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.

在这项工作中，准双曲面齿轮的双螺旋加工方法实现了凹面和凸面的同步切削，并且研究了齿面误差校正的问题。首先，建立了双螺旋齿轮加工的准双曲面齿轮的数学模型。其次，通过测量中心获得牙齿表面离散点的坐标，并计算出离散点的法向误差。第三，建立牙齿表面误差校正模型，并采用Levenberg-Marquard算法，信赖域策略和最小二乘法对牙齿表面误差进行校正。最后，采用信任区域策略对Levenberg-Marquard算法获得的加工参数进行了磨削实验，与最小二乘法相比，它对牙齿表面误差校正的效果更好。牙齿表面误差校正后，最大绝对误差从校正前的30.9 µm减小到6.8 µm，凹面误差的均方根从15.1减小到2.1 µm，凸面误差的均方根从10.8到1.8 µm，凹凸面的平方误差总和从15471减少到358 µm²。验证了采用信赖域策略的Levenberg-Marquard算法对双螺旋法加工的准双曲面齿轮的齿面误差校正具有良好的精度。