Determining the uncertainty of fitting discrete measurement data to a nominal surface

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

Abstrakty

EN

Coordinate measurements are a source of digital data in the form of coordinates of measurement points with a discrete distribution on the measured surface. Geometric deviations of freeform surfaces are determined at each point as normal deviations of these points from the nominal surface (a CAD model). The calculations are preceded by fitting the measurement data to the CAD model. The relations between the workpiece coordinate system and the coordinate system of the machine are described by the transformation parameters. This paper presents the idea of the process of data fitting with the use of the least square algorithm method as well as the way of determining the uncertainty on the assumption that transformation parameters are subject to a cumulative normal probability distribution. The theoretical issues were verified by experiments carried out on a freeform surface obtained in the milling process and characterized by quasi-random geometric deviations.

Słowa kluczowe

EN

coordinate measurement; fitting uncertainty; freeform surface

• Czasopismo: Metrology and Measurement Systems
• Rocznik: 2008
• Tom: Vol. 15, nr 4
• Strony: 595-606
• Opis fizyczny: Bibliogr. 9 poz., rys., wykr.

Twórcy

autor

Poniatowska, M.

• Chair of Materials Engineering and Mechanical Technology, Bialystok Technical University, Poland

Bibliografia

• 1. Chan F. M. M., King T. G., Stout K. J.: “The influence of sampling strategy on a circular feature in coordinate measurements”. Measurement, vol. 19, no. 2, 1996, pp. 73-81.
• 2. Dhanish P. B., Mathew J.: “Effects of CMM point coordinate uncertainty on uncertainties in determination of circular features”. Measurement, vol. 39, 2006, pp. 522-531.
• 3. Yau H. T.: “Uncertainty analysis in geometric best fit”. International Journal of Machine Tools and Manufacture vol. 38, 1998, pp. 1323-1342.
• 4. Chenggang Che, Jun Ni: “A generic coordinate transformation uncertainty assessment approach and its application in machine vision metrology”. International Journal of Machine Tools and Manufacture, vol. 38, 1998, pp. 1241-1256.
• 5. Ratajczyk E.: Coordinate Measurement Technique. OWPW, Warsaw 2005, (in Polish).
• 6. Yau H. T., Menq C. H.: “A unified least-square approach to the evaluation of geometric errors using discrete measurement data”. International Journal of Machine Tools and Manufacture, vol. 36, no 11, 1996, pp. 1269-1290.
• 7. Kiciak P.: The basis of modelling the curves and the surfaces. WNT, Warsaw 2000, (in Polish).
• 8. Kotulski, Z., Szczepiński W.: Error Analysis with Applications In Engineering. WNT, Warsaw 2004, (in Polish).
• 9. Werner A., Poniatowska M.: “Determining errors in complex surfaces machining with the use of CNC machine tools”. Archives of Mechanical Technology and Automation, vol. 26, no. 2, 2006, pp. 211-217.