Algorithmization for Calculating Fractal Parameters of the Relief of a Rough Surface According to GOST R ISO 25178-2-201
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GENERAL PROBLEMS OF METROLOGY AND MEASUREMENT TECHNIQUE ALGORITHMIZATION FOR CALCULATING FRACTAL PARAMETERS OF THE RELIEF OF A ROUGH SURFACE ACCORDING TO GOST R ISO 25178-2-2014
B. N. Markov, D. A. Masterenko, P. N. Emelyanov, and V. I. Teleshevskiy
UDC 621.9.015: 62-408.8
The application of fractal geometry methods for characterizing the properties of surfaces of materials and products is described. The terminology of the standard GOST R ISO 25178-2-2014, “Geometric characteristics of products (GPS). Surface structure. Areal. Part 2. Terms, definitions and parameters of surface structure.” The functions provided by the standard for calculating fractal dimension are presented; algorithms for their calculation in the Mathcad environment are described. We give an example of calculations based on the results of measurements of the heights of surface irregularities of a gauge block, obtained using an atomic force microscope. Keywords: surface, fractal, fractal dimension, Mathcad, volume-scale function, relative area function, diagnostics, cutting tool.
Introduction. In recent years, much attention has been given to the methods of fractal geometry for the description of the surface properties of materials mechanically processed [1–3] or obtained as a result of irradiation with high-current electron and ion beams [3, 4], surfaces of composite materials (nanocomposites) [ 5], surfaces of destruction of products [6]. Also, fractal geometry methods are in demand when analyzing the features of electromagnetic fields after they are scattered by a fractal rough surface [7], when solving tribological problems to determine the parameters of contact interaction of surfaces taking into account their roughness [8]. The problem of diagnostics of cutting tools is relevant at the present time [9–16]. In mechanical engineering, to diagnose a condition, in particular the degree of wear of a cutting tool, one can use the fractal characteristics of its surface. When studying the profiles of cutting edges according to the data of morphological filtration and constructing scale-dependent regularities, it was found that the structure of the edge is fractal-like, and the fractal dimension of the edge changes with wear [17]. The widespread use of fractal methods makes it necessary to unify the quantitative description of surfaces as fractals. The international standard ISO 25178-2:2012, “Geometric product specifications (GPS) – Surface texture: Areal – Pt. 2: Terms, definitions and surface texture parameters,”and its Russian version GOST R ISO 25178-2-2014, “Geometric characteristics of products (GPS). Surface structure. Areal. Part 2. Terms, definitions and parameters of the surface structure,” introduce for the first time the fractal parameters of a rough surface into consideration and methods for their calculation from measurement data are established. Unfortunately, understanding the Russian version GOST R ISO 25178-2-2014 of the ISO 25178-2:2012 standard is hampered by some flaws in the Russian translation which will be discussed in t
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