Methodology of research of the influence of oscillations of the sprung part of wheeled vehicles on the stability of movement

Abstract

For wheeled vehicles, a methodology for studying the effect of relative oscillations of the sprung part on the stability of movement along curved sections of the road has been developed. The peculiarity of these oscillations is that they take into account the nonlinear power characteristics of elastic shock absorbers and damping devices.

Provided that the dynamic process of this part takes place in the vertical plane, its mathematical model is built. It is a system of two nonlinear differential equations of the second order. Given that the maximum values of the resistance forces of damping devices during the movement of wheeled vehicles are much smaller than the maximum values of the elastic forces of the shock absorbers, an approximate analytical solution of the mathematical model is built.

It is based on: the existence of normal forms of oscillations of undisturbed motion of the sprung part; using periodic Ateb functions to describe them; generalization of the main ideas of the Van der Paul method to the equation of perturbed motion.

It is shown that the normal forms of oscillations of the sprung part have this feature, their frequency depends on the amplitude, parameters that describe the elastic properties of the shock absorbers and the resistance of the dampers.

In particular, for the progressive dependence of the elastic properties of the shock absorbers on the deformation, it takes larger values for larger values of amplitude, and for regressive - smaller.

The obtained basic analytical dependences concerning the normal oscillations of the sprung part in combination with the basic principles of mechanics were used to determine the critical speed of steady motion along curvilinear sections of the road.

It is shown that this value takes smaller values for larger values of oscillation amplitudes and smaller values of the parameter that indicates the deviation of the elastic properties of the shock absorbers from the linear law and at the same time larger - for larger values of their static deformation of the sprung part

The results of the work can be the basis for selecting the power parameters of the suspension system in order to maximize the performance of wheeled vehicles, and their reliability is confirmed by the results known for extreme cases.

Key words: sprung and unsprung parts, normal forms of oscillations, stability of motion, deformation, dynamics.