Mathematical Foundation of Railroad Vehicle Systems

AHMED A. SHABANA is University Distinguished Professor and the Richard and Loan Hill Professor of Engineering at the University of Illinois at Chicago, United States. He is a Fellow of the American Society of Mechanical Engineers (ASME), a Fellow of the Society of Automotive Engineering (SAE International), and the author of texts in the areas of dynamics and vibration.

• Preface ix1 Introduction 11.1 Differential Geometry 41.2 Integration of Geometry and Mechanics 91.3 Hunting Oscillations 141.4 Wheel and Track Geometries 171.5 Centrifugal Forces and Balance Speed 221.6 Contact Formulations 261.7 Computational MBS Approaches 281.8 Derailment Criteria 331.9 High-Speed Rail Systems 361.10 Linear Algebra and Book Notations 412 Differential Geometry 452.1 Curve Geometry 462.2 Surface Geometry 542.3 Application to Railroad Geometry 572.4 Surface Tangent Plane and Normal Vector 602.5 Surface Fundamental Forms 622.6 Normal Curvature 692.7 Principal Curvatures and Directions 722.8 Numerical Representation of the Profile Geometry 762.9 Numerical Representation of Surface Geometry 783 Motion and Geometry Descriptions 833.1 Rigid-Body Kinematics 843.2 Direction Cosines and Simple Rotations 863.3 Euler Angles 883.4 Euler Parameters 913.5 Velocity and Acceleration Equations 953.6 Generalized Coordinates 973.7 Kinematic Singularities 1003.8 Euler Angles and Track Geometry 1023.9 Angle Representation of the Curve Geometry 1073.10 Euler Angles as Field Variables 1083.11 Euler-Angle Description of the Track Geometry 1113.12 Geometric Motion Constraints 1143.13 Trajectory Coordinates 1194 Railroad Geometry 1254.1 Wheel Surface Geometry 1264.2 Wheel Curvatures and Global Vectors 1324.3 Semi-analytical Approach for Rail Geometry 1354.4 ANCF Rail Geometry 1424.5 ANCF Interpolation of Rail Geometry 1454.6 ANCF Computation of Tangents and Normal 1464.7 Track Geometry Equations 1484.8 Numerical Representation of Track Geometry 1524.9 Track Data 1554.10 Irregularities and Measured Track Data 1624.11 Comparison of the Semi-Analytical and ANCF Approaches 1695 Contact Problem 1755.1 Wheel/Rail Contact Mechanism 1775.2 Constraint Contact Formulation (CCF) 1835.3 Elastic Contact Formulation (ECF) 1845.4 Normal Contact Forces 1875.5 Contact Surface Geometry 1885.6 Contact Ellipse and Normal Contact Force 1945.7 Creepage Definitions 1995.8 Creep Force Formulations 2035.9 Creep Force and Wheel/Rail Contact Formulations 2135.10 Maglev Forces 2196 Equations of Motion 2256.1 Newtonian and Lagrangian Approaches 2266.2 Virtual Work Principle and Constrained Dynamics 2276.3 Summary of Rigid-Body Kinematics 2326.4 Inertia Forces 2356.5 Applied Forces 2396.6 Newton–Euler Equations 2416.7 Augmented Formulation and Embedding Technique 2446.8 Wheel/Rail Constraint Contact Forces 2546.9 Wheel/Rail Elastic Contact Forces 2596.10 Other Force Elements 2616.11 Trajectory Coordinates 2686.12 Longitudinal Train Dynamics (LTD) 2746.13 Hunting Stability 2806.14 MBS Modeling of Electromechanical Systems 2887 Pantograph/Catenary Systems 2917.1 Pantograph/Catenary Design 2927.2 ANCF Catenary Kinematic Equations 2987.3 Catenary Inertia and Elastic Forces 3047.4 Catenary Equations of Motion 3067.5 Pantograph/Catenary Contact Frame 3087.6 Constraint Contact Formulation (CCF) 3107.7 Elastic Contact Formulation (ECF) 3147.8 Pantograph/Catenary Equations and MBS Algorithms 3177.9 Pantograph/Catenary Contact Force Control 3217.10 Aerodynamic Forces 3227.11 Pantograph/Catenary Wear 324Appendix Contact Equations and Elliptical Integrals 329A.1 Derivation of the Contact Equations 329A.2 Elliptical Integrals 332Bibliography 335Index 355