Schramm / Hiller / Bardini Vehicle Dynamics

Modeling and Simulation
2. Auflage 2018
ISBN: 978-3-662-54483-9
Verlag: Springer
Format: PDF
Kopierschutz: Wasserzeichen (»Systemvoraussetzungen)

E-Book, Englisch, 450 Seiten, eBook

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.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Schramm, Dieter

Hiller, Manfred

Bardini, Roberto

Inhaltsverzeichnis

1;Preface 2nd edition;5
2;Preface;6
3;Contents;7
4;Nomenclature and Definitions;14
4.1;Variables and Physical Quantities;14
4.2;Special Notation for Physical Vectors;14
4.3;Examples for Subscriptions;15
4.4;Examples for “Physical” Vectors and Their Representation;16
4.5;Scalars;16
4.6;Vectors and Matrices;17
4.7;Trigonometric Functions;18
5;1 Introduction;19
5.1;1.1 Problem Definition;19
5.1.1;1.1.1 Modeling Technical Systems;21
5.1.2;1.1.2 Definition of a System;23
5.1.3;1.1.3 Simulation and Simulation Environment;23
5.1.4;1.1.4 Vehicle Models;24
5.2;1.2 Complete Vehicle Model;27
5.2.1;1.2.1 Vehicle Models and Application Areas;29
5.2.2;1.2.2 Commercial Vehicle Simulation Systems;29
5.3;1.3 Outline of the Book;32
5.4;1.4 Webpage of the Book;32
5.5;References;33
6;2 Fundamentals of Mathematics and Kinematics;34
6.1;2.1 Vectors;34
6.1.1;2.1.1 Elementary Algorithms for Vectors;34
6.1.2;2.1.2 Physical Vectors;35
6.2;2.2 Coordinate Systems and Components;36
6.2.1;2.2.1 Coordinate Systems;36
6.2.2;2.2.2 Component Decomposition;36
6.2.3;2.2.3 Relationship Between Component Representations;37
6.2.4;2.2.4 Properties of the Transformation Matrix;39
6.3;2.3 Linear Vector Functions and Second Order Tensors;39
6.4;2.4 Free Motion of Rigid Bodies;41
6.4.1;2.4.1 General Motion of Rigid Bodies;41
6.4.2;2.4.2 Relative Motion;45
6.4.3;2.4.3 Important Reference Frames;48
6.5;2.5 Rotational Motion;49
6.5.1;2.5.1 Spatial Rotation and Angular Velocity in General Form;49
6.5.2;2.5.2 Parameterizing of Rotational Motion;50
6.5.3;2.5.3 The Rotational Displacement Pair and Tensor of Rotation;51
6.5.4;2.5.4 Rotational Displacement Pair and Angular Velocity;53
6.5.5;2.5.5 CARDAN (BRYANT) Angles;54
6.6;References;58
7;3 Kinematics of Multibody Systems;59
7.1;3.1 Structure of Kinematic Chains;59
7.1.1;3.1.1 Topological Modelling;59
7.1.2;3.1.2 Kinematic Modelling;61
7.2;3.2 Joints in Kinematic Chains;63
7.2.1;3.2.1 Joints in Spatial Kinematic Chains;63
7.2.2;3.2.2 Joints in Planar Kinematic Chains;65
7.2.3;3.2.3 Joints in Spherical Kinematic Chains;65
7.2.4;3.2.4 Classification of Joints;66
7.3;3.3 Degrees of Freedom and Generalized Coordinates;68
7.3.1;3.3.1 Degrees of Freedom of Kinematic Chains;68
7.3.2;3.3.2 Examples from Road Vehicle Suspension Kinematics;69
7.3.3;3.3.3 Generalized Coordinates;70
7.4;3.4 Basic Principles of the Assembly of Kinematic Chains;71
7.4.1;3.4.1 Sparse-Methods: Absolute Coordinates Formulation;73
7.4.2;3.4.2 Vector Loop Methods (“LAGRANGE” Formulation);75
7.4.3;3.4.3 Topological Methods: Formulation of Minimum Coordinates;76
7.5;3.5 Kinematics of a Complete Multibody System;78
7.5.1;3.5.1 Basic Concept;78
7.5.2;3.5.2 Block Wiring Diagram and Kinematic Networks;79
7.5.3;3.5.3 Relative Kinematics of the Spatial Four-Link Mechanism;80
7.5.4;3.5.4 Relative, Absolute and Global Kinematics;82
7.5.5;3.5.5 Example: Double Wishbone Suspension;85
7.6;References;87
8;4 Equations of Motion of Complex Multibody Systems;88
8.1;4.1 Fundamental Equation of Dynamics for Point Mass Systems;88
8.2;4.2 JOURDAIN’S Principle;90
8.3;4.3 LAGRANGE Equations of the First Kind for Point Mass Systems;90
8.4;4.4 LAGRANGE Equations of the Second Kind for Rigid Bodies;91
8.5;4.5 D’ALEMBERT’s Principle;93
8.6;4.6 Computer-Based Derivation of the Equations of Motion;95
8.6.1;4.6.1 Kinematic Differentials of Absolute Kinematics;96
8.6.2;4.6.2 Equations of Motion;98
8.6.3;4.6.3 Dynamics of a Spatial Multibody Loop;99
8.7;References;107
9;5 Kinematics and Dynamics of the Vehicle Body;109
9.1;5.1 Vehicle-Fixed Reference Frame;109
9.2;5.2 Kinematical Analysis of the Chassis;112
9.2.1;5.2.1 Incorporation of the Wheel Suspension Kinematics;113
9.2.2;5.2.2 Equations of Motion;115
9.3;References;116
10;6 Modeling and Analysis of Wheel Suspensions;117
10.1;6.1 Function of Wheel Suspension Systems;117
10.2;6.2 Different Types of Wheel Suspension;119
10.2.1;6.2.1 Beam Axles;120
10.2.2;6.2.2 Twist-Beam Suspension;121
10.2.3;6.2.3 Trailing-Arm Axle;122
10.2.4;6.2.4 Trailer Arm Axle;124
10.2.5;6.2.5 Double Wishbone Axles;124
10.2.6;6.2.6 Wheel Suspension Derived from the MacPherson Principle;126
10.2.7;6.2.7 Multi-Link Axles;127
10.3;6.3 Characteristic Variables of Wheel Suspensions;129
10.4;6.4 One Dimensional Quarter Vehicle Models;132
10.5;6.5 Three-Dimensional Model of a MacPherson Wheel Suspension;135
10.5.1;6.5.1 Kinematic Analysis;136
10.5.2;6.5.2 Explicit Solution;140
10.6;6.6 Three-Dimensional Model of a Five-Link Rear Wheel Suspension;145
10.6.1;6.6.1 Kinematic Analysis;145
10.6.2;6.6.2 Implicit Solution;148
10.6.3;6.6.3 Simulation Results of the Three Dimensional Quarter Vehicle Model;153
10.7;References;157
11;7 Modeling of the Road-Tire-Contact;158
11.1;7.1 Tire Construction;159
11.2;7.2 Forces Between Wheel and Road;160
11.3;7.3 Stationary Tire Contact Forces;160
11.3.1;7.3.1 Tires Under Vertical Loads;162
11.3.2;7.3.2 Rolling Resistance;163
11.3.3;7.3.3 Tires Under Longitudinal (Circumferential) Forces;163
11.3.4;7.3.4 Tires Subjected to Lateral Forces;175
11.3.5;7.3.5 Influence of the Camber on the Tire Lateral Force;178
11.3.6;7.3.6 Influence of the Tire Load and the Tire Forces on the Patch Surface;179
11.3.7;7.3.7 Fundamental Structure of the Tire Forces;179
11.3.8;7.3.8 Superposition of Circumferential and Lateral Forces;180
11.4;7.4 Tire Models;183
11.4.1;7.4.1 The Contact Point Geometry;184
11.4.2;7.4.2 Contact Velocity;189
11.4.3;7.4.3 Calculation of the Slip Variables;190
11.4.4;7.4.4 Magic Formula Model;191
11.4.5;7.4.5 Magic Formula Models for Superimposed Slip;193
11.4.6;7.4.6 HSRI Tire Model;194
11.5;7.5 Instationary Tire Behavior;197
11.6;References;198
12;8 Modeling of the Drivetrain;200
12.1;8.1 Drivetrain Concepts;200
12.2;8.2 Modeling;202
12.2.1;8.2.1 Relative Motion of the Engine Block;202
12.2.2;8.2.2 Modelling of the Drivetrain;203
12.2.3;8.2.3 Engine Bracket;204
12.2.4;8.2.4 Modeling of Homokinetic Joints;209
12.3;8.3 Modeling of the Engine;211
12.4;8.4 Relative Kinematics of the Drivetrain;213
12.5;8.5 Absolute Kinematics of the Drivetrain;215
12.6;8.6 Equations of Motion;216
12.7;8.7 Discussion of Simulation Results;217
12.8;References;218
13;9 Force Components;220
13.1;9.1 Forces and Torques in Multibody Systems;220
13.1.1;9.1.1 Reaction Forces;222
13.1.2;9.1.2 Applied Forces;223
13.2;9.2 Operating Brake System;223
13.3;9.3 Aerodynamic Forces;225
13.4;9.4 Spring and Damper Components;227
13.4.1;9.4.1 Spring Elements;227
13.4.2;9.4.2 Damper Elements;228
13.4.3;9.4.3 Force Elements Connected in Parallel;230
13.4.4;9.4.4 Force Elements in Series;230
13.5;9.5 Anti-Roll Bars;231
13.5.1;9.5.1 Passive Anti-Roll Bars;231
13.5.2;9.5.2 Active Anti-Roll Bars;234
13.6;9.6 Rubber Composite Elements;235
13.7;References;237
14;10 Single Track Models;238
14.1;10.1 Linear Single Track Model;238
14.1.1;10.1.1 Equations of Motion of the Linear Single Track Model;239
14.1.2;10.1.2 Stationary Steering Behavior and Cornering;245
14.1.3;10.1.3 Instationary Steering Behavior: Vehicle Stability;248
14.2;10.2 Nonlinear Single Track Model;250
14.2.1;10.2.1 Kinetics of the Nonlinear Single Track Model;250
14.2.2;10.2.2 Tire Forces;253
14.2.3;10.2.3 Drive and Brake Torques;256
14.2.4;10.2.4 Equations of Motion;258
14.2.5;10.2.5 Equations of State;259
14.3;10.3 Linear Roll Model;260
14.3.1;10.3.1 Equation of Motion for the Rolling of the Chassis;261
14.3.2;10.3.2 Dynamic Tire Loads;265
14.3.3;10.3.3 Influence of the Self-steering Behavior;268
14.4;References;270
15;11 Twin Track Models;271
15.1;11.1 Twin Track Model Without Suspension Kinematics;271
15.1.1;11.1.1 NEWTON’s and EULER’s Equations for a Basic Spatial Twin Track Model;274
15.1.2;11.1.2 Spring and Damper Forces;276
15.1.3;11.1.3 NEWTON’s and EULER’s Equations of the Wheels;278
15.1.4;11.1.4 Tire-Road Contact;279
15.1.5;11.1.5 Drivetrain;281
15.1.6;11.1.6 Brake System;283
15.1.7;11.1.7 Equations of Motion;284
15.2;11.2 Twin Track Models with Kinematic Wheel Suspensions;285
15.2.1;11.2.1 Degrees of Freedom of the Twin Track Model;285
15.2.2;11.2.2 Kinematics of the Vehicle Chassis;288
15.2.3;11.2.3 Generalized Kinematics of the Wheel Suspension;290
15.2.4;11.2.4 Wheel Suspension with a Trailing Arm Suspension;295
15.2.5;11.2.5 Kinematics of the Wheels While Using a Trailing Arm Suspension;300
15.2.6;11.2.6 Tire Forces and Torques;303
15.2.7;11.2.7 Suspension Springs and Dampers;304
15.2.8;11.2.8 Aerodynamic Forces;305
15.2.9;11.2.9 Steering;305
15.2.10;11.2.10 Anti-roll Bar;306
15.2.11;11.2.11 Applied Forces and Torques;307
15.2.12;11.2.12 NEWTON’s and EULER’s Equations;308
15.2.13;11.2.13 Motion and State Space Equations;312
15.3;11.3 Simplified Driver Model;312
15.3.1;11.3.1 Controller Concept;312
15.4;11.4 Parameterization;315
15.5;References;316
16;12 Three-Dimensional Complete Vehicle Models;317
16.1;12.1 Modeling of the Complete Vehicle;317
16.1.1;12.1.1 Kinematics of a Rear-Wheel Driven Complete Vehicle Model;318
16.1.2;12.1.2 Kinematics of Front- and Four-Wheel Driven Complete Vehicle Models;327
16.1.3;12.1.3 Dynamics of the Complete Vehicle Model;337
16.2;12.2 Simulation of Motor Vehicles;343
16.2.1;12.2.1 Setup and Concept of FASIM_C++;344
16.2.2;12.2.2 Modular Structure of a Vehicle Model;346
16.2.3;12.2.3 Construction of the Equations of Motion;350
16.2.4;12.2.4 Numeric Integration;356
16.2.5;12.2.5 Treatment of Events;359
16.3;References;360
17;13 Model of a Typical Complex Complete Vehicle;362
17.1;13.1 Modeling of the Complete Vehicle;362
17.2;13.2 Model Verification and Validation;365
17.2.1;13.2.1 Verification;366
17.2.2;13.2.2 Validation;366
17.3;13.3 Parameterized Vehicle Model;374
17.3.1;13.3.1 Definition of a Reference Model;374
17.3.2;13.3.2 Comparison of Parameterized Versus Validated Models;377
17.4;References;381
18;14 Selected Applications;383
18.1;14.1 Simulation of Test Maneuvers;383
18.1.1;14.1.1 Simulation of a Step Steering Input (ISO 7401);383
18.1.2;14.1.2 Simulation of Stationary Circular Travel;386
18.1.3;14.1.3 Simulation of a Double Lane Change;386
18.2;14.2 Simulation of Vehicle Rollover;390
18.2.1;14.2.1 Virtual Proving Grounds;394
18.2.2;14.2.2 Results of the Simulation;398
18.2.2.1;14.2.2.1 Misuse Testing;398
18.2.2.2;14.2.2.2 Ride Over a R400
18.2.2.3;14.2.2.3 Passing Over Embankment;403
18.2.2.4;14.2.2.4 Sand Bed;406
18.3;14.3 Control of the Roll Dynamics Using Active Anti-Roll Bars;409
18.3.1;14.3.1 Passive Anti-Roll Bar;410
18.3.2;14.3.2 Stiffness Distribution Between Front- and Rear Axle;410
18.3.3;14.3.3 Adjustment of the Roll Dynamics by Means of Active Anti-Roll Bars;413
18.3.4;14.3.4 Control Unit Design;413
18.3.5;14.3.5 Response and Disturbance Reaction;417
18.3.6;14.3.6 Roll Torque Distribution with Fuzzy Logic;417
18.3.7;14.3.7 Active Principle;418
18.3.8;14.3.8 Potential of a Roll Torque Distribution;419
18.4;14.4 Driving Simulators;421
18.4.1;14.4.1 Areas of Application and Implementation of Driving Simulators;421
18.4.2;14.4.2 The Control Circuit Driver-Vehicle-Environment;424
18.4.3;14.4.3 Implementation of Driving Simulators;426
18.4.4;14.4.4 Simulation Models and Interfaces;426
18.4.5;14.4.5 Motion Systems;429
18.4.6;14.4.6 Conducting Experiments with Driving Simulators;430
18.4.7;14.4.7 Recording of Measured Values in Simulator Tests;432
18.4.8;14.4.8 Implementation of Simple Driving Simulators;432
18.5;References;441
19;Index;443

Über Autor(innen)

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.