Journal of Jilin University(Engineering and Technology Edition) ›› 2024, Vol. 54 ›› Issue (8): 2149-2155.doi: 10.13229/j.cnki.jdxbgxb.20221359

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Thermal expansion error modeling of feed axis based on principal component regression

Lin JIANG1,2(),Guo-long LI1(),Shi-long WANG1,Kai XU3,Zhe-yu LI1   

  1. 1.College of Mechanical and Vehicle Engineering，Chongqing University，Chongqing 400044，China
    2.Chongqing Machine Tool （group） Co. ，Ltd. ，Chongqing，401300
    3.College of Mechanical Engineering，Chongqing University of Techology，Chongqing 400054，China
  • Received:2022-10-24 Online:2024-08-01 Published:2024-08-30
  • Contact: Guo-long LI E-mail:jianglin@chmti.com;glli@cqu.edu.cn

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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

CLC Number: 

  • TH161

Fig.1

Thermal error modeling process based on temperature sensitive point screening"

Fig.2

Measurement of linear positioning error of the X-axis"

Fig. 3

Installation locations of the temperature sensor"

Fig. 4

Temperature change in Experiment 1"

Fig. 5

Fitting result of the positioning error of X-axis"

Fig. 6

Change curve of thermal expansion slope of X-axis"

Fig.7

Thermal expansion slope prediction results of Experiment 4"

Fig.8

Thermal expansion slope prediction error of Experiment 4"

Table 1

Performance index of prediction results in Experiment 4"

方法RMSEMAE最大残差
FCM-MLR4.54.36.8
FCM-SVR4.03.76.0
PCR1.71.52.8

Table 2

Setting of modeling group and prediction group"

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

Table 3

Selection results of temperature sensitive points"

预测聚类数
234
#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｝

Table 4

RMSE of prediction results"

组聚类数2聚类数3聚类数4PCR
FCM-MLRFCM-SVRFCM-MLRFCM-SVRFCM-MLRFCM-SVR
#16.71.60.71.20.71.31.3
#24.45.25.05.31.75.83.4
#312.62.87.35.37.73.01.8
#49.93.84.54.02.84.61.7
均值8.43.44.44.03.23.72.0
标准差3.61.52.71.93.12.00.9
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