Estimation of form deviation and the associated uncertainty in coordinate metrology

Abstract

Purpose

The uncertainty evaluation for coordinate measuring machine metrology is problematic due to the diversity of the parameters that can influence the measurement result. From discrete coordinate data taken on curve (or surface) the software of these machines proceeds to an identification of the measured feature, the parameters of the substitute feature serve in the phase of calculation to estimate the form error of form, and the decisions made based on the result measurement may be outliers when the uncertainty associated to the measurement result is not taken into account. The paper aims to discuss these issues.

Design/methodology/approach

The authors relied on the orthogonal distance regression (ODR) algorithm to estimate the parameters of the substitute geometrical elements and their uncertainties. The solution of the problem is resolved by an iterative calculation according to the Levenberg Marquard optimization method. The authors have also presented in this paper the propagation model of uncertainties to the circularity error. This model is based on the law of propagation of the uncertainties defined in the GUM.

Findings

This work proposes a model based on ODR to estimates parameters of the substitute geometrical elements and their uncertainties. This contribution allows us to estimate the uncertaintof the form error by applying the law of propagation of uncertainties. An example of calculating the circularity error and the associated uncertainty is explained. This method can be applied to others geometry type: line, plan, sphere, cylinder and cone.

Practical implications

This work interested manufacturing firms by allowing them: to meet the normative, which requires that each measurement must be accompanied by its uncertainty-in conformity assessment, the decision-making must take account of this uncertainty to avoid the aberrant decisions. Informing the operators on the capability of their measurement process

Originality/value

This work proposes a model based on ODR to estimates parameters of the substitute geometrical elements and its uncertainties. without the hypothesis of small displacements torsor, this method integrates the uncertainty on the coordinates of points and can be applied in any reference placemark. This contribution allows us also to estimate the uncertainty of the form error by applying the law of propagation of uncertainties.

Citation

Jalid, A., Hariri, S. and Senelaer , J.P. (2015), "Estimation of form deviation and the associated uncertainty in coordinate metrology", International Journal of Quality & Reliability Management, Vol. 32 No. 5, pp. 456-471. https://doi.org/10.1108/IJQRM-06-2012-0087