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Tyre characteristics and modelling 257 Overinflation Normal inflation Pressure distribution in the tyre contact patch Underinflation Tyre contact patch Fig. 5.11 Pressure distribution in a stationary tyre contact patch 5.4 Tyre force and moment characteristics 5.4.1 Components of tyre force and stiffness The local pressures and stresses distributed over the tyre contact patch can be integrated to produce forces and moments referenced to a local co-ordinate system within the contact patch. Using the SAE tyre axis system the full set of forces and moments is as shown in Figure 5.12. The following section will explain the mechanical characteristics of each force and moment component. The order in which these components are described will be that which most facilitates an understanding of the mechanisms and dependencies rather than following the local order of the SAE tyre axis system. The tractive force F x and lateral force F y depend on the magnitude of the normal force component F z . Hence the normal force is described first. It should also be noted that more than one mechanism will be involved in the generation of each component. The tractive force has formulations involving driving, braking and rolling resistance. The lateral force is dependent on both slip and camber angle. It is also not possible to treat components of force and moment in isolation. It is, for example, necessary to provide a single explanation as to how the self-aligning moment and lateral force resulting from slip angle arise due to stress distributions within the tyre contact patch. Finally the reader should also be reminded that vehicle dynamics is traditionally a subject where various terms are used to describe the same thing. For example, vertical force, normal force and tyre load may be used to mean the same thing by various authors. Other examples where confusion may arise include the use of aligning torque, aligning moment or selfaligning moment, longitudinal or tractive force and lateral or cornering force.
258 Multibody Systems Approach to Vehicle Dynamics SPIN AXIS OVERTURNING MOMENT (M x ) TRACTIVE FORCE (F x ) WC {X SAE } 1 α P ROLLING RESISTANCE MOMENT (M y ) SELF-ALIGNING MOMENT (M y ) {Z SAE } 1 {Y SAE } 1 LATERAL FORCE (F y ) NORMAL FORCE (F z ) Fig. 5.12 Tyre forces and moments shown acting in the SAE tyre axis system The use of the term stiffness can also add confusion to newcomers to the subject area. A traditional static force/displacement approach is used by Moore (1975) to define longitudinal, lateral and torsional stiffness of a tyre. In each case a non-rolling tyre is mounted on a plate and incrementally loaded as indicated in Figure 5.13 until complete sliding occurs. Plotting graphs of force or moment against displacement or rotation allows the stiffness parameters to be obtained from the slopes at the origin. We will see later that terms such as cornering stiffness and aligning moment stiffness are associated with a rolling tyre and should not be confused with the lateral and torsional stiffness defined here. The term longitudinal stiffness can be particularly misleading as another definition is commonly used when longitudinal tractive forces due to driving and braking are discussed. The explanations that follow will initially deal with each force mechanism in isolation, for example lateral forces arising due to slip angle and camber angle are considered separately with no simultaneous longitudinal tractive force. Following this, a more complex treatment involving combinations of the various force components will be addressed. 5.4.2 Normal (vertical) force calculations The calculation of normal force in the tyre is relatively straightforward compared with the calculation of longitudinal or lateral forces. The normal force will, however, always be negative when computed using the SAE tyre axis system. This is not particularly elegant when presenting the dependencies of other force components on the normal force. To overcome this a positive value of this force component is often referred to as vertical force or tyre load. In SAE J670e (SAE Publication, 1976) vertical load is taken as the negative of normal force.
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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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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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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 491 t
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Appendix C: Glossary of terms 493 e
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Appendix C: Glossary of terms 495 m
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Appendix C: Glossary of terms 497 h
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Appendix C: Glossary of terms 499 t
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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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