Vehicle Dynamics (eBook)

Modeling and Simulation

Dieter Schramm, Manfred Hiller, Roberto Bardini (Autoren)

eBook Download: PDF

2017 | 2nd ed. 2018
XXI, 440 Seiten
Springer Berlin Heidelberg (Verlag)
978-3-662-54483-9 (ISBN)

Infos

The authors examine in detail the fundamentals and mathematical descriptions of the dynamics of automobiles. In this context, different levels of complexity are presented, starting with basic single-track models up to complex three-dimensional multi-body models. A particular focus is on the process of establishing mathematical models based on real cars and the validation of simulation results. The methods presented are explained in detail by means of selected application scenarios.

In addition to some corrections, further application examples for standard driving maneuvers have been added for the present second edition. To take account of the increased use of driving simulators, both in research, and in industrial applications, a new section on the conception, implementation and application of driving simulators has been added.

Prof. Dr.-Ing. Dieter Schramm is the head of the Chair of Mechatronics since 2004 and the dean of the Faculty of Engineering at the University of Duisburg-Essen since 2006. Before that time and after he got his Phd in Engineering from the University of Stuttgart he worked over a period of more than 18 years in various positions in the Automotive Industry. Starting as section manager at the Robert Bosch Company he held later positions as head of department and from 1999 as director of engineering and marketing for various product segments and as well as being the CEO of an affiliated company of Tyco Electronics Ltd. His main scientific focus in automotive is on vehicle dynamics and safety, driver assistance systems, electro mobility and driving simulators.

Prof. Dr.-Ing. habil. Dr. H.C. Mult. M. Hiller has been head of the first Chair of Mechatronics in Germany from 1991 to 2004 at the University of Duisburg (today University of Duisburg-Essen). During his time in Duisburg (from 1987) and before that during his time at the University of Stuttgart he has been dealing with modeling and simulation of road vehicles over more than three decades. As a consequence, close collaborations with major car manufacturers and car suppliers in Germany have been established. In particular, detailed multi-body system based simulation models have been designed, thus providing a major contribution to the development of active and passive safety systems, like ESP and rollover-prevention.

Dr.-Ing. Roberto Bardini has been working since March 2000 as a development engineer in the field of vehicle safety, first with the company Audi and since October 2003 with the company BMW. He is engaged in spatial multi-body simulation of occupants and vehicles since his mechanical engineering degree in 1996 at the chair of mechatronics under direction of Professor Hiller. Especially for the design of occupant protection systems for vehicle rollover, he has developed simulation tools that are successfully used in practice.

Inhalt

Preface 2nd edition 5
Preface 6
Contents 7
Nomenclature and Definitions 14
Variables and Physical Quantities 14
Special Notation for Physical Vectors 14
Examples for Subscriptions 15
Examples for “Physical” Vectors and Their Representation 16
Scalars 16
Vectors and Matrices 17
Trigonometric Functions 18
1 Introduction 19
1.1 Problem Definition 19
1.1.1 Modeling Technical Systems 21
1.1.2 Definition of a System 23
1.1.3 Simulation and Simulation Environment 23
1.1.4 Vehicle Models 24
1.2 Complete Vehicle Model 27
1.2.1 Vehicle Models and Application Areas 29
1.2.2 Commercial Vehicle Simulation Systems 29
1.3 Outline of the Book 32
1.4 Webpage of the Book 32
References 33
2 Fundamentals of Mathematics and Kinematics 34
2.1 Vectors 34
2.1.1 Elementary Algorithms for Vectors 34
2.1.2 Physical Vectors 35
2.2 Coordinate Systems and Components 36
2.2.1 Coordinate Systems 36
2.2.2 Component Decomposition 36
2.2.3 Relationship Between Component Representations 37
2.2.4 Properties of the Transformation Matrix 39
2.3 Linear Vector Functions and Second Order Tensors 39
2.4 Free Motion of Rigid Bodies 41
2.4.1 General Motion of Rigid Bodies 41
2.4.2 Relative Motion 45
2.4.3 Important Reference Frames 48
2.5 Rotational Motion 49
2.5.1 Spatial Rotation and Angular Velocity in General Form 49
2.5.2 Parameterizing of Rotational Motion 50
2.5.3 The Rotational Displacement Pair and Tensor of Rotation 51
2.5.4 Rotational Displacement Pair and Angular Velocity 53
2.5.5 CARDAN (BRYANT) Angles 54
References 58
3 Kinematics of Multibody Systems 59
3.1 Structure of Kinematic Chains 59
3.1.1 Topological Modelling 59
3.1.2 Kinematic Modelling 61
3.2 Joints in Kinematic Chains 63
3.2.1 Joints in Spatial Kinematic Chains 63
3.2.2 Joints in Planar Kinematic Chains 65
3.2.3 Joints in Spherical Kinematic Chains 65
3.2.4 Classification of Joints 66
3.3 Degrees of Freedom and Generalized Coordinates 68
3.3.1 Degrees of Freedom of Kinematic Chains 68
3.3.2 Examples from Road Vehicle Suspension Kinematics 69
3.3.3 Generalized Coordinates 70
3.4 Basic Principles of the Assembly of Kinematic Chains 71
3.4.1 Sparse-Methods: Absolute Coordinates Formulation 73
3.4.2 Vector Loop Methods (“LAGRANGE” Formulation) 75
3.4.3 Topological Methods: Formulation of Minimum Coordinates 76
3.5 Kinematics of a Complete Multibody System 78
3.5.1 Basic Concept 78
3.5.2 Block Wiring Diagram and Kinematic Networks 79
3.5.3 Relative Kinematics of the Spatial Four-Link Mechanism 80
3.5.4 Relative, Absolute and Global Kinematics 82
3.5.5 Example: Double Wishbone Suspension 85
References 87
4 Equations of Motion of Complex Multibody Systems 88
4.1 Fundamental Equation of Dynamics for Point Mass Systems 88
4.2 JOURDAIN’S Principle 90
4.3 LAGRANGE Equations of the First Kind for Point Mass Systems 90
4.4 LAGRANGE Equations of the Second Kind for Rigid Bodies 91
4.5 D’ALEMBERT’s Principle 93
4.6 Computer-Based Derivation of the Equations of Motion 95
4.6.1 Kinematic Differentials of Absolute Kinematics 96
4.6.2 Equations of Motion 98
4.6.3 Dynamics of a Spatial Multibody Loop 99
References 107
5 Kinematics and Dynamics of the Vehicle Body 109
5.1 Vehicle-Fixed Reference Frame 109
5.2 Kinematical Analysis of the Chassis 112
5.2.1 Incorporation of the Wheel Suspension Kinematics 113
5.2.2 Equations of Motion 115
References 116
6 Modeling and Analysis of Wheel Suspensions 117
6.1 Function of Wheel Suspension Systems 117
6.2 Different Types of Wheel Suspension 119
6.2.1 Beam Axles 120
6.2.2 Twist-Beam Suspension 121
6.2.3 Trailing-Arm Axle 122
6.2.4 Trailer Arm Axle 124
6.2.5 Double Wishbone Axles 124
6.2.6 Wheel Suspension Derived from the MacPherson Principle 126
6.2.7 Multi-Link Axles 127
6.3 Characteristic Variables of Wheel Suspensions 129
6.4 One Dimensional Quarter Vehicle Models 132
6.5 Three-Dimensional Model of a MacPherson Wheel Suspension 135
6.5.1 Kinematic Analysis 136
6.5.2 Explicit Solution 140
6.6 Three-Dimensional Model of a Five-Link Rear Wheel Suspension 145
6.6.1 Kinematic Analysis 145
6.6.2 Implicit Solution 148
6.6.3 Simulation Results of the Three Dimensional Quarter Vehicle Model 153
References 157
7 Modeling of the Road-Tire-Contact 158
7.1 Tire Construction 159
7.2 Forces Between Wheel and Road 160
7.3 Stationary Tire Contact Forces 160
7.3.1 Tires Under Vertical Loads 162
7.3.2 Rolling Resistance 163
7.3.3 Tires Under Longitudinal (Circumferential) Forces 163
7.3.4 Tires Subjected to Lateral Forces 175
7.3.5 Influence of the Camber on the Tire Lateral Force 178
7.3.6 Influence of the Tire Load and the Tire Forces on the Patch Surface 179
7.3.7 Fundamental Structure of the Tire Forces 179
7.3.8 Superposition of Circumferential and Lateral Forces 180
7.4 Tire Models 183
7.4.1 The Contact Point Geometry 184
7.4.2 Contact Velocity 189
7.4.3 Calculation of the Slip Variables 190
7.4.4 Magic Formula Model 191
7.4.5 Magic Formula Models for Superimposed Slip 193
7.4.6 HSRI Tire Model 194
7.5 Instationary Tire Behavior 197
References 198
8 Modeling of the Drivetrain 200
8.1 Drivetrain Concepts 200
8.2 Modeling 202
8.2.1 Relative Motion of the Engine Block 202
8.2.2 Modelling of the Drivetrain 203
8.2.3 Engine Bracket 204
8.2.4 Modeling of Homokinetic Joints 209
8.3 Modeling of the Engine 211
8.4 Relative Kinematics of the Drivetrain 213
8.5 Absolute Kinematics of the Drivetrain 215
8.6 Equations of Motion 216
8.7 Discussion of Simulation Results 217
References 218
9 Force Components 220
9.1 Forces and Torques in Multibody Systems 220
9.1.1 Reaction Forces 222
9.1.2 Applied Forces 223
9.2 Operating Brake System 223
9.3 Aerodynamic Forces 225
9.4 Spring and Damper Components 227
9.4.1 Spring Elements 227
9.4.2 Damper Elements 228
9.4.3 Force Elements Connected in Parallel 230
9.4.4 Force Elements in Series 230
9.5 Anti-Roll Bars 231
9.5.1 Passive Anti-Roll Bars 231
9.5.2 Active Anti-Roll Bars 234
9.6 Rubber Composite Elements 235
References 237
10 Single Track Models 238
10.1 Linear Single Track Model 238
10.1.1 Equations of Motion of the Linear Single Track Model 239
10.1.2 Stationary Steering Behavior and Cornering 245
10.1.3 Instationary Steering Behavior: Vehicle Stability 248
10.2 Nonlinear Single Track Model 250
10.2.1 Kinetics of the Nonlinear Single Track Model 250
10.2.2 Tire Forces 253
10.2.3 Drive and Brake Torques 256
10.2.4 Equations of Motion 258
10.2.5 Equations of State 259
10.3 Linear Roll Model 260
10.3.1 Equation of Motion for the Rolling of the Chassis 261
10.3.2 Dynamic Tire Loads 265
10.3.3 Influence of the Self-steering Behavior 268
References 270
11 Twin Track Models 271
11.1 Twin Track Model Without Suspension Kinematics 271
11.1.1 NEWTON’s and EULER’s Equations for a Basic Spatial Twin Track Model 274
11.1.2 Spring and Damper Forces 276
11.1.3 NEWTON’s and EULER’s Equations of the Wheels 278
11.1.4 Tire-Road Contact 279
11.1.5 Drivetrain 281
11.1.6 Brake System 283
11.1.7 Equations of Motion 284
11.2 Twin Track Models with Kinematic Wheel Suspensions 285
11.2.1 Degrees of Freedom of the Twin Track Model 285
11.2.2 Kinematics of the Vehicle Chassis 288
11.2.3 Generalized Kinematics of the Wheel Suspension 290
11.2.4 Wheel Suspension with a Trailing Arm Suspension 295
11.2.5 Kinematics of the Wheels While Using a Trailing Arm Suspension 300
11.2.6 Tire Forces and Torques 303
11.2.7 Suspension Springs and Dampers 304
11.2.8 Aerodynamic Forces 305
11.2.9 Steering 305
11.2.10 Anti-roll Bar 306
11.2.11 Applied Forces and Torques 307
11.2.12 NEWTON’s and EULER’s Equations 308
11.2.13 Motion and State Space Equations 312
11.3 Simplified Driver Model 312
11.3.1 Controller Concept 312
11.4 Parameterization 315
References 316
12 Three-Dimensional Complete Vehicle Models 317
12.1 Modeling of the Complete Vehicle 317
12.1.1 Kinematics of a Rear-Wheel Driven Complete Vehicle Model 318
12.1.2 Kinematics of Front- and Four-Wheel Driven Complete Vehicle Models 327
12.1.3 Dynamics of the Complete Vehicle Model 337
12.2 Simulation of Motor Vehicles 343
12.2.1 Setup and Concept of FASIM_C++ 344
12.2.2 Modular Structure of a Vehicle Model 346
12.2.3 Construction of the Equations of Motion 350
12.2.4 Numeric Integration 356
12.2.5 Treatment of Events 359
References 360
13 Model of a Typical Complex Complete Vehicle 362
13.1 Modeling of the Complete Vehicle 362
13.2 Model Verification and Validation 365
13.2.1 Verification 366
13.2.2 Validation 366
13.3 Parameterized Vehicle Model 374
13.3.1 Definition of a Reference Model 374
13.3.2 Comparison of Parameterized Versus Validated Models 377
References 381
14 Selected Applications 383
14.1 Simulation of Test Maneuvers 383
14.1.1 Simulation of a Step Steering Input (ISO 7401) 383
14.1.2 Simulation of Stationary Circular Travel 386
14.1.3 Simulation of a Double Lane Change 386
14.2 Simulation of Vehicle Rollover 390
14.2.1 Virtual Proving Grounds 394
14.2.2 Results of the Simulation 398
14.2.2.1 Misuse Testing 398
14.2.2.2 Ride Over a Ramp 400
14.2.2.3 Passing Over Embankment 403
14.2.2.4 Sand Bed 406
14.3 Control of the Roll Dynamics Using Active Anti-Roll Bars 409
14.3.1 Passive Anti-Roll Bar 410
14.3.2 Stiffness Distribution Between Front- and Rear Axle 410
14.3.3 Adjustment of the Roll Dynamics by Means of Active Anti-Roll Bars 413
14.3.4 Control Unit Design 413
14.3.5 Response and Disturbance Reaction 417
14.3.6 Roll Torque Distribution with Fuzzy Logic 417
14.3.7 Active Principle 418
14.3.8 Potential of a Roll Torque Distribution 419
14.4 Driving Simulators 421
14.4.1 Areas of Application and Implementation of Driving Simulators 421
14.4.2 The Control Circuit Driver-Vehicle-Environment 424
14.4.3 Implementation of Driving Simulators 426
14.4.4 Simulation Models and Interfaces 426
14.4.5 Motion Systems 429
14.4.6 Conducting Experiments with Driving Simulators 430
14.4.7 Recording of Measured Values in Simulator Tests 432
14.4.8 Implementation of Simple Driving Simulators 432
References 441
Index 443

Produkt-Details

• Erscheint lt. Verlag: 3.7.2017
• Zusatzinfo: XXI, 440 p. 306 illus.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: automotive engineering • automotive mechatronics • kinematic-based multibody analysis • Modeling • multibody systems (MBS) • Simulation • Vehicle Dynamics • vehicle system modeling
• ISBN-10: 3-662-54483-0 / 3662544830
• ISBN-13: 978-3-662-54483-9 / 9783662544839