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Contents<br />

vii<br />

4.10.1 Problem definition 202<br />

4.10.2 Velocity analysis 202<br />

4.10.3 Acceleration analysis 214<br />

4.10.4 Static analysis 226<br />

4.10.5 Dynamic analysis 234<br />

4.10.6 Geometry analysis 242<br />

5 Tyre characteristics and modelling 248<br />

5.1 Introduction 248<br />

5.2 Tyre axis systems and geometry 249<br />

5.2.1 The SAE and ISO tyre axis systems 249<br />

5.2.2 Definition of tyre radii 249<br />

5.2.3 Tyre asymmetry 253<br />

5.3 The tyre contact patch 254<br />

5.3.1 Friction 254<br />

5.3.2 Pressure distribution in the tyre contact patch 256<br />

5.4 Tyre force and moment characteristics 257<br />

5.4.1 Components of tyre force and stiffness 257<br />

5.4.2 Normal (vertical) force calculations 258<br />

5.4.3 Longitudinal force in a free rolling tyre (rolling<br />

resistance) 260<br />

5.4.4 Braking force 264<br />

5.4.5 Driving force 267<br />

5.4.6 Generation of lateral force and aligning moment 269<br />

5.4.7 The effect of slip angle 269<br />

5.4.8 The effect of camber angle 272<br />

5.4.9 Combinations of camber and slip angle 276<br />

5.4.10 Overturning moment 277<br />

5.4.11 Combined traction and cornering (comprehensive<br />

slip) 278<br />

5.4.12 Relaxation length 281<br />

5.5 Experimental testing 284<br />

5.6 Tyre modelling 291<br />

5.6.1 Overview 291<br />

5.6.2 Calculation of tyre geometry and velocities 295<br />

5.6.3 Road surface/terrain definition 299<br />

5.6.4 Interpolation methods 299<br />

5.6.5 The ‘Magic Formula’ tyre model 301<br />

5.6.6 The Fiala tyre model 306<br />

5.6.7 Tyre models for durability analysis 308<br />

5.7 Implementation with MBS 314<br />

5.7.1 Virtual tyre rig model 315<br />

5.8 Examples of tyre model data 318<br />

5.9 Case study 6 – Comparison of vehicle handling tyre<br />

models 320<br />

6 Modelling and assembly of the full vehicle 326<br />

6.1 Introduction 326<br />

6.2 The vehicle body 327<br />

6.3 Measured outputs 330<br />

6.4 Suspension system representation 331<br />

6.4.1 Overview 331

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