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Modelling and assembly of the full vehicle 345 REVOLUTE Bell crank Rebound movement Spring damper Anti-roll bar Push rod upper Rotational spring damper Anti-roll bar lower UNIVERSAL SPHERICAL REVOLUTE Rotation REVOLUTE REVOLUTE Push rod Bump movement Fig. 6.20 Modelling of anti-roll bar mechanism in student race car anti-roll bar to rock back and forward as the bell cranks rotate during parallel wheel travel but prevents rotation during opposite wheel travel when the body rolls. As the body rolls the torsional stiffness of the anti-roll bar, modelled with the rotational spring damper, resists the pushing motion of one push rod as the suspension moves in bump on one side and the pulling motion as the suspension moves in rebound on the other side. The small spring damper helps to locate the anti-roll bar with respect to the vehicle chassis and adds to the heave stiffness and damping. Alternative linkage designs are possible that allow the use of a translational spring element and hence allow independent control of damping in roll compared to damping in heave. Such ‘three spring’ systems are common in higher formula motorsports events when allowed by the rules. 6.7 Determination of roll stiffness for the equivalent roll stiffness model In order to develop a full vehicle model based on roll stiffness it is necessary to determine the roll stiffness and damping of the front and rear suspension elements separately. The estimation of roll damping is obtained by assuming an equivalent linear damping and using the positions of the dampers relative to the roll centres to calculate the required coefficients. If a detailed vehicle model is available the procedure used to find the roll stiffness for the front suspension elements involves the development of a model as shown in Figure 6.21. This model includes the vehicle body, this being constrained to rotate about an axis aligned through the front and rear roll centres. The roll centre positions can be found using the methods described in Chapter 4. The vehicle body is attached to the ground part by a cylindrical joint located at the front roll centre and aligned with the rear roll centre. The rear roll centre is attached to the ground by a spherical joint in order to prevent the vehicle sliding along the roll axis. A motion input is applied at the cylindrical
346 Multibody Systems Approach to Vehicle Dynamics SPH Rear roll centre Front roll centre CYL Applied roll angle motion INPLANE INPLANE Fig. 6.21 Determination of front end roll stiffness. (This material has been reproduced from the Proceedings of the Institution of Mechanical Engineers, K2 Vol. 213 ‘The modelling and simulation of vehicle handling. Part 2: vehicle modelling’, M.V. Blundell, page 127, by permission of the Council of the Institution of Mechanical Engineers) joint to rotate the body through a given angle. By requesting the resulting torque acting about the axis of the joint it is possible to calculate the roll stiffness associated with the front end of the vehicle. The road wheel parts are not included nor are the tyre properties. The tyre compliance is represented separately by a tyre model and should not be included in the determination of roll stiffness. The wheel centres on either side are constrained to remain in a horizontal plane using inplane joint primitives. Although the damper force elements can be retained in the suspension models they have no contribution to this calculation as the roll stiffness is determined using static analysis. The steering system, although not shown in Figure 6.21, may also be included in the model. If present a motion input is needed to lock the steering in the straight-ahead position during the roll simulation. For the rear end of the vehicle the approach is essentially the same as for the front end, with in this case a cylindrical joint located at the rear roll centre and a spherical joint located at the front roll centre. For both the front and rear models the vehicle body can be rotated through an appropriate angle either side of the vertical. For the example vehicle used in this text the body was rotated 10 degrees each way. The results for the front end model are plotted in Figure 6.22. The gradient at the origin can be used to obtain the value for roll stiffness used in the equivalent roll stiffness model described earlier. In the absence of an existing vehicle model that can be used for the analysis described in the preceding section, calculations can be performed to estimate the roll stiffness. In reality this will have contributions from the road springs, anti-roll bars and possibly the suspension bushes. Figure 6.23
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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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Modelling and analysis of suspensio
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Tyre characteristics and modelling
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Page 318 and 319: Tyre characteristics and modelling
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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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