A Mathematical Model of the Dynamic Interaction of a Locomotive's Wheelset and Track

The interaction of the wheel and the rail is the physical basis for the movement of rolling stock on railways. In order to reduce the wear rate of wheel sets and rails, it is necessary to create a mathematical model for the interaction of the "wheel-rail" pair, on which one could look at various methods to reduce catastrophic wear. Currently widely used mathematical algorithms with many degrees of freedom of dynamic interaction of a pair of "wheelset rolling stock - railway track" have a number of disadvantages that affect the accuracy of the calculation results. It is necessary to first build the dynamic equations of dynamics in a basic fixed coordinate system, and then introduce a transformation into local coordinate systems. The algorithm proposed by the authors for constructing dynamic equations, taking into account the inclination and elevation of the outer rail over the inner rail, and the speed of the portable movement of the center of mass of the wheelset, allows to avoid all kinds of errors. In this paper, we describe an algorithm for constructing dynamic equations describing the joint motion of a wheel pair and a rail track, as well as an algorithm for solving the dynamic contact problem. The equations of translational and rotational dynamics of a wheel pair of a railway rolling stock (locomotive), the equations of motion of interacting bodies and communications are constructed. Based on the described mathematical algorithms, programs have been developed for calculating the forces of dynamic interaction in the wheel - rail system.