- Email: [email protected]
Injection Mold Design Engineering
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
David O. Kazmer
Injection Mold Design Engineering
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
David O. Kazmer Injection Mold Design Engineering
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
David O. Kazmer
Injection Mold Design Engineering
Hanser Publishers, Munich • Hanser Gardner Publications, Cincinnati
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
The Author: David O. Kazmer, P.E., Ph.D. Department of Plastics Engineering, 1 University Avenue, Lowell, MA 01854, USA Distributed in the USA and in Canada by Hanser Gardner Publications, Inc. 6915 Valley Avenue, Cincinnati, Ohio 45244-3029, USA Fax: (513) 527-8801 Phone: (513) 527-8977 or 1-800-950-8977 www.hansergardner.com Distributed in all other countries by Carl Hanser Verlag Postfach 86 04 20, 81631 München, Germany Fax: +49 (89) 98 48 09 www.hanser.de Your use of the information provided herein is conditioned upon your agreement, and the agreement of your employer or any third party to whom you provide information, to make use of these materials only in accordance with and subject to the following terms and conditions. The information provided herein is made available“as is” without warranty of any kind, either express or implied, including but not limited to the implied warranties of merchantability, fitness for a particular purpose, satisfactory quality, or noninfringement. We may in the future modify, improve or make other changes to the information made available. All the included information may include technical or typographical errors and we will not be responsible for any such errors. Any pricing and other information about products and services contained herein is not an offer to provide such goods or services. You agree not to bring any legal action against the author or publisher based on your use of the provided information. You agree to indemnify and hold the copyright holder and its affiliates, officers, agents, and employees harmless from any claim or demand, including reasonable attorneys‘ fees, made by any third party due to or arising out of your use of the provided information. The sole and maximum liability of the copyright holder, its affiliates and subsidiaries for any reason, and your exclusive remedy for any cause whatsoever, shall be limited to the amount paid, if any, for the provided information. Library of Congress Cataloging-in-Publication Data Kazmer, David. Injection mold design engineering / David O. Kazmer. p. cm. ISBN-13: 978-1-56990-417-6 (hardcover) ISBN-10: 1-56990-417-0 (hardcover) 1. Injection molding of plastics. I. Title. TP1150.K39 2007 668.4‘12--dc22 2007018765 Bibliografische Information Der Deutschen Bibliothek Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über abrufbar. ISBN 978-3-446-41266-8 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 wirting from the publisher. © Carl Hanser Verlag, Munich 2007 Production Management: Oswald Immel Typeset by Manuela Treindl, Laaber, Germany Coverconcept: Marc Müller-Bremer, Rebranding, München, Germany Coverillustration by David O. Kazmer, Lowell, USA Coverdesign: MCP • Susanne Kraus GbR, Holzkirchen, Germany Printed and bound by Druckhaus “Thomas Müntzer” GmbH, Bad Langensalza, Germany
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Preface Mold design has been more of a technical trade than an engineering process. Traditionally, practitioners have shared standard practices and learned tricks of the trade to develop sophisticated molds that often exceed customer expectations. However, the lack of fundamental engineering analysis during mold design frequently results in molds that may fail and require extensive rework, produce moldings of inferior quality, or are less cost effective than may have been possible. Indeed, it has been estimated that on average 49 out of 50 molds require some modifications during the mold start-up process. Many times, mold designers and end-users may not know how much money was “left on the table”. The word“engineering”in the title of this book implies a methodical and analytical approach to mold design. The engineer who understands the causality between design decisions and mold performance has the ability to make better and more informed decisions on an application by application basis. Such decision making competence is a competitive enabler by supporting the development of custom mold designs that outperform molds developed according to standard practices. The proficient engineer also avoids the cost and time needed to delegate decision to other parties, who are not necessarily more competent. The book has been written as a teaching text, but is geared towards professionals working in a tightly integrated supply chain including product designers, mold designers, and injection molders. Compared to most handbooks, this textbook provides worked examples with rigorous analysis and detailed discussion of vital mold engineering concepts. It should be understood that this textbook purposefully investigates the prevalent and fundamental aspects of injection mold engineering. I hope that Injection Mold Design Engineering is accessible and useful to all who read it. I welcome your feedback and partnership for future improvements. Best wishes, David Kazmer, P. E., Ph. D. Lowell, Massachusetts June 1, 2007
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XV 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Overview of the Injection Molding Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Mold Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Mold Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3.1 External View of Mold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3.2 View of Mold during Part Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.3 Mold Section and Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Other Common Mold Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4.1 Three Plate, Multi-Cavity Family Mold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4.2 Hot Runner, Multi-Gated, Single Cavity Mold . . . . . . . . . . . . . . . . . . . . . 11 1.4.3 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.5 The Mold Development Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.6 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2
Plastic Part Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 The Product Development Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Product Definition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Product Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Business and Production Development . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Scale-Up and Launch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.5 Role of Mold Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Design Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Application Engineering Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Production Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 End Use Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Product Design Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.5 Plastic Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Design for Injection Molding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Uniform Wall Thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Rib Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Boss Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Corner Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5 Surface Finish and Textures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.6 Draft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.7 Undercuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17 17 18 18 19 19 19 20 20 21 22 24 26 28 28 29 29 30 31 33 34 35
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
VIII
Contents
3
Mold Cost Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The Mold Quoting Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Cost Drivers for Molded Parts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Effect of Production Quantity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Break-Even Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Mold Cost Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Cavity Cost Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.1 Cavity Set Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.2 Cavity Materials Cost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.3 Cavity Machining Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.4 Cavity Discount Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.5 Cavity Finishing Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Mold Base Cost Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Mold Customization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Part Cost Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Mold Cost per Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Material Cost per Part. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Processing Cost per Part. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.4 Defect Cost per Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37 37 39 40 41 43 44 45 45 46 51 51 53 55 60 60 61 62 65 66
4
Mold Layout Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Parting Plane Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Determine Mold Opening Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Determine Parting Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Parting Plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.4 Shut-Offs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Cavity and Core Insert Creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Height Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Length and Width Dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Adjustments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Mold Base Selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Cavity Layouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Mold Base Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Molding Machine Compatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.4 Mold Base Suppliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Mold Material Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Strength vs. Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Hardness vs. Machinability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.3 Mold-Maker’s Cost vs. Molder’s Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.4 Material Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67 67 67 70 71 73 74 74 75 76 77 77 79 81 83 84 84 85 86 88 89
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Contents
IX
5
Cavity Filling Analysis and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.2 Objectives in Cavity Filling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.2.1 Complete Filling of Mold Cavities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.2.2 Avoid Uneven Filling or Over-Packing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.2.3 Control the Melt Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.3 Viscous Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.3.1 Shear Stress, Shear Rate, and Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.3.2 Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.3.3 Rheological Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.3.4 Newtonian Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.3.5 Power Law Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.4 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.5 Cavity Filling Analyses and Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.5.1 Estimating the Processing Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.5.2 Estimating the Filling Pressure and Minimum Wall Thickness . . . . . . 107 5.5.3 Estimating Clamp Tonnage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.5.4 Predicting Filling Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.5.5 Designing Flow Leaders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.6 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6
Feed System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.2 Objectives in Feed System Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.2.1 Conveying the Polymer Melt from Machine to Cavities . . . . . . . . . . . . 119 6.2.2 Impose Minimal Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 6.2.3 Consume Minimal Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 6.2.4 Control Flow Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 6.3 Feed System Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6.3.1 Two-Plate Mold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6.3.2 Three-Plate Mold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 6.3.3 Hot Runner Molds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 6.4 Feed System Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6.4.1 Determine Type of Feed System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 6.4.2 Determine Feed System Layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 6.4.3 Estimate Pressure Drops. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 6.4.4 Calculate Runner Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 6.4.5 Optimize Runner Diameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 6.4.6 Balance Flow Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 6.4.7 Estimate Runner Cooling Times. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 6.4.8 Estimate Residence Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 6.5 Practical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 6.5.1 Runner Cross-Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 6.5.2 Sucker Pins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
X
Contents
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
6.6
6.5.3 Runner Shut-Offs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 6.5.4 Standard Runner Sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 6.5.5 Steel Safe Designs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
7
Gating Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 7.1 Objectives of Gating Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 7.1.1 Connecting the Runner to the Mold Cavity . . . . . . . . . . . . . . . . . . . . . . . 161 7.1.2 Provide Automatic De-Gating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 7.1.3 Provide Aesthetic De-Gating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 7.1.4 Avoid Excessive Shear or Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . 162 7.1.5 Control Pack Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 7.2 Common Gate Designs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 7.2.1 Sprue Gate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 7.2.2 Pin-Point Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 7.2.3 Edge Gate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 7.2.4 Tab Gate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 7.2.5 Fan Gate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 7.2.6 Flash/Diaphragm Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 7.2.7 Tunnel/Submarine Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 7.2.8 Thermal Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 7.2.9 Valve Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 7.3 The Gating Design Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 7.3.1 Determine Type of Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 7.3.2 Calculate Shear Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 7.3.3 Calculate Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 7.3.4 Calculate Gate Freeze Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 7.3.5 Adjust Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 7.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
8
Venting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 8.1 Venting Design Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 8.1.1 Release Compressed Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 8.1.2 Contain Plastic Melt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 8.1.3 Minimize Maintenance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 8.2 Venting Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 8.2.1 Estimate Air Displacement and Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 8.2.2 Identify Number and Location of Vents . . . . . . . . . . . . . . . . . . . . . . . . . . 186 8.2.3 Specify Vent Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 8.3 Venting Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 8.3.1 Vents on Parting Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 8.3.2 Vents around Ejector Pins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 8.3.3 Vents in Dead Pockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 8.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Contents
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
9
XI
Cooling System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 9.1 Objectives in Cooling System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 9.1.1 Maximize Heat Transfer Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 9.1.2 Maintain Uniform Wall Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 9.1.3 Minimize Mold Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 9.1.4 Minimize Volume and Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 9.1.5 Minimize Stress and Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 9.1.6 Facilitate Mold Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 9.2 The Cooling System Design Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 9.2.1 Calculate the Required Cooling Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 9.2.2 Evaluate Required Heat Transfer Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 9.2.3 Assess Coolant Flow Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 9.2.4 Assess Cooling Line Diameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 9.2.5 Select Cooling Line Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 9.2.6 Select Cooling Line Pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 9.2.7 Cooling Line Routing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 9.3 Cooling System Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 9.3.1 Cooling Line Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 9.3.2 Cooling Inserts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 9.3.3 Conformal Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 9.3.4 Highly Conductive Inserts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 9.3.5 Cooling of Slender Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 9.3.5.1 Cooling Insert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 9.3.5.2 Baffles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 9.3.5.3 Bubblers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 9.3.5.4 Heat Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 9.3.5.5 Conductive Pin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 9.3.5.6 Interlocking Core with Air Channel . . . . . . . . . . . . . . . . . . . . . . 229 9.3.6 One-Sided Heat Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 9.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
10 Shrinkage and Warpage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 10.1 The Shrinkage Analysis Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 10.1.1 Estimate Process Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 10.1.2 Model Compressibility Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 10.1.3 Assess Volumetric Shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 10.1.4 Evaluate Isotropic Linear Shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 10.1.5 Evaluate Anisotropic Shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 10.1.6 Assess Shrinkage Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 10.1.7 Establishing Final Shrinkage Recommendations . . . . . . . . . . . . . . . . . . 245 10.2 Shrinkage Analysis and Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 10.2.1 Numerical Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 10.2.2 “Steel Safe” Mold Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 10.2.3 Processing Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
XII
Contents
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
10.2.4 Semi-Crystalline Plastics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 10.2.5 Effect of Fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 10.3 Warpage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 10.3.1 Sources of Warpage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 10.3.2 Warpage Avoidance Strategies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 10.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 11 Ejection System Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 11.1 Objectives in Ejection System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 11.1.1 Allow Mold to Open . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 11.1.2 Transmit Ejection Forces to Moldings. . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 11.1.3 Minimize Distortion of Moldings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 11.1.4 Actuate Quickly and Reliably . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 11.1.5 Minimize Cooling Interference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 11.1.6 Minimize Impact on Part Surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 11.1.7 Minimize Complexity and Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 11.2 The Ejector System Design Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 11.2.1 Identify Mold Parting Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 11.2.2 Estimate Ejection Forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 11.2.3 Determine Ejector Push Area and Perimeter . . . . . . . . . . . . . . . . . . . . . . 269 11.2.4 Specify Type, Number, and Size of Ejectors . . . . . . . . . . . . . . . . . . . . . . . 271 11.2.5 Layout Ejectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 11.2.6 Detail Ejectors and Related Components . . . . . . . . . . . . . . . . . . . . . . . . . 276 11.3 Ejector System Analyses and Designs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 11.3.1 Ejector Pins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 11.3.2 Ejector Blades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 11.3.3 Ejector Sleeves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 11.3.4 Stripper Plates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 11.3.5 Elastic Deformation around Undercuts . . . . . . . . . . . . . . . . . . . . . . . . . . 285 11.3.6 Core Pulls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 11.3.7 Slides. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 11.3.8 Early Ejector Return Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 11.3.9 Advanced Ejection Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 11.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 12 Structural System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 12.1 Objectives in Structural System Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 12.1.1 Minimize Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 12.1.2 Minimize Mold Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 12.1.3 Minimize Mold Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 12.2 Analysis and Design of Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 12.2.1 Plate Compression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 12.2.2 Plate Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 12.2.3 Support Pillars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Contents
XIII
12.2.4 Shear Stress in Side Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 12.2.5 Interlocks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 12.2.6 Stress Concentrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 12.3 Analysis and Design of Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 12.3.1 Axial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 12.3.2 Compressive Hoop Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 12.3.3 Core Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 12.4 Fasteners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 12.4.1 Fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 12.4.2 Socket Head Cap Screws. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 12.4.3 Dowels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 12.5 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 13 Mold Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 13.2 Coinjection Molds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 13.2.1 Coinjection Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 13.2.2 Coinjection Mold Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 13.2.3 Gas Assist/Water Assist Molding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 13.3 Insert Molds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 13.3.1 Low Pressure Compression Molding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 13.3.2 Insert Mold with Wall Temperature Control . . . . . . . . . . . . . . . . . . . . . . 351 13.3.3 Lost Core Molding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 13.4 Injection Blow Molds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 13.4.1 Injection Blow Molding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 13.4.2 Multilayer Injection Blow Molding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 13.5 Multi-Shot Molds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 13.5.1 Overmolding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 13.5.2 Core-Back Molding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 13.5.3 Multi-Station Mold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 13.6 Feed Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364 13.6.1 Insulated Runner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364 13.6.2 Stack Molds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 13.6.3 Branched Runners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 13.6.4 Dynamic Melt Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 13.7 Mold Wall Temperature Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 13.7.1 Pulsed Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 13.7.2 Conduction Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 13.7.3 Induction Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 13.7.4 Managed Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 13.8 In-Mold Labeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 13.8.1 Statically Charged Film. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 13.8.2 Indexed Film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 13.9 Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
XIV
Contents
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
13.9.1 Split Cavity Molds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 13.9.2 Collapsible Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 13.9.3 Rotating Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 13.9.4 Reverse Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 13.10 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 Appendix A: Plastic Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 Appendix B: Mold Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 B.1 Non-Ferrous Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 B.2 Common Mold Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 B.3 Other Mold Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 B.4 Notes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 Appendix C: Properties of Coolants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398 Appendix D: Statistical Labor Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 D.1 United States Labor Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 D.2 International Labor Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 D.3 Trends in International Manufacturing Costs . . . . . . . . . . . . . . . . . . . . . 401 Appendix E: Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 E.1 Length Conversions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 E.2 Mass/Force Conversions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 E.3 Pressure Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 E.4 Flow Rate Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 E.5 Viscosity Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 E.6 Energy Conversions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 Appendix F: Advanced Derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 Subject Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
Nomenclature
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Mold engineering requires analysis, and so an extensive nomenclature has been developed. L, W, and H refer to the length, width, and height dimensions as shown in Figure 1.
Figure 1:
Length, width, and height nomenclature
Variable names have been selected and consistently used as expected (e.g., T for temperature, C for cost, P for pressure, etc.). R refers to rate-related constants (with time dependence) and κ refers to monetary constants (with cost dependence). To provide clarity, subscripts are unabbreviated throughout most of the book. The nomenclature for many of the variables and their units are as follows. Table 1: Nomenclature
Variable
Meaning
α
Thermal diffusivity [m2/s]
β
Compressibility [1/MPa]
δ
Deflection [m]
δbending
Deflection due to bending [m]
δcompression
Deflection due to compression [m]
δtotal
Deflection due to bending and compression [m]
ε
Strain [m/m]
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
XVI
Nomenclature
Variable
Meaning
εplastic
Plastic’s strain to failure [%]
γ
Shear rate [1/s]
γ max
Maximum allowable shear rate for a plastic melt being molded [1/s]
η
Viscosity [Pa s]
κ
Thermal conductivity [W/m°C]
κinsert
Cost per unit volume of core and cavity insert materials [$/m3]
κmold
Cost of mold metal per kilogram [$/kg]
κplastic
Cost of plastic per kilogram [$/kg]
λ
Tolerance limit [m]
μ
Apparent viscosity for Newtonian model [Pa]
μstatic
Coefficient of static friction [–]
ρ
Density [kg/m3]
ρinsert
Density of core and cavity insert materials [kg/m3]
ρplastic
Density of plastic [kg/m3]
φ
Draft angle [°]
θ
Draft angle [°]
σbuckling
Stress level at which column buckles [MPa]
σcyclic
Imposed cyclic stress [MPa]
σendurance
Maximum allowable stress given cyclic loading [MPa]
σhoop
Hoop stress [MPa]
σlimit
Maximum allowable stress given cyclic loading or yielding [MPa]
σyield
Maximum allowable stress given yield failure [MPa]
τ
Shear stress [Pa]
ν
Specific volume [–]
Ωejectors
Total perimeter of all ejectors [m]
Acavity_Projected
Projected area of the mold cavity [m2]
Acompression
Area exposed to compressive stress [m2]
Aeff
Effective area under stress [m2]
Aejectors
Total area of all ejectors [m2]
Apart
Total surface area of the molded part
Ashear
Area exposed to shear stress [m2]
C
Tolerance coefficient for a standard fit [m2/3]
Cauxiliaries
Total cost of all auxiliaries [$]
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Nomenclature
Variable
Meaning
Cinserts
Total cost of all cavities [$]
Cinsert_finishing
Cost of finishing one set of core and cavity inserts [$]
Cinsert_machining
Cost of machining one set of core and cavity inserts [$]
Cinsert_materials
Cost of materials for one set of core and cavity inserts [$]
Cmold
Total cost of purchasing mold [$]
Cmold/part
Cost of purchasing mold amortized across total production quantity [$]
Cmold_base
Total cost of mold base and modifications [$]
XVII
Cmold_customization Total cost of all customizations of mold base [$] Cmold_steel
Initial purchase cost of mold base or steel [$]
Cpart
Total cost per molded part [$]
Cplastic/part
Cost of material used in molding one part [$]
Cprocess/part
Cost of machinery and labor used to mold one part [$]
CPplastic
Plastic’s specific heat [J/kg °C]
CTE
Coefficient of thermal expansion [1/°C]
CVTE
Coefficient of volumetric thermal expansion [1/°C]
D
Diameter [m]
Dhydraulic
Hydraulic diameter of runner segment [m]
Dpin
Diameter of ejector pin [m]
E
Elastic modulus [GPa]
f
Factory of safety [–]
fcavity_complexity
Factor related to the complexity of the cavity
fcavity_discount
Discount factor related to production of multiple sets of core and cavity inserts
fcycle_efficiency
Factor associated with the efficiency of operating the molding machine
fefficiency
Factor related to the overall efficiency of all machining operations
ffeed_waste
Factor associated with material wasted in molding the feed system
f f f
i cavity_customizing i finishing i mold_customizing
Factor associated with customization of one set of core and cavity inserts Percentage of the molded part’s surface area to be finished in the manner i Factor associated with customizing mold base
fmachine
Factor associated with cost of operating different molding machines and auxiliaries
fmachining
Factor related to the average material removal rate of all machining processes relative to standard milling
fmaintenance
Mold lifetime maintenance factor
fwear
Factor associated with maintenance due to mold wear
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
XVIII
Nomenclature
Variable
Meaning
fyield
Fraction of molded parts that are good
F
Force [N]
Fbuckling
Critical load at which column buckles [N]
Fclamp
Mold force tonnage [metric tons, t]
Feject
Ejection force [N]
Finsertion
Insertion force for interference fit [N]
Ftensile
Maximum tensile force for a socket head cap screw [N]
h
Nominal cavity wall thickness [m]
h∞
Heat transfer coefficient [W/°C]
Hcavity
Height of cavity inserts [m]
Hcore
Height of core inserts [m]
Hinserts
Combined height of core and cavity inserts [m]
HLine
Distance from cavity surface to the center of cooling line [m]
Hmold
Total stack height of mold [m]
Hpart
Maximum height of molded part [m]
I
Moment of inertia [m4]
K
Stress concentration factor [–]
k, n
Reference viscosity and power law index per the power law model [Pan, –]
kplastic
Plastic’s thermal conductivity [W/m °C]
Linserts
Length of core and cavity inserts [m]
Lmold
Length of mold [m]
Lpart
Maximum length of molded part [m]
MFI
Plastic’s melt flow index [g/min]
Mmold
Total mass of mold base [kg]
ncycles
Number of molding cycles [–]
n, τ*, D1, D2, D3, WLF model coefficients A1, A3 ncavities
Number of cavities in mold [–]
ncavities_length
Number of cavities in the length direction [–]
ncavities_width
Number of cavities in the width direction [–]
ncycles
Total number of mold cycles that a mold is operated [–]
nj
Number of j-th portions of mold cavity in mold [–]
nlines
Number of cooling lines [–]
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Nomenclature
Variable
Meaning
nparts
Total production quantity of parts to be molded [–]
P
Pressure [Pa]
Pinject
Pressure required to fill the cavity [Pa]
Qmolding
Total thermal energy of moldings [J]
Q line Q
molding
XIX
Cooling power per cooling line [W] Cooling power [W]
rv
Relative change in the specific volume [–]
R
Radius [m]
Re
Reynold’s number [–]
Rfinishing_cost
Hourly cost of finishing [$/h]
Rifinishing
Rate of finishing the part’s surface in the manner i [m2/h]
Rmachining_cost
Hourly rate of machining [$/h]
Rmachining_area
Rate of machining per unit area [m2/h]
Rmachining_volume
Rate of machining per unit volume [m3/h]
Rmolding_cost
Hourly cost of operating molding machine and operator if required [$/h]
RW
Radius of curvature due to warpage [m]
s
Linear shrinkage rate [m/m]
s⊥
Shrinkage rate perpendicular to flow [m/m]
s//
Shrinkage rate parallel to flow [m/m]
save
Average shrinkage rate [m/m]
tc
Cooling time [s]
tcycle
Cycle time of molding machine [s]
tinsert_area
Time required to machine the cavity surface area for one set of core and cavity inserts [h]
tinsert_finishing
Time required to completely finish one set of core and cavity inserts [h]
tinsert_machining
Time required to perform all machining for one set of core and cavity inserts [h]
tinsert_volume
Time required to machine the cavity volume for one set of core and cavity inserts [h]
tp
Packing time before gate solidification [s]
tresidence
Residence time of the polymer melt [s]
Tc
Mold coolant temperature [°C]
Te
Plastic’s ejection temperature [°C]
Tg
Plastic’s glass transition temperature [°C]
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
XX
Nomenclature
Variable
Meaning
THDT
Plastic’s heat deflection temperature [°C]
Tmelt
Melt temperature [°C]
Twall
Mold wall temperature [°C]
v
Linear melt velocity [m/s]
Vinserts
Combined volume of one set of core and cavity inserts [m3]
Vj
Volume of the j-th portion of mold cavity [m3]
Vpart
Volume of molded part [m3]
V
Volumetric flow rate [m3/s]
Wcavity
Width of core and cavity inserts [m]
Wcheek
Distance from cavity side wall to side of mold [m]
Wmold
Width of mold [m]
Wpart
Maximum width of molded part [m]
Wpitch
Distance between parallel cooling lines [m]
David O. Kazmer
Injection Mold Design Engineering
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
David O. Kazmer Injection Mold Design Engineering
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
David O. Kazmer
Injection Mold Design Engineering
Hanser Publishers, Munich • Hanser Gardner Publications, Cincinnati
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
The Author: David O. Kazmer, P.E., Ph.D. Department of Plastics Engineering, 1 University Avenue, Lowell, MA 01854, USA Distributed in the USA and in Canada by Hanser Gardner Publications, Inc. 6915 Valley Avenue, Cincinnati, Ohio 45244-3029, USA Fax: (513) 527-8801 Phone: (513) 527-8977 or 1-800-950-8977 www.hansergardner.com Distributed in all other countries by Carl Hanser Verlag Postfach 86 04 20, 81631 München, Germany Fax: +49 (89) 98 48 09 www.hanser.de Your use of the information provided herein is conditioned upon your agreement, and the agreement of your employer or any third party to whom you provide information, to make use of these materials only in accordance with and subject to the following terms and conditions. The information provided herein is made available“as is” without warranty of any kind, either express or implied, including but not limited to the implied warranties of merchantability, fitness for a particular purpose, satisfactory quality, or noninfringement. We may in the future modify, improve or make other changes to the information made available. All the included information may include technical or typographical errors and we will not be responsible for any such errors. Any pricing and other information about products and services contained herein is not an offer to provide such goods or services. You agree not to bring any legal action against the author or publisher based on your use of the provided information. You agree to indemnify and hold the copyright holder and its affiliates, officers, agents, and employees harmless from any claim or demand, including reasonable attorneys‘ fees, made by any third party due to or arising out of your use of the provided information. The sole and maximum liability of the copyright holder, its affiliates and subsidiaries for any reason, and your exclusive remedy for any cause whatsoever, shall be limited to the amount paid, if any, for the provided information. Library of Congress Cataloging-in-Publication Data Kazmer, David. Injection mold design engineering / David O. Kazmer. p. cm. ISBN-13: 978-1-56990-417-6 (hardcover) ISBN-10: 1-56990-417-0 (hardcover) 1. Injection molding of plastics. I. Title. TP1150.K39 2007 668.4‘12--dc22 2007018765 Bibliografische Information Der Deutschen Bibliothek Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Preface Mold design has been more of a technical trade than an engineering process. Traditionally, practitioners have shared standard practices and learned tricks of the trade to develop sophisticated molds that often exceed customer expectations. However, the lack of fundamental engineering analysis during mold design frequently results in molds that may fail and require extensive rework, produce moldings of inferior quality, or are less cost effective than may have been possible. Indeed, it has been estimated that on average 49 out of 50 molds require some modifications during the mold start-up process. Many times, mold designers and end-users may not know how much money was “left on the table”. The word“engineering”in the title of this book implies a methodical and analytical approach to mold design. The engineer who understands the causality between design decisions and mold performance has the ability to make better and more informed decisions on an application by application basis. Such decision making competence is a competitive enabler by supporting the development of custom mold designs that outperform molds developed according to standard practices. The proficient engineer also avoids the cost and time needed to delegate decision to other parties, who are not necessarily more competent. The book has been written as a teaching text, but is geared towards professionals working in a tightly integrated supply chain including product designers, mold designers, and injection molders. Compared to most handbooks, this textbook provides worked examples with rigorous analysis and detailed discussion of vital mold engineering concepts. It should be understood that this textbook purposefully investigates the prevalent and fundamental aspects of injection mold engineering. I hope that Injection Mold Design Engineering is accessible and useful to all who read it. I welcome your feedback and partnership for future improvements. Best wishes, David Kazmer, P. E., Ph. D. Lowell, Massachusetts June 1, 2007
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XV 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Overview of the Injection Molding Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Mold Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Mold Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3.1 External View of Mold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3.2 View of Mold during Part Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.3 Mold Section and Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Other Common Mold Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4.1 Three Plate, Multi-Cavity Family Mold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4.2 Hot Runner, Multi-Gated, Single Cavity Mold . . . . . . . . . . . . . . . . . . . . . 11 1.4.3 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.5 The Mold Development Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.6 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2
Plastic Part Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 The Product Development Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Product Definition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Product Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Business and Production Development . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.4 Scale-Up and Launch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.5 Role of Mold Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Design Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Application Engineering Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Production Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.3 End Use Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.4 Product Design Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.5 Plastic Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Design for Injection Molding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Uniform Wall Thickness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Rib Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.3 Boss Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Corner Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.5 Surface Finish and Textures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.6 Draft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.7 Undercuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17 17 18 18 19 19 19 20 20 21 22 24 26 28 28 29 29 30 31 33 34 35
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
VIII
Contents
3
Mold Cost Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 The Mold Quoting Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Cost Drivers for Molded Parts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Effect of Production Quantity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Break-Even Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Mold Cost Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 Cavity Cost Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.1 Cavity Set Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.2 Cavity Materials Cost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.3 Cavity Machining Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.4 Cavity Discount Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1.5 Cavity Finishing Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 Mold Base Cost Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Mold Customization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Part Cost Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Mold Cost per Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Material Cost per Part. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.3 Processing Cost per Part. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.4 Defect Cost per Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37 37 39 40 41 43 44 45 45 46 51 51 53 55 60 60 61 62 65 66
4
Mold Layout Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Parting Plane Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Determine Mold Opening Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Determine Parting Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Parting Plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.4 Shut-Offs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Cavity and Core Insert Creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Height Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Length and Width Dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Adjustments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Mold Base Selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Cavity Layouts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Mold Base Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Molding Machine Compatibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.4 Mold Base Suppliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Mold Material Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 Strength vs. Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Hardness vs. Machinability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.3 Mold-Maker’s Cost vs. Molder’s Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.4 Material Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67 67 67 70 71 73 74 74 75 76 77 77 79 81 83 84 84 85 86 88 89
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Contents
IX
5
Cavity Filling Analysis and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 5.2 Objectives in Cavity Filling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.2.1 Complete Filling of Mold Cavities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.2.2 Avoid Uneven Filling or Over-Packing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.2.3 Control the Melt Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 5.3 Viscous Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.3.1 Shear Stress, Shear Rate, and Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.3.2 Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 5.3.3 Rheological Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.3.4 Newtonian Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.3.5 Power Law Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.4 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.5 Cavity Filling Analyses and Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.5.1 Estimating the Processing Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.5.2 Estimating the Filling Pressure and Minimum Wall Thickness . . . . . . 107 5.5.3 Estimating Clamp Tonnage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 5.5.4 Predicting Filling Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.5.5 Designing Flow Leaders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5.6 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6
Feed System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.2 Objectives in Feed System Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.2.1 Conveying the Polymer Melt from Machine to Cavities . . . . . . . . . . . . 119 6.2.2 Impose Minimal Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 6.2.3 Consume Minimal Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 6.2.4 Control Flow Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 6.3 Feed System Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6.3.1 Two-Plate Mold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6.3.2 Three-Plate Mold. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 6.3.3 Hot Runner Molds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 6.4 Feed System Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6.4.1 Determine Type of Feed System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 6.4.2 Determine Feed System Layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 6.4.3 Estimate Pressure Drops. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 6.4.4 Calculate Runner Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 6.4.5 Optimize Runner Diameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 6.4.6 Balance Flow Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 6.4.7 Estimate Runner Cooling Times. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 6.4.8 Estimate Residence Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 6.5 Practical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 6.5.1 Runner Cross-Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 6.5.2 Sucker Pins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
X
Contents
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
6.6
6.5.3 Runner Shut-Offs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 6.5.4 Standard Runner Sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 6.5.5 Steel Safe Designs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
7
Gating Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 7.1 Objectives of Gating Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 7.1.1 Connecting the Runner to the Mold Cavity . . . . . . . . . . . . . . . . . . . . . . . 161 7.1.2 Provide Automatic De-Gating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 7.1.3 Provide Aesthetic De-Gating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 7.1.4 Avoid Excessive Shear or Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . 162 7.1.5 Control Pack Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 7.2 Common Gate Designs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 7.2.1 Sprue Gate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 7.2.2 Pin-Point Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 7.2.3 Edge Gate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 7.2.4 Tab Gate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 7.2.5 Fan Gate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 7.2.6 Flash/Diaphragm Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 7.2.7 Tunnel/Submarine Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 7.2.8 Thermal Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 7.2.9 Valve Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 7.3 The Gating Design Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 7.3.1 Determine Type of Gate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 7.3.2 Calculate Shear Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 7.3.3 Calculate Pressure Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 7.3.4 Calculate Gate Freeze Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 7.3.5 Adjust Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 7.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
8
Venting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 8.1 Venting Design Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 8.1.1 Release Compressed Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 8.1.2 Contain Plastic Melt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 8.1.3 Minimize Maintenance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 8.2 Venting Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 8.2.1 Estimate Air Displacement and Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 8.2.2 Identify Number and Location of Vents . . . . . . . . . . . . . . . . . . . . . . . . . . 186 8.2.3 Specify Vent Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 8.3 Venting Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 8.3.1 Vents on Parting Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 8.3.2 Vents around Ejector Pins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 8.3.3 Vents in Dead Pockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 8.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Contents
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
9
XI
Cooling System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 9.1 Objectives in Cooling System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 9.1.1 Maximize Heat Transfer Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 9.1.2 Maintain Uniform Wall Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 9.1.3 Minimize Mold Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 9.1.4 Minimize Volume and Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 9.1.5 Minimize Stress and Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 9.1.6 Facilitate Mold Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 9.2 The Cooling System Design Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 9.2.1 Calculate the Required Cooling Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 9.2.2 Evaluate Required Heat Transfer Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 9.2.3 Assess Coolant Flow Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 9.2.4 Assess Cooling Line Diameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 9.2.5 Select Cooling Line Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 9.2.6 Select Cooling Line Pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 9.2.7 Cooling Line Routing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 9.3 Cooling System Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 9.3.1 Cooling Line Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 9.3.2 Cooling Inserts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 9.3.3 Conformal Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 9.3.4 Highly Conductive Inserts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 9.3.5 Cooling of Slender Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 9.3.5.1 Cooling Insert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 9.3.5.2 Baffles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 9.3.5.3 Bubblers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 9.3.5.4 Heat Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 9.3.5.5 Conductive Pin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 9.3.5.6 Interlocking Core with Air Channel . . . . . . . . . . . . . . . . . . . . . . 229 9.3.6 One-Sided Heat Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 9.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
10 Shrinkage and Warpage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 10.1 The Shrinkage Analysis Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 10.1.1 Estimate Process Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 10.1.2 Model Compressibility Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 10.1.3 Assess Volumetric Shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 10.1.4 Evaluate Isotropic Linear Shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 10.1.5 Evaluate Anisotropic Shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 10.1.6 Assess Shrinkage Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244 10.1.7 Establishing Final Shrinkage Recommendations . . . . . . . . . . . . . . . . . . 245 10.2 Shrinkage Analysis and Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 10.2.1 Numerical Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 10.2.2 “Steel Safe” Mold Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 10.2.3 Processing Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
XII
Contents
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
10.2.4 Semi-Crystalline Plastics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 10.2.5 Effect of Fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 10.3 Warpage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 10.3.1 Sources of Warpage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 10.3.2 Warpage Avoidance Strategies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 10.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 11 Ejection System Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 11.1 Objectives in Ejection System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 11.1.1 Allow Mold to Open . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 11.1.2 Transmit Ejection Forces to Moldings. . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 11.1.3 Minimize Distortion of Moldings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 11.1.4 Actuate Quickly and Reliably . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262 11.1.5 Minimize Cooling Interference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 11.1.6 Minimize Impact on Part Surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 11.1.7 Minimize Complexity and Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 11.2 The Ejector System Design Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 11.2.1 Identify Mold Parting Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 11.2.2 Estimate Ejection Forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 11.2.3 Determine Ejector Push Area and Perimeter . . . . . . . . . . . . . . . . . . . . . . 269 11.2.4 Specify Type, Number, and Size of Ejectors . . . . . . . . . . . . . . . . . . . . . . . 271 11.2.5 Layout Ejectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 11.2.6 Detail Ejectors and Related Components . . . . . . . . . . . . . . . . . . . . . . . . . 276 11.3 Ejector System Analyses and Designs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 11.3.1 Ejector Pins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 11.3.2 Ejector Blades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280 11.3.3 Ejector Sleeves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 11.3.4 Stripper Plates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 11.3.5 Elastic Deformation around Undercuts . . . . . . . . . . . . . . . . . . . . . . . . . . 285 11.3.6 Core Pulls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 11.3.7 Slides. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 11.3.8 Early Ejector Return Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 11.3.9 Advanced Ejection Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 11.4 Chapter Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 12 Structural System Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 12.1 Objectives in Structural System Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 12.1.1 Minimize Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 12.1.2 Minimize Mold Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 12.1.3 Minimize Mold Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 12.2 Analysis and Design of Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 12.2.1 Plate Compression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306 12.2.2 Plate Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 12.2.3 Support Pillars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Contents
XIII
12.2.4 Shear Stress in Side Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 12.2.5 Interlocks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 12.2.6 Stress Concentrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 12.3 Analysis and Design of Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 12.3.1 Axial Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 12.3.2 Compressive Hoop Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 12.3.3 Core Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 12.4 Fasteners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 12.4.1 Fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 12.4.2 Socket Head Cap Screws. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 12.4.3 Dowels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 12.5 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 13 Mold Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 13.2 Coinjection Molds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 13.2.1 Coinjection Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 13.2.2 Coinjection Mold Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 13.2.3 Gas Assist/Water Assist Molding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 13.3 Insert Molds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 13.3.1 Low Pressure Compression Molding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350 13.3.2 Insert Mold with Wall Temperature Control . . . . . . . . . . . . . . . . . . . . . . 351 13.3.3 Lost Core Molding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 13.4 Injection Blow Molds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 13.4.1 Injection Blow Molding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 13.4.2 Multilayer Injection Blow Molding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 13.5 Multi-Shot Molds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 13.5.1 Overmolding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 13.5.2 Core-Back Molding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 13.5.3 Multi-Station Mold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 13.6 Feed Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364 13.6.1 Insulated Runner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364 13.6.2 Stack Molds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 13.6.3 Branched Runners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368 13.6.4 Dynamic Melt Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369 13.7 Mold Wall Temperature Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 13.7.1 Pulsed Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372 13.7.2 Conduction Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 13.7.3 Induction Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 13.7.4 Managed Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 13.8 In-Mold Labeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 13.8.1 Statically Charged Film. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 13.8.2 Indexed Film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 13.9 Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
XIV
Contents
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
13.9.1 Split Cavity Molds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381 13.9.2 Collapsible Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 13.9.3 Rotating Cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 13.9.4 Reverse Ejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 13.10 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 Appendix A: Plastic Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390 Appendix B: Mold Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 B.1 Non-Ferrous Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 B.2 Common Mold Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 B.3 Other Mold Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 B.4 Notes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 Appendix C: Properties of Coolants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398 Appendix D: Statistical Labor Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 D.1 United States Labor Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 D.2 International Labor Rates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 D.3 Trends in International Manufacturing Costs . . . . . . . . . . . . . . . . . . . . . 401 Appendix E: Unit Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402 E.1 Length Conversions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 E.2 Mass/Force Conversions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 E.3 Pressure Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 E.4 Flow Rate Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 E.5 Viscosity Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 E.6 Energy Conversions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 Appendix F: Advanced Derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409 Subject Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
Nomenclature
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Mold engineering requires analysis, and so an extensive nomenclature has been developed. L, W, and H refer to the length, width, and height dimensions as shown in Figure 1.
Figure 1:
Length, width, and height nomenclature
Variable names have been selected and consistently used as expected (e.g., T for temperature, C for cost, P for pressure, etc.). R refers to rate-related constants (with time dependence) and κ refers to monetary constants (with cost dependence). To provide clarity, subscripts are unabbreviated throughout most of the book. The nomenclature for many of the variables and their units are as follows. Table 1: Nomenclature
Variable
Meaning
α
Thermal diffusivity [m2/s]
β
Compressibility [1/MPa]
δ
Deflection [m]
δbending
Deflection due to bending [m]
δcompression
Deflection due to compression [m]
δtotal
Deflection due to bending and compression [m]
ε
Strain [m/m]
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
XVI
Nomenclature
Variable
Meaning
εplastic
Plastic’s strain to failure [%]
γ
Shear rate [1/s]
γ max
Maximum allowable shear rate for a plastic melt being molded [1/s]
η
Viscosity [Pa s]
κ
Thermal conductivity [W/m°C]
κinsert
Cost per unit volume of core and cavity insert materials [$/m3]
κmold
Cost of mold metal per kilogram [$/kg]
κplastic
Cost of plastic per kilogram [$/kg]
λ
Tolerance limit [m]
μ
Apparent viscosity for Newtonian model [Pa]
μstatic
Coefficient of static friction [–]
ρ
Density [kg/m3]
ρinsert
Density of core and cavity insert materials [kg/m3]
ρplastic
Density of plastic [kg/m3]
φ
Draft angle [°]
θ
Draft angle [°]
σbuckling
Stress level at which column buckles [MPa]
σcyclic
Imposed cyclic stress [MPa]
σendurance
Maximum allowable stress given cyclic loading [MPa]
σhoop
Hoop stress [MPa]
σlimit
Maximum allowable stress given cyclic loading or yielding [MPa]
σyield
Maximum allowable stress given yield failure [MPa]
τ
Shear stress [Pa]
ν
Specific volume [–]
Ωejectors
Total perimeter of all ejectors [m]
Acavity_Projected
Projected area of the mold cavity [m2]
Acompression
Area exposed to compressive stress [m2]
Aeff
Effective area under stress [m2]
Aejectors
Total area of all ejectors [m2]
Apart
Total surface area of the molded part
Ashear
Area exposed to shear stress [m2]
C
Tolerance coefficient for a standard fit [m2/3]
Cauxiliaries
Total cost of all auxiliaries [$]
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Nomenclature
Variable
Meaning
Cinserts
Total cost of all cavities [$]
Cinsert_finishing
Cost of finishing one set of core and cavity inserts [$]
Cinsert_machining
Cost of machining one set of core and cavity inserts [$]
Cinsert_materials
Cost of materials for one set of core and cavity inserts [$]
Cmold
Total cost of purchasing mold [$]
Cmold/part
Cost of purchasing mold amortized across total production quantity [$]
Cmold_base
Total cost of mold base and modifications [$]
XVII
Cmold_customization Total cost of all customizations of mold base [$] Cmold_steel
Initial purchase cost of mold base or steel [$]
Cpart
Total cost per molded part [$]
Cplastic/part
Cost of material used in molding one part [$]
Cprocess/part
Cost of machinery and labor used to mold one part [$]
CPplastic
Plastic’s specific heat [J/kg °C]
CTE
Coefficient of thermal expansion [1/°C]
CVTE
Coefficient of volumetric thermal expansion [1/°C]
D
Diameter [m]
Dhydraulic
Hydraulic diameter of runner segment [m]
Dpin
Diameter of ejector pin [m]
E
Elastic modulus [GPa]
f
Factory of safety [–]
fcavity_complexity
Factor related to the complexity of the cavity
fcavity_discount
Discount factor related to production of multiple sets of core and cavity inserts
fcycle_efficiency
Factor associated with the efficiency of operating the molding machine
fefficiency
Factor related to the overall efficiency of all machining operations
ffeed_waste
Factor associated with material wasted in molding the feed system
f f f
i cavity_customizing i finishing i mold_customizing
Factor associated with customization of one set of core and cavity inserts Percentage of the molded part’s surface area to be finished in the manner i Factor associated with customizing mold base
fmachine
Factor associated with cost of operating different molding machines and auxiliaries
fmachining
Factor related to the average material removal rate of all machining processes relative to standard milling
fmaintenance
Mold lifetime maintenance factor
fwear
Factor associated with maintenance due to mold wear
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
XVIII
Nomenclature
Variable
Meaning
fyield
Fraction of molded parts that are good
F
Force [N]
Fbuckling
Critical load at which column buckles [N]
Fclamp
Mold force tonnage [metric tons, t]
Feject
Ejection force [N]
Finsertion
Insertion force for interference fit [N]
Ftensile
Maximum tensile force for a socket head cap screw [N]
h
Nominal cavity wall thickness [m]
h∞
Heat transfer coefficient [W/°C]
Hcavity
Height of cavity inserts [m]
Hcore
Height of core inserts [m]
Hinserts
Combined height of core and cavity inserts [m]
HLine
Distance from cavity surface to the center of cooling line [m]
Hmold
Total stack height of mold [m]
Hpart
Maximum height of molded part [m]
I
Moment of inertia [m4]
K
Stress concentration factor [–]
k, n
Reference viscosity and power law index per the power law model [Pan, –]
kplastic
Plastic’s thermal conductivity [W/m °C]
Linserts
Length of core and cavity inserts [m]
Lmold
Length of mold [m]
Lpart
Maximum length of molded part [m]
MFI
Plastic’s melt flow index [g/min]
Mmold
Total mass of mold base [kg]
ncycles
Number of molding cycles [–]
n, τ*, D1, D2, D3, WLF model coefficients A1, A3 ncavities
Number of cavities in mold [–]
ncavities_length
Number of cavities in the length direction [–]
ncavities_width
Number of cavities in the width direction [–]
ncycles
Total number of mold cycles that a mold is operated [–]
nj
Number of j-th portions of mold cavity in mold [–]
nlines
Number of cooling lines [–]
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
Nomenclature
Variable
Meaning
nparts
Total production quantity of parts to be molded [–]
P
Pressure [Pa]
Pinject
Pressure required to fill the cavity [Pa]
Qmolding
Total thermal energy of moldings [J]
Q line Q
molding
XIX
Cooling power per cooling line [W] Cooling power [W]
rv
Relative change in the specific volume [–]
R
Radius [m]
Re
Reynold’s number [–]
Rfinishing_cost
Hourly cost of finishing [$/h]
Rifinishing
Rate of finishing the part’s surface in the manner i [m2/h]
Rmachining_cost
Hourly rate of machining [$/h]
Rmachining_area
Rate of machining per unit area [m2/h]
Rmachining_volume
Rate of machining per unit volume [m3/h]
Rmolding_cost
Hourly cost of operating molding machine and operator if required [$/h]
RW
Radius of curvature due to warpage [m]
s
Linear shrinkage rate [m/m]
s⊥
Shrinkage rate perpendicular to flow [m/m]
s//
Shrinkage rate parallel to flow [m/m]
save
Average shrinkage rate [m/m]
tc
Cooling time [s]
tcycle
Cycle time of molding machine [s]
tinsert_area
Time required to machine the cavity surface area for one set of core and cavity inserts [h]
tinsert_finishing
Time required to completely finish one set of core and cavity inserts [h]
tinsert_machining
Time required to perform all machining for one set of core and cavity inserts [h]
tinsert_volume
Time required to machine the cavity volume for one set of core and cavity inserts [h]
tp
Packing time before gate solidification [s]
tresidence
Residence time of the polymer melt [s]
Tc
Mold coolant temperature [°C]
Te
Plastic’s ejection temperature [°C]
Tg
Plastic’s glass transition temperature [°C]
Injection Mold Design Engineering downloaded from www.hanser-elibrary.com by 128.122.230.132 on February 29, 2016 For personal use only.
XX
Nomenclature
Variable
Meaning
THDT
Plastic’s heat deflection temperature [°C]
Tmelt
Melt temperature [°C]
Twall
Mold wall temperature [°C]
v
Linear melt velocity [m/s]
Vinserts
Combined volume of one set of core and cavity inserts [m3]
Vj
Volume of the j-th portion of mold cavity [m3]
Vpart
Volume of molded part [m3]
V
Volumetric flow rate [m3/s]
Wcavity
Width of core and cavity inserts [m]
Wcheek
Distance from cavity side wall to side of mold [m]
Wmold
Width of mold [m]
Wpart
Maximum width of molded part [m]
Wpitch
Distance between parallel cooling lines [m]