Efficient Multiple-Measurement Technique for Rotationally Symmetric Measurands

Gears are key elements of power transmission systems, and the inspection of their pitch deviation is one of the most important tests done on gears. The specifications of gears are assessed using gear measuring instruments (GMIs) or coordinate measuring machines (CMMs), and the results of the measurements must be validated under an appropriate traceability system. In the traceability system, calibrated gauges whose measuring uncertainties are estimated are necessary. In the case of pitch deviation measurement, special artefacts or gears manufactured with high dimensional accuracy are used as reference gauges. As a calibration method for the pitch deviation standards, authors have proposed themethod based on themultiplemeasurement technique and uncertainty evaluation with analysis of variance (ANOVA). The proposed method performs the accurate calibration for the rotationally symmetric measurands such as pitch deviations; however, the total number of measurements for the calibration tend to be large. In this paper, authors propose a technique for reducing the number of trials based on the symmetry of the measurement for the multiple-measurement technique. First, the evaluation of rotationally symmetric measurands using a multiple-measurement technique and the estimation of its uncertainty based on the analysis of variance are formulated. Second, a technique for reducing the number of measurement trials based on the symmetry of the measurement is discussed. Finally, the proposed calibration method is validated through experiments.