Abstract
This article describes the application of the generalized Pascal triangle for description of fixed variation of the oscillation amplitude of friction force upon frictional interaction of materials, and the region of interest in terms of friction theory and material wear is highlighted. Mathematical models of friction are presented, and their efficiency is confirmed by experimental data.
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Gardner, M., Mathematical Games: Collection, Greenwich, CT: Scientific American, 1967–1971; Moscow: Mir, 1974.
Kuz’min, O.V., Triangle and pyramid of Pascal: properties and generalizations, Soros. Obraz. Zh., 2000, vol. 6, no. 5, pp. 101–109.
Kuz’min, O.V., Obobshchennye piramidy Paskalya i ikh prilozheniya (General Pascal Pyramids and Their Applications), Novosibirsk: Nauka, 2000.
Kremer, N.Sh., Teoriya veroyatnostei i matematicheskaya statistika (Theory of Probability and Mathematical Statistics), Moscow: Yuniti-Dana, 2007, 3d ed.
Gorbatov, V.A., Gorbatov, A.V., and Gorbatova, M.V., Diskretnaya matematika (Discrete Mathematics), Moscow: AST-Astrel’, 2006.
Uspenskii, V.A., Treugol’nik Paskalya (Triangle of Pascal), Moscow: Nauka, 1979.
Penkin, N.S., Penkin, A.N., and Serbin, V.M., Osnovy tribologii i tribotekhniki: uchebnoe posobie (Fundamentals of Tribology and Tribotechnics: Manual), Moscow: Mashinostroenie, 2008.
Breki, A.D., Tribotechnical properties of modified lubricating oils, Cand. Sci. (Tech.) Dissertation, St. Petersburg: S.-Peterb. Gos. Politekh. Univ., 2011.
Breki, A.D., et al., Analysis of load capacity of lubricating compositions with nanoparticles WS2 and WSe2, Vopr. Materialoved., 2012, no. 2 (70), pp. 109–149.
Breki, A.D., Selection principles of effective lubricating oils with dispersed additives for bearing assemblies of automated systems, Materialy 3-i mezhdunarodnoi nauchno-prakticheskoi konferentsii “Sovremennoe mashinostroenie. Nauka i obrazovanie,” 14–15 iyunya 2013 g. (Int. Sci.-Pract. Conf. “Modern Machine Engineering. Sciences and Education,” June 14–15, 2013), St. Petersburg: Politekh. Univ., 2013, pp. 284–90.
Breki, A.D., Didenko, A.L., Kudryavtsev, V.V., Vasilyeva, E.S., Tolochko, O.V., Kolmakov, A.G., Fadin, Yu.A., Sergeyev, N.N., Gvozdev, A.E., Starikov, N.E., and Provotorov, D.A., Synthesis and tribotechnical properties of composite coatings with PM–DADPE polyimide matrix and fillers of tungsten dichalcogenide nanoparticles upon dry sliding friction, Inorg. Mater.: Appl. Res., 2016, vol. 7, no. 4, pp. 542–546.
Breki, A.D., Fadin, Yu.A., Didenko, A.L., Kudryavtsev, V.V., Tolochko, O.V., Vasil’eva, E.S., Gvozdev, A.E., Starikov, N.E., Kalinin, A.A., and Provotorov, D.A., Tribological properties of composite coatings based on DAI polyheteroarylenes with aggregates of nanoparticles of tungsten dichalcogenides, Izv. Tulsk. Gos. Univ., Ser.: Tekh. Nauki, 2015, no. 8 (2), pp. 148–155.
Breki, A.D., Fadin, Yu.A., Didenko, A.L., Kudryavtsev, V.V., Tolochko, O.V., Vasil’eva, E.S., Gvozdev, A.E., Starikov, N.E., and Provotorov, D.A., Tribotechnical properties of composite coatings based on P-OOOD polyheteroarylene with made of tungsten diselenide nanoparticles as the filler, Izv. Tulsk. Gos. Univ., Ser.: Tekh. Nauki, 2015, no. 8 (2), pp. 181–188.
Breki, A.D., Fadin, Yu.A., Didenko, A.L., Kudryavtsev, V.V., Tolochko, O.V., Vasil’eva, E.S., Gvozdev, A.E., Starikov, N.E., and Provotorov, D.A., Tribotechnical properties of composite coatings based on P-ODFO polyheteroarylene with tungsten nanoparticles as the filler, Izv. Tulsk. Gos. Univ., Ser.: Tekh. Nauki, 2015, no. 11 (1), pp. 133–139.
Breki, A.D., Medvedeva, V.V., Fadin, Yu.A., Tolochko, O.V., Vasil’eva, E.S., Sergeev, A.N., Provotorov, D.A., Gvozdev, A.E., and Starikov, N.E., The effect of the lubricant composite material with tungsten disulfide nanoparticles on friction in rolling bearings, Izv. Tulsk. Gos. Univ., Ser.: Tekh. Nauki, 2015, no. 11 (1), pp. 78–86.
Dubinin, A.D., Trenie i iznos v detalyakh mashin (Friction and Wear in Machine Parts), Moscow: Mashgiz, 1952.
Kostetskii, B.I. and Kolesnichenko, N.F., Kachestvo poverkhnosti i trenie v mashinakh (Quality of Surface and Friction in Machines), Kiev: Tekhnika, 1969.
Kostetskii, B.I., Trenie, smazka i iznos v mashinakh (Friction, Lubrication, and Wear in Machines), Kiev: Tekhnika, 1970.
Vinogradov, Yu.M., Trenie i iznos modifitsirovannykh metallov (Friction and Wear of Modified Metals), Moscow: Nauka, 1972.
Gvozdev, A.E., Zhuravlev, G.M., and Kolmakov, A.G., Formation of the mechanical properties of carbon steels in the processes with drawing with thinning, Tekhnol. Met., 2015, no. 11, pp. 17–29.
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Original Russian Text © A.D. Breki, A.E. Gvozdev, A.G. Kolmakov, 2016, published in Materialovedenie, 2016, No. 11, pp. 3–8.
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Breki, A.D., Gvozdev, A.E. & Kolmakov, A.G. Application of generalized pascal triangle for description of oscillations of friction forces. Inorg. Mater. Appl. Res. 8, 509–514 (2017). https://doi.org/10.1134/S2075113317040049
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DOI: https://doi.org/10.1134/S2075113317040049