One of the approaches for the analytical description of the interaction of an elastic wheel with a solid surface

Abstract

The design of branched transmissions of multi-axle vehicles, multistage steering systems and automated workflow control systems requires their preliminary dynamic calculation. These calculations are based on mathematical models of structural elements corresponding to the modern level of development of system theory, i.e. taking into account dynamic interrelations between the system links. The aim of the work is to build a mathematical model of the automobile wheeled propulsor intended for use in the dynamic model of the “car-road” system or models of separate automobile systems. The approach to mathematical modeling of the automobile wheeled propulsor is offered, consisting in its description by methods of the control theory as an element of dynamic system. The method of construction and analysis of the complete system of equations of kinematic bonds superimposed in the contact zone on the movement of points of the external surface of the tire of linear elastic wheel at its perturbed rectilinear rolling on a solid uneven support surface is developed. The method of construction of a transfer matrix of automobile linear elastic wheel at which its structure practically does not depend on features of the settlement scheme of the tyres is developed too in this study. The method of obtaining the tire characteristics necessary for the calculation of the transfer matrix elements by the generalized method of successive approximations, which gives the qualitatively correct results in zero approximation, is proposed. The method of qualitative theoretical analysis of the features of rectilinear stationary rolling of the automobile wheel is given in this paper. The results allow to carry out researches and calculations of dynamic characteristics of automobile systems, units and assemblies directly interacting with the wheel; they can serve as a basis for further improvement of mathematical models of automobile ruts by methods of system theory.