The response of a high-speed train wheel to a harmonic wheel-rail force

The maximum speed of China's high-speed trains currently is 300km/h and expected to increase to 350-400km/h. As a wheel travels along the rail at such a high speed, it is subject to a force rotating at the same speed along its periphery. This fast moving force contains not only the axle load component, but also many components of high frequencies generated from wheel-rail interactions. Rotation of the wheel also introduces centrifugal and gyroscopic effects. How the wheel responds is fundamental to many issues, including wheel-rail contact, traction, wear and noise. In this paper, by making use of its axial symmetry, a special finite element scheme is developed for responses of a train wheel subject to a vertical and harmonic wheel-rail force. This FE scheme only requires a 2D mesh over a cross-section containing the wheel axis but includes all the effects induced by wheel rotation. Nodal displacements, as a periodic function of the cross-section angle 6, can be decomposed, using Fourier series, into a number of components at different circumferential orders. The derived FE equation is solved for each circumferential order. The sum of responses at all circumferential orders gives the actual response of the wheel.