MATHEMATICAL MODELLING OF THE ROLLING SPEED

Abstract

The article shows the consideration of the rolling friction moments (pure rolling) of the wheels on the rail threads and in the bearings of the front axlebox units. and rear bogies of the car with their subsequent replacement by conditional sliding friction. It is noted that if the active force in the form of a projection of the force of gravity and the aerodynamic drag force on the direction of rolling of the car (or release), acting on the car, is greater than the limiting friction force, then simultaneously with rolling, the wheels may also slip on the rail threads. An analytical formula was obtained for finding the difference between the driving forces and all resistance forces when rolling wheels with sliding, which, based on the theorem on the change in the momentum of a material point, made it possible to create a mathematical model for finding the speed of a single car (or cut) on the first profile section of the hump. An analysis of the results of solving the problem of determining the rolling speed of a car has been carried out. It is noted that the theorem on the change in the momentum of a material point for solving the problem of finding the time of rolling down a hill is applicable only when the final speed of the car is known, otherwise solving the problem in such a formulation will be meaningless.