A rotating ring in contact with a stationary load as a model for a flexible train wheel

Abstract

A load moving on a center-fixed ring and the reciprocal problem, namely a rotating ring subjected to a moving load have been used in several works to study the tire dynamics. In contrast, very few papers exist in which the ring model has been used in order to study the dynamics of a train wheel. In this paper, a thin ring model is introduced to model a flexible train wheel with distributed springs acting in the radial, circumferential and rotational directions to study the wheel dynamic response. A so-called “method of images” is applied to solve the governing equations. The idea of this method is that the response of the rotating ring to a stationary load is equivalent to the response of an axially moving, infinitely long beam subjected to a set of loads located equidistantly on the beam. Taking advantage of linearity of the problem, the response is obtained as a superposition of the responses to the individual loads. The method of images combined with the contour integration technique, allows to obtain an exact analytical solution to the problem that includes neither infinite series nor integrals. The exact maximum bending moment in the ring obtained using the method of images is compared to that resulting from a series representation of the solution based on the modal expansion. The results show that many terms in the modal expansion are necessary in order to accurately approximate the exact solution. This means that the method of images is significantly more efficient than the modal expansion method.