Rail profile irregularities are one of the main vibration sources to vehicle and track. In this article a dynamic model of wagon, rail track and its substrate is developed to examine the vertical interaction of the rail track and the wagon system due to random irregularities of track vertical profile. The model consists of a wagon with body, two bogies and four wheels having 21 degrees of freedom. The rail system is treated as a Timoshenko beam supported by sleepers, ballast, subballast, and subgrade. The rail irregularities are assumed to be stationary random and ergodic processes in space, with Gaussian amplitude probability densities and zero mean values. To determine rail-wheel contact forces, Hertzian nonlinear contact theory has been used. The interaction forces between the vehicle and the rail and the vertical acceleration generated in the wagon body due to random irregularities of the track vertical profile with different track grades for different train speeds have been simulated by this model. The results are compared to previous works in the literature.

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