Modeling the impact of wheelsets with flat spots on a railway track

In this paper, we propose a method for calculating the impact of a damaged wheel with a flat spot on a rail. The method allows us to take into account different degrees of the wheelset damage, various types of train cars, locomotives and rails, distance between sleepers, weather conditions, and features of enclosing geological medium. Combined calculations are used to solve the problem. We calculate the pressure of rolling wheelsets on a rail using analytical expressions. We likewise developed analytical expressions to account for the impact of damaged wheels on the rail. We solve a complete system of equations describing the state of a continuous linear-elastic medium in a rail, sleepers, embankment and sedimentary rocks with the possibility of varying the velocities of elastic waves, density, and geometry. To solve this system of equations in the time domain, we use the grid-characteristic method. In this paper, we consider the cases of a train car with intact wheelsets and a train car with a defected wheelset under two train speeds. We calculated the cracks formation in the rail. The simulated results are in good agreement with the norms for transportation of trains with damaged wheelsets to repair stations. This method can be used to develop criteria for transportation of train cars and locomotives with damaged wheelsets depending on specific conditions. In addition, with the help of detailed analysis of elastic wave processes in the railway track, which occur when a train moves and when a wheel with a flat spot strikes the rail, it is possible to study the physics of the railway damage process. Such study allows to develop methods for timely detection of wheel defects in the early stages, timely replacement of wheelsets, and minimizing the railway damage. Furthermore, we proposed an approach for calculating the fatigue cracks, not just shock damages.