基于NURBS曲线拟合的渐开线圆柱齿轮齿形偏差计算  

Calculation of Tooth Profile Deviation of Involute Cylindrical Gear Based on NURBS Curve Fitting

作　　者：晏婷 杨光永[1] 于元滐 戈一航 徐天奇[1] YAN Ting;YANG Guangyong;YU Yuanjie;GE Yihang;XU Tianqi(School of Electrical Information Engineering,Yunnan Minzu University,Kunming 650500)

机构地区：[1]云南民族大学电气信息工程学院,昆明650500

出　　处：《计算机与数字工程》2024年第2期332-336,共5页Computer & Digital Engineering

摘　　要：为了提高现有齿轮齿廓曲线的拟合精度,针对现有的齿形偏差计算方法,提出了一种基于非均匀有理B样条(NURBS)曲线拟合的渐开线圆柱齿轮齿形偏差计算方法。首先,建立渐开线圆柱齿轮齿形误差的理论数学模型,然后根据NURBS曲线拟合原理和三坐标测量机测量的齿廓坐标点,用Matlab编程实现了NURBS曲线对实际齿廓曲线的拟合,结合渐开线等效拟合法,计算出了齿轮的齿形偏差。拟合结果表明,与最小二乘法(LS)的拟合结果对比,NURBS曲线拟合齿廓曲线精度更高,误差小,具有良好的拟合效果。齿形偏差计算结果表明,采用的基于NURBS曲线拟合的齿形偏差与实测值一致,表明该方法准确、有效。In order to improve the fitting accuracy of the existing gear profile curve,aiming at the existing tooth profile deviation calculation methods,a tooth profile deviation calculation method of involute cylindrical gear based on NURBS curve fitting is adopted.Firstly,the theoretical mathematical model of tooth profile error of involute cylindrical gear is established.Then,according to the NURBS curve fitting principle and the tooth profile coordinate points measured by CMM,the fitting of actual tooth profile curve and theoretical tooth profile curve is realized by Matlab programming.Combined with the involute equivalent fitting method,the tooth profile deviation of gear is calculated.The fitting results show that NURBS curve has high precision,small error and good fitting effect.The calculation results of tooth profile deviation show that the tooth profile deviation based on NURBS curve fitting is consistent with the measured values,which shows that this method is accurate and effective.

关 键 词：渐开线齿轮 NURBS曲线拟合 齿形偏差 三坐标测量机 

分 类 号：O141.4[理学—数学]