Geometric Accuracy Characterization of Small-Sized Surfaces Based on Fractal Methods

The traditional evaluation of micro-geometric accuracy of machined surfaces depends on sampling length, evaluation length and other parameters, and can not be used to describe the geometric accuracy of surface topography features at micromachined surface. In this paper, fractal theory is introduced to describe the geometric morphology of surfaces obtained by micro milling, and the theory of Brownian motion was combined to analyze the principle of solving the fractal dimension of machined surface based on the structure function method. Based on Weierstrass-Mandelbrot function, surface contour curves with different fractal parameters were simulated, and the mapping relationship between fractal parameters and contour curve morphology was deeply explored. Finally, the side milling analysis test of micro feature surface was carried out, and the fractal parameters of the contour curve of the feature surface were obtained based on the structure function method, and the advantages and disadvantages of various sampling methods were compared and analyzed. The internal relationship between the fractal parameters and the micro-morphology characteristics and geometric accuracy of the feature surface was deeply revealed based on the mathematical statistics method.