GEOMETRIC ANALYSIS OF AXISYMMETRIC DISK FORGING A Thesis Presented to The Faculty of the Fritz J. and Dolores H. Russ College of Engineering and Technology Ohio University In Partial Fulfillment of the Requirement for the Degree Master of Science by Corey Bevan Raub March, 2000 ACKNOWLEDGEMENT The research that went into this project would not have been possible without the invaluable assistance of many persons. Their expertise and patience have given me the strength and motivation to remain committed through the completion of this work. My thanks and appreciations go out to my advisor, Dr. Bhavin Mehta, who has helped lead me through my educational path and arranged for my funding on this project. I would especially like to thank Daniel Allwine, whose devotion and sincere encouragement has given me the will power to bring this project to an end. I would like to thank the other members of my thesis committee (Dr. Khairul Alam, and Dr. Thomas Scott) for their valuable comments and suggestions and to the Faculty and Staff of the College of Mechanical Engineering for their commitment to higher education. Finally, I would like to thank my parents, Daniel and Linda Raub, for their love, support, and patience in the pursuit of my education. Without their continued support, none of this would have been possible. TABLE OF CONTENTS Approval Page Acknowledgments List of Figures, Illustrations, and Graphs vii 1 INTRODUCTION 1.1 PROJECT DESCRIPTION AND SIGNIFICANCE 1.2 BACKGROUND 2 MANUFACTURING 2.1 FORGING 2.1.1 TYPES OF FORGING 2.1.2 MACHINERY 2.1.3 HEAT TREATMENTS 2.2 OTHER METAL FORMING PROCESSES 2.2.1 CASTING 2.2.2 EXTRUSION 2.2.3 ROLLING AND BENDING 2.2.4 MACHINING 3 GEOMETRIC ANALYSIS OF AXISSYMMETRIC DISK FORGING 3.1 AXISYMMETRIC DISKS 3.2 PROGRAM SIGNIFICANCE 3.3 PROGRAM CONTENTS 3.4 GEOMETRIC ANALYSIS 4 MUTUAL VOLUMETRIC DISCRETIZATION OF AXISSYMMETRIC DISK FORGING 4.1 MUTUAL VOLUMETRIC DISCRETIZATION 38 4.2 DERIVATION OF DISK VOLUME CALCULATIONS 40 4.3 EXAMPLES OF VOLUMETRIC DISCRETIZATIONS 42 5 CONCLUSION 47 REFERENCES APPENDIX A MATHEMATICAL DERIVATIONS A. 1 DERIVATION OF THE PARALLEL LINE SEGMENT MINIMUM DISTANCE FORMULA 54 A.2 DERIVATION OF THE PARTIAL DIFFERENTIATION MINIMUM DISTANCE FORMULA 59 A.3 DERIVATION OF THE VOLUME FORMULAS USED TO COMPUTE THE MUTUAL VOLUMETRIC DISCRETIZATION 62 APPENDIX B PROGRAM FILES B. 1 PROGRAM 1 - PROFILE-FINAL.M B.2 PROGRAM 2 - MlNIMlJM-OFFSET-PROF1LE.M B.3 PROGRAM 3 - MUTUAL DISCRETIZATION GROUP APPENDIX C SAMPLE OUTPUT AND RESULTS C.l MINIMUM DISTANCE OF SEGMENTS (PROGRAM 1) C.2 MINIMUM DISTANCE OF SEGMENTS (PROGRAM 2) C.3 MUTUAL VOLUMETRIC DISCRETIZATION GLOSSARY ABSTRACT vii LIST OF FIGURES, ILLUSTRATIONS, AND GRAPHS Figure 1.1 A young blacksmith uses a hammer and anvil. Figure 2.1 Flow lines in a forged part. Figure 2.2 Set of closed impression dies. Figure 2.3 Smith forging hammer Figure 2.4 Board drop hammer Figure 2.5 Direct extrusion Figure 2.6 Direct extrusion, (b) hollow and (c) semi-hollow cross-sections Figure 2.7 Indirect extrusion, (top) solid, and (bottom) hollow cross-sections Figure 2.8 Forward impact extrusion Figure 2.9 Backward impact extrusion Figure 2.10 Hydrostatic extrusion Figure 2.1 1 Polymer Extrusion Figure 2.1 2 Relative cost for manufacturing an aircraft part Figure 3.1 Axisymmetric closed die forging Figure 3.2 Configuration of a simple four ringed disk profile Figure 3.3 Profile intersection illustration Figure 3.4 Minimum offset illustration Figure 3.5 Illustration of segment minimum distance orientation Figure 3.6 Minimum distance coordinates for two parallel lines Figure 4.1 Ring cross-section Figure 4.2 Simple discretization example Figure 4.3 A second simple discretization example ... Vlll Figure 4.4 Multiple ring discretization example Figure 4.5 The "reverse" discretization Figure 4.6 Configuration of a simple four ringed disk profile Figure Al.l Representation of the minimum distance between two parallel lines Figure A3.1 Configuration of a simple four ringed disk profile Figure A3.2 Ring cross section Figure C1.l Diagram of Program 1 - Example 1 Figure C1.2 Diagram of Program 1 - Example 2 Figure C1.3 Diagram of Program 1 - Example 3 Figure C3.1 Diagram of Original Profiles - Example 1 Figure C3.2 Diagram of Discretized Profiles - Example 1 Figure C3.3 Diagram of Original Profiles - Example 2 Figure C3.4 Diagram of Discretized Profiles - Example 2 CHAPTER 1 --INTRODUCTION -- 1 .l- PROJECT DESCRIPTION AND SIGNIFICANCE This project is in conjunction with the Air Force Research Laboratory at Wright- Patterson Air Force Base in Dayton, Ohio. The project deals with a "simulation and optimization based system for design of multi-stage material processes". Once finished, the system will be used as a manufacturing a001 that will "consider alternative manufacturing sequences and parameters." [25, pp. 2871 There will be uses for such a system in industry, as well as research facilities and academic institutions. In industry, this system will be beneficial in determining the best set of "manufacturing methods and parameters" for a given situation. This system will also aid in the education and training of an assortment of manufacturing processes. Researchers will be able to apply this system to newly defined methods or to help in the improvement of pre-existing methods of manufacturing analysis. Material processes have been improved, during the past 20 years, due to advances in the manufacturing analysis tools. It is now possible to ~unextremely accurate process models with the advancement of computers and "powerful computational tools such as finite-element method (FEM)" that produce results acceptable by industrial analysts. However, these tools require extensive knowledge of the software and of the subject being analyzed. For these reasons alone: ". .New computational tools" need to be developed "that car1 directly assist the designer in making process design decisions such as those involving selection of the sequence of manufacturing operations and specification of processing conditions for each of these operations. Material process design methods that consider alternative materials and processes in order to optimize life-cycle cost should enable the production of components that are lighter, stronger, environmentally compliant, and less expensive than those achieved though conventional design practices." [25, pp. 2871 This project is part of an ongoing development of a design environment that integrates models for materials and manufacturing processes, and allows for the selection and optimization of components such as those used in aircraft structures and engines. [25] The forging of axisymrnetric turbine-engine disks similar to those used in aircraft engines is the focus of this effort. Such a system will "significantly improve productivity and reduce the costs of multistage materials processes such as hot-metal forging." [ll, pp. 11 It will also "allow the evaluation, with respect to quality, performance, and cost of alternate materials, processes, and process parameters for the affordable manufacturing of reliable components." [25, pp. 287-2881 This system is expected to serve as "a tool for the design of multistage materials processes that will allow consideration of alternate routes and parameters for manufacturing both military and commercial components." 124, pp. 11 The benefits of a system, such as this, that will help in the optimization of algorithms for manufacturing 5 are phenomenal. "Optimization algorithms that can vary the sequence and parameters or processing stages . will allow the evaluation of alternative manufacturing sequences and materials to obtain designs optimized for quality, perfomlance and cost." [25, pp. 2881 This system can also be applied to other areas of manufacturing; it is not limited to only the production of metal-formed products and such processes. Current methods of engineering analysis are not directly associated with the idea of "design to cost" and optimization paradigms, and are more useful when considering the "analysis of complex material flow and the evaluation of design choices." A principle concept for this project on a whole was to develop a design tool that would make use of much simpler models. Several reasons were considered for this approach. 1. "Simpler models can predict the most important characteristics of the material behavior during processing in a small fraction of the time taken by a Finite Element Analysis (FEA) run." 2. "They can be connected together to form simulations of multistage processes." 3. "These connected simulations can be controlled by an optimization algorithm that can change parameters of the whole sequence of operations according to predetermined optimality criteria in order to obtain the best combination of processes and process parameters that satisfy desired product quality, performance, and cost requirements." [25, pp. 2891 The approach taken by this type of design tool is primarily aimed at the "conceptual design of processes with potential for becoming a routine tool for problem solving and training." As mentioned, this system can also be applied to other areas of 4 manufacturing. In time, other processes using different materials will be developed that would benefit from such a system. "Emphasis is . " being ". ,. placed on the ability to evaluate alternative manufacturing strategies instead . ." of ". highly sophisticated simulations of a single manufacturing operation." [25, pp. 2921 A design tool such as this will help "predict the cost and properties of a component or system early in the product- realization process, when most of the cost is decided." [24, pp. 11 1.2 - BACKGROUND Forging is a metal forming process used to produce large quantities of identical parts, as in the manufacture of automobiles, and to improve the mechanical properties of the metal being forged, as in aerospace parts or military equipment. The design of forged parts is limited when undercuts or cored sections are required. All cavities must be comparatively straight and largest at the mouth, so that the forging die may be withdrawn.