基于模糊聚类测点优化与向量机的坐标镗床热误差建模

上海交通大学学报（自然版） ›› 2014, Vol. 48 ›› Issue (08): 1175-1182.

基于模糊聚类测点优化与向量机的坐标镗床热误差建模

杨军,梅雪松,赵亮,马驰,冯斌,施虎

(西安交通大学机械制造系统工程国家重点实验室，西安 710049)

收稿日期:2014-01-14 出版日期:2014-08-28 发布日期:2014-08-28
基金资助:
国家高技术研究发展计划(863)资助项目（2012AA040701）

Thermal Error Modeling of a Coordinate Boring Machine Based on Fuzzy Clustering and SVM

YANG Jun,MEI Xuesong,ZHAO Liang,MA Chi,FENG Bin,SHI Hu

(State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an 710049, China)

Received:2014-01-14 Online:2014-08-28 Published:2014-08-28

摘要/Abstract

摘要：

为了研究电主轴系统热特性对机床精度的影响，建立了主轴轴向及径向热误差模型.以精密坐标镗床为对象，采用五点法对主轴热误差进行测量，并分析了转速对主轴热误差及温度场的影响规律.利用模糊聚类分析法对温度变量进行分组优化，选出对热误差敏感的温度变量，建立主轴轴向热伸长及径向热倾角的最小二乘支持向量机（LSSVM）以及多元线性回归（MLRA）的综合热误差模型，并设定了预测优度评价标准.结果表明：模糊聚类分组法能有效降低温度变量间的多重共线性，并提高模型的稳定性；LSSVM模型具备全局寻优的特点，可实现不同工况的高精度预测，预测精度可达90%，且比传统的MLRA模型有更好的通用性以及更强的泛化能力，可作为后期热误差的补偿模型.

关键词: 坐标镗床电主轴, 热误差建模, 模糊聚类分析, 最小二乘支持向量机, 多元线性回归分析

Abstract:

To investigate the effect of the thermal characteristics of a motorized spindle system on the precision of a machine tool, two thermal error modeling of a CNC boring machine spindle were proposed, and a fivepoint method was used to measure the thermal errors of the spindle. The relationships between the spindle speed and temperature field, and thermal errors were analyzed. Then the method combining fuzzy clustering and correlation analysis was presented to optimize temperature variables and select the variables sensitive to thermal error. Subsequently, the least square support vector machine (LSSVM) and multivariable linear regression analysis (MLRA) models were established for axial elongation and radial declinations. The results indicate that the fuzzy cluster can reduce the multicollinearity among temperature variables and improve the stability of the model. Moreover, the LSSVM has better generalization than MLRA under different cutting conditions, and the prediction accuracy could reach up to 90%, which could be used to compensate thermal errors of the machine.

Key words：

Key words: boring machine spindle, thermal error modeling, fuzzy cluster, least square support vector machine (LSSVM), multivariable linear regression analysis (MLRA)

中图分类号:

杨军,梅雪松,赵亮,马驰,冯斌,施虎. 基于模糊聚类测点优化与向量机的坐标镗床热误差建模[J]. 上海交通大学学报（自然版）, 2014, 48(08): 1175-1182.

YANG Jun,MEI Xuesong,ZHAO Liang,MA Chi,FENG Bin,SHI Hu. Thermal Error Modeling of a Coordinate Boring Machine Based on Fuzzy Clustering and SVM[J]. Journal of Shanghai Jiaotong University, 2014, 48(08): 1175-1182.

参考文献

［1］Bryan J B. International status of thermal error research ［J］. Annals of CIRP, 1968, 16(1):203215.

［2］Min X, Jiang S. A thermal model of a ball screw drive system for a machine tool ［J］. Journal of Mechanical Engineering Science, 2011, 1:186225.

［3］Zhao H T, Yang J G, Shen J H. Simulation of thermal behavior of a CNC machine tool spindle ［J］. International Journal of Machine Tools and Manufacture, 2007, 47(6):10031010.

［4］Creighton E, Honegger A, Tulsian A, et al. Analysis of thermal errors in a highspeed micromilling spindle ［J］. International Journal of Machine Tools and Manufacture, 2010, 50(4):386393.

［5］Yang S, Yuan J, Ni J. The improvement of thermal error modeling and compensation on machine tools by CMAC neural network ［J］. International Journal of Machine Tools and Manufacture, 1996, 36(4): 527537.

［6］Zhang Y, Yang J G, Jiang H. Machine tool thermal error modeling and prediction by grey neural network ［J］. International Journal of Advanced Manufacturing Technology, 2012, 59(9):10651072.

［7］Ouafi A E, Guillot M, Barka N. An integrated modeling approach for ANNbased realtime thermal error compensation on a CNC turning center ［J］. Advanced Materials Research, Environmental and Materials Engineering, 2013, 664: 907915.

［8］Hong C F, Ibaraki S C. Observation of thermal influence on error motions of rotary axes on a fiveaxis machine tool by static Rtest ［J］. International Journal of Automation Technology, 2012, 6(2):196204.

［9］Vyroubal J. Compensation of machine tool thermal deformation in spindle axis direction based on decomposition method ［J］. Precision Engineering, 2012, 36(1):121127.

［10］Vissiere A, Nouira H, Damak M, et al. A newly conceived cylinder measuring machine and methods that eliminate the spindle errors ［J］. Measurement Science and Technology, 2012, 23(9):111.

［11］郭前建，杨建国，李永祥, 等. 聚类回归分析在滚齿机热误差建模中的应用［J］. 上海交通大学学报, 2008, 42(7): 10551059.

GUO Qianjian, YANG Jianguo, LI Yongxiang, et al. Application of clustering regression analysis to thermal error modeling of gear hobbing machine ［J］. Journal of Shanghai Jiaotong University, 2008, 42(7): 10551059.

［12］Lin W Q, Xu Y Z, Fu J Z, et al. Thermal error modeling and compensation of spindles based on LSSVM ［C］∥International Technology and Innovation Conference 2006. United Kingdom: IET Conference Publications, 2006(524):841846.

［13］ISO 2303:2007(E), Test code for machine tools Part 3: Determination of thermal effects ［S］. Switzerland: ISO copyright office, 2007.

［14］Leahy R, Wu Z. An optional graph theoretic approach to data clustering: theory and its application to image segmentation ［J］. IEEE Trans on PAMI, 1993, 15(11):11011113.

［15］Vapnik V N. Statistical learning theory ［M］. New York: John Wiley, 1998.

［16］Suykens J A K, De B J, Lukas L, et al. Weighted least squares support vector machines: robustness and sparse approximation ［J］. Neurocomputing, 2002, 48(1):85105.

[1]	李春祥，裴杨从琪，殷潇. 基于Hermite组合核EMD-WT-LSSVM的非平稳非高斯风压预测[J]. 上海交通大学学报, 2019, 53(10): 1249-1258.
[2]	李春祥,殷潇. 基于小波支持向量机的非高斯空间风压内外插预测[J]. 上海交通大学学报（自然版）, 2018, 52(11): 1516-1523.
[3]	罗华毅，王景成，杨丽雯，李肖城. 基于时差系数的城市原水需水量预测应用[J]. 上海交通大学学报（自然版）, 2017, 51(10): 1260-1267.
[4]	姚晓栋1,3,黄奕乔1,马晓波2,薛波3,杨建国1. 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（自然版）, 2016, 50(05): 673-679.
[5]	朱小龙，杨建国，代贵松. 基于AVQ聚类和OIF-Elman神经网络的机床热误差建模[J]. 上海交通大学学报（自然版）, 2014, 48(1): 22-26.
[6]	苏永生, 王永生, 段向阳. 实船喷水推进泵空化识别试验[J]. 上海交通大学学报（自然版）, 2012, 46(03): 404-409.
[7]	张广明, 袁宇浩, 龚松建. 基于改进最小二乘支持向量机方法的短期风速预测[J]. 上海交通大学学报（自然版）, 2011, 45(08): 1125-1129.
[8]	邓卫卫1, 杨慧中1, 2. 一种带监督的仿射传播聚类多模型建模方法[J]. 上海交通大学学报（自然版）, 2011, 45(08): 1172-1175.
[9]	刘涵，尹嵩，刘丁. 基于动态神经网络支持向量机的FPGA实现[J]. 上海交通大学学报（自然版）, 2010, 44(07): 962-0967.