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Modelling and analysis of suspension systems 203 I A E C F B C Z 1 X Y 1 1 O 1 Fig. 4.67 Body 2 J Body 3 D Body 5 G Body 4 H K L P POINT X (mm) Y (mm) Z (mm) A 103 B 127 C 12 D 12 E 122 F 108 G 7 H 156 I 15 J 156 P 0 K 0 L 0 Double wishbone suspension example geometry data 350 142 350 128 491 104 589 127 345 80 345 80 620 89 545 500 540 317 186 678 265 600 0 678 0 178 15 m/s P z a x P L 350 mm a 12.5 mm Fig. 4.68 L Road input definition for velocity analysis simplified by ignoring the compliance in the tyre and the profile of the road hump is taken as a sine function. The local x–z axis taken to reference the geometry of the road hump is located at a point where the vertical velocity V Pz of the contact point P reaches a maximum with a corresponding vertical acceleration A Pz equal to zero. The profile of the road hump can be defined using x z asin ⎛ 2 ⎞ (4.96) ⎝ L ⎠
204 Multibody Systems Approach to Vehicle Dynamics Working in mm and taking the wavelength L as 350 mm and the amplitude a as 12.5 mm, for a total bump height of 25 mm, gives x z 12.5 sin ⎛ ⎞ ⎝ 175 ⎠ We are after the vertical velocity of point P which can be expressed as: dz dt where dx dt dz dx dx dt 15 000 mm/s (4.97) (4.98) and dz 12.5 d 175 cos x ⎛ ⎞ x ⎝175⎠ giving dz 12.5 x cos ⎛ ⎞ 15 000 dt 175 ⎝175⎠ (4.99) (4.100) The maximum value of dz/dt occurs when cos(x/175) 1 and occurs at values of x 0, 350, 700, . . . giving ⎛ dz⎞ ⎝ dt ⎠ The acceleration d 2 z/dt 2 is given by 2 d z 2 dt max 12.5 15 000 3366 mm/s 175 12.5 2 175 2 sin ⎛ x ⎞ 15 000 ⎝175⎠ and has a value of zero at x 0, 350, 700, . . . (4.101) (4.102) This provides inputs for the following velocity and acceleration analyses of V Pz 3366 mm/s A Pz 0 mm/s 2 The approach taken here is to initially ignore the spring damper assembly between points C and I shown in Figure 4.67. Solving for the rest of the suspension system will deliver the velocity {V C } 1 of point C thus providing a boundary condition allowing a separate analysis of the spring damper to follow. Before proceeding with the velocity analysis it is necessary to identify the unknowns that define the problem and the same number of equations as unknowns leading to a solution. The angular velocities of the rigid bodies representing suspension components can be used to find the translational
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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 176 and 177: 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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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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