Research of the Vertical Dynamics of the Supporting Structures of Freight Cars Made of Round Pipes

Purpose. This study is aimed at determining the vertical dynamics of supporting structures of freight cars made of round pipes. Methodology. Mathematical modeling of the dynamic loading of the supporting structures of the main types of freight cars made of round pipes (gondola car, covered car, flat car, hopper car) was carried out. The studies were carried out in a plane coordinate system – the XZ plane. At the same time, it was taken into account that the car is moving in an elastic-viscous track so that the reactions of the track are proportional to both its deformation and the rate of this deformation. The studies were carried out for the case of empty cars. The joint inequality is described by a periodic function. The calculation was performed at a speed of 80 km/h. Differential equations of motion were solved in the MathCad software package using the Runge-Kutta method. Findings. Based on the mathematical modeling of the dynamic loading of the supporting structures of cars made of round pipes, the main indicators of their dynamics were obtained: accelerations acting on the supporting structures in the mass center, forces acting in the spring suspension of bogies, dynamics coefficients. For gondola car, covered car, and hopper car, the acceleration at the mass center of the supporting structure is within 0.4 g, and for a flat car – 0.5 g. It was found that the obtained indicators of the dynamics of cars made of round pipes are within the permissible limits. The accelerations acting on the supporting structures of cars made of round pipes are almost the same as those obtained for prototype cars. At the same time, the motion of cars is assessed as "excellent" for gondola car, covered car, and hopper car and "good" for flat car. Originality. Mathematical modeling of the dynamic loading of the supporting structures of cars from round pipes was carried out and the main indicators of their dynamics were obtained. Practical value. The research carried out will contribute to the creation of recommendations for the design of supporting structures of freight cars of round pipes, and can also be useful developments in the creation of innovative car designs.