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Tyre characteristics and modelling 263 F z F O Rx R l M y = F z x F Rx Rear P Front {X SAE } 1 x F z Fig. 5.17 Generation of rolling resistance in a free rolling tyre patch it will be loaded until it reaches the midpoint of the contact patch and unloaded as it moves to the rear of the contact patch. This and the additional losses due to hysteresis in the side walls lead to a pressure distribution that is not symmetrical as shown for the stationary tyre in Figure 5.11 and has a greater pressure distribution in the front half of the contact patch as shown in Figure 5.17. The pressure distribution implies that the resultant tyre load F z acts through the centre of pressure a distance x forward of the wheel centre. For equilibrium a couple exists that must oppose the tyre load and its reaction acting down through the wheel centre. The couple that reacts the wheel load couple results from the rolling resistance force F Rx acting longitudinally in the negative X SAE axis and reacted at the wheel centre where Fz x FRx (5.17) R l The rolling resistance may also be referenced by a rolling resistance coefficient, this being the rolling resistance force F Rx divided by the tyre load F z . By definition therefore the rolling resistance moment, M y , is F z x and the rolling resistance moment coefficient is x. Rigorous adherence to the sign convention associated with the tyre reference frame is essential when implementing these formulations in a tyre model. In Figure 5.17, to assist understanding, F z is represented as the vertical force acting on the tyre rather than the negative normal force computed in the Z SAE direction. The rolling resistance force is very small in comparison with other forces acting at the contact patch, a rolling resistance coefficient of the order 0.01 being typical for a car tyre. This and the fact that the rolling resistance force
264 Multibody Systems Approach to Vehicle Dynamics may vary by up to 30% of the average value during one revolution (Phillips, 2000) make accurate measurement difficult. 5.4.4 Braking force During braking the activation of the brake mechanism will apply forces to the rotating wheel that at this stage may be treated as a brake torque T B acting about the wheel centre and opposing the rolling motion of the wheel. During this process the tread material in the tyre will begin to slide relative to the road, giving rise to slip. As the angular velocity of the wheel reduces a braking force is generated that tends to move the contact patch rearwards relative to the wheel centre. This effect will introduce circumferential tension in the tread just before entering the contact patch as opposed to the compression noted earlier in this area for a free rolling tyre. As the contact patch distorts rearward during braking compression will instead be generated in the tread just leaving the patch as shown in Figure 5.18. During braking, as for free rolling, as tread material approaches the contact patch the radius will reduce with a consequent reduction in the tangential speed of the tread material relative to the wheel centre. For moderate braking, the tread initially entering the contact patch will initially bend rearward under the action of shear stresses for a short distance before the tangential velocity of the tread material slows to the forward velocity of the tyre R e and slip begins to progressively develop as the tread material moves back through the contact patch. As the tread approaches the rear of the tread the pressure begins to unload releasing the deformation in the tread. The tangential velocity of the tread material begins to increase and the frictional braking force reduces rapidly to zero at the rear of the patch. These actions produce distributions of pressure, slip and longitudinal shear stress of the type shown at the bottom of Figure 5.18 where the shear stress is plotted as negative in accordance with the resultant braking force resolved in the SAE tyre co-ordinate system. It should also be noted that when braking, the pressure distribution tends to differ from that in a free rolling tyre as the peak, and hence resultant tyre load, move further forward in the tyre contact patch. If the resulting braking force is maintained the angular velocity of the tyre will reduce from its free rolling value and will eventually become zero when the wheel is fully locked. A measure of the slip generated can be defined by a slip ratio or percentage slip. In this text the term slip ratio S will be used: S 0 0 B (5.18) where 0 is the angular velocity of the free rolling wheel B is the angular velocity of the braked wheel If we consider the case of a braked wheel it can be seen from equation (5.18) that for the free rolling state the slip ratio will be zero and that for the fully locked and skidding wheel the slip ratio will be 1.0. Multiplying slip ratio by 100 gives the term percentage slip.
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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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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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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 495 m
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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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