Skip to main content
Log in

Application of generalized pascal triangle for description of oscillations of friction forces

  • Published:
Inorganic Materials: Applied Research Aims and scope

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Gardner, M., Mathematical Games: Collection, Greenwich, CT: Scientific American, 1967–1971; Moscow: Mir, 1974.

    Google Scholar 

  2. Kuz’min, O.V., Triangle and pyramid of Pascal: properties and generalizations, Soros. Obraz. Zh., 2000, vol. 6, no. 5, pp. 101–109.

    Google Scholar 

  3. Kuz’min, O.V., Obobshchennye piramidy Paskalya i ikh prilozheniya (General Pascal Pyramids and Their Applications), Novosibirsk: Nauka, 2000.

    Google Scholar 

  4. Kremer, N.Sh., Teoriya veroyatnostei i matematicheskaya statistika (Theory of Probability and Mathematical Statistics), Moscow: Yuniti-Dana, 2007, 3d ed.

    Google Scholar 

  5. Gorbatov, V.A., Gorbatov, A.V., and Gorbatova, M.V., Diskretnaya matematika (Discrete Mathematics), Moscow: AST-Astrel’, 2006.

    Google Scholar 

  6. Uspenskii, V.A., Treugol’nik Paskalya (Triangle of Pascal), Moscow: Nauka, 1979.

    Google Scholar 

  7. 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.

    Google Scholar 

  8. Breki, A.D., Tribotechnical properties of modified lubricating oils, Cand. Sci. (Tech.) Dissertation, St. Petersburg: S.-Peterb. Gos. Politekh. Univ., 2011.

    Google Scholar 

  9. 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.

    Google Scholar 

  10. 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.

    Google Scholar 

  11. 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.

    Article  Google Scholar 

  12. 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.

    Google Scholar 

  13. 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.

    Google Scholar 

  14. 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.

    Google Scholar 

  15. 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.

    Google Scholar 

  16. Dubinin, A.D., Trenie i iznos v detalyakh mashin (Friction and Wear in Machine Parts), Moscow: Mashgiz, 1952.

    Google Scholar 

  17. Kostetskii, B.I. and Kolesnichenko, N.F., Kachestvo poverkhnosti i trenie v mashinakh (Quality of Surface and Friction in Machines), Kiev: Tekhnika, 1969.

    Google Scholar 

  18. Kostetskii, B.I., Trenie, smazka i iznos v mashinakh (Friction, Lubrication, and Wear in Machines), Kiev: Tekhnika, 1970.

    Google Scholar 

  19. Vinogradov, Yu.M., Trenie i iznos modifitsirovannykh metallov (Friction and Wear of Modified Metals), Moscow: Nauka, 1972.

    Google Scholar 

  20. 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.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. E. Gvozdev.

Additional information

Original Russian Text © A.D. Breki, A.E. Gvozdev, A.G. Kolmakov, 2016, published in Materialovedenie, 2016, No. 11, pp. 3–8.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2075113317040049

Keywords

Navigation