基于温度特征提取的数控机床热误差建模
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摘要
在数控机床的热误差补偿技术中,机床温度信息的提取对改善机床的加工精度至关重要。首先对广泛使用的模糊聚类多元线性回归模型在变工况下的性能进行了试验,结果证明:试验工况变化后,该模型预测值失准。通过方差膨胀因子判断,这种现象是由模型自变量的复共线性引起。为了改进上述模型,提出了一种温度特征提取的建模方法,通过特征提取算法,提取模糊聚类优化测点的综合特征,从而得到综合特征自变量,最后利用综合自变量进行回归建模。试验表明,该方法有效消除了复共线性对模型预测精度和鲁棒性的影响,优化后的回归模型均方根误差在4μm以内,可有效预测76%以上误差,相较于其他方法表现出优良的预测性能,易于在其他机床热误差补偿中推广使用。
In thermal error compensation technology on CNC machine tool,it is crucial for improving the accuracy of machine to extract temperature information. Firstly,analyzing the performance of popular model whose temperature point is optimized by fuzzy clustering when operating condition varied. The analysis shows the difference of the operating conditions leads to poor forecast performance of the model. Further analysis shows the poor performance is resulted from multi-collinearity. For the sake of improving the model,a method of optimizing independent variables is proposed. Through a feature extraction algorithm,the method obtains comprehensive feature variables which are extracted from temperature points optimized by fuzzy clustering. Finally,the comprehensive variables are utilized to establish a multiple linear regression model. The experiment results indicated that the proposed method effectively eliminated the influence of multi-collinearity on the accuracy and robustness of the model. The root mean square error of the optimized model was within 4 μm and can forecast over 76 % thermal errors. The method shows a superior performance comparing with other methods and is easier to be applied widely to thermal error modeling of other CNC machine tool.
In thermal error compensation technology on CNC machine tool,it is crucial for improving the accuracy of machine to extract temperature information. Firstly,analyzing the performance of popular model whose temperature point is optimized by fuzzy clustering when operating condition varied. The analysis shows the difference of the operating conditions leads to poor forecast performance of the model. Further analysis shows the poor performance is resulted from multi-collinearity. For the sake of improving the model,a method of optimizing independent variables is proposed. Through a feature extraction algorithm,the method obtains comprehensive feature variables which are extracted from temperature points optimized by fuzzy clustering. Finally,the comprehensive variables are utilized to establish a multiple linear regression model. The experiment results indicated that the proposed method effectively eliminated the influence of multi-collinearity on the accuracy and robustness of the model. The root mean square error of the optimized model was within 4 μm and can forecast over 76 % thermal errors. The method shows a superior performance comparing with other methods and is easier to be applied widely to thermal error modeling of other CNC machine tool.
引文
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[8]魏弦,吴继忠,王允威.数控机床进给系统误差综合补偿[J].现代制造工程,2016(10):1-5.
[9]高峰,刘江,杨新刚,等.基于Fisher最优分割法的机床热关键点优化研究[J].仪器仪表学报,2013(5):1070-1075.
[10]ATTIA M H,FRASER S.A generalized modelling methodology for optimized real-time compensation of thermal deformation of machine tools and CMM structures[J].International Journal of Machine Tools and Manufacture,1999,39(6):1001-1016.
[11]LI Y X,YANG J G,GELVIS T,et al.Optimization of measuring points for machine tool thermal error based on grey system theory[J].The International Journal of Advanced Manufacturing Technology,2008,35(7/8):745-750.
[12]张毅,杨建国.基于灰色理论预处理的神经网络机床热误差建模[J].机械工程学报,2011,47(7):134-139.
[13]YANG H,NI J.Adaptive model estimation of machine-tool thermal errors based on recursive dynamic modeling strategy[J].International Journal of Machine Tools and Manufacture,2005,45(1):1-11.
[14]BEZDEK J C.Numerical taxonomy with fuzzy sets[J].Journal of Mathematical Biology,1974,1(1):57-71.
[15]BEZDEK J C.Cluster validity with fuzzy sets[J].Journal of Cybernetics,1973,3(3):58-73.
[16]余文利,姚鑫骅,傅建中,等.贝叶斯证据框架下的LSSVM多工况数控机床热误差建模[J].中国机械工程,2014(17):2361-2368.
[2]RAMESH R.Error compensation in machine tools—a review Part II:thermal errors[J].International Journal of Machine Tools and Manufacture,2000,40(9):1257-1284.
[3]MIAO E,LIU Y,LIU H,et al.Study on the effects of changes in temperature-sensitive points on thermal error compensation model for CNC machine tool[J].International Journal of Machine Tools and Manufacture,2015,97(6):50-59.
[4]MAYR J,JEDRZEJEWSKI J,UHLMANN E,et al.Thermal issues in machine tools[J].CIRP Annals-Manufacturing Technology,2012,61(2):771-791.
[5]李艳,李英浩,高峰,等.基于互信息法和改进模糊聚类的温度测点优化[J].仪器仪表学报,2015(11):2466-2472.
[6]ABDULSHAHED A M,LONGSTAFF A P,FLETCHER S.The application of ANFIS prediction models for thermal error compensation on CNC machine tools[J].Applied Soft Computing,2015(27):158-168.
[7]魏弦,高峰,李艳,等.龙门机床进给系统热误差模型关键点优化[J].仪器仪表学报,2016,37(6):1340-1346.
[8]魏弦,吴继忠,王允威.数控机床进给系统误差综合补偿[J].现代制造工程,2016(10):1-5.
[9]高峰,刘江,杨新刚,等.基于Fisher最优分割法的机床热关键点优化研究[J].仪器仪表学报,2013(5):1070-1075.
[10]ATTIA M H,FRASER S.A generalized modelling methodology for optimized real-time compensation of thermal deformation of machine tools and CMM structures[J].International Journal of Machine Tools and Manufacture,1999,39(6):1001-1016.
[11]LI Y X,YANG J G,GELVIS T,et al.Optimization of measuring points for machine tool thermal error based on grey system theory[J].The International Journal of Advanced Manufacturing Technology,2008,35(7/8):745-750.
[12]张毅,杨建国.基于灰色理论预处理的神经网络机床热误差建模[J].机械工程学报,2011,47(7):134-139.
[13]YANG H,NI J.Adaptive model estimation of machine-tool thermal errors based on recursive dynamic modeling strategy[J].International Journal of Machine Tools and Manufacture,2005,45(1):1-11.
[14]BEZDEK J C.Numerical taxonomy with fuzzy sets[J].Journal of Mathematical Biology,1974,1(1):57-71.
[15]BEZDEK J C.Cluster validity with fuzzy sets[J].Journal of Cybernetics,1973,3(3):58-73.
[16]余文利,姚鑫骅,傅建中,等.贝叶斯证据框架下的LSSVM多工况数控机床热误差建模[J].中国机械工程,2014(17):2361-2368.