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Tyre characteristics and modelling 265 T B O V R e Compression Rear Tread deformation Front Tension x F B {X SAE } 1 Pressure distribution F z Longitudinal slip Longitudinal shear stress Fig. 5.18 Generation of force in a braked tyre In SAE J670e (SAE Publication, 1976) the sign is reversed to produce a slip ratio of 1.0 for the fully locked wheel, convenient when plotting braking force that is negative in the SAE system against slip ratio: B 0 S (5.19) 0 A further definition that is popular is to substitute V 0 R e into equation (5.18) giving V R S B e (5.20) V
266 Multibody Systems Approach to Vehicle Dynamics Slip angle = 0 Camber angle = 0 Braking force F x (N) F z = 8 kN F z = 6 kN F z = 4 kN F z = 2 kN φ Longitudinal stiffness C s = tan φ 0.0 Slip ratio 1.0 Fig. 5.19 Braking force versus slip ratio It should be noted that slip ratio has been subject to various definitions by researchers and research groups in tyre companies, several are listed in Milliken and Milliken (1995). Some tyre models use R l instead of R e when formulating slip ratio which may require careful consideration when using a general-purpose MBS program to model ABS (Ozdalyan and Blundell, 1998). Plotting curves of braking force, for convenience shown positive here, against slip ratio for a range of tyre loads will generally produce curves of the type shown in Figure 5.19. Examination of the curves in Figure 5.19 reveals that at each vertical load the braking force increases rapidly in a linear manner to reach a peak value that, depending on tyre design and road conditions, would typically occur at a slip ratio anywhere between 0.15 and 0.3. After this point the braking force will level out or reduce as the wheel approaches the fully locked situation. Examination of curves such as these, sometimes called ‘mu-slip’ curves, facilitates an understanding of ABS operation where cycling the brake pressure maintains a slip ratio near the peak braking force position for each wheel on the vehicle. This is desirable not only to maximize braking effort but also to maintain a rolling wheel for cornering and directional stability. An important property of each curve is the slope at the origin, referred to as the longitudinal stiffness, C s . It can be seen that this is not a constant but increases with load which is significant when considering the capability of any tyre model to be used in braking simulations. In Figure 5.19 the curves are shown to pass through the origin. In practice a small vertical offset in longitudinal force will be apparent for a free rolling tyre, this being the rolling resistance discussed earlier. It is important to reiterate that frictional forces are not the property of the tyre alone. The effects of road material and texture, or contamination with water and ice, are also significant. Figure 5.20 demonstrates typical curves of braking force against slip ratio, at a given tyre load for various road conditions (Phillips, 2000). These curves demonstrate that on wet roads peak
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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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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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