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Chebyshevskii Sbornik, 2022, Volume 23, Issue 2, Pages 179–190
DOI: https://doi.org/10.22405/2226-8383-2022-23-2-179-190 (Mi cheb1185) 		 
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. Brekiab, S. E. Alexandrova, A. S. Biela, S. G. Chulkinbc, V. A. Yakhimovicha, A. E. Gvozdevd, A. G. Kolmakove, E. A. Protopopovf

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)
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DOI: https://doi.org/10.22405/2226-8383-2022-23-2-179-190
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.
Funding agency Grant number
Russian Science Foundation 22-19-00178
The work was supported by a grant from the Russian Science Foundation for the priority area of activity of the Russian Science Foundation "Conducting fundamental scientific research and exploratory scientific research by individual scientific groups" to the scientific project: "Application of digital modeling and big data to improve the efficiency of mechanical processing of titanium steam turbine blades and their operation under conditions of drop impact erosion", № 22-19-00178.
Received: 06.03.2022
Accepted: 22.06.2022
Document Type: Article
UDC: 539.621
Language: Russian
Citation: 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., 23:2 (2022), 179–190
Citation in format AMSBIB
\Bibitem{BreAleBie22}
\by A.~D.~Breki, S.~E.~Alexandrov, A.~S.~Biel, S.~G.~Chulkin, V.~A.~Yakhimovich, A.~E.~Gvozdev, A.~G.~Kolmakov, E.~A.~Protopopov
\paper Generalized mathematical model of the dynamics of the change in the friction force at rest and the beginning of sliding
\jour Chebyshevskii Sb.
\yr 2022
\vol 23
\issue 2
\pages 179--190
\mathnet{http://mi.mathnet.ru/cheb1185}
\crossref{https://doi.org/10.22405/2226-8383-2022-23-2-179-190}
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