Establishing Conformity to Tolerances by Coordinate Measuring Machines: A First Step for a Statistical Approach

[+] Author and Article Information
Giulio Barbato

DISPEA, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italygiulio.barbato@polito.it

Daniela D’Agostino, Raffaello Levi

DISPEA, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy

J. Comput. Inf. Sci. Eng 7(1), 81-84 (Dec 11, 2006) (4 pages) doi:10.1115/1.2432901 History: Received September 30, 2005; Revised December 11, 2006

Conformity to tolerances is currently assessed taking into account the maximum material condition. Coordinate measuring machines do not however operate accordingly, a small sample only of points on workpiece surface being actually contacted, with a fairly low chance of hitting the outmost point. That problem should therefore be properly addressed using statistical methods, as currently considered also by the ISO Technical Committee on “Geometrical Product Specifications and Verification.” This paper proposes to associate maximum material with the statistical distribution of maximum; typical examples of saw-tooth and round grooved surface profiles are theoretically examined. An actual surface with a good finish, representing the common case of normal distribution, was experimentally evaluated, showing that the method proposed produces consistent results. Furthermore, the method proposed readily associates results obtained with a statistical confidence interval; the uncertainty of results obtained can thus be assessed at any given confidence level.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Saw-tooth profile parameters

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Figure 2

Parameters of shallow, circular grooves

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Figure 3

Numerical estimate of expected value of maximum M and related 2σ uncertainty versus n virtual points, calculated using N=200 measured points on a nominally plane surface. Standard deviation of residuals was 1.9μm. Asymptotic shape shows that the estimate of M for a sufficiently large value of n offers a good estimate of the maximum over the whole surface (n=∞).

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Figure 4

Experimental estimates of M∞ and related 2σ uncertainties corresponding to N=20, 50, 100, and 200



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