Fractal simulation of rough surface with platform power spectrum

Abstract This study utilizes rough surface data obtained from grinding processes and applies the structure function method and an improved variance method to calculate the fractal dimension and the scale characteristic coefficient, respectively. The Weierstrass Mandelbrot (W-M) function, modified by Majumdar-Bhushan (M-B) and Yan-Komvopoulos (Y-K), is employed to simulate rough surfaces and validate the reliability of fractal parameters. When simulating surface profiles using the W-M function on rough surfaces with a platform power spectrum, the low-frequency cut-off frequency ( ω l ) should be defined as the roll-off frequency ( ω 0 ), rather than the reciprocal of the sampling length. We recalculated the fractal scale coefficient G and compared the simulation results of two correction functions on rough surface profiles. The probability density distribution of the M-B model exhibits a slight bimodal characteristic, whereas the Y-K model more accurately reflects rough surface profiles due to its stochastic nature.