Flow Analysis of Injection Molds

Transcription

1 Peter K. Kennedy Rong Zheng Flow Analysis of Injection Molds 2 nd Edition

2 Kennedy, Zheng Flow Analysis of Injection Molds

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4 Peter Kennedy Rong Zheng Flow Analysis of Injection Molds 2 nd Edition Hanser Publishers, Munich Hanser Publications, Cincinnati

5 The Authors: Dr. Peter Kennedy, Helmet Investments, 141/99 Spring St., Melbourne, Victoria 3000, Australia Dr. Rong Zheng, School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia Distributed in North and South America by: Hanser Publications 6915 Valley Avenue, Cincinnati, Ohio , USA Fax: (513) Phone: (513) Distributed in all other countries by Carl Hanser Verlag Postfach , München, Germany Fax: +49 (89) The use of general descriptive names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. While the advice and information in this book are believed to be true and accurate at the date of going to press, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Library of Congress Cataloging-in-Publication Data Kennedy, Peter (Peter K.) Flow analysis of injection molds / Peter Kennedy, Rong Zheng. -- 2nd edition. pages cm Includes bibliographical references and index. ISBN (hardcover) -- ISBN (e-book) (print) 1. Injection molding of plastics. 2. Mathematical modeling. I. Zheng, Rong, II. Title. TP1150.K dc Bibliografische Information Der Deutschen Bibliothek Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über < abrufbar. ISBN E-Book-ISBN All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying or by any information storage and retrieval system, without permission in writing from the publisher. Carl Hanser Verlag, Munich 2013 Production Management: Steffen Jörg Coverconcept: Marc Müller-Bremer, München Coverdesign: Stephan Rönigk Printed and bound by CPI buch bücher gmbh Printed in Germany

6 To my Father Professor Zhi-Zhong Zheng for his love and professional spirit that have guided my life. Rong Zheng To my Children William and Anthony for their support, understanding and love. Peter K. Kennedy

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8 Acknowledgements We wish to record our sincere thanks to Professors Roger I. Tanner (University of Sydney), H.E.H. Meijer (Technische Universiteit Eindhoven), Xi-Jun Fan (University of Sydney), and Nhan Phan-Thien (National University of Singapore formerly of the University of Sydney). Many results and ideas presented in this book came from their works and from collaborative research work with them and their colleagues. From this book one may see their deep influence on our work. Thanks are also due to Professor Charles Tucker (University of Illinois, Urbana-Champaign), Professors Gerrit Peters, and Patrick Anderson (both of Technische Universiteit Eindhoven) for fruitful discussions and advice from which we benefited. We also want to thank our former Moldflow colleagues in Melbourne, Australia and Ithaca, USA with whom we both used to work. Our interactions with them broadened our knowledge in several different aspects and lead to deep friendships. Their work can also be seen in this book. Much of our early work was conducted with several consortiums located in France and sponsored by Moldflow Corporation and some other industrial partners. In particular, we would like to thank Professors G. Regnier (formerly ENSAM Paris, now Arts et Métiers ParisTech), R. Fulchiron (Université de Lyon), D. Delaunay (Université de Nantes), and Dr. V. Leo (Solvay) for participation in several projects that showed how complex the injection molding process is but nevertheless produced some results that are of practical use. We are indebted to the Australian Cooperative Research Center for Polymers for providing an opportunity of doing collaborative research with research teams from Monash and Sydney Universities. In particular, we were grateful to obtain access to the Australian Synchrotron. Special thanks go to the former Moldflow Corporation (now part of Autodesk Inc.) for providing an excellent working environment and constant support to both of us during the period we were working there. Professors H.E.H. Meijer, Nhan Phan-Thien, and Roger I. Tanner reviewed the draft of the whole book and made very valuable comments and suggestions for improvement; their help is gratefully acknowledged. We also wish to thank the editors of this book s publisher for their patience and professional assistance. On the personal side, we want to thank our families for the love, understanding, and encouragement that sustained us during our confrontation with an important, but difficult, industrial problem.

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10 Preface Injection molding is an ideal process for fabricating large numbers of geometrically complex parts. Many everyday items are injection molded: mobile phone housings, automobile bumpers, television cabinets, compact discs, and lunch boxes are all examples of injection molded parts. Parts produced by the process are also becoming commonplace in less obvious applications. For example, the relatively new area of micro-injection molding is providing new methods of drug delivery and optical couplers [195]. Variations of injection molding that have been developed over the years include co-injection or two-component molding, water injection, and gas-assisted injection molding (GAIM). All these processes provide additional scope for designers of plastic parts. Excellent examples are provided by Neerincx [267] and Neerincx et al. [268, 269]. Indeed it is possible to combine these variations with each other or injection molding to achieve other processes. In particular, Neerincx and Meijer combined GAIM and two-component molding [270] to produce a part with unique qualities. An important characteristic of injection molding, including variations, is that it may not be possible to fix a part defect in production by simply varying process conditions. Frequently the mold must be modified to overcome a problem. This is expensive and costs valuable time. It is far better to avoid problems in the design phase than to fix them in production. Consequentially, simulation of injection molding is industrially valuable. Not surprisingly, there are several commercial companies offering software for simulation of injection molding and its variants. Due to the complexity of the physics of the process, various assumptions are made to simplify the mathematical model used for simulation. Over the years many descriptions of modeling and simulation of injection molding have appeared in academic journals and books. While readily available to specialist readers, an understanding of principles used in simulation software is difficult for nonspecialists to obtain. This is due to the multi-disciplinary nature of simulation software. In particular, aspects of rheology, materials science, and numerical methods are used. There are some excellent books on polymer processing that discuss injection molding. One of the original classics was by Tadmor and Gogos [351]. This was followed by Tucker s book [368] which focused on modeling for computer simulation. More recently, Osswald and Hernández-Ortiz [279] provided an overview of modeling and simulation for polymer processing, while Kamal et al. [190] have produced a book focused on injection molding that discusses variations and other aspects of the injection molding process. Given the importance of injection molding as a process, and the simulation industry that has grown to support it, we believe there is a need for a book that deals solely with modeling and simulation of injection molding. One of the authors wrote a book in 1995 [196] along these lines. It discussed filling and packing phase simulation, but is no longer in print. Moreover, there have been many developments in modeling and simulation since that time. The current book is intended to address this need. It provides a comprehensive description of modeling and simulation of injection molding. While some parts of the book may be relevant

11 X Preface to other polymer forming processes, we assume injection molding is the process under discussion, and so do not deal with variants. The book is divided into two parts and a considerable number of appendices. Each appendix is meant to provide detailed information on the topics discussed in the main parts of the book. Hopefully, moving specialist and routine information into appendices makes the book more readable. Part I is written for the user of simulation software who seeks an explanation of the basic modeling and assumptions made. Modeling and simulation details of filling, packing, residual stress, shrinkage, and warpage of amorphous, semi-crystalline, and fiber filled materials are described. Additionally, it introduces numerical methods for solving mathematical models of the process. This part is intended to be self-contained but presumes knowledge of algebra and calculus at the level of a degree in physical sciences or engineering. Tensor concepts are given in Appendix B. Part II deals with improved modeling. This part is aimed at interested users of software, graduate students, and researchers who are interested in enhancing simulation. A knowledge of the history of simulation is useful for anyone so disposed. Appendix A provides some background on both academic and commercial developments in simulation to around Much of the material presented in Part II covers developments from 2000 to the present. At the time of writing, this information is not implemented in commercial simulation software, and is meant to be a starting point for improvement in modeling and simulation. It presents some models that incorporate more of the physics of the molding process. Although we present some possible approaches, we do not cover all areas of improvement. We do, however, try to reference other approaches to the problems we consider. In particular, we focus on fiber-filled and semicrystalline materials, but some ideas may be applied to amorphous materials. Hopefully it will be a source of ideas that lead to better simulations. Part II uses more advanced ideas of tensor calculus. Where these are not provided in the text, we prescribe external references. We hope our readers enjoy the challenge of modeling and simulating the injection molding process. Injection molding is a technology that has been around for approximately 140 years [172]. However, it was only in the 1950s, with the development of the reciprocating screw method, that the process showed its true potential. Despite the immaturity of computer technology, simulation of injection molding can be traced to 1960 [367]. Since then it has become a field of both academic and commercial interest. Moreover, the physics of injection molding are still being researched. It is this latter aspect that provides us with the hope that this book will inspire others to improve simulation by improved modeling and by taking advantage of the computational power available today and in the future. Peter K. Kennedy and Rong Zheng, Melbourne, Australia, 2013

12 Contents Preface... IX Notation...XXI I The Current Status of Simulation 1 1 Introduction The Injection Molding Process Molding Terminology What is Simulation? The Challenges for Simulation Basic Physics of the Process Why Simulate Injection Molding? How Good is Simulation? Stress and Strain in Fluid Mechanics Stress in Fluids The Stress Tensor The Extra Stress Tensor Rate of Strain Tensor Newtonian and Non-Newtonian Fluids The Generalized Newtonian Fluid Material Properties of Polymers Types of Polymers Amorphous Polymers Semi-Crystalline Polymers Overview of Material Properties for Simulation Viscosity Modeling Viscosity The Viscosity Function... 23

13 XII Contents The Power Law Model The Carreau Model The Cross Model Incorporation of Temperature Effects The Solidification Problem Thermal Properties Specific Heat Capacity Thermal Conductivity Thermodynamic Relationships Expansivity and Compressibility Pressure-Volume-Temperature (PVT) Data Fiber Orientation Shrinkage and Warpage Governing Equations Introduction Mathematical Preliminaries The Material Derivative The Gauss Divergence Theorem Reynolds Transport Theorem Integration by Parts Conservation of Mass Conservation of Momentum Conservation of Energy Relating Specific Energy to Temperature The Energy Equation in Terms of Temperature Boundary Conditions Pressure and Flow Rate Boundary Conditions Temperature Boundary Conditions Mold Deformation Boundary Conditions Thin Cavities Long Cores and Mold Inserts Fiber-Filled Materials Fiber Concentration Jeffery s Equation A Statistical Approach Mechanical Properties Shrinkage and Warpage Runners... 53

14 Contents XIII 5 Approximations for Injection Molding Introduction Material Property Approximations Filling, Packing, and Cooling Analysis The Thermal Source Term in the Energy Equation Viscosity Modeling Specific Heat Capacity Thermal Conductivity Unfilled Amorphous Unfilled Semi-Crystalline Filled Materials No-Flow or Transition Temperature Pressure-Volume-Temperature (PVT) Data Fiber Orientation, Shrinkage, and Warpage Fiber Orientation Analysis Shrinkage and Warpage Analysis Summary of Material Assumptions Governing Equations The 2.5D Approximation Governing Equations in Cartesian Coordinates Conservation of Mass Conservation of Momentum Conservation of Energy Estimation of Relevant Terms Velocity in the z Direction Integration of the Momentum Equations Integration of the Continuity Equation Summary of the 2.5D Approximation Mold Cooling Analysis Fiber Orientation Orientation Tensors Folgar-Tucker Equation Closure Approximations Linear Closure Quadratic Closure Hybrid Closure Orthotropic Closure The Interaction Coefficient... 83

15 XIV Contents 5.9 Shrinkage and Warpage Shrinkage Prediction Residual Strain Methods Residual Stress Models The 2.5D Approximation for Runners Conservation of Mass for Runners Conservation of Momentum for Runners Conservation of Energy for Runners Integration of the Momentum Equation for Runners Integration of the Continuity Equation for Runners Numerical Methods for Solution Midplane Methods Extraction of a Midplane from a 3D Model Dual Domain Analysis for Flow Dual Domain Structural Analysis Warpage Analysis Using the Dual Domain FEM D Analysis Finite Volume Methods A Pseudo-3D Approach Warpage and Shrinkage Analysis in 3D D Analysis of Runner Systems II Improving Molding Simulation Improved Fiber Orientation Modeling Introduction ARD Model Evolution Equation Direct Simulation Calculation of C I RSC Model Suspension Rheology Brownian Dynamics Simulation