基于主成分回归的进给轴热膨胀误差建模

doi:10.13229/j.cnki.jdxbgxb.20221359

摘要/Abstract

摘要：

为进一步提高磨齿机进给轴热误差模型的预测精度，本文提出了基于主成分回归的进给轴热膨胀误差建模方法。通过线性拟合对进给轴定位误差解耦得到热膨胀斜率参数，消除进给轴热膨胀误差的位置相关性，并基于主成分回归算法建立了热膨胀斜率参数与全部测点温度的回归模型。区别于传统方法，主成分回归模型无须进行额外的温度敏感点筛选，分组实验预测结果的均方根误差均值和标准差可达到2.0 μm/m、0.9 μm/m，具有更高的精度和稳定性。

关键词: 机械工程, 进给轴, 热膨胀, 主成分, 斜率参数

Abstract:

To further improve the prediction accuracy of the thermal error model of the feed axis of the gear grinding machine， a thermal expansion modeling method of the feed axis based on principal component regression is proposed in this paper. The slope parameter of thermal expansion is obtained by decoupling the positioning error of the feed axis through a linear fitting， which eliminates the position correlation between the thermal expansion error and the position of feed axis. The regression model between the thermal expansion slope and all the temperature points is established using the principal component regression algorithm. Different from the traditional methods， the principal component regression model does not need additional screening of temperature sensitive points， and the mean value and standard deviation of the root means square errors of the prediction results can reach 2.0 μm/m、0.9 μm/m， which has higher accuracy and stability than conventional methods.

Key words: mechanical engineering, feed axis, thermal expansion, principal components, slope parameter

中图分类号:

TH161

蒋林,李国龙,王时龙,徐凯,李喆裕. 基于主成分回归的进给轴热膨胀误差建模[J]. 吉林大学学报(工学版), 2024, 54(8): 2149-2155.

Lin JIANG,Guo-long LI,Shi-long WANG,Kai XU,Zhe-yu LI. Thermal expansion error modeling of feed axis based on principal component regression[J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(8): 2149-2155.

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方法	RMSE	MAE	最大残差
FCM-MLR	4.5	4.3	6.8
FCM-SVR	4.0	3.7	6.0
PCR	1.7	1.5	2.8

组	建模组	预测组
#1	实验二、三、四	实验一
#2	实验一、三、四	实验二
#3	实验一、二、四	实验三
#4	实验一、二、三	实验四

预测	聚类数
预测	2	3	4
#1	｛T6， T11｝	｛T1， T11， T12｝	｛T1， T9， T11， T12｝
#2	｛T11， T12｝	｛T5， T6， T12｝	｛T5， T6， T9， T12｝
#3	｛T6， T11｝	｛T1， T11， T12｝	｛T1， T9， T11， T12｝
#4	｛T6， T12｝	｛T1， T6， T12｝	｛T1， T6， T7， T12｝

组	聚类数2		聚类数3		聚类数4		PCR
组	FCM-MLR	FCM-SVR	FCM-MLR	FCM-SVR	FCM-MLR	FCM-SVR	PCR
#1	6.7	1.6	0.7	1.2	0.7	1.3	1.3
#2	4.4	5.2	5.0	5.3	1.7	5.8	3.4
#3	12.6	2.8	7.3	5.3	7.7	3.0	1.8
#4	9.9	3.8	4.5	4.0	2.8	4.6	1.7
均值	8.4	3.4	4.4	4.0	3.2	3.7	2.0
标准差	3.6	1.5	2.7	1.9	3.1	2.0	0.9