The non-uniform elasticity of the railway track and its considering in mathematical models of rolling stock of JSC «Russian Railways»

Abstract

The problem of interaction between rolling stock and railway track is relevant and important for railway transport. To date, it has not been fully solved, apparently due to the complexity of the corresponding mathematical models. To solve this problem, it is necessary to change the paradigm of mathematical models, moving from ordinary differential equations to ordinary differential equations with random coefficients. Most researchers in the calculations of the dynamics of the interaction between the railway track and rolling stock, the vertical rigidity of the track is assumed to be a constant value in the longitudinal direction, which is not true. Even in the case of a «velvet» track, its non-uniform elasticity exists, the stiffness above the sleeper and in the inter-sleeper box, according to professors M.F. Verigo and A.Ya. Kogan, differ on the basis of experimental data from All-Union Scientific and Research Institute of Railway Transport. It is also necessary to take into account that the stiffnesses of the left and right wheels are not identical. In the new paradigm of ordinary differential equations with variable, random or parametric coefficients, the concepts of resonance and stability are changing. From the above calculations, it can be seen that with taking into account gravity in the calculations and the parameters of the rolling stock, as well as the stiffness of the track under the left and right wheels, the values of bouncing and lateral pitching increase significantly with increasing speed, which can lead to unloading of the wheel, and as a consequence - to its crawling onto the rail head.