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One of the main methods to predict permeability is a simulation of the motion of wheeled vehicles in different operating conditions, which are based on mathematical models of interaction between elastic tires with deformable irregularities of the support base. Currently in the theoretical study of the interaction of propellers with the ground formed two main directions: analytical method involving a mathematical description of the process under study and the finite element method based on computer simulation. The aim of this study is to develop a mathematical model of rolling elastic wheels on deformable rough reference base, taking into account the deformation of the contact patch at each end of the elementary playground. A mathematical model of the curvilinear rolling of the elastic wheel on an uneven elastic-visco-plastic support base is developed, taking into account the deformation of the contact spot in each finite elementary site; the influence of ground hooks on the parameters of the wheel movement; coupling properties of the support base in the horizontal direction under the action of a vertical load; change in the direction of radial and tangential reactions; elastic- visco-plastic properties of the support base;“history” of loading of each elementary platform of the support base; condition of the support base on its physical and mechanical characteristics.

Mathematical model of interaction of a rolling elastic wheel with elastic-visco-plastic support base taking into account the history of loading