Tooth surface error correction of hypoid gears machined by duplex helical method

Abstract

In this work, synchronous cutting of concave and convex surfaces was achieved using the duplex helical method for the hypoid gear, and the problem of tooth surface error correction was studied. First, the mathematical model of the hypoid gears machined by the duplex helical method was established. Second, the coordinates of discrete points on the tooth surface were obtained by measurement center, and the normal errors of the discrete points were calculated. Third, a tooth surface error correction model is established, and the tooth surface error was corrected using the Levenberg-Marquard algorithm with trust region strategy and least square method. Finally, grinding experiments were carried out on the machining parameters obtained by Levenberg-Marquard algorithm with trust region strategy, which had a better effect on tooth surface error correction than the least square method. After the tooth surface error is corrected, the maximum absolute error is reduced from 30.9 µm before correction to 6.8 µm, the root mean square of the concave error is reduced from 15.1 to 2.1 µm, the root mean square of the convex error is reduced from 10.8 to 1.8 µm, and the sum of squared errors of the concave and convex surfaces was reduced from 15471 to 358 µm². It is verified that the Levenberg-Marquard algorithm with trust region strategy has a good accuracy for the tooth surface error correction of hypoid gear machined by duplex helical method.

Keywords

duplex helical method / hypoid gear / error measurement / Levenberg-Marquard algorithm with trust region strategy / correction of tooth surface error

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