Peculiarities of Implementing Multifractal Analysis of the Milled Surfaces Microrelief

Abstract

Manufacturing parts with a specific surface microrelief, which often determines their functional properties, is essential in various industry sectors. The practicality of studying the state of surface microrelief after various mechanical processing methods is of critical importance. It is crucial to develop specific mathematical approaches for calculating the quantitative characteristics of surface relief, a matter of significant practical interest. This paper aims to identify, discuss, and generalize the main features of implementing multifractal analysis of flat surfaces of steel and aluminum alloy samples formed by face milling with different cutting modes. Multifractal analysis of micrographs of C35 steel and AA2024 aluminum alloy sample surfaces was conducted after dry milling with various cutting modes. The statistical analysis of the area and volumes of spatial microforms reveals a linear relationship between their volumes and the sizes of the elementary cells in the coarse-graining method. This finding provides substantial evidence of fractal symmetry among these surface parameters after forming a periodic spatial relief on the surface due to the cyclic action of the tool’s cutting edge. Recommendations were developed to minimize errors in calculating multifractal parameters based on milled samples’ surface area and volumes of relief-forming microforms. It was established that the analysis of multifractal parameters of the machined surface should consider the cutting process’s physical characteristics. The recommendations developed in this paper showed a strong correlation between Rényi numbers, disorder parameters, and the face milling modes of steel and aluminum alloy.

Keywords

• multifractal spectra
• rényi number
• hausdorff dimension
• disorder parameter
• face milling
• process innovation