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Simulation output and interpretation 419 RC rear cm F FOy F FIz Roll axis F ROy F ROz F RIy A y F RIz RC front Z F FIy Y X F FOz Fig. 7.24 Resulting forces acting at the inner and outer tyres Lateral force F y F y Fig. 7.25 Inner tyre load Static tyre load Outer tyre load Vertical load F z Loss of cornering force due to non-linear tyre behaviour At this stage we must consider the tyre characteristics. The tyre cornering force F y varies with the tyre load F z but the relationship is not linear (as shown in Chapter 5). Figure 7.25 shows a typical plot of tyre lateral force with tyre load at a given slip angle. The total lateral force produced at either end of the vehicle is the average of the inner and outer lateral tyre forces. From the figure it can be seen that F y represents a theoretical loss in tyre force
420 Multibody Systems Approach to Vehicle Dynamics resulting from the averaging and the non-linearity of the tyre. Tyres with a high load will not produce as much lateral force (in proportion to tyre load) compared with other tyres on the vehicle. More weight transfer at either end therefore reduces the total lateral force produced by the tyres and causes that end to drift out of the turn. It should be noted that this behaviour is true for all slip angles of interest; at low slip angles, the cornering stiffness of the tyre is reduced non-linearly with increasing load, promoting a larger slip angle at an axle with a greater roll moment. At saturated slip angles, the peak lateral force is reduced as a proportion of the vertical load, producing a lower coefficient of friction for an axle with a greater roll moment. Thus mechanisms that adjust sub-limit under- and oversteer also adjust departure plough and spin behaviour. Although substantially simplified, the preceding analysis helps with understanding the essential mechanisms in play when a vehicle is cornering. 7.4 Transient effects Vehicle dynamics would be a very simple field if the preceding text described it entirely. However, the pneumatic tyres in use have some features that add complication. The most significant of these is the need for the tyres to have a slip angle in order to generate a lateral force. This can be seen intuitively to lead to the need for a slip angle of the body as a whole (Figure 7.26). The need for a body slip angle gives rise to an additional yaw rate, rotating the body to the correct slip angle, for a brief period near the start of any manoeuvre. There is also a corresponding yaw rate reduction at the end of a manoeuvre required to bring the vehicle back to its trimmed, straight-ahead state. These variations in yaw rate are acutely remarked by even the least skilled driver and greatly influence the emotional reaction of the driver to the car – although the driver might not consciously recognize it. A vehicle that rotates slowly to give the required body slip angle feels sluggish and unresponsive; a vehicle that overshoots and oscillates feels lively and poorly controlled. Subjectively, these two states might be described as Body slip angle, β Forward velocity, u Yaw velocity, Lateral velocity, v Rear axle slip angle, r Front axle slip angle, f Fig. 7.26 Pneumatic tyres give rise to the need for a body slip angle
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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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4 Modelling and analysis of suspens
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Tyre characteristics and modelling
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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 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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