Course Objective:

Introduction to analytical tools for modeling, analysis and design of railway vehicles.




ME 625, ESO 209a (or equivalents)


N. S. Vyas

Other interested faculty members:

Bishakh Bhattacharya, Nachiketa Tiwari

Lectures per week:

3 hrs


PG, UG (III, IV yrs)

Condensed Syllabus:

Railroad Vehicles and Multi-body System Dynamics, Contraint Dynamics, Geometry Problems, Contact Theories, General Multi-body Vehicle Formulations, Specialised Railroad Vehicle Formulations, Linearised Railroad Vehicle Models, Motion Stability, Motion Scenarios (Hunting, Steady Curving, Spiral Negotiations, Twist, Pitch, Roll, Yaw, Sway, Dynamic Curving, Response to discintinuities), Modeling and Simulation.

Lecture-wise Break-up

I. Introduction (2 hrs):

II. Dynamic Formulations (6 hrs):

  • General Displacement, Rotation Matrix, Velocities and Accelerations, Newton-Euler Equations, Joint Constraints, Augmented Formulations, Trajectory Coordinates, Embedding Techniques, Virtual Work

III. Rail and Wheel Geometry (6 hrs):

  • Theory of Curves, Geometry of surfaces, Rail Geometry, Definitions and Terminology, Geometric description of track, Wheel Geometry

IV. Contact and Creep-Force Models (6 hrs):

  • Hertz Theory, Creep Phenomenon, Wheel/Rail contact approaches, Creep-force theories

V. Multibody Contact Formulations (10 hrs):

  • Prameterisation of Wheel and Rail surfaces, Constraint Contact Formulations, Augmented constraint contact formulation, Embedded constraint contact formulation, Elastic Contact Formulation (Algebraic Equations, Nodal Search), Planar Contact Profile Parameters Coupling between surface parameters

VI. Modelling and Simulation (10 hrs):

  • Multi-body and constraint algorithms, Track models, Creep calculations, Measurements Damping Elements, Maglev models, Stability Models

Suggested Textbooks:

  1. Railroad Vehicle Dynamics, Ahmed A. Shabana, Khaled E. Zaazaa, Hiroyuki Sugiyama, CRC Press

  2. Dynamics of Railway Vehicle Systems, Vijay K. Garg, Rao V, Dukkipati, Academic Press

  3. Fundamentals of Rail Wheel Dynamics, A. H. Wickens, Swets & Zeitlinger Publishers, The Netherlands

  4. Handbook of Railway Vehicle Dynamics, Simon Iwnicki, CRC Press

  5. Railway Noise and Vibration, David Thompson, Elsvier

  6. Wheel-rail Interface Handbook, R. Lewis, U. Olofsson, CRC Press