Simulation and modeling of grinding surface topography based on fractional derivatives

Abstract

The grinding surface’s 3-D topography has self-affinity. To more accurately simulate this characteristic, this paper proposes for the first time to construct a grinding surface simulation model based on fractional derivatives, including: utilizing the Weierstrass-Mandelbrot function to simulate the point cloud of the grinding wheel surface; further deriving the trajectory equation based on the He’s fractal derivative; the semi-inverse method is employed to construct the fractional-order variational principle of the vibration equation. Experiments show that the simulation model designed in this paper can predict the surface height more accurately, and is better than the traditional model in the calculation of roughness parameters Sa and Sq. The model is helpful to thoroughly understand the formation mechanism of grinding surface topography, and provides simulation data guidance for machine vision inspection of grinding surface in micron scale.