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Uncertainty associated with form assessment in coordinate metrology

Published online by Cambridge University Press:  05 June 2013

A.B. Forbes
A.B. Forbes*
Affiliation:
National Physical Laboratory, Teddington, Middlesex, UK
*
⋆ Correspondence: Alistair.Forbes@npl.co.uk
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Abstract

In this paper, we describe techniques for evaluating the uncertainties associated with the assessment of form error, i.e., the departure from ideal geometry of a manufactured part, in coordinate metrology. The techniques take into account measurement uncertainty, sampling effects due to the fact that the form error is determined from a finite set of coordinate data points, and the spatial correlation of the form errors. The techniques are designed to be practical, without the need for complex computation.

Keywords

Form errorGaussian processesuncertainty
Type
Research Article
Information
International Journal of Metrology and Quality Engineering , Volume 4 , Issue 1 , 2013 , pp. 17 - 22
Copyright
© EDP Sciences 2013

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References

S.J. Ahn, E. Westkämper, W. Rauh, Orthogonal distance fitting of parametric curves and surfaces, in Algorithms for Approximation IV, edited by J. Levesley, I.J. Anderson, J.C. Mason (University of Huddersfield, 2002), pp. 122–129
Anthony, G.T., Anthony, H.M., Bittner, B., Butler, B.P., Cox, M.G., Drieschner, R., Elligsen, R., Forbes, A.B., Groß, H., Hannaby, S.A., Harris, P.M., Kok, J., Reference software for finding Chebyshev best-fit geometric elements, Precis. Eng. 19, 28–36 (1996) CrossRefGoogle Scholar
Boggs, P.T., Byrd, R.H., Schnabel, R.B., A stable and efficient algorithm for nonlinear orthogonal distance regression, SIAM J. Sci. Statist. Comput. 8, 1052–1078 (1987) CrossRefGoogle Scholar
Carr, K., Ferreira, P., Verification of form tolerances part I: Basic issues, flatness and straightness, Precis. Eng. 17, 131–143 (1995) CrossRefGoogle Scholar
Carr, K., Ferreira, P., Verification of form tolerances part II: Cylindricity and straightness of a median line, Precis. Eng. 17, 144–156 (1995) CrossRefGoogle Scholar
A.B. Forbes, Least squares best fit geometric elements, in Algorithms for Approximation II, edited by J.C. Mason, M.G. Cox (Chapman & Hall, London, 1990), pp. 311–319
Forbes, A.B., Surface fitting taking into account uncertainty structure in coordinate data, Meas. Sci. Technol. 17, 553–558 (2006) Google Scholar
Forbes, A.B., Uncertainty evaluation associated with fitting geometric surfaces to coordinate data, Metrologia 43, S282–S290 (2006) CrossRefGoogle Scholar
A.B. Forbes, H.D. Minh, Form assessment in coordinate metrology, in Approximation Algorithms for Complex Systems, edited by E.H. Georgoulis, A. Iske, J. Levesley, Springer Proceedings in Mathematics (Springer-Verlag, Heidelberg, 2011), Vol. 3, pp. 69–90
H.-P. Helfrich, D. Zwick, ℓ 1 and ℓ ∞ Fitting of Geometric Elements (2002), pp. 162–169
Jiang, X., Zhang, X., Scott, P.J., Template matching of freeform surfaces based on orthogonal distance fitting for precision metrology, Meas. Sci. Technol. 21, 045101 (2010) CrossRefGoogle Scholar
Moroni, G., Petrò, S., Geometric tolerance evaluation: a discussion on minimum zone fitting algorithms, Precis. Eng. 32, 232–237 (2008) CrossRefGoogle Scholar
D. Sourlier, W. Gander, A new method and software tool for the exact solution of complex dimensional measurement problems, in Advanced Mathematical Tools in Metrology II, edited by P. Ciarlini, M.G. Cox, F. Pavese, D. Richter (World Scientific, Singapore, 1996), pp. 224–237
G.E.P. Box, G.C. Tiao, Bayesian Inference in Statistical Analysis (Wiley, New York, Wiley Classics Library, edition 1992, edition 1973)
A. Gelman, J.B. Carlin, H.S. Stern, D.B. Rubin, Bayesian Data Analysis, 2nd edn. (Chapman & Hall/CRC, Boca Raton, 2004)
H.S. Migon, D. Gamerman, Statistical Inference: an Integrated Approach (Arnold, London, 1999)
D.S. Sivia, Data Analysis: a Bayesian Tutorial (Clarendon Press, Oxford, 1996)
M. Evans, N. Hastings, B. Peacock, Statistical distributions (Wiley, 2000)
W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes: the Art of Scientific Computing (Cambridge University Press, Cambridge, 1989), www.nr.com
C.E. Rasmussen, C.K.I. Williams, Gaussian Processes for Machine Learning (MIT Press, Cambridge, 2006)
G.H. Golub, C.F. Van Loan, Matrix Computations, 3rd edn. (John Hopkins University Press, Baltimore, 1996)
A.B. Forbes, Parameter estimation based on least squares methods, in Data Modeling for Metrology and Testing in Measurement Science, edited by F. Pavese, A.B. Forbes, (Birkhäuser-Boston, New York, 2009), pp. 147–176
Zhang, G., Ouyang, R., Lu, B., Hocken, R., Veale, R., Donmez, A., A displacement method for machine geometry calibration, Ann. CIRP 37, 515–518 (1988) CrossRefGoogle Scholar
D. Gamerman, Markov chain Monte Carlo: Stochastic Simulation for Bayesian Inference (Taylor & Francis, New York, 1997)
A.B. Forbes, Structured nonlinear Gauss-Markov Problems, in Algorithms for Approximation V, edited by A. Iske, J. Levesley (Springer, Berlin, 2006), pp. 167–186