基于新陈代谢原理的机床热误差伪滞后建模
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摘要
为了建立预测精度高、泛化性能强的热误差预测模型,提出了一种基于新陈代谢原理的热误差伪滞后预测模型.通过实验研究发现了机床的伪滞后现象,并假设热误差是前一时刻关键点的温升及热误差共同作用的结果,求解出了机床的热关键点及典型工况下的热误差平均滞后时间.并利用遗传算法优化了最小二乘支持向量机的结构参数,基于新陈代谢原理对热误差进行迭代求解,从而建立了机床的热误差伪滞后预测模型.通过对比不同预测模型的预测结果,证明了假设的正确性,并且考虑伪滞后效应的预测模型的预测精度更高、泛化性能更好,能将不同转速的热误差降低90%以上.
In order to establish a thermal error prediction model with high prediction accuracy and generalization performance, a thermal error pseudo-hysteresis prediction model based on metabolic theory is proposed in this paper. The pseudo-hysteresis effect of machine tool is found by experimental research, and it is assumed that the thermal error is the result of the coupled action of the temperature rise at key points and the thermal error of the previous moment, and the thermal key points of the machine tool and the average lag time in the typical working conditions are solved. The genetic algorithm is used to optimize the structural parameters of the least squares support vector machine(LS-SVM). Based on the principle of metabolism, the thermal error is iteratively solved and the thermal error pseudo-hysteresis prediction model of the machine tool is established. The results of different prediction models show that the correctness of the hypothesis and the prediction accuracy of the pseudo-hysteresis prediction model is higher, the generalization performance is better, and the thermal error of different rotational speeds can be reduced by more than 90%.
In order to establish a thermal error prediction model with high prediction accuracy and generalization performance, a thermal error pseudo-hysteresis prediction model based on metabolic theory is proposed in this paper. The pseudo-hysteresis effect of machine tool is found by experimental research, and it is assumed that the thermal error is the result of the coupled action of the temperature rise at key points and the thermal error of the previous moment, and the thermal key points of the machine tool and the average lag time in the typical working conditions are solved. The genetic algorithm is used to optimize the structural parameters of the least squares support vector machine(LS-SVM). Based on the principle of metabolism, the thermal error is iteratively solved and the thermal error pseudo-hysteresis prediction model of the machine tool is established. The results of different prediction models show that the correctness of the hypothesis and the prediction accuracy of the pseudo-hysteresis prediction model is higher, the generalization performance is better, and the thermal error of different rotational speeds can be reduced by more than 90%.
引文
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[12]阳红,向胜华,刘立新,等.基于最优权系数组合建模的数控机床热误差在线补偿[J].农业机械学报,2012,43(5):216.DOI:10.6041/j.issn.1000-1298.2012.05.037 YANG Hong,XIANG Shenghua,LIU Lixin,et al.Online compensation for CNC machine thermal error based on optimal weights-based combined modeling[J].Transaction of the Chinese Society for Agricultural Machinery,2012,43(5):216.DOI:10.6041/j.issn.10001298.2012.05.037
[13]YANG Hong,NI Jun.Dynamic modeling for machine tool thermal error compensation[J].Journal of Manufacturing Science & Engineering,2003,125(2):245.DOI:10.1115/1.1557296
[14]姚焕新,牛鹏程,龚亚运,等.数控机床热误差补偿中分布滞后模型的建立[J].农业机械学报,2013,44(3):246 YAO Huanxin,NIU Pengcheng,GONG Yayun,et al.Establishment of autoregressive distributed lag model in thermal error compensation of CNC machine tools[J].Transaction of the Chinese Society for Agricultural Machinery,2013,44(3):246
[15]苗恩铭,刘义,董云飞,等.数控机床热误差时间序列模型预测稳健性的提升[J].光学精密工程,2016,24(10):2480.DOI:10.3788/ope.20162410.2480 MIAO Enming,LIU Yi,DONG Yunfei,et al.Improvement of forcasting robustness of time series model for thermal error on CNC machine tool[J].Optics and Precision Enginerring.2016,24(10):2480.DOI:10.3788/ope.20162410.2480
[16]VAPNIK V.The nature of statistical learning theory[C]// Conference on Artificial Intelligence.Springer-Verlag,1995:988
[17]SUYKENS J A K,VANDEWALLE J.Least squares support vector machine classifiers[J].Neural Processing Letters,1999,9(3):293
[2] PAHK H J,LEE S W.Thermal error measurement and real time compensation system for the CNC machine tools incorporating the spindle thermal error and the feed axis thermal error[J].International Journal of Machine Tools & Manufacture,2002,20(7):487
[3] 李逢春,王海同,李铁民.重型数控机床热误差建模及预测方法的研究[J].机械工程学报,2016,52(11):154.DOI:10.3901/JME.2016.11.154 LI Fengchun,WANG Haitong,LI Tiemin.Research on thermal error modeling and prediction of heavy CNC machine tools[J].Journal of Mechanical Engineering,2016,52(11):154.DOI:10.3901/JME.2016.11.154
[4] 李永祥,杨建国.灰色系统模型在机床热误差建模中的应用[J].中国机械工程,2006,17(23):2439 LI Yongxiang,YANG Jianguo.Application of gray system model to thermal error modeling on machine tools[J].China Mechanical Engineering,2006,17(23):2439
[5] 刘志峰,潘明辉,张爱平,等.基于灰色线性回归组合模型的机床热误差建模方法[J].高技术通讯,2013,23(6):631.DOI:10.3772/j.issn.1002-0470.2013.06.013 LIU Zhifeng,PAN Minghui,ZHANG Aiping,et al.Thermal error modeling based on the grey-linear regression combination model for machine tools[J].High Technology Letters,2013,23(6):631.DOI:10.3772/j.issn.1002-0470.2013.06.013
[6] 林伟青,傅建中,陈子辰,等.数控机床热误差的动态自适应加权最小二乘支持矢量机建模方法[J].机械工程学报,2009,45(3):178.DOI:10.3901/JME.2009.03.178 LIN Weiqing,FU Jianzhong,CHEN Zichen,et al.Modeling of NC machine tool thermal error based on adaptive best-fitting WLS-SVM[J].Journal of Mechanical Engineering,2009,45(3):178.DOI:10.3901/JME.2009.03.178
[7] 姜辉,杨建国,姚晓栋,等.数控机床主轴热漂移误差基于贝叶斯推断的最小二乘支持向量机建模[J].机械工程学报,2013,49(15):115.DOI:10.3901/JME.2013.15.115 JIANG Hui,YANG Jianguo,YAO Xiaodong,et al.Modeling of CNC machine tool spindle thermal distortion with LS-SVM based on bayesian inference[J].Journal of Mechanical Engineering,2013,49(15):115.DOI:10.3901/JME.2013.15.115
[8] HUANG Yanqun,ZHANG Jie,LI Xu,et al.Thermal error modeling by integrating GA and BP algorithms for the High-speed spindle[J].International Journal Advance Manufacture Technology,2014,71(9/12):1669.DOI:10.1007/s00170-014-5606-0
[9] 王续林,顾群英,杨昌祥,等.基于PSO聚类和ELM神经网络机床主轴热误差建模[J].组合机床与自动化加工技术,2015(7):69.DOI:10.13462/j.cnki.Mmtamt.2015.07.019 WANG Xulin,GU Qunying,YANG Changxiang,et al.Modeling for machine tool thermal error based on PSO clustering algorithm and ELM model preprocessing neural network[J].Modular Machine Tool & Automatic Manufacturing Technique,2015(7):69.DOI:10.13462/j.cnki.Mmtamt.2015.07.019
[10]ZHANG Yi,YANG Jianguo,JIANG Hui.Machine tool thermal error modeling and prediction by grey neural network[J].The International Journal of Advanced Manufacturing Technology,2012,59(9-12):1065.DOI:10.1007/s00170-011-3564-3
[11]谭峰,殷国富,殷勤,等.基于GM-LS-SVM层级模型的数控机床热误差建模[J].中南大学学报(自然科学版),2016,47(12):4028.DOI:10.11817/j.issn.1672-7207.2016.12.010 TAN Feng,YIN Guofu,YIN Qing,et al.CNC machine tool thermal error modeling based on GM-LS-SVM hierarchical model[J].Journal of Zhongnan University,2016,47(12):4028.DOI:10.11817/j.issn.16727207.2016.12.010
[12]阳红,向胜华,刘立新,等.基于最优权系数组合建模的数控机床热误差在线补偿[J].农业机械学报,2012,43(5):216.DOI:10.6041/j.issn.1000-1298.2012.05.037 YANG Hong,XIANG Shenghua,LIU Lixin,et al.Online compensation for CNC machine thermal error based on optimal weights-based combined modeling[J].Transaction of the Chinese Society for Agricultural Machinery,2012,43(5):216.DOI:10.6041/j.issn.10001298.2012.05.037
[13]YANG Hong,NI Jun.Dynamic modeling for machine tool thermal error compensation[J].Journal of Manufacturing Science & Engineering,2003,125(2):245.DOI:10.1115/1.1557296
[14]姚焕新,牛鹏程,龚亚运,等.数控机床热误差补偿中分布滞后模型的建立[J].农业机械学报,2013,44(3):246 YAO Huanxin,NIU Pengcheng,GONG Yayun,et al.Establishment of autoregressive distributed lag model in thermal error compensation of CNC machine tools[J].Transaction of the Chinese Society for Agricultural Machinery,2013,44(3):246
[15]苗恩铭,刘义,董云飞,等.数控机床热误差时间序列模型预测稳健性的提升[J].光学精密工程,2016,24(10):2480.DOI:10.3788/ope.20162410.2480 MIAO Enming,LIU Yi,DONG Yunfei,et al.Improvement of forcasting robustness of time series model for thermal error on CNC machine tool[J].Optics and Precision Enginerring.2016,24(10):2480.DOI:10.3788/ope.20162410.2480
[16]VAPNIK V.The nature of statistical learning theory[C]// Conference on Artificial Intelligence.Springer-Verlag,1995:988
[17]SUYKENS J A K,VANDEWALLE J.Least squares support vector machine classifiers[J].Neural Processing Letters,1999,9(3):293