Abstract: When measuring non-circular gears, it will encounter problems such as mutual coupling of coordinate system error and processing error, many noise points, low measurement efficiency, etc. In order to detect the true condition of the tooth surface, it is necessary to plan measurements of the theoretical tooth surface and to establish a measuring coordinate system. Accordingly, a mathematical model is established based on the relationship between the measurement coordinate system and design coordinate system, which is optimized and solved. At the same time, a mathematical model is established for the relationship between the measurement point and the theoretical point. It also analyses the effect of measurement error on the detection results and compensates the measurement error. Further, the accuracy of this error detection method is verified by coordinate measuring machine error detection experiments. The results show that the degree of mesh distortion of this method is reduced by 15.6% and 6.6% compared to the conventional and unconstrained methods, respectively, thus indicating its correctness and effectiveness.

Key words: non-circular gear, coordinate measuring machine, tooth surface error, measuring coordinate system, error compensation