Research On Fractal Character Of Machined Surface Topography Based On Surface Grayscale Image

The micro-geometry feature of machined surface topography greatly influences its technique performances and functions. There are many factors having intimate relations with surface geometry structure, such as wear resistance, seal capability, fitness, friction, thermal conductivity and electrical conductivity and so on. Studying machined surface topography is one of the important research topics in surface science. Research indicates that rough surfaces have characteristics of randomness, irregularity, self-similarity, self-affinity and multi-scale. As a kind of new mathematic theory, fractal geometry research object is the irregular and random set or system that presents characteristics of self-similarity and self-affinity in the nature. The author of this paper goes at the three-dimensional topography of surface, applies the fractal theory, takes the SEM image of the surface as the research object, and studies the fractal character of machined surface. Research achievements and innovations as bellow:The author introduces the fractal Brownian movement into the research of surface topography, establishes the discrete fractal Brownian increment random field model (DFBIR) and also analyzes the stability to provide an appropriate model for analyzing an object which has characteristic of random fractal feature. On this condition, in this paper several algorithms of computing curved surface fractal dimension Ds are studied and the problem that if many kinds of dimension computation methods are fit for the fractal objects of different property is discussed. By computing several kinds of fractal dimension of machined surface, the author discusses the evaluation parameter of roughness of three-dimensional surface.The study on the surface texture feature is based on DFBIR, defining a kind of surface ascent parameter b to describe the surface relief degree. As a result, the author accomplishes the classification of machined surface and the synthesis evaluation of surface topography by combining the fractal parameter H and the ascent parameter b. The concept of the surface singular feature texture and its evaluation parameter are put forward. The fractal character of surface bearing characteristic is discussed.The fundamental principle and the computation method for the multi-fractal spectrum are researched, the multi-fractal spectrum of sampled surface and the multi-fractal spectrum of surface gradient and its feature parameter are probed into. As evaluation indexes, the altitude homogeneity and the slope homogeneity of surface are respectively evaluated in this paper, and the general conclusion in accordance with the reality is reached accordingly.Based on the DFBIR, the author studies the directivity of surface texture and computes the dimension distribution of every point of surface. On this basis, he also studies FD gradient feature and the Fourier spectrum feature of surface dimension,and deduces a new parameter V to evaluate the directivity of surface. In this way the quantificational evaluation to the directivity of surface has been achieved in this paper.Moreover, the author applies wavelet theory to study the local exiguity property and the structure regulation of fractal surface and brings forth the concept of surface normalization fractal measure. He also deduces a kind of wavelet analysis algorithm to analyze the surface local fractal exponent and the evaluation method of structure regulation, and takes it into practice, then provides an effective research method to analyze further the local fractal feature of machined surface topography.