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Modelling and analysis of suspension systems 235 Table 4.14 Force Comparison of force vectors computed by theory and MSC.ADAMS Force vectors Theory MSC.ADAMS F x (N) F y (N) F z (N) F x (N) F y (N) F z (N) F A31 645.173 2006.948 3412.360 645.173 2006.950 3412.360 F B31 204.112 3022.800 3353.266 204.112 3022.800 3353.270 F C37 116.421 349.263 16 919.843 116.421 349.263 16 919.800 F D34 557.482 4680.486 10 154.217 557.482 4680.490 10 154.200 F E21 557.482 1453.911 47.583 557.482 1453.910 47.582 F F21 0.0 2787.021 91.212 0.0 2787.020 91.212 F G24 557.482 4240.932 138.979 557.482 4240.930 138.794 F H54 0.0 439.554 15.942 0.0 439.554 15.423 Z 1 X 1 Y 1 O 1 m 2 {A G 2 } 1 Plane of {F F 21 } 1 geometric F Y symmetry 2 {F E21 } 1 E • • {ω 2 } 1/2 Body 2 Z 2 O 2 G 2 X • {α 2 2 } 1/2 G m 2 {g} 1 Fig. 4.76 Free-body diagram for suspension lower wishbone Body 2 {F G 24 } 1 20 unknown constraint forces as used in the previous static analysis. Referring back to Chapter 2, however, the reader will realize that the addition of inertial forces and the use of a local body centred co-ordinate system for the moment balance will add to the complexity of the solution. For brevity a full theoretical solution will not be performed here but rather the six equations of motion for Body 2 will be set up using, by way of example, the velocities and accelerations found earlier. The process of setting up the equations of motion for the other bodies would follow in a similar manner. Body 2 can be considered in isolation as illustrated with the free-body diagram shown in Figure 4.76. For the dynamic analysis we can take it that the physical properties of the suspension component, mass, mass moments of inertia, centre of mass location and orientation of the body principal axis system, are all known. The co-ordinate data provided with this example has only provided definitions so far for the locations of points such as those defining suspension
236 Multibody Systems Approach to Vehicle Dynamics Rotate ψ 90d about Z 1 Rotate θ 90d about X 2 Rotate φ 0d about Z 2 Z 1 Z 1 Y 2 Y 2 X 2 Z 2 ψ Y X 1 Y 1 X 2 X 2 O 1 φ O 2 θ Z 2 Fig. 4.77 Definition of body principal axis system using Euler angle rotations mounts and joints connecting the linkages. Mass centre positions have not been provided. For a dynamic analysis the mass centre locations of all moving bodies are required in order to set up the equations of motion. For this example using Body 2 the position of the mass centre G 2 relative to the inertial reference frame O 1 is defined by the position vector {R G2O1 } 1 and assumed to be {R G2O1 } T 1 [7 500 85] mm The mass of Body 2, m 2 , is taken to be 3.5 kg. It should also be noted from Figure 4.76 that the principal axes of Body 2 are located at the mass centre G 2 and are defined by the reference frame O 2 . The transformation from reference frame O 1 to O 2 is obtained through a set of three Euler angle rotations as shown in Figure 4.77. The mass moments of inertia for Body 2, measured about the principal axes of the body O 2 , are taken to be for this example: I 21 I 2xx 1.5 10 3 kg mm 2 I 22 I 2yy 38 10 3 kg mm 2 I 23 I 2zz 38 10 3 kg mm 2 The X 2 Y 2 plane of O 2 is taken to be a plane of geometric symmetry for the part so that all cross products of inertia are zero. The inertia matrix for Body 2 [I 2 ] 2/2 measured from and referred to reference frame O 2 is therefore 3 1.5 10 ⎢ I 2 22 [ ] ⎡ ⎢ ⎢ ⎣ 0 0 0 3 38 10 0 0 0 38 10 From the previous velocity and acceleration analysis we also have { 2 } T 1 [12.266 0 0] rad/s (4.314) { 2 } T 1 [10.642 0 0] rad/s 2 Before progressing to set up the equations of motion we need to do one more calculation to find the acceleration {A G2 } 1 of the mass centre for Body 2: {A G2 } 1 {A G2E } 1 { 2 } 1 {V G2 } 1 { 2 } 1 {R G2E } 1 (4.315) 3 ⎤ ⎥ ⎥ kg mm ⎥ ⎦ 2
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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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Page 208 and 209: 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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