Modeling of the Dynamics of a Carriage Taking into Account the Geometric Nonlinearity of Displacements and Deformation

Abstract

—A mathematical model of a carriage is presented, describing movement taking into account the geometric nonlinearity of displacements and deformations in terms of the body, carriage frames, bolsters and wheel sets. In the design scheme, symmetric linear dimensions can be taken unequal, which allows evaluating the effect of tolerances on dimensions that occur in the manufacture and repair of the car, on the dynamic performance of the car. For the analysis of the dynamics of the car computational methods of numerical integration were used, as well as finding eigenvalues and eigenvectors. The matrix-vector notation of differential equations allowed us to isolate linear and non-linear components. For the linearized model, the eigenvalue problem and the vector are solved, which gives a priori idea of the resonant states of the car in dynamics. Taking into account large angular displacements the equations of the deformations of the elastic connections of the car are obtained. The linearized model is permissible to apply to the study of the oscillations of the car when driving along straight sections of the road and flat curves. The proposed model, which takes into account the geometric nonlinearity of displacements and deformations, should be used to study the dynamics of the car in steep curves.