A Spatial Mathematical Model of the Dynamic Behavior of Modern Rolling Stock in High-Speed Traffic

Abstract

Purpose. The paper aims to develop a spatial mathematical model of the high-speed electric train EKr-1 “Tarpan” taking into account the design features of its first and second stages of spring suspension. Methodology. The design scheme of the electric train is taken as a set of 7 solids connected by ligaments of different rheology. Each of the bodies performs spatial oscillations. In this case, the wheel set is considered as a system with two degrees of freedom (lateral displacement and wagging). The angular and linear displacements of the bodies are considered as generalized coordinates. The resulting mechanical system has 26 degrees of freedom. The differential equations of motion are written using the d'Alembert principle. The kinematic perturbation of oscillations due to movement along unevennesses of the track in both vertical and horizontal directions is considered. The presence of elastic and dissipative viscosities is taken into account in the first and second stages of the spring suspension. The hypothesis of geometric linearity of deformations is accepted. The reactions acting in the longitudinal (in the wheel plane) and transverse directions are taken into account at the point of contact between the wheel and the rail. The longitudinal and transverse reactions are quantitatively described by the nonlinear creep hypothesis. The modeling of hydraulic vibration dampers takes into account their inclined location, which makes it possible to dampen vibrations in the vertical and horizontal directions. Findings. The spatial design scheme of the studied object was chosen. The geometric dependences between the deformations of the ligaments and the generalized coordinates of the design scheme are obtained. The physical dependencies between the reactions of the ties and their deformations are described, taking into account the pneumatic spring suspension system. The differential equations of oscillations for each element of the design scheme are derived. Originality. For the first time, a spatial mathematical model of the dynamic behavior of high-speed railroad rolling stock was constructed, taking into account the peculiarities of the pneumatic spring suspension system, the location of the bindings, and the interaction of the wheelset with the rail track in the vertical and horizontal directions, both in straight and curved sections of the railroad track. Practical value. The development of such a model will make it possible to numerically study its dynamic and safety performance in high-speed traffic conditions at the design stage of high-speed railroad rolling stock and to establish the optimal parameters of the first and second stages of spring suspension, while setting various kinds of kinematic disturbances from the rail track.