Keywords: vehicle-track interaction, dipped joint, contact force, Hertzian spring, infinite beam, finite difference method.

The research described in this paper forms part of an overall research project concerned with the dynamic analysis of steel railway bridges. The project is being carried out in the Department of Civil Engineering at Trinity College Dublin, and is supported by Íarnród Éireann, the national railway company of Ireland. The research documented in this paper is concentrated upon the dynamic interaction between vehicle and track, in isolation from a bridge system.

The paper describes the implementation of a numerical model for the purpose of calculating railway track displacements, and consequent stresses, as a result of the passage of a moving vehicle along a length of railway track. Particular emphasis is placed upon the dynamic effect of the vehicle traversing a dipped track joint. A dipped joint gives rise to two dynamic increments in the contact force between wheel and rail. These are denoted the and forces respectively. There are well known formulae available, which give values for these increments as a function of vehicle velocity [1]. The force increments induce a corresponding increment in the track bending moment. The bending moments obtained from the numerical model described in this paper are compared with those obtained from the formulae.

The overall model consists of two subsystems; the vehicle model and the track model. The vehicle is a simple four degree-of-freedom system based upon a standard railway vehicle model used for dynamic analysis [2]. The track is modelled as a quasi-infinite beam on a continuous elastic foundation using the finite difference technique [3]. A convected coordinate transformation was applied to the standard equation of motion for a beam on an elastic foundation.

Once the transformation was applied it was required to formulate an appropriate stiffness matrix that would approximate to the case where the beam is of infinite length. For this purpose, the beam was truncated into two regions; a finite inner region to be modelled using the finite difference technique, and an outer region representing the continuation of the beam into infinity in both the positive and negative directions. By applying suitable boundary conditions to the finite difference beam it was possible to approximate the influence of the outer region upon the finite beam. This method involves an approximation in the calculation of the boundary support conditions. However, previous dynamic tests applied to this type of beam model formulation have shown good agreement with the expected theoretical response [4].

1

G.H. Cope, "British Railway Track - Design, Construction and Maintenance", The Permanent Way Institution, 1993.

2

Rail Technology Unit, "The Manchester Benchmarks for rail vehicle simulation", 1998.

3

A. Ghali, A.M. Neville, "Structural Analysis - A Unified Classical and Matrix Approach", Chapman & Hall, 1989.

4

D. O'Dwyer, D. Hegarty, B. Basu, "Numerical Modelling of Railway Vehicle Track Interaction with Infinite Beam Track Model", Railway Engineering, 2004.

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