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Modelling and analysis of suspension systems 165 (WC) and another on the spindle axis (SA), taken in this example to be outboard of the wheel centre. The calculation of camber and steer angle is converted from radians to degrees by the factor (180/). 4.5.5 Castor angle and suspension trail Castor angle, , is defined as the angle measured in the side elevation between the steering (kingpin) axis and the vertical. Castor angle is measured in degrees and taken as positive if the top of the steering axis leans towards the rear as shown in Figure 4.26. Suspension trail (TR) is the longitudinal distance in the x direction between the wheel base and the intersection between the steering axis and the ground. The suspension trail generates a measure of stability providing a moment arm for lateral tyre forces that will cause the road wheels to ‘centre’. The suspension trail combines with tyre pneumatic trail, discussed in Chapter 5, and contributes to the steering ‘feel’. 4.5.6 Steering axis inclination and ground level offset The steering axis inclination, , is defined as the angle measured in the front elevation between the steering (kingpin) axis and the vertical. The angle is measured in degrees and taken as positive if the top of the steering axis leans inwards as shown in Figure 4.27. Ground level offset (GO) is the lateral distance in the y direction between the wheel base and the intersection between the steering axis and the ground. The ground level offset is often referred to as the scrub radius as the amount of ‘scrub’ in the tyre as it steers will depend on the magnitude of the ground level offset. (180/π) ATAN(DX(UB,LB)/DZ(UB,LB)) TR DX(WB,LB) DZ(LB,WB) * DX(UB,LB)/DZ(UB,LB) φ Upper ball joint marker (UB) Lower ball joint marker (LB) Z X Fig. 4.26 Wheel base marker (WB) TR Intersection of steering axis with ground Calculation of castor angle and suspension trail
166 Multibody Systems Approach to Vehicle Dynamics GO DY(WB,LB) DZ(LB,WB) * (DY(LB,UB)/DZ(UB,LB)) (180/π) ATAN(DY(LB,UB)/DZ(UB,LB)) UB LB Z GO Wheel base marker (WB) Fig. 4.27 Intersection of steering axis with ground Calculation of steering axis inclination and ground level offset Y 4.5.7 Instant centre and roll centre positions The determination of the instant centre and the roll centre position is more complicated than the previous calculations described here and the following is included to demonstrate the approach that is used with MBS software to establish these positions. The methods used here are based on the traditional graphical (kinematic) type of construction as described by Gillespie (1992). The approach used to program the computations will require the definition of algebraic equations that calculate the gradients and intersection points of the lines used in the construction. For the MSC.ADAMS program, there are two methods that may be used to achieve this in the absence of a dedicated program such as ADAMS/Car: (i) Programming in the input deck using the VARIABLE statement. (ii) Preparing a user-written FORTRAN subroutine and linking with MSC.ADAMS. The methods used to formulate the construction will be dependent on the type of suspension system being considered. Examples are provided here for a double wishbone and a McPherson strut suspension system. For a double wishbone suspension the methods used to determine the instant centre and roll centre position for the front suspension are based on the construction shown in Figure 4.28. The instant centre is found by intersecting two lines projected along the upper and lower arms. The instant centre is the instantaneous centre of rotation for the complete suspension system. The suspension system can be thought of as an equivalent swing arm that pivots about the instant centre. As such the instant centre is also sometimes referred to as the effective swing arm pivot. The roll centre is found by projecting a line between the wheel base and the instant centre. The point at which this line intersects the centre line of the vehicle is taken to be the roll centre.
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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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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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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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