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The need for an accurate mathematical description of the dynamic processes occurring in the running parts of the railway vehicles is substantiated, taking into account the real operating conditions of the rolling stock. A mathematical model of motion of vehicles with a variable structure of a system of nonlinear differential equations of motion is proposed. In the design scheme, material elements are accepted by massive rigid bodies, whose internal deformations are not taken into account in calculations, and by elastic-friction elements with nonlinear characteristics, whose masses are neglected. Between the elements of the system, connections are used that regulate certain relative movements of these elements. Features of dynamic power connections in the «wheel pair-path» system are taken into account, including rolling, sliding and slipping of wheel crests along the lateral faces of railheads arising in motion. To do this, a special technique is used to calculate the longitudinal and transverse forces of wheel-rail friction depending on the redistribution of the relative rates of slippage, lateral attitude, wagging and twitching of the wheel pair. The mathematical model allows one to investigate the movement, dynamic properties of the railway vehicles taking into account the real combinations of the maximum permissible wear of the running parts of the vehicles and the track; choose rational parameters of the railway vehicles for various geometric, rigid and inertial parameters of the running gear of the vehicle. Keywords— railway vehicle; mathematical model; the «wheel pair-track» system, car dinamics; car truck.

Modeling of railway vehicles movement having deviations in content of running parts