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Tyre characteristics and modelling 251 R u V R l R e Rear Front Fig. 5.4 B P C Definition of tyre radii A d A R u V R l P B d C z Fig. 5.5 Deformation of rolling tyre (ii) The static loaded radius is the loaded radius of a stationary tyre inflated to the normal recommended pressure. (iii) The effective rolling radius, R e , is the ratio of the linear velocity of the wheel centre in the X SAE direction to the angular velocity of the wheel. A more detailed treatment of effective rolling radius is provided by Phillips (2000) based on the representation given in Figure 5.5 which allows the effective rolling radius to be related to the unloaded radius and tyre deflection. For the tyre shown in Figure 5.5, the wheel axle is considered fixed and the road moving such that the relative forward velocity of the wheel is V. If a
252 Multibody Systems Approach to Vehicle Dynamics number of equidistant radial lines are drawn on the tyre the number passing point A in a given time must be the same as the number passing point P in the contact patch. If we take d the distance between the radial lines at the tyre outer radius near A d the distance between the radial lines at the contact patch near P then R d u therefore V d (5.2) R e V R d u d (5.3) The tread band is subject to a longitudinal compressive strain within the contact patch where dd d (5.4) dd (1 ) (5.5) therefore R e R u (1 ) (5.6) Assuming that the strain in the contact line is constant we have (assuming sin ( 3 /3!) ( 5 /5!) …) cord 1 BC arc BC sin ≈ 1 6 2 (5.7) From Figure 5.5 we also have (assuming cos 1 ( 2 /2!) ( 4 /4!) …) z Ru( 1 cos ) ≈ Ru 2 2 (5.8) From equations (5.7) and (5.8) we have 1 1 z 3 R u (5.9) From equations (5.6) and (5.9) we have R e R u z 3 (5.10)
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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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Multibody systems simulation softwa
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4 Modelling and analysis of suspens
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Modelling and analysis of suspensio
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Page 224 and 225: Modelling and analysis of suspensio
Page 272 and 273: Tyre characteristics and modelling
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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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