A. D. Breki, S. E. Alexandrov, A. S. Biel, S. G. Chulkin, V. A. Yakhimovich, A. E. Gvozdev, A. G. Kolmakov, E. A. Protopopov, “Generalized mathematical model of the dynamics of the change in the friction force at rest and the beginning of sliding”, Chebyshevskii Sb., 2022, Volume 23, Issue 2,Pages <nobr>179

HISTORY OF MATHEMATICS AND APPLICATIONS

Generalized mathematical model of the dynamics of the change in the friction force at rest and the beginning of sliding

A. D. Breki^ab, S. E. Alexandrov^a, A. S. Biel^a, S. G. Chulkin^bc, V. A. Yakhimovich^a, A. E. Gvozdev^d, A. G. Kolmakov^e, E. A. Protopopov^f

^a Peter the Great St. Petersburg State Polytechnic University (St. Petersburg)
^b Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences (St. Petersburg)
^c St. Petersburg State Marine Technical University (St. Petersburg)
^d Tula State Lev Tolstoy Pedagogical University (Tula)
^e Baikov Institute of Metallurgy and Materials Science (Moscow)
^f Tula State University (Tula)

Abstract: In the article a generalized empirical mathematical model of the dynamics of changes in the friction force at rest and the beginning of sliding is presented. Using the example of the friction of a ball made of ShKh15 steel over $SiO_2$ coatings deposited on flat surfaces made of polycarbonate and polyethylene terephthalate, it is shown that there are deviations from the stationary value of the friction force when sliding over short distances. The developed mathematical model describes the frictional interaction both at a stationary value of the friction force and at deviations from it.

Keywords: friction mathematical model, silicon dioxide coating, polycarbonate, polyethylene terephthalate, gradient of mechanical properties, static friction, sliding friction.

UDC: 539.621

Received: 06.03.2022
Accepted: 22.06.2022

DOI: 10.22405/2226-8383-2022-23-2-179-190