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| A Registration Algorithm With Multiple Tolerance Constraints Based on Satisfaction Function and Gray Correlation |
| LU Zhengxin 1 , LIANG Yongshou 1 , CHU Yasong 2 , REN Junxue 1 |
1. Key Laboratory of High Performance Manufacturing for Aero Engine, Ministry of Industry and Information Technology, Northwestern Polytechnical University, Xi’an 710072, China;
2. Beijing Power Machinery Institute, Beijing 100074, China |
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Abstract 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%.
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2022, 
