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Modelling and analysis of suspension systems 197 The preceding results were all generated using an undamped eigensolution. However, for vehicle ride work, the influence of the dampers is critical. Moreover, the dampers are typically highly non-linear devices. Therefore, a further treatment of the existing MSC.ADAMS model is required once the modal ‘positioning’ (i.e. the undamped frequencies for primary ride, wheel hop and fore–aft compliance) is established. In terms of the modelling approach the only modification here is a change in the motion applied to the jack where the function now represents a sinusoidal input with fixed amplitude but with a frequency that increases as a function of time as illustrated in Figure 4.61. The motion input is referred to as a frequency sweep, sometimes described as a ‘chirp’ – for reasons which are obvious if the resulting signal is audible. The following motion statement is an example of a suitable input function where the amplitude of the road input is fixed at 10 mm and the frequency is increased using the following function from zero to 20 Hz after 80 seconds. MOTION/20, JOINT 20, TRANS ,FUNCTION 10.0 * SIN(TIME/8 * TIME * 360D) Using this simulation we can produce a time history plot showing the change in vertical acceleration of the sprung and unsprung masses of the quarter vehicle model as the simulation progresses. Examination of the response shown in Figure 4.62 reveals that excitation of a system resonance (a ‘mode of vibration’) occurs at two points during the simulation. The first of these corresponds with the natural frequency of the body and the second with the natural frequency of the unsprung mass. Another interpretation of the results obtained here is to perform a Fast Fourier Transform (FFT) so that the results can be plotted in the frequency rather than the time domain as shown in the lower half of Figure 4.62. The simulation was allowed to run for 81.91 seconds with an output sample rate of 100 Hz, giving 8192 points including the zero time point. A single buffer transform was performed on the entire record for each of the signals. Although flawed, this method is adequate for identifying frequency peaks. However, for quantifying amplitude content the underlying presumption Jack part Motion input z r Frequency sweep Time (s) Fig. 4.61 Input of frequency sweep via jack motion
198 Multibody Systems Approach to Vehicle Dynamics case 4 25.0 20.0 15.0 10.0 Body position 5.0 0.0 Wheel position 5.0 10.0 15.0 20.0 25.0 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 Analysis Last_Run Time (s) Length (mm) Length (mm) 1.0 0.1 9.5 Hz damped wheel hop 0.94 Hz damped primary ride 0.01 0.0 Fig. 4.62 10.0 20.0 30.0 Frequency (Hz) Quarter vehicle body vertical acceleration time history 40.0 50.0 that the signal repeats itself after the end of the observation buffer is clearly in error; therefore the magnitude results of this exercise should not be used further. From Figure 4.62 it can be seen that the damped natural frequency of the body occurs at around 0.94 Hz and that the natural frequency of the unsprung mass is about 9.5 Hz. Comparing these values with the previous values, it can be seen they are systematically low. This is to be expected since the addition of a damping ratio reduces the damped natural frequency d when compared with the undamped natural frequency n : d n 1 (4.87) The greatest reduction in frequency comes with the heavily damped wheel hop mode. Observing the change between undamped and damped frequency allows an estimate of the damping ratio to be made. For the two modes the damping ratios can be estimated as 0.07 and 0.48 for primary ride and wheel hop, respectively. The damping of the primary ride is low. However, if the exercise were to be repeated at different amplitudes of excitation, the level of damping in the primary ride is certain to vary since the damper characteristics are highly non-linear. For this reason, the timedomain method and subsequent processing are the preferred methods for evaluating ride behaviour once simplified undamped positioning calculations have been carried out. The next question has to be ‘how does one choose where to position primary ride behaviour?’ In order to answer this, some knowledge of typical road surfaces is required. Road surfaces are, to a first approximation, a random process passing under the car. They can be described by the expression V R 1 K( 2 ) u( ) R 2 (4.88)
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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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Modelling and analysis of suspensio
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Page 170 and 171: 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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