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

• Autorzy: Janecki D. , Zwierzchowski J.

Warianty tytułu

EN

Theoretical background of cylindricity profile evaluation of rotary parts by means of bird-cage measuring method Part 2: A functional approach to profile filtering

• Języki publikacji: PL

Abstrakty

PL

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.

EN

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].

Słowa kluczowe

PL

walcowość; metoda pomiarowa klatki

EN

cylindricity; bird-cage method; profile filtering

• Wydawca: Wydawnictwo PAK
• Czasopismo: Pomiary Automatyka Kontrola
• Rocznik: 2009
• Tom: R. 55, nr 12
• Strony: 1017--1022
• Opis fizyczny: Bibliogr. 10 poz., rys., wykr., wzo

Twórcy

autor

Janecki D.

autor

Zwierzchowski J.

• Wydział Mechatroniki i Budowy Maszyn, Politechnika Świętokrzyska,

Bibliografia

• [1] Janecki D., Zwierzchowski J.: Podstawy teoretyczne oceny profili walcowości obrotowych części maszyn metodą klatki – część pierwsza: zagadnienie optymalnego dopasowania profili, Pomiary Automatyka Kontrola, nr 9, str. 715-722, 2009.
• [2] Krystek M.: Form filtering by splines, Measurement, vol. 18, No 1/1996, pp. 9–15.
• [3] Krystek M.: Discrete L-spline filtering in roundness measure-ments, Measurement, vol. 18, No 2/1996, pp. 129–138.
• [4] Üstüner K.F., Ferrari L.A., Discrete splines and spline filters, IEEE Trans. Circuit and Systems II: Analog and Digital Signal Processing, vol. 39, 1992, pp. 417-422.
• [5] Unser M., Aldroubi A., Eden M., B-spline signal processing: Part I – Theory, IEEE Trans. Signal Processing, vol. 41, 1993, pp. 821-833.
• [6] Feng G., Data smoothing by cubic spline filters, IEEE Trans. Signal Processing, vol. 46, 1998, pp. 2790-2796.
• [7] Janecki D., A generalized L2-spline filter, Measurement, Vol. 42, 2009, pp. 937-943.
• [8] Brinkmann S., Bodschwinna H., Lemke H.W.: Accessing roughness in three–dimensions using Gaussian regression filtering, International Journal of Machine Tools and Manufacture, vol. 41, 2001, pp. 2153–2161.
• [9] ISO TS 16610-22 standard: Geometrical Product Specifications (GPS) - Filtration - Part 22: Linear Profile Filters: Spline Filters.
• [10] ISO/CD TS 16610-31, Geometrical product specifications (GPS) -- Filtration -- Part 31: Robust profile filters: Gaussian regression filters, Under development.