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Journal Nonlinear World №3 for 2014 г.
Article in number:
A parametric method for determining the presence of fractal properties of the electrochemically treated surfaces
Keywords: fractal properties Hurst dimensional electrochemical machining
Authors:
A.A. Potapov - Dr.Sc. (Phys.-Math.), Professor, Leading Research Scientist, Kotel-nikov Institute of Radio Engineering and Electronics of RAS. E-mail: potapov@cplire.ru
O.F. Vyacheslavova - Dr.Sc. (Eng.), Professor, Department «Standardization, metrology and certification», Moscow State University of Mechanical Engineering. E-mail: smis@mami.ru
O.B. Bavykin - Associate Professor of Department «Standardization, metrology and certification», Moscow State University of Mechanical Engineering
Abstract:
This article shows that the fractal analysis of surface is effective in the case where the structure exhibits fractal properties. Well-known approaches assess the presence of fractal properties have a number of drawbacks and limitations that do not allow them to use for the study of fractality surface after electrochemical treatment. However, the properties of exponent Hurst (H) provide an opportunity to develop a parametric method for determining the presence of fractal in structure. The proposed method involves two steps. The first one allows you to assess the presence of fractal properties by checking for compliance with the behavior of the structure of the Gauss law. If the structure is not subject to the normal law is based on the properties of the parameter H, we may say that it is a fractal. The analysis of common approaches determine the presence of Gaussian statistics in the behavior of a random variable has shown that the best way to explore electrochemically treated surface is using of criterion for checking the directional asymmetry and directional criterion checks curvature. The second stage allows to estimate the intensity fractality by the analysis of the fractal properties of the distribution of the random variable for the presence of «heavy tail». It is noted that a convenient tool for this analysis is the graph of Pearson. It is shown that the results of research in the presence of fractal properties of electrochemically treated surfaces are in good agreement with the results of R/S-analysis performed in the Institute of Radioengineering and Electronics of Russian Academy of Sciences.
Pages: 3-12
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