A mathematical model describing the law of contact gliding friction, taking into account changes in the sliding contact states, is proposed for consideration. The generalization of classical linear models of contact friction is carried out by putting in more additive components allowing for new state transitions of frictional interaction. The developed mathematical model makes it possible to give analytic description of the schematic diagram of classical slip coefficient change depending on the load of B.I. Kostetsky and allows adding to
generalized friction law, mathematical model, sliding friction, transition, Fermi-Dirac integral
1. Leonardo da Vinci. Selected works. In 2 vols. Vol.1./ Reprint from the 1935 edition - Moscow: Ladomir, 1995. - 415 p.
2. Amontons Guillaume. De la resistance causée dans les machines, Memoires de l’Academie Royale, Paris 1699. pp. 206-222.
3. Coulomb C.A. Théorie des machines simples, Collection des Mémoires de l’Académie des Sciences de Paris, 10 (1785) 163-332.
4. Kostetsky B.I. Friction, lubrication and wear in machines [Text] / B. I. Kostetsky. - Kiev: Technika, 1970. - 396p.
5. Breki A.D. Tribotechnical characteristics of materials of friction pairs and lubricants in conditions of spontaneous changes in the states of friction contact: dissertation... Doctor of Technical Sciences: 05.02.04 / Alexander Dzhalyulevich Breki; [Place of defense: Peter the Great St. Petersburg Polytechnic University]. - St. Petersburg, 2021. - 378 p.
6. Breki A.D. Tribotechnical characteristics of materials of friction pairs and lubricants in conditions of spontaneous changes in the states of friction contact: abstract of the dissertation. ... Doctor of Technical Sciences: 05.02.04 / Alexander Dzhalyulevich Breki; [Place of defense: Peter the Great St. Petersburg Polytechnic University]. - St. Petersburg, 2021. - 43 p.
7. Alexandrov I.K. A characteristic methodological error in the analysis of frictional forces in a friction pair // Mechanics of machines, mechanisms and materials. 2011. No. 3 (16). pp. 59-63.
8. Akhmatov A.S. Molecular physics of boundary friction. M.: "Fizmatgiz", 1963. - 472 p.
9. Bridgman P.U. The latest works in the field of high pressures [Text] / P. V. Bridgman; Translated from the English by A. I. Lichter; Ed. and with the addition of L. F. Vereshchagin. - Moscow: publishing house and type. State Publishing house of foreign lit., 1948. - 300 p.
10. Breki A.D. Mathematical models of sliding friction of antifriction coatings made of polyamide P-54 on steel 45 / Breki A.D., Chulkin S.G., Stukach A.V. and [others] // Steel. 2020. No. 8. pp. 34-38.
11. Kragelsky I.V. Development of the science of friction. Dry friction / I.V. Kragelsky, V.S. Shchedrov. - Publishing House of the USSR Academy of Sciences Moscow, 1956, -236 p.
12. Kragelsky I.V. Fundamentals of calculations for friction and wear [Text] / I.V. Kragelsky, M.N. Dobychin, V.S. Kombalov. - Moscow: Mashinostroenie, 1977. - 526 p.
13. Kuznetsov V.D. Physics of cutting and friction of metals and crystals [Text]: Selected works / V.D. Kuznetsov; [USSR Academy of Sciences, Siberian Branch, United. learned. advice on phys.-mat. and technical sciences, Sib. phys.-tech. V.D. Kuznetsov Institute, State Scientific Research Institute. in-t of machine science named after. akad. A.A. Blagonravova]. - Moscow: Nauka, 1977. - 310 p.
14. Theory of lubricating action and new materials [Text]: [Collection of articles] / Academy of Sciences of the USSR. Sci. advice on friction and lubricants. - Moscow: Nauka, 1965. - 246 p.
15. Bridgman, P.W., Flow Phenomena in Heavily Stressed Metals, J. Appl. Phys., v.8, no. 5, 1937, pp. 328-336.
16. Koroleva O.N., Mazhukin A.V., Mazhukin V.I., Breslavsky P.V. Analytical approximation of Fermi-Dirac integrals of half-integers and integer orders. modeling, 28:11 (2016), pp. 55-63.
17. Kalitkin N.N., Ritus I.V. Smooth approximation of Fermi-Dirac functions // Journal of Computational Mathematics and Mathematical Physics, 1986, volume 26, number 3, pp. 461-465.
18. GOST R 55266-2012: Electromagnetic compatibility of technical means. Communication network equipment. Requirements and test methods. M.: Standartinform, 2013. - 36 p.
19. Fundamentals of automatic regulation and control / Ed. Ponomareva V. M. and Litvinova A. P. Educational. manual for non-electrical engineering. Specialties of universities. - M.: Higher School, 1974. - 439 p.
