Mathematical model of the formation and development of wave-shaped rail wear when an electric locomotive operates in the traction mode in tangent sections of the track

The problem of wave-shaped rail wear is highly relevant for rail transport. The paper presents a mathematical model of the formation and development of wave-shaped rail wear. The task of estimating vertical wear of the rail head under the axles of electric locomotives passing in the traction mode is considered. A technique has been developed that allows building chain of calculations that determine the formation and development of a wave-shaped rail head wear. A specific calculation example is given, illustrating the process of propagation of a wave-shaped wear from the source of its formation in the direction of train motion. An example of the calculation allows drawing the following conclusions:1. Wave-shaped wear primarily occurs when the shock interaction of the wheel of an electric locomotive moving in the traction mode and a rail thread having imperfections of the rolling surface. Such imperfections, among others, may be a joint with a significant gap or a “step down” in the direction of the locomotive, as well as a welded joint with defect 46.3-4.2. Wavelength of the wave-shaped rail wear, its configuration and amplitude of the fundamental tone are determined mainly by joint oscillations of the wheel-motor unit of the locomotive and the track infrastructure in the field of high-frequency oscillations (120 – 180 Hz).3. Multivariate calculations showed that in steady state, the distribution speed of wave-shaped rail wear in the direction of train motion (as a function of the number of axles of electric locomotives passed in traction mode) is directly proportional to the vertical load at the wheel and rail contact in the slip zone 0≤Q≤F/(2nψk), is inversely proportional to wear resistance C and significantly depends on the parameters of the undercarriage of the electric train and the track superstructure.