基于小波变换的三维粗糙表面分形维数计算方法

基于小波变换提出一种三维粗糙表面分形维数的计算方法。该方法采用小波变换对三维表面形貌数据进行多尺度分解,通过对不同分解尺度下小波系数平方的均值进行函数拟合,继而得到粗糙表面的三维分形维数。为验证提出的方法的正确性与准确性,采用已知参数构建三维分形表面,对不同方法下分形维数的计算结果进行对比分析。对比结果显示,相比原始盒维数法与差分盒维数法,采用提出的小波变换法计算得到的分形维数误差更小。特别是在小波变换过程中选用sym4小波基函数时,分形维数的计算误差最小,误差能够控制在2%以内。将提出的方法应用于磨削表面分形维数的计算,得到了不同粗糙度下磨削表面的分形维数,进而验证了该方法的实用性。提出的方法能够更加精确地计算三维粗糙表面的分形维数,为粗糙表面分形接触模型的构建提供了参数基础。

Fractal Dimension Calculation of Three-dimensional Rough Surface Based on Wavelet Transform

A method for calculating fractal dimension of three-dimensional rough surface based on wavelet transform was proposed. In this method,wavelet transform was used to decompose the three-dimensional surface topography data in multi- scale,and the mean value of the square of the wavelet coefficients under different decomposition scales was fitted by func- tion,then the three-dimensional fractal dimension of the rough surface was obtained. In order to verify the correctness and accuracy of the proposed method,a three-dimensional fractal surface was constructed with known parameters and the results of fractal dimension calculation under different methods were compared and analyzed. The results show that compared with the original box dimension method and the difference box dimension method,the fractal dimension error calculated by the wavelet transform method is smaller. Especially when sym4 wavelet basis function is selected in the process of wavelet transform,the calculation error of fractal dimension is the smallest,and the error can be controlled within 2%. The method was applied to calculate the fractal dimension of grinding surface. The fractal dimension of grinding surface under different roughness was obtained,which verified the practicability of the method. The method presented can calculate the fractal dimension of three-dimensional rough surface more accurately,which provides a parameter basis for the construction of fractal contact model of rough surface