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Abstract. This paper investigates the influence of wheel defects on the development of rail defects up to a state where rail prompt replacement becomes necessary taking into account different models of the dynamic contact between a wheel and a rail. In particular, the quasistatic Hertz model, the linear elastic model and the elastoplastic Aleksandrov-Kadomtsev model. Based on the model of the wheel-rail contact the maximum stresses are determined which take place in the rail in the presence of wheel defects (e.g. flat spot, weld-on deposit, etc.). In this paper, the solution of the inverse problem is presented, i.e., investigation of the influence of the strength of a wheel impact upon rails on wheel defects as well as evaluation of the stresses emerging in rails. During the motion of a railway vehicle, the wheel pair position in relation to rails changes significantly, which causes various combinations of wheel-rail contact areas. Even provided the constant axial load, the normal stresses will substantially change due to the differences in the radii of curvature of contact surfaces of these areas, as well as movement velocities of railway vehicles.

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The paper presents semi-analytical approaches to the method of evaluating strain-stress mode of railway rails when a part of the solution is in the form of ramp functions whose rate of change cannot be adequately considered using the standard method of finite elements. The proposed model of a multipoint boundary value problem allows for effective evaluation of the rail’s work against the changing of its profile, i.e. due to its wear.