In adaptive machining of near-net-shape formed parts

traditional registration algorithms cannot effectively constrain the form and position tolerances. To solve this problem

a registration algorithm with multiple tolerance constraints is proposed based on the satisfaction function and gray correlation

in which the balance relationship among different tolerances is converted to a multi-objective co-optimization problem. Firstly

evaluation method and representation form of each tolerance of the part are determined. The deviation of the measured data from the theoretical model is regarded as a margin in solving of profile tolerance. Then deviation of each tolerance is evaluated by the satisfaction function

and correlation degrees among different tolerances are calculated based on the gray correlation theory. At last

a solution function with non-linear least squares form under constraints is constructed with the Lagrange method. Parameters of rigid transformation are solved with the BFGS algorithm (Broyden

Fletcher

Goldfarb

Shanno algorithm). Finally

the proposed algorithm is verified on a precision forged blade. The result shows that the qualification rate of profile tolerance increases from 96.86% to 99.40%.