Aiming at the complex nonlinear relationship between temperature rise and spindle thermal error caused by multiple heat sources of numerical control (NC) machine tool, a spindle thermal error prediction model (hereinafter referred to as thermal error model) based on chicken swarm optimization (CSO) algorithm and support vector machine (SVM) was proposed. Taking the spindle unit of a precision NC machine tool as the research object, the axial thermal deformation under idle state was measured by five-point measurement method, and the temperatures of four key temperature measuring points of the machine tool were collected using thermocouple sensor. Based on SVM theory, 75% data samples were randomly selected for training, and then the spindle thermal error model was constructed. Among them, CSO algorithm was used to optimize the penalty parameter c and kernel parameter g of SVM model to improve the prediction ability and robustness of the thermal error model. The remaining 25% of the samples were used as the test data set to verify the thermal error model.The spindle thermal error under different working conditions was predicted using CSO-SVM model, and the predicted results were compared with the measured results.The results showed that when the spindle rotate speed was 3 000 r/min, the average prediction accuracy of CSO-SVM model was as high as 97.32%, which was 6.53% and 4.68% higher than that of multiple linear regression model and SVM model based on particle swarm optimization, respectively; when the spindle rotate speed was 2 000 and 4 000 r/min, the average prediction accuracy of CSO-SVM model was 92.53% and 91.82% respectively, indicating that the model had high prediction ability and good robustness. CSO-SVM model has strong practicability and engineering application value.
Fig.2 Schematic of principle of five-point measurement
序号
T1
T2
T3
T4
位置
前轴承
主轴箱
立柱
床身
Table 1Key temperature measuring points of machine tool
Fig.3 Distribution of key temperature measuring points of machine tool
Fig.4 Measuring platform of machine tool temperature and spindle thermal error
Fig.5 Temperature variation curve of key measuring points of machine tool at rotate speed of 3 000 r/min
Fig.6 Variation curve of spindle thermal error at different rotate speeds
Fig.7 CSO algorithm flow
Fig.8 Thermal error prediction results of CSO-SVM model at rotate speed of 3 000 r/min
Fig.9 Comparison of prediction accuracy of different models
Fig.10 Thermal error prediction results of CSO-SVM model under different working conditions
Fig.11 Prediction result of spindle radial thermal drift error of CSO-SVM model at rotate speed of 3 000 r/min
[1]
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， 2000， 40（9）： 1257-1284. doi：10.1016/s0890-6955(00)00010-9
doi: 10.1016/s0890-6955(00)00010-9
[2]
WENG L， GAO W， LV Z， et al. Influence of external heat sources on volumetric thermal errors of precision machine tools［J］. The International Journal of Advanced Manufacturing Technology， 2018， 99： 475–495. doi：10.1007/s00170-018-2462-3
doi: 10.1007/s00170-018-2462-3
[3]
LI Y， ZHAO W， LAN S， et al. A review on spindle thermal error compensation in machine tools［J］. International Journal of Machine Tools and Manufacture， 2015， 95： 20-38. doi：10.1016/j.ijmachtools.2015.04.008
doi: 10.1016/j.ijmachtools.2015.04.008
[4]
邓小雷，林欢，王建臣，等.机床主轴热设计研究综述［J］.光学精密工程，2018，26（6）：1415-1429. doi：10.3788/OPE.20182606.1415 DENG Xiao-lei， LIN Huan， WANG Jian-chen， et al. Review on thermal design of machine tool spindles［J］. Optics and Precision Engineering， 2018， 26（6）： 1415-1429.
doi: 10.3788/OPE.20182606.1415
[5]
要小鹏，殷国富，李光明.基于OE-CM算法的机床主轴热误差建模与补偿分析［J］.中国机械工程，2015，26（20）：2757-2762. doi：10.3969/j.issn.1004-132X.2015.20.011 YAO Xiao-peng， YIN Guo-fu， LI Guang-ming. Thermal error modeling and compensation analysis based on OE-CM algorithm for machine tool spindles［J］. China Mechanical Engineering， 2015， 26（20）： 2757-2762.
doi: 10.3969/j.issn.1004-132X.2015.20.011
[6]
颜宗卓，陶涛，侯瑞生，等.机床电主轴热特性卷积建模研究［J］.西安交通大学学报，2019，53（6）：1-8. doi：10.7652/xjtuxb201906001 YAN Zong-zhuo， TAO Tao， HOU Rui-sheng， et al. Convolution modeling for thermal properties of motorized spindle in machine tools［J］. Journal of Xi'an Jiaotong University， 2019， 53（6）： 1-8
doi: 10.7652/xjtuxb201906001
[7]
姚晓栋，黄奕乔，马晓波，等.基于时间序列算法的数控机床热误差建模及其实时补偿［J］.上海交通大学学报，2016，50（5）：673-679. doi：10.16183/j.cnki.jsjtu.2016.05.005 YAO Xiao-dong， HUANG Yi-qiao， MA Xiao-bo， et al. Thermal error modeling and real-time compensation of CNC machine tools based on time series method［J］. Journal of Shanghai Jiaotong University， 2016， 50（5）： 673-679.
doi: 10.16183/j.cnki.jsjtu.2016.05.005
[8]
LI T， LI F， JIANG Y， et al. Thermal error modeling and compensation of a heavy gantry-type machine tool and its verification in machining［J］. The International Journal of Advanced Manufacturing Technology， 2017， 92： 3073-3092. doi：10.1007/s00170-017-0353-7
doi: 10.1007/s00170-017-0353-7
[9]
高卫国，王伟松，张大卫，等.考虑结构热变形的机床进给系统热误差研究［J］.工程设计学报，2019，26（1）：29-38. doi：10.3785/j.issn.1006-754X.2019.01.006 GAO Wei-guo， WANG Wei-song， ZHANG Da-wei， et al. Research on thermal error of machine tool feed system considering structural thermal deformation［J］. Chinese Journal of Engineering Design， 2019， 26（1）： 29-38.
doi: 10.3785/j.issn.1006-754X.2019.01.006
[10]
LIU Y， MIAO E， LIU H， et al. Robust machine tool thermal error compensation modelling based on temperature-sensitive interval segmentation modelling technology［J］. The International Journal of Advanced Manufacturing Technology， 2020， 106： 655-669. doi：10.1007/s00170-019-04482-8
doi: 10.1007/s00170-019-04482-8
[11]
YAO X， HU T， YIN G， et al. Thermal error modeling and prediction analysis based on OM algorithm for machine tool’s spindle［J］. The International Journal of Advanced Manufacturing Technology， 2020， 106： 3345-3356. doi：10.1007/s00170-019-04767-y
doi: 10.1007/s00170-019-04767-y
[12]
王维，杨建国，姚晓栋，等.数控机床几何误差与热误差综合建模及其实时补偿［J］.机械工程学报，2012，48（7）：165-170，179. doi：10.3901/JME.2012.07.165 WANG Wei， YANG Jian-guo， YAO Xiao-dong， et al， Synthesis modeling and real-time compensation of geometric error and thermal error for CNC machine tools［J］. Journal of Mechanical Engineering， 2012， 48（7）： 165-170， 179.
doi: 10.3901/JME.2012.07.165
[13]
谭峰，殷鸣，彭骥，等.基于集成BP神经网络的数控机床主轴热误差建模［J］.计算机集成制造系统，2018，24（6）：1383-1390. doi：10.13196/j.cims.2018.06.007 TAN Feng， YIN Ming， PENG Ji， et al. CNC machine tool spindle thermal error modeling based on ensemble BP neural network［J］. Computer Integrated Manufacturing System， 2018， 24 （6）： 1383-1390.
doi: 10.13196/j.cims.2018.06.007
[14]
LI G， KE H， LI C， et al. Thermal error modeling of feed axis in machine tools using particle swarm optimization-based generalized regression neural network［J］. Journal of Computing and Information Science in Engineering， 2020， 20（2）： 1-13. doi：10.1115/1.4045292
doi: 10.1115/1.4045292
[15]
CHENG Q， QI Z， ZHANG G， et al. Robust modelling and prediction of thermally induced positional error based on grey rough set theory and neural networks［J］. The International Journal of Advanced Manufacturing Technology， 2016， 83： 753-764. doi：10.1007/s00170-015-7556-6
doi: 10.1007/s00170-015-7556-6
[16]
朱星星，赵亮，雷默涵，等.精密进给系统热误差的协同训练支持向量机回归建模与补偿方法［J］.西安交通大学学报，2019，53（10）：40-47. doi：10.7652/xjtuxb201910006 ZHU Xing-xing， ZHAO Liang， LEI Mo-han， et al. Co-training support vector machine regression modeling and compensation for thermal error of precision feed system［J］. Journal of Xi'an Jiaotong University， 2019， 53（10）： 40-47.
doi: 10.7652/xjtuxb201910006
[17]
LI Q， LI H. A general method for thermal error measurement and modeling in CNC machine tools’ spindle［J］. The International Journal of Advanced Manufacturing Technology， 2019， 103： 2739-2749. doi：10.1007/s00170-019-03665-7
doi: 10.1007/s00170-019-03665-7
[18]
LIU H， MIAO E， ZHUANG X， et al. Thermal error robust modeling method for CNC machine tools based on a split unbiased estimation algorithm［J］. Precision Engineering， 2018， 51： 169-175. doi：10.1016/j.precisioneng.2017.08.007
doi: 10.1016/j.precisioneng.2017.08.007
[19]
黄智，贾臻杰，邓涛，等.基于支持向量机的静压转台热误差补偿［J］.浙江大学学报（工学版），2019，53（8）：1594-1601. HUANG Zhi， JIA Zhen-jie， DENG Tao， et al. Thermal error compensation of static pressure turntable based on support vector machine［J］. Journal of Zhejiang University （Engineering Science）， 2019， 53（8）： 1594-1601.
[20]
李宾，申国君，孙庚，等.改进的鸡群优化算法［J］.吉林大学学报（工学版），2019，49（4）：1339-1344. LI Bin， SHEN Guo-jun， SUN Geng， et al. Improved chicken swarm optimization algorithm［J］. Journal of Jilin University （Engineering and Technology Edition）， 2019， 49（4）： 1339-1344.
