基于刀倾法的螺旋锥齿轮齿面误差修正算法研究

摘要

针对螺旋锥齿轮齿面偏差识别方程的特点及采用最小二乘法求解此方程的不足,提出采用截断奇异值分解(TSVD)法与L曲线法进行求解,并且将此方法和最小二乘法进行了比较.研究表明:对小轮凹面,采用TSVD法与L曲线法,方程求解误差为0.051 571,而采用最小二乘法,方程求解误差为0.895 63;对小轮凸面,采用TSVD法与L曲线法,方程求解误差为0.043 882,而采用最小二乘法,方程求解误差为0.353 76.采用TSVD法与L曲线法求解此齿面偏差识别方程更精确,且得到的解都有意义.%According to the characteristics of the tooth surface deviation identification model of spiral bevel gear and defects of the least squares method solving, TSVD and the L curve method were proposed. The identification equation was solved to use TSVD and the L curve method and the least squares method separately. The research results show, to the concave, using TSVD and the L curve method, the equation solution error is 0. 051 571, but using the least squares method, the equation solution error will be 0.895 63; to the convex, using TSVD and the L curve method, the equation solution error is 0.043 882, but using the least squares method, the equation solution error will be 0. 353 76. Using TSVD and the L curve method this tooth surface deviation identification equation is solved more precisely, and the obtained solutions are meaningful.