Fractal characterization of nano anisotropic rough surface

With the development of ultra-precision equipment, the roughness of contact surface can reach the nanometer level, and the surface morphology has a significant impact on surface contact, friction, wear and lubrication. At present, the surface morphology description is mainly based on the measurement, which is scale dependent, and the statistical parameters obtained by different sampling length and measurement resolution are different, so it is impossible to realize the accurate characterization of nanoscale rough surface. Because the rough surface is self-affine, another method can be introduced to characterize the rough morphology, fractal theory. The simulated rough surface has the advantage that it is not limited by the sampling length, and can realize the unique characterization of the rough surface. In this study, a nanoscale anisotropic three-dimensional fractal surface is established based on W-M model, and the relationships between fractal dimension D, roughness coefficient G, contour arithmetic mean deviation Sa and contour height standard deviation Sq are studied based on statistical principle.