The effect of anisotropy on the interaction of the caterpillar propeller with the soil during the vehicle turn

Abstract

The article discusses the force interaction of the caterpillar propeller with the ground during the vehicle turn. Since more than 70 % of soil reactions are inherently friction forces, the article is based on the Fyodor Opeiko mathematical theory of friction. According it, the resulting force and the moment of friction are interrelated quantities determined by the position of the instantaneous center of sliding. With increasing the moment of friction, the force decreases and vice versa. Since any caterpillar mover has lugs, its interaction with the soil in the longitudinal and transverse directions becomes different. In the frame-work of the adopted approach, the anisotropy of the force interaction of the propulsion with the soil is ex-pressed in various friction coefficients in the longitudinal and transverse directions. In addition, there is a fundamentally different nature of the interaction with the soil. In the transverse direction, a clean cut is observed. In the longitudinal direction, before the start of the cut, the soil is crushed due to its elastic properties. The article presents a mathematical model of the force interaction of a caterpillar propeller with soil, taking into account the anisotropy of the interaction. The elastic properties of the soil in the longitudinal direction are taken into account due to the variable coefficient of friction introduced under the integral sign. Hyperbolic tangent is used as a function, since it allows one to introduce the smallest number of empirical coefficients. Based on the presented mathematical model of force interaction, numerical calculations were performed. The results are presented in graphical form, which allows to visually as-sess the effect of anisotropy. The calculations showed that the differences in the values of the friction force due to taking into account anisotropy can reach 50 %, and the moment of friction up to 10 %.