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A Low Computational Cost Nonlinear Formulation for Multibody Railroad Vehicle Systems

[+] Author Affiliations
Graham G. Sanborn, Ahmed A. Shabana

University of Illinois at Chicago, Chicago, IL

Jason R. Heineman

Ensco, Inc., Springfield, VA

Paper No. DETC2007-34522, pp. 1847-1856; 10 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


In this investigation, a multibody system formulation for the nonlinear dynamics of railroad vehicles is developed. This formulation, which permits developing simplified models for the forces acting on rail cars, allows the analysis of long trains at a low computational cost. In the dynamic models developed using the formulation proposed in this investigation, each rail car can be represented as a single rigid body. The configurations of the bodies in a train model are defined with respect to trajectory coordinate systems which follow a space curve whose geometry is defined at a preprocessing stage. In the formulation presented in this study, the number of degrees of freedom of an arbitrary body can be varied from one to six degrees of freedom. The principal degree of freedom of an arbitrary body is the arc length along the space curve. This degree of freedom defines the location of the origin and the orientation of the body trajectory coordinate system. The other five degrees of freedom define the location and orientation of the body with respect to the body trajectory coordinate system. The nonlinear equations of motion of the bodies in a train model are developed using the three-dimensional Newton-Euler equations. These equations are then expressed in terms of the trajectory coordinates and their derivatives. To this end, a velocity transformation is obtained by expressing the Cartesian and angular velocities of the bodies in terms of the time derivatives of the trajectory coordinates. Various force element models particular to rail cars are developed in this study. These forces include tractive effort, and air brake and dynamic brake forces, as well as a model of available wheel-rail adhesion. Additionally, various types of couplers are formulated as force elements, allowing the modeling of connections between cars. Resistance forces are also modeled in order to be able to simulate rolling, curve, and air resistance forces that may act on the cars during the train operations.

Copyright © 2007 by ASME
Topics: Vehicles , Railroads



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