Interaction between a railway track and uniformly moving tandem wheels

Interaction among loaded wheels via railway track is studied. The vertical parametric oscillations of an infinite row of identical equally spaced wheels, bearing constant load and uniformly moving over a railway track, are calculated by means of Fourier series technique. If the distance between two consecutive wheels is big enough, then one can disregard their interaction via the railway track and consider every wheel as a single one. In this case, however, the Fourier series technique represents an appropriate computation time-saving approximation to a Fourier integral transformation technique that describes the oscillations of a single moving wheel. Two schemes are considered. In the first scheme, every wheel bears the same load. In the second one, consecutive wheels bear contrarily directed loads of the same magnitude. The second scheme leads to simpler calculations and so is recommended to model the wheel–track interaction. ilway track periodicity due to sleeper spacing is taken into account. Each period is the track segment between two adjacent sleepers. A partial differential equation with constant coefficients governs the vertical oscillations of each segment. Boundary conditions bind the oscillations of two neighbour segments and provide periodicity to the track. ear deformation in the rail cross-section strongly influences the parametric oscillations. It also causes discontinuity of the rail centre-line slope at any point, where a concentrated transverse force is applied. Therefore, Timoshenko beam properties with respect to the topic of this paper are discussed. ction between a railway track and a bogie moving at moderate speed is studied. The study points to influence of the bogie frame oscillations on variation in the wheel–rail contact force over the sleeper span. The simplified bogie model considered includes only the primary suspension. A static load applied to the bogie frame centre presents the vehicle body.