Моделювання динаміки колісних транспортних засобів під час руху шляхом із нерівностями

Abstract

The paper outlines the main provisions of the methodology for analytical research of the individual road irregularities impact on the longitudinal-angular oscillations of the wheeled vehicle sprung body. A flat system of three bodies (front, rear bridges, sprung part), whose relative motion is in the vertical plane, was chosen as the physical model for the research. Its peculiarity is that the sprung and unsprung parts interact with each other as elastic shock absorbers with non-linear characteristics of the restoring force. As for road irregularities, it is considered that they are described by smooth functions and the tires are in constant contact with the supporting surface during the wheeled vehicle movement. A mathematical model of the sprung part dynamics was built, which is a second-order nonlinear differential equation with the following feature: its right-hand side is a piecewise continuous function. Based on physically justified assumptions, the differential equation solution was constructed, which describes the relative longitudinal-angular oscillations of the sprung part. It is based on the idea of using: the special periodic Ateb-functions to construct the solution of differential equations with exponential nonlinearity; the construction of asymptotic approximations using the specified functions for new classes of differential equations. Taken together, the above made it possible to obtain differential equations in the standard form, which describe the amplitude-frequency characteristics of the sprung part oscillations. As for the individual irregularities influence on the sprung part dynamics, the amplitude of the longitudinal-angular oscillations of the exit from the irregularity is smaller: at higher vehicle speed; for suspension systems with a regressive change law of the restoring force of elastic shock absorbers; at smaller values of their static deformation for the progressive characteristic of the suspension system (and at larger values for the regressive one). Analytical dependences were obtained, calculations were made and dependences were constructed that describe the amplitude and frequency of these oscillations caused by the irregularities parameters and motion speed.The obtained results can be a basis not only for evaluating the quality of the suspension system, but also for developing algorithms for managing the suspension stiffness in order to improve operational characteristics.