Comparison of methods for estimating the fractal dimension of microprofiles of surface roughness

A brief overview of new approaches to characterizing the surface quality of metalworking products is given. These approaches are based on mathematical procedures involving a large amount of computation, including fractal methods. A comparative analysis of methods for estimating the fractal dimension of microprofiles of the surface roughness of a steel alloy part obtained as a result of electric discharge treatment has been carried out. Micro-profiles with a given fractal dimension are formed using the structural and functional method based on Brownian motion. The fractal dimension was calculated by two analyzed methods – spectral and the method of constructing the area-scale function, and compared with a given value. The accuracy of the calculated values is estimated. It is established that when estimating the fractal dimension over the entire frequency range of the signal power spectrum, the spectral method can be used, but the error in determining the fractal dimension will be greater than when using the method of constructing the area-scale function. In addition, when estimating the fractal dimension of the roughness of the surface profile of a material by the spectral method, additional filtering, smoothing and centering using weight windows is required, which leads to signal truncation.

Truncation distorts the high-frequency components of the signal and underestimates the fractal dimension. It is established that the estimation of the fractal dimension of real microprofiles of surfaces by constructing the area-scale function is more correct than estimating this value using the spectral method. Therefore, to determine the fractal dimension of microprofiles of surfaces, it is recommended to use the method of constructing the area-scale function. The results obtained will be useful in processing measurement information in accordance with modern standards in the field of geometric characteristics of surfaces, including in the development of software for measuring roughness.

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