent strain rate response to applied stress or elongational viscosity is important [116]. Figure 9.38 shows time-dependent nature of PP extensional or elongational viscosity. Shear viscosity is also considered a measure of PP resistance to applied stress, as seen for modified and unmodified PP at 1700C (Fig. 9.39) [117]. The very tight helical structure of the PP molecule provides for relatively good stiffness and chemical resistance but does not allow for a high degree of intermolecular entanglement. Intermolecular and side chain entanglements are major contributors to melt elasticity or "melt strength". Without these effects, PP elongational and shear viscosities are relatively low and the transition between the solid polymer modulus and the elastic strength of the melt is quite abrupt, as seen in schematic in Fig. 9.40 [118]. And as noted shortly, the initially low value for elongational viscosity means that the polymer can quickly sag during heating. The morphology or crystalline architecture of PP has been studied for decades. The crystalline structure consists of a super-lattice containing large hexagonal P-crystallites and small monoclinic a-crystallites [119-121]. P-crystallites begin to melt at about 147°C and some remain recognizable at 155°C. a-crystallites begin to melt around 152°C and may persist to 162°C. The way in which the PP sheet is extruded and cooled alters the balance between a- and P-crystallites and the propensity for one type to dominate the super-lattice. The crystallites melt relatively slowly during heating and polypropylene crystallizes relatively slowly from the melt to a crystallinity level of approximately 70%, as seen in Table 2.4.
Sag Test There is no single agreed-upon test for sheet formability [117,118]. Nor is there an agreed-upon way to determine whether a, polymer can be heated to the forming temperature without excessive sagging. As discussed in Chapter 4, initial sheet sag can be determined from: (9.56) where y is the extent of sag, a is a Roark-Young scale factor, b is the sheet width, q is the weight of the sheet, h is the sheet thickness and E is the temperature-depen-
Temperature,0C
Solid Phase Forming of PP Shear Rate = 0.001 s"1
Viscosity, MPa*s
Thermoforming of HIPS
HIPS Ml=3
PP MF=0.7
Melt Thermoforming of PP
Reciprocal Absolute Temperature, 103/Tf 0K"1 Figure 9.37 Temperature-dependent viscosity for polypropylene, PP, homopolymer and high-impact polystyrene, HIPS. Redrawn from [55]
dent tensile modulus. As is apparent, sag increases with decreasing modulus and increasing temperature. Heavy-gage sheet shows much greater initial sheet sag and wide sheet sags much more than narrow sheet. Once the top portion of the sheet has passed the neutral axis, sheet sag is determined from flexible cable or catenary theory. As shown in Fig. 9.41 [122], if the sheet initially b units wide has sagged y units, the arc length, s, at distance x from the clamp is given as: (9.57) where q' is the sheet weight per unit width, =q/b and T0 is the tensile load at the clamp. The amount of sag is given as: (9.58) The maximum amount of sag occurs at x = L/2, as: (9.59)
Viscosity, MPa s
High Melt Strength PP
Conventional Homopolymer PP
Time, s
Viscosity, MPa«s
Figure 9.38 Relative time-dependent viscosities for conventional and high melt strength polypropylenes, PP
5% Acrylic-Modified
Unmodified
Shear Rate, s 1 Figure 9.39 Viscosities of unmodified and 5% acrylic-modified polypropylene, PP. Redrawn from [117]
Modulus, MPa
Solid Forming Region
Thermoforming Region
Amorphous Polymer
PP
Temperature Figure 9.40 Temperature-dependent modulus of polypropylene, compared with an amorphous polymer with same room temperature modulus
Figure 9.41 Geometric characteristics for catenary sag
The tensile load at any point x from the clamp is given as: (9.60) Or with substitution: (9.61) The maximum tensile load occurs when y = y max . Typically, the amount of sag, y max , is measured as a function of temperature. As is apparent, if the sheet weight is
Dimensionless Sag Figure 9.42 Effect of span, as p • y/to, on extent of sag, as p • x/to
Dimensionless Span
known, the tensile strength of the polymer at that amount of sag is obtained from Equation 9.60. The equations are derived for one-dimensional sag. Thermoforming considers planar two-dimensional sag. As a result, Equation 9.59 is written in terms of polymer density, p, lb/in3 or g/cm3 and tensile strength, to, lbf/in2 or Pa. The relationship is rewritten as: (py/t0) = cosh(px/t 0 )-l
(9.62)
Since the equation is transcendental, it is best solved graphically. Figure 9.42 shows the relationship between py/to and px/to. Since it is usually the case that the span value, x = b/2, is fixed and y, the extent of sag, is measured, Fig. 9.42 is also the relationship between y/x and (px/to). Example 9.5 illustrates how these functions are related. Keep in mind that these equations may not yield entirely practical results. For example: • • • • •
The arithmetic assumes that the sheet is initially uniform in temperature, The arithmetic assumes that the sheet is isothermal during sag, The arithmetic assumes that the sheet is only clamped along two edges. Although this approximates sagging conditions in roll-fed thermoforming, this is not the way most sag experiments are conducted [116,117], The sheet thickness decreases as the sheet stretches. This means that the sheet weight decreases as the sheet stretches. Although this can be accounted for, it further assumes that the sheet is stretching uniformly, The arithmetic assumes elastic deformation of the sheet. As a result, the predicted amount of sag is time-independent,
• • •
The effect of sheet thickness on the extent of sag is not a factor. According to Equation 9.62, the only material parameters are the sheet tensile strength and the polymer density, The arithmetic assumes a catenary shape to the sheet, and The arithmetic assumes that the sheet simply pivots in the clamp and does not account for any reinforcement by the clamp during sagging. Example 9.5 Correlation Between Catenary Sag and Hot Strength A 36-in span of HDPE cannot sag more than 4 inches. Determine its sag if its hot tensile strength is 100 lbf/in3, 10 lbf/in2, and 1.0 lbf/in2. Then determine its sag if a sag band is used. The density of HDPE is 0.96 g/cm3 = 0.0347 lb/in3. Equation 9.62 becomes: to
f
, /0.0347 -IA
t "|
ydeflectlon = o^347 = LC°Sh V n r ) 1 The following table obtains: tOj
Ydeflection?
lbf/in2
L = 36 in
100 10 1
0.056 0.56 5.8
i n
L = 18 in 0.014 0.14 1.4
As seen in Fig. 9.43 [123], isothermal sag is time-dependent. Elongational stretching force is related to elongational viscosity [96]. Elongational viscosity, r|e, is the ratio of applied extensional stress, Te, to strain rate or rate of deformation, e:
Sag Rate
Extensional Viscosity
If the amount of sag increases linearly with time, as shown in Fig. 9.44, the extensional viscosity is constant. If the rate of sag increases with time, the extensional viscosity is decreasing. And if the rate of sag decreases with time, the extensional
Time
Time
Figure 9.43 Conceptual relationship between time-dependent isothermal sag and time-dependent extensional viscosity for polypropylene, PP
3% Modifier
Sag Distance, cm
Unmodified
4% Modifier
5% Modifier
Sag Time, min Figure 9.44 Experimental time-dependent sag for polypropylene, PP having various levels of acrylic modifier added, redrawn from [124]
viscosity is increasing. This is seen in schematic in Fig. 9.44 [124]. An extensional strain growth function, M: ^e = %,o exp (Met) (9.64) is a measure of strain-hardening or -softening. If M > 1, the polymer strain-hardens and the rate of sag decreases with time. If M < I5 the polymer strain-thins and the rate of sag increases with time. As seen in Fig. 9.45 [125], neat and mineral-filled homopolymer polypropylene show increasing sag rates with time, indicating M < 1 or strain softening. On the other hand, the modified PP shows decreasing sag rate, indicating M > 1, or strain hardening. Sag occurs in parison blow molding [126]. Technically, parison sag is not predicted using either an elastic approach using linear creep compliance or elastic modulus [127], or the viscous approach that relates the sag rate to elongational viscosity [128]. As with sag in thermoforming ovens, parison sag is neither a constant stress process nor a constant strain rate process. In other words, the correct material approach is to consider the polymer as a viscoelastic liquid. Additional tests for formability are given in Chapter 10. Modified Polypropylenes As noted above, the addition of fillers does not necessarily change the ability of a crystalline polymer to be thermoformed in the melt state. Filled polypropylene,
Sag Distance, cm
Oven Temperature = 2400C Virgin PP
Mineral-Filed PP Polyolefin Alloy
Oven Time, min Figure 9.45 Comparison of time-dependent sag characteristics of neat and mineral-filled polypropylene, PP, homopolymer with polyolefin alloy. Redrawn from [125] and used with permission of copyright owner
usually filled with about 20% (wt) talc, has been thermoformed on conventional equipment since the 1970s. The filler adds stiffness to the melt and provides nucleating sites for crystallization as the sheet cools on the mold surface. The finished parts are opaque, have a semi-gloss finish, exhibit lowered impact strength and split resistance, and are difficult to rim roll. Care is required in heating to keep the sheet temperature below about 1700C. These low forming temperatures imply more difficult forming, very short transfer and forming times, shallow draw and a lack of sharp detail in the formed parts. Excessive heating will result in sag characteristics of the unfilled polymer. The complex morphology and low melt strength of the neat homopolymer combine to cause uncontrollable sagging and to prevent traditional commercial thermoforming. As a result, PP was first commercially formed in the solid state using high air pressure. Currently there are two ways of altering PP to make it melt formable: • High molecular weight or high melt strength polypropylene [129]. Although increasing the molecular weight increases the polymer resistance to tensile load, it also makes traditional extrusion more difficult [118]. Increasing the molecular weight distribution increases the melt strength of the polymer without substantially increasing its viscosity at normal extrusion shear rates [130]. Increasing the dispersity index, a measure of molecular weight distribution, from 5 or 6 to 10 or
Sag Time, s
Melt Flow Rate, MFR, dg/min Figure 9.46 Effect of molecular weight, as melt flow rate, MFR, on sag time for polypropylene, PP, homopolymer. Redrawn from [131] and used with permission of copyright owner
•
more dramatically increases the formability window for PP. Figure 9.46 shows the effects of increased molecular weight or reduced melt flow index on the time required to sag PP a fixed amount [131]. Figure 9.47 shows the effects of increased molecular weight distribution on this same time [132]. The results are asymptotic for both cases. Figure 9.48 shows that increased molecular weight distribution is effective for both homopolymer and copolymer grades of PP [133]. Copolymer or modified polypropylene [117,134,135]. The primary objective of copolymerization is to increase molecular entanglements by altering the polymer backbone stiffness or by adding end-groups or bulky side chain branches. This increases the melt viscosity of the polymer. Acrylic acid graft copolymer to 5% (wt) is one example, as shown in Fig. 9.39. The effect of copolymer concentration on sag resistance is shown in Fig. 9.44 [136]. As another example, a proprietary blend of olefins reduces the extent of sag when compared with homopolymer and mineral-filled homopolymer (Fig. 9.45) [137].
Sag Time, s
Molecular Weight Distribution, M ^ M n Figure 9.47 Effect of molecular weight distribution on sag time for polypropylene, PP, homopolymer, melt flow rate held constant. Redrawn from [131] and used with permission of copyright owner
Most of the work with modified PP has been with thin-gage sheet, in the thickness range of 20 to 60 mil, 0.020 to 0.060 in or 0.5 to 1.5 mm. As is apparent from Equations 9.59 and 9.62, increased sheet thickness and increased sheet width exacerbates sheet sag. However, work with viscosity-modified PP indicates that most of the formability improvements with thin-gage sheet are translatable to heavy-gage sheet. All of the methods being promoted to improve polypropylene thermoformability add substantial cost, in reduced extrusion rate or increased material cost, to the base polymer. In certain cases [117], some of this cost is recovered in reduced cycle times (Fig. 9.49) [138]. As with any diluent, there is concern that the modifiers may alter the chemical resistance, microwavability, oil resistance, autoclavability, moisture resistance, FDA status, taste and odor acceptability and recyclability of polypropylene. Other information is given in [139,140].
Next Page
High Melt Strength Homopolymer
Time, s
High Melt Strength Copolymer
PP Copolymer PP Homopolymer
Sag Distance, cm Figure 9.48 Comparison of time-dependent sag distance for traditional polypropylene, PP, and high melt strength polypropylene, PP, for both homopolymer and copolymer grades. Redrawn from [133] and used with permission of copyright owner
Sheet Temperature,°C
Process Window for Acrylic-Modified PP
Process Window for PP
Heating Time, s Figure 9.49 Comparison of process windows of neat and acrylic modified polypropylene, PP, homopolymers. Redrawn from [138] and used with permission of copyright owner
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9.8
Thermoforming Foam Sheet
Flat low-density foam sheet is produced by mixing polymers with appropriate foaming agents and extruding through special sheet dies. Although polystyrene and polyethylene are the most common polymers processed into foam sheet, other polymers such as polypropylene, styrene-maleic acid or SMA, polyethylene terephthalate or PET and modified polyphenylene oxide or mPPO are also available as foam sheet. The technical details of making fine-celled, dimensionally stable extruded low-density foam sheet are covered in detail elsewhere [141,142]. Polystyrene-based foam sheet is shaped into products such as automotive headliners, disposable meat trays, burger and pizza boxes, egg cartons, hot drink cups and other disposable products. Polyolefin foam sheet is shaped into automotive trunk liners and shaped underlayment for carpeting. US polystyrene low-density foam thermoforming is estimated at 500 MIb or 225 Mkg, nearly all for packaging and automotive applications [2]. US polyolefin low-density foam thermoforming is estimated at 100 MIb or 45 Mkg. Much of the discussion will focus on forming polystyrene foam. Forming of polyolefin foams follows the same general concepts.
Cell Architecture—Actual v. Ideal When pressurized gas-laden melt is extruded through die lips, the rapid drop in melt pressure allows the dissolved gas to come from solution, nucleate and form bubbles. Very early bubble growth is inertia-controlled. That is, bubble growth rate decreases with increasing polymer viscosity. Relatively quickly, bubble growth rate decreases as the polymer melt in the region around the bubble is depleted of gas and the bubble growth becomes diffusion-controlled. For low-density foams, as the bubbles continue to grow, the regions between bubbles thin to form membranes. The final bubble growth stage is controlled by elongational viscosity or melt elasticity of the polymer in the membrane. Foam cell size is affected by nucleant concentration, gas concentration, melt elasticity, and diffusivity of gas in polymer, among other parameters. Typically, foam cells are quite uniform in dimension, as shown in Fig. 9.50. Foams are usually discussed in terms of their architectural elements. Nearly all thermoplastic foams are closed-cell foams. Nearly all thermoplastic foams have membranes that are uniformly thick across their surfaces. And nearly all thermoplastic foams have membrane intersections that are not much thicker than the neighboring membranes. Foam architecture is usually considered as either regular dodecahedrons with fiveedged membranes, Fig. 9.5 IA, or regular tetrakidecahedrons, 14-edged structures having six four-edged membranes and eight six-edged membranes, Fig. 9.5IB. Simpler architectural models include three-dimensional cube-in-cube and two-dimensional square-in-square models, Figures 9.51C and 9.51D, respectively [143]. It is apparent from Fig. 9.50 that although real foam cells are relatively uniform in shape, it is only by chance that they achieve one of the several regular architectural models. Figure 9.52 shows the theoretical relationship between polystyrene foam density, cell
Figure 9.50 Scanning electron micrograph of low-density polystyrene foam. Scale bar is 500 um or 0.020 in
size and cell wall thickness [145]. Table 9.12 shows other relationships for low-density polystyrene foam. Example 9.6 shows these relationships for a typical polystyrene foam used for meat trays. Note that the thickness of polymer is very small, on the order of 50 |im or so, compared with the thickness of the foam sheet, on the order of 5 mm or so. Even more important, the experimental end-to-end dimension of a randomly coiled 60,000 molecular weight polystyrene molecule is about 1 x 10~6 in or 0.025 jim. For the foam of Example 9.6, the cell wall thickness is 80 microinches Table 9.12 Cell Architectural Dimensions for Polystyrene [145] Foam density (lbf/in2)
Cell size (x 10 " 3 in)
Cell wall thickness ( x 10 - 6 in)
Volume percent of solid (%)
Number of cells per ft3 (xlO 9 )
16.0 8.0 8.0 4.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 1.0 0.5
10 20 40 40 40 32 16 8 4 2 1 40 40
974 880 1760 834 400 320 160 80 40 20 10 190 87.1
24.3 12.1 12.1 6.0 2.94 2.94 2.94 2.94 2.94 2.94 2.94 1.41 0.651
1.3 0.19 0.024 0.025 0.027 0.051 0.41 3.3 26.0 210 1700 0.027 0.027
Ratio of cell size to cell wall thickness
10.3 22.7 22.7 48.0 100 100 100 100 100 100 100 210 459
A)
B)
C)
D)
Figure 9.51 Various classical foam architectural shapes
or 2 um. Thus if the polymer in the cell wall has no orientation, the cell wall is only about 80 molecules thick. Even with substantial orientation, typical cell walls are on the order of a few hundred molecules thick. Example 9.6 Cell Dimensions for a Meat Tray Polystyrene Foam Consider a 2 Ib I ft3, 0.200 in thick polystyrene foam used in meat tray applications. If the typical cell dimension is 200 jum, determine the typical cell wall thickness, the number of cells per unit volume, the number of cells in the foam thickness direction,
the thickness of polymer in the sheet thickness direction and the volume fraction of solid. The cell dimension is 0.008 in. From Fig. 9.52, the cell wall thickness is 80 microinches or 2 jim. From Table 9.12, the volume of foam contains less than 3% polystyrene. The rest, 97%, is cell gas. There are 3.3 x 109 cells/ft3. For 0.200 in thick of foam sheet, there are: 3.3 x 109 x -^- x 0.200 = 3.8 x 105 cells/in2 172o The number of cells in the sheet thickness direction is given as: O200 0.008 The number of cell membranes is thus 25 + 1 = 26. The thickness of plastic in the sheet thickness direction is: 26 x 80 x 10~6 = 2.0 mil, 0.002 in or 50 jim
Cell Wall Thickness (x 10~4in)
Density=O.128g/cm3
Cell Size (in) Figure 9.52 Classical relationship between polystyrene, PS foam density, cell size and cell wall thickness. Redrawn from [145] and used with permission of copyright owner
These models are used primarily to predict mechanical and thermal performance of thermoplastic foams. As is shown below, the square-in-square model is used to determine how a foam responds to conduction and radiant energy transmission.
Radiant Energy Transmission The three primary modes of energy transmission, conduction, convection and radiation, are applied to heating foam sheet. Convection involves energy transfer between the foam sheet and the air in the oven as well as microcirculation of cell gases during heating. As with heating of most plastic sheet, sheet surface convection is considered small when compared with conduction and radiation. Low-density foam is a good thermal insulator or a poor thermal conductor. The thermal conductivity of low-density foam is calculated from: kfoam*kg +(2/3)(l-c№p
(9.65)
where k f o a m is the thermal conductivity of the foam, k g is the thermal conductivity of the gas, k p is the thermal conductivity of the polymer and c|) is the volume fraction of the gas phase. The thermal conductivity of gas is always less than that for the polymer, as seen in Table 9.13. As a result, thermal conductivity of foam decreases with decreasing foam density, as illustrated in Example 9.7. As noted in Chapter 3, on heating the sheet, the material property for transient heat conduction is thermal diffusivity: CXf = k f /p • c p f
(9.66)
where p is the foam density and c p f is the heat capacity of the foam. Density-dependent thermal diffusivity values for polystyrene and PVC foams are shown in Fig. 9.53 [146]. The thermal diffusivity for most thermoformable foams is about the same as that for the unfoamed polymer. As noted many times herein, the rate of conduction energy transfer is a function of the Fourier number: 2
Fo = ocG/L
(9.67)
The time to heat to a specific forming condition is then proportional to the square of the thickness. Foams cannot be heated efficiently to their forming temperature with conduction alone. Example 9.7 Effect of Foam Density on Room Temperature Thermal Conductivity Determine the thermal conductivity of fresh 2 Ib/ft3 or 32 kg /m3 polystyrene foam blown with R-Il. What is the value if the foam is blown with n-butane? What is the value if the foam is blown with CO2? What is the value if the foam cells contain only air? What is the value if the foam is 4 Ib/ft3 or 64 kg/m3 and the cells contain air? The thermal conductivity of low-density foam is calculated from:
From Table 9.13, the volume percent of polymer in 2 lb/ft3 foam is 2.94%. Thus <\> = 1 - 0.0294 = 0.9706. Similarly, <)> for 4 lb/ft3 foam is 0.94. The R-value is given as the reciprocal of the British unit thermal conductivity per inch of foam thickness: R-value = l/kBtu.in = 0.1443/kw From Table 9.13, the thermal conductivities (in W/m • k) of the various gases and the polystyrene are: Trichlorofluoromethane (R-Il) n-Butane Carbon Dioxide Air Polystyrene (PS)
0.0074 0.0159 0.0166 0.0260 0.16
The calculated thermal conductivities (W/m • K) and R-values for the foams are: Foam thermal conductivity [W/m • K]
R-value
2 2 2 2
lb/ft3 PS/R-11 lb/ft3PS/n-Butane lb/ft3/CO2 lb/ft3/Air
0.0105 0.0190 0.0197 0.0291
13.7 7.6 7.3 5.0
4 4 4 4
lb/ft3 PS/R-11 lb/ft3 PS/n-Butane lb/ft3/CO2 Ib/ft3/air
0.0138 0.0223 0.0230 0.0324
10.5 6.5 6.3 4.5
Radiation transfer through very thin membranes is the key to efficient and uniform heating of low-density foams. Energy uptake during radiant heating of foams has not been measured. However, extensive studies of radiant energy transmission through foams have been done in conjunction with insulation. For this area, energy transfer is considered in terms of effective thermal conductivities: kf,eff
==
k CO nd H" *^rad H~ ^conv
(9.0o)
The last two are artificial conductivities. The overall effect of cell gas convection energy transfer is considered small for all but very low density foams having very large cells [149]. There have been many attempts to predict k rad , the artificial effective radiative thermal conductivity [150-154]. The Rosseland approximation solves the general equation for radiation through optically thick media [155]. For low-density foams, the equation is written as: (9.69)
Table 9.13 Room Temperature Thermal Conductivities of Foaming Agent Gas and Plastic [146,147] Gas
Thermal conductivity (Btu/ft • h • 0F)
(W/m • K)
Air Nitrogen Carbon dioxide Water vapor Propane n-Butane i-Butane n-Pentane Methanol Ethanol Dichloromethane (methylene chloride) Trichloromethane (chloroform) Trichlorofluoromethane (R-Il) Dichlorodifluoromethane (R-12) Dichlorofluoromethane (R-21) Chlorodifluoromethane (R-22) Trichlorotrifruoroethane (R-113) Dichlorotrifluoroethane (R-123) Dichlorofluoroethane (R-14 Ib) Difluoroethane (R-152a) Tetrafluoroethane (R-134a) Chlorodifluoroethane (R-142b)
0.0150 0.0151 0.0096 0.0103 0.0103 0.0092 0.0094 0.0078 0.0117 0.0091 0.0070 0.0070 0.0043 0.0055 0.0057 0.0068 0.0065 0.0060 0.0058 0.0054 0.0081 0.0054
0.0260 0.0261 0.0166 0.0178 0.0178 0.0159 0.0163 0.0135 0.0203 0.0157 0.0122 0.0121 0.0074 0.0095 0.0099 0.0118 0.0112 0.0104 0.0100 0.0094 0.0141 0.0094
Plastic
Thermal conductivity
Cellulose acetate (CA) Cellulose acetate butyrate (CAB) Cellulose propionate (CAP) Polyoxymethylene (Acetal or POM) Polycaprolactam (Nylon 6 or PA 6) Polyhexamethylene adipamide (Nylon 66 or PA 66) Polycarbonate (PC) Low-density polyethylene (LDPE) High-Density polyethlene (HDPE) Polymethyl methacrylate (PMMA) Modified polyethylene oxide (mPPO) Polypropylene (PP) Polystyrene (PS) SAN High-impact polystyrene (HIPS) ABS Polyethylene terephthalate (PET) Rigid polyvinyl chloride (RPVC) Polyvinylidene fluoride Polytetrafluoroethylene (PTFE) Fluoroethylene copolymer (FEP)
(Btu/ft • h • 0F)
(W/m • K)
0.156 0.179 0.116 0.173 0.168 0.133 0.121 0.185 0.231 0.104 0.133 0.127 0.092 0.104 0.104 0.104 0.144 0.092 0.075 0.133 0.150
0.27 0.31 0.20 0.30 0.29 0.23 0.21 0.32 0.40 0.18 0.23 0.22 0.16 0.18 0.18 0.18 0.25 0.16 0.13 0.23 0.26
Thermal Diffusivity (cm2/s)
Polystyrene (PS)
Polyvinyl Chloride (RPVC)
Density (g/cm3) Figure 9.53 Density-dependent thermal diffusivity for polystyrene, PS, and rigid polyvinyl chloride, RPVC, foams. Redrawn from [146] and used with permission of copyright owner
where qr is the radiant flux into the foam, x is the distance into the foam, K is the extinction coefficient and eb is the radiative emissive power, given as: eb = al^
(9.70)
where a is the Stefan-Boltzmann constant and Ts is temperature of the source, in absolute degrees. With substitution, Equation 9.54 becomes:
When this is combined with the conduction equation, the result is an energy uptake equation for low-density foams:
qt « | \ + (2/3)(l - <\>)kp + ^ l GT^j g
(9.72)
Measured values of the extinction coefficient, K, range from about 15 cm"1 to 45 cm^1 [156,157]. Example 9.8 demonstrates that the radiation effect is many times greater than that by conduction. Since the effective radiative conductivity is so great, the energy transmission into the foam is very rapid. As a result, the temperature gradient through radiantly heated low-density foam is on the order of a few degrees, as seen in Fig. 9.54 [158]. This figure also shows that the foam heats in a manner similar to nonwoven matte, indicating that membrane effects such as internal reflections and absorption and reradiation are small.
Example 9.8 Relative Effects of Conduction and Radiation Energy Transmission Determine the relative values for conduction and radiation conductivities of a 2 Ib/ft3 or 32 kg/3 polystyrene foam containing air in the cells. K= 15 cm'1. The heater temperature is 4000F. The absolute heater temperature is 477 K. a, the Stefan-Boltzmann constant value, is 0.5674 x 10~ 10 kW/m 2 K4. The value for the effective radiation thermal conductivity is: 16 16-0.5674 x IQ- 10 k
-
=
K aTs
=
'(4?7)
iJVW
krad = 0.0657 W/m • K The conduction thermal conductivity of this foam is given in Example 9.7 as: kcond = 0.0291 W/m -K The total rate of energy transfer through the foam is: ktotal = 0.0657 + 0.0291 = 0.0948 W/m • K The total energy transfer is 226% greater than that predicted from simple conduction heat transfer. Radiation accounts for nearly 70% of the total energy transfer.
Surface
Heater Temperature = 500 F
Temperature Increase, °F
at 0.070 in PS Foam Non-Woven PP
Non-Woven PP PS Foam Air
Oven Time, s Figure 9.54 Measured time-dependent surface and inner temperatures for polystyrene, PS foam and non-woven polypropylene, PP mat
Cell Gas Pressure @ 104 0C, kPa
Total Cell Gas
Air CFC-12
Time, h Figure 9.55 Time-dependent internal cell gas pressure showing air pressure, CFC-12 pressure and total cell gas pressure. Redrawn from [159]
Internal Cell Gas Pressure As gas-laden melt issues from the extruder die, bubbles form and grow and the foam cools until the increasing polymer strength and decreasing gas pressure balance. This is shown in schematic in Fig. 9.55 [159]. At that point, the internal cell gas pressure is slightly greater than one atmosphere absolute. As the foam cools to room temperature, internal cell gas pressure drops to 0.2 to 0.5 atmospheres absolute (Fig. 9.56) [160]. With time, air diffuses into the cells and the foaming gas diffuses out. The rate of foaming gas diffusion depends on its diffusivity. Diffusivity depends on the size of the gas molecule and the type of polymers. For polystyrene, certain classes of gases such as the HCFCs have very low diffusivity values and so remain in the foam for years. Others, such as butane and CO2, diffuse very quickly. For polyolefins, hydrocarbons and HCFCs diffuse very quickly whereas water vapor does not. Internal cell gas pressure therefore is quite time-dependent in the weeks following extrusion. It is important to know what the initial cell gas pressure is prior to heating since cell gases are rapidly expanded during reheating of the foam for the thermoforming step. In addition to cell gas pressure, some foaming gas always remains dissolved in the cell walls (Fig. 9.57) [161]. This residual gas affects foam reheating in two ways: •
The glass transition temperature of polystyrene is affected by blowing agents that act as small molecule lubricants. The typical effect is a linear decrease in Tg with blowing agent concentration:
Cell Volume
Temperature
Blowing Agent Concentration in Cell Wall
Cell Gas Pressure
Time
Full Expansion
Cell Wall Concentration (g/g Polymer)
Figure 9.56 Schematic time-dependent foam characteristics. Adapted from [159]
Hypothetical
n-Pentane i-Pentane
n-Butane Propane
i-Butane
Boiling Temperature (0C) Figure 9.57 Relationship between cell wall concentration and boiling point of foaming agent for polystyrene, PS. Adapted from [159]
(9.73)
•
where C is blowing agent concentration (g/g), and a is an empirical coefficient having a range of about 400 to 10000C. From Fig. 9.57, the residual concentration of n-pentane in polystyrene is 0.017. For a = 800, Tg of the foam is 13.5°C below that of the unfoamed polymer. This means that the foam has a lower forming temperature than the unfoamed polymer. The blowing agent gas in the cell wall will diffuse into the cell as the foam is reheated. While the partial pressure of this small amount of gas is low, it does contribute to the total cell gas pressure during "secondary foaming" or sheet expansion.
Forming Window for Foam As foam sheet is heated, the internal cell gas pressure increases and the cell walls soften. Gas pressure at fixed volume is related to absolute temperature as: P/PO = T/TO
(9.74)
where T 0 is initial or room temperature and P 0 is the cell gas pressure at initial temperature. Example 9.9 demonstrates this effect. Secondary foaming or oven expansion occurs because the polymer cannot resist internal cell gas pressure at the temperature. As seen in Fig. 9.58 for 4 lb/ft3 or 64 kg/m3, the experimental expansion ratios lie in a broad band between 1 and 2 over the sheet surface temperature range of 500C to 1200C [162]. As shown in Example 9.9, variation in room temperature internal cell gas pressure from sample to sample can dramatically affect the temperature where measurable secondary expansion begins. The nature of the heating source also changes the temperature-dependent secondary expansion curve, as seen in Fig. 9.59 [163]. The downward-turning curves indicate that excessive cell collapse or burn is occurring. This is an indication that energy transfer into the foam is strongly dependent on the source temperature, as seen in Equation 9.72. Note also in this figure that secondary expansion is very small with traditional convection oven heat transfer. Since convection energy can only be thermally conducted into the foam, this illustrates the relative importance of radiant heating of foams. The temperature-dependent expansion ratio can be predicted with substantial arithmetic and assumptions. In Fig. 9.60 [164], the predicted value envelope compares favorably with the experimental data. Example 9.9 Temperature Effect on Cell Gas Pressure Fresh foam has a room temperature (25° C) cell gas pressure of 0.5 atmospheres absolute. What is the cell gas pressure at 85° C? What is the cell gas pressure at this temperature for aged foam having a cell gas pressure of 1.5 atmosphere absolute at room temperature? Using Equation 9.59, the fresh foam cell gas pressure at 85°C is: P = 0.5 • (273 + 85)/(273 + 25) = 0.60 atmospheres absolute
The aged foam cell gas pressure at 85°C is: P = 1.5 • (273 + 85)/(273 + 25) = 1.8 atmospheres absolute If the polymer in the aged foam is sufficiently soft at 85°C, the foam will expand. The maximum amount of expansion is given by: P*v = Povo where P* is atmospheric pressure, or: v /v o
= p o /p* = 1.8/1 = 1.80
As seen in Fig. 9.58 [162], the measured expansion ratio is between about 1.25 and 1.6. This implies that the polymer offers some resistance to expansion. The lower forming temperature for polystyrene foam is the glass transition temperature of the blowing agent-impregnated sheet. The exact value depends on the blowing agent concentration but is probably 100C to 200C below the glass transition temperature for the unfoamed polymer. Secondary expansion can occur a few degrees below this temperature if initial internal cell gas pressure is high and the polymer has
Expansion Ratio, t/t 0
64 kg/m3 PS Foam
Surface Temperature,°F Figure 9.58 Experimental surface temperature-dependent secondary expansion ratio for 4 lb/ft3 or 64 kg/m3 polystyrene, PS foam. Open circles are heater temperature = 8000F. Closed circles are heater temperature = 9000F. Open triangles are heater temperature = 10000F. Open squares are 2500F hot air convection oven temperature. Lines represent 95% confidence limits
Heater Temperature = 900°F
Expansion Ratio, t/t 0
Gent-Thomas Strut Models
250°F Isothermal Convection Oven
T
g
Surface Temperature, F Figure 9.59 Experimental secondary expansion ratio for 4 lb/ft3 or 64 kg/m3 polystyrene, PS foam with heater temperature as parameter. Gent-Thomas expansion models represent closed and open celled foam responses [163]
a relatively gradual drop in tensile modulus just below the unfoamed polymer glass transition temperature. The upper forming temperature is the temperature where surface cell collapse or "burn" occurs. As seen in Fig. 9.59, this temperature is greatly dependent on the radiant heater temperature. It appears that at radiant heater temperatures of approximately 2600C, the upper forming temperature is 1200C or so. At radiant heater temperatures of 4800C, the upper forming temperature is 95°C or so. Thus the forming window can range from nearly 00C to as much as 400C. The low value for the upper forming temperature directly affects the drawability of foam sheet. Figure 9.61 [165] shows the very narrow forming range and low values for areal draw ratio for polystyrene foam as compared with those for unfoamed polystyrene. Table 9.14 compares draw ratios for laminated and unlaminated 4 lb/ft3 or 64 kg/m3 polystyrene sheet of several thicknesses [166]. Keep in mind that polystyrene is quite brittle near its glass transition temperature. Furthermore, draw-down is restricted by internal cell gas pressure which tends to support the cell walls against deformation. These factors combine with the low forming temperature to limit vacuum-formed foam products in depth of draw and detail. If excessive force is applied, as with plug assist, the sheet will tear.
Expansion Ratio, t/t 0
Theoretical
Experimental Bounds
Surface Temperature, F Figure 9.60 Comparison of experimental and theoretical secondary expansion ratios for 4 lb/ft3 or 64 kg/m3 polystyrene, PS foam. Shaded area represents heater temperature range of 5000F to 10000F
Matched die molds are used to achieve deeper draws and finer detail. Typically, the molded part wall thickness is less than the expanded sheet thickness. This allows the foam to compress while stretching. This helps stabilize the stretching process by minimizing cell wall collapse and membrane tearing. This stabilization allows for relatively deep draws. Nevertheless, cell wall rupture is apparent when matched die molding is used. Molding pressures are less than 100 lbf/in2 or 0.7 MPa and usually 40 to 50 lbf/in2 or 0.28 to 0.34 MPa. The Forming Equipment Traditional roll-fed thermoforming equipment is used to form low-density polystyrene foam even though sheet thickness can exceed 0.200 in or 5 mm. Since sheet heating is critical, ovens are designed to handle as many as five shots. This
H:D
Areal Draw Ratio
Unfoamed PS
PS Foam
Temperature (0C) Figure 9.61 Temperature-dependent areal draw ratio or H:D for foamed and unfoamed polystyrene
Table 9.14 Maximum H:D Draw Ratio for Laminated and Unlaminated Polystyrene Foam [166] (Note: 4 lb/ft3 or 64 kg/m3 polystyrene foam with 0.010 in or 0.25 mm polystyrene sheet lamination) Thickness of foam (in)
(mm)
0.010 0.030 0.050 0.080 0.100
0.25 0.76 1.27 2.03 2.54
H:D, Unlaminated
H: D, Laminated
0.3:1 0.5:1 0.7:1 0.9:1 1.2:1
0.4:1 0.7:1 0.9:1 1.1:1 1.5:1
allows for extended preheating and careful final heating of the sheet to prevent catastrophic cell collapse. Although traditional pin-chains are common, pins that are longer and larger in diameter are sometimes used with thicker sheet. Owing to the relatively low sheet temperatures, there is very little sheet sag although the sheet increases in thickness as discussed above. And the mold clamping section should be more robust in order to handle the weight of the matched dies. Foam sheet is usually not pattern- or zone-heated. As a result, metal rod heaters are sufficient for foam thermoforming. In-press and in-line trimming are common methods of separating the formed parts from the non-product web. Polystyrene foam processing experiences many of the problems encountered with unfoamed polystyrene. If the foam is blown with a volatile hydrocarbon, static charge can be a source of ignition as the sheet exits the extruder. Trim dust and fibers are always quite tenacious. The web is frequently passed through a two-roll nip to densify it prior to shredding or regrinding for recycling. Since cell collapse is catastrophic, overheated sheet can drop very quickly into the lower heaters. Rapidly opening or withdrawing heater sections are important modifications to any forming press. Shutters have been used over lower heaters. Carbon dioxide is sometimes injected into the heater section in the case of polystyrene foam fire. This polymer generates soot particles that hang in the ambient air and can contaminate product for hours or days after the fire. A thin sheet of unfoamed polymer is usually hot laminated to foam to improve cut resistance and drawability (Table 9.14). If the laminated sheet or capsheet is sufficiently thick, the sheet, not the foam, dominates the drawing characteristic of the laminate. However, the laminate cannot be overheated without catastrophic cell collapse.
9.9
Other Forming Technologies
The term thermoforming correctly encompasses any technology that involves heating and forming of thermoplastic sheet goods. As a result, many processes that are not identified as thermoforming incorporate thermoforming essentials. This section highlights some of these.
Interdigitation In the 1970s, a technique for mechanically deforming heated thermoplastic sheet was patented [167]. The basic concept involves impaling hot plastic sheet on cold mechanical "fingers". Two aspects of the technique have been commercialized. Interdigitation, or the "joining of fingers", produces a three-dimensional honeycomblike structure by simultaneously impinging digits or fingers perpendicularly in two directions into hot sheet (Fig. 9.62). These interdigitated thermoplastic polymers
Figure 9.62 Example of interdigitated structure, high-impact polystyrene, HIPS
compete with traditional honeycomb structures, are considerably less costly to produce, but appear to have only about 30% of the crush strength of honeycomb structures of the same density. The primary mode of failure for an interdigitated structure is buckling of the fingers. Thin-gage interdigitated products are produced either on special machines, where the heated sheet is passed at constant rate between two mating double belts that contain the opposing steel fingers as shown in Fig. 9.63, or on conventional jog-stop thermoforming equipment. Heavy-gage interdigitated products are produced on conventional shuttle presses. Applications include carpet underlayment that does not have the wicking and water absorption of foam and core structures for laminated decking and shaped dunnage where strength is needed at low cost. Mechanical shaping can be combined with traditional thermoforming to produce straight sidewall containers. The technique is called "cuspation-dilation" or "C-D" (Fig. 6.40) [168]. The key is articulation of the plug or finger to form the sidewall ribs and bottom of the container. Vacuum- or pressure-forming can follow to ensure adequate contact of the sheet with the mold surface during cooling, thus minimizing shrinkage effects and maintaining sharpness of detail.
Oven
Pin-Chain
Roll Stock
lnterdigitator
Figure 9.63 Schematic of interdigitation for the production of three-dimensional planar thermoformed structures
Sealed Air Cushion/Dunnage A thin-gage version of twin sheet thermoforming competes with low-density polyolefin foams in shock mitigating applications. The product is known generically as trapped air wrap, sealed air film or "bubble pack". The last is also a trade name. Four to 8 mil, 0.004 to 0.008 in or 0.1 to 0.2 mm cast or uniform biaxially blown polyethylene film is radiantly heated at a constant throughput rate and formed against a dimpled vacuum roll (Fig. 9.64) [169]. A second film is then heat-sealed against the first. This is done either on the vacuum roll by pressing the second film against the first using a heated mating roll or in a separate in-line step. Air is trapped in the dimples between the two films, thus providing shock mitigation. The energy absorption characteristics depend almost entirely on the compressibility of the air in the dimple. The primary mode of failure is microscopic tearing at the heat sealed edge. Radiant Oven Vacuum Roll
Take-off
Take-off
Take-up
Warm Mating/Pressure Roll Figure 9.64 Schematic of trapped air wrap for shock mitigation
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80. O.C. Raspor and H. Bongartz, "Solid-Phase Forming and Coforming of High-Performance Thermoplastics", Eng. Plast., 1: 5 (1988), pp. 323-338. 81. M. Cakmak and A. Dutta, "Instrumented Thermoforming of Advanced Thermoplastic Composites II", Polym. Compos., 12: 5 (Oct 1991), pp. 338-353. 82. M. Cakmak and A. Dutta, "Instrumented Thermoforming of Advanced Thermoplastic Composites III", Polym. Compos., 12: 5 (Oct 1991), pp. 354-369. 83. R. Scherer and K. Friederich, "Inter- and Intraply-Slip Flow Processes During Thermoforming of CF/PP-Laminates", Compos. Mfg., 2: 2 (1991), pp. 92-96. 84. M. Hon and K. Friederich, "Thermoforming of High Performance Composites with Thermoplastic Matrices", Eng. Plast., 5: 2 (1992), pp. 86-100. 85. T. Sin, A. Datta, J.P. DeSouza and D.G. Baird, "Thermoforming of In-Situ Reinforced Thermoplastic Composites", SPE ANTEC Tech. Papers, 37(1991), pp. 933-940. 86. T.A. Martin, "Deformation Characteristics and Formability of Fiber-Reinforced Thermoplastic Sheets", Compos. Manuf., 3: 3 (1992), pp. 165-172. 87. R.K. Okine, "Formable Avanced Thermoplastic Composite Sheet Based on an Excess Filament Length Concept", J. Thermoplast. Compos. Mat., 5(1992), pp. 152-165. 88. A.B. Strong and P. Hanwiller, "Incremental Forming of Large Thermoplastic Composites", Adv. Compos., 4: 5 (Sep/Oct 1989), pp. 56-66. 89. N G . McCrum, CP. Buckley, and CB. Bucknall, Principles of Polymer Engineering, Oxford Univ. Press, Oxford (1988), Figure 6.25, p. 247. 90. R.C. Harper, "Thermoforming of Thermoplastic Matrix Composites", Part II, SAMPE J., 28: 3 (May/Jun 1992), Figure 2, pp. 9-17. 91. R.C. Harper, "Thermoforming of Thermoplastic Matrix Composites", Part II, SAMPE J., 28: 3 (May/Jun 1992), Figure 5, pp. 9-17. 92. Anon., "Large-Section Components on Missile Airframe Thermoformed of Thermoplastic Composites", Adv. Compos., 6: 2 (Mar/Apr 1991), pp. 6, 10. 93. R.C Harper, "Thermoforming of Thermoplastic Matrix Composites". Part II, SAMPE J., 28: 3 (May/Jun 1992), pp. 9-17, Figure 4. See also R. Monks and M. Naitove, "Technology Update: Advanced Composites, 37: 3 (Mar 1991), pp. 48-55. 94. J.A. Boldt and J.P. Chanani, "Solid-Tool Machining and Drilling", in CA. Dostal, Ed., Engineered Materials Handbook. Vol. 1: Composites, ASM International, Metals Park OH (1987), pp. 667-675. 95. R.C Progelhof, J.G. Quintiere and J.L. Throne, "Temperature Distribution in Semitransparent Plastic Sheets Exposed to Symmetric, Unsymmetric and Pulsed Radiant Heating and Surface Cooling", J. Appl. Polym. ScL, 77(1973), pp. 1227-1252. 96. R.C Progelhof, J.L. Throne and J.G. Quintiere, "Some Clues to Thermoforming Transparent Plastic Sheet", SPE J., 29: 1 (Jan 1973), pp. 35-37. 97. J.L. Throne, R.C. Progelhof and J.G. Quintiere, "Cyclical Radiant Heating of Semi-Transparent Sheets—Some Clues to Thermoforming", SPE ANTEC Tech. Papers, 17 (1972), pp. 820-824. 98. L.K. Kochar and J.L. Throne, "Thermoforming Multilayer Sheet. I: General Criteria", J. Plast. Film Sheet., 5(1989), pp. 186-208. 99. L.K. Kochar and J.L. Throne, "Thermoforming Multilayer Sheet. I: General Criteria", J. Plast. Film Sheet., 5 (1989), Figure 9b. 100. A. Schuster, Astrophys. J., 21 (1905), pp. 234-247. Cited in D.H. Menzel, Selected Papers on the Transfer of Radiation, Dover Publications, New York (1966). 101. L.K. Kochar and J.L. Throne, "Thermoforming Multilayer Sheet. I: General Criteria", J. Plast. Film Sheet., 5 (1989), Figure 10. 102. L.K. Kochar and J.L. Throne, "Thermoforming Multilayer Sheet. I: General Criteria", J. Plast. Film Sheet., 5(1989), Figure 11a, lib. 103. L.K. Kochar and J.L. Throne, "Thermoforming Multilayer Sheet. I: General Criteria", J. Plast. Film Sheet., 5 (1989), Figure 12. 104. A.C. Peterson, Applied Engineering Mechanics: Strength of Materials, 2nd Ed., Allyn and Bacon, Inc., Boston (1982), Figure 5-17, 5-19.
105. E. Galli, "Twin-Sheet Thermoforming: Cost-Effective Alternative for Large Parts", Plast. Des. Forum, 75:5 (Sep/Oct 1990), pp. 35-40. 106. Anon., "Double Thermoforming—A Twin-Sheet Vacuum Forming Process for the Production of Hollow Goods", Plastverarbeiter, 43: 3 (Mar 1992), pp. 34-36. 107. Anon., "Producing Hollow Products by Twin Sheet Forming", Plast. Rubber WkIy, # 1328 (24 Mar 1989), p. 9. 108. Jack Schreiffer and P.V. Muhlethaler report that Dupont twin-sheet molded ping-pong balls of 0.020-inch cellulose acetate nitrate at Leominster MA in 1935. 109. J.L. Throne, Thermoplastic Foams, Chapman & Hall, New York (1994), Table 11.2. 110. C M . Mulcahy and E.M. Berns, "Thermoforming Takes on More Engineering Applications", Plast. Eng., 46: 1 (Jan 1990), pp. 21-25. 111. D. Bank, "Structural Blow Molding", Seminar given at Plastics Product Designers Forum, Boston MA (13-15 Sep 1994), Papago Plastics, Inc., 240 Burrows St., Rochester NY 14606. 112. R.C. Progelhof and J.L. Throne, Polymer Engineering Principles. Properties, Processes, and Tests for Design, Hanser Publishers, Munich (1993), pp. 471-475. 113. J.L. Throne, Thermoplastic Foams, Sherwood Publishers, Hinckley OH (1996), Section 11.6, "Hollow Objects". 114. W.R. Roller, "Twin Sheet Thermoforming", paper presented at SPE Thermoforming Conference, South Bend IN (Sep 1993). 115. G. Menges and D. Weinand, "Modelling the Stretching Process in Thermoforming", Kunststoffe, 78 (1988), BiId 3, pp. 456-460. 116. D. Hylton, "Laboratory Techniques for Predicting Material Thermoformability: A Review", SPE ANTEC Tech. Papers, 37(1991), Figure 3, pp. 580-583. Note: There is no temperature indication on this figure. 117. R.W. Johnson and CS. Ilenda, "Modifiers That Improve the Thermoformability of Polypropylene", SPE ANTEC Tech. Papers, 38: 1 (1992), pp. 501-505, especially Figure 1. 118. D. Hylton and C Cheng, "The Effect of Molecular Weight and Molecular Weight Distribution on Extrusion and Thermoforming Properties of Polypropylene", SPE ANTEC Tech, Papers, 34 (1988), Figure 1, pp. 491-495. 119. F J . Padden and H.D. Keith, "Spherulitic Crystallization in Polypropylene", J. Appl. Phys., 30 (1959), pp. 1479-1484. 120. H.D. Keith, F J . Padden, M.M. Walter and H.W. Wychoff, "Evidence for a Second Crystal Form of Polypropylene", J. Appl. Phys., 30 (1959), pp. 1485-1488. 121. H. Gross and G. Menges, "Influence of Thermoforming Parameters on the Properties of Thermoformed PP", SPE ANTEC Tech. Papers , 28 (1982), pp. 840-843. 122. J.L. Meriam, Mechanics: Part l~Statics, John Wiley & Sons, New York (1952), Figure 52, pp. 184-186. 123. R.W. Johnson and CS. Ilenda, "Modifiers That Improve the Thermoformability of Polypropylene", SPE ANTEC Tech. Papers, 38: 1 (1992), pp. 501-505, especially Figure 3. 124. D. Hylton, "Laboratory Techniques for Predicting Material Thermoformability: A Review", SPE ANTEC Tech. Papers, 37(1991), Figure 2, pp. 580-583. 125. A.S. Scheibelhoffer, A.S. Wimolkiatisak, B.L. Leonard and D.Chundury, "Highly Thermoformable Polyolefin Alloys", SPE ANTEC Tech Papers 39: 1 (1993), Figure 2, pp. 629-632. 126. K.F. Wissbrun and J.M. Dealy, "Melt Rheology and Blow Molding", in D.V. Rosato and D.V. Rosato, Eds., Blow Molding Handbook: Technology, Performance, Markets, Economics—The Complete Blow Molding Operation, Hanser Publishers, Munich (1989), Chapter 17. 127. G. Ajroldi, "Determination of Rheological Parameters from Parison Extrusion Experiments", Polym. Eng. ScL, 18 (1976), pp. 742-749. 128. D.H. Sebastian and J.R. Dearborn, "Elongation Rheology of Polyolefins and Its Relation to Processibility", Polym. Eng. Sci., 23 (1983), pp. 572-575. 129. K.E. McHugh and K. Ogale, "High Melt Strength Polypropylene for Melt Phase Thermoforming", SPE ANTEC Tech. Papers, 36(1990), pp. 452-455. 130. M.R. Drickman and K.E. McHugh, "Balancing Extrusion and Thermoforming Capability for Polypropylene", SPE ANTEC Tech. Papers 38: 1 (1992), pp. 496-500.
131. D. Hylton and C. Cheng, "The Effect of Molecular Weight and Molecular Weight Distribution on Extrusion and Thermoforming Properties of Polypropylene", SPE ANTEC Tech, Papers, 34 (1988), Figure 3, pp. 491-495. 132. D. Hylton and C. Cheng, "The Effect of Molecular Weight and Molecular Weight Distribution on Extrusion and Thermoforming Properties of Polypropylene", SPE ANTEC Tech, Papers, 34 (1988), Figure 4, pp. 491-495. 133. K.E. McHugh and K. Ogale, "High Melt Strength Polypropylene for Melt Phase Thermoforming", SPE ANTEC Tech. Papers, 3(5(1990), Figure 1, pp. 452-455. 134. A.S. Scheibelhoffer, A.S. Wimolkiatisak, B.L. Leonard and D. Chundury, "Highly Thermoformable Polyolefin Alloys", SPE ANTEC'Tech. Papers, 39: 1 (1993), pp. 629-632. 135. K.A. Albert, CA. Cruz, J.P. Palm and R.W. Johnson, "Acrylic Modified Polypropylene for Thin Gage Thermoforming: Improved Processing Properties and Economics", SPE ANTEC Tech. Papers, 39: 1 (1993), pp. 633-637. 136. R.W. Johnson and CS. Ilenda, "Modifiers That Improve the Thermoformability of Polypropylene", SPE ANTEC Tech. Papers, 38: 1 (1992), Figure 3, pp. 501-505. 137. A.S. Scheibelhoffer, A.S. Wimolkiatisak, B.L. Leonard and D. Chundury, "Highly Thermoformable Polyolefin Alloys", SPE ANTEC Tech. Papers, 39: 1 (1993), Figure 2, pp. 629-632. 138. K.A. Albert, CA. Cruz, J.P. Palm and R.W. Johnson, "Acrylic Modified Polypropylene for Thin Gage Thermoforming: Improved Processing Properties and Economics", SPE ANTEC Tech. Papers, 39: 1 (1993), Figure 1, pp. 633-637. 139. P. Mapleston, "Thermoforming PP: Here Come the New Processes, New Materials", Mod. Plast. Int., 19: 8 (Aug 1989), pp. 40-43. 140. R.D. Leaversuch, "What Does it Take to Run Melt-Formable PP?", Mod. Plast., 66: 4 (Apr 1989), pp. 73-76. 141. J.L. Throne, Thermoplastic Foams, Sherwood Publishers, Hinckley OH (1996), Section 5.2, "Extrusion". 142. D. Klempner and K.C Frisch, Eds., Handbook of Polymeric Foams and Foam Technology, Hanser Publishers, Munich (1991). 143. J.L. Throne, Thermoplastic Foams, Sherwood Publishers, Hinckley OH (1996), Figure 9.5A-E. 144. CJ. Benning, Plastic Foams: The Physics and Chemistry of Product Performance and Process Technology. Volume 1: Chemistry and Physics of Foam Formation, Wiley-Inter science, New York (1969), Figure 65. 145. CJ. Benning, Plastic Foams: The Physics and Chemistry of Product Performance and Process Technology. Volume 1: Chemistry and Physics of Foam Formation, Wiley-Interscience, New York (1969), Table XIII. 146. J.L. Throne, Thermoplastic Foams, Sherwood Publishers, Hinckley OH (1996), Table 4.8. 147. H. Saechtling, International Plastics Handbook for the Technologist, Engineer and User, 2nd Ed., Hanser Publishers, Munich (1987), p. 395, Table 100. 148. J.L. Throne, Thermoplastic Foams, Sherwood Publishers, Hinckley OH (1996), Figure 9.102. 149. J.A. Valenzuela and L.R. Glicksman, "Thermal Resistance and Aging of Rigid Urethane Foam Insulation", Proceeding of DOE-ORNL Workshop on Mathematical Modeling of Roof, Conf-811179, Atlanta GA (3-4 Nov 1981), pp. 261-262. 150. F J . Norton, "Thermal Conductivity and Life of Polymer Foams", J. Cell. Plast., 3 (1967), pp. 24-29. 151. R.E. Skochdopole, "The Thermal Conductivity of Foamed Plastics", Chem. Eng. Prog., 57: 10 (Oct 1961), pp. 57-62. 152. R.C Progelhof, J.L. Throne and R.R. Ruetsch, "Methods for Predicting the Thermal Conductivity of Composite Systems", Polym. Eng. Sci., 16(1916), pp. 618-625. 153. D.A. Brandreth and H.G. Ingersoll, "Accelerated Aging of Rigid Polyurethane Foam", J. Cell. Plast., 7(5(1980), pp. 235-238. 154. D.W. Reitz, "A Basic Study of Gas Diffusion in Foam Insulation", MS Thesis, Massachusetts Institute of Technology, Cambridge MA (May 1983). 155. M. Sinofsky, "Property Measurement and Thermal Performance Prediction of Foam Insulations", MS Thesis, Massachusetts Institute of Technology, Cambridge MA (Jan 1984), p. 24.
156. M.A. Schuetz, "Heat Transfer in Foam Insulation", MS Thesis, Massachusetts Institute of Technology, Cambridge MA (May 1982), p. 141. 157. C H . Stern, "Radiation Characteristics of Rigid Foam Insulation", BS Thesis, Massachusetts Institute of Technology, Cambridge MA (May 1982). 158. J.L. Throne, "Polystyrene Foam Sheet Expansion During Heating", J. Polym. Eng., 6 (1986), Figure 3, pp. 313-344. 159. J.G. Burt, "The Elements of Expansion of Thermoplastics. Part II", J. Cell. Plast., 24(1978), pp. 341-345. 160. J.L. Throne, Thermoplastic Foams, Sherwood Publishers, Hinckley OH (1996), Figure 9.105. 161. J.L. Throne, Thermoplastic Foams, Sherwood Publishers, Hinckley OH (1996), Figure 6.20B. 162. J.L. Throne, "Polystyrene Foam Sheet Expansion During Heating", J. Polym. Eng., (5(1986), Figure 5, pp. 313-344. 163. J.L. Throne, "Polystyrene Foam Sheet Expansion During Heating", J. Polym. Eng., 6(1986), Figure 6, pp. 313-344. 164. J.L. Throne, "Polystyrene Foam Sheet Expansion During Heating", J. Polym. Eng., (5(1986), Figure 19, pp. 313-344. 165. J.L. Throne, Thermoplastic Foams, Sherwood Publishers, Hinckley OH (1996), Figure 10.15. 166. J.L. Throne, Thermoplastic Foams, Sherwood Publishers, Hinckley OH (1996), Table 10.2. 167. D.G. Keith and A.E. Flecknoe-Brown, "Cuspation: A New Technique in High-Speed DeepDraw Thermoforming", Mod. Plast., 56: 12 (Dec 1979), pp. 62-64. 168. A. Brockschmidt, "Thermoforming Barrier Containers: How It's Different", Plastics World, 42:9 (Sep 1984), Figure on p. 71. 169. J.L. Throne, Thermoplastic Foams, Sherwood Publishers, Hinckley OH (1996), Figure 11.26A. 170. J.L. Throne, "Rotational Molding", in M. Narkis and N. Rosenzweig, Eds., Polymer Powder Technology, Chapman & Hall, Ltd., London (1994).
10 Set-Up Protocols, Troubleshooting, and the Economics of Thermoforming 10.1
Introduction
10.2 Setting Up a Thermoforming Machine—Protocols A New Polymer Setting Up a New Mold Setting the Mold Stops Dry-Cycling the Mold Checking the Vacuum Attaching Cooling to the Mold The Sheet Delivery System Setting the Oven Conditions Forming Step—Simple Vacuum Forming Changing Temperature Conditions Activating the Assists Pressure Boxes General Objectives 10.3 Troubleshooting the Forming Process 10.4 Energy and Materials Cost The Energy Audit Cost of Extrusion Cost of Regrind Competitive Costs of Polymers 10.5 General Processing Economics Rules of Thumb Global Production Costs Manufacturing Efficiencies The Learning Curve 10.6 Isolated Venture Costs 10.7 New Venture Economics Entrepreneurial Risks 10.8 The Incremental Operation 10.9 Comparative Process Economics 10.10 References
10,1
Introduction
The business of thermoforming depends on several fundamental concepts. Modern machines are designed to produce parts, repetitively, day in and day out, with relatively little maintenance or attention. Businesses require that these machines make money. Profitable businesses require that the machine make quality parts that can be sold at values greater than their total manufacturing costs. Profit is the expected return on investment for taking the risk of being in business. The keys to business success are quality and accountability. To make products from sheet, the interaction of the sheet with the process parameters should be thoroughly understood. The quality of the product depends on: • • •
The skill of the operator, The selection of quality raw materials, and An adequate quality control of all incoming and outgoing materials.
This is shown in schematic in Fig. 10.1. Since energy consumption is an important factor in thermoforming, energy audits are necessary, as shown in Fig. 10.2. Money, as cash flow, is also treated in this fashion in Fig. 10.3. In previous chapters, the technical and marketing aspects of thermoforming have been analyzed in detail. In this chapter, the focus is on the business aspects of thermoforming. Good finished parts cannot be made from imperfect sheet material. Incoming materials quality and the condition of regrind materials for reprocessing into additional sheet require management awareness and dedication. In order to become and remain competitive, an understanding of current processing practices in other, non-thermoforming areas such as extrusion, calendering, milling and casting, must be understood. This understanding allows the thermoformer to establish meaningful quality standards for his/her products. Accountability has become immeasurably easier with the successful development of small, inexpensive computers
Purchased Sheet
Ancillary Parts,Components Packing Materials
Consumed Materials,
Packaged Finished Products to Customer Regrind to Reprocessing Retains,Give-Aways,Take-Homes Valueless Scrap
Surface Treatments
Figure 10.1 Steady-state material balance in thermoforming
Water
Electricity
Waste Heat Waste Water
Plant Operation
Flue Gas to Environment
Fuel
Figure 10.2 Steady-state energy balance in thermoforming
SWB of Employees Accounts Payable Accounts Receivables
Plant Operation Taxes.lnsurance Profit
Figure 10.3 Steady-state cash flow in thermoforming
and attendant accounting and storage software. Even the smallest business now has the capability of keeping detailed records on: • • • • • • • •
Payroll, Incoming materials inventory, Outgoing materials inventory, Work in progress, Regrind, Accounts receivables, Accounts payables, and Many other accounting techniques [I].
The rapid development of barcoding1 has opened new opportunities for keeping track of things such as: • • • • • •
Incoming materials, including delivery dates, warehouse location, and any receivable materials tests, Outgoing product, including day and time of production, machine, shift, operators), storage location and all inspection information, All work in progress and all rework, including reasons for delays and reasons for reworking, All regrind, whether rolled web or reground cut-sheet chip, All molds, including original manufacturing date, reworking dates, total production information, storage procedures, and warehouse location, All incoming machinery spare parts and warehouse locations.
Despite these aids, the thermoform business person must still have a basic understanding of the various elements of his/her specific business that make up cash balances and annual operating costs. The thermoform business person is usually concerned with at least one of three general categories of business: •
•
•
Existing business, where the costs required to produce a product are similar to the already-known costs to produce a similar product. Existing product business is usually considered as fitting into an on-going thermoforming effort whose costs are essentially time-independent or steady-state, Isolated new business, where a new business is begun in a location that is remote from the current business area and/or where the existing business is not thermoforming. Classic examples of isolated new business ventures include: • Manufacture of thermoformed parts that replace nonthermoformed products such as sheet metal or fiber-glass-reinforced thermosets with thermoformed products, and • Incorporation of thermoforming as part of a forward- or backward integration, such as adding thermoforming containers to a manufacturing operation or thermoforming an assembly component that was previously purchased, and Incremental business, where a new product line is added to an existing business. The incremental venture combines certain aspects of steady-state production costs and new venture costs.
The isolated new business venture requires the most analysis, since not only is the value of the product initially unknown, but long-term effects of energy costs, money 1
PC-based software enables customized barcodes to be created and printed directly on PSAbacked labels. This allows any size company to create its own data-logging scheme using barcodes and laser scanners. Some suppliers are: Bear Rock Technologies, 4140 Mother Lode Dr., Suite 100, Shingle Springs CA 95682, 916-672-0244 River City Grafix, 11765 West Avenue, Suite 321, San Antonio TX 78216, 210-496-5109 Riversedge, 10902 Forest Summit, San Antonio TX, 78233, 210-590-9528 T.A.L. Enterprises, 2022 Wallace St., Philadelphia PA 19130, 215-763-5096.
Table 10.1 Nature of the New Thermoforming Product on Business Structure Nature of the new product/business
Existing
Incremental
Isolated new venture
Nature of business
Existing
New
Effect on general operation Effect on equipment Effect on site Effect on labor Effect on sales/service Effect on management Effect on R&D Effect on facilities Nature of polymers Debugging of Machine Polymers Facilities Molds Debugging time Start-up costs Accuracy of cost analysis
None, steady state None None None None None Little None New or well-known
New product on existing business Existing, expansion New or modification Existing expansion Expansion Expansion, retraining None Moderate Expansion New
None Some None Moderate Immediate to week None to slight +5%
Some Some Moderate Moderate Week to month Moderate +15%
Significant Significant Significant Significant Months to year Significant +25% or more
New expansion New New expansion New hires New hires New, training Significant New, ground-up New
costs and inflation are also unknown. Isolated ventures require careful analysis of competitive processes as well. For these reasons, major emphasis is placed on understanding the elements of the isolated venture. Some important elements of each of these business strategies are given in Table 10.1. Businesses also depend on the ability to convert new ideas to income in minimum time at minimum cost. Most of the early discussion focused on the technical aspects of how plastic sheet responds to its environment. However, there are many times when theory and sound reasoning must be replaced with traditional check-lists accumulated through hands-on experience. Two general "fix-it" sections are included here: • •
Setting up the thermoforming system with a new polymer and/or a new mold, and Finding out why the product is not forming correctly.
Many quality control tests have been discussed throughout the technical sections of this book. Some of these are summarized in this chapter as well.
10.2
Setting Up a Thermoforming Machine—Protocols
There are many occasions when it is necessary to rapidly spiral in on operating conditions for a new plastic or a new mold. Certain protocols are possible to help speed this process1. A New Polymer The most important first step when considering thermoforming a new polymer is to collect as much information about the polymer as possible. This is true whether the sheet is cut heavy-gage for shuttle or rotary presses or is thin-gage for roll-fed operations. For example, the morphological nature of the polymer is needed: •
A polymer that is amorphous has no melting temperature. Typically, amorphous polymers such as styrenics, vinyls, acrylics, amorphous polyesters and polycarbonates have similar forming characteristics: • The polymer softens over a wide temperature range, • The polymer generally has good to excellent melt strength, • The polymer usually has controllable sag, and in some cases, no sag at all, and • The polymer has a wide forming window. • Crystalline polymers have finite melting temperature ranges. Some melt over a relatively broad temperature range usually greater than 100C. Low-density polyethylene is an example. Others melt over a very narrow temperature range usually less than 1°C. Nylon 66 or PA 66 is an example. Others, such as polypropylene and high-density polyethylene, have melting temperatures in the 1 to 100C range. Crystalline polymers have similar forming characteristics: • The polymer softens and melts over a narrow temperature range, • The polymer may exhibit excessive sag and poor melt strength, • The polymer may exhibit high shrink and warping characteristics, and • The polymer usually has a narrow forming window. In addition to general forming characteristics, certain polymers may exhibit other undesirable characteristics such as: • • • • 1
Color change, particularly yellowing. PVC and PET are polymers that show this tendency, Loss in molecular weight with the resulting loss in physical properties. PET, PVC and PA 6 are polymers that show this tendency, Outgassing, odor and excessive smoke. ABS, PVC and mPPO are polymers that show these tendencies, and Loss of embossing or surface gloss. ABS and RPVC are polymers that show these tendencies.
Portions of this section are abstracted from notes provided by Don Carroll, Consultant, with permission [2].
Filled and reinforced polymers offer additional general characteristics that must be addressed prior to thermoforming. For example: •
Filled polymers usually require higher forming pressures but the forming temperature usually is restricted by the forming temperature of the neat polymer. Excessive sag occurs if the filled polymer temperature is raised substantially above that for forming the neat polymer, • Reinforced polymers usually require higher forming pressures and probably matched dies for molding. The forming temperature is usually substantially higher than the forming temperature for the neat matrix. The fiber reinforcement keeps the sheet from sagging substantially even at very high sheet temperatures. • Colorants and pigments may change the way in which the polymer absorbs radiant energy. Typically, polymers colored with metallic oxide pigments and carbon will heat much more rapidly than the natural polymers. Even though the forming window is not dramatically changed by pigmenting, the time to achieve the forming window is. Some of the inherent forming characteristics of a polymer can be deduced by observing how the homologous series of polymers form. For example, the forming window for a new impact polystyrene is not expected to be substantially different than the forming window for other, well-known impact polystyrenes. The same is true for polyethylenes and cellulosics. On the other hand, not all polyvinyl chlorides form the same. Polyvinyl chloride formability depends on the adducts that are compounded into the polyvinyl chloride resin. Certain adducts improve the extrusion characteristics but are detrimental to the thermoforming hot strength. Other adducts improve the forming range but shorten the high-temperature exposure time. In addition to the general characteristics of the polymer, information regarding the polymer mechanical properties should be obtained. Information that is useful to the designer includes: • • • • • • •
Impact strength, including Notched and Drop weight, Heat distortion temperature, Continuous service temperature, Coefficient of linear expansion, Shrinkage, Thermal conductivity and thermal diffusivity, and Chemical resistance.
No new polymer can be offered to the thermoformer without having been extruded. For initial trials, only virgin sheet is used, unless the customer requires 100% regrind only. The first-hand knowledge of the extruder in dealing with extrusion aspects of the polymer is important in determining proper handling protocol. The extruder should be able to provide the thermoformer with the following information: •
Sheet preparation conditions, including drying, storage, and unusual sheet orientation problems,
• • • • •
Unusual sag conditions, Extrusion time and temperature conditions, Unusual handling conditions, such as splittiness or brittleness, Potential maximum regrind level, and Safety precautions, including obnoxious gases or odors, discoloration, and the like.
Concern about the sheet quality is usually less critical with prototype set-up operations than with manufacturing operations. Nevertheless, the extruder and thermoformer should agree on acceptable standards for the initial prototyping, process and product trials. Standards should include: • • • • • •
Gage, width and length dimensional tolerances, Sheet flatness and squareness, Sheet orientation, across the sheet, in the sheet direction, sheet to sheet and pallet to pallet (or roll to roll), General appearance including surface defects and moisture level, The nature of the trimming and whether dust or slivers are apparent, and Molecular weight or IV for PET, melt index for polyethylenes and melt flow rate for polypropylenes.
Then some simple tests are needed. Sheet orientation should be checked on several sheets. The orientation of the sheet is determined with the test described in Section 8.11 [4]. The formability of the sheet and its forming range are determined with the funnel test described in Appendix 7.1. The technique is used in the following way: • • • • •
A heating protocol is defined. One such protocol is given in [3]. This protocol is used throughout the test. Sheet is heated to a fixed temperature, then formed into a 60° metal funnel. The formed cone is removed and the thickness of the bottom center of the shape is measured. The process is repeated at a slightly higher sheet temperature, say, 5°C. As noted in Chapter 7, the local thickness ratio is the reciprocal of the local areal draw ratio. The temperature-dependent formability of the sheet can be easily determined, as shown in Fig. 10.4 for PVC.
The equipment needed for this technique is very inexpensive. A 4-in to 6-in diameter metal funnel can be obtained at any feed store. A toaster oven will suffice for the heating source and a shop vacuum system will work for the vacuum source. The funnel is connected to the vacuum system ,with a section of heavy rubber hose. The sheet is clamped in a simple book mold using vise grips. Another test uses the draw-down into a two-dimensional radius as a measure of the formability. As noted in Chapter 7, the relationship between local sheet thickness and drawn radius is: (10.1)
Areal Draw Ratio, R^
Geon 87313
Geon 87651
Oven Temperature,0F Figure 10.4 Temperature-dependent maximum areal draw ratio for two types of polyvinyl chloride, PVC. Data obtained using 60° cone
Figure 10.5 shows the relationship between R/ho and sheet temperature. The temperature-dependency of h/ho is obtained from Equation 10.1. The circle-grid technique is used in many ways. For example, it is routinely used in trouble-shooting to determine whether zonal heaters are functioning properly. It is also helpful in determining the relative effect of plugs and billow prestretching on material reallocation1. The technique is very simple. The sheet surface is scribed with a standard cross-hatch of, say, 1 in or 25 mm squares. A circle is drawn at the axis of each set of crossing lines (Fig. 10.6). After forming, the circles are examined and measured, as follows: •
If the final shape is still a circle, the local areal draw ratio is:
"•-£-©' 1
(102)
The standard method of applying the circle-grid pattern to the sheet is to use indelible ink. A rubber stamp is useful for small parts. A silk screen is used for larger surfaces. For troubleshooting, the entire surface does not need to be circle-gridded. Frequently, a template is placed over the critical area through which the pattern is marked. This technique must be used with care when the sheet is very thin or is transparent. High carbon- or iron-content ink will preferentially absorb radiant energy, leading to sheet wrinkling and questionable localized drawing. Dye-based inks are more acceptable.
Reduced Radius, R/ho
H=D/2
RPVC
OPS 5
CA
1
JVCLDPE
S-B PET
FPVC
CAP PA1HDPE'
PVCA Design
CAB
Minimum
Sheet Temperature,0C Figure 10.5 Temperature-dependent corner radius for several polymers
Figure 10.6 Circle-grid pattern for stretching characteristics of thermoformed shapes
The local thickness ratio is again the reciprocal of the areal draw ratio: (10.3) More importantly, the sheet has been uniformly biaxially oriented in the local area. If the final shape is an ellipse, Fig. 10.8, the local areal draw ratio is: (10.4)
R A =(r 2 /ab)
•
Figure 10.8 Nonuniform biaxial or uniaxial stretching with circle-grid pattern
where a is the major half-axis and b is the minor half-axis of the ellipse. The local thickness ratio is the reciprocal of this local areal draw ratio. The sheet has been nonuniformly biaxially oriented in the local area. If the final shape is an ellipse where b, the minor half-axis, equals the initial radius, R, the local areal draw ratio is:
The sheet has been uniaxially oriented in the local area. If the final shape is tear-drop in shape, Fig. 10.9, no inference can be drawn about the local extent of orientation. It is suggested that the test be rerun using smaller circles in this area. If the polymer is found to be satisfactory for the application, the thermoformer and extruder must negotiate the standards and guidelines for production quality sheet product. The correct procedure for this negotiation is described in Chapter 8. •
Setting Up a New Mold The thermoformer should work with the mold maker throughout the manufacture of the mold to ensure that the mold meets the required specifications. A typical checklist is given as Table 10.2. Any standard checklist should include:
R. = Indeterminate A
Figure 10.9 Tear-drop or nonuniform elongation with circle-grid pattern
Table 10.2 Setting up a Thermoformer—The Check List Prior to the Mold Leaving the Mold Maker • Check surface texture, polish • Look for oil, grease leaks • Check all mechanical actions Cams Slides Hinges Plugs • Review aspects of coolant lines Proper layout Chip-free • Check vacuum lines Chip-free • C J « * v a c u u m holes All open • Dry-cycle mold action • Pressurize coolant lines • If P°sslble: . Place rubber sheet over mold cavity Apply vacuum and observe draw-down Put Mold on Platen • Center • Align • Level • Set stops • Set platen movement rate Check platen velocity • Realign at top of stop • Relevel at top of stop • Dry-cycle mold on platen • Align and time each ancillary element • Install vacuum line Smooth interior line Minimum number of L's and T's • Test vacuum seal Place gasketed metal plate with pressure gage, petcock over cavity Measure rate of evacuation • Test the vacuum hole configuration LDPE film or rubber sheet over mold t
Measure rate of evacuation • Install coolant hoses Ma folds Insulate hoses Use oversize quick-disconnects • Apply coolant to mold 10-20 0 F below HDT of polymer Allow steady-state, hour(s) Check for leaks • Check mold temperature Surface thermocouple
Infrared probe Thermography • Look for regions of differential temperature Slides Hinges Plugs Ribs, bosses, gussets • Recheck platen/mold level • Dry-cycle hot mold Check all alignments Check for metal-to-metal interference, binding Remachine rather than lubricate Set Sheet Delivery System # Coordinate/time sheet delivery with mold dry-cycle # Set sheet deHvery sequence
first?
then set load/unload sequence Set Oven Conditions • Set top heater bank to fixed, constant temperature across all heaters # Wait for steady-state heater cycling— minutes # Measure individual heater temperature Thermocouple Infrared Thermography # Shut off top heater bank, allow to cool # Repeat with bottom heater bank # Clean, reposition photo-eye for sag limit # Adjust lower over to accomodate expected sheet sag # Clean, reposition in-oven infrared Calibrate infrared if possible Check, clean air/water coolant to infrared detector Reset Safeguards •
Table 10.2 (Continued) Observe time-dependent temperature, color, smoke, odor Remove from oven when sag, temperature indicates sheet is formable Allow sheet to cool without forming Measure sheet time-dependent temperature as sheet cools in ambient air Repeat with circle-gridded sheet Look for abnormal orientation during heating, cooling • Repeat with circle-gridded sheet but now engage mold action without ancillary elements Check to see if sheet covers mold periphery Watch drape into mold to observe initial contact points • Repeat but now apply vacuum Observe the nature of draw-down, particularly around male portions of female mold Measure temperature of free surface if possible Set Forming process Temperature . Repeat but now adjust temperature zones to achieve better stretch profile • Continue temperature zone adjustment until it appears that no additional benefit can be obtained.
•
Setting Forming Process Assists • If billow prestretching is to be used— Use circle-gridded sheet to initially stretch without molding Check extent of stretch to see if sheet forms aneurysm, blow-out Change zonal temperature profile to accomodate prestretching • If plug assist is to be used— Make certain that every other means of material reallocation has been tried first Activate plug slowly at first to ensure stretching is occurring where it is needed Measure final part wall thickness to ensure sheet is stretching correctly Measure sheet temperature to ensure sheet is at proper temperature Examine final part to ensure sheet is not against mold or plug surface during stretching • If pressure forming is to be used— Make certain that all other molding aspects—temperature, prestretching, mo d element J actuation-are completely understood and functional before using pressure box
Mold surface texture and/or polish. This is most important if the polymer is crystalline, if the part is transparent or is used as an optical part, or if the part is to be pressure-formed. Any imperfection, including machining and polishing marks, burrs, dents or local deglossed areas may make the product unacceptable. • Mechanical action. Cams, ejection mechanisms, slides, hinged areas, and plug assists, if part of the mold design, should work flawlessly while on the mold maker's work table. The thermoformer may wish to "dry cycle" these mechanical devices while the mold is still at the mold maker, to ensure that the actions will work flawlessly over many cycles. Usually such actions are pneumatically driven. A simple pneumatic system with proper valves and timers will usually suffice for this type of testing. During this cycling, the thermoformer should check for oil or grease leaks. • Coolant lines. The lines should be chip-free and properly threaded for large-diameter fittings. Manifolds should be provided where multiple coolant lines are used. These should be mounted directly to the mold base. Lines should be pressurized to at least twice expected maximum coolant line pressure and the
• •
pressure should be kept on the lines and monitored for at least 72 hours to ensure that there are no internal cracks or leaks. Other connections. Vacuum lines should be chip-free and large enough to accommodate adequate vacuum lines. Vacuum holes should be chip-free and all should be demonstrated to be open between the mold cavity and the vacuum box. Surface preservatives, conditioners. Sometimes blueing or other surface coatings are applied during machining. These, any other surface coatings such as shipping greases, rust or oxide inhibitors, and all oils and greases should be removed prior to starting the mold in service.
When the mold is ready to be installed in the thermoforming machine, all the above elements should be carefully checked again to ensure that there has been no damage during shipping. The mold should be carefully mounted to the top or bottom platen, taking care to center the mold on the platen. A heavy off-center mold can rapidly wear guide-pins or guide-rods flat on one side. The mold should be carefully leveled to the rails or sheet frame. For small molds and/or platens, this can be done manually. For large molds and/or platens, this is usually done with optical devices such as a surveyor's laser. The leveling tolerance is usually established by the machinery builder but should not exceed 0.005 in (125 |im) in any direction on platens that are less than 48 in (1.2 m) on a side. Setting the Mold Stops Once the mold is positioned on the platen, the hydraulic/pneumatic action of the machine should be started. At this point, the mold should not be plumbed for cooling or auxiliary actions such as cams or ejection bars. The mold should be raised or lowered to the final position and the level again checked against the sheet frame or rails. The tolerance should be exactly the same as before. If not, the mold guide rails and the mold lifting mechanism must be checked for out-of-tolerance conditions. The mold should then be stopped at the half-way point and the level check repeated. The mold stops should be set to move to this position at the slowest rate. The mold motion is then observed during its movement from one stop to another. A laser leveler or bubble spirit level is used. If an electronic position indicator is used, the local mold velocity is charted. If there is any hesitation or racking, it is necessary to pinpoint the region and correct the problem before continuing. If the platen velocity can be controlled along the path between stops, its initial speed should be relatively high but should decrease rapidly as the platen approaches its maximum position. This minimizes hydraulic valve hammer or pneumatic piston wear. Dry-Cycling the Mold Once all the stops are in place, the mold is "dry cycled" for some time to ensure that all stops are locked in and all sliding surfaces are fully lubricated. The ancillary mold elements are then connected to their appropriate power supplies but only after it
Vacuum Gauge Steel Plate Bleed
Rubber Gasket
Figure 10.10 Apparatus for determining effectiveness of applied vacuum for given mold cavity design
appears that the mold and platen are functioning nominally. The positioning and timing of each of the slides, unscrewing devices, cams and plug assists must be treated separately. Once each of these devices has been properly tuned and the entire mold is functioning as expected, the vacuum line is installed. Again the vacuum line should have a smooth interior, should be of minimum length with as few elbows and tees as possible and there should be no constriction between the vacuum box and the vacuum surge tank, Chapter 6. A metal plate containing a vacuum gauge and a petcock valve to atmosphere is then placed on the mold surface and gasketed or sealed with metal tape (Fig. 10.10). Vacuum is then applied to the mold and the rate of evacuation is measured. The time needed to get to 50%, 75%, 90% and 95% of the maximum vacuum supplied by the vacuum system is recorded. This is shown in schematic in Fig. 10.11. As discussed in detail in Chapter 6, the ideal maximum vacuum is 28^ in Hg or 35 Torr. Vacuum of 25 in Hg or 125 Torr is barely adequate. With proper arithmetic, the evacuation rate, in in3/s or cm3/s, can be determined. The evacuation rate should be constant with time. If the evacuation rate decreases rapidly with time, the surge tank is too small. If the time required to evacuate the cavity is long, there are insufficient vacuum holes or there is serious constrictions in the vacuum system, Chapter 6. As soon as the vacuum in the cavity has reached 95% of the maximum vacuum supplied by the vacuum system, the petcock is opened and the valve to the vacuum surge tank closed. The time it takes for the surge tank to achieve the original vacuum value is the vacuum recovery time. This value should be less than the time required to evacuate the cavity. If not, the vacuum pump is too small. If the system is run at this rate, the vacuum pump will run continuously and the vacuum in the mold cavity will never achieve maximum value.
Checking the Vacuum A piece of flexible PVC or LDPE film or rubber sheet is now placed in the clamp frame and the press cycle is activated. The sheet should cover the mold surface. It must be clamped tightly before the vacuum system engages. If the sheet does not seal
Surge Tank Pressure
High, 23-25" Hg
Incomplete Surge Tank Recovery Time
Rubber Diaphragm Solid Plate
Cavity Evacuation Time
Surge Tank Recovery Time
Near Vacuum Pump Capacity, 28" Hg Figure 10.11 Time-dependent vacuum in mold cavity, using solid plate of Fig. 10.10 or rubber sheet. Figure also shows time-dependent nature of surge tank vacuum recovery
the cavity, air will leak under it and the effect of the vacuum will be compromised. One way of achieving good initial seal is to bring the mold deeper into the sheet during platen travel. Other ways include cavity isolators, peripheral clamping frames and cavity dams. The rate at which the flexible sheet is drawn into the mold cavity should be compared with the rate at which air was evacuated from the cavity when the rigid plate was used. Since the initial volume of air is the same, the initial evacuation rate should be the same. However, the film acts as a flexible bladder, keeping the pressure on the mold cavity side of the vacuum holes at or close to atmospheric. As a result, the overall evacuation rate should be greater than that with the metal plate (Fig. 10.11). If not, air may be leaking around the film/mold interface. Another cause is that the sheet may be covering too many vacuum holes early in the draw. Additional vacuum holes are then required and these must be placed in two- and three-dimensional regions last covered by the sheet.
Attaching Cooling to the Mold If the system is satisfactory to this point, coolant hoses are installed. Again, large diameter lines are required everywhere. If quick-disconnect fittings are used, they must be oversized so that the flow channel through the body of the fitting is the same diameter as that in the hoses. Since the temperature rise in any coolant line should not exceed 5°F or 3°C, for large molds, coolant lines should be manifolded to achieve this. Again, pressure drops into and out of manifolds should be minimized
by using the largest possible fittings. The manifolds should be mounted directly on the mold base. Platen motion should not drag coolant hoses. If hot water, steam or oil is used as coolant, all hoses must be of appropriate design and should be insulated. If chilled water or glycol-water mixture is used as coolant, all hoses should be oversized and again should be insulated. After all lines are pressure-tested, the coolant system is turned on and the mold allowed to achieve constant temperature. This may take an hour or more. The mold is considered to be at constant temperature when the coolant lines show no change in temperature over several minutes. The practical beginning mold temperature should be 100F to 200F or 60C to 11°C below the polymer 66 lbf/in2 or 0.455 MPa heat distortion temperature. It is now necessary to determine the uniformity in mold surface temperature. This is done in one of three ways: •
•
•
Surface thermocouple. A thermocouple is pressed against the mold surface and held until the reading stabilizes. The temperature at that point is recorded. This technique is repeated at many places on the mold surface, particularly on vertical surfaces and thin mold sections. Infrared pyrometer. The infrared temperature is measured without direct contact with the mold. The probe emissivity should be adjusted to accommodate reflective mold materials rather than non-reflective plastics. Again the temperature is monitored at many places on the mold surface. Infrared thermal imaging. This new technique takes a video scan of the entire two-dimensional surface at one time. Only one reading is needed and the results are displayed on a video screen for all to see and comment on.
Particular attention must be paid to male portions of female molds, such as ribs, bosses or gussets, and to any element that undergoes mechanical action, such as hinged sections, cams or slides. Active cooling of these elements is usually limited by the mold design. If any portion of the mold seems cool, a major decision must be made whether to run the mold knowing of this limitation. If the part is critical, this decision must be made on a high level and must include the mold maker and the customer. This decision is particularly important if chill marks are typically a problem with the particular polymer. When the mold reaches constant temperature, the platen should be dry cycled to ensure that the thermal expansion has not interfered with the platen travel or rate of travel. All slides, cams and plugs should function without binding or squealing. If an element binds, it must be removed and machined to tolerance. Simply lubricating the element will ultimately lead to oil contamination of the product and binding or squealing some time in the future. In addition, the level of the platen should not have changed with increased mold temperature. If it has, the platen will need to be re-leveled.
The Sheet Delivery System Once the isothermally hot press and mold system are functioning, the sheet delivery system is interfaced with it. This is usually a simple matter of adjusting the speed of
rotation for a rotary machine or the speed of the chain drive for a roll-fed machine. However, in some cases, automatic load and unload stations must be properly sequenced as well. The delivery system is brought into sync first. Then the loading and unloading stations are attended to. Setting the Oven Conditions The heating portion of the process is now addressed. At this point, the platen motion and all mold element actuation efforts are stopped, although the heat to the mold remains on. The top elements on the primary oven are switched on and allowed to achieve an equilibrium or steady state condition, as indicated by cyclical on-off control1. The elements should be set at a flat temperature profile across the heater surface. As with mold temperature measurement, heater measurement is made with a direct contact thermocouple, an infrared pyrometer or by thermal imaging. As with mold temperature measurement, the thermal imaging gives the most rapid and easily interpreted result. Although it is possible to detect a burned-out metal wire or rod heater by current flow means, it is difficult to detect a defective heater that is showing an intermittent short or hot spot. Ceramic heaters with liquid crystal temperature indicating coatings are now available to help maintain fully functional heaters. The recorded temperatures are then calibrated against the power input to the individual element. The top heaters should be switched off and the unit allowed to cool before the bottom heaters are tested. The bottom heaters are tested in the same fashion as the top heaters. Once this exercise is completed, the lower heater spacing from the clamp frame or the pin-chain is adjusted to accommodate sheet sag. At that time, the photoelectric eye should be cleaned and positioned to detect critical sag conditions. If through-the-oven-wall infrared sheet temperature monitoring is used, the quartz lens should be removed and cleaned, the water or air line to the cooling collar around the sensor should be cleaned and the sensor should be recalibrated at this time. The outboard lip of the oven is then positioned to prevent the sagging sheet from touching it as it exits the oven. At this point, proper safeguards that were removed for calibration are now replaced. Pinch-points and hot zones must be isolated. Electronic barriers and mechanical cages must be closed properly. Personnel must don protective equipment such as gloves, ear plugs, and sleeve protectors. Fire protection must be in place and emergency exits and warning lights actuated. 1
Note that the set-up described here is strictly valid only for ceramic and rod heaters. Quartz and the new halogen heaters operate on an entirely different principle, Chapter 3, and as a result, cannot be calibrated in this fashion. To ensure that all the quartz elements are functional, the quartz heaters are turned on in zones and the incandescence from each quartz element observed. If a quartz tube is burned out, the element will be black. Since the quartz heater has essentially no thermal feedback control, it must be switched off as soon as it has been found to be functional. Gas-fired burners and catalytic surface burners are easily monitored with a simple thermocouple in the middle of the burner. The natural-gas supply safety system requires the thermocouple to sense whether the burner is on. As a result, the system is either on or off and its status is clearly indicated.
Forming Step—Simple Vacuum Forming The sheet is now readied for forming. For cut sheet forming, several sheets are marked with the circle-grid pattern. For roll-fed sheet, a strip of sheet that could form eight to ten shots is cut from the roll. The circle-grid pattern is marked along the entire length of the sheet. For cut sheet forming, an ungridded sheet is placed in the clamp frame and rotated into the primary oven. Observers record the time, a temperature somewhere on the sheet, and the extent of sag. When the sheet sag is great, the sheet temperature is high, or the sheet is smoking, the sheet is then rotated over the stationary mold. The mold motion is not activated however. The hot sheet is observed for warping, discoloration, and abnormal stretching as it cools in free space. The sheet surface temperature is recorded as a function of time in the ambient air. If sheet sag and the forming temperature window appear satisfactory, a second sheet that has been circle-grid marked is clamped and heated to about the desired time and temperature. As with the first sheet, the second sheet is allowed to cool in ambient air. The extent of stretch and any abnormal stretching areas are determined by observing the changes in circle characteristics, as discussed earlier. At this point, no adjustments should be made to the temperature field. This is very important. Another circle-gridded sheet is then clamped and heated. This time, the platen and mold are allowed to penetrate the sheet but all ancillary actions such as cams, cavity isolators, peripheral seals, pre-blowing or plug assist stretching, and slides are locked out. In addition, vacuum is not applied to the sheet. Instead the sheet is allowed to drape into the mold. This allows the operator to see and verify the first points of contact of the sheet with the mold. This step is repeated but now maximum vacuum is applied. This simple vacuum forming step forms the basis for all additional manipulations of the sheet. At this point, free sheet surface temperature is measured as a function of time, using an infrared pyrometer. Thermal labels, tabs or crayon-type sticks can also be used to determine local sheet temperature. These data give baseline values for the cooling rate of the sheet. This step should be repeated several times to ensure that the sheet is in fact forming the same way every time. What is sought is uniformity in draw-down into three-dimensional corners, stretching over male portions of the mold, drawdown uniformity into multicavity molds, and regions of thinness and potential tearing. It is understood that it may be necessary to activate some of the ancillary aspects of the mold, such as hinged sections, in order to get the part out of the mold cavity. Note that this exercise may not yield manufacturing data. When a single sheet is loaded in a rotary press and rotated through the complete cycle, the thermal duty on the oven is frequently substantially less than when every frame contains a sheet. As a result, the actual cycle time for a one-at-a-time trial will usually be different than that for steady-state production. This is true for roll-fed units as well. In particular, if a sheet of 10 to 12 shots is fed continuously to ensure that the sheet is forming the same each time, the last sheets of the short roll will assuredly form differently than the first.
Changing Temperature Conditions At this point, the forming press is acting as a simple flat plate heater and vacuum former. The next series of steps depends on the confidence and experience of the operator. Recall that raising overall heater temperature simply shortens cycle time. If the sheet is thinning in one specific region, the heater temperature in that region must be lowered or equivalently, the heater temperatures everywhere else increased. Webbing is the result of high heater temperature and so the temperatures in the web region must be lowered. Increasing heater temperature on heavy-gage sheet can result in surface burn or blister. Increasing heater temperature on saggy materials can result in dropping the sheet onto the lower heater. Although the temperature profile change seems to give the most rapid effect on forming conditions, temperature effects do not take place instantaneously. Heaters require time to achieve new steady-state values and the air in the oven takes even longer to steady out. Circle-gridded sheets are very functional when determining the somewhat subtle effects of differential energy input on material reallocation on the mold surface.
Activating the Assists Once it is apparent that the sheet is being vacuum formed in the best manner possible using only temperature as a means of reallocating plastic, the assists can now be activated. Consider simple billow prestretching. This can be done by pneumatically inflating the sheet prior to insertion of a male mole or by everting the inflation into a female mold. Or it can be done by drawing the sheet with vacuum. Billow prestretching is the simplest means of prestretching the sheet. A photoelectric eye is usually employed to stop the inflation pressure. The interactive timing of inflation and mold motion is important as well. If prestretching is used with zone or pattern heating, some adjustment in the heating profile is usually needed in order to minimize bubble blow-out or aneurysm. The prestretching rate is controlled by simple air-flow valves. As a result, initial prestretching can be very rapid and final prestretching can be very slow. Plug assists are very difficult to install and operate correctly. As a result, they should be the last elements to be employed during mold start-up. The plug process control variables include: • • • • •
Plug temperature, Surface texture of the plug, Rate of plug travel, The time when plug travel is initiated, and The differential pressure across the stretching sheet.
All the variables but plug temperature and surface texture can be time-dependent. Articulated plugs offer yet another dimension of plug motion. It is important to remember that the action of a plug is quite localized. The majority of sheet thickness
distribution and redistribution should be accomplished, without plug assist, by other means such as temperature and pre-inflation. All too often, plug assists are only used when the operators and engineers cannot find any other way of forming the part.
Pressure Boxes There must be adequate justification to add more than one atmosphere of pressure to the forming process. Pressure forming requires the addition of a pressure vessel that must be correctly interactively sequenced along with the other mold and press activities. Pressure is usually not applied prematurely, simply because other mold activities usually take precedence. Typically pressure is applied late in the forming process. If the pressure application is delayed too long, the polymer may cool so much that the extra pressure to deform is insufficient. As with plug assist, pressure forming should be one of the last features to add to a start-up process.
General Objectives The primary objective of new mold or new plastic start-up is molding consistent parts having relatively uniform wall thicknesses without degradation or deterioration of the polymer. Initially, effort is focused on just getting the polymer to stretch reasonably well. Once this is achieved, effort moves toward optimization of the forming process. Usually the sheet heating time dominates the total cycle and so is the first part of the process to undergo optimization. Depending on the length of the production run and the cost and complexity of the part being formed, this may be the only process effect to be optimized. This is particularly true if sheet make-up is also changed. For example, start-up usually uses only virgin sheet. Once the product is forming well, regrind is added to the virgin sheet. The nuances of the forming character of the sheet now change and fine tuning progresses at the expense of further process optimization. Custom molders are faced with the added burden of needing to remove and reinstall molds at frequent intervals. The protocol described above for new molds and new polymers must necessarily be shortened to enable production in the shortest time interval. Computer storage of vital information about machine settings, including mold positions, stops, timing sequences, temperatures at various zones and transfer rates aids the progress in rapid mold change. Nevertheless, the experienced operator is always on the lookout for excessive mold element wear, over-zealous coatings of corrosion inhibitor, worn hoses, loose connections, out-oflevel platens, heaters that are losing efficiency and mold coolant lines that are plugging with scale. These long-term effects can substantially increase the time needed to get an old mold back into production.
10.3
Troubleshooting the Forming Process
Good quality parts begin with good quality sheet. The interface between the thermoformer and the sheet producer is in many respects similar to that between the thermoformer and the customer of his formed parts. The sheet producer needs to sell product to the thermoformer at a profit and the thermoformer needs to buy quality product from the sheet producer at the best price. In addition to agreeing on price and delivery, the thermoformer and the sheet producer must agree on quality, in writing. An example of a typical purchasing specification check list was given as Table 8.12. As discussed in Chapter 8, extrusion is the common way of producing thermoplastic sheet for thermoforming. The overview of extrusion was included to help the thermoformer understand the various aspects of the conversion process that most affect the quality of the thermoformer's raw material. The thermoformer does not need to be able to troubleshoot the extrusion process. Nevertheless, he/she should generally know what aspects of the conversion process are most apt to generate less-than-acceptable sheet goods. More importantly, the thermoformer must understand that writing very stringent specifications may cause the sheet converter to use very expensive procedures and that these very expensive procedures will undoubtedly be reflected in the final sheet unit cost. Table 10.3 gives a brief troubleshooting guide for extruded sheet product. Sheet is also produced by calendering and compression molding.
Table 10.3 Troubleshooting the Extrusion Process—A Brief Guide Problem
Probable cause
Suggested course of action
Die lines in sheet
Plate-out buildup
Remove and clean die Determine nature of plate-out, review polymer recipe with resin supplier, extruder
Erratic gauge control
Non-uniform thermal environment around die
Check for draft sources around die and correct Insulate die with fiberglass baffles
Surging in extruder
Uneven melt conditions in extruder Erratic polymer feed
Raise heat in first zones of extruder Check feed throat for bridging Make certain hopper level is constant
Die pressure fluctuation
Clogged screen or disk pack
Replace screen and clean out plugged one Go to slide plate screen changer Go to continuous screen changer
Orange peel surface
Surface viscosity in die too high
Raise die temperature Raise heat in last zones of extruder (Continued)
Table 10.3 (Continued) Problem
Dark specks and streaks
Probable cause
Suggested course of action
Surface shrinking unevenly during cooling
Raise chill roll temperature Raise die temperature
Polymer degrading
Lower melt temperature Reduced screw speed Modify screw to decrease flight clearance Modify screw to decrease compression ratio Clean die lips Pull screw and examine for pitted chrome Check die design and streamline if necessary Clean hopper and securely cover Pull screw and examine screw shank for oily or carbonaceous buildup If using regrind, examine regrind for contamination Examine virgin polymer pellets for black speck contamination
Contaminants in melt
Lines in machine direction
Damage or corruption on die lips
Surface scratches on chill roll Polymer hang-up between die lip and die body
Curved lines in crossmachine direction
Melt bank too large Melt folding
Gels in sheet
Melt has cold spots Polymer crosslinking
Disassemble die and clean thoroughly; examine with 30X loupe for corrosion Take scrapings of build-up, chemically analyze and determine if build-up is from polymer Clean and optically examine chill rolls. Resurface if necessary Check mating surfaces for misalignment, damaged areas Check die design and streamline if necessary Reduce melt bank to pencil-thick diameter Check extruder output to determine if surging is occurring. If so, add melt pump Increase heat in last zone of extruder Increase die temperature Reduce heat in first zone of extruder Reduce screw speed to minimize shear heating Reduce regrind level Examine regrind for contamination Increase antioxidant package in polymer
Table 10.3 (Continued) Problem
Probable cause
Suggested course of action
Dull spots on sheet surface
Sheet picking plate-out off chill roll
Increase first chill roll temperature Discuss alternate adduct packages with resin supplier Clean flow channels in chill roll
Nonuniform cooling in chill roll Sheet intermittently lifting from chill roll
Use air knife to hold hot sheet against first chill roll
Brittle sheet
For certain polymers such as ABS, PET, polymer is too wet
Thoroughly dry polymer Thoroughly dry regrind
Hazy sheet
Polymer crystallizing— typical of PET, PP
Thoroughly dry polymer Increase melt temperature Reduce first chill roll temperature Reduce melt bank Increase extrusion rate Review adduct package with polymer supplier Increase or decrease melt temperature to determine general effect Increase or decrease first chill roll temperature to determine general effect Polymer wet; thoroughly dry polymer Polymer degrading; lower melt temperature, reduce residence time Adduct decomposition; review adduct package with polymer supplier
Adduct package wrong
Microscopic bubbles inside sheet
Internal holes in sheet
Moisture Air
Degrading polymer
Decomposing adducts
Dry polymer Dry regrind Seal hopper or use inert gas layer Increase heat in first zones of extruder Decrease heat in last zones of extruder Increase back pressure on melt pump Decrease screw speed Decrease temperature profile throughout extruder Decrease back pressure on melt pump Reduce regrind concentration Review adduct package with resin supplier (Continued)
Table 10.3 (Continued) Problem
Probable cause
Suggested course of action
Melt freeze off
Melt temperature too low
Increase die temperature Increase heat in last zone of extruder Check for burned-out heater bands Intermittent when screens are changed; preheat screens
Screen too cold Surface roughness in sheet
Contamination Unmelted pellets
Moisture Trapped air
Unpolished low spots
Insufficient roll stack polish
Check incoming virgin resin for contamination Check regrind for contamination Increase heats on first zones of extruder Decrease extruder throughput rate Increase gear pump back pressure Change screw to higher compression ratio screw Switch to barrier screw Dry polymer thoroughly Move extruder die closer to chill roll Use air knife to hold sheet against chill roll Lay sheet on roll at 300° to 330° angle Increase melt bank diameter slightly Check vertical alignment of chill roll and die Increase melt bank diameter Adjust vertical alignment of chill roll and die Adjust die lips to increase flow in low spots Increase roll stack temperature Decrease roll gap Increase bottom roll speed slightly
Even if all apparent sheet imperfections are absent, and even if great care has been taken to design out polymer and process elements that interfere with the production of acceptable and quality parts, process problems still occur during start-up and during any normal process run. Many reoccurring processing problems are grouped in Table 10.4 [17]. The probable causes of each of these problem classes are assessed in Table 10.5 [17] along with some suggested methods to correct or eliminate them. Most of these problem classes are characteristic of heavy-gage sheet although some pertain to thin-gage sheet or film as well. Many pertain to all forming
Table 10.4 Categories of Thermoformed Part Process/Product Problems—I [17] • • • • •
Bubbles or blisters Incomplete forming or poor detail Sheet scorching Blushing or change in color intensity Sheet whitening
• • • • •
Webbing, bridging, wrinkling Nipples or nibs on mold side of formed part Excessive sag Sag variation between sheet blanks Chill marks or "mark-off' lines on part
• • • • •
Bad surface markings Shiny streaks Excessive post shrinkage or distortion after part removal from mold Warpage Poor wall thickness distribution, excessive local thinning
• • • • •
Nonuniform or bulging prestretch bubble Shrink marks on part, particularly in corners or inside radius of molds Deep draw corners too thin Part sticking to mold Sheet sticking to plug assist
• Part tears during forming • Cracking in corners during use
operations. Recently, another grouping of process problems, primarily for thin-gage forming, has been published (Table 10.6) [5]. Many of the problem areas are similar or identical to those of the earlier list. The probable causes of each of these problem classes are given in Table 10.7, where the causes are also grouped as the result of problems in: •
Production,
•
Tool,
• • •
Forming machine, Polymer material, and Design.
Although no suggested courses of action are recommended, it is apparent that the appropriate response is to negate or neutralize the probable cause. Certain classes of polymers such as CPET, PP and foams, require specialized forming procedures. Specialized troubleshooting techniques are usually required when processing these polymers. For example, Table 9.6 gives a troubleshooting guide for CPET.
Table 10.5 Trouble-Shooting Guide to Thermoforming—Primarily Heavy-Gage1 Problem
Probable cause
Suggested course of action
Blisters
Heating too rapidly
Lower heater temperature Use slower heating Increase distance between heaters and sheet Blow air across sheet surface during heating Pre-dry sheet Preheat sheet Heat from both sides Do not remove moisture barrierfilmuntil ready to use Require sheet supplier to provide dry sheet Check heater output, power consumption Use pattern heating Order correct formulation
Excess moisture
Uneven heating Wrong sheet type or formulation Incomplete forming, poor detail
Sheet too cold
Clamp frame cold prior to sheet insetion Insufficient vacuum Vacuum not applied rapidly enough
Applied pressure too low 1
Adapted from [17], by permission of the copyright owner
Heat sheet longer Raise heater temperatures Use more heaters Change to more efficient heater design If problem localized, check heater bank for problems Preheat frame Check vacuum holes for obstruction Increase number of vacuum holes Increase diameter of vacuum holes Use vacuum slots rather than holes Surge tank/pump too small Vacuum line/valves too small Too many bends in vacuum line Corrugated vacuum line used Vacuum leaks Increase air pressure Use plug, silicone slab rubber, or bladder as pressure assist
Scorched sheet
Sheet surface too hot
Shorten heat cycle Use slower, soaking heat Consider convection heating
Blushing or color intensity change
Insufficient heating
Lengthen heating cycle Raise heater temperature Change to more efficient heaters Reduce heater temperature Shorten heating cycle If localized, check heater efficiencies Consider convection heating/surface cooling Warm mold Heat assist Try heavier gage sheet Try more elastic formulation Change mold design Transfer sheet faster Increase forming rate Increase mold, plug temperature Reduce draw ratio Increase draft angles Increase corner radius Change sheet formulation Change polymers Retest regrind for problems Check percentage of regrind
Excessive heating
Mold too cold Assist too cold Sheet is stretched too far Sheet cools before fully formed Poor mold design Polymer not suitable Excessive, poor use of regrind Whitening
Stretching below forming temperature Sheet dry-colored
Increase sheet temperature Increase forming speed Poor extrusion Polymer unsuitable for pigmentation Local blemishes removed with hot air gun
Webbing, bridging, wrinkling
Sheet too hot, drape into forming area
Shorten heating cycle Increase heater distance Lower heater temperature Air-cool just before forming (Continued)
Table 10.5 (Continued) Problem
Probable cause
Suggested course of action
Webbing, bridging, wrinkling (continued)
Resin melt strength too low, sheet sag
Change to lower MI olefin Increase orientation Use very low heater temperature Increase or decrease TD-to-MD orientation ratio Check vacuum system Add more vacuum holes Rotate sheet 90° Redesign mold Use plug/ring assist Use female mold rather than male mold Use assist blocks to pull out wrinkles Increase radii/draft angles For many parts on a mold, move them apart For multi-part molds, use part isolators, grids Speed up assist and/or mold travel Redesign grid/plug/ring assists
Orientation mismatch Insufficient vacuum Preferential bridging Excess draw ratio, poor mold design/layout
Nibs or nipples on formed parts
Sheet too long Vacuum holes too large
Excessive sag
Sheet too hot Melt index too high
Sheet area excessive Chill marks, striations
Plug assist temperature too low Mold temperature too low
Reduce heating cycle Reduce heater temperature Plug holes, redrill Reduce heating cycle Reduce heater temperature Use lower MI olefin Change resins Increase sheet orientation Pattern heat to reduce sheet center temperature Add sag bands Increase plug temperature Use wood, synthetic plug Cover plug with wool, felt, fabric Increase mold temperature
Poor mold temperature control
Sheet too hot Wrong forming technique Wrong polymer
Surface blemishes
Ghosts in details, rim on roll-fed Indentations Poor vacuum Plasticizer accumulation
Mold too hot Mold too cold Improper mold composition Rough mold surface Dirt Atmospheric dust Contaminated polymers
Reconfigure cooling, heating channels Add more coolant channels Increase coolant flow rate Increase coolant channel diameter Inspectflowpath for debris, plugging, rust Reduce heating cycle Cool sheet surface with air prior to forming Change forming rate Change forming technique Change to higher tensile strength resin, lower MI olefin polymer Matched die mold misaligned Mold hesitates in travel—check guides, alignment Mold surface too smooth—roughen Increase vacuum hole area Sheet cast against smooth roll, air trapping Increase vacuum hole area If localized, check for plugged vacuum holes Clean mold periodically Reduce mold temperature Regulate mold temperature Do not allow mold to "see" heaters Shorten heating cycle Reduce mold temperature Increase mold temperature Change mold materials Try machined aluminum molds Polish mold Use aluminum molds Clean mold, sheet Clean thermoforming area Enclose former Usefilteredair for blow-off Check regrind for dirt Check resin, sheet supplier (Continued)
Table 10.5 (Continued) Problem
Probable cause
Suggested course of action
Surface blemishes (continued)
Scratched sheet
Review sheet handling procedures Use surface paper protection Polish sheet prior to forming Use sag bands to keep sheet from touching mold edge Increase mold daylight
Drag marks on roll-fed sheet
Shiny streaks
Local overheating
Check heater temperature Check heating pattern, zones Air-cool locally Reduce heating cycle Increase heater-to-sheet distance
Post-forming shrinkage, distortion
Time on mold too short
Increase cooling time Decrease coolant temperature Use free-surface cooling Change free-surface cooling to water mist Check for restricted coolant flow Use cooling fixtures Reduce mold temperature Increase coolant flow rate
Mold too hot Warped parts
Uneven part cooling
Poor polymer distribution in part wall
Poor mold design
Change coolant channel configuration Check for blocked coolant channels Direct free-surface cooling to warped area Use prestretching or plug assist Poor temperature uniformity Out-of-spec sheet thickness Vacuum holes in wrong place Increase vacuum hole area Redesign rim area to stiffen Add moat to mold at trim line Unplug vacuum holes
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Table 10.5 (Continued) Problem
Probable cause
Suggested course of action
Poor material allocation (continued)
Sheet slips from frame (continued)
If retainer springs are used, change to higher temper springs
Uneven sheet thickness Uneven heating
Nonuniform prestretch bubble
Periodic drafts Non-uniform air inflation
Inadequate vacuum
Mold surface too smooth Part shrinking during forming Shrink marks Inadequate air pressure
Very thin corners
Incorrect forming technique Sheet too thin Sheet temperature variation
Check with sheet supplier Tighten quality control on extrusion Heat sheet slowly, in hot air Check heater efficiency Change to more efficient heaters Improve heater temperature control Change to pattern heating Enclose oven, forming area Check air flow Install baffles if necessary Preheat blow air Vacuum leaks Vacuum surge tank, pump inadequate Plugged vacuum holes Vacuum hole area inadequate Roughen mold surface Change to lower conductivity mold material Increase forming pressure Increase mold temperature Change to less elastic polymer Reduce free-surface cooling Increase air flow rate Increase air pressure Increase cycle time under pressure Try plug assist Increase sheet thickness Check material allocation Switch to pattern heating Increase forming rate
Variation in mold temperature Incorrect polymer Parts stick in mold
Part temperature too high Inadequate draft Mold undercuts
Sticking in one spot
Wooden mold Rough mold surface Very smooth surface-olefins
Sheet sticks to plug
Plug temperature too high
Wooden plug Plug speed too high
Change coolant line configuration Check free-surface cooling Use stiffer polymer Use more elastic polymer Increase cooling time Lower mold temperature Reduce heating cycle time Rework mold for more draft Use female mold Remove part early, thenfixtureuntil cool Consider more sophisticated ejection system Use pulling cores, breakaway frame Decrease depth of texture Uneven mold temperature Uneven sheet temperature prior to forming Vacuum break inadequate Check for local mold damage Lubricate with dry mold release Polish, especially corners Use dry mold release Add antiblock to polymer Roughen mold surface slightly Inadequate vacuum break Try female mold if excessive shrinkage Reduce plug temperature Use dry mold release Use permanent mold coating Use felt/cloth/wool/fabric covering Coat with lubricant Use felt/cloth/wool/fabric covering Switch to temperature-controlled plug material Reduce plug penetration rate Increase air pressure behind plug Decrease air pressure ahead of plug (Continued)
Table 10.5 (Continued) Problem
Probable cause
Suggested course of action
Sheet tears while forming
Mold design Sheet too hot
Increase corner radius Decrease sheet temperature Preheat sheet, then bring to forming temperature slowly Sheet thickness may not be uniform Increase heating time Preheat sheet Depth of draw excessive for polymer, see resin supplier Change forming technique Decrease plug penetration rate Increase inflation rate Increase draw-down rate
Sheet too cold Improper polymer Forming conditions improper
Corner cracking in service
Stress concentration
Under-designed
Increase radii Corner too cold during forming Increase mold temperature Increase sheet temperature Increase forming rate Prestretch sheet Decrease free-surface cooling Decrease plug rate of penetration Change to ESCR resin Reevaluate design
Next Page Table 10.6 Categories of Thermoformed Part Process/Product Problems—II [5] • • • •
Blisters or bubbles Poor forming and bad detail Product surface distorted Color changes Whit ma ks
• • • • •
Webbing, bridging or wrinkling Mold side bumps Chill marks Surface marks Surface shiny . t . , t. • Excessive post-forming shrinkage or distortion • Warped or twisted part
10.4
• Thin corners • Thin surfaces • Thin sides „ ,•, ,. ., • # Poor wall thickness distribution • Post-forming cracking • Shrink marks • Too much sag • Pre-blow/vacuum bubble variation • Material sticks to plug assist • Material tears during forming • Demolding problems
Energy and Materials Cost
Every business, regardless of size, should operate on micro-economics. That is, an economics balance should be made on every part produced1. With some modifications, the global concepts of Figs. 10.1 through 10.3 are directly applicable to every part produced. There is a general tendency to lump production costs into a "machine hour cost". Although this is acceptable for a "Class C" estimate, it should never be the norm for day-to-day price forecasting. This is discussed in more detail below. The Energy Audit Thermoforming is an energy-intensive business. Recently, the re-emergence of gasfired heaters has sparked another round of economic focus on power consumption. As discussed in detail in Chapter 3, there are many ways of heating a plastic sheet. The nature of the energy source is strongly dependent on the nature of the polymer and the sheet thickness. In other words, the optimum energy source is usually not the most economic energy source [6]. Care must be taken when considering a simple substitution, since other non-energy cost factors such as maintenance, time-dependent energy efficiency of the heating unit, and installation costs can temper an otherwise obvious selection. The decision to replace current heaters with more efficient units should be made only after a thorough energy audit is made on each 1
It is apparent that if the forming shop is producing a few hundred outdoor signs or swimming pool, the cost associated with each part can be carefully monitored. It is not apparent that this same philosophy holds if the forming shop is molding unit dose cups or margarine tubs. Nevertheless, the general approach is valid if applied to, say, each 1000 units or each hour of production.
Previous Page Table 10.6 Categories of Thermoformed Part Process/Product Problems—II [5] • • • •
Blisters or bubbles Poor forming and bad detail Product surface distorted Color changes Whit ma ks
• • • • •
Webbing, bridging or wrinkling Mold side bumps Chill marks Surface marks Surface shiny . t . , t. • Excessive post-forming shrinkage or distortion • Warped or twisted part
10.4
• Thin corners • Thin surfaces • Thin sides „ ,•, ,. ., • # Poor wall thickness distribution • Post-forming cracking • Shrink marks • Too much sag • Pre-blow/vacuum bubble variation • Material sticks to plug assist • Material tears during forming • Demolding problems
Energy and Materials Cost
Every business, regardless of size, should operate on micro-economics. That is, an economics balance should be made on every part produced1. With some modifications, the global concepts of Figs. 10.1 through 10.3 are directly applicable to every part produced. There is a general tendency to lump production costs into a "machine hour cost". Although this is acceptable for a "Class C" estimate, it should never be the norm for day-to-day price forecasting. This is discussed in more detail below. The Energy Audit Thermoforming is an energy-intensive business. Recently, the re-emergence of gasfired heaters has sparked another round of economic focus on power consumption. As discussed in detail in Chapter 3, there are many ways of heating a plastic sheet. The nature of the energy source is strongly dependent on the nature of the polymer and the sheet thickness. In other words, the optimum energy source is usually not the most economic energy source [6]. Care must be taken when considering a simple substitution, since other non-energy cost factors such as maintenance, time-dependent energy efficiency of the heating unit, and installation costs can temper an otherwise obvious selection. The decision to replace current heaters with more efficient units should be made only after a thorough energy audit is made on each 1
It is apparent that if the forming shop is producing a few hundred outdoor signs or swimming pool, the cost associated with each part can be carefully monitored. It is not apparent that this same philosophy holds if the forming shop is molding unit dose cups or margarine tubs. Nevertheless, the general approach is valid if applied to, say, each 1000 units or each hour of production.
Table 10.7 Thermoforming Troubleshooting Guide—Primarily Thin-Gage1 Possible causes Material
Problem
Production
Tooling
Machine
Blisters or bubbles
Material too hot Material heated too quickly Forming vacuum/pressure too slow Forming vacuum/pressure not turned off Forming vacuum/pressure too short Cooling too soon
Heating intensity too high Incorrect heating pattern Insufficient screening of heater bank
High moisture content Too much release agent Incorrect formulation
Poor forming, bad detail
Material too cold Draft over the material Grid absorbs too much heat, not polished Forming vacuum/pressure too slow Forming vacuum/pressure too short Cooling too soon Demolded while too warm Operational sequence too slow
Too hot Too smooth—not grit blasted No venting Not enough vacuum holes or holes too small Missing vacuum holes Incorrect vacuum hole placement Vacuum channels clogged Wrong air supply No venting Insufficient sealing Hollow, suction volume too large Not enough vacuum holes or holes too small Missing vacuum holes Incorrect vacuum hole placement Drawing edge too small Vacuum channels clogged Wrong air supply
Area within clamp frame too small Clamping frame too cold Clamping frame not sealed Clamping frame not polished Insufficient seal Dirty vacuum filter Incorrect heating pattern Insufficient screening of heater bank
Hard to form Poor heat retention
Product surface distorted
1
Courtsey of [15]
Too rough Mold dirty
Material not cleaned, static Contains impurities Too much release agent
Design
Color changes
White marks
Webbing, bridging or wrinkling
Mold side bumps
Material too cold Plug advances too fast Plug assist too cold Mold advances too slow Forming vacuum/pressure too late Forming vacuum/pressure too slow Material too cold Plug advances too fast Plug assist too cold Mold advances too slowly Forming vacuum/pressure too late Forming vacuum/pressure too slow Cooling too long Demolded while too cold Material too hot No or incorrect form assist grid Assist grid advances too slowly No plug assist Plug advances too slowly Forming vacuum/pressure too fast Not enough forming vacuum/ pressure Forming vacuum/pressure not turned off Insufficient preblow Forming vacuum/pressure too slow Not enough forming vacuum/ pressure Operational sequence too slow
Too cold Not enough draft Edges, corners too sharp
Incorrect heating
Incorrect formulation Too much or inconsistent regrind content
Incorrect draw ratio Insufficient draft Corners too sharp
Too hot Not enough draft Eges, corners too sharp No venting
Table jerks or moves too slowly Incorrect heating
Too thin Incorrect formulation Too much or inconsistent regrind content
Incorrect draw ratio Insufficient draft Corners too sharp
Too cold Too hot Not enough draft Edges, corners too sharp Spacing too small
Incorrect heating Incorrect heating pattern Insufficient screening of heater bank
Wrong sheet orientation Incorrect formulation
Incorrect draw ratio Insufficient draft Corners too sharp
Too hot Too smooth, not grit blasted Drawing edge too small Spacing too small
Incorrect heating pattern Insufficient screening of heater bank
Thickness variations
(Continued)
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Warped or twisted part
Grid absorbs too much heat, not polished Cooling too soon Uneven cooling Demolded while too warm Clamping edge not immediately removed Products placed crooked after removal
Too cold Too hot Too smooth, not grit blasted Missing vacuum holes Incorrect vacuum hole placement Vacuum channels clogged
Clamping frame not polished Inconsistent heating Incorrect heating pattern
Thickness variations High shrinkage
Incorrect draw ratio Insufficient ribbing
Thin corners
Grid absorbs too much heat, not polished Insufficient preblow No plug assist Forming vacuum/pressure too late Forming vacuum/pressure too fast Operational sequence too slow
Plug assist too small Plug assist too rough Plug assist not centered
Incorrect heating pattern Insufficient screening of heater bank
Too thin Thickness variations
Incorrect draw ratio
Thin surfaces
Material too cold Too much preblow No plug assist
Plug assist too small Plug assist too rough
Thin sides
Material too cold Insufficient preblow Plug assist too early Plug assist too cold Mold advances too fast Forming vacuum/pressure too late Forming vacuum/pressure too slow
Too rough Edges, corners too sharp Drawing edge too small Spacing too small Plug assist too big
Incorrect heating pattern Insufficient screening of heater bank Area within clamping frame too small Incorrect heating pattern Insufficient screening of heater bank
Incorrect draw ratio
Incorrect draw ratio
(Continued)
Table 10.7 (Continued) Possible causes Material
Problem
Production
Tooling
Machine
Poor wall thickness distribution
Material too cold Draft over material Material touches mold during heating Material sag during heating No or incorrect form assist grid Insufficient preblow Too much preblow No plug assist Plug assist too early Plug assist too cold Forming vacuum/pressure too early Forming vacuum/pressure too late Forming vacuum/pressure too slow Uneven cooling Operational sequence too slow
Too cold Too hot Edges and corners too sharp Inconsistent spacing Plug assist too small Plug assist too big Plug assist too rough Plug assist not centered
Area within Thickness clamping frame variation Wrong sheet too large orientation Area within Incorrect formuclamping frame lation too small Clamping frame too small Clamping frame not polished Inconsistent heating Table jerks or moves too slow Incorrect heating pattern Insufficient screening of heater bank
Post forming cracking
Material too cold Plug assist too cold Mold advances too slowly Cooling too soon Demolded while too cold
Too cold
Clamping frame too cold Incorrect heating
Shrink marks
Not enough forming vacuum/pressure
Too smooth— not grit blasted Not enough vacuum holes or too small
Insufficient seal
Design
High shrinkage
Too much sag
Material too hot No material support
Preblow/ vacuum bubble variation
Draft over material
Inconsistent heating Thickness Incorrect heating pattern Insufficient screening of heater bank
Polymer sticks to plug assist
Plug assist too hot
Improper plug material
Polymer tears during forming
Material too hot Material heated too quickly Material too cold Insufficient preblow
Too cold Too rough Edges, corners too sharp Drawing edge too small Inconsistent spacing
Demolding problems
Mold returns too fast Cooling too long Incorrect demolding pressure Demolded while too warm
Too cold Too hot Too rough Not tapered enough Too much undercut No venting
Wrong sheet orientation Incorrect formulation
Area within clamping frame too small Inconsistent heating Heating intensity too high Incorrect heating pattern Insufficient screening of heater bank
Contains impurities Hard to form Narrow forming window Poor heat retention Release agent missing Too much or inconsistent regrind content
Corners too sharp
High shrinkage
Insufficient taper Corners too sharp
Release agent missing
thermoformer. One recommended method is to install electric power meters on each unit. For high-energy heaters, separate units should be installed on both the upper and lower heater banks. Nevertheless, in the US today, natural gas is between 3 and 7 times cheaper than electricity on the same energy unit basis, Table 10.81. The average is about 5. 1
This excludes Alaska where cheap gas and expensive electricity make the ratio in excess of 15.
Table 10.8 Cost of Electricity and Gas to Industrial Users State
Electricity1 (cents/kWh)
Natural gas2 ($/1000 ft3)
Natural gas (cents/kWh3)
Ratio, electricity to natural gas
Alabama Alaska Arizona Arkansas California
4.46 5.96 5.67 4.95 6.74
3.01 1.18 4.14 3.10 3.66
0.962 0.377 1.324 0.991 1.170
4.6 15.8 4.3 5.0 5.8
Colorado Connecticut Delaware District of Columbia Florida
4.49 7.93 4.71 5.43 5.27
2.24 4.79 3.20 NA 3.21
0.716 1.532 1.023 — 1.027
6.3 5.2 4.6 — 5.1
Georgia Hawaii Idaho Illinois Indiana
4.79 7.71 2.59 5.50 4.33
3.41 NA 3.00 3.73 3.30
1.091 — 0.959 1.193 1.055
4.4 — 2.7 4.6 4.1
Iowa Kansas Kentucky Louisiana Maine
4.00 4.90 4.19 4.26 6.71
3.47 2.60 3.29 1.83 4.14
1.110 0.831 1.052 0.585 1.324
3.6 5.9 4.0 7.3 5.1
Maryland Massachusetts Michigan Minnesota Mississippi
5.51 8.50 5.72 4.26 4.56
3.54 4.33 4.13 3.06 2.53
1.132 1.385 1.321 0.979 0.809
4.9 6.1 4.3 4.4 5.6
Missouri Montana Nebraska Nevada New Hampshire
4.72 2.89 4.02 4.96 7.70
2.92 3.53 2.78 4.02 4.56
0.934 1.129 0.889 1.286 1.458
5.1 2.6 4.5 3.9 5.3
New Jersey New Mexico New York North Carolina North Dakota
7.70 4.84 6.15 5.00 4.64
3.43 3.04 5.31 3.35 3.27
1.097 0.972 1.698 1.071 1.046
7.0 5.0 3.6 4.7 4.4
Table 10.8 (Continued) State
Electricity1 (cents/kWh)
Natural gas2 ($/1000 ft3)
Natural gas (cents/kWh3)
Ohio Oklahoma Oregon Pennsylvania Rhode Island
4.13 3.95 3.17 6.32 9.11
4.15 1.99 3.34 3.88 4.68
1.327 0.636 1.068 1.241 1.497
3.1 6.2 3.0 5.1 6.1
South Carolina South Dakota Tennessee Texas Utah
4.19 4.59 4.66 4.13 3.96
2.95 3.37 3.20 2.07 3.95
0.943 1.078 1.023 0.662 1.263
4.4 4.3 4.6 6.2 3.1
Vermont Virginia Washington West Virginia Wisconsin Wyoming
6.98 4.27 2.38 3.67 4.04 3.52
3.28 4.02 2.78 2.79 3.81 2.68
1.049 1.286 0.889 0.892 1.218 0.857
6.7 3.3 2.7 4.1 3.3 4.1
Total U.S.
4.85
2.82
0.902
5.4
1 2 3
Ratio, electricity to natural gas
Data reflect rates in 1991 and were supplied by the Edison Electric Institute, Washington DC Data for 1992 are from American Gas Association, Arlington VA These values assume 100% conversion of methane to CO2 and H 2 O. The heat of combustion of CH4 is 383,036 Btu/lb-mol. There are 359 ft3/lb-mol at standard conditions. Therefore the energy generated by methane combustion is 1.067 x 106 Btu/1000 ft3. There are 3413 Btu per kWh. Therefore the energy generated is 312.7 kWh/1000 ft3. This value was used to convert $/1000 ft3 to cents/kWh. Again, this assumes 100% combustion. Actual combustion is not 100% efficient
Cost of Extrusion The thermoformer purchases the extruder's finished product. The thermoformer's initial material cost is the cost of the polymer plus the extruder's conversion cost. The thermoformer must understand that thermoforming products are sold by the area, as cost per square foot or square meter. The converter sells his product by the weight, as cost per pound or kilogram. The conversion cost is usually a function of the degree of difficulty of the extrusion and the mass throughput, in lb/h or kg/h. For most commodity polymers such as PE, PP and PS, the conversion cost asymptotically approaches a minimum value of about $0.12/lb in 1992 US dollars (Fig. 10.12) [7]. Typically, for production runs of 1000 lb/h, sheet conversion costs are about $0.20/lb. For higher performance polymers or polymers that require special attention such as PVC, PET and PMMA, conversion costs are approximately double the values shown in Fig. 10.12. If the product is to be used for medical or biomedical applications, regrind may not be allowed. In this case, the material cost in the product, $MC, is:
Production Cost 0/lb
Extruder Capacity, Ib/h Figure 10.12 Throughput-dependent minimum production cost [1992] for sheet extrusion. Redrawn from [7] and used with permission of copyright owner
Example 10.1 Material Cost for a Polycarbonate Medical Appliance A 12-in x 12-in medical appliance is to be thermoformed of 0.250-in thick polycarbonate. Polycarbonate costs $1.25/Ib and has a density of 1.2 g/cm3. The initial sheet dimension is 18 in square. Determine the material cost if the conversion cost is SO.40/Ib and the trim cannot be reused. The part volume is:
O A - 1 I ^ U - O 2 O 8 ft3 1728 The part weight is: 0.0208 x 1.2-62.4= 1.56 Ib The fraction of trim, Y, is:
The cost of the unit weight of the sheet is: $1.25+ $0.40 $ M C = 1-0.556 = $ 3 ' 7 2 / l b The material cost of the part is: $3.72 x 1.56 = $5.80 Approximately 66% of the material cost of the part is in conversion and trim that is unusable.
(10.6) where $V is the virgin polymer cost, $C is the conversion cost, and Y is the fraction of sheet that is trim. Example 10.1 shows the importance of conversion costs. Cost of Regrind Regrind was considered in detail in Section 7.2. The steady-state cost of regrind was given as Equation 7.12: (7.12) where $X is the cost of reprocessing the trim per unit weight. The cost of reprocessing includes costs such as grinding, drying, re-extrusion into pellets for easier handling but it does not include the cost of re-extruding the trim into sheet. This cost may also include warehouse costs, labor costs in handling the trim, and shipping costs. Example 10.2 illustrates the role regrind costs play on total material costs. Examples 7.5 and 7.6 illustrate other aspects of regrind costs. Example 10.2 Material Cost for a Polycarbonate Fresnel Lens A 12-in x 12-in Fresnel lens is to be thermo formed of 0.250-in thick polycarbonate. Polycarbonate costs $1.25/Ib and has a density of 1.2 g/cm3. The initial sheet dimension is 18 in square. Determine the material cost if the conversion cost is $0.40/Ib. The trim can be reused and its reprocessing cost is $0.30/Ib including drying and repelletizing.
The part and sheet weights of Example 10.1 are used here. The part weight is 1.561b. Equation 7.12 is the operative expression: * ™ , $C + Y-$X g 1 o c , $0.40+ 0.556-$0.30 F = $V + — j — ^ - = $1.25 + — = $2.53/lb The total cost for the part is: $2.53- 1.56 = $3.94 Note that the use of regrind reduces the part cost from $5.80 in Example 10.1 to $3.94, a $1.86 savings. Nevertheless the cost of reusing the trim is still about half the total material cost. Competitive Costs of Polymers Selection of the cheapest polymer that will meet the customer's performance criterion will not always yield the cheapest part. Some of the reasons for this are apparent and others are not:
•
The cheaper polymer may be much more difficult to extrude than a more expensive one, • The cheaper polymer may not have the intrinsic strength or modulus of a more expensive one and so may need to be slightly thicker, resulting in: Longer heating cycles, Longer cooling times, and Greater trimming problems, • The cheaper polymer may be more difficult to heat, • The cheaper polymer may sag more, making it more difficult to thermoform uniformly, resulting in: Increased mold costs for gridding, Longer heating cycles, and Maintenance problems with elements such as sag bands, • The cheaper polymer regrind may need special treatment such as: Extensive drying, Degassing for foams, or Repelletizing, • The cheaper polymer may have restrictions on the fraction of polymer that can be recycled owing to: Thermal or oxidative degradation, Greater loss in physical properties such as impact strength, and Greater color change. • If the full amount of cheaper polymer trim generated cannot be recycled, the excess must be discarded and this cost factored into the actual material cost. Not all these factors are always operative or significant. A recent software guide has been developed that allows side-by-side comparison of several candidate polymers [8]. This package has been reworked and is available through The Society of Plastics Engineers Thermoforming Division. Table 10.9 gives an example of the results of this software program. Side-by-side candidate polymer comparisons can also be made by repeating the single polymer economics described below. Typically, the more expensive the polymer is, the less important the exact economic details of the process become.
10.5 General Processing Economics Thermoforming competes with many other polymer molding technologies, including FRP, compact injection molding, structural foam injection molding, blow molding and rotational molding. It also competes with non-polymer technologies such as sheet metal and forging. The standard method of cost analysis begins with a quick "Class C" estimate of the cost of the thermoformed plastic part, to determine if the polymer cost is competitive. If so, more advanced analyses are employed to determine more accurate costs.
Table 10.9 Cost Comparison—ABS, HDPE and Modified PP (Adapted from [8]1) Dimensions of sheet: 33.75 in x 23.25 in x 0.187 in Materials to be considered: ABS, HDPE and Modified PP Number of parts: 2000 Number of parts/sheet: 2 ABS
HDPE
MPP
INPUT Production Information Set-up time Cycle time (s) Percent trim (%) Percent reject (%) Finish time/part (s) Material loss in regrind (%)
— 125 30 2 30 2
— 210 30 3 30 2
— 127 30 3 30 2
Costs Cost of sheet ($/lb) Trim credit (% of CM)2 Regrind cost ($/lb) Line time cost ($/h)3 Set-up cost, flat charge ($)4 Finishing cost ($/h)
1.50 30 0.10 100.00 150.00 15.00
0.50 30 0.10 100.00 150.00 15.00
0.90 30 0.10 100.00 150.00 15.00
5,62 2,041 41 1,021 5,734.7 114.6 1,685.0 1,799.7
5.06 2,062 62 1,031 5,217.2 156.5 1,518.1 1,674.6
4.77 2,062 62 1,031 4,916.8 147.5 1,430.7 1,578.2
OUTPUT Production Information Sheet weight (Ib) Total number parts made Number defective parts Total number sheets needed Total weight of sheet needed (Ib) Reject (Ib) Trim (Ib) Sheet to be reground (Ib) Costs per part Cost per sheet ($) Cost per part Sheet ($) Line time ($) Additional line time ($) Set-up cost ($) Finishing ($) Regrinding ($) Credit for regrind ($) Total cost per part ($) Total Costs Cost of sheet ($) Cost of line time ($) Cost of additional line time ($) Cost of set-up ($)
8.425
2.530
4.292
4.301 1.736 0.035 0.075 0.125 0.090 (0.397) 5.966
1.304 2.917 0.090 0.075 0.125 0.084 (0.123) 4.472
2.213 1.764 0.055 0.075 0.125 0.079 (0.209) 4.101
8,602 3,472 71 150
2,609 5,833 180 150
4,425 3,528 109 150
(Continued)
Table 10.9 (Continued)
Cost of finishing ($) Cost of regrinding ($) Credit for regrind ($) Total cost OUTPUT—INITIAL RUN COST Total job cost ($) Total cost per part ($) Sheet cost per part ($) Percent of sheet cost per total (%) Forming cost per part ($) Percent of form cost per total (%) OUTPUT—ONGOING RUN COST5 Total job cost ($) Total cost per part ($) Sheet cost per part ($) Percent of sheet cost per total (%) Forming cost per part ($) Percent of form cost per total (%) OUTPUT—PRODUCTIVITY Total sheet used (Ib) Total number sheets used Thermoforming line time (h) Total parts made 1
2 3
4 5
ABS
HDPE
MPP
250 180 (794) 11,931
250 167 (246) 8,944
250 158 (418) 8,202
12,725.10 6.363 4.301 67.6 2.062 32.4
9,189.25 4.595 1.304 28.4 3.291 71.6
8,619.80 4.310 2.213 51.4 2.097 48.6
11,931.45 5.966 3.904 65.4 2.062 34.6
8,943.66 4.472 1.181 26.4 3.291 73.6
8,202.21 4.101 2.004 48.9 2.097 51.1
5,217 1,031 60.1 2,062
4,917 1,031 36.4 2,062
5,735 1,021 35.4 2,041
The software used to obtain these values was donated by Rohm & Haas to Society of Plastics Engineers, Inc., Brookfield Center CT. The program has been checked and reformatted by SPE Thermoforming Division CM is compounded material The overall line time cost, $/h, is used in the calculation of cost of line time and cost of additional line time. It is not used in the individual values by resin The flat set-up cost is used in the calculation of cost of set-up but not in line time cost times set-up time Includes recycle credit
Rules of Thumb The largest element in the price of any plastic article made of a commodity polymer is the cost of the polymer. It is well-known [9] that injection molded parts are less than about 2.75 times the polymer costs for 98% of the cases studied, and less than 1.8 to 2.1 times for 50% of the cases. The range of 1.5 to 10 includes all polymers and all processes. The "factor of two" rule evolved from this observation: A first approximation of the manufacturing cost is obtained by doubling the polymer cost.
More expensive resins require more labor to produce a useful product [10]. Although labor costs increase with increasing unit polymer cost, they do not increase in direct proportion to the polymer cost. Therefore the multiplier for more expensive polymers should be less than that for commodity polymers. For thermoforming, the fixed and variable burden should also be less sensitive to polymer costs. One rule of thumb is a power-law [16]: $L^($V) n
(10.7)
where 0 < n < 1. When n = 0, the cost is independent of polymer cost, or any other cost. When n = 1, the cost is directly proportional to resin costs. For most chemical and plastics operations, 0.4 < n < 0.8. The "six-tenths rule" is frequently quoted: $L «(SV) 0 - 6
(10.8)
where $L is the cost of direct and indirect labor and $V is the cost of the polymer. The same rule of thumb holds for fixed and variable burden, $FVB: $FVB^($V) 06
(10.9)
External costs, on the other hand, increase with the most expensive polymers, as seen in Table 10.10. The ratio here is selling price per unit polymer cost, and so the ratio is substantially greater than 2. The nature of conversion from polymer to finished goods also has an influence on the selling price range (Table 10.11). Typically, injection molding and blow molding are more highly automated, more energy efficient and less labor intensive than other conversion processes. The thermoforming polymer cost must include a cost to convert the pellets to sheet. The most probable thermoforming ratio of 3 to 4 in this table agrees well with the general ratio range of 2.8 to 4 in Table 10.11. These ratios should be used only to get an approximate cost for a conceptual part and not for comparative process analysis. More detailed comparisons follow.
Table 10.10 Thermoformed Part Selling Price Range Polymer
Polymer Labor cost cost
LDPE, GPS, HDPE, 1 PP, PVC
0.65 to 1
PET, ABS, PPS, Cellulosics
1
PA 6, PA 66, POM, PC, PMMA PI, PESO2, PEEK
Fixed/variable Manufacturing External Selling charges price burden cost 3.15 to 3.5
0.5
3.65 to 4
0.4 to 0.75 1.25
2.65 to 3
0.4
3.05 to 3.4
1
0.3 to 0.5
2.0 to 2.5
0.5
2.8 to 3.0
1
0.25 to 0.4 1.0
2.25 to 2.4
0.6
2.85 to 3.0
1.5
1.0
Table 10.11 Comparative Plastics Process Selling Price Range1 [9] Process
Range
Average part range
Compression molding Injection molding Blow molding Extrusion Thermoforming Reinforced construction
2 to 10 1.5 to 5 1.5 to 5 2 to 5 2 to 10 2 to 5
3 to 2 to 2 to 3 to 3 to 3 to
1
5 3 3 4 5 4
Polymer cost factor = 1
Global Production Costs For the simplest case, where an existing business is producing a single product, the unit cost for that product is obtained by dividing the average global cost of the business in a given unit of time by the average number of products produced in that time: ^1 , , ^1 Business Expenses Global Part Cost = —— -^(10.10) Number of Parts Approximate costs for several products are obtained this way with proper proportioning of business expenses. The items that make up typical manufacturing plant operating costs are given in Table 10.12. Plant operation is considered "steady state" when supplemental orders for currently manufactured goods are quoted. When new products similar to currently manufactured goods are quoted on, the operation can also be considered "steady state", even though additional personnel and/or operating costs are incurred. This is true only so long as the unit manufacturing time to produce
Table 10.12 Manufacturing Plant Operating Costs Operating labor Maintenance labor Supervision Top management Overhead employees—guards, cafeteria Technical support Clerical support—secretaries, computers Payroll benefits Utilities Fuel Steam Electricity Water cooling and treatment
Polymers Additives, admixtures and adducts Molds, cutters, jigs, fixtures Auxiliary materials—paint, appliques Supplies Maintenance materials Overhead materials Local taxes Insurance Contract services—cleaners, consultants Demurrage Containers, cartons, pallets
Table 10.13 Existing Business Thermoformed Part Balance Sheet Inventory of raw materials, month X Additional purchases, month X Inventory of raw materials, month X - I Cost of raw materials consumed, month X
— — ( —) —
Direct wages, month X Direct utilities, month X Other direct expenses, month X Direct manufacturing expense, month X
— — — =
Payroll overhead, month X Plant overhead, month X Other indirect expenses, month X
— — —
Indirect manufacturing expense, month X Depreciation, month X
— ( —)
Indirect costs, month X Net cost of work in progress, month X
=
Production costs, month X Inventory of finished goods, month X Inventory of finished goods, month X - I New inventory cost, month X Gross profit, month X Sales, month X
= = =
— (—) =
= •—_ =
the new product is a small faction, 3 to 8% or so, of the typical product manufacturing time. For a steady-state operation, the unit time global cost is obtained as shown in Table 10.13. Some items need definition: •
•
Raw materials are all elements that go into the final product, such as: Polymer sheet, Additives and admixtures, such as: Surface-applied antistats, Finishing and decorating materials, Purchased components, such as: Inserts and Decorations, and so on. Direct wages are paid to Direct laborers. These are the people who contact the materials during processing. Direct laborers include: Thermoform machine operators, Trimmers, Dock and warehouse workers, Quality control inspectors,
•
•
•
•
Packers, and Their immediate supervisors. Since it is hard to separate direct and indirect utilities, to apportion the amount of power required to operate thermoformers from that required to power the buildings and grounds, utilities are usually considered to be direct utilities. Note that direct manufacturing cost simply represents the material and direct labor costs. Indirect costs deal specifically with: Benefit package to direct laborers, Specific cost of the facility to house direct laborers, and Depreciation of the processing and ancillary equipment. The plant overhead specifically excludes the cost of indirect labor people such as: Management, Technical staff, Sales, Clerical and Support staff. The cost of their salaries, wages and benefits or SWB, is subtracted from the gross profit. The net cost of work in progress is usually a small but potentially significant fraction of the total manufacturing cost. Work in progress is material that has been moved from inventory to the work stations, already formed, trimmed, inspected, or packed and not yet in finished product inventory. It can be assumed that these goods have values not much greater than raw material value. Occasionally, finished products are awaiting "rework" and so have values only slightly less than finished goods value. Many cost reduction efforts focus on minimizing the net cost of work in progress.
The gross profit is the sales revenue less production costs and increases in inventory value, Table 10.14. The net profit, before taxes is the gross profit less SAR 1 [H]. Note that SAR includes the total cost or SWB of all indirect labor, including top management. For the 1991-1993 period, SAR for the polymer industry was about 20% of the gross revenue [H]. If a single product is produced, the unit production cost and unit net profit is obtained by simply dividing the global production cost and the net profit by the number of good or salable pieces produced. Further, if all forming machines are the same and produce parts at the same through put rate, for the same number of clock hours, at the same efficiency, then an accurate value for machine hour cost or MHC, is obtained from: M H C =
Production Cost Number Machines x Hours per Machine
1
For example, if four identical machines each operated 500 h/month at a steady state monthly production costs of $100,000, the average machine hour cost is $50/h. In 1
SAR, is sales, adminstration and other costs such as R&D. SG&A, being sales, general and administrative costs, is considered to be equivalent.
Table 10.14 Thermoformed Part Balance Sheet for Net Profit Sales, month X New inventory, month X Production costs, month X Gross profit, month X Administration Sales, marketing Advertising Technical service R& D
= (= ) (= ) = (—) ( —) (—) ( —) (-)
SAR, month X Net profiit before taxes, month X
(= )
(= ) =
general, machine hour cost is the sum of the total annualized cost to operate a given machine, excluding SAR. The total annual production cost, APCTotal, is: APCTotal = Z M1 • hi
(10.12)
where M1 is the machine hour cost of the ith machine and hi is the annual number of hours that machine is run. Today, computerized accounting procedures allow accurate record-keeping on individual machines, and so such inaccurate estimates are no longer used for final cost analyses. Manufacturing Efficiencies Overall product efficiency is the actual number of good or salable parts, divided by the ideal number that can be obtained from a given amount of material. Process efficiency is the actual number of parts produced in a given period of time, divided by the ideal number that could be produced in that same time period. Individual efficiencies make up these efficiencies. Care must be taken in applying efficiency factors, since they strongly influence part production cost and can penalize it if not applied correctly: Not all efficiency factors are multiplicative.
Although thermoforming machines are designed to operate continuously, they rarely do so. The industry average is 70% to 80% or 6100 to 7000 hours per year, Table 10.15. Machine efficiency depends on the start-up condition of the thermoformer. Start-up times for forming new products on new molds with new polymers are substantially longer than for momentary shut-downs, at break for example. Start-up procedures and protocols were discussed earlier in this chapter. Table 10.16 gives some ranges for typical start-up times. Operators are required for all times except during maintenance, mold changeover or lack of business. Industry average is about 75% or 6600 hours per year.
Table 10.15 Thermoforming Machinery Efficiencies Nature of time Scheduled maintenance Emergency maintenance Shut-down, no business or mold changeover On but idle, not forming Running, start-up, set-up, shut-down, no product, see Table 10.16 for specific start-up times Running but off-spec parts Running quality product
Machine clock time
Percent of total time
X X
3 1 20 2 2
X X
2 70
Table 10.16 Thermoforming Machine Start-up Times1 Stock
Start-up condition
Time since last operation
Roll Sheet
Restart after momentary stop
Minutes
Roll
After extended shut-down
Hours
Sheet
Cycle time 4 to 10 cycles 1 to 2 cycles 10 cycles to 1 hour 2 to 4 cycles
Both
Cold start, old mold, known polymer
Weeks
1 to 2 hours
Both
Cold start, old mold, new polymer but
NA
2 to 4 hours
NA
4 to 20 hours
NA
20 to 40 hours
homologous to old polymers Both
Cold start, old mold, new polymer
Both Cold start, new mold, new polymer 1 Cycle = time on mold NA = Not applicable
Operator efficiency is about 80%, although it is slightly lower on evening shifts, weekends and for 10 or 12 hour days. Supervision is required to man machines for at least one-half shift per year. This estimate is obtained from: o • Tf Machine Time 1 n A n , Supervisor Time = — —— —1 (10.13) : |_Operator Time x Operator EfficiencyJ Example 10.3 illustrates this. Industry standard for direct supervision on forming machines is about 20% to 30%. For those parts where process cycle time controls production cycle time, labor efficiency usually does not affect the number of good parts produced. Instead, it serves to directly affect the production costs on each good part. On the other hand, when the production rate is labor-controlled, as might be the case where extensive finishing and post-forming operations are needed, labor efficiency contributes directly to the overall manufacturing efficiency.
Example 10.3 Direct Supervisory Time on Thermoforming The thermoforming machine is operated 67% of the time. An operator is used 75% of the time at 80% efficiency. Determine the amount of time supervision is required. Direct supervision time is given from Equation 10.12: Supervisor Time =
' — 1 = 0.117 or 11.7% of the year 0.75 * 0.8
0.117 • 8760 h/y = 1022 h/y or a supervisor is needed approximately 20 hours per week. Although machine efficiency allows good parts to run about 70% of the year, there are product losses due to the inherent nature of the process (Table 10.17). The most significant of these are forming defects. For certain products, such as transparent goods, surface blemishes and distortion are major reasons for product losses. Thus, product efficiency is usually 80% to 90%, but the nature of rejection of unsalable product depends strongly on its end use. Example 10.4 is an in-depth review of the costs associated with an on-going or "steady-state" thermoforming operation. The interaction of manufacturing efficiencies used in this example are not always applicable in every case. Machine hour costs should always be calculated from overall material and energy balances and raw materials should always include purchase prices of assembly components. Example 10.4 Costing a Part in an On-going Forming Operation Two thousand VCR covers are to be manufactured of smoky PMMA. Determine the manufacturing cost if these covers are part of an ongoing thermoforming operation. The input data are given as needed in the example. Material Cost The unit size is 18 in x 12 in x 4 in deep. The average thickness is 0.100 in. The areal draw ratio is given as: /18-12 + 2 - 4 - 1 2 + 2 - 4 - 1 8 \ = 2 1 1 V 18-12 / Assume initial sheet thickness is given as: h o «2.11 -0.100 = 0.211 in Material in part: Part volume = 0.211 • 18 • 12 = 45.6 in3 Sheet dimensions are assumed to be 24 in x 16 in x 0.211. Therefore the sheet volume is: Sheet volume = 0.211 • 24 • 16 = 81.0 in3 The percent trim is 43.7%.
PMMA cost is $1.65/lb plus $0.35/lb conversion cost or $2.00/lb. The density of PMMA is 75 lb/ft3. Therefore, the part and sheet weights and the part and sheet material costs are: Part weight =
' = 1.98 Ib: Part material cost = $2 • 1.98 = $3.96 1728
Sheet weight =
' = 3.52 Ib: Sheet material cost = $2 • 3.52 = $7.03 1728
Machine Cost I Efficiency Machine hour cost is $100/hour. This assumes labor, overhead, SWB, but excludes profit. Steady-state cycle time is 3 minutes and is based on about 30 s/mm. The process efficiency is 90%. The set-up time is 2 hours plus 10 unsalable parts. The down-time is 10% of the run-time plus 12 unsalable parts. The set-up time and down-time cost is $100/hour. Quality control retains 100 good parts. The time to produce good parts is: =
(2000+100) 0.9 • 20
S
Material Balance Good parts shipped: Good parts retained: Bad parts, 2 x 117: Set-up rejects: Down-time rejects: Total production
2000 100 234 10 12 2356
Overall Material Costs Purchased sheet: Purchased sheet cost: Salable product: Salable product cost:
2356 2356 2000 2000
• 3.52 = 8293 Ib • $7.03 = $16,586.24 • 1.98 - 3960 Ib • $3.96 = $7,920.00
Assume a trim sheet value of $0.35/lb. The trim credit is then: Trim: Trim credit: Net material cost:
8293 - 3960 = 4333 Ib 4333 • $0.35 = $1,516.55 $16,586.24 - $1,516.55 = $15,069.69
Unit Cost Net material cost: Machine hour cost: [117 + 2 + 0.1 • 117] • $100 = 130.7 hours • $100 = Finishing, including routering, edge polishing, packaging: $15/hour- 130.7 h
$15,069.69
$13,070.00
$1,960.50
Appliques, metallic tape, package materials, $1.95 per good unit $3,900.00 Manufacturing cost: $34,000.19 Manufacturing cost per salable unit: $17.00 Cost per unit weight of salable unit: $8.59/lb $7920 Material cost efficiency: —— = 52.6% $15,069.69 3960
Material weight efficiency:
8293
= 47.8%
Table 10.17 Thermoformed Part Efficiency Nature of loss
Percent
Comment on types of failure
Sheet damage in shipment
—
Sheet fails incoming inspection Damage in warehouse Damage during drying
—
Sheet supplier's responsibility, return for credit. Blemishes, off-color, unacceptable orientation. Same as above. Corner damage, crushed roll cores. Handling, blistering, marring of soft surfaces. Cracks in edges of brittle materials, scuffing. Overheating, grain wash, discoloration. Thermally sensitive polymers such as PVC, ABS. Too thin, uneven wall thickness, blisters, webs. Serious if part dimensions are critical, extreme draw-down, low temperature. Chill marks, blemishes. Low mold, sheet temperature. Dull saws, knives, routers cause split, surface melting, produces excessive dust, threads. Sheet imperfections such as gels and draw lines become more apparent after heating and forming. Transparent, thin polymers. Awkward, bulky parts difficult to handle. Long-term inventory more susceptible. Also, samples, cut-aparts, take-homes, and so on.
0 to 1 1
Damage in transit to machine
0 to 1
Thermal loss
0 to 1
Poorly formed
3 to 5
Mold stripping damage
1 to 2
Trimming damage
1 to 2
Reject by final inspection— polymer, sheet flaws
1
Packing damage Damage in warehouse, miscellaneous causes
0 to 1 1 to 2
Customer returns Total
2 to 3 10 to 20
Per-Unit Cost
Number of Units
Figure 10.13 An example of the learning curve
The Learning Curve Efficiencies in the production of new products are lower than those for established products, as seen in Table 10.16. As production continues, learned skills and shortcuts reduce the manufacturing cost per piece. This is usually referred to as the Learning Curve (Fig. 10.13). Learning curve arithmetic is used to predict the cost of future parts: • •
Let Y be the cumulative average cost per unit. This includes production time, manufacturing cost and so on. Let X be the cumulative production, in units. Then: Y = KXn
•
(10.14)
Where K is the effective cost of the first unit and n is the slope of the learning curve. Typically, — 1 < n < 0. If Y1 is the cost of the first run of X1 units, then the average unit cost of the second run is: Y1[CX2ZX1)"+' - 1 ] [(X 2 ZX 1 )-1]
( w n )
where X 2 is the number of units of the second run. Further, C x , the cost of the last unit in the production of X units, is: C x = K[X n + 1 - (X - l ) n + 1J
(10.16)
Example 10.5 illustrates the learning curve. Note that the analysis in this example is global and assumes that a detailed process analysis is well established.
Next Page
Example 10.5 Determination of the Cost for a Subsequent Run Consider the "steady state" data of Example 10.4, where 2000 units were produced. Assume that the costs given represent the third order of identical units. The first order was for 1000 units and cost $24.30 each to manufacture. The second was for 1800 units and cost $20.30 each to manufacture. The projected cost of the third order of 2000 is found as follows. X 1 = 1000, Y 1 = $24.30, X 2 =1800, Y 2 = $20.30. The first two lots, 1000+1800 = 2800, were manufactured at a cumulative unit cost of: $24.30 • 1000 + $20.30 • 1800 ^ 1 ^ = $2L?3 2800 Thus: In Y = In K + n In X In 24.3O = In K + n In 1000 In 21.73 = In K + n In 2800 n = -0.1086 K = $51,472, the unit cost of the first piece sold. The average unit cost for each of the next 2000 units is given as: Y = $2L73
[(4800/280O)0-89' - 1] [(4800/280O)-I] = $ 1 8 - 7 6
The cost of the last unit made in the second run, number 2800, is given as: C x = $51.472[(2800)0891 - (2799)0891] = $19.31 The learning curve characteristic is given as: LCC = 100 In" 1 (n In 2) = 92.7%
In addition to using the learning curve to predict costs of subsequent products, the slope of the learning curve yields information on production efficiencies. The Learning Curve Characteristic, LCC, is defined as: LCC= 100 e ( n l n 2 )
(10.17)
where n is the slope of the learning curve. If LCC = 100%, learning by experience is not possible and outside influences govern the process. If LCC is less than 60% or so, learning has been expensive, the initial process was very inefficient, or the product was brought to market before the process was fully debugged. Established processing and product schemes have LCCs in the range of about 90% to 95%.
10.6
Isolated Venture Costs
Previous Page
Simple steady-state cost analyses are not recommended when a new business venture is considered. A new venture implies staffing and equipping a new, ground-up facility at a site remote from current operations. All projected manufacturing costs are based on production estimates obtained from accurate market research. Thorough market analysis is mandatory for major installations. Operating expenses, capital costs, and processing costs are far easier to predict than sales and profits. Errors in manufacturing cost projections have much less influence on project profitability than changes in selling price, selling volume, raw material costs, and distribution and transportation costs. In addition to accurate, detailed market size and price projections, it is important to fully understand the impact of two other elements of the proposed business venture: • •
Competition from other thermoformers, and Competition from other processors.
Successful business ventures encourage imitators. This effect must be included in long-range sales and profit projections and forecasts. More significant to the early success of the venture is the effect of the potential simultaneous realization of the same or similar new product by two or more businesses. If the venture has a strong likelihood of this event, sales and profit projections must reflect it in lowered expectations of market penetration. Sales projections are frequently time-dependent, showing market penetration to saturation or maturation over a finite number of years. Saturation is followed by a decline in sales as new products replace the now-mature ones. Profits, on the other hand, should continue to increase throughout the growth and maturation time, as production costs follow down the learning curve. Careful market analysis is needed to ascertain the time to maturation and the percent penetration at that time. This value or range in values is the basis for production cost development. Manufacturing cost, production cost, and fabricating cost are considered here as identical and interchangeable terms. The cost to produce a salable product is partitioned in one of several ways. One way is in terms of direct and indirect costs: Production Costs = Direct Costs + Indirect Costs
(10.18)
Direct costs are all those elements that are directly related to the production of goods: Direct Costs = Direct Labor + Direct Materials + Other Direct Expenses
(10.19)
As noted earlier, direct labor is the cost for those people directly connected to or in contact with the product, from receipt of raw materials to loading of finished product. Typically direct laborers are: • •
Machine operators, Supervisors,
• • • •
Foreman, Materials handlers, Finishers, and Inspectors.
Direct labor benefits packages can be included in direct labor costs. Inclusion must be so indicated in any cost analysis, however. Direct materials are all those materials that are consumed to produce the final product. Direct materials costs should include credits for recovery of trim or unsalable product: Direct Materials Cost = Incoming Materials Cost — Returns + Reclaim Recovery Credit (10.20) Mold costs are not direct materials costs. Other direct costs include: • • •
The power needed to produce the goods, Packaging materials costs, if not already included in the direct materials costs, and Outbound freight charges.
All other costs are indirect costs. These include: • • • • • • • • •
Facility costs, Indirect labor and benefits costs, Depreciation or amortization of facilities, Mold and mold repair costs, Repairs and maintenance costs, Expendable supplies, Rentals and royalties costs, Utilities costs except those that are included in direct costs, Security, cafeteria and stockroom costs, and so on.
Production costs are also partitioned into those costs that are proportional to production rate and those that are not: Production Costs = Variable Costs -f Fixed Costs + Semivariable Costs
(10.21)
A fixed cost is one that is independent of production rate. Some typical fixed costs are: • • • • • • • •
Insurance, Property taxes, Plant management, Engineering personnel, Laboratory personnel, Maintenance supervision, Plant security, Maintenance shops such as tool-room and mold repair room,
• • • • • • • • •
Stockroom, Depreciation of facility, Depreciation of ancillary machinery, laboratory equipment, computers, electrical equipment, Depreciation and maintenance of cafeteria, roads, parking lots, sewers, fences, Fire protection costs and fees, Accounting, Purchasing, Quality control, all aspects, and Traffic dispatching.
Variable costs are those that are proportional to the production rate. These costs include: • • • • • •
Raw material, Operating labor, Materials handling, Royalties and rentals, Supervision, and Operating supplies.
Semivariable costs are those that increase with increasing production rate but not necessarily in direct proportion. Some costs plateau or peak with production rate. Examples are: • • • • • •
Depreciation of equipment, Maintenance, Repair and replacement, Mold costs, Utilities, and Outbound freight, to some extent.
There are general accounting software programs available for most office computers. None are specific enough to yield production costs for new thermoforming business ventures. Several aspects of production cost projections must be reviewed when developing new business schemes. Some of the concepts that follow are also used in Example 10.9, an illustration of projected costs for a new venture. As noted, the new production rate is time-dependent. All production costs must be clearly accounted for. But no production cost should be counted more than once. Depreciation is a measure of the falling value of a piece of equipment. Special purpose equipment should be depreciated at a rate faster than that for general purpose equipment1. Mold costs should not include installation. Care must be taken 1
Federal guidelines dictate the appropriate lifetime of equipment for tax purposes. Business has some option as to rate of depreciation and the practical lifetime of the equipment. Equipment should be replaced when it is apparent that new technologies are making the current equipment too costly to operate. Certainly, no business should keep obsolete or inefficient equipment just because it has not been fully depreciated for tax purposes.
when accounting for the cost of molds. Occasionally, mold costs are amortized over a fixed number of years and so become semivariable costs. Or mold costs are charged against a specific number of sold parts. Current practices set mold costs aside, to be so noted in the projected production cost summary. The costs of mold installation and repair are variable costs and should be included in all projected production cost analyses, however1. Once the marketing and early cost incentives indicate a business need for a new thermoforming business venture, determination of the optimum scheme for fabricating the requisite goods follows. Necessary fabrication equipment is researched. If the new product can be fabricated on already-available equipment, specifications are prepared and quotations requested. If available equipment needs to be modified or if specialized equipment is needed, development laboratories of equipment suppliers should be contacted to determine cost and availability to run demonstrations or trials of the to-be-formed parts. Obvious decisions must be made on the capacity of the equipment, given the needed production rate at market maturity. An oversized forming press can be inefficient and costly on a per unit basis, particularly if it sits idle for lengthy periods. An undersized press, on the other hand, may require additional maintenance costs and incremental costs of added shifts to maintain production rate. A table listing all capital cost items and associated installation costs should be made at this time. When the proposed processing scheme has been accepted by engineering and management and the requisite equipment lists approved by all, production cost analyses follow. In the analysis of Example 10.6 discussed below, the purchase price of the equipment is assumed to be known. Further, it is assumed that the part design is relatively complete and so the unit material cost is known. Typically, a production layout schematic is prepared (Fig. 10.14). It shows approximate equipment location, floor space, warehouse space, and so on. The process is then "walked through and timed" and manpower allocated. With this information and the estimates of other indirect cost, a quick product cost study, similar to the "steady-state" example, Example 10.4, is done. This will allow a "go-no-go" decision to be made on economic feasibility. Expected manufacturing efficiencies must be carefully thought out at this point and included in this study. Other elements must be included in the projected production costs in addition to standard material and labor costs. Depreciation and profit are two. Depreciation is usually considered as the tax-free portion of the difference between income and expenditure. The average annual depreciation is obtained by dividing some measure of the net cost of an item of fixed capital, by its useful life. There are several ways of discounting the item: • • •
Straight-line depreciation, Declining balance, Double-declining balance,
1
For custom molders, mold costs are usually borne by the customer. However, the custom molder should make certain that mold installation, maintenance, and repair costs are properly accounted for in the unit cost of the part quoted to the customer.
Dock Material Quality Assurance Raw Material Inventory
Computer Inventory Control [RM]
Materials Transfer to Work Station LoadingFormingUnloading
Inventory Control [WS]
Forming Inspection
Trimming, Finishing, Assembly
Dock to Extruder Trim Inventory
Finished Product Inspection
Trim Inventory Control [T]
Trim Transfer to Warehouse
Packaging, Labeling Trim Recovery, Identification
Finished Product Transfer to Warehouse Inventory Control [FP] Finished Product Inventory Dock Figure 10.14 Typical thermoforming materials flow layout
• •
Sum of years digits, and Sinking fund.
These methods are compared in standard economics texts [12,13]. Consider the simple straight-line depreciation. If F is the fixed value of the capitalized item, S is its scrap value, and N is its useful life, then the average annual depreciation for any year, D SL , is given as: (10.22) The book value, BV, after n years is: (10.23) For the sum-of-years digits depreciation, D SY : (10.24)
The equipment book value after n years is: (10.25) The annual depreciation and book value at the nth year for sum-of-years digits and straight-line depreciation schemes are illustrated in Example 10.6. Example 10.6 Comparison of Depreciation Rates for Thermoforming Equipment A $100,000 former has a $10,000 scrap value after 10 years. Determine its book value after 5 years using straight-line depreciation. Compare the value with sum-of-years digits depreciation. Table 10.18 gives a comparison of straight-line and sum-of-years digits depreciation for this example. After 5 years using straight-line depreciation, the former book value is $55,000. For sum-of-years digits depreciation, the former book value is $34,550. Table 10.18 Annual Depreciation and Book Value Schemes for Thermoform Machinery (Capital Cost = $100,000, Scrap Value - $10,000, Useful Life = 10 Years) Year
Sum-of-years digits
0 1 2 3 4 5 6 7 8 9 10
Annual depreciation ($) 18000 16360 14730 13100 11450 9820 8180 6550 4910 3300 1640
Straight line Book value ($) 100000 83640 68910 57450 49270 34550 26360 19820 14910 11640 10000
Annual depreciation ($) 9000 9000 9000 9000 9000 9000 9000 9000 9000 9000 9000
Book value ($) 100000 91000 82000 73000 64000 55000 46000 37000 28000 19000 10000
It is assumed for an isolated venture that external financial sources are to be sought. The interest on borrowed monies is the inducement offered to the lender to accept the risk of the venture. Interest rates vary but are usually greater than the prevailing prime lending rate. The capitalized cost of equipment, FK, should include the interest on borrowed money. This is given as: (10.26)
where M is the number of payment years and i is the interest rate fraction. Example 10.7 shows how the capitalized cost of equipment compares with its purchase price. Example 10.7 The Cost of Money The S 100,000 piece of equipment described in Example 10.6 is to be financed with an 8-year note at 15% interest. Determine the actual cost of the equipment. Is it cheaper to finance it for 10 years at 12% interest?
The capitalized cost of the equipment, including the interest is given as:
= $143,710 Thus $143,710 - $100,000 = $43,710 is the interest paid on the money over the 8 year period of time. For M = 10 and i = 0.12, FK = $142,740. Or financing it over 10 years saves $970 or less than 1% of the capital cost. When a business is begun, monies must be set aside for working capital and start-up capital. Start-up capital is the amount of financial resources needed to meet immediate costs to begin the business. In reality, these costs are part of the working capital costs, but usually concentrated at the very beginning of the program. Some of these costs might be: •
• • • • • • •
Initial interest on borrowed monies for Architect's fees, Site evaluation, Site preparation, Building construction, Building permits and operating licenses, Equipment installation, Equipment start-up costs, including labor, Personnel living expenses, Initial payment on raw materials, Contingency fees and expenses, Utilities deposits, and so on.
Working capital is the amount of money needed to meet day-to-day operating expenses (Table 10.19). Initially, nearly all working capital is start-up capital. Within a few months of established production, start-up costs should be small when compared with net costs for materials and accounts (Fig. 10.15). Projected production costs must ultimately focus on profit. For a business to succeed, a reasonable fraction of the selling price of the product must be returned as profit. Two types of profitability are normally considered:
Table 10.19 Working Capital Costs
• •
Inventories
Raw materials Intermediate materials, warehoused Ancillary materials, purchased components, packaging Finished product, unpacked, shipment-ready
Start-up costs
Payrolls Supplies Raw materials Utility deposits
Money
Emergency funds Monies to cover [accounts receivables minus accounts payable]
Running costs
Inventory control Warehousing Transportation Insurance deposits Taxes, prepayments only
Rate of return on investment, ROI, and Discounted cash flow.
Rate of return is a traditional way of measuring profitability: ""ualProfit (10 27) Invested Capital Unfortunately, there are many ways of defining profit and invested capital. Profit could be net annual profit before or after taxes. Or it could be annual cash income before or after taxes. Capital can be:
Working Capital Costs
Fractional ROI =
A
Working Capital
Non-Start-Up Costs
Start-Up Costs
Time Figure 10.15 Schematic of time-dependent working capital costs. Figure adapted from [16] and used with permission of McGraw-Hill Book Company, copyright owner
• • • •
The original invested capital, Depreciated investment, Current investment, or Time-averaged investment.
If the fractional rate of return, ROI, is based on the initial cash investment, F, and the net annual profit after taxes, PAT, the ROI is: PAT ROI = -pr(10.28) The net annual cash income after taxes, CIAT, is the sum of the net annual profit after taxes and the average annual depreciation, regardless of the depreciation method: CIAT = PAT+ D (10.29)
Rate of Return, r, %
Again, D is obtained from the appropriate depreciation scheme. The effect of depreciation on ROI is shown in Fig. 10.16 [13]. ROI methods have been refined to include more carefully calculated items such as land value appreciation and initial start-up costs. Similarly, there are other traditional techniques as payback period, the time needed for net cash flow to recoup original fixed capital costs. Typically, all these techniques lack the flexibility to account for the time-dependent nature of new ventures. Profitability must be a quantification of the attractiveness of taking a risk, Discounted cash-flow rate of return, i, and net present worth, NPW, are two such quantifying method. Cash flow, CF, is essentially the transient money supply. Cash-flow value is much greater at the beginning of a project than when the project is fully established. Initially, cash flow is negative. Start-up costs are not balanced by incoming sales revenues. Eventually, start-up costs drop to zero, working capital costs stabilize, and incoming monies exceed expenditures. This produces a positive
Time, yr
Figure 10.16 Time-dependent rate-of-return for sum-ofyears digits depreciation, i is interest rate of return, based on net annual profit after taxes, f is depreciation rate, and P is gross rate of return, ratio of net annual cash income to total capital cost. P = i + f. Figure redrawn from [13] and used with permission of McGraw-Hill Book Company, copyright owner
Discounted Cash Flow, DCF, 106$
Time, yr Figure 10.17 Example of time-dependent annual discounted cash flow. Figure redrawn from [13] and used with permission of McGraw-Hill Book Company, copyright owner
cash flow (Fig. 10.17) [13]. Cumulative cashflow or CCF is the sum of unit time cash flows. The break-even point is the number of years required to recoup the invested money1. The present value, P, of & future sum of money, f, is given as: P = f-d = ^
(10.30)
where d is the discount factor, i is now the discounted cash-flow rate of return, and m is the number of years. The discounted cash-flow rate of return is also known as the profitability index, PI or the true rate of return. IF CF is the annual cash flow, the annual discounted cash flow, DCF, is: (10.31) The net present worth, NPW, is the running sum of the annual discounted cash flows to the year M: (10.32) To obtain a suitable value for i, the discounted cash-flow rate of return, the net present work is assumed to go to zero in year M: (10.33) Since i is implicit in this equation, the appropriate value is obtained by iteration, graphical means or table interpolation. The effective use of NPW to obtain the 1
In the examples that follow, it is assumed that all the capital costs are required at the very beginning of the project. In reality, capital costs are usually ongoing throughout the lifetime of the project, particularly as competitive pressures force manufacturing to become more efficient.
discounted cash-flow rate of return depends on the accuracy of annual cash-flow estimates. Sound venture decisions depend on an accurate interpretation of NPW versus discounted cash-flow rate of return. Several points are worth noting here. First, depreciation is not considered a separate expense. Instead, it is deducted from the annual cash flow before the net present worth is calculated. The discounted cash-flow rate of return represents the fraction of money returned on the investment plus sufficient funds to repay the initial investor, interest on borrowed monies, taxes and expenses. Tables 10.21 and 10.22 illustrate the interactions of cash flow, net present worth and discounted cash-flow rate of return for a made-up example, Example 10.8. Created values for annual sales and expenses are used here. To achieve a zero net present worth value at 10 years, the discounted cash-flow rate of return must be 14.2%. The break-even point, where actual costs are recouped, occurs shortly after 5 years. Example 10.8 An Example of Discounted Cash Flow and Net Present Worth A S 1,000,000 forming machine is purchased and installed in a new part of the plant. The new plant cost is $40,000 and S 160,000 working capital is needed to get the operation going. The annual expenses increase with time according to: Annual expenses = Sl 00,000 + N • Sl 0,000 The depreciation value of the machine is zero after 10 years. The plant and land is worth $200,000 after 10 years. The output from this machine yields the following annual sales: Year 0 Year 2 Year 3 Year 5 Year 8
to 1 to 4 to 7 to 10
-0$1,500,000 1,000,000 800,000 400,000
Determine the discounted cashflow and net present worth after 5 years and after 10 years.
Table 10.20 reviews the data. In Table 10.21, it is seen that the cash flow at 5 years is $225,000. At 10% discount, the cash flow is $140,000 and the net present worth is -$165,000. At 10 years, the cash flow is $50,000 + the proceeds from the sale of the plant and land. At 10% discount, the cash flow is $97,000 and the net present worth is $217,000. The 10 year "break-even" discount rate is about 14.2%. The payback period or PBP is defined in terms of the discounted cash-flow rate of return. Simply, it represents the ratio of capital expenditures to cash flow. For a single capital investment, F, and an annual cash flow, CF, the payback period is just: (10.34)
Table 10.20 Net Present Worth [NPW] and Discounted Cash-Flow Rate-of-Return [i] [F] [S] [N] [WC] [L] [K = F + WC + L] [D] [E] [$]
Capital equipment cost, one-time Scrap value Process NPW = 0 in [N] = 10 years Working capital cost Cost of land Total capital cost Annual SL depreciation, D = [F - S]/N Annual Expenses = $100,000 + N • $10,000 Annual Sales: Year 0 to 1 -0Year 2 $1,500,000 Year 3 to 4 $1,000,000 Year 5 to 7 $800,000 Year 8 to 10 $400,000
$1,000,000 -0160,000 40,000 1,200,000 100,000
If the net present worth to the nth year is: (10.35) then PBP = d'. If n = oo, PBP = (l/i)max. For example, if the payback period is 5 years, the maximum discounted cash-flow rate of return is just 20%. The equations presented so far assume no inflation. If a general average inflation, I, is included, the net present worth becomes: (10.36) And the effect on discounted cash-flow rate of return is to generate a new rate of return, called the effective discounted cash-flow rate of return, ie: (10.37) For example, if i = 20% with an inflation rate of I = 10%, the effective value of ie would be only 9.1%. Other terms are reduced in similar manners.
10.7
New Venture Economics
The previous sections serve to introduce certain important general accounting terms. Example 10.9 illustrates how these are applied to a new venture, again defined as a stand-alone, remote facility. In this example, the costs are based on buying land and constructing a building to house the production facilities. Further, equipment is purchased as capital equipment, to be depreciated over a reasonable time. Alternate costing methods should include renting facilities and leasing equipment.
Table 10.21 Net Present Worth Year
0 1 2 3 4 5 6 7 8 9 10
1
Sales (103 $) [$]
Expenses (103 $) [E]
Income (103 $) $-E = i
Depreciation [D] (103 $)
Taxable Income I - D = TI (103 $)
50% Tax (103 $) T = 0.5 TI
Total capital cost (103 $)
0 0 1500 1000 1000 800 800 800 400 400 400
0 110 120 130 140 150 160 170 180 190 200
0 -110 1380 870 860 550 540 530 220 210 200
0 100 100 100 100 100 100 100 100 100 100
0 -210 1280 770 760 450 440 430 120 110 100
0 0 640 385 380 225 220 215 60 55 50
1200 0 0 0 0 0 0 0 0 0 -200
7100
1550
5550
1000
4550
2330
1000
Discount factor, d, given in Table 10.22
Cash flow (103 $) [CF]
-1200 -210 640 385 380 225 220 215 60 55 250
Discounted cash flow (103 $) [DCF] = [CF]d
Net present worth, (103 $) [NPW]
i = 10%
i=15%
i = 10%
i=15%
-1200 -191 528 298 260 140 124 110 28 23 97
-1200 -183 484 253 217 119 95 81 20 16 62
-1200 -1391 -863 -565 -305 -165 -41 69 97 120 217
-1200 -1383 -899 -646 -429 -317 -222 -141 -121 -105 -43
Table 10.22 Discount Factor, d = ( l + i ) ~ n Year
i= 0
=10%
=15%
=20%
=30%
=40%
0 1 2 3 4 5 6 7 8 9 10
1 1 1 1 1 1 1 1 1 1 1
LOOO 0.909 0.826 0.751 0.683 0.621 0.524 0.513 0.467 0.424 0.386
1.000 0.870 0.756 0.658 0.572 0.497 0.432 0.376 0.327 0.284 0.247
1.000 0.833 0.783 0.579 0.482 0.402 0.335 0.279 0.233 0.194 0.162
1.000 0.769 0.592 0.455 0.350 0.269 0.207 0.159 0.123 0.0943 0.0725
1.000 0.714 0.510 0.364 0.260 0.186 0.133 0.0949 0.0678 0.0484 0.0346
Example 10.9 New Business Venture—CPET Dinner Trays A new business is being considered. The product is CPET dinner trays, 8 x 10 x 3/4-in deep. The finished part average wall thickness is 0.030 in, the areal draw ratio is 1.34, the initial sheet thickness is 0.030 • 1.34 & 0.040 in, and the on-mold cycle time is 12 s. After careful evaluation, engineering selects a special purpose, roll-fed thermoformer with rapid-response high-temperature quartz heaters, sheet temperature monitoring and feed back control, but with essentially standard camelback trimming equipment. Part layout on its platen yields 4 trays per cycle with 50% trim. The fixed capital cost for the unit is $645,000, as detailed in Table 10.23. The one-time capital costs, including building and land, is estimated to be $2,205,000. The former selected by engineering has a maximum production rate of: MPR = (24 - 365) h/y • (unit/cycle) • (cycleIh) = 10,500,000 unitsIy Through careful discussions with prospective customers, an estimate of the selling price is determined1. In this study, marketing estimates that 4,000,000 unitsIy can be sold at about $1.75/unit. They estimate that sales will build to this level in 2 years and plan on discontinuing the product line after 5 years. Price elasticity allows discounting to achieve 6,000,000 units !year. One shift, 2000 h/y, produces a maximum of 2,400,000 units Iyear. Therefore, a three-shift operation without weekends is indicated. The sheet is to be purchased in 1000-lb rolls at $0.90/Ib. Owing to loss in IV of PET, it is decided to restrict regrind level to 10%. The rest of the trim is sold at auction for $0.20/Ib. Additional data are given in Table 10.24. Management has found capital investment monies at 10%, a semiskilled labor force at $10/h, plus $4/h benefits and no shift differential. Only half the labor force is needed the first year. Management would like NPW= 0 in five years. Therefore the capital equipment is to be internally straight-line depreciated over 5 years. The building and equipment scrap values are given in Table 10.23. The land does not decrease in value during this time. Molds are expected to last at least 1,000,000 1
A good guess of the selling price of the product must be made early in any venture analysis to determine if the effort is worth pursuing. The Class C estimate discussed earlier is a good starting point.
Table 10.23 Fixed Capital Costs and Mold Costs Thermoformed CPET Tray Fixed capital costs Item
Capital costs (103 $)
Scrap value (103 $)
5 year SL depreciation (103 $)
Installation (103 $)
Thermoformer, roll-fed Trim station and web roll-up Web regrind Ancillary equipment, mold heaters, warehouse equipment Contingency
450 75 20 35
45 8 4 5
65
10 0
129
Building, 40,000 ft2 @ $35 (including heated warehouse) Land, 4 acres @ $40,000 (fully improved)
1400
400
200*
160
160
0
2205
560
329
645
Total capital cost
72
72
Mold costs Steel molds, 4-cavity, channeled for oil heat Unit cost = $5000 Lifetime = 1,000,000 units Contingency = 20% Cost to produce 2,000,000 good parts: 3.175 x 1.2 = 3.81, say 4 @ $5000 = $10,000 Cost to produce 4,000,000 good parts: 6.35 x 1.2 = 7.6, say 8 @ $5000 = $20,000 * Normally buildings are depreciated over 20 or 30 years. This value is used for this example only.
units and cost S5,000 each, Table 10.23. Engineering estimates that the special purpose machine will be functional only about 70% of the clock operating time. They expect good parts 90% of the functional machine time. Three shifts, 6000 h/y, will produce: Good parts Iy = 6000 (h/y) • 4 • (5 • 60) • 0.9 • 0.7 = 4,500,000 Each shift requires the following direct labor force: 2 machine operators, 1 materials handler, 1 supervisor, 1 QC/inspector, and the following indirect labor: 1 maintenance man per shift, 1 shipping clerk per shift, 1 mold man per shift, 1 handyman per shift, and 1 shop secretary per day.
Table 10.24 Sheet Material Cost Thermoformed CPET Tray Sheet material cost = $2/kg or $0.90/lb Sheet contains 10% regrind Scrap value of regrind = $0.45/kg or $0.20/lb Density of PET = 1.37 g/cm3 Material used in single tray: 20.3 • 25.4 • 0.1 = 51.6 cm3 or 32.1 in 3 51.6 cm3 • 1.37 = 70.6 g or 0.156 Ib Web - 50% sheet = 70.6 g or 0.156 Ib Total single tray weight = 141.2 g or 0.311 Ib Code
Item
Nl MT
Actual number of trays needed, =No./(0.9 • 0.7) Material used
Mt
Material sold as trays
R
Material reclaimed (MT-Mt) Fraction recovered in new sheet, 0.1-MT Amount sold as scrap (R-F') Scrap value* Gross polymer cost* Net material cost* (G-VS)
F' S' VS G MC
2 x 106 trays/y 3.175 x 106 448,000 kg 968,0001b 141,000 kg 311,0001b 307,000 kg 676,000 Ib 45,000 kg 99,000 Ib 262,000 kg 577,000 Ib $118,000 $896,000 $778,000
4 x 106 trays/y 6.35 x 06 895,000 kg 1,975,0001b 282,000 kg 620,0001b 613,000 kg 1,355,000 Ib 90,000 kg 198,000 Ib 577,000 kg 1,157,000 Ib $235,000 $1,790,000 $1,555,000
* Values are based on metric values only
Power company costs are estimated to be S5 per machine operating hour. Annual property taxes are $60,000 or about 2.7% of fixed capital cost. The industry range is usually 1.5 to 3%. No local tax abatement is given. Annual insurance is $30,000 or about 1.4% of the fixed capital cost. The industry range is usually 1 to 2%. Determine the return on investment or profitability index for a range of unit selling prices that bracket marketing's selling price estimate. Then determine price elasticity at 6,000,000 units per year. Table 10.24 gives the material cost for the CPET tray. Table 10.25 summarizes line item elements that make up the operating expenses, Tables 10.26 and 10.27 list the labor costs and SAR, Table 10.28 itemizes the working capital costs without start-up, and Table 10.29 lists the start-up costs. Direct manufacturing costs represent approximately 67 to 75% of the total operating expenses. Start-up costs and working capital costs represent the rest. When the optimum selling price is unknown, a net present worth table is constructed, with a range in selling price values and several values of the discounted cash-flow rate of return. The net present worth is then determined, Table 10.30. In Table 10.31, price elasticity is also determined by
Table 10.25 Manufacturing Costs, Thermoformed CPET Tray (Values in 103 $) Year 1
Costs Direct manufacturing costs Raw materials, Table 10.24 Operating labor, Table 10.26 Utilities Maintenance, Table 10.26 Labor Supplies
775 160 13
1550 300 26
418 48
72 72
1044 Indirect manufacturing costs (excluding SAR, taxes) Labor, Table 10.26 Benefits, all labor, Table 10.26 Operating supplies, expenses Molds, Table 10.23
1044
216 152 110 20 488
SAR, Table 10.27 Property taxes Insurance
Year 2-5
312 248 150 40 488
331 60 30 422
2020
2020
750
750
405 60 30 422
495
495
Total manufacturing costs Working capital costs, Table 10.28 Start-up expenses, Table 10.29
1954 515 452
3265 1029
Operating expenses
2921
4294
evaluating the net present worth range for 6 million units per year, 50% more than marketing projections1. Figure 10.18 and Fig. 10.19 show the effect of discounted cash-flow rate of return on net present worth for 4 and 6 million units/year, respectively. Figure 10.20 shows the effect of selling price as well as the effect of price elasticity on the profitability index. 1
Equation 10.7 is also applicable to production costs. Here the expenses are considered to increase according to: Expenses = A • (Units)"
(10.38)
where A is a base value and n has the range 0 < n < 1. For n = 0.65, a 50% increase in production rate should increase production expenses by 30%. This value was used to generate the expense data of Table 10.31.
As is apparent from this example, the selling price of the product is strongly dependent on the cost of money, through the discount rate, and the production rate. Typically, selling price and net present worth are usually plotted against the discount
Table 10.26 Labor Costs, Thermoformed CPET Tray Item Number of good trays needed Minimum hours to produce good trays Actual hours to produce good trays, operating hours Number of shifts at 2000 h/shift year Assumed number of shifts Total labor, DL - 5/shift Minimum DL cost @ $10/h DL cost based on shifts Maintenance labor, total Maintenance cost @ $12/h Maintenance supplies, = maintenance cost Additional indirect labor, total Foreman Mold shop Shipping clerk Shop secretary Handyman Indirect labor cost @ $12/h Total labor force Benefits @ $4/h, all labor (2000 h/yr)
Year 2-5
Year 1 2,000,000 1,667 2,646
4,000,000 3,333 5,291
1.3 1* 8* $132,000 $160,000 2 $48,000 $48,000
2.7 3 15 $265,000 $300,000 3 $72,000 $72,000
2 2 2 1 2
3 3 2 2 3
9 $216,000 19 $152,000
13 $312,000 31 $248,000
* One shift + overtime
rate, as shown in Figs. 10.18 to 10.20, based on the data of Example 10.9. Again, this example is much simpler than reality, since all the equipment is purchased at one time, the production rate is steady-state and money is procured at a fixed interest rate. Once the basic elements of the process and ancillary costs are well understood, a simple computer program is written to provide more accurate, rapid, and complete price v. capacity v. expense profiles. This program is then used to develop other business scenarios and to compare such effects as overtime pay v. additional shift addition.
Entrepreneurial Risks Many new ventures are proposed by entrepreneurs. Venture capitalists frequently require that entrepreneurial projects pay a risk factor, in excess of the discounted cash-flow rate of return. Since, in theory, working capital and for the most part, costs for buildings and grounds are fully recoverable, any added risk factor should be applied only to those costs for items that are lost by premature project termina-
Table 10.27 Sales, Administration, Research [SARJ Costs, Thermoformed CPET Tray Item
Year 1
Administration, plant manager Operations manager Sales, marketing Purchasing Technical service, engineering
Year
2-5
$95,000 — 55,000 40,000 55,000
$95,000 55,000 55,000 40,000 55,000
Benefits, 35%
$245,000 $86,000
$300,000 $105,000
SAR
$331,000
$405,000
Table 10.28 Working Capital Costs Excluding Start-up Costs Thermoformed CPET Tray Item
Year 1
Year 2-5
Net accounts (Receivables-Payables) 10% annual product value, 3X polymer cost, (net) raw materials inventory, 30 days Finished product inventory, 30 days at 3X polymer cost
$233,000
$465,000
$65,000 $194,000
$129,000 $388,000
Contingencies, 20%
$492,000
$492,000 $23,000
Working capital costs
$515,000
$982,000
$1,029,000
Table 10.29 Start-Up Costs—First Year Only Thermoformed CPET Tray Item
$982,000 $47,000
Cost (103 $)
Installation costs, Table 10.23 Permits, utilities deposits Outside equipment rental, start-up Personnel on-site living expenses, personnel hiring costs Initial payment on raw materials Interest on start-up monies Contingency fees, expenses
72 5 35 50 120 120 50
Total start-up expenses
452
tion or business liquidation. If CAC is the cost of allocated capital and RR is the risk rate, the minimum acceptable rate, MAR, is: MAR = CAC+ RR
(10.39)
This is written in terms of the discounted cash-flow rate of return as: 1+ i = (1 + BIR) • (1 + MAR)
(10.40)
where BIR is the best risk-free interest rate, from banks, bonds or treasury notes. The net return on invested capital, i, is: i, Net Return = Gross Return — Payback of Capital — Interest on Borrowed Capital — Taxes — Other Expenses
(10.41)
Therefore, the net return, i represents the entrepreneurial return for managing the capital used in the venture. And MAR then becomes the entrepreneurial risk factor. Example 10.10 illustrates this. Example 10.10 The Entrepreneurial Risk Factor Consider a discounted cash-flow rate of return of i — 20%. If the best risk-free interest rate available from a local bank, BIR is 10%, determine the entrepreneurial risk rate. Determine the risk-free income on $100,000. And then obtain the I entrepreneurial effective tax-free income. From Equation 10.40, the entrepreneurial risk rate, MAR is:
1
MAR = T l ± ^ - l = 1 ^ - 1 =0.0909 or 9.1%
I For $100,000 deposited in a bank at 10%, if half is borrowed at 15%, say, II and 50% corporate taxes are paid, the risk-free income is: I
$50,000 • 0.10 - 0.15 • 0.5 • $50,000 = $1250 The BIR is then $1250/$100,000 = 0.0125 or 1.25%. If the same money is invested in a project with an after-tax return of 10%, the entrepreneurial risk factor is:
I
MAR = - ^ - - 1 = 0.0864
or
8.6%
or $8600 on $100,000. If the entrepreneur had invested his own money in the venture, he would have achieved an after-tax return of 50% of 10% or 5% on Ji! $50,000 or $2500 on $100,000. Therefore, by managing the venture rather I than investing in it, the entrepreneur obtains an effective tax-free income of I $8600 - $2500 = $6100 on his $100,000 effort. This is nearly 5 times better than the risk-free income route via banks.
Table 10.30 Net Present Worth (NPW) and Discounted Cash-Flow Rate of Return Thermoformed CPET Tray 4,000, 000 units per year s filing at $ 2.00 per un it Year Sales (103 $)
Expenses Income Deprecia- Taxable 50% Tax Total cap. cost income (103 $) (10 3 $) tion (103 $) (103 $) (103 $) (103 $)
Cash flow (10 3 $)
Discounted cash flow i = 10% 20%
0 1 2 3 4 5
0 4000 8000 8000 8000 8000
0 2921 4294 4294 4294 4294
0 1079 3706 3706 3706 3706
0 329 329 329 329 329
0 750 3198 3198 3198 3198
0 375 1599 1599 1599 1599
-2205 0 0 0 0 560
-2205 -2205 341 375 1321 1599 1201 1599 1092 1599 1341 2159
Net present worth 30%
-2205 -2205 288 312 1180 947 728 926 560 771 581 868
i = 10%
20%
30%
-2205 -1864 -543 658 1750 3091
-2205 -1893 -713 213 948 1852
-2205 -1917 -970 -242 318 899
4,000,000 units per year selling at $1.75 per unit Year Sales (103 $)
Expenses Income Deprecia- Taxable 50% Tax Total cap. cost (103 $) tion income (103 $) (103 $) (103 $) (103 $) (103 $)
Cash flow (103 $)
Discounted cash flow i = 10% 20%
0 1 2 3 4 5
0 3500 7000 7000 7000 7000
0 2921 4294 4294 4294 4294
0 579 2706 2706 2706 2706
0 329 329 329 329 329
0 250 2370 2370 2370 2370
0 125 1185 1185 1185 1185
-2205 0 0 0 0 560
-2205 -2205 114 125 979 1185 890 1185 809 1185 1084 1745
-2205 104 875 686 571 701
Net present worth 30%
i = 10%
-2205 -2205 96 -2091 702 -1112 539 -222 415 587 469 1671
20%
30%
-2205 -2101 -1226 -540 31 732
-2205 -2109 -1407 -868 -453 16
Table 10.31 Net Present Worth (NPW) and Discounted Cash-Flow Rate of Return Thermoformed CPET Tray 6,000,000 units per year selling at $1.60 per unit Year Sales (103 $)
Expenses* Income Deprecia- Taxable 50% Tax Total cap. income (103 $) (103 $) tion (103 $) cost (103 $) (103 $) (103 $)
Cash flow (103 $)
Discounted cash flow i = 10% 20%
0 1 2 3 4 5
0 4800 9600 9600 9600 9600
0 3797 5582 5582 5582 5582
0 821 4018 4018 4018 4018
0 329 329 329 329 329
0 492 3689 3689 1844 3689
0 246 1844 1844 1599 1844
-2205 0 0 0 0 560
-2205 -2205 246 224 1844 1523 1844 1385 1844 1259 2404 1493
-2205 205 1361 1068 889 966
Net present worth 30%
i = 10% 20%
-2205 -2205 189 -1981 1092 -458 839 927 645 2186 647 3679
-2205 -2000 -639 429 1318 2284
30% -2205 -2016 -924 -85 560 1207
6,000,000 units per year selling at $1.40 per unit Year Sales (103 $)
Expenses* Income Deprecia- Taxable 50% Tax Total cap. income (103 $) (103 $) (103 $) tion cost (103 $) (103 $) (103 $)
Cash flow (103 $)
Discounted cash flow i = 10% 20%
0 1 2 3 4 5
0 4200 8400 8400 8400 8400
0 3797 5582 5582 5592 5582
0 403 2818 2818 2818 2818
0 329 329 329 329 329
0 74 2489 2489 2489 2489
* Expenses increased 30% for increased throughput
0 37 1244 1244 1244 1244
-2205 0 0 0 0 560
-2205 -2205 37 34 1244 1011 1244 934 1244 850 1804 1120
-2205 31 918 720 600 725
Net present worth 30%
i = 10% 20%
30%
-2205 28 736 566 435 486
-2205 -2171 -1160 -226 624 1744
-2205 -2177 -1441 -875 -440 45
-2205 -2174 -1256 -536 44 769
Net Present Worth, NPW, 106$, Year 5
$2.00/Unit
$1.75/Unit
Discounted Cash Flow Rate of Return, %
Net Present Worth, NPW, 106 $, Year 5
Figure 10.18 Discounted cash-flow rate of return-dependent net present worth for annual thermoform molding of 4,000,000 crystallized polyethylene terephthalate, CPET trays at year 5
$1.60/Unit $1.40/Unit
Discounted Cash Flow Rate of Return, % Figure 10.19 Discounted cash-flow rate of return-dependent net present worth for annual thermoform molding of 6,000,000 crystallized polyethylene terephthalate, CPET trays at year 5
Discounted Cash Flow Rate of Return, %
6 Milion 4 Milion
Selling Price, $/Unit
Figure 10.20 Price sensitivity analysis for thermoform molding of crystallized polyethylene terephthalate, CPET trays at year 5
10.8
The Incremental Operation
An incremental expansion usually includes addition of a new, dedicated process to an existing plant operation to produce a new product (Table 10.1). If the new process and/or product is very similar to existing operations, the costs are projected from existing business costs. If the new process and/or produce is substantially different from current products, a new business venture plan should be considered. In this case, certain costs such as: • •
Start-up costs, and Stand-alone ancillary facilities costs including Land, Cafeteria, Power substations, and Parking lots,
are reduced or eliminated. If a modified new venture plan is used, most incremental operating costs are usually much better documented than those for isolated ventures. The information collection procedures are essentially the same however, as shown in Table 10.32. Emphasis is then on determination of the feasibility of expansion at the existing location. In addition to physical location, there are legitimate concerns of adequate space for: • •
Materials handling, Loading dock,
Table 10.32 Information Collection Procedure, Incremental Operation Determine market size, share, elasticity Determine characteristics of product—material, design parameters Determine cycle times, scrap level Polymer material specifications, regrind usage, polymer costs Develop details on process, equipment, cost, delivery Assess current warehouse, dock, parking, office space utilization Determine labor requirements Determine power requirements, costs Determine cost of plant addition, refurbishing Obtain management assessment of incremental SAR
• • • • •
Parking, Toilets, Traffic control, Office space, Cafeteria space, and so on.
The adequacy of: • • • •
Sewers, Power, HVAC, and Other utilities,
must also be assessed. If the new process and/or product is technically more advanced than current systems, the availability of a trainable labor supply must be assessed as well. The efficiency of in-plant materials distribution is an important factor in siting any addition. Intrinsically inefficient schemes may require entire plant rehabilitation and this cost must be included in the incremental venture cost analysis1. The proposed equipment for many systems may be similar or identical to existing equipment. Therefore the initial process efficiencies may be relatively high. For modest incremental systems development, the financial burden is frequently underwritten by the existing business. If this is done, however, management must prudently avoid rate-of-return comparisons between the proposed incremental operation and the current business. The financial status of all efforts, including new efforts, must always be assessed against the best available risk-free ventures and not against continuing in-house operations. Example 10.11 illustrates those elements of an isolated venture that are altered to fit an incremental operation.
1
The reason for this is apparent. If the new process and/or product had never been conceived, the current functioning of the operation would have continued undisturbed, regardless of how inefficient it was. Therefore the entire cost of rehabilitation must be carried by the new venture.
Example 10.11 Thermoformed Camper Top—Incremental Operation Consider the addition of a camper top production line to an operation currently producing shower stalls, soaking tubs and wading pools. Current ancillary real property is assumed adequate but a 40,000 ft2 cement block building is needed for the production equipment. The new thermoformer and trimming equipment are identical to existing equipment, although with improved processing controls. The parts formed from PMMA/ABS hot laminated sheet are to be backed with sprayed-up fiberglass-reinforced polyester resin, FRP. This process is new to the corporation. Start-up is assumed to be immediate once equipment delivery and installation are completed. Start-up costs are expected to increase working capital costs by only 10% the first year. Working capital costs are twice net accounts, or receivables minus payables. From experience, the net accounts run about 30% of the annual raw material costs. The final design wall thickness is 0.080 in PMMA/ABS and 0.175 in FRP. Six good camper tops per hour are to be produced on a two shift operation. Production efficiency is expected to be 95%. Shift labor is estimated at 20 direct, including maintenance and 20 indirect people. The labor cost is SlO/h with $4/h benefits. Determine the unit production cost the first year and every year thereafter, if the operation is designed for a 5 year life and a 10 year life. Determine the approximate selling price per unit.
Table 10.33 gives a review of the fixed capital costs for this incremental addition. Straight-line depreciation is given for both 5 years and 10 years. The building is assumed to have a $400,000 value at the end of the project lifetime. The part dimensions and sheet requirements are given in Table 10.34. The polymer material cost of each good unit is about $215. Additional material costs include window structures and ancillary hardware so that the total product material cost is about $385 per unit. For 24,000 units per year, manufacturing costs are more than $15 million dollars, Table 10.35. Year one includes 10% start-up cost surcharge. The discounted cash-flow rate of return and NPW for both 5 year and 10 year production times are given in Table 10.36. A unit selling price of $725 was used to create this table. At this selling price, for a 5 year neutral NPW, the profitability index, i, is about 15%. For a 10 year neutral NPW, the profitability index, i, is about 28.5%. Price elasticity and the effect of other depreciation schemes are obtained by proper substitution into the arithmetic in Tables 10.33 to 10.36.
10.9
Comparative Process Economics
Thermoforming is a competitive technology. In thin-gage, it competes with: • •
Paper, Paper-board,
Table 10.33 Fixed Capital Cost Thermoformed Camper Top (Equipment has zero value after depreciation) Item
Shuttle thermoformer—two station FRP spray-up equipment Ovens, saws Ancillary equipment Contingency
Capital cost (103 $)
SL depreciation 1Oy 5y (103 $) (103 $)
Salvage (xlO 3 $)
435 210 130 100 100 975
195
98
-0-
Building, 40,000 ft2 @ $35
1400
280
140
400
Total
2375
475
238
400
• • • • •
Paper pulp, Plastic-coated paper, Expanded polystyrene foam, Aluminum, and Roll-sheet steel,
and with: • • •
Plastics extrusion, Stretch-blow molding, and Injection-blow molding.
In heavy-gage, it competes with: • • • • • • • •
Plastics rotational molding, Injection molding, Blow molding, Fiberglass-reinforced polyester resin or FRP as spray-up molding, or lay-up molding, Sheet molding compounds or SMC, Bulk molding compounds or BMC, Sheet metal forming, and Metal die casting.
In certain areas such as equipment cabinets, boxes and containers, thermoforming competes directly with injection molding, blow molding and rotational molding. The comparative characteristics of these processes are outlined in Table 10.37 [10]. Generally when thermoforming is compared with these processes, it is characterized as having higher raw material costs and scrap and lower equipment and mold costs.
Table 10.34 Polymer Material Cost Thermoformed Camper Top Part dimension = 1270 x 2540 x 508 mm deep = 50 x 100 x 20 in deep Part thickness: PMMA/ABS = 2.03 mm or 0.080 in FRP = 4.5 mm or 0.175 in Areal draw ratio: [1270 • 2540] + 2 • [1270 • 508] + 2 • [2540 • 508] _ [1270 • 2540] ~ ' Initial thermoplastic sheet thickness = 4.5 mm or 0.175 in Part weight: PMMA/ABS = 1.2 [g/cm3] • 127 • 254 • 0.45 = 17.4 kg or 38.0 Ib FRP =1.2 [g/cm3] -2.2- 127-254-0.45 = 38.3 kg or 84.31b 55.7 kg or 122.3 Ib Scrap, zero value: PMMA/ABS (40%) 17.4 • 0.4 = FRP (30%) 38.3-0.3=
7.0 kg or 15.0 Ib 11.5 kg or 25.31b 18.5 kg or 40.31b
Total polymer weight: PMMA/ABS FRP
24.4 kg or 53.0 Ib 49.8 kg or 109.6 Ib 74.2 kg or 162.61b
Sheet material cost: PMMA/ABS $5.00/kg • 24.4 = $122.00 FRP $1.65/kg-49.8= $82.17 $204.17 Material cost per good unit: $204.17/0.95 = $214.92 Ancillary materials cost: Aluminum trim, metal rails, window assemblies, hardware decoration, decals (purchased) $155.00 [Assumes all hardward is recoverable] Shipping crate Total product material cost
$15.00 $384.92
Three decades ago, a major study [14] compared conversion costs for fabricating a 12 in x 12 in x 0.125 in thick five-sided box of LDPE. Four processes were compared: • •
Thermoforming, Injection molding,
Table 10.35 Manufacturing Costs, 1000 $ Thermoformed Camper Top Item Direct manufacturing costs: Raw materials Labor, including maintenance Utilities Other direct costs Indirect manufacturing costs: Labor Benefits, all labor Operating supplies, expenses Molds
Year 1
Year 2 +
9,238 800 40 200 10,278
9,238 800 40 200 10,278
800 640 240 10 1,690
Incremental SAR, 10% labor Incremental property taxes, insurance
160 20 180
Total manufacturing costs Working capital Start-up costs, 10% working capital Expenses Expenses, $ per good unit
• •
10,278
800 640 240 10 1,690
1,690
1,690
180
160 20 180
180
12,148 3,110 311 3,411
10,278
12,148 3,110
3,411 15,559 $648.29
3,110
3,110 15,258 $635.75
Blow molding, and Rotational molding.
It was anticipated that thermoforming would be the most economical for the production of relatively few units, owing to its low capital and mold costs. And injection molding was expected to be the most economical at high production rates, owing to its lower material and labor costs. The analysis has been redone to 1992 economics using the appropriate machine hour costs and scale factors described earlier and are displayed here in Tables 10.38 and 10.39. The machine hour costs are assumed to be applicable at 100,000 units per year, Table 10.40. Polymer material costs are given in Table 10.41. Process cycle times, scrap percentage, and process efficiencies are estimated from typical processing units [10,15]. Mold, material and finishing costs are representative of the specific processing unit, as well. The comparative manufacturing costs are given in Table 10.42. The thermoforming process yields the lowest unit manufacturing cost for 100,000 parts. Injection molding yields the lowest unit manufacturing cost at one million units. The high machine hour costs for the thermoforming process used in [14] is the primary reason for the relatively flat unit price curve (Fig. 10.21). This is a reflection of the more labor intensive burden carried by thermoforming nearly 30 years ago. However, even at a more-modern machine hour cost scale factor, the inherently higher raw material costs eventually eliminates
Table 10.36 Net Present Worth, Thermoformed Camper Top Five-year SL depreciation Year
0 1 2 3 4 5
Sales (103 $)
0 17400 17400 17400 17400 17400
Expenses (103 $)
0 15559 15258 15258 15258 15258
Income (103 $)
0 1841 2142 2142 2142 2142
Depreciation (103 $)
Taxable income (103 $) 0 1366 1667 1667 1667 1667
0 475 475 475 475 475
50% Tax (103 $)
0 683 834 834 834 834
Total cap. cost*, (103 $) -2686 0 0 0 0 400
Cash flow (103 $)
Discounted cash flow
-2686 683 834 834 834 1234
Net present worth
i = 10%
20%
i = 10%
20%
-2686 621 689 626 570 766
-2686 569 653 483 402 496
-2686 -2065 -1376 -750 -180 586
-2686 -2117 -1464 -981 -579 -83
Ten-year SL depreciation Year Sales (103 $)
Expenses Income Deprecia- Taxable 50% Tax Total cap. (103 $) tion (103 $) income (103 $) cost*, 3 (10 $) (103 $) (103 $)
Cash flow (103 $)
Discounted cash flow i = 10% 20%
0 1 2 3 4 5 6 7 8 9 10
0 17400 17400 17400 17400 17400 17400 17400 17400 17400 17400
0 15559 15258 15258 15258 15258 15258 15258 15258 15258 15258
0 1841 2142 2142 2142 2142 2142 2142 2142 2142 2142
0 238 238 238 238 238 238 238 238 238 238
0 1603 1904 1904 1904 1904 1904 1904 1904 1904 1904
0 952 952 952 952 952 952 952 952 952 952
-2686 0 0 0 0 0 0 0 0 0 400
* One-time start-up charge added as depreciation cost in the example, only
-2686 -2686 801 728 952 786 952 715 952 650 952 591 952 499 952 488 952 445 952 404 1352 522
Net present worth 30%
-2686 -2686 -2686 667 661 -1958 745 564 -1172 551 433 -457 193 459 333 784 383 256 1283 319 197 1771 266 151 2216 222 117 2620 185 90 3142 219 98
20%
30%
-2686 -2019 -1274 -723 -264 119 438 704 926 1111 1330
-2686 -2070 -1506 -1073 -740 -484 -287 -136 -19 71 169
Table 10.37 General Characteristics of Comparative Plastics Processes1 Characteristic
Thermoforming
Injection molding
Blow molding
Rotational molding
Polymer form Variety of polymers Raw material cost
Sheet Good Price includes extrusion to sheet Low rubber content Economically required Colored sheet Controllable
Pellets or granules Excellent Standard
Pellets Very good Standard
Powder Fair to limited Price includes grinding
All Immediate
Somewhat restricted Immediate
Concentrates Moderate
Concentrates Difficult
No thermally sensitive polymers Usually not practical Dry blend Very difficult
SMC, PUR, foams Very many
Difficult Very limited
Not feasible Very limited
Possible Many
Moderate to low Fair
Highest Excellent
High Fair to good
Moderate to low Poor to fair
Rim clamp Excellent Mechanical and vacuum Gentle
Butt Limited Hydraulic or mechanical Moderate
Butt Limited to good Mechanical
Tongue and groove Good Mechanical
Moderate
Severe
Corner draw-down and wall uniformity Air, mold core Air, stripper plate
Gating and weld lines Mold core Ejector pins
Pinch-off and wall uniformity Mold core and air Push pins and air
Wall uniformity
10 to 100
1000 to 100,000
100 to 1000
10
Types of polymers Scrap reuse Color Processability of thermally sensitive polymers Thermoset polymers Variety of mold materials Mold cost Mold maker reliability Mold closure Nonferrous tooling Method of holding polymer in mold Thermal cycling of mold Major trial and error problems Cooling method Part release mechanism Life of molds, 103
Air and water quench Manual and air
Operating pressure, atm Operating temperature, 0C Controlling portion of cycle Skill of operator Man to machine interaction Filling methods Part removal Part wall uniformity Flash Inserts Material orientation
Stress retention Method of controlling distortion, warp Method of forming hollow part2 Primary mechanical mode of part failure Surface finish Surface Texture 1 2
-1 to 5
100 to 1000
5 to 50
Oto 1
Room to 200
150 to 300
100 to 250
200 to 350
Heating and cooling
Cooling
Blowing
Heating
Low to moderate Normally high
Moderate to high Nil to low
High Low
Low Very high
Manual to automatic Manual to semiautomatic Fair Highest, trim Possible to questionable Biaxially oriented to uniaxially oriented High Heating
Automatic
Automatic
Automatic
Automatic
Manual to semiautomatic Manual
Excellent Low to very low Feasible but costly
Good to very good Moderate to high Feasible
Fair Moderate to low Feasible
Oriented
Unoriented
High to moderate Pressure
Uniaxially to biaxially oriented High Cooling
Welding and twinsheet forming Thin corners
Welding
Intrinsic
Intrinsic
Weld line
Thin side walls, poor pinch-off
Poor tensile strength
Excellent Good to very good
Excellent Excellent
Very good Very good
Good Good
Adapted from [10] by permission of Marcel Dekker, Inc. See also Table 9.6
Little to none Air and water cooling
Table 10.38 Plastic Process Scale Factors Updated from [14] Cost, $ = A (1000 Units) n Manufacturing cost, n
Process
Thermoforming Injection molding Blow molding Rotational molding
Polymer material cost
Mold cost, n
n
A
-0.14 -0.40 -0.51 -0.11
6.359 13.29 23.41 4.356
0.41 0.45 0.22 0.73
0.5 to 0.89* 0.53 0.45 0.34
* In [14], the upper value was quoted. Modern thermoforming processes indicate that the lower value is more appropriate
Table 10.39 Typical Machine Hour Costs Plastics Processing—19921 Process
Range ($/h)
Average ($/h)
Compression molding, <200T Injection molding, <150T Extrusion, 3-in extruder Rotational molding, rotary Thermoforming, shuttle Blow molding, extrusion, gallon bottle
75 100 30 30 50 80
80 120 55 50 65 90
1 2
to to to to to to
130 180 65 100 105 115
Updated and supplemented from [9] Adapted from [10] by permission of Marcel Dekker, Inc
Table 10.40 Machine Hour Costs for Comparative Process Analysis, Five-Sided Box for 100,000 Units Process
Cycle Time (min)
Parts (h^ 1 )
Total time, 100% efficiency (h)
Overall* efficiency (%)
Actual hours (h)
Machine hour cost ( $/h)
Total machine hour cost, (1000 $)
TF, 2-up IM, 1-up BM, 1-up RM, 2-up
7 3 4 10
17 20 15 12
5880 5000 6670 8330
85 90 85 75
6920 5560 7850 11110
65 120 90 50
346 667 707 556
* Combined machine and labor efficiencies
Table 10.41 Material Costs for Comparative Plastics Processes, Five-Sided LDPE Box Weighting 3 Ib or 1.36 kg Process
Thermoforming Injection molding Blow molding Rotational molding 1 2 3
Scrap
Gross material weight
(%)
(Ib)
(kg)
25 8 15 203
3.75 3.24 3.45 3.60
1.70 1.47 1.57 1.64
Material form
Sheet Pellets Pellets Powder
Material cost
($/lb)
(S/kg)1
Total (1000 $)2
0.70 0.45 0.45 0.55
1.54 1.00 1.00 1.21
262 146 155 198
Includes trim recovery value For 100,000 units Includes center section of 2-up forming
Blow Molding
Unit Cost, $
Rotational Molding
Thermoforming-Oid
Thermoforming-Modified
Injection Molding
Annual Production, Million Units Figure 10.21 Production-dependent unit cost for competitive processes for manufacturing a fivesided box, 12 x 12 x 12 x 0.125 in or 300 x 300 x 300 x 3.2 mm
thermoforming as a competitive economic process as the number of units increases. This is a typical analysis for heavy-gage parts. For thin-gage parts, on the other hand, thermoforming competes quite well with injection molding at any production level.
Table 10.42 Comparative Process Costs, Five-Sided Box 12 in x 12 in x 0.125 in thick Bold face values indicate minimum unit cost Process
TF-OId1 TF-Mod2 IM BM RM
Machine hour cost*
Material cost*
Material finishing costs*
Mold cost*
Total mfg costs*
Mfg cost/unit ($ unit)
100
300
1000
100
300
1000
1100
300
1000
100
300
1000
100
300
1000
100
300
1000
346 346 667 707 556
919 600 1193 1159 808
2686 1094 2260 1993 1217
262 262 146 155 198
674 674 282 265 527
1898 1898 582 1413 1824
28 28
53 53
110 110
53 53
104 104
212 212
19 19 81 41 16
31 31 133 52 36
50 50 228 68 87
655 655 894 956 823
1677 1358 1608 1580 1475
4744 3152 3070 3686 3340
6.55 6.55 8.94 9.56 8.23
5.59 4.53 5.36 5.27 4.92
4.74 3.15 3.07 3.69 3.34
* Global costs are in 1000$ per 1000 units 1 Machine hour costs are based on a scale factor, n = 0.89 2 Machine hour costs are based on a scale factor, n = 0.50
10.10
References
1. Interested readers should review the following book: Anon., The Guide to Accounting Software for Microcomputers, CTS, Rockville MD, 1-800-433-8015. 2. D. Carroll, "Set-Up Routines", handout provided at Thermo forming, University of WisconsinMilwaukee Seminars, Milwaukee WI (7-10 Jun 1993), Trevose PA (14-17 Jun 1993). 3. L.K. Kochar and J.L. Throne, "Thermoforming Multilayer Sheet. I: General Criteria", J. Plasat. Film Sheet., 5(1989), pp. 186-208. 4. A typical standard is Procurement and Supply Form SP-IOl, Chrysler Corporation, P.O. Box 2866, Detroit MI 48288. 5. Anon., "Thermoforming Troubleshooting Guide", Kiefel Systems, Succasunna NJ (1994). 6. M. Heil, "Entwicklungsperspektiven beim Warmformen technischer Teile", Kunststoffe 84 (1994), pp. 1420-1424. 7. F.R. Nissel, "Sheet Extrusion Systems for Thermoformers, Or Should You Make Your Own Sheet?", Presented at SPE Thermoforming Conference, Midland MI (20-22 Sep 1992), Figure 4. 8. R.A. Jarma and D.M. Brinker, "Acrylic Polyolefm Modifier-Value Analysis", Rohm & Haas, Bristol PA (14 JuI 1993). 9. G.L. Graf, Jr., "Applied Economics", in E. Baer, Ed., Engineering Design for Plastics, Reinhold Publishing Co., New York (1964), p. 1146. 10. J.L. Throne, Plastics Process Engineering, Marcel Dekker, New York (1979), pp. 850-859. 11. S.L. Mintz, "Spotlight on SG&A", CFO, 10: 12 (Dec 1994), pp. 63-65. 12. W.D. Baasel, Preliminary Chemical Engineering Plant Design, Elsevier, London (1976), Chapter 1. See also F.A. Holland, F.A. Watson and J.K. Wilkinson, Introduction to Process Economics, John Wiley & Sons, New York (1983). 13. F.A. Holland, F.A. Watson and J.K. Wilkinson, "Process Economics", in R.H. Perry, D.W. Green, and J.O. Maloney, Eds., Perry's Chemical Engineers' Handbook, 6th Ed., McGraw-Hill Book Co., New York (1984), Section 2.5. 14. A.D. Little Consulting Corporation, Boston NA, 1966. This report was detailed in J.L. Throne, Plastics Process Engineering, Marcel Dekker, New York (1979), pp. 853-854. 15. Z. Tadmor and C G . Gogos, Principles of Polymer Processing, John Wiley & Sons, New York (1979), pp. 11-22. 16. H.E. Mills, "Costs of Process Equipment", in H. Popper, Ed., Modern Cost-Engineering Techniques, McGraw-Hill Book Co., New York (1967), p. 111. 17. Wm.K. McConnell, Jr., SPE Industrial Thermoforming Symposium and Workshop, Arlington TX (12-14 March 1985).
Appendix A Abbreviations for Thermoformable Polymers Referred to in Text
Abbreviation
Definition
ABA ABS APET BOPP
Poly (aery lonitrile-butadiene acrylate). Poly(acrylonitrile-butadiene-styrene). Amorphous PET. Biaxially oriented polypropylene. Usually thin-gage. Also known as OPP. Cellulose acetate. One of the family of cellulosics that includes CN, CAP, CAB.
CA CAB CAP CPET CN ECTFE EPDM EPM ETFE EVA EVOH FEP FPVC FRP GR-UPE HDPE HIPS LDPE
Cellulose acetate butyrate. Sometimes called cellulose butyrate. Cellulose acetate propionate. Also called cellulose propionate or just propionate. Crystallized or crystallizing PET. Reserved for high-heat products where PET crystallinity exceeds about 20%. Cellulose nitrate. Polyethylene-chlorotrifluoroethylene copolymer. See also FEP. Ethylene-propylene-diene monomer-based thermoplastic elastomer. Also known as a norbornene-based elastomer. Ethylene-propylene copolymer. See also TPE. Polyethylene-tetrafluoroethylene copolymer. See also FEP. Polyethylene vinyl acetate. Polyethylene vinyl alcohol. Used as a barrier film in packaging applications. Fluoroethylene-based polymer. The extrusion and molding grade of PTFE. Flexible PVC. Also called plasticized PVC or soft PVC. Glass-fiber reinforced unsaturated polyester resin. Also known as GR-UPE. Glass-fiber reinforced unsaturated polyester resin. High density polyethylene (sp.gr. = 0.96 g/cm3). Also called lowpressure or hard polyethylene. High-impact polystyrene. Also called rubber-modified polystyrene. Low-density polyethylene (sp.gr. = 0.92 g/cm3). Also called highpressure or soft polyethylene.
Abbreviation
Definition
MIPS
PAI PaMS PAN
Medium-impact polystyrene. Also called rubber-modified polystyrene. Modified PPO. A soluble blend of PPO and styrenics. Oriented polypropylene. Usually thin-gage. Oriented polystyrene. Usually thin-gage. Polyamide. Also called nylon. Generic unless followed with numbers such as PA 6 for polycaprolactam. Polyamide-imide. High-temperature amorphous polymer. Poly-oc-methyl styrene. Also known as PAMS. Poly aery lonitrile.
PA 6 PA 66 PBT PCDP PEN
Polycaprolactam or nylon 6. Poly(hexamethylene diamine/adipic acid) or nylon 66. Polybutylene terephthalate. Polydicyclopentadiene. Polyethylene naphthanate.
PC PCTFE PE PEEK PEI
Polycarbonate. Polychlorotrifluoroethylene. See also FEP. Polyethylene, generic. See also HDPE and LDPE. Polyetheretherketone. Polyetherimide.
PET
Polyethylene terephthalate. Also called thermoplastic polyester or just polyester. Usually the amorphous type of PET or APET. Polyethylene terephthalate. The acronym used for recycling PET. Polyfluoroethylene polymer. See FEP. Polyimide. Polymethyl methacrylate. Also known as "acrylic" although this term can include other types of acrylates as well.
mPPO OPP OPS PS
PETE PFEP PI PMMA POM PP PPA PPO PPS PS PTFE
Polyoxymethylene. Also known as polyacetal or just acetal. Can include the copolymer as well. Polypropylene. Polyphthalamide. Poly-/»-phenylene oxide. An intractable polymer unless mixed with other polymers such as styrenics. Polyphenylene sulfide. Polystyrene. Usually refers to the generic family of styrenics, including unmodified or crystal polystyrene and impact grades. See also MIPS and HIPS. Poly tetr afl uoroethy lene. (Continued)
Abbreviation
Definition
PUR
Polyurethane. Linear or thermoplastic polyurethane is thermoformable. In certain cases, thermoset polyurethane film and low density foam can be thermoformed as well. Polyvinyl acetate. Used as a release agent in mold preparation. Polyvinyl butyral. Polysulfone. Also given- as PSO2. Polyvinyl chloride. See also RPVC and FPVC. Polyvinylidene chloride. Also known as polyvinyl dichloride. Used primarily as a barrier film in packaging applications. Polyvinyl fluoride. Polyvinylidene fluoride. Also known as PVF2. Used as a barrier film in packaging applications.
PVAc PVB PSO PVC PVDC PVF PVDF PVOH PVK RPVC SMA TPE
Polyvinyl alcohol. Used as a mold parting agent. Polyvinyl carbazole Rigid PVC. Also called unplasticized PVC. Polystyrene-maleic anhydride copolymer. Thermoplastic elastomer. Although once considered a specific product, now generic designation. Not normally thermoformed.
TPO TPX UHMWPE XLPE
Thermoplastic elastomer, usually polyolefinic. Polymethylpentene. Ultrahigh molecular weight polyethylene. Crosslinked polyethylene. Usually thin-gage or foamed.
Appendix B Typical Conversion Factors Used in Thermoforming (US Customary to Metric, Metric to US Customary) European metric
Multiply by
To get US units
Multiply by
x 39.37 x 10"6 x 0.0394
= inch = mil
x 25.4 x 103 x 25.4
= lbf = ft/h = ft 2 /h
x 2.2 x 4.448 x 0.00847 x 0.258
To get European Metric
kgf Newton (N) cm/s cm2/s
x 0.454 x 0.225 x 118.1 x 3.875
gm/cm3 kg/m3 1/min
x 62.4 x 0.0624 x 0.0353
= lbm/ft3 = lbm/ft3 = ft3/min
x 0.016 x 16.03 x 28.32
= g/cm3
atm Pascal (Pa) MPa GPa MN/mm2 MN/m2
x x x x x x
= lbf/in2 (psi) = lbf/in2 (psi) = lbf/in2 (psi) = 1000 lbf/in2 = lbf/in2 (psi) = lbf/in2 (psi)
x 0.068 x 6895 x 0.006895 x 0.006895 x 6895 x 0.006895
= atm = Pascal = MPa = GPa = MN/mm2 = MN/m 2
kW
x 3413
= Btu/h
x 0.000293
14.696 0.000145 145 145 0.000145 145
= lbf
= Newton (N) = cm/s = cm2/s
= 1/min
(Continued)
European metric
Multiply by
To get US units
Multiply by
To get European Metric
kW/m2 W/cm2 cal/cm2 • s cal/g • 0C W • s/kg • 0C
x317.1 x3171 x13277
= Btu/ft2h = Btu/ft2h = Btu/ft2h
x 0.003154 x 0.0003154 x 7.54 x 10"5
= kW/m2 = W/cm2 = cal/cm2 • s
x 1.00 x 0.000239
= Btu/lb°F = Btu/lb°F
x 1.00 x4184
= cal/g-°C =W-s/kg-°C
J/m J/m2
x 0.01875 x 4.755 x 10-4
= ft-lb/in = ft-lb/in2
x 53.34 x2103
= J/m = J/m2
kg/m • s
x 2415
= lb/ft-h
x4.14x 10~4
= kg/m- s
2
2
kW/m • jim
x317.1
= B t u / f t h -urn
x 0.003154
= kW/m 2 -^im
kW/m • 0C W/cm • 0C cal/s • cm • 0C cal/s • cm • 0C
x 578 x 57.79 x 241.9 x 2903
= Btu/fth°F = Btu/ft-h-°F = Btu/fth°F = Btu- in/ft 2 - h - 0F
x 0.00173 x 0.0173 x 0.004134 x 3.445 x 10-4
= kW/m-°C = W/cm-°C = cal/s-cm-°C = cal/s-cm- 0C
cal/s - C m - 0 C W/cm2 • 0C kW/m2 • 0C
x 7376 x 1761 x 176.1
= Btu/ft2h°F = Btu/ft2h°F
x 1.356 x 10~4 x 5.68 x 10-4 x 0.00568
= cal/scm2oC = W/cm2oC = kW/m2oC
Pa-s
x 1.45 x 10"4
= lb f -s/in 2
x 6895
= Pas
Appendix C Glossary of Thermoforming Terms
A Asperities Amorphous polymers Absorptance
Microscopic surface roughness. Polymers that exhibit no melting points. That fraction of radiant energy that is retained by the sheet.
B Biaxial deformation Billow Biot number Black body Blend Book value Bursting time
Stretching in two directions. Prestretching sheet by inflation with air pressure. A dimensionless ratio of internal to external heat transfer, Bi = hL/k. A body that emits the maximum amount of radiant energy at a given wavelength. Physical mixing of two or more polymers. Depreciated value of a machine. Time to burst a membrane that is biaxially inflated under a known differential pressure.
C
Cauchy strain Chill mark Computer-Aided Design Computer-Aided Engineering Conduction Convection Constrained deformation Copolymer Creep compliance Crystalline polymers Cut sheet
Tensor function of the extent of deformation. A surface blemish on a formed part. Computer design of part wall thickness using geometry or FEM. Also shown as CAD. Computer control of the thermoforming process. Also shown as CAE. Energy transfer by direct solid contact. Energy transfer by moving or flowing fluids. Sheet stretching with a portion in contact with the mold. Polymer with two sets of monomers, such as HIPS. A function related to retardation time. Polymers that exhibit melting points. Usually, heavy-gage sheet, fed one at a time to rotary or shuttle thermoformers. (Continued)
D Deformation Depth of draw Discounted cash-flow rate of return Draw ratio
Stretching. Also, draw ratio. Profitability index or true rate of return, A gross measure of the extent of sheet stretching. A measure of the area of thickness of the sheet after being formed into a mold to that before forming.
E Effective discounted cash-flow rate of return Elastic liquid Enthalpy Entrepreneurial risk factor Equilibration Eversion
The discounted cash-flow rate of return adjusted for inflation. A polymer that has both fluid and solid characteristics. A thermodynamic measure of the intrinsic heat content of a polymer. The additional cost of a speculative venture. Allowing a sheet to reach uniform temperature after the heating source is removed. Transfer of a bubble shape from above a horizontal plane to below it.
F FEM Finite Element Method Fourier number Fracture toughness Free surface
Finite Element Method. A computer technique for predicting how a sheet of plastic deforms under load. A dimensionless time, Fo = oc0/L2. A measure of the stress intensity at a crack tip needed to propagate a sustained fracture. The sheet surface not in contact with the mold surface.
G Galerkin weighted residual method Gels Glass transition temperature Global cost Gray body Gray body correction
A common numerical method for including boundaries in FEM problems. Hard, resinous particles in plastic sheet. The temperature range above which a brittle or tough polymer becomes rubbery. The overall cost of a business. A body emitting a fixed fraction of the maximum amount of energy, regardless of the wavelength. In net radiant energy interchange, the factor that accounts for energy factor interchange that is lower than black body interchange.
H Heat
flux
Heat transfer
Heavy-gage Homopolymer Hot creep test
The energy incident on a surface element per unit time, in W/in2, W/m2, or Btu/ft2 • h. A measure of the effectiveness of energy transport between a flowing fluid and coefficient a solid surface. Also known as convection heat transfer coefficient. Commonly, sheet having a thickness greater than 3 mm or 0.120 inches. A polymer from a single set of monomers such as PS. Application of a constant uniaxial load to a tensile strip of plastic that has been heated above its glass transition temperature.
/
Index In-situ trimming
To move a sheet forward a fixed length. In roll-fed technology, trimming that takes place while the formed sheet is still on the mold surface. Also called in-mold trimming.
K Kirksite
A zinc-based alloy metal used in prototype or shortrun tooling.
L Learning curve Lumped-parameter model
The cost to produce a given part as a function of the number of parts produced. An approximate mathematical heat transfer model that assumes no thermal gradient across the plastic sheet thickness.
M Machine hour cost Material allocation Maxwell
fluid
Melt temperature Mode III antiplane pure shear
The cost required to run a machine for one hour, all labor and overhead costs included. The theory that material on a given spot on a plastic sheet will always reside at the same location on the final part. A model fluid comprised of elastic springs and viscous dashpots in series. The temperature range above which a crystalline polymer changes from a rubbery solid to a viscoelastic liquid. A technical term describing the nature of nibbling or shear cutting in part trimming. (Continued)
Mooney rubbery solid
A material that follows a simple linear form for the strain energy function.
N Newtonian viscosity Node Non-Newtonian viscosity Nusselt number
A measure of the linear resistance of a molecularly simple fluid to applied shear. A junction or intersection, used in finite difference equations or FEM. A measure of the resistance of a molecularly complex fluid such as a polymer to applied shear. A dimensionless ratio of convection to conduction heat transfer for flowing fluids.
O Orientation
The amount of residual or frozen-in stretch in a plastic sheet, usually in a given direction.
P Pattern heating
Peclet number (J)(T)
Pin-chain Plug Poisson's ratio Prandtl number Pressure forming Price elasticity Pseudo-convection heat
The practice of selectively applying gauze, tissue or welded wire to a sheet, usually heavy-gage, to achieve uniform heating rate. A dimensionless product of Reynolds number and Prandtl number. A material design parameter, related to the secant modulus of the polymer and the rate of change of strain energy with the first principal invariant of the Cauchy strain tensor. Chains used to accurately feed roll-fed sheet. A mechanical device used to aid or assist sheet stretching prior to total contact with the mold. A measure of the volumetric change in material while it undergoes nonuniform deformation. A dimensionless ratio of fluid physical properties. Commonly, differential pressure across the sheet in excess of 2 atm or 30 lbf/in2. The effect of quantity on unit selling price. A measure of the effectiveness of radiant energy interchange between heat source transfer coefficient and sink. Also known as radiation heat transfer coefficient.
R Radiation Rate of return Reflectance
Electromagnetic energy transfer or interchange. Ratio of annual profit to invested capital. The fraction of radiant energy that is reflected at the surface of a sheet.
Replication Retardation time Reynolds number Roll-fed
Faithful imaging of the mold surface by the hot formed sheet. A measure of the ratio of viscous to solid characteristics in a polymer. A dimensionless ratio of inertial to viscous forces, for flowing fluids. Thin-gage sheet, fed continuously into the thermoformer.
S Sag bands Set temperature Soaking time Sonic velocity Steady-state Stefan-Boltzmann Strain Strain energy function Strain rate Stress Surge tank Syntactic foam
In continuous-sheet thermoformers, metal support bands that run the length of the oven to support the hot sheet and to help minimize sheet sag. The temperature below which a part can be removed from the mold without appreciable distortion. Equilibration time. The speed of sound, for air exiting a mold cavity through vent holes. Income equals outgo, with no accumulation. A radiation constant, =0.5674 x 10~10 kW/m2 •0C4 or =0.1714 x 10~8 Btu/ft • h •0R4. Polymer static response to applied stress. In solid mechanics, the amount of energy that occurs when a polymer is extended under stress. The slope of the elongation-time curve for a polymer. Externally applied load per projected area of a material. The tank between the vacuum pump and the mold, to allow near-uniform differential pressure to be applied during forming. A mixture of sintered inorganic foam spheres and plastic foam matrix, used in plugs. The common matrices are epoxy and polyurethane.
T Terpolymer Thermal diffusivity Thermoplastics Thermosets Thin-gage Transmittance
A polymer with three sets of monomers, such as ABS. A material property measure of the rate of energy transmission, oc = k/p • cp. Two-dimensional organic molecules. Three-dimensional organic molecules. Commonly, sheet thickness less than 1.5 mm or 0.060 in. The fraction of incident energy that is transmitted through a polymer sheet. (Continued)
Trim Trouton viscosity
That portion of the sheet that is not part of the final product. A measure of the resistance of a fluid to applied uniaxial stress, elongational viscosity.
U Unconstrained deformation Free-form sheet stretching without mold contact. Uniaxial deformation Sheet stretching in one dimension. V View factor Virgin
A measure of the fraction of radiant interchange that occurs between primary sources and sinks. Unprocessed.
W Watt density Wavelength
Wavenumber Web
Heater output rating. A measure of the nature of incident electromagnetic radiation. Ultraviolet: 0 to 0.38 um Visible: 0.38 um to 0.70 um Near Infrared: 0.70 um to 3 um Far Infrared: 3 um to 20 um Reciprocal of wavelength in radiation. During draw-down, a fold of plastic that cannot be stretched flat against a mold surface.
Y Yield point Young's modulus
The polymer stress/strain level below which plastic recovers elastically. The initial stress per unit strain of a polymer under uniaxial tensile load.
Author Index
Adkins, J.E. 240, 279 Ajroldi, G. 717, 745 Albert, K.A. 719, 720, 721F, 746 Alfrey, T., Jr. 61, 62F, 103, 233, 279 Allard, R. 262, 281 Alongi, P. 11, 53, 649, 741 Arenz, R J . 216, 278 Armstrong, R.C. 206f, 226, 232F, 233, 241, 278-280 Arpaci, V.S. 168, 195 Arruda, E.M. 241, 281 Ashby, M.F. 66, 66F, 67F, 103 Avrami, M. 655, 656, 741
Baasel, W.D. 812, 843 Baer, E. 327, 380 Bahadur, S. 226, 226T, 247, 278, 281 Baird, D.G. 683, 744 Bakker, M. 4, 6F, 52, 70, 7OT, 104, 364, 365T, 380, 623, 624, 647 Baldwin, R.L. 73, 104 Bank, D. 706, 745 Bartos, O. 241, 279, 281, 539, 542F Basile, P. 547, 549, 579 Bassani, J.L. 247, 281 Batterman, S.D. 247, 281 Beall, G. 4T, 18, 53, 329, 380, 567F, 568, 573, 576, 678, 679, 743 Belova, E.A. 513, 580 Benjamin, B.S. 573, 577 Benjamin, W.P. 387, 390, 392, 467 Benning, C J . 503, 574, 723, 723T, 725F, 746 Berghmans, H. 658, 742 Berins, M.L. 584, 586F, 644 Berns, E.M. 678, 701, 743, 745 Bichgalter, V.I. 513, 576 Bikales, N.M. 72, 72, 92, 104, 352, 354F, 358T, 380, 583f
Bird, R.B. 206f, 226, 232F, 232, 241, 278, 280, 294, 379 Boldt, J.A. 687, 744 Bongaerts, H. 584, 584T, 590, 593T, 607, 608F, 610, 611, 613, 613F, 618T, 629F, 644, 645, 647 Bongartz, H. 683, 744 Boyce, M.C. 241, 281 Brain, R.R. 675, 677, 742 Brandreth, D.A. 727, 746 Breuer, H. 607, 608F, 609F, 628, 603F, 646, 648 Brinken, F., 76, 104, 140, 141F, 195 Brinker, D.M. 794, 795-796T, 843 Brockschmidt, A. 447, 448F, 468, 674, 742, 739, 747 Brown, A.I. 136T, 196 Bruins, P.F. 4, 6F, 52, 213, 214, 225, 227, 229F, 267T, 277 Brydson, J.A. 65, 66, 67F, 78, 103, 206f, 233, 279, 587, 644 Buckley, C P . 217, 218F, 280, 682, 684, 685F, 743, 744 Bucknell, C B . 217, 218F, 278, 682, 684, 685F, 743, 744 Burdeinaya, T.A. 513, 580 Burgess, D. 327, 380 Burns, M. 395, 468, 488, 578 Burt, J.G. 731, 73IF, 732F, 747
Caddell, R.M. 347, 381 Cakmak, M. 683, 744 Cammons, R.R. 547, 549, 579 Carley, J.F. 233, 237, 239T, 249, 279, 282, 489, 490, 495, 574, 583f, 595, 596, 596F, 597, 598F, 602, 603F, 604, 605F, 628, 630F, 645, 648 Carroll, D. 753f, 843 Chanani, J.P. 687, 744
Italic = Reference location, F = Figure, f = Footnote, T = Table
Chaney, C. 387, 388T, 389, 467 Chang, H. 435, 469, 501, 576 Charrier, J.-M. 55, 76, 103, 262, 281 Chastain, C. 475, 574 Cheng, C. 711, 719, 719F, 745, 746 Childs, E.S. 4, 6F, 6T, 7, 8, 52 Chudinov, P.B. 513, 577 Chundury, D. 717, 718F, 719, 745, 746 Churchill, S.W. 294, 379 Coates, J. 83, 104 Cobbs, W.H., Jr. 657, 742 Coleman, B.D. 241, 280 Crawford, R J . 206f, 490, 503, 514, 515, 578, 615E, 646 Croft, D.R. 188, 192, 196, 315, 379, 659, 742 Cruz, C , Jr. 273, 283 Cruz, C A . 719, 720, 721F, 746 Cummings, D.S. 395, 468, 488, 574
Daane, R.A. 435, 469, 501, 576 Datta, A. 683, 744 Dealy, J.M. 215, 216F, 257, 277, 111, 745 Deanin, R.D. 58, 70, 7OT, 103, 104, 622T, 646, 679, 682F, 743 Dearborn, J.R. 717, 745 DeLorenzi, H.G. 241, 281, 521, 527F, 528F, 575 Dempsey, R.E. 65, 103, 652, 655, 741 Denson, C D . 207, 207T, 216, 226, 262, 264, 277 DeSousa, J.P. 683, 744 Di Pede, S. 683, 743 Domininghaus, H. 79, 79F, 80, 80F, 8IF, 104, 107, 194, 199, 210, 21 IF, 212F, 224, 226, 225F, 227F, 228F, 243, 246F, 247F, 25IF, 252F, 254F, 255F, 256F, 257F, 258F, 259, 277-281, 679, 681T, 743 Donnell, R. 679, 743 Dostal, C A . 374, 376T, 381, 687, 744 Drickman, M.R. 718, 745 Driscoll, S.B. 547, 549, 576 DuBois, J.H. 2, 52 Dunning, L.A. 675, 742
Dusinberre, G.M. 315, 380, 659, 742 Dutta, A. 683, 744
Ehlers, G.L.F. 327, 380 Elias, H.-G. 650, 650T, 741 Erwin, L. 226, 278 Eshbach, O.W. 405, 406, 407T, 467, 468
Farnham, S.E. 3, 52 Fenner, R.T. 583f Finney, R.H. 244, 281 Flecknoe-Brown, A.E. 738, 747 Fleming, M.F. 683, 743 Florian, J. 42, 53, 186, 187, 195, 196, 198, 277, 335F, 340, 355, 363, 364, 367, 380, 457, 468 Ford, H. 534, 575 Foster, J. 675, 743 Frados, J. 55, 103, 127, 127F, 194, 369, 381 Franey, J. 183, 185, 186F, 195 Frankenhauser, B. 238T, 239, 240F, 279 Fredrickson, A.G. 206f Friederich, K. 683, 743 Frisch, K.C. 722, 746 Fruzzetti, R.E. 655, 741 Fukase, H. 513, 515, 575, 577 Funt, J.M. 226, 234, 236, 237, 238T, 239T, 278
Galli, E. 696, 744 Gallo, R J . 216, 226, 262, 278 Gartland, R.H. 652, 654, 655, 655T, 741 Gawrilow, LK. 513, 577 Ghafur, M.O. 239, 281 Gheen, W.L. 490, 576 Ghosh, A. 262, 281 Gibson, L J . 66, 66F, 67F, 103 Glachter, R. 55, 103 Glicksman, L.R. 727, 746 Gogos, C G . 82, 82F, 104, 225, 278, 327, 380, 654, 741, 836, 843 Golike, R . C 657, 742 Gonzolez, H. 226, 278
Italic = Reference location, F = Figure, f = Footnote, T = Table
Goodier, J.N. 504, 574 Goodman, T.R. 310, 379 Gornick, G. 658, 742 Graf, G.L., Jr. 796, 798T, 843 Green, A.E. 240, 279 Green, D.W. 812, 843 Griffin, O.M. 372, 373, 381 Groeninckx, G. 658, 742 Gross, H. 168, 195, 235, 279, 710, 745 Gruenwald, G. 52, 53, 323, 328, 340, 355, 358T, 380, 425, 426, 468, 499, 574, 595, 645 Gurnee, E.F. 61, 62F, 103
Haas, T.W. 183, 185, 186F, 195 Haessly, W.P. 239, 281 Halldin, G.W. 244, 281 Han, C D . 206f, 226, 278 Harms, J.F. 675, 742 Harper, R . C 684, 685F, 686F, 744 Harris, R.L. 213, 214, 226, 227, 229F, 267T, 277 Hartmann, K.-H. 50F, 53 Hartnett, J.P. 290, 29IT, 310, 379, 444, 469 Hassager, O. 206f, 225, 232F, 233, 241, 278, 279, 280 Heil, M. 783, 843 Heneczkowski, M. 549, 549T, 550T, 551T, 579 Hensen, F. 583f, 584, 584T, 590, 593T, 607, 608F, 609F, 610, 611, 613, 613F, 617, 618T, 620, 621, 621F, 622T, 628, 629F, 630F, 644, 645, 647, 648 Hertzberg, R.W. 348, 349F, 350, 350F, 351, 380 Hieber, C A . 290, 379 Hoger, A. 29, 31, 32T, 35, 36T, 53, 144T, 165, 185, 186F, 187F, 195, 507, 577 Holland, F.A. 812, 843 Holman, J.P. 88, 88F, 104, 156, 156F, 195, 300, 359, 379, 380 Holt, D.L. 227, 228T, 231, 232T, 240, 249, 279, 499, 504, 505, 505F, 574 Hon, M. 683, 744 Hoover, K.C. 225, 231, 260F, 266, 278
Howard, J.B. 72, 72F, 104 Howell, H.G. 501, 541, 576 Howell, J.R. 662, 742 Huebner, K.H. 523, 575 Hylton, D. 227, 229F, 244, 279, 282, 711, 715, 717, 717F, 718, 719, 719F, 745, 746
Ilenda, C S . 711, 713F, 715, 716, 745, 746 Imada, K. 244, 281 Ingersoll, H.G. 727, 746 Irvine, T.F., Jr. 310, 379 Isayev, A.I. 241, 283, 521, 527F, 575 Ito, K. 513, 539, 577 Iwaaki, A. 513, 577
Jarma, R.A. 794, 795-796T, 843 Johnson, R.W. 711, 713F, 715, 716, 719, 720, 721F, 745, 746 Jolicoeur, C 547, 549, 576 Joye, D.D. 216, 226, 264, 278
Kamal, M.R. 290, 379 Kampf, G. 224, 278 Karynak, G. 674, 742 Keith, D.G. 738, 747 Keith, H.D. 710, 745 Kempthorn, J.T. 210, 279 Kenig, S. 290, 379 Kern, D.Q. 289, 289T, 379 Khorshied, S.A. 541, 556, 576 Kinloch, A J . 349, 351, 351T, 380 Klempner, D. 722, 746 Kmetz, M. 514, 577 Kobayashi, A. 334, 336F, 340, 341T, 342, 342F, 343T, 345, 345F, 346T, 368, 368F, 369T, 370-371T, 380, 501, 576 Kochar, L.K. 687, 688, 689, 690, 694, 695F, 744, 755, 843 Korican, J. 374, 376T, 381 Kossler, I. 92, 104 Kothandaraman, C P . 295, 295T, 379 Kouba, K. 239, 241, 281, 523, 539, 542F, 575
Italic = Reference location, F = Figure, f = Footnote, T = Table
Kovach, G.P. 14, 53 Kraybill, R.R. 148T, 150, 195 Kreith, F. 88, 104, 111, H l F , 122, 132, 133T, 135, 136T, 165, 194, 195, 295, 295T, 379, 659, 742 Krone, J.R. 683, 683F, 743 Kumar, A. 244, 281 Kunio, T. 513, 577
Lai, M.O. 227, 228T, 231, 232T, 240, 249, 279, 499, 504, 505, 505F, 574 Landel, R.F. 216, 278 Leaversuch R D 720 746 Leonard, B.L. 717, 718F, 719, 745, 746 Levy, S. 583f, 595, 596, 596F, 597, 598F, 602, 603F, 604, 605F, 628, 630F, 645, 648
Li C S 290 379 Liao,M.K. 290, 379 Lightfoot, E.N. 294, 379 Lilley, D.G. 188, 192, 196, 315, 379, 659, j42 Lodge, A.S. 251, 280, 501, 541, 576 Lodge, C. 679, 743 Loepp, D. 631, 63IT, 648 Lorntson, J.M. 226, 231, 23IF, 233F, 278 Lui, S.K.L. 490 503, 514, 515, 574
Macklin, S J . 675, 742 Macosko, C W . 231, 23IF, 233F, 278 Mallon, P J . 683, 743 Malloy, R.A. 573, 576 Maloney, J.O. 812, 843 Malpass, V.E. 209, 210, 211, 212, 225, 226, 227, 277 Manson, J.A. 351, 380 Mapleston, P. 720, 746 Marangou, M. 262, 281 Marco, S.M. 136T, 196 Markovitz, H. 241, 280 Martin, E.L. 623, 647 Martin, T.A. 683, 744 McConnell, W m I , Jr. 4T, 33, 52, 53, 81, 104, 127, 153T, 194, 308, 308F,
327, 379, 451, 468, 633, 634-636T, 648, 772, 773T, 774-782T, 843 McCrum, N.G. 217, 218F, 278, 682, 684, 685F, 743, 744 McHugh, K.E. 610, 646, 718, 719, 721F, 745, 746 McKelvey, J.M. 217, 218T, 278, 281 McTaggart, L.S. 652, 741 Meissner, J. 226, 278 Menges, G. 168, 195, 235, 239, 279, 281, 745
Menzel, D.H. 689, 744 Meriam, J X . 270, 270F, 281, 712, 745 Michaeli, W. 583f, 598, 599F, 600F, 602, 603F, 604F, 616, 626, 628, 629F, 645, 647 > 648 Middleman, S. 263, 281 Miles, M J . 244, 281 Miller > R M 389 > 3 8 8 T > 453 > 467> 468 Mills, H.E. 797, 843 Mills > N J - 244 > 281 Mills > N - L - 651 > 741 Minagawa, N. 628, 648 Mintz > S L - 800 > 843 Mizra > F A 241» 281> 521 > 575 Monks, R. 684, 686F, 744 Mooney, M. 238T, 279, Al5, 574 Moskovskii, C L . 513, 576 Mucke, W. 617, 618T, 619F, 620F, 647 Mulcahy, C M . 678, 701, 743, 745 Muller, H. 55, 103
Naitove, M. 684, 686F, 744 Nakamura, K. 244, 281 Narkis, M. 499, 514, 515, 574, 704T, 706, 747 Neid, H.F. 521, 527F, 528F, 576 Neiman, Y a . C 513, 575 Nelson, E.D. 547, 549, 576 Nichols, N. 674, 742 Nied, H.F. 241, 281 Nielsen, L.E. 70, 7OT, 104, 347, 380 Nietzert, W.A. 513, 565, 565F, 576 Nikitin, Y.V. 513, 577
Italic = Reference location, F = Figure, f = Footnote, T = Table
Nissel, F.R. 624, 626, 628F, 647, 791, 792F, 843 Noll, W. 241, 279 Norton, F J . 727, 746
O'Bradaigh, C M . 683, 743 Oelze, H. 513, 567F, 568, 576 Ogale, K. 610, 646, 718, 719, 721F, 745, 746 Ogden, R.W. 236, 239, 279 Ogorkiewicz, R.M. 71, 7IT, 104, 227, 234, 240, 278 Okine, R.K. 683, 744 Osmers, H.R. 176T, 195, 404, 467 Overbergh, N. 658, 742
Padden, F J . 711, 745 Palm, J.P. 719, 720, 72IF, 746 Park, J.Y. 226, 278 Peng', S. 216, 278 Perry, J.H. 146T, 196 Perry, R.H. 812, 843 Peterson, A.C. 46Of, 468, 691, 744 Petrie, CJ.S. 205, 206f, 226, 234, 260, 263, 277-281, 283, 513, 539, 577 Pipes, R.B. 683, 743 Platzer, N. 162F, 195 Poehlein, G.W. 216, 226, 264, 278 Pollock, M. 226, 278 Popper, G. 797, 843 Potente, H. 76, 104, 140, 141F, 195 Powell, P.C. 322, 323F, 380 Progelhof, R.C. 3, 4T, 52, 58, 61, 64, 64T, 66, 68F, 74, 74T, 75, 75F, 76, 76T, 77, 77T, 84, 103, 104, 181, 181T, 183, 185, 186F, 195, 199, 202, 203, 203F, 213, 222, 223F, 224, 224F, 225F, 234, 243, 249F, 250F, 277-280, 322, 326, 348T, 380, 415, 573, 574, 576, 584, 585F, 589, 589F, 590, 591T, 621, 622, 624F, 644, 647, 662, 675, 687, 688, 696, 706, 727, 742, 744, 745, 746 Przygocki, W. 652, 741 Pye, R.G.W. 404, 442, 454, 456, 467, 468
Quintiere, J.G. 183, 195, 687, 688, 696, 744
Ragab, A.R. 541, 556, 577 Raspor, O.C. 683, 743, 744 Rauwendaal, C. 583f9 595, 596F, 597, 602, 604, 605T, 606, 616, 616F, 624, 62'7F, 645, 647 Reitz, D.W. 727, 746 Rhee, B.O. 290, 379 Richardson, P.N. 583f Rivlin, R.S. 236, 279 Roark, R J . 267, 268, 268T, 281, 423, 428, 437, 468 Rohsenow, W.R. 290, 29IT, 379, 444, 469 Roller, W.R. 710, 745 Rosato, D.V. 590, 591, 592T, 594, 594F, 595F > 644 > 645> 717 > 745 Rosen > S L - 2O6f> 377-378T, 379, 381 Rosenzweig, N. 499, 514, 515, 574, 704T, 706 > 747 Ruetsch, R.R. 84, 104, 727, 746 R an Y > M E - 262 > 263 > 281
Saechtling, H. 65, 103, 210, 210F, 21 IF, 242, 242F, 243F, 244F, 277, 280, 679, 680F, 728T, 743, 746 Sakiadis, B.C. 83, 104 Salazkin, K.A. 513, 558, 559F, 576 Saunders, D.W. 236, 281 Savonuzzi, A. 675, 742 Scheibelhoffer, A.S. 717, 718F, 719, 745, 746 Scheiner, L.L. 675, 711, 712, 712F, 743 Scherbak, V.V. 513, 577 Scherer, R. 683, 743 Scheryschew, M.A. 513, 577 Schmidt, H J . 513, 577 Schmidt, L.R. 233, 235, 237, 238T, 239T, 249, 279, 282, 489, 490, 495, 499, 503505, 574 Schneider, P J . 165, 166F, 168, 169F, 172, 174F, 178F, 179, 179F, 195, 290, 291T, 379, 444, 469
Italic = Reference location, F = Figure, f = Footnote, T = Table
Schrage, D.A. 403, 403T, 467 Schreiber, H.P. 547, 549, 576 Schrieffer, J. 678, 743 Schuetz, M.A. 729, 746 Schuster, A. 689, 744 Schut, J.H. 333, 380 Sebastian, D.H. 717, 745 Semerdjiev, S. 437, 437F, 469 Shapiro, A.H. 414, 468 Shea, J.W. 547, 549, 576 Sheryshev, M.A. 513, 558, 559F, 576 Shlyakhova, T.G. 513, 577 Shrivastava, S. 262, 281 Shutov, F.A. 623, 625T, 647
742
X S £ '1 7 4 i "gletn R W 42Lf43T i t t
dingieion, r^.w. i^-z 1101, iyo ^^^ c. n A, Sinofsky, M . 727, 7/f/C 746 Skee, S. 387, 388T, 389, 467
oi i_i o T^ crvr ^^^ Skoblar, S.K. 595, 645 Skochdopole, R.E. 727, 746 Smets, G. 658, 742 Smoluk, G. 595, 645 Song, W.N. 240, 241, 279, 281, 521, 523, 534, 536F, 543, 544F, 575 Sors, L. 384, 467 Souders, M. 405, 406, 407T, 467, 468 Steinberg, A.H. 3, 52, 675, 742 Stephenson, M J . 263, 281 Stern, C H . 729, 746 Stewart, W.E. 294, 379 Storr, L.D. 623, 647 Streeter, V.L. 405, 406, 407T, 414, 467, 468 Subramanyan, S. 295, 295T, 379 Suh, N.P. 436, 468 Sung, N.H. 436, 468
Tadmor, Z. 82, 82F, 104, 226, 278, 327, 380, 499, 514, 515, 574, 654, 741, 836, 843 Takayanagi, M. 244, 281 Tanner, R.I. 241, 280, 539, 579 Taylor, C A . 241, 281 Taylor, G.A. 527, 529F, 576
Thorp, M.E. 397, 399T, 467 Timoshenko, S. 504, 574 Tock, R.W. 226, 231, 260F, 266, 278 Treloar, L.R.G. 236, 237, 238T, 239T, 240, 257, 279, 281, 527, 529F, 575 Tsuge, K. 216, 278 Turner, S. 475, 476f, 574, 576
Valenzuela, J.A. 727, 746 ' K E ' 7 3 ' 104 Vll f M A 513 ^ ' ' 576 ^5^^380^ ^
Van Holde
^^?rSvf V
^
^
l f m 28h 521
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355< -jc/;x ^^7T7 IQH /ion /io£ 3 5 6 ^ , 3 5 6 1 , 3 5 7 r , 3 ^ , 490, 496, ' ' ' 8 ^ ' , !: / ' ^ ^ ^
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Voskresensku, A.M. 513, 576
Wagner, M.H. 241, 280 j . H . 683, 683F, 743 Walter, M.M. 711, 745 Wang, K.K. 290, 379 Ward, L.G. 675, 742 Warnecke, H J . 238T, 239, 240F, 279 Watson, F.A. 812, 843 Weinand, D. 94, 95, 95F, 96F, 104, 105, 155, 155F, 158, 158F, 184, 185F, 186, 195, 214, 215F, 239, 243, 248F, 250F, 277, 280, 281, 676, 677F, 709, 743, 745 Welty, J.R. 659, 742 White, C H . 209, 210, 211, 212, 226, 277 White, J.L. 226, 233, 234, 236, 278, 583f, 604, 605T, 606, 606F, 628, 645, 648 Wilkinson, J.K. 812, 843 Williams, J.G. 237, 238T, 239F, 249, 277F, 278A, 279, 281, 504, 533, 534, 575 Wimolkiatisak, A.S. 717, 718F, 719, 745, 746 Wineman, A. 242f, 280 Wissbrun, K.F. 717, 745
Waiker?
Italic = Reference location, F = Figure, f = Footnote, T = Table
Wlochowicz, A. 652, 741 Wood, D.T. 405, 467 Wood, R. 13, 13F, 53 Woodhams, R.T. 683, 743 Wooldridge, J.M. 22, 25T, 53 Worbye, J. 402, 467 Wu, R. 262, 281 Wychoff, H.W. 710, 745 Wyeth, N.C. 651, 741
Young, R.L. 349, 351, 351T, 380 Young, W.C. 267, 268, 268T, 281, 423, 428, 437, 468
Zablau, N. 683, 743 Zerillo, J. 678, 679T, 743 Zhoyolev, LV. 513, 558, 559F, 576 Ziabicki, A. 64, 64T, 103, 657, 741
Italic = Reference location, F = Figure, f = Footnote, T = Table
Index A = Appendix, E = Example, f = Footnote, F = Figure, T = Table
Index terms
Links
A ABS
2 74 119E 243 379 753
ABS/PVC
8 78 135 251F 441
14 109 189E 338 485E
72F 109E 221E 344 486E
96F
73 118 235E 369 614
227
ABS Calendering drying of
584 618T
infrared absorption
93F
moisture in sheet
640
multilayer sheet
623
sheet appearance of
642
static charge on
642
Absorptance
183
Absorption colorant effect on
93
94
95F
pigment effect on
93
94
96F
Absorptivity Definition
135
Discussion
92
Absorptivity
112
136T
This page has been reformatted by Knovel to provide easier navigation.
862
863
Index terms
Links
Acrylonitrile-butadiene-styrene terpolymersee ABS Allocation, polymer sheet-see also Reallocation, polymer sheet, Distribution, polymer sheet Allocation, polymer sheet
471
510
510F
Allocation, polymer sheet billowing, during start-up
767
circle-grid test for of
756
plug assist, during start-up
767
plug assist effect on
507
507F
preblowing effect on
503
505F
prestretching effect on
512
Aluminum, plug material Amorphous polymer
758
439 443F
441 444F
8
207
508F
442
442F
Analysis, thermomechanical
224
Angel hair
340
359
362F
364
APET
338 676
339
379
441
217
219
219E
221E
Areal draw ratio-see also Draw ratio Areal elongation-see Draw ratio, areal Arrhenius equation Bursting
266
ASA
243
Avrami equation
656
252F
B Barcoding
751
Barrier polymers Beam bending, discussion
751f
28 511
511F
This page has been reformatted by Knovel to provide easier navigation.
443
666
864
Index terms Beer’s law
Links 93
Beta gage, sheet thickness Biaxially oriented sheet, discussion Biot number
definition
184
185
688
690
125E
165
168
169
169F
170E 189 308
171E 193 661
174 194
174F 300E
175 306F
622
623
623f
624F
835 841T
836 842F
838T 842T
840T
841
696
697T
601 12
125
Birefringence, in orientation
621
Blister pack, discussion
12
Blister pack
16
Blocking, effect
643
Blocking, ways of minimizing
643
Blow molding accumulator, competition
11
competition
28
competition to thermoforming industrial injection, competition
11
Blown film process
263
Bosses, dimensions
565
Brittle strength, polymer, discussion
358
Bursting
264
Bursting time
266
566F
Business existing, discussion
751
forming, discussion
749
incremental
752T
752T
incremental, discussion
830
isolated, competition
808
831
832E
This page has been reformatted by Knovel to provide easier navigation.
865
Index terms
Links
Business (Continued) isolated, costs, discussion
808
isolated, discussion
751
752T
isolated, protocol for
811
812F
new, discussion
751
752T
record keeping
750
751
C CAD-see Computer-aided design CAE-see Computer-aided engineering Calaendering roll stack configuration thin sheet
587 586F 584
Camel-back trimmer
15
15F
start-up, discussion
814
815F
venture
823
working, discussion
814
Capital
815T
815F
817F
Cash flow balance
750F
cumulative
817
discounted
816
817
discussion
816
817
Cauchy strain tensor defined
248f 236
Cavity isolator Cell-cast sheet, PMMA Cellulose acetate, infrared absorption
14
51
587 89
89F
2
3
617
618T
Cellulosic-see also CA, CAB, CAP Cellulosic drying of
5
This page has been reformatted by Knovel to provide easier navigation.
84
754
866
Index terms
Links
Chamfer
517E
design
459
Chatter line
557
Chill mark
441f
causes of
565
mold temperature effect on
558
plug temperature effect on
559
460
460F
460f
543
676f
764
663
663F
663T
664T
756f 766
757
757F
758
449
449F
557
558F
Chill roll-see also Roll stack Chill roll simulation for PET
662
condition for PET
662
Circle-grid test during start-up
756 758F 767
Clamp cavity
449
edge
463F
peripheral
448
sheet, discussion
448
with coining
449
with ejection
451
with trimming
449
Clamping
450 450F
383
sheet, discussion
38
44
Coefficient of thermal expansion
85T
321T
Coextrusion
586
Coining
449
competition with pressure forming
450
450E
28 679
Compression molding comparison
2
This page has been reformatted by Knovel to provide easier navigation.
867
Index terms
Links
Compression molding (Continued) competition Computer-aided design, discussion Computer-aided engineering
28 508 477F
multilayer
510
plug assist
509
prestretching
509
Computer-aided mold design
477
Computer-aided part design
477
Computer-aided structural analysis
477
509
Computer prediction boundary condition
192
heat transfer
188
Conduction boundary condition
123
definition
13
into mold
286
steady-state
121
transient
121
110
121
514
514E
241
521
121F
Cone draw-down into truncated, draw ratio Constitutive equation of state
513 574A 205
Convection boundary condition
123
definition
13
forced, in ovens
14
free surface
286
mold coolant
286
Conversion to sheet, discussion
111
583
This page has been reformatted by Knovel to provide easier navigation.
523
868
Index terms
Links
Coolant oil as
297E
water as
296E
Coolant channel, discussion
404
Coolant channel design
404
404F
contraction
406
expansion
406
orifice
406
407
760
763
discussion
303
304F
forced convection
303
307
natural convection
303
305
water mist
303
Coolant lines, during start-up
408E
764
Cooling, free surface
Cooling, in ambient air
303
Cooling cycle
285
286
start-up protocol
755
757F
temperature dependency of
565
566F
balance sheet at steady state
798
capitalized
813
313
313E
799
799T
800
799T
800
800f
826T
direct, isolated business
808
809
direct/indirect labor
797
fixed, isolated business
809
fixed/variable burden
797
Corner radius
Cost
SAR
fixed capital global production
822T
833T
798
labor
826T
machine hour, competitive
840T
This page has been reformatted by Knovel to provide easier navigation.
869
Index terms
Links
Cost (Continued) machine hour
800
manufacturing, isolated business
808
manufacturing
796
798
material
823T
834T
material, competitive
841T
mold, accounting for
810
mold
824T
811
811f
835T
822T
energy
783
790
790T
extrusion
791
792F
792E
forming, discussion
794
796
797
forming, general
794
797
797T
forming, software for
794
795T
813
814E
polymer
793
794
regrind
793
793E
operating
798
798T
polymer
796
money
process, competitive production, isolated business
793
793E
840T
841T
842T 808
809
835
836
838T
842F
841
842T
815F
816
817f
826T
3 38 545
5 285 650
7 339 773
13 340
37 441
cooling formed part plug of
668
669
crystallization rate, effect of heater temperature on
666
667F
competitive processes semivariable, isolated business
810
start-up
814
variable, isolated business
810
working capital CPET
827T
This page has been reformatted by Knovel to provide easier navigation.
870
Index terms
Links
CPET (Continued) crystallization rate, effect of temperature on
666
forming
649
forming conditions
666
lamination of
643
mold design for
668
mold temperature
666
multilayer sheet
623
nucleants in
652
patents on
652
pressure for forming
668
pressure forming
676
thermoforming equipment for
666
trimming of
670
troubleshooting forming process of
670
671T
Crack propagation, rate
351
352T
Creep, hot
226
Creep, isochronous
237
Creep test, hot
213
Crystalline melting temperature
286
Avrami equation
656
crystalline level
651
transition temperatures Ziabicki equation
667F
668
654
214
215
658T
650T 658
Crystallization cold
199f
on mold
285
orientation-induced
652
thermally induced
652
Crystallization rate DSC determination of
658
This page has been reformatted by Knovel to provide easier navigation.
871
Index terms
Links
Crystallization rate (Continued) DTA determination of
658
hot-stage microscope determination of
655
CTFE
210
Cut-sheet forming clamping
13 13
shuttle press
33F
Cut-sheet forming-see also thermoforming categories Cutting characteristics, in trimming
341T
343T
compression
352
mechanics
334
335
355 357T
355F
shear steel rule die
352
thermal
372
thermal, melting rate
372
water jet
374
Cutting force, defined
356F
356T
373E 375F
376T
354
D Dam
558F
design
459
Debugging time Deformation
459F
752T 220
biaxial, defined
202
biaxial
241
250
elongational
201
202
260
extensional-see also Deformation, elongational
This page has been reformatted by Knovel to provide easier navigation.
260F
357F
872
Index terms
Links
Deformation (Continued) extensional
207
solid phase
206
uniaxial, defined
202
uniform biaxial, defined
202
Depreciation average annual
811
816
discussion
810
810f
methods for
811
812
Depth-of-draw, discussion
813
15
Design concept feasibility
477
dimensional tolerance on
472
environmental effects on
472
mechanical behavior on
472
polymer characteristics on
472
Design check list appearance
474T
application
473T
discussion
472
environmental
474T
general
473T
part function
474T
part limitation
476T
Design criteria, discussion
471
Design philosophy, discussion
476
Dewpoint, of air for drying
617
Disperity index Disposables
618
61 4
Disposables-see also thin-gage categories
This page has been reformatted by Knovel to provide easier navigation.
813E
873
Index terms
Links
Distributed parameter model
659
boundary conditions on
660
669
669F
DMA
224
Double step, design on male mold
459
459F
Draft angle
558
561
562F
17
17F
252E
253E
231 492E 498
488 493E
489 496F
490 493E
495 498E
495E
496
effect on wall thickness
518E
Drape forming
2
definition
14
Draw-down-see Draw ratio Draw-down
215
Draw-down rate
557
Draw ratio-see also Depth-of-draw, H:D, Areal draw ratio, Linear draw ratio Draw ratio
214
areal
214 491 497
areal, common shapes
491T
areal, definition
16
areal, discussion
471
areal, practical limit
565
areal, prestretching effect on
505
areal, truncated cone
577
discussion
471
Hid, definition linear
578
16 488 496F
linear, definition
16
linear, discussion
471
linear, practical limit
565
linear, truncated cone
578
494 498
This page has been reformatted by Knovel to provide easier navigation.
874
Index terms
Links
Draw ratio (Continued) temperature-dependent
503
504F
367
368E
3
16
Dryer design
618
619F
Drying, discussion
617
Dye, infrared effect
185
186
186T
labor
801
802
803E
manufacturing, discussion
801
803
803E
803
803E
234
235E
Drilling Drink cups
369T
370T
E Efficiency
part
805T
process
801
product
801
Ejection system
383
Elastic liquid
205
Elastic liquid-see also Viscoelastic liquid Elastic solid
234
Elongation, ultimate
213
Emissivity
112
definition
136T
134
Energy audit, discussion
783
Energy balance
750F
Energy cost, by state
790T
Enthalpy
107
defined
82
790
Enthalpy-see also Polymer enthalpy, Polymer heat capacity EPDM
239
This page has been reformatted by Knovel to provide easier navigation.
260
875
Index terms Epoxy, plug material Equilibration definition
Links 439
441
177F
285
176
Equilibration time computed
177
178F
178E
179F
180E
763
763F
591T
592T
593T
590
594
594F
588T
588F
180
Euler buckling-see Plate buckling EVA
28
Evaculation rate, during start-up EVOH
762 28
Extension biaxial, uniform
257
258E
biaxial
207
257
207
257
annular die for
584
587
heat buildup owing to shear
597
597E
pressure in
596
597
screen pack for
591
594
single-screw, characteristics
590
591
single-screw, compression ratio
589
589T
single-screw, melt pumping section of
590
single-screw, plasticating section of
590
single-screw, residence time in
614
single-screw, screw design for
589
589F
595
595F
biaxial-see also Deformation, biaxal Extension, uniaxial
258E
Extension, unaxial-see also Deformation, uniaxial Extruder
single-screw, solids conveying section of
589
single-screw
587
tandem
587
590F
588
This page has been reformatted by Knovel to provide easier navigation.
876
Index terms
Links
Extruder (Continued) twin-screw Extrusion
587 2
3
aspects affecting thermoforming
583
blown film
584
cost
508
CPET
659
discussion
583
economic penalty
583
foam
587
property penalty
583
residence time
583
sheet die, heat buildup owing to shear
601
sheet die, pressure in
598
661
sheet die
587
598
599F
single-screw
583
thickness range
585F
584T
thin sheet
584
twin-screw, discussion
604
606
607
605T
605F
606F
twin-screw, types Extrusion-see also Sheet, extrusion
F Failure criteria
472
FEA-see Finite Element Analysis Female forming-see Vacuum forming FEP
243
fluoropolymer, infrared absorption
92F
mold release
457
mold surface
434
255F
This page has been reformatted by Knovel to provide easier navigation.
600F
877
Index terms
Links
Fiber effect on tensile strength
210
reinforcing
679
Fiber-forming polymers, trimming
285
Fiber spinning
263
Filler, effect on tensile strength
210
Film, definition
680F
12
Film resistance coolant
287F
free surface
287F
Finger strain tensor
241
Finite difference equation model
659
Finite Element Analysis
510 525F
522 526F
523 527
523F 527F
comparison with data
522F
527
528F
529F
541
542F
543
543
544F
computational time, discussion
522
discussion
521
Galerkin weighted residual
523
internal energy function
523
K-BKZ model
539
mesh selection
524
Newton-Raphson iteraton
523
node
521
plug assist
524
plug design
539
sheet removal from plug
541
stability
524
3-dimension
521
2-dimension
521
web prediction
525F
526
This page has been reformatted by Knovel to provide easier navigation.
524
544
878
Index terms
Links
Foam architecture
57f
bubble growth discussion
722
cell architecture
722
723
723F
724F
724E
725F
depth of draw in
735
736
737F
forming equipment
736
738
forming pressures for
736
forming window for
733
heating of
726
internal cell gas pressure in
731
molecular diffusivity in
731
nucleants for
722
723T
724
733E
731F
732F
733
radiant transmission, Rosseland approximation
727
radiant transmission through
726
727
729
730E
secondary expansion in
733
734
734F
735
736F thermal conductivity of thermal diffusivity in Foam sheet
726
726E
729F 556
discussion
12
Food containers
16
convenience
3
Forging, competition
28
Form-fill-seal
16
discussion
12
7
7T
Forming billow
20
20F
billow drape
20F
20
billow snap-back
25T
This page has been reformatted by Knovel to provide easier navigation.
735F
879
Index terms
Links
Forming (Continued) billow vacuum
20
21F
cell architecture, discussion
722
CPET
649
651
26
27F
25T
125
drape, plug-assisted
22
23F
embossed sheet
26
filled polymer
649
flocked sheet
25
diaphragm drape
679
foam
649
foam sheet, discussion
722
free blow
18F
18
immersion
22
24F
matched mold metallized sheet
25T 25
multilayer
649
687
mulilayer, trapped air
740
740F
plug-assisted
19
plug-assisted reverse draw
22
24F
polyolefin foam sheet
722
PP, discussion
709
710
pressure
18F
18
pressure, CPET
676
pressure, discussion
687
671
36
pressure, during start-up
768
pressure, effect on detail
674
675
pressure, heavy-gage
677
678
678F
pressure, plug-assisted
19
22
23F
pressure, PP
675
676
676F
pressure, safety concerns for
675
678
pressure, thin-gage
675
This page has been reformatted by Knovel to provide easier navigation.
674
880
Index terms
Links
Forming (Continued) pressure, with prestretching
677
pressure-bubble immersion
22
24F
675
677
pressure box for printed circuit board sheet
26
printed sheet
26
PS foam sheet
722
PSA-applied sheet reinforced polymer, problems reinforced polymer safety concerns slip
25 685
686
687
26
649
679
683
685F
686F
707
708
37 25T
splitty plastic
26
start-up, heavy-gage
766
start-up, thin-gage
766
trapped sheet
127
127F
twin-sheet
649
696
twin-sheet, air injection
701
702F
twin-sheet, competition to
696
697T
27
27F
twin-sheet, heavy-gage twin-sheet, historical
696f
twin-sheet, products of
696
twin-sheet, seal area, adhesion
704
704T
twin-sheet, seal area, compressive force
707
707F
twin-sheet, seal area, design
707
709F
702 705T
702F
703
703F
twin-sheet, simultaneous
701
701F
702F
705T
twin-sheet, tack-off
710
710F
twin-sheet, thin-gage
28
28F
twin-sheet, sequential
vacuum
683F
708F
701
25T This page has been reformatted by Knovel to provide easier navigation.
704
881
Index terms
Links
Forming (Continued) vacuum, plug-assisted
22
22F
25T
vacuum snap-back
21
21F
25T
very thin sheet
26
Forming process troubleshooting, discussion troubleshooting
769 773T
783T
Forming station ancillary
31
discussion
31
drive
31
drive units pressure Forming temperature lower normal
32T 31
32
69T
230F
233
115
116
116F
117F
118F
119F
120F 116F
117F
118F
116F
117F
118F
682
682F
115
116
119F
120F
range
8
upper
115
116
119F
120F
198
222E
definition
115
256
effect of fillers on
679
680
Fouling factor, defined
289
289T
165 171E 306F
168 174 315f
169F 174F 444E
170 188 445F
170E 306 661
3
338
355
451
456
Forming window
Fourier number
FPVC
545
This page has been reformatted by Knovel to provide easier navigation.
882
Index terms Fracture energy defined
Links 350E 348
Fracture mechanics, in trimming
340
Fracture toughness, defined
349
Free surface cooling
285
Friction factor
421F
defined
294
Funnel test
260
prior to start up
755
755
G Gamma gage, sheet thickness GEA
601 496F
GEA-see also Geometric Element Analysis Gear pump Geometric Element Analysis
594
595
595F
596
596F
496F 515
513 515F
513F 516F
514
514E
comparison with data
522F
converging wall
516F
517
518
design protocol
515
520
521
elements of
516F
517
one-side lay-down
516F
518
parallel wall
516F
517
plug design
536
shallow part
519
519F
sheet removal from plug
541
543F
three-dimensional corner
516F
517
two-dimensional corner
516F
517
519
520F
This page has been reformatted by Knovel to provide easier navigation.
883
Index terms Glass transition temperature
Links 56
69T
62
65
66
66F 199f 231
67F 202 286
78 207 358
83 217
199 220E
effect of blowing agent on
731
733
Gray body correction factor
136E
definition
135
Grooving
367
H H:D
488
496
496F
practical limit
565
truncated cone
574
575
5
28
56
58
109
109E 231F 349 451
118 246F 355 651
119E 285 369
189E 338 373E
207 340 441
139
139F
139
140E
HDPE
Heat balance, cyclic Heat capacity defined
302 107F 82
Heat capacity-see also Polymer heat capacity, Polymer enthalpy Heat conduction equation
305
mold, cooling
308
Heat distortion temperature
69T
Heat flux
122
constant, application
138
constant, approximation
167
constant
127
This page has been reformatted by Knovel to provide easier navigation.
884
Index terms
Links
Heat flux (Continued) definition
112
113F
Heat removal from part cyclical transient
287
steady state
287
288
Heat transfer, transient computer model
314
finite difference
315
Heat transfer coefficient
660
661
111
124
124T
124E
145
146 148T 298E
146T 149F 300
147 150 305
147E 288f 309T
148E 294
interfacial
290
291T
overall
288
radiation, definition
126 146E
147E
661
142T
144T
151
convection
radiation
126E
144
interfacial
289
290F
overall
288
292E
Heat transfer resistance
Heater edge loss
154
Heater ceramic
30
efficiency examples
140
141F
152
153T
128
gas-fired, catalytic
30
gas-fired, direct
30
gas-fired, indirect
30
halogen
30
This page has been reformatted by Knovel to provide easier navigation.
885
Index terms
Links
Heater (Continued) heavy-gage formers, discussion
45
lamps
30
local energy input
155
46 155F
157F
158F
150E
150F
151
151E
152F
spacing
162
163F
start-up conditions for
765
117
168
171T
173E
161
162F
metal plate
30
metal resistance rod
29
nickel-chrome
29
pattern, during start-up quartz
767 30
rod
Heating energy efficiency heavy-gage, guidelines heavy-gage pattern, discussion pattern
108T
110
193 14 174E 106 160E
thin-gage, guidelines
193
thin-gage
116
zone, discussion
106
164
zone-see also Pattern heating, Zonal heating Heating methods, summarized
29
Heating oven, discussion
29
Heating time Heavy-gage, definition Heavy-gage thermoforming, in-line
149F 12 13F
Heavy-gage thermoforming-see also Cut-sheet forming
This page has been reformatted by Knovel to provide easier navigation.
886
Index terms HIPS
Links 72F
135
210
227
338
840T
841T
441 HIPS, sheet appearance of
642
HIPS/PVDC lamination
628
Hooke's law, defined
202
Hookean
202
Hot-melt adhesive Hot strength, defined Hyatt, J.W.
203F
28 208 3
Hyperelastic analysis, defined Hyperelasticity
235f 205
I Impact forming Index of refraction, in orientation
28 621
Inflation effect on rate of return
819
sheet
215
tube
215
Infrared radiant heating
13
Infrared wavelength range
88
216
216F
88T
Injection molding comparison
2
competition
11
competition to thermoforming
835
836
838T
842F
841
842T
foam
696
697T
gas-assisted
696
697T
Interdigitation, as a forming method
738
739
739F
Interest on money, simple
813
Interfacial resistance, computer model
318
319T
319F
This page has been reformatted by Knovel to provide easier navigation.
740F
887
Index terms IPS
Links 754
IV-see PET, intrinsic viscosity of
K K-BKZ equation
741
K-BKZ model-see also Finite Element Analysis K-BKZ model Keratin
539
541
542F
543
7 58 246F
25 71 352
51 168 456
55 232F
806
806F
807
807E
3
L Lake, causes of
565
Laminar flow, coolant
405
Laminated honeycomb
696
Laminated object manufacturing-see Rapid prototyping Latex, solution casting
585
Law of mixtures linear, defined
547
linear, property type
548T
logarithmic, defined
547
logarithmic, property type LDPE
Learning curve, discussion
548T
Learning curve characteristic-see Learning curve Linear draw ratio-see also Draw ratio Liquid viscoelastic
205
This page has been reformatted by Knovel to provide easier navigation.
56 232E
888
Index terms
Links
Liquid (Continued) viscous
201
LLDPE
25
LLDPE as nucleant in CPET
654
LOM-see also Rapid prototyping LOM
478
Loss factor-see Loss tangent Loss tangent, defined
223
Lumped-parameter, approximation
127
164
165T
166E
19F
19
557
166F
659 in cooling
304
model, boundary conditions on
661
M Machinery, innovations in
11
Male forming-see Drape forming Matched die molding
14
Material balance
749F
Maxwell-Voigt viscoelastic model
223F
224F
22
223F
233
234F
67F
78
199f
359
364
Maxwell viscoelastic model Melt strength, hot
220
Melting temperature-see also Melting point Melting temperature
66
Metal forming, competition
28
Microcrack
352
formation
339
generation
285
Moat design
557
558F
458
458F
This page has been reformatted by Knovel to provide easier navigation.
202
889
Index terms Mode I fracture
Links 352
354F
347
349F
Mode II fracture, defined
347
349F
Mode III fracture, denned
347
349F
defined
Modulus creep
267T
flexural, hot
211F
212F
loss
226F
227F
228F
682
683
loss, defined
223
reindorced polymer
680
storage, defined
223
684
685F
Moisture adsorption
617
effect on sheet quality
640
equilibrium content
617
619F
383
401
Mold aluminum aluminum, properties
402
402T
cooling on non-metallic
309
311E
discussion
383
female, draft angle
558
561
562F
fiberboard
386
387
387T
388F
flipper in
452F
hinge in
452
452F
453
453F
male, draft angle
558
561
562F
materials, discussion
383
metal, other
403
nickel
400
non-metallic
309
311E
plaster
383
384
plaster, finishing
389
387
This page has been reformatted by Knovel to provide easier navigation.
388T
389
890
Index terms
Links
Mold (Continued) plaster, reinforcement
389
plaster, repair
389
plastic
383
plastic, coolant channel
397
plastic, epoxy
394
plastic, gel-coat, recipe
389f 384 395
391T
plastic, gel-coat
390
plastic, internal support
392
393F
plastic, polyurethane
395
396T
plastic, reinforcement
390
plastic, SMC
400
plastic, unsaturated polyester resin, recipe
390
production, discussion
400
prototype
384
service requirements
383
Mold, steel surface finish surface texture swing in
403T 383
402
403
433
434
434F
435F
436
436E
436
437
438
453F
white metal
397
white metal, coolant channel
399
white metal, properties
399
white metal, spray-up
397
wood
383
wood, finishing
386
wood, properties
399F
399T
white metal, reinforcement
coolant
394F
392T
plastic, unsaturated polyester resin
steel, properties
389
398
398F
386f
385T 384
This page has been reformatted by Knovel to provide easier navigation.
434f
435
891
Index terms
Links
Mold design cammed section
454
collapsing core
454
included hinge
455F
moving elements, discussion
454
pressure forming
678
reinforcement, encapsultaion of
453
slide
454
stripper plate/bar
455
undercut, discussion
452
unscrewing section
454
Mold mark
679
679T
456
456F
457F
676f
Mold materials coefficient of thermal expansion
86T
density
86T
heat capacity
86T
thermal conductivity
86T
thermal diffusivity
86T
Mold protocol, during startup
759T
Mold release discussion
456
permanent
457
temporary
457
Mold surface, discussion
383
Mold temperature
69T
Molecular weight distribution
61F
discussion
62
effects on
62
457
Mooney-Rivlin model
205
237f
239F
524f
Mooney model
237
238T
258E
278A
Morphology, effect of extrusion on
583
This page has been reformatted by Knovel to provide easier navigation.
892
Index terms mPPO
Links 77
sheet appearance of
642
foam
722
Multi-cavity forming
614
753
695
696
696E
14
Multilayer sheet delamination, causes of
644
delamination of
694
discussion
623
energy absorption in
688
689
689F
690
690F
forming of
687
691
692
694
695F
forming window for
691
691F
692
heating of
687
688
688F
lamination, measurement of
643
lamination, quality of
643
thin-gage, trapped air
740
tie layers in
623
two-flux method
689
via coextrusion
624 630
626 631
626F
627F
628
via lamination
628
630
630F
631
Murphy's oil soap
388
388f
244
245
740F
N Neck-down
208
Necking
230
Necking-see also Yield as localized drawing during forming Neo-Hookean
676f 676 249
model, denned
236
238T
model
237
238T
This page has been reformatted by Knovel to provide easier navigation.
248f
893
Index terms
Links
Neo-Hookean (Continued) modulus
252E 278A
response
206T
Net Present Worth
816 820T 837T
Newton's law
205
Newtonian viscosity
205
Nibbling, defined
355
Nibbling force
253
253E
254E
256
817 828T
818 829T
818E 830F
819T 833E
217
233
63 369
78 451
81
92
356E
Normal stress difference
233
Notch sensitivity in formed part
565
NPW-see Net Present Worth Nusselt number defined
373 298
Nylon
58 352
Nylon-see also PA, PA 6, PA 66 glass-reinforced
2
infrared absorption
90F
plug material
439
441
Nylon-6
243
256F
Nylon-66
243
257F
O Off-gassing dissolved gases
199
lubricant
199
moisture
199
processing aid
199
This page has been reformatted by Knovel to provide easier navigation.
894
Index terms Ogden model
Links 205
239
240
352
441
244
524f
757
758
539 OPP-see also Oriented PP OPP
25
OPS-see also Oriented PS OPS
25
Orientation biaxial
620
biaxial, blown film
620
biaxial, tentering
620
birefringence in
621
cross-direction
620
621
machine-direction
620
621
sheet, cross-direction
583
608
sheet, machine-direction
583
608
sheet, start-up
755
sheet, test for
637
638
756
specification of
637
638
639
58
352
621F
Oriented HDPE, properties
70T
PET, properties
70T
PMMA, properties
70T
PP, properties
70T
PS, properties
70T
Ovenable containers
3
P PA
26
moisture sensitivity of regrind
545
notch sensitivity
565
PA-6-see also Nylon 6
This page has been reformatted by Knovel to provide easier navigation.
451
895
Index terms PA-6 PA-66 PAN
Links 2
243
256F
753
243
257F
650
753
571F
572
572E
224 368
226F 369
28
Part design dimensional tolerance on
565
edge, discussion
569
edge, heavy-gage, adhesive trap
570F
edge, heavy-gage
569
edge, twin-sheet
569f
guidelines, general
555
guidelines, prestretch
559
guidelines, process
556
guidelines
561
rim, discussion
569
rim rolling
569
570
573
573E
slot formation
568
568F
source of performance on variability
573
577
stiffening elements
566
567F
Part removal system, discussion
471
Pattern heating, screen material
557
Payback period
818
819
PBT
243
258
617
618T
243
258
58 338 792E
127 339
PBT PC
568
29
Parts design, discussion
drying of
569F
moisture sensitivity of regrind
545
stresses in formed
565
182 352
This page has been reformatted by Knovel to provide easier navigation.
896
Index terms
Links
PE-see also HDPE, LDPE PE
2
55
243
573
791
58 92 250F 753
64 96F 349 755
Penetration model, described
310
Performance criteria, discussion
471
PET
26 65F 182 352 791
28 73 199 573
51 78 243 614
drying of
617
618T
620F
infrared absorption
92F
moisture in sheet
640
moisture sensitivity of regrind
545
multilayer sheet
623
sheet appearance of
642
static charge on
642
stresses in formed
565
Pigment, infrared effect
185
187F
534
535F
536F
512
512F
Plane strain analysis stretching
540F
Plate, definition Plate buckling, discussion Plug
12 511 14
articulated bullet-nosed
383
447F
446F
coolant design
441
444E
effect on textured sheet
560
560F
flat
446F
metal
441
plastic
441
This page has been reformatted by Knovel to provide easier navigation.
897
Index terms
Links
Plug (Continued) prestretch depth ring
560
560F
446F
syntactic
559
temperature control on
764
thin-gage, discussion
51
wood
386
Plug assist
25
during start-up
441
767
Plug assist-see also Plugs Plug characteristic
439
Plug design
445
446
447T
448
blunt-nosed
529 543
530 544F
differential pressure effect
540
542F
439
discussion
446F
447
447F
530F
531
532E
527
530
530F
531
536F
531F Finite Element Analysis
539
force balance
533
534
534E
535F
Geometric Element Analysis
536
537F
538F
539F
Geometric Element Analysis-see also Geometric Element Analysis, Plug design shape
507
spherical
531F
533
tapered
540
542F
temperature
507
Plug mark-off
434
Plug material
439
properties
440T
Plug temperature
441f
543
559
This page has been reformatted by Knovel to provide easier navigation.
898
Index terms PMMA
Links 2
3
7
8
58
70 96F 218 249F 791
74 127 219E 338
78 176T 227 339
84 182 239F 344
95F 185F 243 349
63 754
77 755
92
biaxially oriented, properties of
622T
drying of
618T
infrared absorption
91F
molecular weight
62
notch sensitivity
565
stresses in formed
565
PMMA/ABS lamination
628
Poisson's ratio defined
202
in trimming
347
348T
Polyamide biaxially oriented, properties of
622T
drying of
617
618T
extrusion
584
594
moisture in sheet
640
Polyazole, solution casting
585
Poly butadiene, mold surface
434
Polycarbonate
58
drying of
617
infrared absorption
91F
moisture in sheet
640
Polyethylene
56 224
biaxially oriented
620
extrusion
584
618T
58 228F
This page has been reformatted by Knovel to provide easier navigation.
899
Index terms
Links
Polyethylene (Continued) infrared absorption
90F
low-density, extrusion of
594
molecular weight Polyethylene terephthalate
61
62F
58
63
594
596
610
Polyethylene terephthalate-see also PET, CPET extrusion of regrind property loss Polyimide
546T 78
infrared absorption
92F
solution casting
585
Polyisobutylene
65
243
259
66F
260F
109
437f
Polymer absorption bands
94T
addition, chemical structure
59T
addition
57
aliphatic
58
amorphous
63
amorphous, modulus
57F
amorphous, phase diagram
68F
amorphous, start-up on
753
amorphous, stress-strain
79F
amorphous, thermoforming window
81
aromatic
58
chain mobility, discussion
70
comparative size condensation condensation, chemical structure crosslinked, discussion crosslinked, modulus
56T 58 60T 56 57F
This page has been reformatted by Knovel to provide easier navigation.
265
265F
900
Index terms
Links
Polymer (Continued) crystalline
63
crystalline, modulus
57F
crystalline, phase diagram
68F
crystalline, sag
451
crystalline, start-up on
753
crystalline, stress-strain
80F
crystalline, thermoforming window
81
definition
55
density
110
enthalpy
82F
filled, start-up on
754
gas permeation resistance, discussion
72
heat capacity, defined
82
109
82F
heat capacity
83T
85T
infrared-transparent
182
183F
infrared absorption
89T
infrared spectra
87
laminate, discussion
78
modulus
79F
molecular weight, definition
58
molecular weight, discussion
55
molecular weight, number-average
58
molecular weight, weight-average
58
orientation TOT orientation, properties
70
processing characteristics, summary
97T
radiation absorption characteristics
132T
reinforced, start-up on
754
specific heat
110
steric hindrance
71
stress-crack resistance, discussion
72
71T
This page has been reformatted by Knovel to provide easier navigation.
901
Index terms
Links
Polymer (Continued) thermal conductivity
85T
thermal properties of
110
thermoplastic, discussion
55
thermoset, definition
55
vinyl
58
110
Polymer adduct
74T
blowing agent
77
discussion
74
fiber reinforcement
77
77T
filler
76
76T
plasticizer
74
Polymer blend, discussion
74
Polymer copolymerization discussion
73
Polymer crystallinity Avrami
65
effects on
63
Polymer crystallization, half-time
64
Polymer crystallization rate
64T
Polymer foams
57f
Polymer morphology, discussion Polymer properties, start-up
65F
63 754
Polymethyl methacrylate cell-cast
587
moisture in sheet
640
Polyolefin
84 545
drying of
617
foam
229F
232T
12
Polyphenylene oxide-see also mPPO This page has been reformatted by Knovel to provide easier navigation.
372
441
902
Index terms Polyphenylene oxide Polypropylene
Links 74 58 273E
63
extrusion
584
594
infrared absorption
90F
71
73
227
430E
456
456F
Polypropylene-see also PP
Polystyrene
65
Polystyrene-see also PS drying of
618T
extrusion
584
foam, lamination of
628
infrared absorption
90F
multilayer sheet
628
Polyurethane crosslinked
57
mold surface
434
thermoplastic, infrared absorption
91F
thermosetting
285
Polyvinyl acetate
74
Poly vinyl chloride-see also PVC, RPVC, FPVC calendering
584
flexible
584
rigid
584
rigid, extrusion of
594
596
352
441
429
430F
POM
587
Poppet valve-see also Vent, poppet valve Poppet valve Porous metal, manufacturer
424T
This page has been reformatted by Knovel to provide easier navigation.
903
Index terms PP
biaxially oriented biaxially oriented, properties of
Links 3
5
13
18
19
25 65 234 340 451 610F 791
28 78 243 349 456 610f
38 81 247F 355 545 614
51 84 248F 369 573 755
58 168 285 441 610 773
294
295
295T
436 438E
437
437F
438
438F
555
557
565
14
15
620 622T
PP/PVDC lamination
628
PPS
368
Prandtl number
373
defined Pressure, effect on surface texture inflation
249
Pressure forming discussion during start-up
768
textured surface
561
Pressure system, discussion
29
Prestretching
503
air pressure
506T
discussion
505F
14
29
double-bubble
461
461F
restraint
461
461F
36
37
gross
799T
800
net
799T
800
Process control, discussion Profit
801T
This page has been reformatted by Knovel to provide easier navigation.
904
Index terms Profitability, discussion
Links 814
815
549
549T
Profitability index-see Rate of return, discounted cash-flow Property value loss declining, property type
548
offset
548
power-law proportional, property type
552E
5 70 95F 221E 339 369
8 73 96F 224 344 379
14 74 135 243 349 573
28 77 182 251F 355 791
19
78
548T 548 548T
proportional
547
protocol for determining
551
Prototyping, objective of
551T
548T
offset, property type power-law, property type
550T
552
486
Prototyping, rapid-see Rapid prototyping Prototyping PS, biaxially oriented, properties of PS
478 622T 3 58 84 210 338 368
PS-see also HIPS biaxially oriented foam
620 12
notch sensitivity
565
sheet appearance of
642
static charge on
642
stresses in formed
565
This page has been reformatted by Knovel to provide easier navigation.
905
Index terms PTFE
Links 80
89
349
369
infrared absorption
93F
modulus
80F
mold release
457
mold surface
434
plug material
439
sag band coating
451
PUR Foam
210
243
254F
81F
441
27
Purchase order, importance of PVC
477 2
3
5
8
14
25 72 207 244F 267T
30 74 214 245F 441
58 84 227 254E 753
65 89 239 255E 754
71 182 243 262F 791
617
618T
PVC-see also PFVC, RPVC drying of glass transition temperature
75
infrared absorption
91F
plasticizer addition
75F
sheet appearance of
642
PVC/PMMA
176T
lamination
628
multilayer sheet
623
PVDC
28
78
Q Quality, thin-film
587
This page has been reformatted by Knovel to provide easier navigation.
906
Index terms
Links
R Radiation black body, definition
129
130
130F
131
131E
131T
132T
133T
133E
134E
13
111
111F
128
gray body, definition
134
135
135F
infrared
111
128
129
Radius, design
459
460
460F
Rapeseed oil, drilling
369
Rapid prototyping
395
487
layered paper molding
487
488
layered sheet molding
487
489F
polymer droplet
488
powder fusion
487
489F
stereolithography
395
487
489F
816
824
825
816
817
818
818E
819T
820T 833E
821T 837T
828T
829T
830F
184
184E
38f
478
585
cascade, discussion
553
554
554F
discussion
544
boundary condition definition
Rate of return discounted cash-flow
effective discounted cash-flow
123
129T
819
true-see Rate of return, discounted cash-flow Redistribution polymer sheet, advantages of
512
polymer sheet
471
Reflectance
183
Refrigerator liners Regrind
3
Regrind-see also Trim
This page has been reformatted by Knovel to provide easier navigation.
554E
907
Index terms
Links
Regrind-see also Trim (Continued) economics
545
fiber-reinforced polymer
545
generation of
461
material property loss during
545
546T
mechanical property loss, theory
579A
579F
580A
steady-state
579A
579F
580A
cascade
553
554
554F
554E
closed-loop
546
547F
cost of
508
economics of
484
485E
steady-state
484
485E
616
617E
Reprocessing 555
Residence time extruder
614
mean
614
615E
plug flow
614
615E
Residence time distribution
615
616
616F
Residual stress
199
Retardation time
234
235E
235F
defined
234
Return on investment
815
816
Reynolds number
405
416F
294
294E
Rheology, defined
206
206f
Reometer, strain
214
215F
Rheometry, extensional
226
defined
419
Rim material amount, force balance effect on draw ratio Rim rolling
499F
500
502E
499
500
500E
450 This page has been reformatted by Knovel to provide easier navigation.
501F
502E
908
Index terms
Links
Risk factor, entrepreneurial
823
824
825
825E
Rivlin model
236
238T
239
240
240F
Rod heater, spacing
556
556F
3
13
15F
607
608
609F
ROI-see Return on investment Roll-fed forming-see also thermoforming categories Roll-fed forming Roll stack bank on configuration of
608F
cooling v. crystallinity
610
discussion
607
function
607
temperature effect
610F
609F
610F
610
42
43F
44F
four-station
42
44F
three-station
42
43F
11
28
835
836
838T
840T
841T
842F
841
842T
213 355 756F
229F 369
243 545
344 614
352 753
198 201F
199 221E
200
200F
269 274E
269F 277
270
272F
Rotary press
Rotational molding, competition RPVC
Rubbery sheet
201
S Safety, during start-up
765
Sag
51 201
as determined by photoelectric eye
765
catenary
199 276
This page has been reformatted by Knovel to provide easier navigation.
909
Index terms
Links
Sag (Continued) discussion
266
during start-up
765
initial, definition
267
initial
267F
268
268F
268T
270
270F
271
273F
274E
276
277
344
368
292F
293F
273E
parabolic polymer sheet
556
reinforced polymer sheet
556
temperature effect
275E
tensile, definition
268
Sag band, discussion
451
SAN
243
247F
Schmidt model
237
238T
Scrap
38f
definition
276E
478f
Scrapless thermoforming
3
Set temperature
286
Shape factor, cooling
289
Shear modulus, in trimming
347
291
Sheet custom size, economics
483
dimensional tolerance on
566
extrusion
2
3
specifications, discussion
633
634T
standard size, economics
483
virgin, defined
632
virgin + regrind, defined
633
637
Sheet appearance color
642
discrete marks
641
This page has been reformatted by Knovel to provide easier navigation.
910
Index terms
Links
Sheet appearance (Continued) discussion
641
effect of process on quality
641
surface marks
641
surface protection of surface texture
643f 642
Sheet characteristic, start-up
754
755
Sheet die, coextrusion
624
627F
Sheet dimension discussion
637
tolerance on
637
638E
638E
639
Sheet flatness, specification of Sheet handling
29
Sheet orientation-see Orientation Sheet quality discussion
632
effect of moisture on
640
start-up
755
Sheet squareness, specification of Sheet strength, hot
638E
639
271
Sheet texture by roll stack
607
processing effects on
642
Sheet thickness control by roll stack
607
die gap control of
602
monitoring
601
ultrasonic measurement of
643
Sheet transfer
604F
29
Sheet trimming deckles
610
611
612F
This page has been reformatted by Knovel to provide easier navigation.
911
Index terms
Links
Sheet trimming (Continued) discussion
610
611
dust
611
guillotine
611
razor blade
611
613F
discussion
461 464
462 464F
heavy-gage
461
optimization
461
thin-gage
463
Shift factor
181
Sheet utilization 462F 465E
182
Shift factor-see also W-L-F equation Shower stalls
3
Shrinkage amorphous polymer
563
constrained, defined
322
constrained, discussion
324
constrained, effect on draft angle
329
329E
constrained, rate of cooling effect
326
328F
constrained, stress relaxation effect
326
327E
crystalline polymer
563
discussion
320
mold temperature effect on
557
thermoformable polymers
325T
unconstrained, defined
322
unconstrained, effects on
323
Shuttle press Signs
33F
42
43F
3
Silicone rubber, mold surface
434
SLA-see Rapid prototyping, Stereolithography
This page has been reformatted by Knovel to provide easier navigation.
462E
463E
912
Index terms Slotting
Links 367
Smoke-see also Off-gassing Smoke
198
199
Soaking time-see Equilibration Solid elastic, rubber elastoplastic Solution casting, film
201 202f 585
Specific heat-see also Heat capacity, Enthalpy Specific heat
107F
Specific volume temperature-dependent Specific volume
320
320f
199F
Spring-back, reinforced sheet
568
Stanton number, defined
294
295
Start-up costs
752T
discussion machine, protocol
768 759T
mold, protocol
758
759T
760
on virgin sheet only
768
polymer
753
protocol, polymer
753
temperature monitoring
764
765
766
Static charge, discussion
642
643
643f
Static mixer
594
595
595F
Steel rule die
331
331F
332F
cutting edge
361
361F
discussion
359
hardening
360
mounting
363
363F
This page has been reformatted by Knovel to provide easier navigation.
596
596F
913
Index terms
Links
Steel rule die (Continued) resharpening
362
Stereolithography
395
478
STP-see Scrap less thermoforming STP
28
Strain defined
202
engineering
204
Hencky
204
true
204
ultimate
213
Strain energy function coefficients defined
239T 235
Strain hardening
214
Strain invariants, Wagner form
241
Strain rate
209
226 229F
234
265
209
210
212
228
228F
230F
240
243F
244F
245F
Strain recovery, discussion Stress defined
202
engineering
204
true
204
Stress-strain curve
214
curve, ductile
209F
data
242
242F
engineering
204
205
242
243
isochronous
246F true
205
This page has been reformatted by Knovel to provide easier navigation.
914
Index terms
Links
Stress-strain (Continued) uniaxial
244
Stress-strain-rate of strain
198
226
Stress concentration factor
350T
350F
Stress intensity factor
351T
352
defined
233
349
Stretch factor-see Draw ratio, areal Stretching, biaxial, equal
236
237
207F 226
208 228F
215 278A
216
216F
208 237
208F
226
228
236
227F
228F
Stretching, biaxial-see also Deformation, biaxial, Extension, biaxial Stretching, biaxial Stretch, uniaxial-see also Deformation, biaxial, Extension, biaxial Stretching, uniaxial Stretching-see also Deformation, Elongational Stretching
202
Stripper plate
455
discussion
51
Surge tank
33
discussion
34
32
Swimming, sheet
198
199
Syntactic foam, plug material
439
441
properties
442T
T Take-up roll, discussion
611
613F
613E
Tan δ
224
225F
226F
defined
223
Tan δ-see also Loss tangent This page has been reformatted by Knovel to provide easier navigation.
915
Index terms Temperature, thermal imaging
Links 764
Temperature measurement infrared
30
thermistor
30
thermocouple
30
Temperature monitoring during start-up
764
765
infrared
764
766
209 213F
210 214F
ASTM
475
476
criteria
474
475
dynamic mechanical
222
224
part performance effect
473
product
473
Tensile strength, hot
766 210F 215
211F
212
840T
841T
Testing
Textured sheet forming Thermal conductivity, discussion Thermal diffusivity definition
562 84 85T 84
Thermal expansion coefficient
476
87
87
Thermal expansion coefficient-see also Coefficient of thermal expansion Thermoforming applications
7
7T
competition
835
836
838T
842F
841
842T
competition to, heavy-gage
834
competition to, thin-gage
833
continuous sheet, definition
13
cut-sheet, definition
13
834
This page has been reformatted by Knovel to provide easier navigation.
916
Index terms
Links
Thermoforming (Continued) definition
2
description history
106 2
3
machinery, direct contact
51
machinery, heater discussion
51
machinery, heavy-gage check-list
38
39T
machinery, heavy-gage dual-oven shuttle press
42
43F
machinery, heavy-gage shuttle press
42
43F
machinery, heavy-gage rotary press
42
43F
machinery, overview, discussion
29
30T
machinery, pin-chain rails
50
51
machinery, thin-gage check-list
46
46T
machinery, vertical, discussion
51
market growth
5
6F
markets
4
9T
polymers converted in
5T
6T
roll-fed, definition
13
thin-gage, drink cup
50F
thin-gage, form-fill-seal
50F
window, discussion
4T
44F
81
Thermomechanical degradation extrusion effect
545
regrind
545
thermoforming effect
545
Thin-gage, definition
12
Thread, formed single-sheet
563
564F
twin-sheet
562
564F
TMA-see Analysis, thermomechanical
This page has been reformatted by Knovel to provide easier navigation.
917
Index terms
Links
TPE
456
TPO
349
Transmissivity, discussion
92
Transmittance
183
Trapped sheet forming
25T
Treloar, L.R.G.
257
Trim
508
545
definition
478
478f
determination of extent of
479
479F
source of
478
479
25
480E
481E
482E
359
362F
364
Trim-in-place-see Trimming, in-mold Trim dies, heated
359
Trim dust
285
elimination of
339
643
Trim hairs-see also Angel hair Trim hairs
285
Trim press, discussion Trim region, accuracy factors
29 336
Trimming abrasion cutting
335
336F
abrasive wheel
344
345F
346T
336F
337F
automatic, heavy-gage
15
compression
334
defined
329
devices
329
dinking
38
discussion
15
forged die
367
heavy-gage
331
in-line
38
330F 38
285
51
This page has been reformatted by Knovel to provide easier navigation.
918
Index terms
Links
Trimming (Continued) in-mold
38 383
in-situ
51
333
334F
344
344E
364
365F
38
machined die
367
manual, heavy-gage
15
manual
38
microfibers multi-axis router
340 38
multiple-edged tool
342
342F
notching
363
364F
polymer response to
338
338F
post-molding operations
333
punch-and-die
334
335F
registry
337
337F
router, multi-axis
332
332F
routering
335
336F
shear
334
336F
337F
single-edged tool
340
341
341F
steel-rule die
38
summary
376
377T
378T
tabbing
363
364
364F
thermal
335
336F
thin-gage
333
water-jet, heavy-gage
15
Trimming press, in-line
285
Troubleshooting, forming process
769
heavy-gage
774T
thin-gage
784T
772
Troubleshooting, sheet extrusion
769
769T
Trouton viscosity
205
233
773T
379
783T
This page has been reformatted by Knovel to provide easier navigation.
335F
919
Index terms Tub surrounds Turbulent flow, coolant Twin-sheet formers
Links 3 405 43
44
Twin-sheet forming air temperature during
557
blow pin location
559
Twin-sheet thermoforming-see also Forming, twin-sheet
U UHMWPE, molecular weight
62
62F
UHMWPE
56
89
562
563F
761
762
21
560
17F
17
Undercut design
354
369
762F
763
763F
V Vacuum, during start-up Vacuum box Vacuum forming definition
14
during start-up
766
schematic
16F
Vacuum hole-see also Vent hole dimension
558
location
558
Vacuum pressure norm
559F
556
Vacuum pump discussion
32
specifications
36T
Vacuum system
411F
412F
411
412
413
413E
414
414E
415
416
416F
417
design
This page has been reformatted by Knovel to provide easier navigation.
920
Index terms
Links
Vacuum system (Continued) design criteria
33
34E
35E
discussion
32
evacuation rate
33
pressure drop
33
recovery time
34E
34
Vent, poppet valve
429
430F
Vent, porous plug
429
429F
Vent, slot
427
427F
428
428F
418E 422E 425E
420 423E 426
420E 423 426E
421 425F 427
432
432F
430E
Vent-see Vent hole, Vent, slot, Poppet valve Vent hole
383
design
417 422 425
discussion
411
fiberboard
386
388F
location
430 433F
431
431F
plaster
388
154
154E
vacuum system wood
33 386
View factor
138
definition
152
Viscoelastic linear
222
liquid
205
model
240
model, fading memory
241
solid model
260
Viscoelasticity
242f
linear, defined
206
206T
This page has been reformatted by Knovel to provide easier navigation.
921
Index terms
Links
Viscoelasticity (Continued) nonlinear, defined
206
206T
elongational
217
217f
elongational, defined
205
Viscosity
extensional, biaxial
232T
264
extensional
231F
231
232F
Newtonian
205
non-Newtonian
205 218F
218T
shear
217f
shear, defined Visible wavelength range
205 88
88F
222
234F
W-L-F equation
181
181T
217
219
Wall thickness
211
253
508
509
effect on mold feature
561
561F
local
198
part, discussion
471
prediction, discussion
510
structural aspects of
511
Voigt-Kelvin viscoelastic model
W
Web-see also Trim Web definition
478
478f
formation, discussion
457
458
458F
458
458F
Web breaker discussion
457
material for
458
Web catcher, discussion
457
This page has been reformatted by Knovel to provide easier navigation.
510
922
Index terms
Links
Y Yield
230
Yielding, stress-strain
208
Young's modulus
208
defined
202
in trimming
347
209 348
Z Ziabicki equation
658
This page has been reformatted by Knovel to provide easier navigation.
