Estimation Method of Ideal Fractal Parameters for Multi-Scale Measurement of Polished Surface Topography

A surface topography characterization parameter system based on fractal parameters has been established, and several estimation methods for these fractal parameters have been suggested accordingly. Since scale dependence exists in these conventional methods, it is necessary to find an estimation method for characterization parameters with uniqueness. An estimation method for ideal fractal parameters for multi-scale measurement of polished surface topography is proposed in this study. Polished surfaces of two materials, WC-Ni and 9Cr18Mo, are measured under multi-scale for frequency component analysis. This study proposes an estimation method for ideal fractal parameters based on a modified determination method for the scale-free region and the decomposition of frequency components into three classifications. The reasonable results verify the existence of ideal fractal parameters: for the WC-Ni surface, ideal fractal dimension D = 1.3 and scale coefficient G = 2.23×1020 μm; for the 9Cr18Mo surface, ideal fractal dimension D = 1.2 and scale coefficient G = 3.33×1033 μm. Additionally, it is revealed that the scale-dependent components conform to the same regulation on the same instrument by comparing the results of two materials. The conclusions of this study are expected to support tribology research and mechanical engineering related to surface topography.