基于互信息法和改进模糊聚类的温度测点优化
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摘要
基于热误差模型进行机床热误差补偿是保证数控机床加工精度的一种有效方法,温度测点的布置和辨识会直接影响热误差建模的精确性和鲁棒性。本文提出一种互信息和改进模糊聚类法相结合的机床热关键点优化方法。以机床不同位置处的多个测点温度值及工件热变形作为分析数据,通过计算温度变量与热变形之间的平均互信息量,获得其综合关联度矩阵,确定二者之间的相关性后初选温度变量。根据改进模糊聚类法、F统计量和复判定系数对初选的温测点进行聚类,并结合温度变量与热变形之间的综合关联度值提取机床热关键点,从而实现测点优化。将基于该方法所得到的热误差模型与采用变量分组优化法获得的热误差模型进行比较,结果显示采用该方法进行热误差建模,机床X轴和Y轴的热变形预测精度得到显著提高,有利于改善加工精度。
Thermal error modeling is an effective method to ensure the machining accuracy of NC machine tool thermal error using thermal error compensation,whose accuracy and robustness are directly affected by the arrangement and identification of the temperature measuring points. A new method combining mutual information and improved fuzzy clustering is presented to optimize the thermal key points of the machine tool. All temperature measuring points of the machine and thermal deformation of the workpiece are employed as analysis data,and their average mutual information is calculated to obtain their comprehensive correlative matrix and determine the correlation between them. The temperature variables are optimized. After that,the thermal key points are determined with comprehensive correlative matrix by combining the temperature variables clustered based on the improved fuzzy clustering method,the F-statistic and complex coefficient. The established thermal error model based on the method is compared with that built from the temperature key points selected using variable grouping optimization. The results show that the thermal error model is more accurate by which the prediction accuracy of thermal deformation along X axis and Y axis is greatly increased,which shows that the method is more feasible and practicable to improve the machining precision of NC machine tool.
Thermal error modeling is an effective method to ensure the machining accuracy of NC machine tool thermal error using thermal error compensation,whose accuracy and robustness are directly affected by the arrangement and identification of the temperature measuring points. A new method combining mutual information and improved fuzzy clustering is presented to optimize the thermal key points of the machine tool. All temperature measuring points of the machine and thermal deformation of the workpiece are employed as analysis data,and their average mutual information is calculated to obtain their comprehensive correlative matrix and determine the correlation between them. The temperature variables are optimized. After that,the thermal key points are determined with comprehensive correlative matrix by combining the temperature variables clustered based on the improved fuzzy clustering method,the F-statistic and complex coefficient. The established thermal error model based on the method is compared with that built from the temperature key points selected using variable grouping optimization. The results show that the thermal error model is more accurate by which the prediction accuracy of thermal deformation along X axis and Y axis is greatly increased,which shows that the method is more feasible and practicable to improve the machining precision of NC machine tool.
引文
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[16]王时龙,杨勇,周杰,等.大型数控滚齿机热误差补偿建模[J].中南大学学报,2011,42(10):3066-3072.WANG SH L,YANG Y,ZHOU J,et al.Modeling of thermal error compensation of large-scale numerical control gear hobbing machine[J].Journal of Central South University,2011,42(10):3066-3072.
[2]YANG S,YUAN J,NI J.Accuracy enhancement of a horizontal machining center by real-time error compensation[J].Journal of Manufacturing Systems,1996,15(2):113-124.
[3]YANG J G,YUAN J X,NI J.Thermal error mode analysis and robust modeling for error compensation on a CNC turning center[J].International Journal of Machine Tools and Manufacture,1999,39(9):1367-1381.
[4]范金梅,徐黎明,赵晓明,等.机床热误差补偿中温度传感器布置策略的研究[J].仪器仪表学报,2005,26(8):963-964.FAN J M,XU L M,ZHAO X M,et al.Sensor placement strategy for thermal error compensation on machine tools[J].Chinese Journal of Scientific Instrument,2 0 0 5,2 6(8):9 6 3-9 6 4.
[5]CREIGHTON E,HONEGGER A,TULSIAN A.Analysis of thermal errors in a high-speed micromilling spindle[J].International Journal of Machine Tools and Manufacture,2 0 1 0,5 0(4):3 8 6-3 9 3.
[6]高峰,刘江,李艳,等.基于Kohonen自组织竞争网络的机床温度测点辨识研究[J].中国机械工程,2014,25(7):862-866.GAO F,LIU J,LI Y,et al.Identification of temperature measuring points for machine tools with kohonen self-organizing competitive network[J].China Mechanical Engineering,2014,25(7):862-866.
[7]郑学刚,赵宇,吴洪涛.机床热误差建模及检测系统模块设计[J].电子测量与仪器学报,2009,23(9):74-78.ZHENG X G,ZHAO Y,WU H T.Thermal error modeling and detection system module design in machine tools[J].Journal of Electronic Measurement and Instrument,2009,23(9):74-78.
[8]杨建国,邓卫国,任永强,等.机床热补偿中温度变量分组优化建模[J].中国机械工程,2004,15(6):478-481.YANG J G,DENG W G,REN Y Q,et al.Grouping optimization modeling by selection of temperature variables for the thermal error compensation on machine tools[J].China Mechanical Engineering,2004,15(6):478-481.
[9]张伟,叶文华.基于灰色关联和模糊聚类的机床温度测点优化[J].中国机械工程,2014,25(4):456-460.ZHANG W,YE W H.Optimization of temperature measuring points for machine tools based on grey correlation and fuzzy clustering analysis[J].China Mechanical Engineering,2014,25(4):456-460.
[10]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,2013,34(5):1070-1075.GAO F,LIU J,YANG X G,et al.Study on optimization of thermal key points for machine tools based on Fisher optimal segmentation method[J].Chinese Journal of Scientific Instrument,2013,34(5):1070-1075.
[11]余时伟,黄廷祝,刘晓云,等.显著图引导下基于偏互信息的医学图像配准[J].仪器仪表学报,2013,34(6):1218-1225.YU SH W,HUANG T ZH,LIU X Y,et al.Partial mutual information based medical image registration guided by saliency maps[J].Chinese Journal of Scientific Instrument,2013,34(6):1218-1225.
[12]MAES F,COLLIGNON A,VANDERMEULEN D,et al.Multimodality image registration by maximization of mutual information[J].IEEE Transactions on Medical Imaging,1997,16(2):187-198.
[13]唐永波,桂卫华,彭涛,等.基于互信息变量选择的变压器油中溶解气体浓度预测[J].仪器仪表学报,2013,34(7):1492-1498.TANG Y B,GUI W H,PENG T,et al.Prediction method for dissolved gas concentration in transformer oil based on variable selection of mutual information[J].Chinese Journal of Scientific Instrument,2013,34(7):1492-1498.
[14]赵瑞月,梁睿君,叶文华.基于模糊聚类与偏相关分析的机床温度测点优化[J].机械科学与技术,2012,31(11):1767-1771.ZHAO R Y,LIANG R J,YE W H.Optimization of temperature measuring points for machine tools based on fuzzy clustering and partial correlation analysis[J].Mechanical Science and Technology,2012,31(11):1767-1771.
[15]RAMESH R,MANNAN M A,POO A N.Error compensation in machine tools a review part II:Thermal errors[J].International Journal of Machine Tools and Manufacture,2 0 0 0,4 0(9):1 2 5 7-1 2 8 4.
[16]王时龙,杨勇,周杰,等.大型数控滚齿机热误差补偿建模[J].中南大学学报,2011,42(10):3066-3072.WANG SH L,YANG Y,ZHOU J,et al.Modeling of thermal error compensation of large-scale numerical control gear hobbing machine[J].Journal of Central South University,2011,42(10):3066-3072.