The Fractal Behavior and Fractal Characterization of Rough Surfaces

Fractal geometry is a new method recently developed to describe the irregular performance.The profiles of ground surfaces and turned surfaces were obtained by the contact profiler.The fractal behavior of these profiles was then investigated and discussed.Moreover,the concept and definition of the characteristic roughness for a rough surface was proposed in order to evaluate the rough level of surfaces.The results show that the rough surfaces will present strong fractal behavior within a certain scale,which can be measured by contact profilers and its fractal dimension can also be estimated with proper methods.A bifractal behavior is shown on ground surfaces and turned surfaces,the second fractal scale depends on the corelation length of profiles.The first fractal dimension relates to roughness of profiles in a negative power function.However,it is found that fractal dimensions are not enough for characterizing the roughness of surfaces as result of the relative measures in multiscales.The characteristic roughness consists of both the similarity of fractal dimension and the absolute representation of scale parameter,which can be used as a parameter to evaluate roughness.The characteristic roughness can not only make a multi scale measurement of rough surfaces but also show high sensitivity and accuracy in characterizing roughness.