Geodesic
Generalized mathematical model of the dynamics of the change in the friction force at rest and the beginning of sliding
Čebyševskij sbornik, Tome 23 (2022) no. 2, pp. 179-190.

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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. 
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     title = {Generalized mathematical model of the dynamics of the change in the friction force at rest and the beginning of sliding},
     journal = {\v{C}eby\v{s}evskij sbornik},
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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. Čebyševskij sbornik, Tome 23 (2022) no. 2, pp. 179-190. http://geodesic.mathdoc.fr/item/CHEB_2022_23_2_a11/

[1] Breki A. D., Tribotekhnicheskie kharakteristiki materialov par treniya i smazochnykh sred v usloviyakh samoproizvolnykh izmenenii sostoyanii friktsionnogo kontakta, dissertatsiya ... doktora tekhnicheskikh nauk: 05.02.04, FGAOU VO «Sankt-Peterburgskii politekhnicheskii universitet Petra Velikogo», Sankt-Peterburg, 2021, 378 pp.

[2] Verkhovskii A. V., Avraamov V. M., “Yavlenie predvaritelnykh smeschenii pri troganii s mesta katka”, Izvestiya Tomskogo politekhnicheskogo instituta, 61:1 (1947), 53–54

[3] Verkhovskii A. V., “Yavlenie predvaritelnogo smescheniya pri troganii nesmazannykh poverkhnostei s mesta”, Zhurnal prikladnoi fiziki, 3:3-4 (1926), 72–74

[4] Rankin J. S., “The elastic range of friction”, Philosophical Magazine, 8:2 (1926), 806

[5] Maksak V. I., Doschinskii G. A., “Issledovanie yavlenii uprugogo predvaritelnogo smescheniya v svyazi s problemoi tochnosti v mashino- i priborostroenii”, Izvestiya Tomskogo politekhnicheskogo instituta, 225 (1972), 208–211

[6] Tomlinson G. A., “A molecular theory of friction”, Philosophical Magazine Series, 7 (1929), 935–939 | DOI

[7] Khaikin S. E., Salomonovich A. E., Lisovskii L. P., “O silakh sukhogo treniya”, Sb. nauch. tr., Trenie i iznos v mashinakh, 1, AN SSSR, M., 1939, 468–479

[8] Schedrov B. C., “Predvaritelnoe smeschenie na uprugo-vyazkom kontakte”, Sb. nauch. tr., Trenie i iznos v mashinakh, 5, AN SSSR, M., 1950, 101–110

[9] Kragelskii I. V., Mikhin N. M., “O prirode kontaktnogo predvaritelnogo smescheniya tverdykh tel”, Doklady AN SSSR, 153:1 (1963), 78–81

[10] Konyakhin I. R., Teoriya predvaritelnykh smeschenii primenitelno k voprosam kontaktirovaniya detalei, Izdatelstvo Tomskogo un-ta, Tomsk, 1965, 115 pp.

[11] Mitrofanov B. P., O deformatsii diskretnogo kontakta, Avtoreferat dis. na soiskanie uchenoi stepeni kandidata tekhnicheskikh nauk, Tomskii politekhn. in-t im. S. M. Kirova, Izd-vo Tom. un-ta, Tomsk, 1964, 14 pp.

[12] Shilko C. B., “Variatsionnyi analiz predvaritelnogo smescheniya pri uprugom kontaktirovanii. Ch.1: Raschet parametrov NDS”, Trenie i iznos, 13:5 (1992), 795–800

[13] Shilko C. B., “Variatsionnyi analiz predvaritelnogo smescheniya pri uprugom kontaktirovanii. Ch.2: Opredelenie kharakteristik treniya i iznosa”, Trenie i iznos, 13:6 (1992), 973–978

[14] Shilko S. V., Kukhorev L. P., “Metodika i rezultaty issledovaniya metallopolimernogo kontaktnogo sopryazheniya v usloviyakh predvaritelnogo smescheniya”, Trenie i iznos, 28:1 (2007), 101–109

[15] Zhuravlev V. F., “K istorii zakona sukhogo treniya”, Doklady Akademii nauk, 433:1 (2010), 46–47

[16] Zhuravlev V. F., “K istorii zakona sukhogo treniya”, Izvestiya Rossiiskoi akademii nauk. Mekhanika tv-go tela, 2013, no. 4, 13–19

[17] Zhuravlev V. F., “500 let istorii zakona sukhogo treniya”, Vestnik Moskovskogo gosudarstvennogo tekhnicheskogo universiteta im. N.E. Baumana. Seriya Estestvennye nauki, 2014, no. 2 (53), 21–31

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