Podstawy teoretyczne oceny profili walcowości obrotowych części maszyn metodą klatki Część II: Metoda filtracji wykorzystująca podejście funkcjonałowe

W celu rozdzielenia składowych kształtu od składowych falistości i chropowatości stosuje się filtry cyfrowe dolnoprzepustowe. W pracy opracowano metodę filtracji profili walcowości zaobserwowanych metodą "klatki". Wykorzystuje ona tzw. podejście funkcjonałowe. Pozwala to na eliminację efektu brzegowego oraz zapewnia, że w punktach przecięcia trajektorii skanowania wartości promienia przefiltrowanych profili okrągłości i prostoliniowości są równe.

It is assumed that roughness, waviness and form constitute the geometrical surface structure. The components of form with the longest wavelengths can now be extracted using digital low-pass filters. In the case of cylindrical surfaces, the assessment of form requires that a profile be filtered with the aim of eliminating the waviness and roughness constituents. The filtration process selected for a profile registered with the bird-cage method should provide filtration both roundness and straightness profiles. Additionally, it is logical requiring the values of the radii of the filtered roundness and straightness profiles be equal at the points of intersection of the scanning trajectories. The profiles under study were filtered using the so called functional approach, which was introduced to surface metrology by Krystek [2, 3] and further developed by other re-searchers [7]. According to the approach, a filtered profile is modeled as a spline, which assumes a required smooth form due to local stresses proportional to the value of a deviation. The major advantage of the functional approach is the elimination of the boundary effect, which occurs during filtration of straightness profiles. Although it is relatively simple to directly generalize the functional approach to the filtration of a cylindricity profile registered with the bird-cage method (26), the problem is very difficult to solve because of its dimension. Therefore, simplified approach has been applied. First, we filtered each profile separately using the pre-determined methods for roundness and straightness profiles. Subsequently, we filtered the profiles by introducing additional equality conditions (33), which assured profile continuity at the points of intersection of the cylinder scanning trajectories. The proposed two-step filtration algorithm can be combined with the procedure of profile matching discussed in Ref. [1].