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University of Warwick institutional repository: http://go.warwick.ac.uk/wrap A Thesis Submitted for the Degree of PhD at the University of Warwick http://go.warwick.ac.uk/wrap/1238 This thesis is made available online and is protected by original copyright. Please scroll down to view the document itself. Please refer to the repository record for this item for information to help you to cite it. Our policy information is available from the repository home page. Finite Element Modelling and Simulation for a 'Smart' Tyre by Wayne Hall A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Engineering School of Engineering, University of Warwick January 2003 To Angie and Patrick Contents Contents ............................................................................................ List Figures of .................................................................................. List Tables of ...................................................................................... x Acknowledgments .............................................................................. xi Declaration ....................................................................................... xii Summary .......................................................................................... xiii Notation AV .......................................................................................... Chapter 1: Introduction I ....................................................................... 1.1 Automobile Tyres 2 .......................................................................... 1.2 'Smart' Tyres 3 .............................................................................. 1.3 Thesis Motivation 4 ......................................................................... 1.4 Thesis Outline 5 ............................................................................. Chapter 2: Automobile Tyres, Tyre Behaviour Modelling 8 and ........................ 2.1 Introduction 8 .............................................................................. 2.2 Tyre Construction 8 ........................................................................ 2.3 Sizes Load Rating 10 and ................................................................. 2.4 Forces Moments 10 and ................................................................. 2.5 Rolling Resistance 12 .................................................................... 2.6 Tractive Properties 13 ..................................................................... H 2.7 Comering Characteristics 16 ............................................................. 2.7.1 SHpAngle 17 ........................................................................ 2.7.2 CamberAngle 19 ...................................................................... 2.7.3 Concity Ply Steer 20 and ............................................................ 2.8 CombinedBraking Cornering 21 and .................................................... 2.8.1 Brush Model 23 ...................................................................... 2.8.2 Magic FonnulaModel 24 ........................................................... 2.9 Finite ElementModels 26 .................................................................. 2.9.1 Implicit Integration 27 ............................................................... 2.9.2 Explicit Integration 30 ............................................................... 2.10Summary 31 ................................................................................. Chapter 3: Experimental Work to Characterise Tyre Behaviour in the Contact Patch 32 ............................................................................................... 3.1 Introduction 32 ............................................................................. 3.2 Experimental Tyre 33 ...................................................................... 3.3 Testing Equipment 34 ...................................................................... 3.3.1 Load-DeflectionMachine 34 ........................................................ 3.3.2 Flat Bed Tyre TestingMachine 35 ................................................. 3.3.3 Rolling Drum TestingMachine 36 ................................................. 3.4 Tyre Experiments 37 ...................................................................... 3.4.1 Stationary Experiments 37 .......................................................... 3.4.2 Flat Bed Experiments 37 ........................................................... 3.4.3 Rolling Dnim Experiments 38 ...................................................... 3.5 Results Discussion:Stationary Experiments 39 and ................................... 3.6 Results Discussion: Flat Bed Experiments 41 and ..................................... 3.6.1 Free-RoHingCharacteristics 42 .................................................... 3.6.2 CorneringCharacteristics Shp Angle 46 and .................................... 3.6.3 CorneringCharacteristics CamberAngle 48 and ................................ 3.7 Results Discussion:Rolling Drum Experiments 50 and ............................. 3.7.1 Free-Rolling Characteristics Normal Load 50 and ............................. 3.7.2 Free-Rolling Characteristics Speed 52 and ..................................... 3.7.3 Cornering Characteristics Slip Angle 54 and .................................... 3.7.4 Cornering Characteristics Camber Angle 57 and ................................ iii 3.8 Summary 57 ................................................................................. Chapter 4: Finite Element Models for Simulation of Microscopic Tyre Behaviour 60 0.00.0 0060 4.0........... 0000................................................................ 4.1 Introduction 60 ............................................................................. 4.2 Mesh Generation 60 ........................................................................ 4.2.1 Tyre Components 63 ............................................................... 4.2.2 SteelWheel 67 ....................................................................... 4.3 Material Properties 67 ..................................................................... 4.4 Rubber Compounds 67 .................................................................... 4.5 Mooney-Rivlin Equation 70 .............................................................. 4.6 Reinforcements 74 ......................................................................... 4.7 Contact Friction 76 and .................................................................. 4.8 Summary 80 ................................................................................. Chapter 5: Simulation Stationary (Non-Rolling) Tyre Behaviour 81 of ............... 5.1 Introduction 81 ............................................................................. 5.2 StationarySimulations 81 .................................................................. 5.3 Normal Loading Simulation 82 ........................................................... 5.3.1 WheelFit Inflation Phase 84 and .................................................. 5.3.2 Normal Loading Phase 87 ......................................................... 5.4 Longitudinal Lateral Loading Simulations 88 and ..................................... 5.4.1 TransverseLoading Phase 88 ...................................................... 5.4.2 RestartFfles ....................................................................... 89 5.5 Selection Analysis Results 89 of .......................................................... 5.6 Results Discussion: Normal Loading Simulation 90 and ............................. 5.6.1 ParametricStudy ............................................................... 93 5.6.2 Normal PressureDistribution ................................................. 95 5.7 Results Discussion:Longitudinal Lateral Loading Simulations 98 and and ....... 5.8 Summary 99 ................................................................................. Chapter 6: Simulation Rolling Tyre Behaviour 100 of .................................... 6.1 Introduction 100 ............................................................................ 6.2 ComputationalConsiderations 100 ...................................................... iv 6.3 Rolling Simulations 101 .................................................................... Fit Inflation, Normal Loading Phase 101 6.3.1 Wheel and and .................... 6.3.2 Rolling Phase 102 ................................................................... 6.4 Tyre Damping 103 ......................................................................... 6.5 Results Discussion: LS-DYNA 950d. 103 and version ................................ Discussion: LS-DYNA 960 104 6.6 Results and version .................................. between LS-DYNA 950d 960 108 6.7 Incompatibility version and ...................... 6.8 Internal Stresses Strains III and ......................................................... 6.8.1 At Lateral Tyre Centre 113 the .................................................... from Lateral Tyre Centre 117 6.8.2 At +30mrn and +55mm the ..................... 6.9 Summary 122 ................................................................................ Work 123 Chapter7: Review, Conclusions and Recommendations for Further ..... 7.1 Thesis Review 123 .........................................................................

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