Estimating and Extracting of the Surface Profile Waviness by Use of the Spatial Notch Filters in the Roughness Profile Analysis

Classical surveying of the machined surface quality is performed very often with using roughness profile recording by means of contact mechanical profilometer [4-7]. Also classical attitude to the profile run elaboration is to regard it as to a curve composed of the three main components: shape – treated mostly as deterministic, waviness – treated essentially as deterministic with some probabilistic component, and roughness itself – treated to as purely probabilistic. The question is: how to estimate this three components quantitatively and extract for individual evaluation. In our works we have developed methodical procedures of profile elaboration divided into three major steps: shape estimation and extraction with using polynomials of the order fitted to the evaluated profile, waviness estimation and extraction with using spatial filtering methods employing so called notch filters, statistical roughness estimation with using the set of tests and methods devoted especially to roughness runs of the purely probabilistic type. The notch filters are filters cutting out one, well determined spatial frequency λ0 from the spectrum of frequencies related with investigated profile. The second but not less important advantage of this choose, was the phase characteristics of this filter, which tends rapidly to zero outside the “notch” band, not distorting unfiltered spatial signal. The width of cutting “notch” is controlled with using one independent variable Q. Our methodology is based upon cutting out a set of frequencies from the profile, tuned separately for to achieve as well reflection of the periodic impulse-like signal as possible, due to the well known theorem of decomposing physical, periodical signals into their harmonic components. In our researches we have employed the set of 8 filters providing us with good results even with profiles “scared” with substantial tracks of periodically acting tool. Of course, it is still possible to employ even greater number of filters, due to their low numerical complexness. Also the comparison has been performed with the profile not affected by waviness for to convince, that this type of filter simply do not affect the probabilistic roughness component. All of the profile elaboration stages have been checked due to their spatial spectrum with using classical tool – FFT transform of the roughness profile autocovariance function. As the major check of the proposed procedure correctness, i.e. proper extraction of the waviness component without disturbing of the statistical roughness parameters we assumed checking of the shape factor Rq/Ra before and after waviness extraction, which turned to be the same at the good level of accuracy. Our results, basing on simple and fundamental frequency analysis seems to be the good alternative to much complicated and time consuming analysis based on wavelet transforms in different forms.