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Modelling and assembly of the full vehicle 351 6.9 Modelling of vehicle braking In Chapter 5 the force and moment generating characteristics of the tyre were discussed and it was shown how the braking force generated at the tyre contact patch depends on the slip ratio as the wheel is braked from a free rolling wheel with a slip ratio of zero to a fully locked wheel where the slip ratio is unity. In this section we are not so much concerned with the tyre, given that we would be using a tyre model interfaced with our full vehicle model to represent this behaviour. Rather we now address the modelling of the mechanisms used to apply a braking torque acting about the spin axis of the road wheel that produces the change in slip ratio and subsequent braking force. Clearly as the vehicle brakes, as shown in Figure 6.26, there is weight transfer from the rear to the front of the vehicle. Given what we know about the tyre behaviour the change in the vertical loads acting through the tyres will influence the braking forces generated. As such the braking model may need to account for real effects such as proportioning the braking pressures to the front and rear wheels or the implementation of anti-lock braking systems (ABS). Before any consideration of this we need to address the mechanism to model a braking torque acting on a single road wheel. If we consider a basic arrangement the mechanical formulation of a braking torque, based on a known brake pressure, acting on the piston can be derived from Figure 6.27. The braking torque B T is given by B T npAR d (6.13) where n the number of friction surfaces (pads) the coefficient of friction between the pads and the disc p the brake pressure A the brake piston area R d the radius to the centre of the pad Note that depending on the sophistication of the model the coefficient of friction may be constant or defined as a run-time variable as a function of brake rotor temperature. Obtaining such data is usually relatively easy, but the calculation of rotor temperature can be a little more involved. Weight transfer Brake torque Deceleration x z Brake torque Fxbr Fxbf Fig. 6.26 Fzr Braking of a full vehicle Fzf
352 Multibody Systems Approach to Vehicle Dynamics Figure 6.28 shows typical specific heat capacity versus temperature characteristics for different brake rotor materials. Brake rotor temperature, T, can be calculated using the expression: TT0 BT thAc ( TTenv) mc (6.14) where T 0 initial brake rotor temperature (K) brake rotor spin velocity (rads second 1 ) t time (seconds) h brake rotor convection coefficient (Wm 2 K 1 ) A c convective area of brake disc (m 2 ) T env environmental temperature (K) m mass of brake rotor (kg) c specific heat capacity of brake rotor (J kg 1 K 1 ) B T Brake pad Brake disc R d F R A F N P Brake piston Fig. 6.27 800 700 600 c (J/kg/deg C) 500 400 300 200 Braking mechanism Cast iron Stainless Alu MMC Carbon 100 0 0 100 200 300 400 500 600 700 800 Temperature, deg C Fig. 6.28 Specific heat capacity, c, versus temperature, T (Farr, 1999)
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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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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 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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