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Katanaeva M., Lartseva T., Yudaev S. et al. International Journal of Emerging Trends in Engineering Research. 2020. Vol. 8. No. 8. P. 4378-4382.

To determine the surface quality of the machine parts, traditional methods based on the direct measurements of the microcracks are used. The results do not allow assessing the correlation of the surface layer quality and the given values. The approach developed recently measures the parameters of the surface layer using fractal analysis and solves this problem. To define the fractal dimension of the surface layer the modern digital stationary surface analyzers were used. As a result, it is possible to save the profile as a text file. This file is a time series consisting of the roughness heights of the surface elements. Having such a two-dimensional profile diagram, it is possible to calculate the fractal dimension in a computer program. This program will calculate the uploaded time series. Nowadays mathematicians use Fractan for time series fractal analysis. The results of the precision analysis of the data showed that Fractan has low precision in estimations of the time series fractal parameters. So Fractan cannot be used for the fractal analysis of the machine parts surface layer. The simultaneous use of the stationary surface analyzer and a computer program to estimate the Hurst exponent in order to define fractal characteristics of the material surface layer is proposed. Fractal analysis using the computer program Fractan shows low accuracy. A computer program written in VBA to calculate fractals of the time series is developed. The algorithms used in the program estimate the Hurst exponent with high accuracy.    

Added: Sep 13, 2020