Railroad Vehicle Dynamics: A Computational Approach

by Shabana; Ahmed A.

• ISBN13: 9781420045819
• ISBN10: 1420045814
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-07-23
• Publisher: CRC Press

Summary

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.

Table of Contents

Preface	p. xi
Acknowledgments	p. xv
Introduction	p. 1
Railroad Vehicles and Multibody System Dynamics	p. 2
Generality	p. 2
Nonlinearity	p. 4
Implementation of Railroad Vehicle Elements	p. 6
Constrained Dynamics	p. 9
Geometry Problem	p. 11
Differential Geometry	p. 12
Rail and Wheel Geometry	p. 14
Contact Theories	p. 17
Creep Forces	p. 17
Wheel/Rail Creep Theories	p. 18
General Multibody Railroad Vehicle Formulations	p. 18
Constraint Contact Formulation	p. 19
Elastic Contact Formulation	p. 20
Specialized Railroad Vehicle Formulations	p. 20
Linearized Railroad Vehicle Models	p. 23
Motion Stability	p. 24
Motion Scenarios	p. 27
Hunting	p. 28
Steady Curving	p. 28
Spiral Negotiation	p. 30
Twist and Roll	p. 30
Pitch and Bounce	p. 31
Yaw and Sway	p. 31
Dynamic Curving	p. 31
Response to Discontinuities	p. 32
Dynamic Formulations	p. 35
General Displacement	p. 36
Rotation Matrix	p. 37
Direction Cosines	p. 38
Simple Rotations	p. 41
Euler Angles	p. 41
Euler Parameters	p. 45
Velocities and Accelerations	p. 49
Velocity Vector	p. 49
Acceleration Vector	p. 50
Generalized Orientation Coordinates	p. 51
Singular Configuration	p. 53
Newton-Euler Equations	p. 58
Joint Constraints	p. 62
Spherical Joint	p. 62
Revolute Joint	p. 63
Cylindrical Joint	p. 64
Prismatic Joint	p. 65
Augmented Formulation	p. 66
Trajectory Coordinates	p. 70
Velocity and Acceleration	p. 72
Equations of Motion	p. 74
Embedding Technique	p. 76
Coordinate Partitioning and Velocity Transformation	p. 77
Elimination of the Constraint Forces	p. 78
Reduced-Order Model	p. 78
Interpretation of the Methods	p. 80
Kinematic and Dynamic Equations	p. 80
Augmented Formulation	p. 83
Embedding Technique	p. 84
D'Alembert's Principle	p. 85
Virtual Work	p. 86
Rail and Wheel Geometry	p. 89
Theory of Curves	p. 90
Arc Length and Tangent Line	p. 90
Curvature and Torsion	p. 91
Geometry of Surfaces	p. 92
Tangent Plane and Normal Vector	p. 94
First Fundamental Form	p. 95
Second Fundamental Form	p. 96
Normal Curvature	p. 99
Principal Curvatures and Principal Directions	p. 100
Rail Geometry	p. 103
Definitions and Terminology	p. 106
Geometric Description of the Track	p. 108
Computer Implementation	p. 111
Track Segment Types	p. 112
Linear Representation of the Segments	p. 112
Derivatives of the Angles	p. 114
Track Preprocessor	p. 116
Track Preprocessor Input	p. 117
Numerical Integration	p. 118
Track Preprocessor Output	p. 120
Use of the Preprocessor Output during Dynamic Simulation	p. 121
Wheel Geometry	p. 123
Contact and Creep-Force Models	p. 127
Hertz Theory	p. 128
Geometry and Kinematics	p. 128
Contact Pressure	p. 133
Computer Implementation	p. 138
Creep Phenomenon	p. 140
Wheel/Rail Contact Approaches	p. 145
Exact Theory of Rolling Contact	p. 146
Simplified Theory of Rolling Contact	p. 147
Dynamic and Quasi-Static Theory	p. 147
Three- and Two-Dimensional Theory	p. 147
Creep-Force Theories	p. 147
Carter's Theory	p. 147
Johnson and Vermeulen's Theory	p. 149
Kalker's Linear Theory	p. 150
Heuristic Nonlinear Creep-Force Model	p. 153
Polach Nonlinear Creep-Force Model	p. 154
Simplified Theory	p. 156
Kalker's USETAB	p. 159
Multibody Contact Formulations	p. 161
Parameterization of Wheel and Rail Surfaces	p. 162
Track Geometry	p. 163
Wheel Geometry	p. 165
Constraint Contact Formulations	p. 165
Contact Constraints	p. 166
Constrained Dynamic Equations	p. 167
Augmented Constraint Contact Formulation (ACCF)	p. 168
Embedded Constraint Contact Formulation (ECCF)	p. 171
Position Analysis	p. 172
Equations of Motion	p. 173
Elastic Contact Formulation-Algebraic Equations (ECF-A)	p. 174
Elastic Contact Formulation-Nodal Search (ECF-N)	p. 177
Comparison of Different Contact Formulations	p. 178
Planar Contact	p. 179
Intermediate Wheel Coordinate System	p. 181
Distance Traveled	p. 182
Profile Parameters	p. 184
Coupling between the Surface Parameters	p. 185
Implementation and Special Elements	p. 187
General Multibody System Algorithms	p. 188
Constrained Dynamics	p. 188
Penalty and Constraint Stabilization Methods	p. 189
Generalized Coordinates Partitioning	p. 191
Identification of the Independent Coordinates	p. 194
Numerical Algorithms - Constraint Formulations	p. 194
Augmented Constraint Contact Formulation (ACCF)	p. 195
Embedded Constraint Contact Formulation (ECCF)	p. 201
Numerical Algorithms - Elastic Formulations	p. 205
Elastic Contact Formulation Using Algebraic Equations (ECF-A)	p. 206
Elastic Contact Formulation Using Nodal Search (ECF-N)	p. 208
Calculation of the Creep Forces	p. 210
Higher Derivatives and Smoothness Technique	p. 211
Track Preprocessor	p. 214
Change in the Length Due to Curvature	p. 216
Use of the Preprocessor Output during Dynamic Simulation	p. 218
Deviations and Measured Data	p. 219
Track Deviations	p. 220
Measured Track Data	p. 222
Track Quality and Classes	p. 223
Special Elements	p. 225
Translational Spring-Damper-Actuator Element	p. 227
Rotational Spring-Damper-Actuator Element	p. 230
Series Spring-Damper Element	p. 231
Bushing Element	p. 232
Maglev Forces	p. 236
Electrodynamic Suspension (EDS)	p. 236
Electromagnetic Suspension (EMS)	p. 237
Modeling of Electromagnetic Suspensions	p. 237
Multibody System Electromechanical Equations	p. 240
Static Analysis	p. 242
Augmented Constraint Contact Formulation	p. 242
Embedded Constraint Contact Formulation	p. 244
Line Search Method	p. 245
Continuation Method	p. 246
Numerical Comparative Study	p. 247
Simple Suspended Wheelset	p. 247
Complete Vehicle Model	p. 248
Specialized Railroad Vehicle Formulations	p. 255
General Displacement	p. 236
Trajectory Coordinate System	p. 256
Body Coordinate System	p. 258
Generalized Trajectory Coordinates	p. 259
Velocity and Acceleration	p. 260
Velocity of the Center of Mass	p. 260
Acceleration of the Center of Mass	p. 261
Angular Velocity and Acceleration	p. 262
Equations of Motion	p. 264
Trajectory Coordinate Constraints	p. 265
Numerical Example	p. 266
Use of the Cartesian Coordinates	p. 269
Single-Degree-of-Freedom Model	p. 272
Two-Degree-of-Freedom Model	p. 277
Linear Hunting Stability Analysis	p. 280
Model 1	p. 287
Model 2	p. 288
Creepage Linearization	p. 291
Background	p. 291
Transformation and Angular Velocity	p. 295
Matrix Identities	p. 295
Definition of the Angular Velocity	p. 296
Euler Angles	p. 298
Linearization Assumptions	p. 300
Longitudinal and Lateral Creepages	p. 301
Spin Creepage	p. 305
Newton-Euler Equations	p. 306
Concluding Remarks	p. 309
Contact Equations	p. 313
Elliptical Integrals	p. 319
References	p. 321
Index	p. 333
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