关键词: W-M函数, 分形粗糙表面, 特征长度尺度参数, 小波分解

Abstract: db2 wavelet decomposition of simulated profiles generated by W-M function with known G is executed. From the decomposition results, it is found that the wavelet decomposition parameters have obvious regularity. Based on this, a new approach to identify the characteristic length scale parameter G of a rough surface profile is proposed. The characteristic length scale parameters of the rough surface profile generated by W-M function and fractional brownian motions as well as actual machined surface profile are calculated using the proposed approach. The results are compared with the calculation results of other four kinds of methods such as the power spectral density method. But the calculation results are not of the same order of magnitude from the different methods. For simulated profiles generated by W-M function, the results from the wavelet method presented are the closest to the theoretical value. By contrast the values of the other methods differ by orders of magnitude from the theoretical value, and the errors are shown to increase with the decrease of fractal dimensions. The power spectral density method has the largest error with the calculation exceeding the theoretical value dramatically, and the error of the equations method follows, then structure function method follows. The calculating error of the equation in the literature[6] is smaller. For the simulated profiles generated by fractional brownian motions, the wavelet method and the equation in the literature[6] and structure function method give the similar calculation results as the wavelet method in this paper. For the actual profile, the wavelet method and the equation from the literature[6] give similar results. In general, the wavelet method is similar to the equation from the literature[6] and the validity of the wavelet method is proved.

Key words: characteristic length scale parameter, fractal rough surface, wavelet decomposition, W-M function