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Modelling and analysis of suspension systems 163 Using the instant axes method the left and right steer axes can be computed from the suspension’s compliance matrix. The process involves locking the spring to prevent wheel rise and applying an incremental steering torque or force. The resulting translation and rotation of the wheel carrier parts can then be used to compute the instant axis, and hence steer axis of rotation for each wheel carrier. Note that the formulations of suspension output that follow are for a quarter vehicle suspension model located on the right side of the vehicle using the general vehicle co-ordinate system in this text with the x-axis pointing to the rear, the y-axis to the side and the z-axis upwards. Needless to say users must ensure the formulations are consistent with the vehicle co-ordinate system and the side of the vehicle being considered to ensure the correct sign for the calculated outputs. For each of the suspension characteristics discussed a typical system variable calculation is provided. This will assist users of MBS programs who need to develop their own calculations without access to the automated outputs in a program such as ADAMS/Car. 4.5.3 Bump movement, wheel recession and half track change As stated earlier it can be the practice to impart vertical motion to a suspension system at either the wheel centre or wheel base. In the following example the displacements at the wheel centre are used to determine the suspension movement. The displacements at the wheel base would be corrected for camber, steer and castor angle changes and dependent on the suspension geometry. On the real vehicle the displacements of the tyre contact patch relative to the road wheel would also result due to the effects of tyre distortion. This is discussed later in Chapter 5. Bump movement (BM) is the independent variable and is taken as positive as the wheel moves upwards in the positive z direction relative to the vehicle body. Similarly wheel recession (WR) and half track change (HTC) are taken as positive as the wheel moves back and outwards in the positive x and y directions respectively. The displacements are obtained simply by comparing the movement of a marker at the wheel centre (WC) relative to an initially coincident fixed marker on the ground (FG). The displacements are shown in Figure 4.24 where the MSC.ADAMS system variable format is used to describe the outputs. 4.5.4 Camber and steer angle Camber angle, , is defined as the angle measured in the front elevation between the wheel plane and the vertical. Camber angle is measured in degrees and taken as positive if the top of the wheel leans outwards relative to the vehicle body as shown in Figure 4.25. The steer or toe angle, , is defined as the angle measured in the top elevation between the longitudinal axis of the vehicle and the line of intersection of the wheel plane and road surface. Steer angle is taken here as positive if the front of the wheel toes towards the vehicle. Both camber and steer angle can be calculated using two markers located on the wheel spindle axis. In this case a marker is used at the wheel centre
164 Multibody Systems Approach to Vehicle Dynamics Wheel centre marker (WC) BM HTC Fixed ground marker (FG) Y Z BM DZ(WC,FG) HTC DY(WC,FG) WR DX(WC,FG) WC FG Z WR X Fig. 4.24 Bump movement, wheel recession and half track change γ SA γ WC Z Y γ (180/π) ATAN(DZ(WC,SA)/DY(SA,WC)) X Y WC δ δ (180/π) ATAN(DX(WC,SA)/DY(SA,WC)) δ SA Fig. 4.25 Calculation of camber angle and steer angle
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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 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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