Covariance in 3D measurement uncertainty evaluation

Peter Benko, Trevor Toman

Abstract

The accepted way of expressing measurement results is through an estimated value and its associated measurement uncertainty. Part of the uncertainty evaluation is also to consider mutual sources of uncertainties, called covariance. This paper will describe a CMM 3D measurement and its uncertainty evaluation. A 3D measurement considered here is a length measurement in three orthogonal directions along the x, y, z axes of a Cartesian coordinate system. When a point in 3D space is located it is considered to be a direct method of measurement. However, when it comes to geometrical features such as the radius of a circle (hole), sphere, cylinder, cone etc. the measurement should be considered as an indirect method of measurement. Therefore, for both the above-mentioned methods, the procedure given by ISO/IEC Guide 98-3:2008 is to apply the law of propagation in uncertainty. Standards such as ISO 10360 and VDI/VDE 2617 supply guidelines for the understanding of uncertainty contributions to 3D measurement uncertainty, and standard ISO 15530-3 describes techniques for determining uncertainty. However, these standards do not consider uncertainties having a mutual source to be dealt with as covariance. This study presents a new approach to evaluating measurement uncertainty for 3D measurement, which helps to conclude where in 3D space the measurement is most affected by uncertainties.

Keywords

Uncertainty, covariance, error, CMM, 3D measurement, straightness, squareness

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IMEKO TC

TC10 - Measurement for Diagnostics, Optimization and Control

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