Mathematical model of oscillations of a railway tank car with partial fillingunder shunting collision

Abstract

Abstract This article is devoted to simulating longitudinal vibrations of the tank car in case of partial filling with liquid during shunting collision. A brief overview of studies of the movement of solid bodies with liquid was performed. The design scheme of cars, represented by a 4-mass system with elastically-dissipative connections, has been developed. A system of differential equations of car motion according to the main equation of dynamics has been compiled. The mathematical model of liquid cargo oscillations based on shallow water theory is derived. In integration, the characteristic method and Euler method are applied. It is envisaged to transfer parameters between the mathematical model of cars (tank acceleration) and the mathematical model of liquid load (pressure forces on the bottoms). The methodology is implemented in the C++ Builder programming environment. According to the developed method, a study of the shunting collision with the tank at incomplete filling was carried out. The dependence of the reaction in the automatic coupling on time has two bursts. The maximum reaction is also dependent on the impact rate and the degree of filling of the tank.