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Tyre characteristics and modelling 271 SIDE VIEW Pressure p Limit lateral stress p Slipping starts Lateral stress Front Tyre contact patch Rear TOP VIEW M z = F y x pt F y Slipping starts Lateral stress Direction of wheel heading Direction of wheel travel x pt Pneumatic trail Fig. 5.23 Generation of lateral force and aligning moment due to slip angle angles, when the lateral stress shape is substantially triangular, there is a nearly linear relationship between lateral force and slip angle. In general this linearity only extends to 1 or 2 degrees of slip angle. As the slip angle increases, the amount of rubber involved in sliding gradually extends from the rear of the tyre contact patch until all the rubber is sliding and the lateral stress follows the boundary limit p distribution. Since the form of the pressure distribution is a measure of the tyre load (F z ), it follows that the maximum lateral force F y max is found from F y max F z (5.22) In practice this maximum is achieved at slip angles above 20 degrees for most tyres. Figure 5.24 shows a typical plot of lateral force F y with slip angle for increasing tyre load with the camber angle set at zero. For the convenience of plotting results in the positive quadrant negative slip angle is used in this plot. From the plot it can be seen that the cornering stiffness C is the gradient of the curve measured at zero slip angle at a given tyre load. As the tyre load increases so does the cornering stiffness although it will be seen later that at higher tyre loads the magnitude of the cornering stiffness begins to level off. In Figure 5.24 the curves are shown to pass through the
272 Multibody Systems Approach to Vehicle Dynamics Camber angle = 0 Lateral force F y (N) F z = 8 kN F z = 6 kN F z = 4 kN F z = 2 kN φ Cornering stiffness C = tan Fig. 5.24 Slip angle (degrees) Plotting lateral force versus slip angle origin. In practice a small offset in lateral force will be apparent at zero slip angle due to the effects of conicity and plysteer discussed earlier. Looking back to Figure 5.23 it can be seen that as the shape of the lateral stress distribution is approximately triangular the lateral force F y acts through the centroid of this area that is to the rear of the wheel centre line by a distance referred to as the pneumatic trail. Inspection of Figure 5.23 should indicate that as the slip angle increases the line of action of F y moves forward reducing the pneumatic trail eventually to zero. The aligning moment M z is the product of the lateral force and the pneumatic trail and will reduce accordingly eventually becoming negative usually for lightly loaded tyres at high slip angles. In these situations the extent of sliding occurs to such an extent throughout the contact patch that the lateral stress distribution approaches the shape of the p curve moving the centroid through which F y acts forward of the centre. A typical plot of aligning moment with slip angle, for a given tyre load and zero camber angle, is shown in Figure 5.25. From the plot it can be seen that the aligning moment stiffness is the gradient of the curve measured at zero slip angle at a given tyre load. The aligning moment curve is nearly linear at low slip angles and reaches a maximum value for most tyres at a slip angle of 4 to 6 degrees. The gradient of the curve measured at a zero slip angle is the aligning moment stiffness. In Figure 5.25 the curves are shown to pass through the origin. In practice a small offset in aligning moment will be apparent at zero slip angle due to the effects of conicity and plysteer discussed earlier. 5.4.8 The effect of camber angle The lateral force that arises due to an inclination of the tyre from the vertical is referred to as camber thrust. The SAE definition of positive camber angle is taken for the top of the tyre leaning outwards relative to the vehicle. The fact that this differs from side to side does not lead to consistency when developing a tyre model. For understanding it is useful to remember that
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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 244 and 245: 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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