Anisotropic 3D rough surface reconstruction model based on fractal method and its application in contact characteristics

This study proposes a novel anisotropic model based on fractal theory for three-dimensional (3D) rough surface reconstruction to improve the large error associated with isotropic models. The proposed model comprises a fractal-based two-dimensional (2D) contour curve, a conversion operator and a coefficient vector ratio. The effects of the virtual random curve and fractal-based 2D contour curve in the conversion operator are discussed. The largest height ratio of the virtual contour curve and the measured surface discrete point curve of each column are used in the coefficient vector ratio. The rough surface is also smoothed using a five-point cubic smoothing algorithm. Compared with the isotropic model, the proposed model resembles the measured surface more closely with an average fitting error reduction of 49.84% and 64.7% before and after smoothing, respectively. The surface exhibits horizontal and vertical textures that can be controlled by the fractal dimension and roughness in the X and Y directions. Additionally, an asperity contact model is established and analysed. The proposed modelling method for anisotropic 3D rough surface contact condition is more consistent with the measured surface model. The transverse and longitudinal textures of the anisotropic surface can be changed by the fractal dimension and fractal roughness in the X and Y directions. This research provides insights into characterising 3D rough surfaces of high-precision gears and improving nominal contact area accuracy.