Railroad vehicle dynamics : a computational approach

The methods of computational mechanics have been used extensively in modeling many physical systems. The use of multibody-system techniques, in particular, has been applied successfully in the study of various, fundamentally different applications.

Railroad Vehicle Dynamics: A Computational Approach presents a computational multibody-system approach that can be used to develop complex models of railroad vehicle systems. The book examines several computational multibody-system formulations and discusses their computer implementation. The computational algorithms based on these general formulations can be used to develop general- and special-purpose railroad vehicle computer programs for use in the analysis of railroad vehicle systems, including the study of derailment and accident scenarios, design issues, and performance evaluation.

The authors focus on the development of fully nonlinear formulations, supported by an explanation of the limitations of the linearized formulations that are frequently used in the analysis of railroad vehicle systems. The chapters of the book are organized to guide readers from basic concepts and definitions through a final understanding of the utility of fully nonlinear multibody- system formulations in the analysis of railroad vehicle systems.

Railroad Vehicle Dynamics: A Computational Approach is a valuable reference for researchers and practicing engineers who commonly use general-purpose, multibody-system computer programs in the analysis, design, and performance evaluation of railroad vehicle systems.

Preface	p. xi
Acknowledgments	p. xv
Chapter 1 Introduction	p. 1
1.1 Railroad Vehicles and Multibody System Dynamics	p. 2
1.1.1 Generality	p. 2
1.1.2 Nonlinearity	p. 4
1.1.3 Implementation of Railroad Vehicle Elements	p. 6
1.2 Constrained Dynamics	p. 9
1.3 Geometry Problem	p. 11
1.3.1 Differential Geometry	p. 12
1.3.2 Rail and Wheel Geometry	p. 14
1.4 Contact Theories	p. 17
1.4.1 Creep Forces	p. 17
1.4.2 Wheel/Rail Creep Theories	p. 18
1.5 General Multibody Railroad Vehicle Formulations	p. 18
1.5.1 Constraint Contact Formulation	p. 19
1.5.2 Elastic Contact Formulation	p. 20
1.6 Specialized Railroad Vehicle Formulations	p. 20
1.7 Linearized Railroad Vehicle Models	p. 23
1.8 Motion Stability	p. 24
1.9 Motion Scenarios	p. 27
1.9.1 Hunting	p. 28
1.9.2 Steady Curving	p. 28
1.9.3 Spiral Negotiation	p. 30
1.9.4 Twist and Roll	p. 30
1.9.5 Pitch and Bounce	p. 31
1.9.6 Yaw and Sway	p. 31
1.9.7 Dynamic Curving	p. 31
1.9.8 Response to Discontinuities	p. 32
Chapter 2 Dynamic Formulations	p. 35
2.1 General Displacement	p. 36
2.2 Rotation Matrix	p. 37
2.2.1 Direction Cosines	p. 38
2.2.2 Simple Rotations	p. 41
2.2.3 Euler Angles	p. 41
2.2.4 Euler Parameters	p. 45
2.3 Velocities and Accelerations	p. 49
2.3.1 Velocity Vector	p. 49
2.3.2 Acceleration Vector	p. 50
2.3.3 Generalized Orientation Coordinates	p. 51
2.3.4 Singular Configuration	p. 53
2.4 Newton-Euler Equations	p. 58
2.5 Joint Constraints	p. 62
2.5.1 Spherical Joint	p. 62
2.5.2 Revolute Joint	p. 63
2.5.3 Cylindrical Joint	p. 64
2.5.4 Prismatic Joint	p. 65
2.6 Augmented Formulation	p. 66
2.7 Trajectory Coordinates	p. 70
2.7.1 Velocity and Acceleration	p. 72
2.7.2 Equations of Motion	p. 74
2.8 Embedding Technique	p. 76
2.8.1 Coordinate Partitioning and Velocity Transformation	p. 77
2.8.2 Elimination of the Constraint Forces	p. 78
2.8.3 Reduced-Order Model	p. 78
2.9 Interpretation of the Methods	p. 80
2.9.1 Kinematic and Dynamic Equations	p. 80
2.9.2 Augmented Formulation	p. 83
2.9.3 Embedding Technique	p. 84
2.9.4 D'Alembert's Principle	p. 85
2.10 Virtual Work	p. 86
Chapter 3 Rail and Wheel Geometry	p. 89
3.1 Theory of Curves	p. 90
3.1.1 Arc Length and Tangent Line	p. 90
3.1.2 Curvature and Torsion	p. 91
3.2 Geometry of Surfaces	p. 92
3.2.1 Tangent Plane and Normal Vector	p. 94
3.2.2 First Fundamental Form	p. 95
3.2.3 Second Fundamental Form	p. 96
3.2.4 Normal Curvature	p. 99
3.2.5 Principal Curvatures and Principal Directions	p. 100
3.3 Rail Geometry	p. 103
3.4 Definitions and Terminology	p. 106
3.5 Geometric Description of the Track	p. 108
3.6 Computer Implementation	p. 111
3.6.1 Track Segment Types	p. 112
3.6.2 Linear Representation of the Segments	p. 112
3.6.3 Derivatives of the Angles	p. 114
3.7 Track Preprocessor	p. 116
3.7.1 Track Preprocessor Input	p. 117
3.7.2 Numerical Integration	p. 118
3.7.3 Track Preprocessor Output	p. 120
3.7.4 Use of the Preprocessor Output during Dynamic Simulation	p. 121
3.8 Wheel Geometry	p. 123
Chapter 4 Contact and Creep-Force Models	p. 127
4.1 Hertz Theory	p. 128
4.1.1 Geometry and Kinematics	p. 128
4.1.2 Contact Pressure	p. 133
4.1.3 Computer Implementation	p. 138
4.2 Creep Phenomenon	p. 140
4.3 Wheel/Rail Contact Approaches	p. 145
4.3.1 Exact Theory of Rolling Contact	p. 146
4.3.2 Simplified Theory of Rolling Contact	p. 147
4.3.3 Dynamic and Quasi-Static Theory	p. 147
4.3.4 Three- and Two-Dimensional Theory	p. 147
4.4 Creep-Force Theories	p. 147
4.4.1 Carter's Theory	p. 147
4.4.2 Johnson and Vermeulen's Theory	p. 149
4.4.3 Kalker's Linear Theory	p. 150
4.4.4 Heuristic Nonlinear Creep-Force Model	p. 153
4.4.5 Polach Nonlinear Creep-Force Model	p. 154
4.4.6 Simplified Theory	p. 156
4.4.7 Kalker's USETAB	p. 159
Chapter 5 Multibody Contact Formulations	p. 161
5.1 Parameterization of Wheel and Rail Surfaces	p. 162
5.1.1 Track Geometry	p. 163
5.1.2 Wheel Geometry	p. 165
5.2 Constraint Contact Formulations	p. 165
5.2.1 Contact Constraints	p. 166
5.2.2 Constrained Dynamic Equations	p. 167
5.3 Augmented Constraint Contact Formulation (ACCF)	p. 168
5.4 Embedded Constraint Contact Formulation (ECCF)	p. 171
5.4.1 Position Analysis	p. 172
5.4.2 Equations of Motion	p. 173
5.5 Elastic Contact Formulation-Algebraic Equations (ECF-A)	p. 174
5.6 Elastic Contact Formulation-Nodal Search (ECF-N)	p. 177
5.7 Comparison of Different Contact Formulations	p. 178
5.8 Planar Contact	p. 179
5.8.1 Intermediate Wheel Coordinate System	p. 181
5.8.2 Distance Traveled	p. 182
5.8.3 Profile Parameters	p. 184
5.8.4 Coupling between the Surface Parameters	p. 185
Chapter 6 Implementation and Special Elements	p. 187
6.1 General Multibody System Algorithms	p. 188
6.1.1 Constrained Dynamics	p. 188
6.1.2 Penalty and Constraint Stabilization Methods	p. 189
6.1.3 Generalized Coordinates Partitioning	p. 191
6.1.4 Identification of the Independent Coordinates	p. 194
6.2 Numerical Algorithms - Constraint Formulations	p. 194
6.2.1 Augmented Constraint Contact Formulation (ACCF)	p. 195
6.2.2 Embedded Constraint Contact Formulation (ECCF)	p. 201
6.3 Numerical Algorithms - Elastic Formulations	p. 205
6.3.1 Elastic Contact Formulation Using Algebraic Equations (ECF-A)	p. 206
6.3.2 Elastic Contact Formulation Using Nodal Search (ECF-N)	p. 208
6.4 Calculation of the Creep Forces	p. 210
6.5 Higher Derivatives and Smoothness Technique	p. 211
6.6 Track Preprocessor	p. 214
6.6.1 Change in the Length Due to Curvature	p. 216
6.6.2 Use of the Preprocessor Output during Dynamic Simulation	p. 218
6.7 Deviations and Measured Data	p. 219
6.7.1 Track Deviations	p. 220
6.7.2 Measured Track Data	p. 222
6.7.3 Track Quality and Classes	p. 223
6.8 Special Elements	p. 225
6.8.1 Translational Spring-Damper-Actuator Element	p. 227
6.8.2 Rotational Spring-Damper-Actuator Element	p. 230
6.8.3 Series Spring-Damper Element	p. 231
6.8.4 Bushing Element	p. 232
6.9 Maglev Forces	p. 236
6.9.1 Electrodynamic Suspension (EDS)	p. 236
6.9.2 Electromagnetic Suspension (EMS)	p. 237
6.9.3 Modeling of Electromagnetic Suspensions	p. 237
6.9.4 Multibody System Electromechanical Equations	p. 240
6.10 Static Analysis	p. 242
6.10.1 Augmented Constraint Contact Formulation	p. 242
6.10.2 Embedded Constraint Contact Formulation	p. 244
6.10.3 Line Search Method	p. 245
6.10.4 Continuation Method	p. 246
6.11 Numerical Comparative Study	p. 247
6.11.1 Simple Suspended Wheelset	p. 247
6.11.2 Complete Vehicle Model	p. 248
Chapter 7 Specialized Railroad Vehicle Formulations	p. 255
7.1 General Displacement	p. 236
7.1.1 Trajectory Coordinate System	p. 256
7.1.2 Body Coordinate System	p. 258
7.1.3 Generalized Trajectory Coordinates	p. 259
7.2 Velocity and Acceleration	p. 260
7.2.1 Velocity of the Center of Mass	p. 260
7.2.2 Acceleration of the Center of Mass	p. 261
7.2.3 Angular Velocity and Acceleration	p. 262
7.3 Equations of Motion	p. 264
7.4 Trajectory Coordinate Constraints	p. 265
7.4.1 Numerical Example	p. 266
7.4.2 Use of the Cartesian Coordinates	p. 269
7.5 Single-Degree-of-Freedom Model	p. 272
7.6 Two-Degree-of-Freedom Model	p. 277
7.7 Linear Hunting Stability Analysis	p. 280
7.7.1 Model 1	p. 287
7.7.2 Model 2	p. 288
Chapter 8 Creepage Linearization	p. 291
8.1 Background	p. 291
8.2 Transformation and Angular Velocity	p. 295
8.2.1 Matrix Identities	p. 295
8.2.2 Definition of the Angular Velocity	p. 296
8.3 Euler Angles	p. 298
8.4 Linearization Assumptions	p. 300
8.5 Longitudinal and Lateral Creepages	p. 301
8.6 Spin Creepage	p. 305
8.7 Newton-Euler Equations	p. 306
8.8 Concluding Remarks	p. 309
Appendix A Contact Equations	p. 313
Appendix B Elliptical Integrals	p. 319
References	p. 321
Index	p. 333

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