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Tyre characteristics and modelling 259 F x F x Longitudinal stiffness x x F y Lateral stiffness F y y y T z Torsional stiffness T z φ Fig. 5.13 Measurement of stiffness in a non-rolling tyre φ It is generally sufficient to treat the tyre as a linear spring and damper when computing the vertical force component. The calculation of the vertical force F z acting at point P in the tyre contact patch has a contribution due to stiffness F zk and a contribution due to damping F zc . These forces act in the direction of the {Z SAE } 1 vector shown in Figure 5.14: F z F zk F zc (5.12) F zk k z z (5.13) F zc c z V z (5.14) where c 2.0 m k z t z and m t mass of tyre k z radial tyre stiffness radial damping ratio z tyre penetration V z rate of change of tyre penetration
260 Multibody Systems Approach to Vehicle Dynamics m t k z c z z {XSAE } 1 P {Z SAE } 1 Fig. 5.14 Vertical tyre force model based on a linear spring damper A linear model of tyre vertical force may need to be extended to a nonlinear model for applications involving very heavy vehicles or studies where the tyre encounters obstacles in the road or terrain of a similar size to the contact patch or smaller. This could also be applicable for parallel work in the aircraft industry where established tyre models have been formulated to simulate the behaviour of the aircraft on the runway, particularly on landing, and potential problems with wheel shimmy (Smiley, 1957; Smiley and Horne, 1960). Where a non-linear model of vertical tyre force is required the most straightforward approach would be to represent the stiffness-based component of the force by a cubic spline interpolation of measured static force–displacement data. 5.4.3 Longitudinal force in a free rolling tyre (rolling resistance) Under normal driving conditions a tyre is continually subject to a wide range of tractive driving and braking forces. This section discusses the formulation of driving and braking forces under pure slip conditions, i.e. straight-line motion only. The more complex situation of combined slip, for example simultaneous braking and cornering, is addressed later in this chapter. As a starting point it can be shown that slip will always be present in the tyre contact patch even in the absence of tractive driving and braking forces. Consider first the free rolling tyre shown in Figure 5.15 and the mechanism that leads to the generation of longitudinal slip. The model used in Figure 5.15 has simplifications but will help to develop an initial understanding. As the tyre rolls forward the radius reduces as tread material approaches point A at the front of the tyre contact patch. At this point we can say that the forward velocity V of the wheel relative to the road surface is given by V R e (5.15)
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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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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 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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