机械加工表面形貌分形特征的计算方法

The Calculation Methods for the Fractal Characteristics of Surface Topography

提出应用小波变换计算表面形貌分形特征参数 ,基于 Weierstrass- Mandelbrot函数 ( W- M函数 )和 Majumdar- Bhushan函数 ( M- B函数 )这 2种常用于表征和模拟机械加工表面轮廓曲线的标准分形函数 ,验证了小波变换计算分形维数具有很高的精度。与其它计算表面形貌分形维数的方法进行了比较 ,结果表明小波变换方法的稳定性和准确性好。应用小波变换计算了不锈钢和铜 2种材料的机械加工表面的分形维数。

In this paper ta new method of calculation the fractal dimensions by Wavelets transform is proposed. Based on the Wererstrass-Mandelbrot function and Majumdar-Bhushan function with known fractal dimensions which are commonly used to simulate the surface profile, it is validated that wavelet transform can calculate accurately the fractal dimensions. And the results are more veracious than Rescaled range analysis method along with other six methods applied for calculation the fractal dimensions, which are Box dimension method, Yard stick method, Covariation method, Structure function method, Variation method and Power Spectrum method. The fractal characteristics of the tested surfaces are estimated for pool nuclear boiling experiments. It is appeared the wavelet transform method is the powerful tool for research on the fractal surface.