计量学报2025，Vol.46Issue(9)：1371-1376,6.DOI:10.3969/j.issn.1000-1158.2025.09.18
标准渐开线的单圆弧最佳拟合方法
The Optimal Fitting Method of Standard Involute Using Single Arc
摘要
Abstract
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 23.0 µm.The unconstrained least squares method improves the accuracy with a peak-to-peak value of 19.9 µm.The approximately equal peak-valley least squares method yields the best performance with a peak-to-peak value of 18.3 µm and the most balanced distribution of positive and negative deviations.This method is suitable for high-precision applications requiring consistent deviation control.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Key words
geometric measurement/involute profile/arc fitting/least squares method/constraint conditions/fitting deviation分类
通用工业技术引用本文复制引用
王家平,林虎,石照耀,杨国梁..标准渐开线的单圆弧最佳拟合方法[J].计量学报,2025,46(9):1371-1376,6.基金项目
国家自然科学基金(52227809) （52227809）
