Determination of the principal coordinates in solving the problem of the vertical dynamics of the vehicle using the method of mathematical modeling

Abstract

Attention to the theory of rolling stock oscillations is due primarily to the fact that oscillatory processes, which inevitably arise as a result of driving along a usually uneven road, degrade almost all the basic properties of rolling stock. The article considers oscillations of a four-axle vehicle with a double spring suspension. The study of oscillations with a finite number of degrees of freedom is simplified if we introduce the principal coordinates of this system. To simplify the finding of the principal coordinates, free and forced oscillations of the sprung parts of the vehicle are investigated. It is assumed that the body of the vehicle has two degrees of freedom: lateral motion and wabbling; bouncing and pitching of trolleys will be neglected. The total number of degrees of freedom of the model is two. Having set-up the kinetic and potential energy and using the Lagrange equations, a system of differential equations was obtained. Consideration of forced oscillations of a system with two degrees of freedom is greatly simplified when moving to the principal coordinates. The problem of the vertical dynamics of the rolling stock is simplified in the transition to the principal coordinates. The resulting differential equations of free and forced oscillations of the system in the principal coordinates are two independent second-order linear differential equations, which greatly simplifies their solution.