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.

摘要

本文研究了双重螺旋法同步切削准双曲面齿轮凹凸两面的齿面误差修正问题。首先, 建立了双重螺旋法切削准双曲面齿轮的数学模型;其次, 通过测量中心得到齿面离散点的坐标, 计算离散点的法向误差;第三, 建立了齿面误差修正模型, 并采用含信赖域策略的Levenberg-Marquard 算法和最小二乘法对齿面误差进行修正;最后, 利用对齿面误差的修正效果更好的含信赖域策略的Levenberg-Marquard 算法得到的加工参数对齿面进行磨削实验。实验结果表明, 对齿面误差进行修正后, 最大绝对误差从初始的30.9 µm 降低为6.8 µm, 凹面误差均方根从初始的15.1 µm 降低为2.1 µm, 凸面误差均方根从10.8 µm 降低为1.8 µm, 凹凸两面误差平方和从初始的15471 µm2 降低为358 µm2。验证了含信赖域策略的Levenberg-Marquard 算法对双螺旋法切削准双曲面齿轮的齿面误差修正具有良好的精度。