Special features in the application of fractal analysis for examining the surface microrelief formed at face milling
DOI:
https://doi.org/10.15587/1729-4061.2017.96403Keywords:
fractal analysis, surface roughness, face milling, surface relief areaAbstract
A method of fractal analysis is applied to describe the relief surface area, which is formed at face milling of plates at different values of the workpiece feed. Microphotographs of the samples’ surface served as input data for calculating the fractal parameters of the microrelief surface area. Here we discuss the most favorable conditions for obtaining photographic images of the samples.
The implementation of the method of fractal analysis was achieved in accordance with the rough partition method by the standard procedure. Data on the relief surface area of real samples, which composed the base set of measure for the fractal analysis, were calculated by the interpolation method based on data on the chromaticity of different pixels in a photograph.
We obtained dependences between the magnitudes of fractal parameters for the surface area at the rate of feed for the workpieces made of steel 35 and alloy D16T. It is demonstrated that an increase in the feed from 50 mm/min to 400 mm/min leads to an increase in the values of Hausdorff dimensions for surface relief area of the articles at the area of its analyzed surface of 5×5 mm2 from 2.55 to 2.68, and at the area of 1×1 mm2 – from 2.43 to 2.51.
A proposal is put forward on the possibility of using fractal characteristics to quantitatively describe the surface microrelief of samples after face milling.References
- Feder, J. (1988). Fractals. New York: Springer US, 283. doi: 10.1007/978-1-4899-2124-6
- Bozhokin, S. V., Parshin, D. A. (2001). Fraktalyi i multifraktalyi. Izhevsk: NITs «Regulyarnaya i haoticheskaya dinamika», 128.
- Bavyikin, O. B., Vyacheslavova, O. F. (2013). Fraktalnyiy analiz poverhnostnogo sloya materiala. Moscow: Nobel Press, 110.
- Sayles, R. S., Thomas, T. R. (1978). Surface topography as a nonstationary random process. Nature, 271 (5644), 431–434. doi: 10.1038/271431a0
- Mandelbrot, B. B. (1983). The fractal geometry of nature. New York: Freeman, 498.
- Godreche, C., Luck, J. M. (1990). Multifractal analysis in reciprocal space and the nature of the Fourier transform of self-similar structures. Journal of Physics A: Mathematical and General, 23 (16), 3769–3797. doi: 10.1088/0305-4470/23/16/024
- Pavelescu, D., Tudor, A. (2004). On the roughness fractal character, the tribological parameters and the error factors. Proceedings of the Romanian Academy. Ser. A, 5 (2).
- Moskvin, P., Kryzhanivskyy, V., Rashkovetskyi, L., Lytvyn, P., Vuichyk, M. (2014). Multifractal analysis of areas of spatial forms on surface of ZnxCd1−xTe–Si (111) heterocompositions. Journal of Crystal Growth, 404, 204–209. doi: 10.1016/j.jcrysgro.2014.07.012
- Moskvin, P. P., Kryizhanovskiy, V. B., Rashkovetskiy, L. V., Litvin, P. M., Vuychik, N. V. (2014). Multifraktalnaya parametrizatsiya prostranstvennyih form na poverhnosti geterokompozitsiy ZnxCd1-xTe – Si (111) i ee vzaimosvyaz s usloviyami sinteza sloev. Zhurnal fizicheskoy himii, 88 (7-8), 1194–1200.
- Brandt, Z. (2003). Analiz dannyih. Statisticheskie i vyichislitelnyie metodyi dlya nauchnyih rabotnikov i inzhenerov. Moscow: Mir, OOO «Izdatelstvo AST», 686.
- Belkyn, E. A. (2008). Geometrycheskoe modelyrovanye mykrorelefa. Izvestyia OrelHTU. Ser. «Fundamentalnye i prykladnye problemу tekhnyky i tekhnolohyy», 12–19.
- Vstovskiy, G. V., Kolmakov, A. G., Bunin, I. Zh. (2001). Vvedenie v multifraktalnuyu parametrizatsiyu struktur materialov. Moscow: Tsentr «Regulyarnaya i haoticheskaya dinamika», 116.
- Vstovsky, G. V., Kolmakov, A. G., Terentjev, V. F. (1999). Using Multifractal Information for Quantitative Evaluation of Broken Symmetries of Materials Structure. Materials Science (Medžiagotyra). Kaunas, Technologija, 9 (2), 62–65.
- Klymenko, S. A., Melnijchuk, Yu. O., Vstovskyj, G. V. (2009). Fraktalna parametryzaciya struktury materialiv, yix obroblyuvanist rizannyam ta znosostijkist rizalnogo instrumentu. Kyiv: INM im. V. M. Bakulya, 172.
- Kartuzov, V. V., Dmitrishina, Ya. Yu. (2015). Multifraktalnyiy analiz mikrostruktur alyuminievyih splavov, obrabotannyih elektrogidroimpulsnyim metodom. Elektronnaya obrabotka materialov, 51 (2), 31–35.
- Generalova, A. A. (2011). Kolichestvennaya otsenka topologii poverhnosti detaley mashin na osnove teorii fraktalov. Perspektivyi nauki, 1, 68–76.
- Perec, A. (2015). Feasibility study on the use of fractal analysis for evaluating the surface quality generated by waterjet. Tehnicki Vjesnik-Technical Gazette, 22 (4), 879–883. doi: 10.17559/tv-20140128231244
- Gwyddion. Available at: http://gwyddion.net
- Melnychuk, P. P., Loiev, V. Yu., Kryzhanivskyi, V. B. (2007). Prohnozuvannia yakosti ploskoi poverkhni pry tortsevomu frezeruvanni. Visnyk Zhytomyrskoho derzhavnoho tekhnolohichnoho universytetu, 2 (41), 19–28.
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