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Analysis of the Fractal Structure of Rough Friction Surfaces to Establish Transient Regimes of Frictional Contact

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Abstract

It is shown that friction fracture surfaces can be self-affine with a local fractal dimension. However, the intersection of such a self-affine surface with a plane gives similar contour lines, which are undoubtedly self-similar. The above considerations regarding the fractal properties of fracture surfaces give reason to believe that a rough surface in contact with metallic bodies in the process of friction is also self-similar. This article presents the fractal dimensions of the transient contact regimes (from elastic to elastoplastic and from elastoplastic to plastic contact) for self-affinity curves, which are the curves of the reference surface at various combinations of material parameters: Poisson’s ratio, hardness, and modulus of elasticity. In the calculations, the Minkowski dimension, calculated by the cellular method, was taken as the fractal dimension of curved reference surfaces. This method, based on the consideration of contact interaction, formed the basis of the method for calculating the contact characteristics of bodies, taking into account their macroshape and the roughness of friction surfaces. The results of the study are of great importance for the development of engineering methods for calculating homogeneous and inhomogeneous rough bodies.

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REFERENCES

  1. Mandelbrot, B.B., The Fractal Geometry of Nature, New York: W.H. Freeman, 1982.

    Google Scholar 

  2. Janahmadov, A.Kh. and Javadov, M.Y., Synergetics and Fractals in Tribology, Materials Forming, Machining and Tribology, Cham: Springer, 2016. https://doi.org/10.1007/978-3-319-28189-6

  3. Hasegawa, M., Liu, J., Okuda, K., and Nunobiki, M., Calculation of the fractal dimensions of machined surface profiles, Wear, 1996, vol. 192, nos. 1–2, pp. 40–45. https://doi.org/10.1016/0043-1648(95)06768-x

    Article  CAS  Google Scholar 

  4. Ivanova, V.S., Balankin, A.S., Bunin, I.Zh., and Oksogoev, A.A., Synergetics and Fractals in Material Science, Terent’ev, E.N., Ed., Moscow: Nauka, 1994.

  5. Edgar, G.A., Measure, Topology, and Fractal Geometry, Undergraduate Texts in Mathematics, New York: Springer, 1990. https://doi.org/10.1007/978-1-4757-4134-6

  6. Bulat, A.F. and Dyrda, V.I., Fraktaly v geomekhanike (Fractals in Geomechanics), Kiev: Naukova Dumka, 2005.

  7. Berry, M.V. and Hannay, J.H., Topography of random surfaces, Nature, 1978, vol. 273, no. 5663, pp. 573–573. https://doi.org/10.1038/273573a0

    Article  ADS  CAS  Google Scholar 

  8. Sayles, R.S. and Thomas, T.R., Topography of random surfaces (reply), Nature, 1978, vol. 273, no. 5663, pp. 573–573. https://doi.org/10.1038/273573b0

    Article  ADS  CAS  Google Scholar 

  9. Dauskardt, R.H., Haubensak, F., and Ritchie, R.O., On the interpretation of the fractal character of fracture surfaces, Acta Metall. Mater., 1990, vol. 38, no. 2, pp. 143–159. https://doi.org/10.1016/0956-7151(90)90043-g

    Article  CAS  Google Scholar 

  10. Mandelbrot, B.B., Self-affine fractals and fractal dimension, Phys. Scr., 1985, vol. 32, no. 4, pp. 257–260. https://doi.org/10.1088/0031-8949/32/4/001

    Article  ADS  MathSciNet  Google Scholar 

  11. Voss, R.F., Random fractals: Characterization and measurement, Scaling Phenomena in Disordered Systems, Pynn, R. and Skjeltorp, A., Eds., New York: Plenum Press, 1985, pp. 1–11.

    Google Scholar 

  12. Lee, Y.-H., Carr, J.R., Barr, D.J., and Haas, C.J., The fractal dimension as a measure of the roughness of rock discontinuity profiles, Int. J. Rock Mech. Min. Sci. Geomechanics Abstracts, 1990, vol. 27, no. 6, pp. 453–464. https://doi.org/10.1016/0148-9062(90)90998-h

    Article  Google Scholar 

  13. Kragel’skii, I.V., Trenie i iznos (Friction and Wear), Moscow: Mashgiz, 1968.

  14. Bowden, F.P. and Tabor, D., The Friction and Lubrication of Solids, Oxford: Clarendon Press, 2001.

    Book  Google Scholar 

  15. Janahmadov, A.Kh., Javadov, M.Y., and Dyshin, O.A., Diagnosis of the contact interaction of solid bodies at friction using fractal analysis methods, J. Sci. Appl. Eng. Q., 2014, vol. 4, pp. 5–16.

    Google Scholar 

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Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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  1. Azerbaijan National Aviation Academy, AZ1045, Baku, Azerbaijan

    A. Kh. Janahmadov

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  1. A. Kh. Janahmadov
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Correspondence to A. Kh. Janahmadov.

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Translated by I. Moshkin

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Janahmadov, A.K. Analysis of the Fractal Structure of Rough Friction Surfaces to Establish Transient Regimes of Frictional Contact. J. Frict. Wear 44, 391–396 (2023). https://doi.org/10.3103/S1068366623060053

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