Studies of the coefficient of friction. Derivation of the analytical equation of the Hersey-Shtribek diagram

A study of the friction coefficient based on a semi-empirical equation for the Guersey-Striebeck diagram was carried out in this paper. An analytical equation for the coefficient of friction versus shear rate, which fully describes the friction of rubbing surfaces under various conditions, is currently absent. In connection with this problem, an attempt was made to obtain an analytical equation based on a relation with four empirical constants - a, b, c, d, and a review of the resulting equation was also carried out. Using the variation of parameters and numerical simulation, graphs of the dependence of the coefficient were constructed. It has been established that the constant a is a parameter characterizing the coefficient of static friction, b - characterizes such properties as density, strength, deformation coefficients, i.e. elastic characteristics of rubbing bodies, as well as the initial degree of roughness, c is an unambiguously uncertain parameter, most likely related to the linear load and the ability of the lubricant to adapt to loads, d is a coefficient characterizing the steady or viscous friction mode. Thus, a comparative analysis of the dependency graphs of the obtained equation and the Guersey-Striebeck diagram indicates their similarity, which makes this equation more preferable than any other empirical relationships and can be used to solve engineering problems.