Validation and uncertainty analysis of a reduced self-calibrating method for pitch measurements of cylindrical gears

Abstract

The three-rosette method is a well-established self-calibrating error-separation method used for highly accurate pitch calibrations of cylindrical gears on coordinate measuring machines or gear measuring machines. It is based on the principle of circle closure and uses multiple measurements in different relative positions of the gear with respect to the measuring device. However, since its measurement effort is proportional to the square of the number of teeth, the method is of limited usability for gears with a large number of teeth. In this paper, a reduced method which requires much fewer measurements is described. This method is based on the same error model and is still self-calibrating. The measurement uncertainties for this method are only slightly higher than for the complete method. After an introduction to the three-rosette method, this paper describes the impact of the number and choice of the measured relative positions on the measurement uncertainty. Moreover, the problem of an erroneously determined gear axis is addressed. Finally, the effectiveness of the reduced three-rosette method is shown in intercomparison measurements with four participants. The obtained E n scores show that the reduced three-rosette method allows pitch calibrations with nearly the same accuracy as can be achieved with the complete method. The reduced three-rosette method is part of the TraCIM online service (https://tracim.ptb.de) of the Physikalisch-Technische Bundesanstalt (PTB) allowing software manufacturers or calibration laboratories to obtain a certificate for their algorithms of the reduced three-rosette method after a successfully performed software test. Moreover, calibration laboratories can receive accreditation by the German national accreditation body (DAkkS) for pitch calibrations performed by using the reduced three-rosette method.