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Tyre characteristics and modelling 255 Direction of sliding Tyre material Adhesive forces due to molecular bonding Fig. 5.8 Road surface Frictional force component due to adhesion F F Loading Unloading δ Fig. 5.9 Hysteresis in rubber conditions such as high tyre pressures. The concept of a coefficient of friction associated with static and sliding conditions will, however, prove useful for describing the tyre models used later in this chapter. For tyres the friction generated between the tread rubber and the road surface is generated through two mechanisms these being adhesion and hysteresis. The adhesive component, shown in Figure 5.8, results from molecular bonds generated between the exposed surface atoms of rubber and road material in the contact area. This is the larger component of friction on dry roads but is greatly reduced when the road surface is contaminated with water or ice. Hence the use of ‘slick’ tyres, with no tread and increased surface contact area, for racing on dry roads. In order to understand the hysteresis mechanism consider a block of rubber subjected to an increasing and then a decreasing load as shown in Figure 5.9. As the rubber is loaded and unloaded it can be seen that for a given displacement the force F is greater during the loading phase than the unloading phase. If we continue to consider the situation where a non-rotating tyre is sliding over a non-smooth surface with a coefficient of friction assumed to
256 Multibody Systems Approach to Vehicle Dynamics Direction of sliding Loading Unloading Fig. 5.10 Road surface Loading and unloading of tyre rubber in the contact patch be zero it can be seen from Figure 5.10 that an element of rubber in the contact patch will be subject to continuous compressive loading and unloading. In the idealized situation of no friction as the tyre slides over the irregular road surface compressive forces normal to the surface are generated as the rubber is loaded and unloaded. Due to the hysteresis in the rubber the sum of the loaded forces is greater than the sum of the unloaded forces resulting in, for example here, a resultant braking force opposing the direction of sliding. 5.3.2 Pressure distribution in the tyre contact patch In order to understand the manner by which forces and moments are generated in the contact patch of a rolling tyre an initial appreciation of the stresses acting on an element of tread rubber in the contact patch is required. Each element will be subject to a normal pressure p and a shear stress acting in the road surface. In theory the element will not slip on the road if p where is the coefficient of friction between the tread rubber and the road surface. The pressure distribution depends on tyre load and whether the tyre is stationary, rolling, driven or braked. The pressure distribution is not uniform and will vary both along and across the contact patch. In order to understand the mechanics involved with the generation of forces and moments in the contact patch some simplification of the pressure distribution will be adopted here starting with Figure 5.11 where typical pressure distributions in the tyre contact patch for a stationary tyre and the effects of inflation pressure are considered. Generally the pressure rises steeply at the front and rear of the contact patch to a value that is approximately equal to the tyre inflation pressure. Overinflation causes an area of higher pressure in the centre of the contact patch while underinflation leads to an area of reduced pressure in the centre of the patch. When the tyre is rolling it will be shown later that pressure distribution in the contact patch is not symmetric and is greater towards the front of the contact patch.
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Multibody Systems Approach to Vehic
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Multibody Systems Approach to Vehic
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Contents Preface Acknowledgements N
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Contents vii 4.10.1 Problem definit
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Contents ix 8.2.1 Active suspension
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Preface This book is intended to br
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Preface xiii vehicle design process
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Acknowledgements Mike Blundell In d
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Nomenclature xvii {z I } 1 Unit vec
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Nomenclature xix O n Frame for part
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Nomenclature xxi p Magnitude of re
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1 Introduction The most cost-effect
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Introduction 3 subsequent ‘classi
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Introduction 5 Fig. 1.4 Linearity:
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Introduction 7 While apparently a s
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Introduction 9 3. The body yaws (ro
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Introduction 11 Aspiration Definiti
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Introduction 13 Decomposition: Synt
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Introduction 15 The best multibody
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Introduction 17 shows good correlat
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Introduction 19 generated in numeri
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Introduction 21 1.9 Benchmarking ex
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2 Kinematics and dynamics of rigid
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Kinematics and dynamics of rigid bo
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3 Multibody systems simulation soft
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4 Modelling and analysis of suspens
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Page 228 and 229: Modelling and analysis of suspensio
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Tyre characteristics and modelling
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Modelling and assembly of the full
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7 Simulation output and interpretat
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Simulation output and interpretatio
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down and even more difficult to asc
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8 Active systems 8.1 Introduction M
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Active systems 443 mechanical actua
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Active systems 445 Table 8.1 MSC.AD
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Active systems 447 Body acceleratio
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Active systems 449 impressions of t
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Active systems 451 For this reason,
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Appendix A: Vehicle model system sc
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Appendix B: Fortran tyre model subr
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Appendix C: Glossary of terms Agili
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Appendix C: Glossary of terms 489 a
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Appendix C: Glossary of terms 495 m
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Appendix C: Glossary of terms 501 s
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References 503 Blundell, M.V. The m
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References 505 Hudi, J. AMIGO - A m
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References 507 Palmer, D. Course no
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References 509 European ADAMS News
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Index Abuse loads, 148 3 g bump, 14
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Index 513 Elk Test, 1 El-Nasher, 29
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Index 515 generalised translational
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Index 517 steer axis inclination, 1
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