Affiliation:
1. School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, China
Abstract
The three-point sinuosity (TPS) method is proposed to calculate the fractal dimension of surface profile accurately. In this method, a new measure, TPS is defined to present the structural complexity of fractal curves, and has been proved to follow the power law. Thus, the fractal dimension can be calculated through the slope of the fitted line in the log–log plot. The Weierstrass–Mandelbrot (W–M) fractal curves, as well as the real surface profiles obtained by grinding, sand blasting and turning, are used to validate the effectiveness of the proposed method. The calculation values are compared to those obtained from root-mean-square (RMS) method, box-counting (BC) method and variation method. The results show that the TPS method has the widest scaling region, the least fit error and the highest accuracy among the methods examined, which demonstrates that the fractal characteristics of the fractal curves can be well revealed by the proposed method.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Geometry and Topology,Modeling and Simulation
Cited by
13 articles.
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