Non-linear vibration analysis of a 2-DOF railway vehicle model under random rail excitation

Abstract

With increase in the axle load and wagon speed, the cost of damage to rail track and wagon components increases significantly. This leads to widespread interests in the investigation of the dynamic interactions of the rail track and the wagon. Rail irregularities are one of the important vibration sources of the rail track structure and train. These irregularities have generally random distribution that are assumed to be stationary random and ergodic processes in space, with Gaussian amplitude probability densities and zero mean values. In this paper, the dynamic response of the railway vehicle due to random irregularity of rail track is analysed. The wagon is modelled as a two degrees-of-freedom non-linear model where includes non-linear spring and linear damper of primary suspension system. The Hertzian contact theory is used to obtain the relationship between normal contact force and the displacement of the mass centre of the wheel. Using the method of multiple scales the analytical approximate response of the railway vehicle due to track irregularities is obtained. The amplitudes of vibrations of the vehicle and the interaction forces between the vehicle and the rail for different line grades and train speeds have been analysed analytically by this model. According to the results, rail irregularities have more effect on the vertical acceleration of the vehicle than the train speed.