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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.

A coordinated calculation of two processes -locomotives turnover and servicing -is described. Locomotives turnover is calculated by optimization system Labyrinth and servicing by dynamic transportation problem. Service programs integrate these processes. A model of coordinated arrival of locomotives at servicing stations is proposed. The calculation consists of three interrelated steps. The first step is the calculation of the optimal locomotive turnover without considering servicing constraints. Service program SP-1 determines stations where forced stops will take place according to the necessity of servicing and forms the basic location of locomotives for further movement to servicing stations. The second step is the calculation of the optimal arrival of locomotives at servicing stations. Service program SP-2 provides location and release time of each locomotive after servicing. The third step is the calculation of a train schedule with the consideration for the location of stopped train sets and the appearance of locomotives after servicing. Servicing program SP-3 forms the united results.

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