According to the results of derailment investigations, the ensuring of train traffic safety was found to be a paramount and urgent task. The growth of freight density and speed of movement on the railway network leads to a significant increase in the number of damaged wheels and rails and, as a result, to an increase in the level of force interaction during load transfer, which provokes the likelihood of a wagon derailment. The operation safety level of rolling stock on railways is determined mainly by the presence of a car derailment stability margin, which depends on the vertical dynamics and the coefficient kdv, which changes throughout the entire time of movement and, accordingly, on the technical condition of the car and the track as a whole. The vertical addition to each element of this “wheel-rail” system depends on many factors, therefore, the level of operational safety of the car, as a mechanical system, is determined mainly by its sprung and non-sprung car parts. The calculation schemes used to study the stability of unperturbed motion are non-linear systems. Non-linearities occur due to the gaps in axle boxes, side bearings and similar connections, non-linearity of the interaction forces of wheels with rails and, at present, also in some types of spring suspension. When moving in a curve, the cart is known to perform a complex movement. The rotation and transverse displacement of the bogie is prevented by frictional forces between the wheels and the rails. The bogie is affected by a part of the centrifugal force, unbalanced by the elevation of the outer rail and depending on the speed of movement, as well as by the guiding force from the side of the outer rail. It is known the process of a car movement results in the appearance of horizontal transverse (relative to the direction of movement) forces, which are determined by the level of interaction between the wheel flanges and the rails. The nature of the perturbed movement of the car leads to the appearance of horizontal transverse with respect to the axis of the path of movement. At relatively low speed, the forces that arise after wearing out of the gaps in the track and when the wheel flanges rest against the rail heads, at a certain level of irregularities, are not dangerous for the wheel-rail system. But with an increase in the speed of the car, these forces increase so that there is a threat to traffic safety as the likelihood of derailment increases.
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