Assessing the Mathematical Model of a Passenger Railroad Car Crossing through Stochastic Technical Stability Test

This article presents a definition of stochastic technical stability that was applied to test a mathematical model of a passenger railroad car crossing a turnout with a speed exceeding 160 km/h. The disturbances occurring in the track are presented in the form of the realization of a stochastic process, illustrating the change of the track gauge. The presented method can be used to study both nonlinear models with random disturbances of mechanical and electrical systems. The definition of stability makes it possible to verify Lyapunov's stability for a nonlinear system and with track disturbances. A nonlinear mathematical model of a passenger carriage was subjected to an STS test by means of motion perturbations resulting from changes in the track gauge and wheelset motion in a direction transverse to the track axis. The main aim of this paper was to determine the influence of various factors and technical conditions on the assessment of the stability of various means of transport. The analysis presented can be used to assess the dynamics of electric vehicles, whose mechanical parameters differ from those of combustion vehicles at present. The STS approach was used to determine the region of stable motion in the Lyapunov sense. To ascertain the wheelset transverse motion trajectory, simulations were run. For a single-point contact, the likelihood of discovering the wheelset in the stable motion region with respect to the rail was calculated. This is actually the wheel's only point of contact with the rail. The research findings are offered based on the conducted study.

The values of the vertical and transverse forces for the motion through the turnout are taken from the work. Studying this type of stability is a very convenient tool for verifying the stability of real objects with disturbances.