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Tyre characteristics and modelling 283 Steady state Slip angle c l last d l dt Integration time step t 0 Fig. 5.36 t last t Time (s) Build-up of slip angle in an MBS model to represent tyre lag where last is the value of l computed at the last successful integration time step t is the current simulation time t last is the time for the last successful integration time step An estimate of the term ( c l )/ in equation (5.25) can be obtained from (5.27) Combining equations (5.26) and (5.27) allows the value of l required to compute lateral force at the current time step to be obtained from ⎛ c l⎞ l tt ⎝ (5.28) Using data for the baseline vehicle used throughout this text it is possible to carry out a calculation to estimate a time delay, tyre lag, for a vehicle travelling at 100 kph. The load on the tyre F z is taken as 4500 N and the radial stiffness of the tyre k z is taken as 160 N/mm. From this it is possible to calculate the static tyre deflection z : Fz z 28.1 mm (5.29) kz Referring back to equation (5.10) the effective rolling radius, R e , can be calculated using the tyre deflection z from equation (5.29) and an unloaded tyre radius, R u , of 318.5 mm from R c l c last e R 309.1 mm u z 3 last ⎠ ( ) last (5.30) Typically a tyre would roll through between 0.5 and 1 revolution (Gillespie, 1992) in order to develop the lateral force following a change in slip angle. If we assume that the tyre must complete 0.5 revolutions then for a speed of 100 kph the tyre lag on this vehicle is 0.035 s.
284 Multibody Systems Approach to Vehicle Dynamics 5.5 Experimental testing In order to obtain the data needed for the tyre modelling required for simulation a series of tests may be carried out using tyre test facilities, typical examples being the machines that are illustrated in Figures 5.37 and 5.38. The following is typical of tests performed (Blundell, 2000) used to obtain the tyre data that supports the baseline vehicle used throughout this text. Fig. 5.37 High Speed Dynamics machine for tyre testing formerly at Dunlop Tyres Ltd (courtesy of Dunlop Tyres Ltd) Fig. 5.38 Flat Bed Tyre Test machine at Coventry University
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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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7 Simulation output and interpretat
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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 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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