基于移动最小二乘法的渐开线齿轮齿廓曲线拟合方法

摘要

针对现有渐开线齿轮齿廓曲线拟合方法精度不高的缺点，提出了一种用移动最小二乘法（MLS）拟合齿廓曲线的新方法，并通过齿距偏差的计算对该方法进行了实例验证。利用三坐标测量机对某齿轮进行测量，得到齿廓数据点和齿距偏差；根据移动最小二乘法原理和实验数据，用 MATLAB编程实现了齿廓曲线的拟合；根据拟合结果，利用图解法计算出了左齿廓齿距偏差。与最小二乘法（LS）的拟合结果的对比表明，用移动最小二乘法拟合齿廓曲线精度更高，误差更小，具有良好的拟合效果。齿距偏差计算结果表明，单个齿距偏差和齿距累积偏差与实测值一致，表明该方法准确、有效。研究结果可为齿廓曲线的拟合和齿距偏差的计算提供参考。%Aiming at the problem of low precision for fitting method of profile curve of involutegears ,the MLS was used to fit tooth profile curve and was validated by an example about the calculationof pitch deviation .At the beginning ,CMM was used to measure a gear and the measured data aswell as the pitch deviation were exported after the test .And then ,with the principle of MLS methodand the measured data ,the profile curve was obtained by MATLAB .At last ,the MLS fitting methodwas used to fit the profile curve .By contrasting with the fitting results of least square ,MLS methodused to fit profile curve can get higher precision and smaller error .The calculation results of toothpitch deviation show that :both the individual circular pitch errors and the total cumulative pitch errorsagree with the experimental ones ,and the MLS method has been proved to be accurate and efficient ,which can provide a kind of beneficial reference for the calculation of tooth pitch deviation and fittingof tooth profile curves .