Perpendicularity assessment and uncertainty estimation using coordinate measuring machine

Abstract

The validation of the conformity of parts according to the ISO 98-4 standard, cannot be achieved without an accurate estimation of the measurement uncertainty, which can become difficult when it comes to a complex measurement strategy to control a geometrical specification of a mechanical part using a Coordinate Measuring Machine (CMM). The purpose of the study in this paper is to analyze the measurement strategy following the Geometric Product Specification (GPS) Standard, to estimate the associated uncertainty of the different parameters of each step, to be able to achieve the uncertainty of the measurement of a given specification (perpendicularity error in our study) using the Guide to the expression of uncertainty in measurement (GUM). This uncertainty will be thereafter validated by a Monte Carlo simulation, and an interlaboratory comparison will be conducted to compare the obtained results according to the ISO 13528 standard. Our contribution is based on a more accurate estimation of the measurement strategy's parameters uncertainties. This approach can also be used by accredited calibration laboratories (ISO 17025) or in the general case in the control of perpendicularity specification of mechanical parts using a coordinate measuring machine. A case study has been conducted, controlling a perpendicularity specification with a tolerance limit of 15 µm, after the calibration of the CMM to obtain the variance-covariance matrices. The mechanical part perpendicularity error (12.55 µm) was below the limit, however, was judged “not conform” when considering the estimated uncertainty (4.06 µm) and the interlaboratory comparison was satisfactory despite the difference of the acceptance criterion.