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Small-modulus gears, which are essential for motion transmission in precision instruments, present a measurement challenge due to their minuscule gear gaps. A high-precision measurement method under the influence of positioning errors is proposed, enabling precise evaluation of the machining quality of small-modulus gears. Firstly, a compound measurement platform for small-modulus gears is developed. Using a 3D model of the measurement system, the mathematical relationships governing motion transmission between various components are analyzed. Secondly, the formation mechanism of gear positioning error is revealed and its important influence on measurement accuracy is discussed. An optimization method for spatial coordinate transformation matrices under positioning errors of gears is proposed. Thirdly, the study focuses on small-sized gears with a modulus of 0.1 mm and a six-level accuracy. Based on the aforementioned measurement system, the tooth profile measurement points are collected in the actual workpiece coordinate system. Then, gear error parameters are extracted based on the established models for tooth profile deviation and pitch deviation. Finally, the accuracy and effectiveness of the proposed measurement method are verified by comparing the measurement results of the P26 gear measuring center.
Niu et al. (Wed,) studied this question.