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Modelling and analysis of suspension systems 161 In each case the parameters are presented as XY plots with the bump movement as the independent variable usually on the x-axis. The calculation of these outputs can be programmed to create a variable that is derived directly from measured system variables or is based on a trigonometric or algebraic derivation. It should be noted that parameters such as the camber angle determined here are measured relative to the vehicle body which is assumed to be fixed and should not be confused with the camber angle measured between the tyre and the road surface discussed later in Chapter 5. The vertical motion is imparted to the wheel using a body to represent a jack with the wheel centre constrained to remain in the plane of the jack using an inplane joint primitive as described in Chapter 3 and shown in Figure 4.22. The motion applied to the translational joint between the jack and the ground will be that needed to move the wheel between the rebound and bump positions. If, as is usual, the model is defined in a position midway between these it is often the practice to define the motion as sinusoidal with a cycle of 1 second. This would provide results in the bump position at 0.25 second the rebound position at 0.75 second and allow for presentation purposes smooth animation of continuous cycles. Running the analysis for 1 second with, say, 80 output steps would ensure that output is calculated in the full bump and rebound positions. The motion statement applied to the translational joint that would accomplish this for a suspension where the total movement between the rebound and bump is 200 mm would be MOTION/04, JOINT 04, TRANS, FUNCTION 100 * SIN(TIME * 360D) I J INPLANE MOTION Bump movement (mm) 100 100 Bump 0.25 0.5 0.75 1.0 Rebound Time (s) Fig. 4.22 Input of vertical motion at the wheel centre
162 Multibody Systems Approach to Vehicle Dynamics Note that the TIME variable is in seconds and is converted to degrees within the function to represent one cycle over 1 second of simulation time. It should also be noted that if the movement is not symmetric, that is to say that the distance moved in bump is different to that moved in rebound, a more complicated function will be needed for the motion input. In the following example the suspension is required to move 110 mm into the bump position and 90 mm into the rebound position. It is still desirable to have an overall sinusoidal motion for animation purposes and so an arithmetic IF is used in the function to switch the amplitude at the half cycle position of 0.5 second as follows: MOTION/04, JOINT 04, TRANS ,FUNCTION IF(TIME0.5: 110*SIN(TIME*360D), 0.0 ,90 * SIN(TIME * 360D)) 4.5.2 Suspension steer axes Suspension characteristics, such as castor angle, suspension trail and the steering axis inclination, require an initial computation of the suspension system steer axis. Generally the concept of a steer axis is straightforward when considering, for example, the double wishbone system described earlier. In such a case it is easy to see that the wheel will steer about an axis passing through the lower and upper ball joints. For a McPherson strut suspension system, the steer axis may be defined to pass through a point located at the lower ball joint and a point located where the upper part of the strut is mounted to the vehicle body. Note that this line is not necessarily parallel to the sliding axis of the upper part of the strut. For some suspensions, such as a multi-link system, the location of the steer axis is not immediately evident from the suspension geometry. In these cases it is necessary that the software be programmed to calculate the steer axis as the instant axis of rotation of the wheel carrier parts. Geometric steer axis Instant steer axis Fig. 4.23 Geometric and instant steer axes of a suspension system
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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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