批量弧齿锥齿轮热处理变形齿面偏差的自助法统计模型

Bootstrap Statistical Model of Tooth Surface Deviation of Heat Treatment Deformation of Batch Spiral Bevel Gears

针对齿轮材料、数控铣齿方法和热处理规范均相同的同一批次的弧齿锥齿轮,基于自助法对少量齿面偏差样本数据进行自助再抽样,得到大量的样本数据,建立了批量弧齿锥齿轮齿面偏差的自助法统计模型;计算了齿面测量顺序点的概率特征值,利用k-s检验了其是否符合正态分布,并选取估计真值、估计区间等参数,描述了其统计规律和结果;通过三次NURBS曲面拟合方法,得到了整批次齿面偏差变化规律,实现了整批次齿面精度的有效评价。该自助法统计模型为指导齿面加工参数修正和高效稳定生产提供了理论依据。

Aiming at the same batch of spiral bevel gears with the same gear material,NC milling method and heat treatment specification,a bootstrap resampling is carried out on a small number of tooth surface devia⁃tion sample data based on the bootstrap method,a large number of sample data are obtained and a bootstrap sta⁃tistical model of batch spiral bevel gear tooth surface deviation is established;the probability characteristic val⁃ue of the sequential points of tooth surface measurement is calculated,and whether they conform to the normal distribution is tested by k-s;the estimated true value,estimated interval and other parameters are selected to describe their statistical laws and results;through the cubic NURBS surface fitting method,the variation law of the tooth surface deviation of the whole batch is obtained,and the effective evaluation of the tooth surface accu⁃racy of the whole batch is realized.The bootstrap statistical model provides a theoretical basis for guiding the modification of tooth surface processing parameters and efficient and stable production.