Calculation of the fractal dimensions of machined surface profiles

The optimal method calculating the fractal dimension of a machined surface profile is discussed in this paper. Through the analysis of the results calculated by use of the Weiestrass-Mandelbrot fractal function with known fractal dimensions, the variation method is found to be the best one for calculating the fractal dimensions of the surface profiles among the power spectrum method, the cover method and the rectangular cell counting method. By this method, the fractal dimensions of the surface profiles machined by turning, electrical discharge machining and grinding are evaluated. Furthermore, the relation between the fractal dimensions and the machining conditions are also investigated. In the case of turning, the fractal dimensions of surface profiles decrease with the change of the feed rate whereas the nose radius. The fractal dimensions of the electrical discharge machining surface profiles hardly vary with an increase of the peak discharge currents and the pulse durations. The fractal dimensions of the surface profiles machined by grinding do not change with the grain sizes of grinding wheels.