Computer Aided Optimization of Tube Hydroforming Processes By Pinaki Ray, B.Eng. This thesis is submitted to Dublin City University as the fulfilment of the requirement for the award of the degree of Doctor of Philosophy Supervisor: Dr Bryan J. Mac Donald, B.Eng. M.Sc. Ph.D. Centre for Intelligent Design Engineering Analysis and Simulation School of Mechanical and Manufacturing Engineering Dublin City University March 2005 DECLARATION I hereby certify that this material, which I now submit for assessment on the programme of study leading to the award of Doctor of Philosophy, is entirely my own work and has not been taken from the work of others save and to the extent that such work has been cited and acknowledged with in the text of my work. Signed: 1U _______________________ Date: Pinaki Ray ID: 51178672 Acknowledgements There are many individuals who have assisted me during my research study. I would like to thank you all. In particular, I would like to acknowledge the contributions of Dr Bryan J. Mac Donald for his supervision, guidance, help and his constructive suggestions and comments. I am indebted to him for the moral support extended to me. 1 would like to thank the academic staff for any help they gave me over the course of my work, especial thanks to Prof M S J Hashmi (Head of School, School of Mechanical and Manufacturing Engineering). I am especially grateful to Mr Liam Domnican and Mr Keith Hickey for their technical support and help throughout this work. I wish to thank all of my fellow postgraduate students with in Dublin City University for their support and friendship. Special thanks are due to my parents Mr Becliu Ram Ray and Mrs Ina Ray, my sisters Ms Somali Ray, Dr Mrs Chaitali Ray, my brother-in-law Dr Amit Neogi and, my wife Mrs Panchali Ghosh for their endless encouragement and support during my studies, without which I may not have got this far. Computer Aided Optimization of Tube Hydroforming Processes Pinaki Ray B.Eng. ABSTRACT Tube hydroforming is a process of forming closed-section, hollow parts with different cross sections by applying combined internal hydraulic forming pressure and end axial compressive loads or feeds to force a tubular blank to conform to the shape of a given die cavity. It is one of the most advanced metal forming processes and is ideal for producing seamless, lightweight, near net shape components.. This innovative manufacturing process offers several advantages over conventional manufacturing processes such as part consolidation, weight reduction and lower tooling and process cost. To increase the implementation of this technology in different manufacturing industries, dramatic improvements for hydroformed part design and process development are imperative. The current design and development of tube hydroforming processes is plagued with long design and prototyping lead times of the component. The formability of hydroformed tubular parts is affected by various physical parameters such as material properties, tube and die geometry, boundary conditions and process loading paths. Finite element simulation is perceived by the industry to be a cost-effective process analysis tool and has the capability to provide a greater insight into the deformation mechanisms of the process and hence allow for greater product and process optimization. Recent advances in the non-linear metal forming simulation capabilities of finite element software have made simulation of many complex hydroforming processes much easier. Although finite element based simulation provides a better understanding of the process, trial-and-error based simulation and optimization becomes very costly for complex processes. Thus, powerful intelligent optimization methods are required for better design and understanding of the process. This work develops a better understanding of the forming process and its control parameters. An experimental study of ‘X’ and ‘T’-branch type tube hydroforming was undertaken and finite element models of these forming processes were built and subsequently validated against the experimental results. Furthermore these forming processes were optimized using finite element simulations enhanced with numerical optimization algorithms and with an adaptive process control algorithm. These new tools enable fast and effective determination of loading paths optimized for successful hydroforming of complex tubular parts and replace trial-and-error approaches by a more efficient customized finite element analysis approach. Keywords: Tube hydroforming, Finite element analysis, LS-DYNA, Forming load paths, Optimization, Adaptive process control I 3.2.1. The hydroforming machine specification 48 3.2.2. Machine control and data recording system 49 3.2.3. Operation procedure 49 3.3. Experimental Forming of ‘X’ and ‘T’-branch components 51 3.3.1. Study of machine consistency and repeatability 5 3 3.3.2. Experimental design 56 3.3.3. Experiment results 57 3.4. Finite element simulation ofX and T-branch components 60 3.4.1. CAD and Finite element modelling 60 3.4.2. Contact definition 62 3.4.3. Material model 63 3.4.4. Boundary conditions, constraints and loading 64 3.4.5. Finite element solution control parameters 65 3.4.6. Results and analysis 66 3.5. Summary of Chapter 3 86 Chapter 4: Part And Process Design Consideration Of Tube Hydroforming Components 4.1. Introduction 87 4.2. Consideration in finite element modelling of tube hydroforming processes 87 4.2.1. Types of finite element formulations 87 4.2.2. Types of Finite Elements 88 4.2.3. Element size 89 4.3. Factors affecting the hydroformability characteristics of the process . 92 4.3.1. Geometric factors 92 4.3.1.1. Effects of initial tube length (spline length) 93 4.3.1.2. Effects of initial tube wall thickness 96 4.3.1.3. Effect of die radius 96 4.3.2 Process parameters 98 4.3.2.1. Effects of friction 98 4.3.2.2. Effects of loading paths 101 4.4. Experimental verification 104 III 4.5. Summary of Chapter 4 107 Chapter 5: Determine Loading Paths Using Finite Element Simulations and Optimization Technique 5.1. Introduction 108 5.2. Overview of the optimization process 109 5.3. Theory of optimization 112 5.3.1. Optimization Method-Subproblem approximation method 114 5.3.1.1. Function Approximations 115 5.3.1.2. Minimizing the Subproblem Approximation 116 5.3.1.3. Convergence 118 5.4. Application of the optimization technique in tube hydroforming - Process Parameter Design 119 5.4.1. Design Variables and Design Limits 121 5.4.2. Objective Function 124 5.4.3. Constraint functions (State Variables) 124 5.5. X and T-branch tube hydroforming (asymmetric expansion) 125 5.5.1. Results 128 5.6. Summary of Chapter 5 138 Chapter 6: Determination of Feasible Forming Loading Paths Using Adaptive Simulation Concepts 6.1. Introduction 139 6.1.1. Adaptive simulation concept 142 6.2. Development of ‘Fuzzy Load Control Algorithm’ 145 6.2.1. Process control limits 145 6.2.2. Design of the load control algorithm 155 6.2.2.1. Fuzzification of the input variables and application of fuzzy rules 163 6.2.2.2. Calculation of the membership function 166 6.2.2.3. Fuzzy inference, defuzzification and calculation of output parameters 166 6.3. Application of the load control algorithm for determination of feasible load paths 172 IV 6.3.1. Asymmetric expansion -X and T-branch tube hydroforming processes 172 6.3.1.1. Finite element modelling, loading and solution 172 6.3.1.2. Results 174 6.3.2. Simulation of an automobile structural component with a complex geometry 181 6.3.2.1. Finite element modelling, loading and solution 181 6.3.2.2. Results 183 6.4. Summary of Chapter 6 189 Chapter 7: Discussion 190 Chapter 8: Conclusions And Recommendation For Future Work 8.1. Conclusions 204 8.2 Thesis contribution 207 8.3. Future work 208 References 211 Appendix A Finite Element Simulation Using Implicit Finite Element Code A-i Appendix B Parametric Finite Element Modelling and Optimization Using Subproblem Optimization Method A-xii Appendix C Adaptive Load Control Algorithm A-x vi i Appendix D List of publications A-xxxvi V Nomenclature Symbol Definition Dimension c Sonic wave propagation velocity m/s i Element characteristic length m t Time s E Young’s modulus N/m2 s Strain P Density K g/m 3 V Poisson’s ratio Yield strength N/m2 (Used in Optimization Simulation) f Objective function F Feed mm g State variable h State variable n Number of design variable P Pressure N /m 2 T Simulation time m-s x Design variable w State variable «i Tolerance limit P i Tolerance limit n Tolerance limit (Used in Adaptive Simulation) f Feed mm Af Incremental feed mm P Pressure N/m2 Ap Incremental pressure N/m2 t Time m-s At Incremental time m-s Vn Normal velocity mm/m-s As Strain difference VI List of Figures Fig. No. Description Page No, Fig 1.1.1 Advantages of hydroforming over conventional manufacturing process 2 Fig 1.1.2 Automotive application of hydroforming 2 Fig 1.1.3 Setup of a typical tube hydroforming process with different stages of operation 3 Fig 2.3.1 Geometry of the bulge 10 Fig 2.3.2 Flexible dies used for bulge forming 12 Fig 2.3.3 Part of the tubular blank subjected to bulge pressure 13 Fig 2.3.4 Geometrical mode of expansion during the initial stage of bulging 14 Fig 2.3.5 Failure modes of tube hydroforming processes 16 Fig 2.3.6 Deformation of a circle to an ellipse 17 Fig 2.3.7 Graphical representation of pure, proportional large deformation in 2D strain space 17 Fig 2.3.8 The forming limit curve 18 Fig 2.3.9 The various failure limits to a simple sheet forming 18 Fig 2.3.10 Forming