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Modelling and analysis of suspension systems 195 wheel vertical motion. Some practitioners quote this as a motion ratio of 1.43:1 and some as 0.699:1. It is very important the definition of motion ratio as quoted is understood before the number is used since it is not always true that the spring moves less than the wheel. Using the motion ratio, the wheel rate due to the spring can be seen to be 31.96/1.43 2 15.63 N mm 1 . Reassessing the classical calculations, the estimated ride frequency is now 0.874 Hz, with a ride rate of 14.24 N mm 1 . The estimated frequency is now less than that calculated using the full model (which was 0.954 Hz), suggesting there is some additional stiffness or reduced mass in the mode of vibration. Examining the model again, the so-called ‘ride rate’ (k eqv ) can be taken directly (Figure 4.60). In the case of this particular suspension geometry, the ride rate is 14.97 N mm 1 . The difference between the two ride rates may be attributed to additional rates arising from the suspension bushes; these are commonly referred to as ‘parasitic’ rates. Although that term implies something undesirable about them, they are generally small and do not degrade the suspension behaviour unduly. It may be noted, however, that the difference between the two results is not fully accounted for by the difference in wheel rate. For this particular example, using the analytical solution for the two-mass solution we may calculate ‘effective’ masses and stiffnesses for each mode of vibration. In the results from the full linkage model, these effective masses and stiffnesses are reported in the results file. They are known as ‘modal’ mass and stiffness values. For the model in question, these values are given as: Primary ride mode: 17.2232 N mm 1 479.355 kg Wheel hop mode: 177.019 N mm 1 38.552 kg It is clear then that there is some other stiffness influence on the ride rate within the model that is not readily apparent to the user. Similarly, the mass is larger than the mass associated with the body alone. This acknowledges 5000.0 MOTION_12.Element_Force.Z case4 4500.0 Force (newton) 4000.0 3500.0 3000.0 2500.0 100.0 50.0 0.0 50.0 100.0 Analysis: Last_Run Length (mm) 2003-08-05 20:38:59 Fig. 4.60 Wheel rate measured from full linkage model
196 Multibody Systems Approach to Vehicle Dynamics the fact that several components are in motion with different velocities when the modes of vibration are excited and thus are storing kinetic energy. For an appreciation of these and other differences between the simplified and detailed model, the kinetic and strain energy tables calculated by MSC.ADAMS can be examined in some detail. Table 4.9 shows the output from the calculations directly. It can be seen that the kinetic energy for the primary ride mode is contained almost entirely in the body mass. However, it will be noted that 472/0.985 479 kg; thus the kinetic energy table shows the contributions of the other components in the model to the modal mass. The largest of the other contributors to the modal mass are the suspension arms and damper. For the strain energy results, it can be seen that the compliance in the lower arm bushes and the damper lower bush contribute significantly to strain energy storage in the primary ride mode of vibration. Table 4.9 ADAMS/Linear output tables ************************ Mode number = 1 Damping ratio = 2.20914E-11 Undamped natural freq. = 9.54000E-01 Cycles per second Generalized stiffness = 1.72232E+01 User units Generalized mass = 4.79355E+02 User units Kinetic energy = 2.18135E-01 Percentage distribution of Kinetic energy | X Y Z RXX RYY RZZ RXY RXZ RYZ +-------------------------------------------------------- PART/20 | PART/1 | 98.50 PART/10 | 0.06 0.04 0.02 PART/11 | 0.03 0.02 PART/12 | 0.22 0.05 PART/13 | 0.30 PART/14 | 0.34 0.03 0.01 0.01 PART/15 | 0.04 0.01 PART/16 | 0.08 PART/17 | 0.01 0.20 0.01 +-------------------------------------------------------- Percentage distribution of Strain energy | Total X Y Z RXX RYY RZZ +-------------------------------------------------------- BUSH/16 | 0.01 0.01 BUSH/17 | 0.01 0.01 BUSH/19 | 0.14 0.14 BUSH/21 | 16.32 0.06 2.47 13.78 SFOR/1029 | 5.35 0.01 0.55 4.79 SFOR/2728 | SFOR/2526 | SFOR/3233 | SPRI/2324 | 37.71 0.19 0.25 37.27 GFOR/16 | 20.16 2.38 17.27 0.02 0.49 GFOR/17 | 2.56 0.22 1.79 0.13 0.42 +--------------------------------------------------------
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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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4 Modelling and analysis of suspens
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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 495 m
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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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