A novel mathematical model for the accurate measurement of face gears by considering the geometric deviations of multiple teeth

In contact coordinate measurement, measurement error sources would affect the establishment of the workpiece coordinate system (WCS) and the exact measurement for the points on the complicated surfaces. This issue would be more complicated for face gears with complex features, especially when having huge machining errors. To address the above problem, this paper proposes a novel precise mathematical model to measure face gears for the geometric deviations of multiple teeth, including the deviations of tooth surfaces, pitch, and tooth thickness. An iterative method is presented to establish the WCS on machines by considering multiple reference points on different teeth. Subsequently, the correction model of measured points is established, and the sensitivity analysis is conducted. Further, a multi-objective optimization is proposed to comprehensively compensate for measurement errors, and the algorithm is given. The experiment of a face gear with huge overcut tooth surfaces validates the proposed method is effective and robust.