Research on Tooth Profile Error of Non-circular Gears Based on Complex Surface Theory

In view of the complex shape and structure of non-circular gears, it is difficult to measure the machining errors of non-circular gears, and the complex surface theory is proposed to measure the errors. Firstly, the Euclidean transformation matrix is used to establish the error evaluation function, and the scanner is used to digitally scan the non-circular gears, collect the coordinates of the data points on the tooth surface. Then, the non-uniform rational B-spline function is used to accurately describe the tooth surface and reconstruct the tooth surface. Finally, the theoretical data are matched with the reconstructed tooth surface by coordinate transformation to calculate the tooth surface error. The feasibility of the proposed algorithm is proved by a calculation example, which provides a reference for further accurate detection of the non-circular gear tooth surface error.