Open AccessMATHEMATICAL MODEL OF SPATIAL OSCILLATIONS OF A RAILWAY FOUR-AXLE AUTONOMOUS TRACTION MODULE
Author(s) -
František Bures
Publication year - 2021
Publication title -
zbìrnik naukovih pracʹ ukraïnsʹkoï deržavnoï akademìï zalìzničnogo transportu/zbìrnik naukovih pracʹ
Language(s) - English
Resource type - Journals
eISSN - 2413-3795
pISSN - 1994-7852
DOI - 10.18664/1994-7852.194.2020.230168
Subject(s) - traction (geology) , axle , dissipative system , mathematical model , equations of motion , differential equation , inertial frame of reference , mechanical system , track (disk drive) , classical mechanics , mathematics , physics , engineering , mathematical analysis , structural engineering , mechanical engineering , quantum mechanics , statistics
A description of the original mathematical model of spatial oscillations of a four-axle autonomous traction module during its movement along straight and curved sections of the railway track is proposed. In this case, the design of a four-axle autonomous traction module is presented as a complex mechanical system, and the track is considered as an elastic-viscous inertial system. The equations of motion were compiled using the Lagrange method of the ІІ kind. For each of the solids, the kinetic energy is determined by the Koenig theorem. The potential energy component is obtained by the Clapeyron theorem, as the sum of the energies accumulated in the elastic elements of the system during their deformations. The dissipative energy was also taken into account when compiling the equations of motion. Generalized forces that have no potential, in this case, include the forces of interaction between wheels and rails, which are determined using the creep hypothesis. It is important to note that the model takes into account the forces in the bonds between the bodies of the system and the spatial displacements of the rigid bodies of the mechanical system, taking into account possible restrictions. Moreover, the mathematical model developed by the author is a system of differential equations of the 100th order. This mathematical model is the base for further theoretical studies of the dynamics of railway four-axle autonomous traction modules in single motion or when moving as part of a train. To solve the resulting system of differential equations, the author develops special software that allows for complex theoretical studies of spatial oscillations of a four-axle autonomous tractionmodule to determine the indicators of its dynamic loading and traffic safety.