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Modelling and assembly of the full vehicle 361 The purpose of the STEP FUNCTION is to define a change of state in the expression that is continuous. The step function can be used to factor a force function by ramping it on over a set time period. In this case the driving torque is being switched on between time 0 and time 1 second. This is important because it is necessary to perform an initial static analysis of the vehicle at time 0 when Va 0 and the torque must not act. As can be seen a ‘reference’ (desired) state is needed, an error term is defined by the difference between the current state and the reference state and finally, responses to that in terms of throttle or brake application to adjust the speed back towards the reference value. There are two possible approaches; the simplest provides a speed ‘map’ for the track, similar to the curvature map description of it. More elaborately, it is possible to examine the path curvature map locally and decide (through a knowledge of the ultimate capabilities of the vehicle, perhaps) whether or not the current speed is excessive, appropriate or insufficient for the local curvature and use brakes or engine appropriately. For the development of vehicles, open loop throttle or brake inputs may be preferable and are sometimes mandated in defined test manoeuvres, rendering the whole issue of speed control moot. In many ways the skill of the competition driver lies entirely in this ability to judge speed and adjust it appropriately. It is also a key skill to cultivate for limit handling development and arguably for road driving too, so as not to arrive at hazards too rapidly to maintain control of the vehicle. For this functionality, some form of preview is essential. It is both plausible and reasonable to run a ‘here and now at the front axle’ model for the path follower and a ‘previewing’ speed controller within the same model, described in subsequent sections. 6.12 The steering system 6.12.1 Modelling the steering mechanism There are a number of steering system configurations available for cars and trucks based on linkages and steering gearboxes. The treatment in the following sections is limited to a traditional rack and pinion system. Space does not permit discussion of the modelling of power steering or steer-bywire here. For the simple full vehicle models discussed earlier, such as that modelled with lumped mass suspensions, there are problems when trying to incorporate the steering system. Consider first the arrangement of the steering system on the actual vehicle and the way this can be modelled on the detailed linkage model as shown in Figure 6.36. In this case only the suspension on the right-hand side is shown for clarity. The steering column is represented as a part connected to the vehicle body by a revolute joint with its axis aligned along the line of the column. The steering inputs required to manoeuvre the vehicle are applied as motion or torque inputs at this joint. The steering rack part is connected to the vehicle body by a translational joint and connected to the tie rod by a universal
362 Multibody Systems Approach to Vehicle Dynamics Steering column part MOTION Steering motion applied at joint REV Revolute joint to vehicle body COUPLER Steering rack part TRANS Translational joint to vehicle body Front suspension Fig. 6.36 Modelling the steering system. (This material has been reproduced from the Proceedings of the Institution of Mechanical Engineers, K2 Vol. 213 ‘The modelling and simulation of vehicle handling. Part 2: vehicle modelling’, M.V. Blundell, page 129, by permission of the Council of the Institution of Mechanical Engineers) joint. The translation of the rack is related to the rotation of the steering column by a coupler statement that defines the ratio. An example of a statement that would define the ratio is COUPLER/510502,JOINTS 501,502,TYPE T:R ,SCALES 8.45D,1.0 In this case joint 501 is the translational joint and 502 is the revolute joint. The coupler statement ensures that for every 8.45 degrees of column rotation there will be 1 mm of steering rack travel. Attempts to incorporate the steering system into the simple models using lumped masses, swing arms and roll stiffness will be met with a problem when connecting the steering rack to the actual suspension part. This is best explained by considering the situation shown in Figure 6.37. The geometry of the tie rod, essentially the locations of the two ends, is designed with the suspension linkage layout and will work if implemented in an ‘as-is’ model of the vehicle including all the suspension linkages. Physically connecting the tie rod to the simple suspensions does not work. During an initial static analysis of the full vehicle, to settle at kerb height, the rack moves down with the vehicle body relative to the 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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4 Modelling and analysis of suspens
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Modelling and analysis of suspensio
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Tyre characteristics and modelling
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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 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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