基于梯度下降算法的空间直线度误差评定  

Evaluation of Spatial Straightness Error Based on Gradient Descent Algorithm

作　　者：尹忠伟 于大国[1,2] 李梦龙 王健 Yin Zhongwei;Yu Daguo;Li Menglong;Wang Jian(School of Mechanical Engineering,North University of China,Taiyuan 030051,China;不详)

机构地区：[1]中北大学机械工程学院 [2]山西省深孔加工工程技术研究中心

出　　处：《工具技术》2021年第12期127-130,共4页Tool Engineering

基　　金：国家自然科学基金(51875532);山西省回国留学人员科研资助项目(HGKY2019065);中北大学德州研究生分院基金(2020004JJ)。

摘　　要：针对空间直线度误差评定问题,采用梯度下降算法对深孔直线度误差评定、坐标系旋转、测量点投影和最小覆盖圆等进行研究。引入被测零件测量点数据,基于梯度下降算法建立数学模型,求出拟合直线的方向向量,并根据方向向量与投影面夹角、投影面投影线与坐标轴夹角对测点坐标进行坐标转换,将空间直线度问题转换为平面最小包容区域。采用MATLAB软件编写相应程序,运用该程序对空间直线度误差进行实例计算,将计算结果与其它直线度误差评定算法进行对比,得出以下结论:梯度下降算法应用于深孔直线度检测,对测点数据进行计算处理可以得到精度较高的直线度误差,适用于对精度要求较高的场合。Aiming at the problem of spatial straightness error evaluation,the gradient descent algorithm is applied to deep hole straightness error evaluation,coordinate system rotation,measurement point projection,minimum coverage circle and other aspects.The measurement point data of the measured part is introduced,a mathematical model based on the gradient descent algorithm is established,and the direction vector of the fitted line is calculated.According to the angle between the direction vector and the projection plane,and the angle between the projection line of the projection plane and the coordinate axis,the coordinates of the measurement points are transformed.The problem of spatial straightness is converted into the problem of the plane minimum containment area.The spatial straightness error is calculated by MATLAB,and the calculation result is compared with other straightness error evaluation algorithms.The results show that the gradient descent algorithm is applied to the straightness detection of deep holes,and the measured point data is calculated and the straightness error with higher precision is obtained,which is suitable for occasions requiring high precision.

关 键 词：空间直线度 梯度下降算法 坐标系转换 深孔 

分 类 号：TH124[机械工程—机械设计及理论]