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Modelling and assembly of the full vehicle 341 Traditional leaf spring Simple equivalent spring model SAE 3-link model Bush Link Link Link Lumped mass/beam elements Bush Masses Beams Fig. 6.15 Leaf spring modelling strategies The next approach is based on modelling the leaf spring as three bodies (SAE 3-link model) interconnected by bushes or revolute joints with an associated torsional stiffness that provides equivalent force–displacement characteristics as found in the actual leaf spring. The last approach shown in Figure 6.15 uses a detailed ‘as is’ approach representing each of the leaves as a series of distributed lumped masses interconnected by beam elements with the correct sectional properties for the leaf. This type of model is also
342 Multibody Systems Approach to Vehicle Dynamics complicated by the need to model the interleaf contact forces between the lumped masses with any associated components of sliding friction. 6.6 Anti-roll bars As shown in Figure 6.16 anti-roll bars may be modelled using two parts connected to the vehicle body by revolute joints and connected to each other by a torsional spring located on the centre line of the vehicle. In a more detailed model the analyst could include rubber bush elements rather than the revolute joints shown to connect each side of the anti-roll bar to the vehicle. In this case for a cylindrical bush the torsional stiffness of the bush would be zero to allow rotation about the axis, or could have a value associated with the friction in the joint. In this model the connection of the anti-roll bars to the suspension system is not modelled in detail, rather each anti-roll bar part is connected to the suspension using an inplane joint primitive that allows the vertical motion of the suspension to be transferred to the anti-roll bars and hence produce a relative twisting motion between the two sides. A more detailed approach, shown in Figure 6.17, involves including the drop links to connect each side of the anti-roll bar to the suspension systems. The drop link is connected to the anti-roll bar by a universal joint and is connected to the suspension arm by a spherical joint. This is similar to the modelling of a tie rod as discussed in Chapter 4 where the universal joint is used to constrain the spin of the link about an axis running along its length, this degree of freedom having no influence on the overall behaviour of the model. The stiffness K T of the torsional spring can be found directly from fundamental torsion theory for the twisting of bars with a hollow or solid circular cross-section. Assuming here a solid circular bar and units that are consistent with the examples that support this text we have GJ KT (6.3) L where G is the shear modulus of the anti-roll bar material (N/mm 2 ) Right anti-roll bar part Revolute joints to vehicle body REV INPLANE REV Torsional spring Left anti-roll bar part Front wheel knuckle INPLANE Front wheel knuckle Fig. 6.16 Modelling the anti-roll bars using joint primitives
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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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Tyre characteristics and modelling
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Modelling and assembly of the full
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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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