Publikacje

Abstract:

The median line of a cylinder measured with the cross-section method is determined on the basis of the centre points of the mean circles of several subsequent cross-sections roundness profiles. Basically, the same principles could be used in the generatrix method. There may be, however, a large scatter of results due to a small number of measurement points with predetermined height coordinates and the occurrence of a waviness component in the cylindricity profile. The method for determination of the median line discussed in this paper involves filtering the measured points by applying the functional approach, as suggested by Krystek in Refs. [2, 3]. It is assumed that the coordinates of the measured median line points minimise the functional (13). One component of the functional assures appropriate approximation of the centres of the mean circles by means of the median line, and the other, termed the cost of curve bending, assures suitable smoothness of the median line eliminating the effect of the waviness components. A similar concept was employed in the bird-cage method, which is actually the combination of the cross-section and generatrix method. In this method, the median line points defined with the cross-section method are taken into account with appropriately greater weight than the points measured with the generatrix method (17). In the examples provided, the median line of a polished roller with a strong waviness component was determined for different cylindricity measurement methods.

B I B L I O G R A F I A[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., Zwierzchowski J.: Podstawy teoretyczne oceny profili walcowości obrotowych części maszyn metodą klatki - część druga: metoda filtracji wykorzystująca podejście funkcjonałowi, Pomiary Automatyka Kontrola, nr 12, str. 1017-1022, 2009.
[8] Janecki D., Adamczak S.: Least-Squares versus minimum-zone deviations, XVI IMEKO World Congress, Wiedeń, Austria 2000, pp. 133-138.

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Podstawy teoretyczne oceny profili walcowości obrotowych części maszyn metodą klatki - część trzecia: Wyznaczanie linii środkowej walca zaobserwowanego