摘要
为提高标准渐开线齿廓的拟合精度,提出一种基于最小二乘法的单圆弧最佳拟合方法。以标准渐开线二维方程为基础,推导出以拟合圆正交距离和渐开线正交距离2种表征拟合偏差的表达式,并提出无约束平方和最小准则与波峰波谷近似相等平方和最小准则2种判定方法。实验中将3点快速拟合法、无约束平方和最小拟合法及波峰波谷近似相等平方和最小拟合法进行对比发现:3点快速拟合法峰峰值23.0μm,拟合精度较低;无约束平方和最小准则拟合法峰峰值为19.9μm,拟合精度有所提升;波峰波谷近似相等平方和最小准则拟合法最优,峰峰值18.3μm,且正负偏差分布最为均衡,适用于高精度且需控制偏差一致性的场景。
To improve the fitting accuracy of the standard involute profile,a best-fit method based on the least squares approach using a single circular arc is proposed.Based on the two-dimensional equation of the standard involute,expressions for fitting deviation characterized by the orthogonal distance to the fitting arc and the orthogonal distance to the involute are derived.Two evaluation criteria are introduced:the unconstrained least squares criterion and the approximately equal peak-valley squared error minimization criterion.In experiments,the three-point rapid fitting method,the unconstrained least squares fitting method,and the approximately equal peak-valley least squares fitting method are compared.The results show that the three-point rapid fitting method has the lowest fitting accuracy with a peak-to-peak value of 23.0µm.The unconstrained least squares method improves the accuracy with a peak-to-peak value of 19.9µm.The approximately equal peak-valley least squares method yields the best performance with a peak-to-peak value of 18.3µm and the most balanced distribution of positive and negative deviations.This method is suitable for high-precision applications requiring consistent deviation control.
作者
王家平
林虎
石照耀
杨国梁
WANG Jiaping;LIN Hu;SHI Zhaoyao;YANG Guoliang(College of Mechanical and Electrical Engineering,China University of Mining and Technology(Beijing),Beijing 100083,China;Beijing Engineering Research Center of Precision Measurement Technology and Instruments,Beijing University of Technology,Beijing 100124,China;National Institute of Metrology,Beijing 100029,China)
出处
《计量学报》
北大核心
2025年第9期1371-1376,共6页
Acta Metrologica Sinica
基金
国家自然科学基金(52227809)。
关键词
几何量计量
渐开线齿廓
圆弧拟合
最小二乘法
约束条件
拟合偏差
geometric measurement
involute profile
arc fitting
least squares method
constraint conditions
fitting deviation
作者简介
第一作者:王家平(1998-),男,山东东营人,中国矿业大学(北京)机械与电气工程学院在读研究生,研究方向为精密测量技术与仪器。Email:739255606@qq.com;通讯作者:林虎(1984-),男,广西陆川人,中国计量科学研究院副研究员,主要从事齿轮计量等方面研究。Email:linhu@nim.ac.cn。
