Finite element analysis of vibration excited by rail-wheel interaction

Abstract

In previous attempts reported in the open literature on modelling rail/wheel dynamics, beam theories are commonly employed to model the rail and rail-wheel contact can be considered by linear or nonlinear contact springs. As the contact force is expected to have a strong influence on the rail corrugation, the predicted contact force is often the key interest. It is noted to be a rather smooth function of time and is different from, for instance, the rail acceleration which contains a considerable amount of high frequency content. On the other hand, finite element method has evolved into a widely accepted numerical simulation tool for engineering analysis. Despite its applicability to many physical phenomena, three-dimensional finite element simulation of rail-wheel dynamic interaction remains to be a computationally formidable task due to the minute size of the rail-wheel instantaneous contact zone. In this thesis, a beam and a plane finite element models are constructed to examine the rail-wheel dynamic interaction. The beam finite element model composes of two-dimensional Timoshenko beam elements whilst contact is mimicked by using a nonlinear contact spring. On the other hand, the plane finite element model composes of plane elements. While very small elements are used on the contacting surfaces, i.e. the wheel rim and rail top, the element size away from the surfaces is kept large in order to reduce the number of elements. To transit the mesh from dense to coarse, different transition meshes are examined and the one showing the best accuracy is employed. Meanwhile, two different ways of simulated contact are examined. The chosen method of kinematic constraint can deliver a reasonable accuracy and, unlike the penalty method, would not reduce the critical time increment in explicit time integration. The contact forces predicted by the beam and plane finite element models are compared. It is noted that the trends of the contact forces predicted by two finite element models show good agreements with each other. However, the plane finite element model has several advantages in the simulations of rail/wheel dynamics over the beam finite element model. The effects of high wheel speed and multiple rolling wheels on rail/wheel dynamics are investigated. It is found that both the high wheel speed and multiple rolling wheels on a rail lead to more severe rail vibrations. Owing to its advantages in the simulations of rail/wheel dynamics, the plane finite element model is then applied to examine the damping capacities of tuned mass damper which is a promising means for reducing the rail vibration. The predicted rail acceleration reveals that the rail vibration can be attenuated considerably when the tuned mass damper is installed.