Computational model for fractal dimension of anisotropic gear surfaces based on improved structure function method

Abstract This paper analyzes the computational errors inherent in the structure function method (SFM) and proposes an improved method considering the effect of sampling length. The results reveal that smaller fractal dimensions correlate with larger calculation errors. While increasing the sampling length reduces errors, it is not the optimal solution. Compared with the traditional method, the improved structure function method (ISFM) markedly reduces computational errors across varying sampling lengths. Specifically, the computational maximum mistake diminishes from 16.55% to 0.46%. Then, an experimental method is introduced to approximate the fractal dimension of actual tooth profiles by extending the sampling length, which validates the accuracy of ISFM. Based on the ISFM, extensive experimental testing of tooth surface profile data establishes an interval model between the fractal dimension and surface roughness. This revised model corrects the inherent errors of traditional models and is more consistent with the actual rough surfaces. The interval values of fractal dimensions outputted are more consistent with the observed phenomenon, where the same roughness value can correspond to multiple contour curves exhibiting different fractal dimensions.