2006:341 CIV MASTER’S THESIS Simulation and Validation of Tire Deformation under Certain Load Cases HENRIK ANDERSSON MASTER OF SCIENCE PROGRAMME Mechanical Engineering Luleå University of Technology Department of Applied Physics and Mechanical Engineering Division of Computer Aided Design 2006:341 CIV • ISSN: 1402 - 1617 • ISRN: LTU - EX - - 06/341 - - SE Eine einfache Formel genügt nicht mehr, auch wenn sie magisch ist — Michael Gipser Abstract This master’s thesis deals with computer aided simulations of mechanical systems in the automotive industry. The specific target of simulation is the pneumatic tire and its behaviour. The aim is to establish a method to use computer simulations for shortening the development cycle and reducing the need for testing and physical prototypes. The work has been separated into several steps, starting with a thorough information study, continuing with creative methods and concept creation. Later on, an evaluation of the concepts has been performed, to find the best approach to continue working on. The selected concepts from the evaluation were further developed to result in the final simulation method. The results of the simulations have then been validated against measurements. A proposal for further work in the subject has been made, as well as ideas for other projects. Keywords Tire simulation, Vehicle simulation, Product development process. i Preface The work presented in this masters thesis is to obtain the Master of Science degree in Mechanical Engineering, with specialization in Computer Aided Engineering. This the- sis has been written at the BMW Group Research and Innovation Center (FIZ) in Munich Germany, during the second half of 2006. The thesis project was initiated and granted by Mr. Robert Hartl, head of the wheel design team at the Wheel and Tire department EF-33 at BMW. I wish to express my appreciation to my supervisor at BMW, Thomas Kellner for all his help and support during my time at BMW in Munich and to my examiner Tobias Larsson at Luleå University of Technology. Many thanks also goes to Erich Rott and Jens Holtschulze, as well as all the other colleagues at the BMW Research and Innovation Center for their help during my thesis. Finally, I would like to thank my family and friends for their support during the entire thesis work. Munich, November 30th, 2006 —————————————- Henrik Andersson ii Contents Contents List of Figures vi List of Abbreviations viii List of Symbols ix 1. Introduction 1 1.1. Tire clearance . 1 1.1.1. Purpose . 2 1.1.2. Schematic overview . 3 1.2. Observations . 11 1.3. Problem formulation . 11 2. Theory 12 2.1. Product design & Development processes . 12 2.1.1. Introduction to product development . 12 2.1.2. Design space exploration phase . 13 2.1.3. Roadmap phase . 13 2.1.4. Concept Design & Prototyping . 14 2.1.5. Detail design & Manufacturing . 16 2.2. Simulation in Engineering . 16 2.2.1. The simulation process . 16 2.2.2. Simulation in Automotive Engineering . 17 2.3. Product Lifecycle Management . 17 2.3.1. Computer Aided Design . 18 2.3.2. Computer Aided Engineering . 19 2.4. Theory of ground vehicles . 23 2.4.1. Vehicle dynamics . 24 2.4.2. Tires . 28 2.5. Programming languages . 49 2.5.1. MATLAB . 49 2.5.2. Python . 49 2.5.3. C/C++ . 49 2.5.4. FORTRAN . 49 3. Method 50 3.1. Design space exploration . 50 3.1.1. Benchmarking . 50 3.1.2. Related technologies . 52 3.2. Roadmap . 54 3.2.1. Mission statement . 54 iii Contents 3.2.2. Product characteristics . 54 3.2.3. Thesis delimitation . 55 3.3. Concept design . 55 3.3.1. Brainstorming . 55 3.3.2. Concepts . 56 3.3.3. Evaluation of concepts . 58 3.4. Detailed design . 60 3.4.1. Concept refinement . 60 3.4.2. Input data for simulations . 62 3.4.3. Output from simulation models . 63 3.4.4. Initial model verification and validation . 64 3.4.5. Final testing and validation . 66 4. Results 69 4.1. Measurements . 69 4.2. Concepts . 70 4.2.1. FTire concept . 70 4.2.2. RMOD-K 7 concept . 71 4.2.3. Mathematical/Empirical Concept . 71 5. Discussion and conclusion 72 5.1. General conclusions . 72 5.1.1. Simulations . 73 5.1.2. Physical/MBS tire models . 73 5.1.3. Finite element models . 74 5.2. Concept results . 75 5.2.1. FTire concept . 75 5.2.2. RMOD-K 7 concept . 76 5.2.3. Mathematical/Empirical concept . 77 5.3. Sources of errors . 78 5.3.1. Tire simulation models . 78 5.3.2. Tire parameterization . 78 5.3.3. Pressure variations . 79 5.3.4. Contour and deformation measurement . 79 5.4. Future work . 80 5.4.1. Validation of the tire models and parametrized data . 80 5.4.2. Additional test rig measurements . 80 5.4.3. Improvement of simulation models . 81 5.4.4. MBS full vehicle simulations . 81 5.4.5. Universal Tire model . 82 6. Summary 83 A. Appendix: Results 84 A.1. Measurement data . 85 A.2. Measured tire contour . 94 A.3. Tire contour validation . 96 A.4. Comparison of deformations . 98 A.5. Modification of the RMOD-K model . 109 iv Contents References 113 Index 120 v List of Figures List of Figures 1.1. Volumetric decomposition of a BMW 3 SERIES Sedan (E90) . 3 1.2. Overview of the tire clearance process . 4 1.3. ETRTO Standards for generating the static envelope contour . 5 1.4. Measurement of deformation on test vehicle . 6 1.5. Post-processing in Catia of the measured tire deformation . 6 1.6. Sectors for measuring tire deformation . 7 1.7. Different types of RHK geometries . 7 1.8. Example of SRHK, combination of RHK for different tire dimensions . 8 1.9. RGB for front and rear wheels . 9 1.10. Foam mounted on inside of wheel well . 9 1.11. Definition of tire deformation . 10 2.1. Schematic description of a simulation process . 17 2.2. Illustration of the axle loads . 25 2.3. Theory of cornering . 27 2.4. Design of a radial tire . 30 2.5. Illustration of the naming conventions for rims and tires . 31 2.6. Comparison of SAE and ISO axis systems . 32 2.7. Friction circle . 33 2.8. Tire/Road friction interaction . 34 2.9. Friction dependence on relative velocity . 35 2.10. Friction dependence on contact pressure . 35 2.11. Description of slip angle phenomenon . 36 2.12. Cambering effects . 38 2.13. MTS Flat-Trac CT tire test rig . 40 2.14. Pacejka’s Magic Formula . 42 2.15. Discretization of FTire flexible ring model . 44 2.16. Cross-section representation in the flexible ring model . 45 2.17. Structure representation in the FETire model . 45 2.18. Structure representation in the RMOD-K 7 Flexible belt model . 47 3.1. Simple tire model used in Volkswagen study . 51 3.2. Statistics of tire deformation . 56 3.3. Adams tire model . ..