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Simulations of Dynamic Braking of Railroad Vehicles Using Trajectory Coordinates

[+] Author Affiliations
Claudio Mellace, Antonio Gugliotta

Politecnico di Torino, Vercelli, Italy

Tariq Sinokrot, Ahmed A. Shabana

University of Illinois at Chicago, Chicago, IL

Paper No. DETC2007-34016, pp. 1785-1793; 9 pages
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4806-X | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME


One of the important issues associated with the use of the trajectory coordinates in railroad vehicle simulations is the ability of such coordinates in dealing with braking and traction scenarios. In existing specialized railroad computer algorithms, the trajectory coordinates instead of the absolute Cartesian coordinates are often used. In these algorithms, track coordinate systems that travel with constant speeds are employed to define the configuration of the components in railroad vehicle systems. As the result of using a prescribed motion for these track coordinate systems, the simulation of braking and/or traction scenarios becomes difficult or even impossible, as reported in recent investigations [2]. The assumption of the prescribed motion of the track coordinate systems can be relaxed, thereby allowing the trajectory coordinate systems to be effectively used in modeling braking and traction scenarios. It is the objective of this investigation to demonstrate that by using track coordinate systems that can have an arbitrary motion, the trajectory coordinates can be used as the basis for developing computer algorithms for modeling braking and traction scenarios. To this end, a set of six generalized trajectory coordinates is used to define the configuration of each rigid body in the railroad vehicle system. This set of coordinates consists of one absolute coordinate, which is an arc length that represents the distance traveled by the body, and five relative coordinates. The arc length parameter defines the location of the origin and the orientation of a track coordinate system that follows the motion of the body. The other five relative coordinates are two translations that define the position of the origin of body coordinate system with respect to the track coordinate system in directions lateral and normal to the track, and three Euler angles that define the orientation of the body coordinate system with respect to its track coordinate system. The independent state equations of motion associated with the trajectory coordinates are identified and integrated forward in time in order to determine the trajectory coordinates and velocities. The results obtained in this study show that when the track coordinates systems are allowed to have an arbitrary motion, the resulting set of trajectory coordinates can be used effectively in the study of braking and traction conditions. The numerical examples presented in this paper include two different vehicle models subjected to several braking conditions. The results obtained are compared with the results obtained using the absolute Cartesian coordinate based formulations which allow modeling braking and traction scenarios.

Copyright © 2007 by ASME



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