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Modelling and analysis of suspension systems 153 Spring Upper mount Damper Wheel knuckle (stub axle) (kingpin) Lower bushes (mounts) Road wheel Lower wishbone (control arm) Connection to rack Track rod Lower ball joint Track rod end Fig. 4.15 McPherson strut suspension system established and will be discussed further in the next section of this chapter. The output from this type of analysis is mainly geometric and allows results such as camber angle or roll centre position to be plotted graphically against vertical wheel movement. The inclusion of bush compliance in the model at this stage will depend on whether the bushes have significant influence on geometric changes in the suspension and road wheel as the wheel moves vertically relative to the vehicle body. With the development of multi-link type suspensions, such as the rear suspension on the Mercedes Model W201 (von der Ohe, 1983), it would appear difficult to develop a model of the linkages that did not include the compliance in the bushes. This type of suspension was used as a benchmark during the IAVSD exercise (Kortum and Sharp, 1993) mentioned in Chapter 1 comparing the application of multibody systems analysis programs in vehicle dynamics. This modelling issue is best explained by an example using the established double wishbone suspension system. The modelling of the suspension using bushes to connect the upper and lower arms to the vehicle body is shown in Figure 4.16. Vertical motion is imparted to the suspension using a jack part connected to the ground part by a translational joint. A translational motion is applied at this joint to move the jack over a range of vertical movement equivalent to moving between the full bump and full rebound positions. Although the jack is shown below the wheel in Figure 4.16 the jack is connected to the wheel using an inplane joint primitive acting at either the wheel base or the wheel centre as described in Chapter 3. The joint primitive constrains the wheel centre or wheel base to remain in the plane at the top of the jack but does not constrain the wheel to change
154 Multibody Systems Approach to Vehicle Dynamics BUSHES SPHERICAL BUSHES REVOLUTE SPHERICAL MOTION UNIVERSAL SPHERICAL INPLANE MOTION TRANSLATIONAL Fig. 4.16 Double wishbone suspension modelled with bushes. (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 121, by permission of the Council of the Institution of Mechanical Engineers) Table 4.2 Degree-of-freedom calculation for suspension system with bushes Component Number DOF ΣDOF Parts 6 6 36 Translationals 1 5 5 Revolutes 1 5 5 Universals 1 4 4 Sphericals 3 3 9 Inplanes 1 1 1 Motions 2 1 2 ΣDOF for system 10 orientation or to move in the lateral or longitudinal directions. A zero motion input is applied at the revolute joint connecting the wheel to the wheel knuckle in order to constrain the spin freedom of the wheel. For the suspension modelled in this manner it is possible to calculate the degrees of freedom for the system as shown in Table 4.2. The double wishbone suspension model shown in Figure 4.16 can be simplified to represent the bushes connecting the upper arm and the lower arm to the vehicle body by revolute joints as shown in Figure 4.17. For the suspension modelled in this manner it is possible to calculate the degrees of freedom for the system as shown in Table 4.3.
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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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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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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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