Geodesic
On the evolution of mathematical models of friction sliding of solids
Čebyševskij sbornik, Tome 21 (2020) no. 4, pp. 327-332.

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The paper provides information about the evolution of mathematical models of sliding friction of solids. It is Shown that taking into account deviations from the Leonardo da Vinci-Amonton-Coulomb law, it is necessary to Refine it using the correction function of the normal force. A mathematical model of the generalized sliding friction law has been created that takes into account the abrupt changes in the linear dependence of the friction force on the normal force.
Keywords: Leonardo da Vinci–Amonton–Coulomb law, mathematical model of friction, gen-eralized law of friction, abrupt change. 
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A. D. Breki; S. G. Chulkin; A. E. Gvozdev; O. V. Kuzovleva. On the evolution of mathematical models of friction sliding of solids. Čebyševskij sbornik, Tome 21 (2020) no. 4, pp. 327-332. http://geodesic.mathdoc.fr/item/CHEB_2020_21_4_a26/

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[4] Breki A., Nosonovsky M., “Ultraslow frictional sliding and the stick-slip transition”, Applied Physics Letters, 113:24 (2018), 241602 | DOI

[5] Breki A.D., Nosonovsky M., “Einstein's viscosity equation for nanolubricated friction”, Langmuir: the ACS journal of surfaces and colloids, 34:43 (2018), 12968–12973 | DOI

[6] Breki A.D., Vasilyeva E.S., Tolochko O.V., Didenko A.L., Nosonovsky M., “Frictional properties of a nanocomposite material with a linear polyimide matrix and tungsten diselinide nanoparticle reinforcement”, Journal of Tribology, 141:8 (2019), 082002 | DOI

[7] Breki A.D., Gvozdev A.E., Kolmakov A.G., “Semiempirical mathematical models of the pivoting friction of SHKH15 steel over R6M5 steel according to the ball-plane scheme with consideration of wear”, Inorganic Materials: Applied Research, 10:4 (2019), 1008–1013 | DOI

[8] Breki A.D., Kolmakov A.G., Gvozdev A.E., Sergeev N.N., “Investigation of the pivoting friction of SHKH15 steel over R6M5 and 10R6M5-MP steel with the use of mathematical modeling”, Inorganic Materials: Applied Research, 10:4 (2019), 927–932 | DOI

[9] Breki A.D., Aleksandrov S.E., Tyurikov K.S., Kolmakov A.G., Gvozdev A.E., Kalinin A.A., “Antifriction properties of plasma-chemical coatings based on SiO2 with MoS2 nanoparticles under conditions of spinning friction on SHKH15 steel”, Inorganic Materials: Applied Research, 9:4 (2018), 714–718 | DOI