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Tyre characteristics and modelling 291 5000.0 TYRE BRAKING FORCE TEST – TYRE B 195/65 R15 Vertical load increments – 1 kN 2 kN 3 kN 4 kN 4000.0 Braking force (N) 3000.0 2000.0 1000.0 0.0 0.1 0.3 0.5 0.0 0.2 0.4 0.6 Slip ratio 0.7 0.8 0.9 1.0 Fig. 5.48 Braking force with slip ratio of comparable tyre test machines gave differences between minimum and maximum measured values of up to 46%. Given the complexities of the tyre models that are described in the following section the starting point should be a set of measured data that can be used with confidence to form the basis of a tyre model. 5.6 Tyre modelling 5.6.1 Overview The modelling of the forces and moments at the tyre contact patch has been the subject of extensive research in recent years. A review of some of the most common tyre models was provided by Pacejka and Sharp (1991), where the authors state that it is necessary to compromise between the accuracy and complexity of the model. The authors also state that the need for accuracy must be considered with reference to various factors including the manufacturing tolerances in tyre production and the effect of wear on the properties of the tyre. This would appear to be a valid point not only from the consideration of computer modelling and simulation but also in terms of track testing where new tyres are used to establish levels of vehicle performance. A more realistic measurement of how a vehicle is going to perform in service may be to consider testing with different levels of wear or incorrect pressure settings. One of the methods discussed by Pacejka and Sharp (1991) focuses on a multi-spoke model developed by Sharp where the tyre is considered to be a series of radial spokes fixed in a single plane and attached to the wheel hub. The spokes can deflect in the radial direction and bend both circumferentially and laterally. Sharp provides more details on the radial spoke model approach in Sharp and El-Nashar (1986) and Sharp (1990, 1993). The other
292 Multibody Systems Approach to Vehicle Dynamics Translational motion inputs to represent road surface irregularities Simple spring damper tyre model Fig. 5.49 A simple tyre model for ride and vibration studies. (This material has been reproduced from the Proceedings of the Institution of Mechanical Engineers, K1 Vol. 214 ‘The modelling and simulation of vehicle handling. Part 3: tyre modelling’, M.V. Blundell, page 4, by permission of the Council of the Institution of Mechanical Engineers) method of tyre modelling reviewed is based on the ‘Magic Formula’ that will be discussed in more detail later in this section. Another review of tyre models is given by Pacejka (1995), where the influence of the tyre is discussed with regard to ‘active’ control of vehicle motion. The radial-spoke and ‘Magic Formula’ models are again discussed. Before considering tyre models in more detail it should be stated that tyre models are generally developed according to the type of application the vehicle simulation will address. For ride and vibration studies the tyre model is often required to transmit the effects from a road surface where the inputs are small but of high frequency. In the simplest form the tyre may be represented as a simple compression-only spring and damper acting between the wheel centre and the surface of the road. The simulation may in fact recreate the physical testing using a four-poster test rig with varying vertical inputs at each wheel. A concept of the tyre model for this type of simulation is provided in Figure 5.49 where for clarity only the right side of the vehicle is shown. In suspension loading or durability studies the tyre model must accurately represent the contact forces generated when the tyre strikes obstacles such as potholes and road bumps. In these applications the deformation of the tyre as it contacts the obstacle is of importance and is a factor in developing the model. These sort of tyre models are often developed for agricultural or construction type vehicles used in an off-road environment and dependent on the tyre to a larger extent in isolating the driver from the
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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 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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