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Form Assessment in Coordinate Metrology

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Approximation Algorithms for Complex Systems

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 3))

Summary

A major activity in quality control in manufacturing engineering in- volves comparing a manufactured part with its design specification. The design specification usually has two components, the first defining the ideal geometry for the part and the second placing limits on how far a manufactured artefact can depart from ideal geometry and still be fit for purpose. The departure from ideal geometry is known as form assessment. Traditionally, the assessment of fitness for purpose was achieved using hard gauges in which the manufactured part was physi- cally compared with the gauge. Increasingly, part assessment is done on the basis of coordinate data gathered by a coordinate measuring machine and involves fitting ge- ometric surfaces to the data. Two fitting criteria are commonly used, least squares and Chebyshev, with the former being far more popular. Often the ideal geome- try is specified in terms of standard geometric elements: planes, spheres, cylinders, etc. However, many modern engineering surfaces such as turbine blades, aircraft wings, etc., are so-called ‘free form geometries’, complex shapes often represented in computer-aided design packages by parametric surfaces such as nonuniform ra- tional B-splines. In this paper, we consider i) computational approaches to form assessment according to least squares and Chebyshev criteria, highlighting issues that arise when free form geometries are involved, and ii) how reference data can be generated to test the performance of form assessment software.

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Authors and Affiliations

  1. National Physical Laboratory, Teddington, TW11 0LW, UK

    Alistair B. Forbes & Hoang D. Minh

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  1. Alistair B. Forbes
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  2. Hoang D. Minh
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Editors and Affiliations

  1. , Dept. of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom

    Emmanuil H Georgoulis

  2. Abt. Mathematik, Universität Hamburg, Bundesstr. 55, Hamburg, 20146, Germany

    Armin Iske

  3. Dept. Mathematics and, Computer Science, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom

    Jeremy Levesley

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Forbes, A.B., Minh, H.D. (2011). Form Assessment in Coordinate Metrology. In: Georgoulis, E., Iske, A., Levesley, J. (eds) Approximation Algorithms for Complex Systems. Springer Proceedings in Mathematics, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16876-5_4

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