A multi-body system approach for finite-element modelling of rail flexibility in railroad vehicle applications

Abstract

In this investigation, a non-linear finite-element formulation for modelling the rail structural flexibility in multi-body railroad vehicle systems is presented. Two different types of interpolations are used in the kinematic equations developed in this study; the geometry interpolation and the deformation interpolation. In the proposed formulation, the rails can have arbitrary geometry, which is described using the isoparametric geometric interpolation. The coordinates of the polynomials used in this interpolation represent constant position and gradient coordinates, which can be used to describe accurately the rail geometry. On the other hand, the rail deflections are described using the deformation interpolation and the non-linear finite-element floating frame of reference formulation. In the formulation proposed in this investigation, the rail tangent and normal vectors as well as other geometric parameters such as the curvature and torsion at the wheel/rail contact points are expressed in terms of the rail deformation coordinates. The non-linear dynamic coupling between the rail geometry and the vehicle dynamics is also considered in the formulation proposed in this paper. In particular, the coupling between the rail deformation and geometry, contact coordinates, and the non-linear vehicle dynamics is taken into consideration. Furthermore, the longitudinal, lateral, and spin creepages are expressed in terms of the rail deformations, which are the result of the wheel/rail contact forces. This non-linear coupled analysis allows for more accurate prediction of the railroad vehicle dynamics. The main outcome of this study is the development of a new procedure that allows building a complex track model that includes significant details using a finite-element preprocessor computer program. The detailed track model can be used as an input to a general purpose flexible multi-body computer program for a non-linear analysis that accounts for the dynamic coupling between the track flexibility and the vehicle coordinates. Numerical results are presented in order to demonstrate the use of the formulation proposed in this study.