Evaluation of the wavelet transform method for machined surface topography 2: fractal characteristic analysis

In this paper, a new method based on wavelet transform is proposed as a means for studying the fractal characteristics of rough surfaces. Through estimation of normal mathematical curves with known fractal dimensions, generated by the Weierstrass-Mandelbrot function, Majumdar-Bhushan function, Fractal Brownian motion (including three methods: the Midpoint FBm, the Additions FBm, the Interpolated FBm) and Interposed method (Kiesswetter curve), it is validated that the wavelet transform method can accurately calculate the fractal dimension. These fractal functions have been used to simulate some surface profiles. The results indicate that the Wavelet transform method is the most precise in its calculation of the fractal dimensions of the curves. It obtains more accurate results than seven other methods, named the Box counting method, the Yardstick method, the Co-variation method, the Structure function method, the Variation method, the Power Spectrum method and the Rescaled range analysis method. Precisely calculating the fractal dimensions of the curves is the first step in characterising machined surface topography. In addition, this paper aims to further develop the evaluation procedure for the fractal characteristics of machined surface topography.