In-process error compensation for tooth form grinding works - (robust error estimation algorithm against the measuring error and experimental result of the in-process grinding error compensation)

Robust error compensation algorithm for tooth furor grinding works of an involute spur gear is proposed. The proposed algorithm is insensitive for the measurement error of the tooth form profile data. Relationship between indirect measurement quantity; the grinding error and direct measurement quantity; the tooth profile data are expressed by an implicit function. Error propagation analysis for the implicit model is derived using implicit derivative of the model function. Error ellipsoid of the indirect measurement quantity, which expresses the projection of the error hyper sphere of the direct measurement quantity, is defined. By taking the structural restrictions of the grinding error model into the least square calculation of the error estimation, the primary axis length of the error ellipsoid became smaller, which means the algorithm became more insensitive fur the measuring error. Proposed algorithm was implemented on an in-process measuring system with personal computer. Accurate grinding error compensation was confirmed by experimental results.