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A problem of optimal cylindricity profile matching

Janecki D., Zwierzchowski J., Cedro L.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2015

Vol. 63, nr 3

771--779

The bird-cage strategy used for measuring cylindricity is reported to be the most effective, as it provides the most detailed information about an analyzed object. The average values of profiles measured with the cross-section and the generatrix strategies may differ slightly, yet this may result from some design imperfections of the measurement instruments used. In this study, the problem of optimal profile matching is formulated and solved. As a result, the differences between the values of the registered profiles at the points of intersection of the scanning trajectories can be minimized.

Podstawy teoretyczne oceny profili walcowości obrotowych części maszyn metodą klatki Część I: Zagadnienie optymalnego dopasowania profili

Janecki D., Zwierzchowski J.

Pomiary Automatyka Kontrola

2009

R. 55, nr 9

715-722

Metoda klatki pomiaru profili walcowości dostarcza najwięcej informacji o mierzonym przedmiocie. Jednak w wyniku pewnych niedokładności przyrządów pomiarowych wartości średnie profili zaobserwowanych metodą przekrojów poprzecznych i wzdłużnych mogą się nieznacznie różnić. W pracy sformułowano i rozwiązano zagadnienie optymalnego dopasowania profili, co pozwala zminimalizować różnice wartości promienia profilu w punktach przecięcia trajektorii skanowania przedmiotu.

The bird-cage method applied to measurement the cylindricity of rotary objects combines the principles of the cross-section and the generatrix methods, see Fig 1. Cylindricity measurement results obtained by means of the bird-cage method, show that the values of the profile radius at the points of intersection of scanning trajectories at the cross and longitudinal sections are slightly different. The difference may be due to the occurrence of measurement noise and instrument vibrations or the design imperfections of the sensor system. Note that the measurement conditions for the cross-section method are different from those for the generatrix method. This causes different distribution of forces acting on the sensor tip. As a result, the profile achieved by the cross-section method can be slightly shifted in relation to the profile achieved by the generatrix method (see Fig. 2 and Table 1). In order to reduce these errors a problem of optimal profile matching is formulated and solved. Values of the profiles in each section are shifted in such a way that the difference in the radii at the points of intersection of the scanning trajectories is the smallest as possible. To do this, a square index of profile matching (20) is defined and the required values of profile shifts (16)-(19) are derived from necessary conditions of optimality. The observed profiles are modified in accordance with the formulae (25)-(26). Additionally, it is also shown that it is possible to correct the difference in the rotation axis position during roundness measurements with the spindle in rotary motion and during straightness measurements with the spindle at standstill. The effects of the application of the profile matching algorithms are analyzed basing on the measurements of two rollers with a diameter of 52 mm and a height of 100 mm, each. One specimen was polished and the other was grounded. Results of the experiments show that due to the optimal profile matching, the root-mean-square of the difference in the radii at the points of intersection of the scanning trajectories may be decreased from several to several dozen times depending on the level of the waviness component (see Figures in Section 3).