Fitting spatial models of geometric deviations of free-form surfaces determined in coordinate measurements

• Autorzy: Poniatowska M. , Werner A.
• Języki publikacji: EN

Abstrakty

EN

Local geometric deviations of free-form surfaces are determined as normal deviations of measurement points from the nominal surface. Different sources of errors in the manufacturing process result in deviations of different character, deterministic and random. The different nature of geometric deviations may be the basis for decomposing the random and deterministic components in order to compute deterministic geometric deviations and further to introduce corrections to the processing program. Local geometric deviations constitute a spatial process. The article suggests applying the methods of spatial statistics to research on geometric deviations of free-form surfaces in order to test the existence of spatial autocorrelation. Identifying spatial correlation of measurement data proves the existence of a systematic, repetitive processing error. In such a case, the spatial modelling methods may be applied to fitting a surface regression model representing the deterministic deviations. The first step in model diagnosing is to examine the model residuals for the probability distribution and then the existence of spatial autocorrelation.

Słowa kluczowe

EN

geometric deviations; free-form surface; coordinate measurements; spatial modelling; spatial autocorrelation

• Wydawca: Komitet Metrologii i Aparatury Naukowej PAN
• Czasopismo: Metrology and Measurement Systems
• Rocznik: 2010
• Tom: Vol. 17, nr 4
• Strony: 599--610
• Opis fizyczny: Bibliogr. 19 poz., rys., tab., wykr.

Twórcy

autor

Poniatowska M.

autor

Werner A.

• Bialystok University of Technology, Division of Production Engineering, Wiejska 45C, 15-351 Bialystok, Poland,

Bibliografia

• [1] ElKott, D.F., Veldhuis, S.C. (2007). Cad-based sampling for CMM inspection of models with sculptured features. Eng. Comp., 23, 187-206.
• [2] Obeidat, S.M., Raman, S. (2009). An intelligent sampling method for inspecting free-form surfaces. Int. J. Adv. Manuf. Technol., 40, 1125-1136.
• [3] Adamczak, S. (2008). Surface geometric measurements. Warszawa: WNT. (in Polish).
• [4] Dong, W.P., Mainsah, E., Stout, K.I. (1996). Determination of appropriate sampling conditions for threedimensional microtopography measurement. Int. J. Mach. Tools Manuf., 36, 1347-1362.
• [5] Pawlus, P. (2004). Mechanical filtration of surface profiles. Measurement, 35, 325-341.
• [6] Adamczak, S., Janecki, D., Makieła, W., Stępień, K. (2010). Quantitative comparison of cylindricity profiles measured with different methods using Legendre-Fourier coefficients. Metrol. Meas. Syst., 17(3), 233-244.
• [7] Szabatin, J. (2003). Signal theory fundamentals. Warszawa: WKŁ. (in Polish).
• [8] Pawlus, P. (2004). Mechanical filtration of surface profiles. Measurement, 35, 325-341.
• [9] Poniatowska, M. (2009). Research on spatial interrelations of geometric deviations determined in coordinate measurements of free-form surfaces. Metrol. Meas. Syst., 16(3), 501-510.
• [10] Cliff, A.D., Ord, J.K. (1981). Spatial Processes. Models and Applications. London: Pion Ltd.
• [11] Kopczewska, K. (2007). Econometrics and Spatial Statistics. Warszawa: CeDeWu. (in Polish).
• [12] Hu, S.M., Li, J.F., Ju, T., Zhu, X. (2001). Modifying the shape of NURBS surfaces with geometric constrains. Comp. Aided Des., 33, 903-912.
• [13] Wang, W.K., Zhang, H., Park, H., Yong, J.H.,. Paul, J.C, Sun, J.G. (2008). Reducing control points in lofted B-spline surface interpolation using common knot vector determination. Comp. Aided Des., 40, 999-1008.
• [14] Upton, G.J.G., Fingleton, B. (1985). Spatial Data Analysis by Example. John Willey & Sons.
• [15] Piegl, L., Tiller, W. (1997). The NURBS book. 2nd ed. New York: Springer-Verlag,.
• [16] Brujic, D., Ristic, M., Ainsworth, I. (2002). Measurement-based modification of NURBS surfaces. Comp. Aided Des. 34, 173-183.
• [17] Hansford, D., Farin, G. (2002). Curve and Surface Constructions. Handbook of Computer Aided Design. Elsevier Science B.V., Amsterdam, 165-192.
• [18] Juhász, I., Hoffmann, M. (2004). Constrained shape modification of cubic B-spline curves by means of knots. Comp. Aided Des., 36, 437-445.
• [19] Poniatowska, M. (2008). Determining uncertainty of fitting discrete measurement data to a nominal surface. Metrol. Meas. Syst., 15(4), 595-606.