基于支持向量回归机的数控机床几何误差元素建模研究  

Research on Geometric Error Modeling of CNC Machine Tools Based on Support Vector Regression

作　　者：周恒飞 叶文华[1] 郭云霞[1] 梁睿君[1] 章婷[1] ZHOU Hengfei;YE Wenhua;GUO Yunxia;LIANG Ruijun;ZHANG Ting(College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)

机构地区：[1]南京航空航天大学机电学院

出　　处：《航空制造技术》2019年第17期50-57,共8页Aeronautical Manufacturing Technology

基　　金：国家自然科学基金(51575272)

摘　　要：针对数控机床几何误差元素建模时面临的误差样本数据少且呈非线性的问题,研究在小样本数据集非线性回归分析中具有独特优势的支持向量回归机,并基于此建立数控机床几何误差元素的预测模型。分析现有几何误差检测中常用的九线法所存在的测量选点难和计算累积误差等问题,提出增加每条测量线垂直方向直线度的测量和修正误差项计算模型的改进方法。以高斯径向基核函数为支持向量回归模型的核函数,运用交叉验证法,选取合适的模型参数,求解凸二次规划问题,进而建立几何误差元素的预测模型。以QLM27100–5X五轴龙门机床X轴为例,基于改进的九线法进行测量辨识得到几何误差样本数据,然后分别基于支持向量回归机和最小二乘法建立几何误差元素预测模型,对比两个模型的预测精度,结果显示,前者的预测均方差值MSE为0.0238,小于后者的0.072,验证了支持向量回归模型在小样本集下具有更高的预测精度。Aiming at the problem that the data samples are small and nonlinear in the modeling of geometrical error items of CNC machine tools, the SVR (support vector regression) with unique advantages in the nonlinear regression analysis of small sample data sets is studied, and based on which the geometric error prediction model of CNC machine tools is established. This paper analyzes the problems of the difficulty of measuring points and the calculation of cumulative error in the nine-line method commonly used in the detection of geometric error, and then proposes an improved method to increase the measurement of the straightness of each measurement line and the calculation model of the correction error term. The Gaussian Radial basis kernel function is chosen as the kernel function of the SVR model, and the cross-validation method is used to select the appropriate model parameters to solve the convex quadratic programming problem, and then the geometric error prediction model is established. Taking the X-axis of the QLM27100–5X five-axis gantry machine as an example, the geometric error sample data is obtained by measuring and identifying based on the improved nine-line method, and then the geometric error item prediction model is established based on the support vector regression machine and the least squares method respectively, and the prediction accuracy of the two models is compared. The results show that the predictive MSE of the former is 0.0238, which is less than 0.072 of the latter. It proves that the support vector regression model has higher predictive accuracy in small sample set.

关 键 词：支持向量回归机 数控机床 几何误差 预测模型 九线法 

分 类 号：TG659[金属学及工艺—金属切削加工及机床]