An Analysis of the Multiscale Structure of Surfaces with Various Finishes

Even with the various surface finishing techniques, all surfaces are rough with different structures and geometric characteristics over multiple scales. In this work, a profilometer is utilized to measure the profiles of different rough surfaces, and the profiles are characterized using a variety of statistical, spectral, and fractal methodologies. Three different methods are implemented in calculating the fractal dimension, D, and these three methods are then compared. The relationship between the fractal dimension and the fractal scaling constant, G, is investigated as well. The measured rough profiles are also compared with Weierstrass-Mandelbrot (W-M) function–generated rough profiles using the characterization results of the measured profiles. After comparing a series of statistical and fractal parameters, which are calculated based on the surface profile data of the original and regenerated profiles, it can be found that the W-M function does not always appear to be very suitable for representing measured rough profiles. Another important conclusion is that many measured profiles are not always consistent with the quality of self-affinity that many of the popular fractal models assume. Therefore, a discrepancy exists between idealized fractal equations and real profiles. However, these findings are limited to the measurement resolution and specific surfaces considered in this work.