高速数控机床电主轴热误差机理分析与建模研究
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摘要
热误差是影响高速数控机床加工精度的主要原因，而电主轴单元是数控机床的最大热源，主轴热变形直接影响整台机床的性能。电主轴单元的热误差补偿技术是当前现代精密工程的研究热点问题，尤其是电主轴热误差预测模型的精度和鲁棒性是广受关注的难点问题。结合卧式加工中心用电主轴动态与热态特性研究项目，本文对电主轴单元热源及其传热机制的量化、关键测温点的优化选择、不同工况下热误差建模方法进行了深入的分析与研究，并通过数值仿真及实验研究证实本文研究成果可有效地提高热误差模型预测精度，为改善电主轴加工精度提供坚实基础。主要研究内容包括：
（1）进行了电主轴单元温度场的研究。通过详细分析热误差形成机理可知，电主轴单元温度场分布不均衡是导致形成热误差的主要原因。分析电主轴两个内热源的发热量发现其大小均与主轴转速有密切关系，根据各自特点分别建立了热源与速度的数学关系式。应用传热学理论，建立了主轴单元的热传递模型，并推导出主轴单元复杂热边界的热传递方程。建立了基于热-结构耦合的电主轴有限元分析模型，利用有限元法研究电主轴高速运转中温度场的变化规律，并进行了实验验证。
（2）针对电主轴热误差建模技术中温度布点选取的问题，提出了优化热关键点的新方法。根据测得的温度和热误差数据序列，借助于聚类分析的模糊聚类法将测温点进行分组，并且建立了灰色关联分析模型，综合分析和评价电主轴温度场分布中的各测温点与主轴热误差的相关程度，从各组温度测点中选出对热误差变化最敏感的点，采用修正可决系数最终选出最佳测温点组合。对温度测点的筛选，减小了选择温度变量和建模所需的时间，优化了测温时热传感器的布局。并提出根据不同实验条件和要求优化选择关键测温点的策略。
（3）提出了分别采用改进神经网络方法和自回归分析法进行电主轴热误差建模的基本原理及方法，建立了遗传算法优化神经网络模型和基于温度的多元自回归分析模型，并且研究了各建模方法的性能特点。根据两种模型对电主轴热误差产生机理的不同表述形式，比较二者的计算效率和拟合精度。通过对比可看出，二者的具体预测范围不同，对短期预测精度要求高的情况选用自回归模型较好，而遗传神经网络模型更适合于对中长期预测要求高的情况。在综合比较几种常用建模方法的性能基础上，结合灰色理论弱化数据序列波动性的特点和自回归分析理论反映随机性成分的特点，并充分利用RBF神经网络特有的自适应非线性信息处理能力，建立了基于RBF神经网络的组合预测模型。实验结果表明，基于RBF的电主轴热误差组合预测模型能够有效地提高预测精度。
（4）为了提高两种不同工况下热误差模型的精度和鲁棒性，提出了将两种工况特征均能很好反映且预测精度较高的组合预测模型。该模型首先建立能准确描述各加工情况特点的热误差模型——灰色模型和自回归分析模型，并通过模糊逻辑自动调节不同预测值的权值，使组合模型在不同工况下预测值均更接近于实际值。通过对恒速连续运转和速度逐步递进两种典型工况的预测和分析，结果表明提出的基于模糊逻辑组合预测模型的精度较高和泛化能力较强。为电主轴、数控机床应用于各种不同工况的热误差预测和误差控制提供了一条思路。
Thermal errors have become the major contributor to the inaccuracy of machinetools. The motorized spindle is the main heat source and thermal deformation ofmotorized spindle impact the performation of the whole machine tool directively. Inthe thermal error compensation technology, the accuracy and robustness of the thermalerror model is one of hot and difficult problems in modern precision engineering. Thisdissertation studies on the following key techniques about this subject: quantitativeanalysis of heat source and heat transfer mechanism, the optimization of the thermalkey points and motorized spindle thermal error modeling method in different operatingconditions. Conclusions from this dissertation are all verified by simulation andexperiment application. The main research contents are shown as follows:
(1) Temperature field of motorized spindle are distributed in unbalance, whichleads to thermal error. The heat generations of two internal heat sources are closerelated with speed of spindle, and the relationship between heat source and speed isestablished. Using the basic theory of heat transfer, the heat transfer model is foundand the heat transfer equations for complex temperature boundarys of spindle unit arederived. The model of motorized spindle is built and analyzed by FEM. Thetemperature field of spindle is obtained, by applying thermal and structural loads onthe FEA model. Finally, the correctness of theoretical analysis is validated byexperiments.
(2) According to the choice of temperature sensors placement in thermal errormodeling, a new method for optimizing the locations of thermal sensors is proposed.Temperature measuring points are divided into groups by using fuzzy clusteringmethod, in terms of the measured temperatures and thermal errors. Grey relationalmodel is adopted to analyze emphasis of each measured point to thermal error intemperature field distribution of motorized spindle and the most sensitive points arepicked out. The best combinations is choosed by using the modified coefficient ofdetermination, which will reduce the number of temperature sensors and the modelingtime. Finally, the optimized strategy of chosing the variable is presented depending ondifferent test conditions and request.
(3) The neural network model based genetic algorithm and autoregression modebased on temperature are put forward respectively and the performances of twomodeling method are studied. According to different representations of generation mechanism of motorized spindle thermal error, operation efficiency and curve fitprecision of these two models are compared. The results indicate that the estimationranges of two models are different, that the MVAR model has higher forecast precisionin short-term prediction, while the GARBF neural network model has higher forecastprecision in mid-long term forecasting. Finally, by comparing several commonmodeling methods, an autoregressive analysis model and a gray dynamic model areused to predict thermal error respectively and on the basis of those models, a hybridprediction model based on radial basis function neural network is proposed. The testresults show that the prediction of the combined prediction model for motorizedspindle thermal errors is effectively improved.
(4) According to the generation mechanism of motorized spindle thermal error, thecombined forecasting model based on the fuzzy logic is proposed under two typicalworking conditions. The model can be expected to improve the forcasting accuracy byusing autoregressive analysis method and grey system theory combined with differentweight. The combined model synthetically uses the above methods and makes the bestuse of them. Through the prediction study on thermal error model under the constantrunning condition and the progressive running condition in experiment platform ofmotorized spindle, experiment results demonstrates intelligence combinationforcasting model has higher precision and stronger robustness, which provides newideas for forecasting and controling thermal error.
（1）进行了电主轴单元温度场的研究。通过详细分析热误差形成机理可知，电主轴单元温度场分布不均衡是导致形成热误差的主要原因。分析电主轴两个内热源的发热量发现其大小均与主轴转速有密切关系，根据各自特点分别建立了热源与速度的数学关系式。应用传热学理论，建立了主轴单元的热传递模型，并推导出主轴单元复杂热边界的热传递方程。建立了基于热-结构耦合的电主轴有限元分析模型，利用有限元法研究电主轴高速运转中温度场的变化规律，并进行了实验验证。
（2）针对电主轴热误差建模技术中温度布点选取的问题，提出了优化热关键点的新方法。根据测得的温度和热误差数据序列，借助于聚类分析的模糊聚类法将测温点进行分组，并且建立了灰色关联分析模型，综合分析和评价电主轴温度场分布中的各测温点与主轴热误差的相关程度，从各组温度测点中选出对热误差变化最敏感的点，采用修正可决系数最终选出最佳测温点组合。对温度测点的筛选，减小了选择温度变量和建模所需的时间，优化了测温时热传感器的布局。并提出根据不同实验条件和要求优化选择关键测温点的策略。
（3）提出了分别采用改进神经网络方法和自回归分析法进行电主轴热误差建模的基本原理及方法，建立了遗传算法优化神经网络模型和基于温度的多元自回归分析模型，并且研究了各建模方法的性能特点。根据两种模型对电主轴热误差产生机理的不同表述形式，比较二者的计算效率和拟合精度。通过对比可看出，二者的具体预测范围不同，对短期预测精度要求高的情况选用自回归模型较好，而遗传神经网络模型更适合于对中长期预测要求高的情况。在综合比较几种常用建模方法的性能基础上，结合灰色理论弱化数据序列波动性的特点和自回归分析理论反映随机性成分的特点，并充分利用RBF神经网络特有的自适应非线性信息处理能力，建立了基于RBF神经网络的组合预测模型。实验结果表明，基于RBF的电主轴热误差组合预测模型能够有效地提高预测精度。
（4）为了提高两种不同工况下热误差模型的精度和鲁棒性，提出了将两种工况特征均能很好反映且预测精度较高的组合预测模型。该模型首先建立能准确描述各加工情况特点的热误差模型——灰色模型和自回归分析模型，并通过模糊逻辑自动调节不同预测值的权值，使组合模型在不同工况下预测值均更接近于实际值。通过对恒速连续运转和速度逐步递进两种典型工况的预测和分析，结果表明提出的基于模糊逻辑组合预测模型的精度较高和泛化能力较强。为电主轴、数控机床应用于各种不同工况的热误差预测和误差控制提供了一条思路。
Thermal errors have become the major contributor to the inaccuracy of machinetools. The motorized spindle is the main heat source and thermal deformation ofmotorized spindle impact the performation of the whole machine tool directively. Inthe thermal error compensation technology, the accuracy and robustness of the thermalerror model is one of hot and difficult problems in modern precision engineering. Thisdissertation studies on the following key techniques about this subject: quantitativeanalysis of heat source and heat transfer mechanism, the optimization of the thermalkey points and motorized spindle thermal error modeling method in different operatingconditions. Conclusions from this dissertation are all verified by simulation andexperiment application. The main research contents are shown as follows:
(1) Temperature field of motorized spindle are distributed in unbalance, whichleads to thermal error. The heat generations of two internal heat sources are closerelated with speed of spindle, and the relationship between heat source and speed isestablished. Using the basic theory of heat transfer, the heat transfer model is foundand the heat transfer equations for complex temperature boundarys of spindle unit arederived. The model of motorized spindle is built and analyzed by FEM. Thetemperature field of spindle is obtained, by applying thermal and structural loads onthe FEA model. Finally, the correctness of theoretical analysis is validated byexperiments.
(2) According to the choice of temperature sensors placement in thermal errormodeling, a new method for optimizing the locations of thermal sensors is proposed.Temperature measuring points are divided into groups by using fuzzy clusteringmethod, in terms of the measured temperatures and thermal errors. Grey relationalmodel is adopted to analyze emphasis of each measured point to thermal error intemperature field distribution of motorized spindle and the most sensitive points arepicked out. The best combinations is choosed by using the modified coefficient ofdetermination, which will reduce the number of temperature sensors and the modelingtime. Finally, the optimized strategy of chosing the variable is presented depending ondifferent test conditions and request.
(3) The neural network model based genetic algorithm and autoregression modebased on temperature are put forward respectively and the performances of twomodeling method are studied. According to different representations of generation mechanism of motorized spindle thermal error, operation efficiency and curve fitprecision of these two models are compared. The results indicate that the estimationranges of two models are different, that the MVAR model has higher forecast precisionin short-term prediction, while the GARBF neural network model has higher forecastprecision in mid-long term forecasting. Finally, by comparing several commonmodeling methods, an autoregressive analysis model and a gray dynamic model areused to predict thermal error respectively and on the basis of those models, a hybridprediction model based on radial basis function neural network is proposed. The testresults show that the prediction of the combined prediction model for motorizedspindle thermal errors is effectively improved.
(4) According to the generation mechanism of motorized spindle thermal error, thecombined forecasting model based on the fuzzy logic is proposed under two typicalworking conditions. The model can be expected to improve the forcasting accuracy byusing autoregressive analysis method and grey system theory combined with differentweight. The combined model synthetically uses the above methods and makes the bestuse of them. Through the prediction study on thermal error model under the constantrunning condition and the progressive running condition in experiment platform ofmotorized spindle, experiment results demonstrates intelligence combinationforcasting model has higher precision and stronger robustness, which provides newideas for forecasting and controling thermal error.
引文
[1]吴南星.高速高精度数控车床结构动力学特性与仿真技术研究:[东南大学博士学位论文].南京:东南大学,2004,1-2
[2]张伯霖,杨庆东,陈长年.高速切削技术及应用.北京:机械工业出版社,2002,61-93
[3]张伯霖,张志润,肖曙红.超高速加工与机床的零传动.中国机械工程,1996,7(5):37-41
[4] Bryan J B. International status of thermal error research. In: CIRP Ann-Manu-facturing Technology.1990,39(2):645-656
[5]洪迈生,苏恒,熊诗波等.数控机床运动误差检测技术.组合机床与自动化技术,2002,1:18-22
[6]洪迈生,苏恒,熊诗波等.数控机床运动误差检测技术.组合机床与自动化技术,2002,2:52-53
[7]倪军.数控机床误差补偿研究的回顾及展望.中国机械工程,1997,8(1):29-33
[8] Weck M, McKeown P, Bonse R, et al. Reduction and compensation of thermal errorin machine tools. In: CIRP Ann-Manufacturing Technology,1995,44(2):589-598.
[9] Ferrerira P M, Liu C R. A method for estimating and compensating quasistatic err-ors of machine tools. Journal of Engineering for Industry,1993,115(1):149-159.
[10] Robert B Aronson. War against thermal expansion.Manufacturing Engineering,1996,116(6):45-50.
[11]杨建国.数控机床误差综合补偿技术及应用:[上海交通大学博士学位论文].上海:上海交通大学,1998,48-61
[12] Mou J. A method of using neural networks and inverse kinematics for machinetool error estimation and correction.Journal of Manufacturing Science and Engi-neering,1997,119:247-254.
[13] Wang K C. Thermal error modeling of a machining center using grey systemtheory and adaptive network-based fuzzy inference system. In: IEEE Conf onCybernetics and Intelligent System. Bangkok,2006,1-6
[14] Krulewich D A. Temperature integration model and measurement point selectionfor hermally induced machine tool errors. Mechatronics,1998(8):395-412
[15] Stolz G J. Numerical solutions to an inverse problem of heat conduction forsimple shapes. Journal of Heat Transfer,1960,82:20-26
[16] Sparrow E M, Haji-Sheikh A, Lundgren T S. The inverse problem in transient heatconduction. Journal of Applied Mechanics.1964,86:369-375
[17] Jarny Y, Ozisik M N, Bardon J P. A general optimization method using adjointequation for solving multidimensional inverse heat conduction. InternationalJournal of Heat Mass Transfer,1991,34(11):2911-2919.
[18] Hensel E. Inverse Theory and Applications for Engineers. Englewood: PrenticeHall Press,1991,35-46
[19] Himeno N, Hinata S, Yanadori M. A simple method of Measuring thermo-physic-cal properties by stepwise heating. Trans JSME B,1992,187-192:59-545(inJapanese)
[20] Monde M. Analytical method in inverse heat transfer problem using Laplace tran-sform technique. International Journal of Heat Mass Transfer2000,43:3965-3975
[21] Huang C H, Yan J Y, Chen H T. Function estimation in predictting temperature-dependent thermal conductivity without internal measurements. Journal of Ther-mophysics and Heat Transfer,1995,9(4):667-673
[22] Hayashi H, Watanabe M and Inaba H. Measurement of thermal expansion coeffi-cient of LaCrO3. Thermochimica Acta,2000,359(1):77-85
[23] Abdel-Aal H A, Smith S T. On friction-induced temperatures of rubbing metallicpairs with temperature-dependent thermal properties, Wear,1998,216:41-59
[24] Sawaf B, Ozisik M N. Determining the constant thermal conductivities of ortho-tropic materials by inverse analysis. International Communications in Heat andMass Transfer,1995,22(2):201-211
[25] Jalali-Heravi M, Fatemi M H. Prediction of thermal conductivity detection res-ponse factorsusing an artificial neural network，Journal of Chromatography A,2000,897(1-2):227-235
[26] Jedrzejewski J, Kaczmarek J, Kowal Z, et al. Numerical optimization of thermalbehavior of machine tools. Annals of the CIRP-Manufacturing Technology,1990,39(1):379-382
[27] Choi J K, Lee D G. Thermal characteristics of the spindle bearing system with agear located on the bearing span. International Journal of Machine Tools andManufacture,1998,38:1017-1030
[28] Choi J K, Lee D G. Characteristics of a spindle bearing system with a gear locatedon the bearing span. International Journal of Machine Tools&Manufacture,1997,37(2):171-181
[29] Gibson A O, Stein J L. A finite element model of thermaloly induced angular con-tact spindle bearing loads. The International Mechanical Engineering Congressand Exposition, Anaheim, California,1998,33-38
[30] Tuomaala P, Piira K, Vuolle M. A rational method for the distribution of nodes inmodeling of transient heat conduction in plane slabs. Building and Environment.2000,35:397-406
[31] Zverev I A, Eun In-Ung, Chung W J, et al. Thermal model of high-speed spindleunits. Journal of Mechanical Science and Technology,2003,17(5):668-678
[32] Zverv I A, Pyoun Y S, Lee K B, et al. An elastic deformation model of high speedspindles built into ball bearings. Journal of Materials Processing Technology,2005,170(3):270-278
[33]肖曙红,郭军,张伯霖.高速电主轴热-结构耦合特性的有限元分析.机械设计与制造,2008,9:96-98
[34] Xiao S H, Guo J, Zhang B L. Research on the motorized spindle’s thermal proper-ties based on thermo-mechanical coupling analysis. In: Technology and Innova-tion Conf,2006(6-7):1479-1483
[35] Dai W L, Woodward P R. Numerical simulations for nonlinear heat transfer in asystem of multimaterials. Journal of Computational Physics,1998,139(1):58-78
[36] Bossmanns B, Tu J F. A thermal modle for high speed motorized spindles.International Journal of Machine Tools and Manufacture,1999,39:1345-1366.
[37] Bossmanns B. Thermo-mechanical modeling of motorized spindle systems forhigh speed milling:[dissertation]. West Lafayette: Purdue University,1997,53-81
[38] Bossmanns B, Tu J F. A power flow model for high speed motorized spindles-heatgeneration characterization. Journal of Manufacturing Science and Engineering,2001,123(3):494-505
[39] Lin C W, Tu J F, Kamman J. An integrated thermo-mechanical-dynamic model tocharacterize motorized machien tool spindles during very high speed rotation.International Journal of Machine Tools and Manufacture,2003,43(10):1035-1050
[40] Prabhu Raja V, Thyla P R, Radhakrishnan P. A strategy of investigation on thethermal behaviour of motorised spindles under high speed machining. Interna-tional Journal of Computer Applications in Technology,2006,27(1):1-11
[41] Tu J F, Stein J L. Active thermal preload regulation for machine tool spindles withrolling element bearing. Journal of Manufacturing Science and Engineering,1996,118(4):499-505
[42] Aramaki H, Shoda Y, Morishita Y, et al. The performance of ball bearing withsilicon nitride ceramic balls in high speed spindles for machine tools. Journal ofTribology,1988,110(4):693-698
[43] Jorgensen B R, Shin Y C. Dynamies of machine tool spindle/bearing systemsunder thermal growth. Journal of Tribology,1997,119(4):875-882
[44] Ohishi S, Matsuzaki Y. Experimental investigation of air spindle unit thermalcharacteristics. Precision Engineering,2002,26(01):49-57
[45] Li H Q, Shin Y C. Analysis of bearing configuration effects on high speed spind-les using an integrated dynamic thermo-mechanical spindle model. InternationalJournal of Machine Tools and Manufacture,2004,44(4):347-364
[46] Li H Q, Shin Y C. Integrated dynamic thermo-mechanic modeling of high speed spindles: part1: model development. Journal of Manufacturing Science and Engi-neering,2004,126(1),148-158
[47] Li H Q, Shin Y C. Integrated dynamic thermo-mechanic modeling of high speedspindles: part2. solution procedure and validations. Journal of ManufacturingScience and Engineering,2004,126(1):159-167
[48] Harris T A. Rolling Bearing Analysis. New York: John Wiley and Sons, Inc,1984,26-42
[49]杨启威.轴承系统温度场分析.轴承,1997(3):2-6
[50] Camera A, Favarato M, Militano L, et al. Analysis of the thermal behavior of amachine tool table using the finite element method.CIRP Ann-ManufacturingTechnology,1976,25(1)
[51] Spur G, Hoffmann E, Paluncic Z, et al. Thermal behavior optimization of machinetools [J]. Annals of CIRP–Manufacturing Technology,1988,37(1):401-405
[52] Zhang G, Wang C, Hu X. Error compensation of coordinate measuring machine.CIRP Ann-Manufacturing Technology,1985,34(1):445-448
[53]李永祥.数控机床热误差建模新方法及其应用研究:[上海交通大学博士学位论文].上海:上海交通大学,2007,7-10
[54]赵海涛.数控机床热误差模态分析、测点布置及建模研究:[上海交通大学博士学位论文].上海:上海交通大学,2007,1-2
[55] Venugopal R. Thermal effects on the accuracy of numerically controlled machinetools (numerical methods, experimental):[dissertation]. West Lafayette: PurdueUniversity,1985,105-118
[56] Domnez M A, Blomquist D S, Hocken R J, et al.A general methodology for ma-chine tool accuracy enhancement by error compensation. Precision Engineering,1986,8(4):187-196
[57] Chen J S. A study of thermally induced machine tool errors in real cutting condi-tions.International Journal of Machine Tools and Manufacture,1996,36(12):1401-1411
[58] Chen J S, Yuan J, Ni J. Thermal error modeling for real-time error compensation.International Journal of Advanced Manufacturing Technology1996,12(4):266-275
[59] Chen J S, Ling C C. Improving the machine accuracy through machine tool metro-logy and error correction. The International Journal of Advanced ManufacturingTechnology,1996,11:198-205
[60] Veldhuis S C, Elbestawi M A. A strategy for the compensation of errors in five-axis machining. CIRP Annals-Manufacturing Technology,1995,44(1):373-377
[61] Lee J, Kramer B M. Analysis of machine degradation using a neural networkbased pattern discrimination model. Journal of Manufacturing Systems,1993,38(2):379-387
[62] Yang S, Yuan J, Ni J.The Improvement of thermal error modeling and compen-sation on machine tools by neural network. International Journal of MachineTools and Manufacture,1996,36(4):527-537
[63] Srinivasa N, Ziegert J. Prediction of thermally induced time-variant machine toolerror maps using a fuzzy ARTMAP neural network. Journal of ManufacturingScience and Engineering,1997,119(4):623-630
[64] Ramesh R, Mannan M, Poo A. Thermal error measurement and modelling inmachine tools. Part I: Influence of varying operating conditions. InternationalJournal of Machine Tools and Manufacture,2003,43(4):391-404
[65] Ramesh R, Mannan M, Poo A, et al. Thermal error measurement and modelling inmachine tools. Part II: Hybrid bayesian network-support vector machine model.International Journal of Machine Tools and Manufacture,2003,43(4):405-419.
[66] Kim S, Cho D. Real-time estimation of temperature distribution in a ball-screwsystem. International Journal of Machine Tools and Manufacture,1997,37(4):451-464
[67] Janeczko J. Machine-tool thermal compensation. Tooling and Production,1989,55(5):60-65.
[68] Jedrzejewski J, Modrzycki W. A new approach to modelling thermal behaviour ofa machine tool under service conditions.CIRP Annals-Manufacturing Technology,1992,41(1):455-458.
[69] Jedrzejewski J, Modrzycki W. Intelligent supervision of thermal deformations inhigh precision machine toos. In: Proc of Int Conf on Manufacturing Automationand Systems Technology, Applications, Design, Organisation and Management,and Research. Manchester, UK,1997,457-462
[70] Fraser S, Attia M, Osman M. Modelling, identification and control of thermaldeformation of machine tool structure. Part1: Concept of generalized modeling.Journal of Manufacturing Science and Engineering,1998,120(3):623-631
[71] Fraser S, Attia M, Osman M. Modelling, identification and control of thermaldeformation of machine tool structure. Part2: Generalized transfer functions.Journal of Manufacturing Science and Engineering,1998,120(3):632-639
[72] Fraser S, Attia M, Osman M. Modelling, identification and control of thermaldeformation of machine tool structure. Part3: Real-time estimation of heat sour-ces. Journal of Manufacturing Science and Engineering,1999,121(3):501-508
[73] Fraser S, Attia M, Osman M. Modelling, identification and control of thermaldeformation of machine tool structure. Part4: A multi-variable closed-loop con-trol system. Journal of Manufacturing Science and Engineering,1999,121,(3):509-516
[74] Fraser S, Attia M, Osman M. Modelling, identification and control of thermaldeformation of machine tool structure. Part5: Experimental verification.Journal of Manufacturing Science and Engineering,1999,121(3):517-523.
[75] Wang Y, Zhang G, Moon K et al. Compensation for the thermal error of multi-axismachining center. Journal of Materials Processing Technology,1998,75(1-3):45-53.
[76] Moriwaki T, Shamoto E J. Analysis of thermal deformation of an ultraprecision airspindle system. Manufacturing Technology,1998,47(1):315-319
[77] Moriwaki T. Thermal deformation and its on-line compensation of hydro staticallysupported precision spindle, Annals of the CIRP.1988,37(1):393-396
[78] Moriwaki T, et al. Thermal deformation of an ultraprecision machine tool due toenvironmental temperature change (in Japanese), Trans. of JSME(C),1997,63(615):4025-4030
[79] Lee J H, Lee J H, Yang S H. Thermal error modeling of a horizontal machiningcenter using fuzzy logic strategy[J]. Journal of Manufacturing Processes,2001,3(2):120-127
[80] Lee J H, Yang S H. Statistical optimization and assessment of a thermal errormodel for CNC machine tools. International Journal of Machine Tools and Ma-nufacture,2002,42:147-155
[81] Pahk H J, Lee S W. Thermal error measurement and real time compensationsystem for the CNC machine tools incorporating the spindle thermal error andthe feed axis thermal error. International Journal of Machine Tools and Manu-facture,2002,20:487-494
[82] Ko T J, Gim T W, Ha J Y. Particular behavior of spindle thermal deformation bythermal bending. International Journal of Machine Tools and Manufacture,2003,43:17-23
[83] Yang H, Ni J. Dynamic modeling for machine tool thermal error compensation.Journal of Manufacturing Science and Engineering,2003,125(2):245-254
[84] Yang H, Ni J. Adaptive model estimation of machine tool thermal errors based onrecursive dynamic modeling strategy. International Journal of Machine Tools andManufacture,2005,45:1-11
[85] Zhu J. Robust thermal error modeling and compensation for CNC machine tools:
[dissertation].America, Michigan: The University Of Michigan,2008,16-25
[86] Lo C H, Yuan J, Ni J. An application of real-time error compensation on a turn-ing center. International Journal of Machine Tools and Manufacture1995,35(12):1669-1682
[87] Chen J S, Yuan J X, Ni J, et al. Real-time compensation for time-variant volu-metric error on a machining center. Journal of Engineering for Industry,1993,115(4):472-479
[88] Lei C L, Rui Z Y. Thermal error modeling and compensating of motorized spin-dle based on improved neural network. Advanced Materials Research,2010,129-131:556-560
[89] Magalhaes M H, Ballini R, Molck P, et al. Combining forecasts for naturestreamflow prediction. Annual Conference and Meeting of the North AmericanFuzzy Information Processing Society. Piscataway NJ, USA: IEEE,2004,1:390-394
[90] Cagdas H A, Erol E, Ufuk Y. Forecast combination by using artificial neuralnetworks. Neural Processing Letters,2010,32(3):269-276
[91] Yang H, Ni J. Dynamic neural network modeling for nonlinear, nonstationarymachine tool thermally induced error. International Journal of Machine Toolsand Manufacture,2005,45:455-465
[92] Kang Y, Chang C W, Huang Y R, et al. Modification of a neural network utilizinghybrid filters for the compensation of thermal deformation in machine tools.International Journal of Machine Tool and Manufacture,2007,47(2):376-387
[93] Attia M, Kops L. System approach to the thermal behavior and deformation ofmachine tool structures in response to the effect of fixed joints. Journal of Engi-neering for Industry,1981,103(1):67-72
[94] Weck M, Mckeown P, Bonse R, et al. Reduction and compensation of thermalerrors in machine tools. CIRP Annals-Manufacturing Technology,1995,44(2):589-598
[95]陈子辰.热模态理论和机床热态精度控制策略研究:[浙江大学博士学位论文].杭州:浙江大学,1989:23-36
[96]陈子辰等.热敏感度和热偶合度研究.见:全国机床热误差控制和补偿研究会议论文集.杭州:浙江大学出版社,1992:86-94
[97]戴庆贺.应用西门子CNC@功能补偿车床主轴热误差.制造技术与机床,1998,3:36-37
[98]杨建国,薛秉源.数控机床热误差鲁棒建模新方法及实时补偿.制造技术与机床,1998,6:8-12
[99] Du Z C, Yang J G, Yao Z Q, et al. Modeling approach of regression orthogonalexperiment design for the thermal error compensation of a CNC turning center.Journal of Material Processing Technology,2002,129:619-623
[100]杨建国,薛秉源. CNC车削中心热误差模态分析及鲁棒建模.中国机械工程,1998,9(5):31-35
[101]项伟宏,郑力,刘大成等.机床主轴热误差建模.制造技术与机床,2000,11:12-15
[102]穆塔里夫阿赫迈德,项伟宏,郑力.加工中心主轴热误差实验分析与建模.组合机床与自动化加工技术,2002,9:15-19
[103]杨庆东.数控机床热误差补偿建模方法.制造技术与机床,2000,2:10-15
[104]杨庆东.神经网络补偿机床热变形误差的机器学习技术.机械工程学报,2000,36(1):92-96
[105] Yang Q D. Study of the thermal deformation on a coordinate measuring machineand compensation via a neural network model.International Journal of FlexibleAutomation and Integrated Manufacturing,1999,7:129-147
[106] Yang Q D. Linear regression and neural net models applied to thermal errorcompensation in machine tools.European Journal of Mechanical and Environ-mental Engineering,1999,44:146-152
[107]吴昊,杨建国,张宏韬等.精密车削中心热误差鲁棒建模与实时补偿.上海交通大学学报,2008,42(7):1064-1072
[108] Zhao Haitao,Yang Jianguo,Shen Jinhua.Simulation of thermal behavior of a CNCmachine tool spindle. International Journal of Machine Tools&Manufacture,2007,47:1003-1010
[109]谈小龙,徐卫亚,刘大文等.高边坡变形的组合预测模型及其应用.水利学报,2010,41(3):294-299
[110]王维强,牛振东,曹玉娟等.基于ARMA-TS-GARCH有限混合模型的交通数据分析.中南大学学报:自然科学版,2010,41(5):1860-1864
[111]李永祥,杨建国,郭前建等.数控机床热误差的混合预测模型及应用.上海交通大学学报,2006,40(12):2030-2034
[112]曾勇红,王锡凡,冯宗建.基于混合自回归滑动平均潜周期模型的短期电价预测.西安交通大学学报,2008,42(2):184-188
[113]闫嘉钰,杨建国.数控机床热误差的最优线性组合建模.上海交通大学学报,2009,43(4):633-637
[114] Hatamura Y, Nagao T, Mitsuishi M, et al. Development of an intelligent machin-ing center incorporating active compensation for thermal distortion. CIRPAnnals-Manufacturing Technology,1993,42(1):549-552
[115] Chen J S, Hsu W Y. Characterizations and models for the thermal growth of amotorized high speed spindle. International Journal of Machine Tools andManufacture,2003(43):1163-1170
[116] Chen J S, Chen K W. Bearing load analysis and control of a motorized highspeed spindle. International Journal of Machine Tools and Manufacture,2005,3(45):1487-1493
[117] Li S H, Zhang Y Q, Zhang G X. A study of pre-compensation for thermal errorsof NC machine tools. International Journal of Machine Tools and Manufacture,1997,37(12):1715-1719
[118]张奕群,李书和,刘安伟等.基于主轴转速的机床热误差状态方程模型.仪器仪表学报,1998,19(5):460-463
[119]李书和,张奕群,王东升等.数控机床热误差的建模与预补偿.计量学报,1999,20(1):49-52
[120] Gull M. Contouring accuracy assessment of CNC machine tools-a user’s view. In:Proc Int Conf on Laser Metrology and Machine Performance.1997,401-412
[121] Attia M H, Kops L. Thermometric design considerations for temperature moni-toring in machine tools and CMM structures．The International Journal ofAdvanced Manufacturing Technology1993,8:311-319
[122] Statham A, Martin D, Blackshaw M S. Assessing the thermal distortion causedby spindle rotation of a machining centre using the draft standard ISO/DIS230-3.In: Proc3rd Int Conf on Laser Metrology and Machine Performance.1997:101-111
[123] Ni J. Study on online identification and forecasting compensatory control ofvolumetric errors for multiple axis machine tools:[dissertation]. Madison: Uni-versity of Wisconsin,1987,23-34
[124] Chen J S. Computer-aided accuracy enhancement for multi-axis CNC machinetool. International Journal of Machine Tools and Manufacture,1995,35(4):593-605
[125] Srinivasa N, Ziegert J C, Mize C D. Spindle thermal drift measurement using thelaser ball bar. Precision Engineering,1996,18:118-28
[126] Jywe W Y, Chen C J. The development of a high-speed spindle measurement sys-tem using a laser diode and a quadrants sensor. International Journal of MachineTools and Manufacture,2005,45:1162-1170
[127] Chang C F, Chen J J, Chen T R. A theory thermal growth control techniques ofhigh speed spindles. In: Proc of Int Conf on Advances in Electronics and Micro-electronics. Washington,2008,96-101
[128]高赛,曾理江,殷纯永等.基于单光束干涉仪的机床主轴热误差实时测量.计量学报,2001,22(1):1-6
[129]商鹏.基于球杆仪的高速五轴数控机床综合误差建模与检测方法:[天津大学博士学位论文].天津:天津大学,2008,45-55
[130] Wang K C,Tseng P C,Lin K M.Thermal error modeling of a machining centerusing grey system theory and adaptive network-based fuzzy inference system.Trans JSME C,2006,49(4):1179-1187
[131] Kurtoglu A. The accuracy improvement of machine tools. CIRP Annals-Manu-facturing Technology,1990,39(1):417-419
[132] Chen J. Fast calibration and modeling of thermally-induced machine tool errorsin real machining. International Journal of Machine Tools and Manufacture,1996,37(2):159-169
[133]张德贤,刘筱连,师汉民等.神经网络在数控机床热变形控制中的应用.制造技术与机床,1995,1:8-11
[134]张奕群,李书和,张国雄. Kalman滤波器在机床热误差建模中的应用．航空精密制造技术,1997,33(1):16-18
[135]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.中国机械工程,2004,15(6):478-451
[136]邓卫国,杨建国,任永强等.精密车削中心热误差测试和优化建模.机械制造,2004,42(7):22-26
[137]林伟清,傅建中,许亚洲等.基于LS-SVM与遗传算法的数控机床热误差辨识温度传感器优化策略.光学精密工程,2008,16(9):1682-1687
[138] Zhao C L, Wang Y Q. Optimization of Measuring Points Based on the GreySystem Theory for Spindle of CNC Machine Tool. Proc of the IEEE Int Conf onMechatronics and Automation, Changchun, China,2009:686-690
[139]郭军.基于热接触分析的电主轴热态特性研究:[广东工业大学硕士学位论文].广州:广东工业大学,2005,36-41
[140] YASDA Precison Tools K.K.支撑YADSA的核心技术. www.yasda.co.jp,2007
[141] Avallone E A, Baumeister T. Marks’standard handbook for mechanical engineers,9thed, New York: McGraw Hill,1987,56-81
[142] Jordan H E. Engergy-efficient electric motors and their applications. New York:2ndEd, Plenum Press,1994,85-98
[143] Boglietti A, Ferraris P, Lazzari M. Power derating for inverter fed inductionmotors.In: Proc of Industry Applications Society Annual Meeting. Piscataway,1994,1:55-61.
[144] Palmgren A. Ball and Roller Bearing Engineering,3rded. Philadelphia: Burbank,1959,87-106
[145] Burton R A，Staph H E.Thermally Activated Seizure of Angular Contact Bearillg.Trans ASJE,1967,10(4):408-417
[146] Ni J. CNC Machine accuracy enhancement through real-time error compensation.Journal of Manufacturing Science and Engineering,1997,119(4B):717-725.
[147]高新波.模糊聚类分析及其应用.西安：西安电子科技大学出版社,2004,2-6
[148]杨纶标.模糊数学原理及应用.广州:华南理工大学出版社,2005,3-32
[149] Zadeh L A. Fuzzy sets. Information and Control,1965,8(3):338-353
[150]刘思峰,郭天榜,党耀国等.灰色系统理论及其应用.北京:科学出版社,1999(第二版),50-76
[151]罗佑新,张龙庭,李敏等.灰色系统理论及其在机械工程中的应用.长沙:国防科技大学出版社,2001,20-31
[152] Anderson R T, Choudhary G, Johnson E N. Comparison of RBF and SHL NeuralNetwork Based Adaptive Control. Journal of Intelligent and Robotic Systems,2009,54:183-199.
[153]姜绍飞.基于神经网络的结构优化与损伤检测.北京:科学出版社,2002,32-34
[154] Guo Z X, Wong W K, Leung S Y S, et al. A genetic-algorithm-based ptimizationmodel for scheduling flexible assembly lines. The International Journal of Ad-vanced Manufacturing Technology,2008,36:156-168
[155] Sahoo G B, Ray C. Predicting flux decline in crossflow membranes using artifi-cial neural networks and genetic algorithms. Journal of Membrane Science,2006,283:147-157.
[156]佟德纯,张黛华.时序分析与工程应用.上海:上海交通大学出版社,1990,5-13
[157]杨叔子.时间序列分析的工程应用(上册).武汉:华中科技大学出版社,2007,255-268
[158]傅立.灰色系统理论及其应用.北京:科学技术文献出版社,1992,21-28
[159] Chen C T. Extensions of the TOPSIS for group decision-making under fuzzyenvironment. Fuzzy sets and Systems,2000,114:1-9
[160]陈耀茂.模糊理论.台北:五南图书出版有限公司,2002,89-102
[161] Visioli A. Fuzzy logic based set-point weight tuning of PID controllers. IEEETrans. on Systems, Man and Cybernetics, Pt.A.1999,29(6):587-592.
[162] Lee J H, Lee J H, Yang S H. Thermal error modeling of a horizontal machiningcenter using fuzzy logic strategy. Journal of Manufacturing Processes,2001,3(2):120-127
[2]张伯霖,杨庆东,陈长年.高速切削技术及应用.北京:机械工业出版社,2002,61-93
[3]张伯霖,张志润,肖曙红.超高速加工与机床的零传动.中国机械工程,1996,7(5):37-41
[4] Bryan J B. International status of thermal error research. In: CIRP Ann-Manu-facturing Technology.1990,39(2):645-656
[5]洪迈生,苏恒,熊诗波等.数控机床运动误差检测技术.组合机床与自动化技术,2002,1:18-22
[6]洪迈生,苏恒,熊诗波等.数控机床运动误差检测技术.组合机床与自动化技术,2002,2:52-53
[7]倪军.数控机床误差补偿研究的回顾及展望.中国机械工程,1997,8(1):29-33
[8] Weck M, McKeown P, Bonse R, et al. Reduction and compensation of thermal errorin machine tools. In: CIRP Ann-Manufacturing Technology,1995,44(2):589-598.
[9] Ferrerira P M, Liu C R. A method for estimating and compensating quasistatic err-ors of machine tools. Journal of Engineering for Industry,1993,115(1):149-159.
[10] Robert B Aronson. War against thermal expansion.Manufacturing Engineering,1996,116(6):45-50.
[11]杨建国.数控机床误差综合补偿技术及应用:[上海交通大学博士学位论文].上海:上海交通大学,1998,48-61
[12] Mou J. A method of using neural networks and inverse kinematics for machinetool error estimation and correction.Journal of Manufacturing Science and Engi-neering,1997,119:247-254.
[13] Wang K C. Thermal error modeling of a machining center using grey systemtheory and adaptive network-based fuzzy inference system. In: IEEE Conf onCybernetics and Intelligent System. Bangkok,2006,1-6
[14] Krulewich D A. Temperature integration model and measurement point selectionfor hermally induced machine tool errors. Mechatronics,1998(8):395-412
[15] Stolz G J. Numerical solutions to an inverse problem of heat conduction forsimple shapes. Journal of Heat Transfer,1960,82:20-26
[16] Sparrow E M, Haji-Sheikh A, Lundgren T S. The inverse problem in transient heatconduction. Journal of Applied Mechanics.1964,86:369-375
[17] Jarny Y, Ozisik M N, Bardon J P. A general optimization method using adjointequation for solving multidimensional inverse heat conduction. InternationalJournal of Heat Mass Transfer,1991,34(11):2911-2919.
[18] Hensel E. Inverse Theory and Applications for Engineers. Englewood: PrenticeHall Press,1991,35-46
[19] Himeno N, Hinata S, Yanadori M. A simple method of Measuring thermo-physic-cal properties by stepwise heating. Trans JSME B,1992,187-192:59-545(inJapanese)
[20] Monde M. Analytical method in inverse heat transfer problem using Laplace tran-sform technique. International Journal of Heat Mass Transfer2000,43:3965-3975
[21] Huang C H, Yan J Y, Chen H T. Function estimation in predictting temperature-dependent thermal conductivity without internal measurements. Journal of Ther-mophysics and Heat Transfer,1995,9(4):667-673
[22] Hayashi H, Watanabe M and Inaba H. Measurement of thermal expansion coeffi-cient of LaCrO3. Thermochimica Acta,2000,359(1):77-85
[23] Abdel-Aal H A, Smith S T. On friction-induced temperatures of rubbing metallicpairs with temperature-dependent thermal properties, Wear,1998,216:41-59
[24] Sawaf B, Ozisik M N. Determining the constant thermal conductivities of ortho-tropic materials by inverse analysis. International Communications in Heat andMass Transfer,1995,22(2):201-211
[25] Jalali-Heravi M, Fatemi M H. Prediction of thermal conductivity detection res-ponse factorsusing an artificial neural network，Journal of Chromatography A,2000,897(1-2):227-235
[26] Jedrzejewski J, Kaczmarek J, Kowal Z, et al. Numerical optimization of thermalbehavior of machine tools. Annals of the CIRP-Manufacturing Technology,1990,39(1):379-382
[27] Choi J K, Lee D G. Thermal characteristics of the spindle bearing system with agear located on the bearing span. International Journal of Machine Tools andManufacture,1998,38:1017-1030
[28] Choi J K, Lee D G. Characteristics of a spindle bearing system with a gear locatedon the bearing span. International Journal of Machine Tools&Manufacture,1997,37(2):171-181
[29] Gibson A O, Stein J L. A finite element model of thermaloly induced angular con-tact spindle bearing loads. The International Mechanical Engineering Congressand Exposition, Anaheim, California,1998,33-38
[30] Tuomaala P, Piira K, Vuolle M. A rational method for the distribution of nodes inmodeling of transient heat conduction in plane slabs. Building and Environment.2000,35:397-406
[31] Zverev I A, Eun In-Ung, Chung W J, et al. Thermal model of high-speed spindleunits. Journal of Mechanical Science and Technology,2003,17(5):668-678
[32] Zverv I A, Pyoun Y S, Lee K B, et al. An elastic deformation model of high speedspindles built into ball bearings. Journal of Materials Processing Technology,2005,170(3):270-278
[33]肖曙红,郭军,张伯霖.高速电主轴热-结构耦合特性的有限元分析.机械设计与制造,2008,9:96-98
[34] Xiao S H, Guo J, Zhang B L. Research on the motorized spindle’s thermal proper-ties based on thermo-mechanical coupling analysis. In: Technology and Innova-tion Conf,2006(6-7):1479-1483
[35] Dai W L, Woodward P R. Numerical simulations for nonlinear heat transfer in asystem of multimaterials. Journal of Computational Physics,1998,139(1):58-78
[36] Bossmanns B, Tu J F. A thermal modle for high speed motorized spindles.International Journal of Machine Tools and Manufacture,1999,39:1345-1366.
[37] Bossmanns B. Thermo-mechanical modeling of motorized spindle systems forhigh speed milling:[dissertation]. West Lafayette: Purdue University,1997,53-81
[38] Bossmanns B, Tu J F. A power flow model for high speed motorized spindles-heatgeneration characterization. Journal of Manufacturing Science and Engineering,2001,123(3):494-505
[39] Lin C W, Tu J F, Kamman J. An integrated thermo-mechanical-dynamic model tocharacterize motorized machien tool spindles during very high speed rotation.International Journal of Machine Tools and Manufacture,2003,43(10):1035-1050
[40] Prabhu Raja V, Thyla P R, Radhakrishnan P. A strategy of investigation on thethermal behaviour of motorised spindles under high speed machining. Interna-tional Journal of Computer Applications in Technology,2006,27(1):1-11
[41] Tu J F, Stein J L. Active thermal preload regulation for machine tool spindles withrolling element bearing. Journal of Manufacturing Science and Engineering,1996,118(4):499-505
[42] Aramaki H, Shoda Y, Morishita Y, et al. The performance of ball bearing withsilicon nitride ceramic balls in high speed spindles for machine tools. Journal ofTribology,1988,110(4):693-698
[43] Jorgensen B R, Shin Y C. Dynamies of machine tool spindle/bearing systemsunder thermal growth. Journal of Tribology,1997,119(4):875-882
[44] Ohishi S, Matsuzaki Y. Experimental investigation of air spindle unit thermalcharacteristics. Precision Engineering,2002,26(01):49-57
[45] Li H Q, Shin Y C. Analysis of bearing configuration effects on high speed spind-les using an integrated dynamic thermo-mechanical spindle model. InternationalJournal of Machine Tools and Manufacture,2004,44(4):347-364
[46] Li H Q, Shin Y C. Integrated dynamic thermo-mechanic modeling of high speed spindles: part1: model development. Journal of Manufacturing Science and Engi-neering,2004,126(1),148-158
[47] Li H Q, Shin Y C. Integrated dynamic thermo-mechanic modeling of high speedspindles: part2. solution procedure and validations. Journal of ManufacturingScience and Engineering,2004,126(1):159-167
[48] Harris T A. Rolling Bearing Analysis. New York: John Wiley and Sons, Inc,1984,26-42
[49]杨启威.轴承系统温度场分析.轴承,1997(3):2-6
[50] Camera A, Favarato M, Militano L, et al. Analysis of the thermal behavior of amachine tool table using the finite element method.CIRP Ann-ManufacturingTechnology,1976,25(1)
[51] Spur G, Hoffmann E, Paluncic Z, et al. Thermal behavior optimization of machinetools [J]. Annals of CIRP–Manufacturing Technology,1988,37(1):401-405
[52] Zhang G, Wang C, Hu X. Error compensation of coordinate measuring machine.CIRP Ann-Manufacturing Technology,1985,34(1):445-448
[53]李永祥.数控机床热误差建模新方法及其应用研究:[上海交通大学博士学位论文].上海:上海交通大学,2007,7-10
[54]赵海涛.数控机床热误差模态分析、测点布置及建模研究:[上海交通大学博士学位论文].上海:上海交通大学,2007,1-2
[55] Venugopal R. Thermal effects on the accuracy of numerically controlled machinetools (numerical methods, experimental):[dissertation]. West Lafayette: PurdueUniversity,1985,105-118
[56] Domnez M A, Blomquist D S, Hocken R J, et al.A general methodology for ma-chine tool accuracy enhancement by error compensation. Precision Engineering,1986,8(4):187-196
[57] Chen J S. A study of thermally induced machine tool errors in real cutting condi-tions.International Journal of Machine Tools and Manufacture,1996,36(12):1401-1411
[58] Chen J S, Yuan J, Ni J. Thermal error modeling for real-time error compensation.International Journal of Advanced Manufacturing Technology1996,12(4):266-275
[59] Chen J S, Ling C C. Improving the machine accuracy through machine tool metro-logy and error correction. The International Journal of Advanced ManufacturingTechnology,1996,11:198-205
[60] Veldhuis S C, Elbestawi M A. A strategy for the compensation of errors in five-axis machining. CIRP Annals-Manufacturing Technology,1995,44(1):373-377
[61] Lee J, Kramer B M. Analysis of machine degradation using a neural networkbased pattern discrimination model. Journal of Manufacturing Systems,1993,38(2):379-387
[62] Yang S, Yuan J, Ni J.The Improvement of thermal error modeling and compen-sation on machine tools by neural network. International Journal of MachineTools and Manufacture,1996,36(4):527-537
[63] Srinivasa N, Ziegert J. Prediction of thermally induced time-variant machine toolerror maps using a fuzzy ARTMAP neural network. Journal of ManufacturingScience and Engineering,1997,119(4):623-630
[64] Ramesh R, Mannan M, Poo A. Thermal error measurement and modelling inmachine tools. Part I: Influence of varying operating conditions. InternationalJournal of Machine Tools and Manufacture,2003,43(4):391-404
[65] Ramesh R, Mannan M, Poo A, et al. Thermal error measurement and modelling inmachine tools. Part II: Hybrid bayesian network-support vector machine model.International Journal of Machine Tools and Manufacture,2003,43(4):405-419.
[66] Kim S, Cho D. Real-time estimation of temperature distribution in a ball-screwsystem. International Journal of Machine Tools and Manufacture,1997,37(4):451-464
[67] Janeczko J. Machine-tool thermal compensation. Tooling and Production,1989,55(5):60-65.
[68] Jedrzejewski J, Modrzycki W. A new approach to modelling thermal behaviour ofa machine tool under service conditions.CIRP Annals-Manufacturing Technology,1992,41(1):455-458.
[69] Jedrzejewski J, Modrzycki W. Intelligent supervision of thermal deformations inhigh precision machine toos. In: Proc of Int Conf on Manufacturing Automationand Systems Technology, Applications, Design, Organisation and Management,and Research. Manchester, UK,1997,457-462
[70] Fraser S, Attia M, Osman M. Modelling, identification and control of thermaldeformation of machine tool structure. Part1: Concept of generalized modeling.Journal of Manufacturing Science and Engineering,1998,120(3):623-631
[71] Fraser S, Attia M, Osman M. Modelling, identification and control of thermaldeformation of machine tool structure. Part2: Generalized transfer functions.Journal of Manufacturing Science and Engineering,1998,120(3):632-639
[72] Fraser S, Attia M, Osman M. Modelling, identification and control of thermaldeformation of machine tool structure. Part3: Real-time estimation of heat sour-ces. Journal of Manufacturing Science and Engineering,1999,121(3):501-508
[73] Fraser S, Attia M, Osman M. Modelling, identification and control of thermaldeformation of machine tool structure. Part4: A multi-variable closed-loop con-trol system. Journal of Manufacturing Science and Engineering,1999,121,(3):509-516
[74] Fraser S, Attia M, Osman M. Modelling, identification and control of thermaldeformation of machine tool structure. Part5: Experimental verification.Journal of Manufacturing Science and Engineering,1999,121(3):517-523.
[75] Wang Y, Zhang G, Moon K et al. Compensation for the thermal error of multi-axismachining center. Journal of Materials Processing Technology,1998,75(1-3):45-53.
[76] Moriwaki T, Shamoto E J. Analysis of thermal deformation of an ultraprecision airspindle system. Manufacturing Technology,1998,47(1):315-319
[77] Moriwaki T. Thermal deformation and its on-line compensation of hydro staticallysupported precision spindle, Annals of the CIRP.1988,37(1):393-396
[78] Moriwaki T, et al. Thermal deformation of an ultraprecision machine tool due toenvironmental temperature change (in Japanese), Trans. of JSME(C),1997,63(615):4025-4030
[79] Lee J H, Lee J H, Yang S H. Thermal error modeling of a horizontal machiningcenter using fuzzy logic strategy[J]. Journal of Manufacturing Processes,2001,3(2):120-127
[80] Lee J H, Yang S H. Statistical optimization and assessment of a thermal errormodel for CNC machine tools. International Journal of Machine Tools and Ma-nufacture,2002,42:147-155
[81] Pahk H J, Lee S W. Thermal error measurement and real time compensationsystem for the CNC machine tools incorporating the spindle thermal error andthe feed axis thermal error. International Journal of Machine Tools and Manu-facture,2002,20:487-494
[82] Ko T J, Gim T W, Ha J Y. Particular behavior of spindle thermal deformation bythermal bending. International Journal of Machine Tools and Manufacture,2003,43:17-23
[83] Yang H, Ni J. Dynamic modeling for machine tool thermal error compensation.Journal of Manufacturing Science and Engineering,2003,125(2):245-254
[84] Yang H, Ni J. Adaptive model estimation of machine tool thermal errors based onrecursive dynamic modeling strategy. International Journal of Machine Tools andManufacture,2005,45:1-11
[85] Zhu J. Robust thermal error modeling and compensation for CNC machine tools:
[dissertation].America, Michigan: The University Of Michigan,2008,16-25
[86] Lo C H, Yuan J, Ni J. An application of real-time error compensation on a turn-ing center. International Journal of Machine Tools and Manufacture1995,35(12):1669-1682
[87] Chen J S, Yuan J X, Ni J, et al. Real-time compensation for time-variant volu-metric error on a machining center. Journal of Engineering for Industry,1993,115(4):472-479
[88] Lei C L, Rui Z Y. Thermal error modeling and compensating of motorized spin-dle based on improved neural network. Advanced Materials Research,2010,129-131:556-560
[89] Magalhaes M H, Ballini R, Molck P, et al. Combining forecasts for naturestreamflow prediction. Annual Conference and Meeting of the North AmericanFuzzy Information Processing Society. Piscataway NJ, USA: IEEE,2004,1:390-394
[90] Cagdas H A, Erol E, Ufuk Y. Forecast combination by using artificial neuralnetworks. Neural Processing Letters,2010,32(3):269-276
[91] Yang H, Ni J. Dynamic neural network modeling for nonlinear, nonstationarymachine tool thermally induced error. International Journal of Machine Toolsand Manufacture,2005,45:455-465
[92] Kang Y, Chang C W, Huang Y R, et al. Modification of a neural network utilizinghybrid filters for the compensation of thermal deformation in machine tools.International Journal of Machine Tool and Manufacture,2007,47(2):376-387
[93] Attia M, Kops L. System approach to the thermal behavior and deformation ofmachine tool structures in response to the effect of fixed joints. Journal of Engi-neering for Industry,1981,103(1):67-72
[94] Weck M, Mckeown P, Bonse R, et al. Reduction and compensation of thermalerrors in machine tools. CIRP Annals-Manufacturing Technology,1995,44(2):589-598
[95]陈子辰.热模态理论和机床热态精度控制策略研究:[浙江大学博士学位论文].杭州:浙江大学,1989:23-36
[96]陈子辰等.热敏感度和热偶合度研究.见:全国机床热误差控制和补偿研究会议论文集.杭州:浙江大学出版社,1992:86-94
[97]戴庆贺.应用西门子CNC@功能补偿车床主轴热误差.制造技术与机床,1998,3:36-37
[98]杨建国,薛秉源.数控机床热误差鲁棒建模新方法及实时补偿.制造技术与机床,1998,6:8-12
[99] Du Z C, Yang J G, Yao Z Q, et al. Modeling approach of regression orthogonalexperiment design for the thermal error compensation of a CNC turning center.Journal of Material Processing Technology,2002,129:619-623
[100]杨建国,薛秉源. CNC车削中心热误差模态分析及鲁棒建模.中国机械工程,1998,9(5):31-35
[101]项伟宏,郑力,刘大成等.机床主轴热误差建模.制造技术与机床,2000,11:12-15
[102]穆塔里夫阿赫迈德,项伟宏,郑力.加工中心主轴热误差实验分析与建模.组合机床与自动化加工技术,2002,9:15-19
[103]杨庆东.数控机床热误差补偿建模方法.制造技术与机床,2000,2:10-15
[104]杨庆东.神经网络补偿机床热变形误差的机器学习技术.机械工程学报,2000,36(1):92-96
[105] Yang Q D. Study of the thermal deformation on a coordinate measuring machineand compensation via a neural network model.International Journal of FlexibleAutomation and Integrated Manufacturing,1999,7:129-147
[106] Yang Q D. Linear regression and neural net models applied to thermal errorcompensation in machine tools.European Journal of Mechanical and Environ-mental Engineering,1999,44:146-152
[107]吴昊,杨建国,张宏韬等.精密车削中心热误差鲁棒建模与实时补偿.上海交通大学学报,2008,42(7):1064-1072
[108] Zhao Haitao,Yang Jianguo,Shen Jinhua.Simulation of thermal behavior of a CNCmachine tool spindle. International Journal of Machine Tools&Manufacture,2007,47:1003-1010
[109]谈小龙,徐卫亚,刘大文等.高边坡变形的组合预测模型及其应用.水利学报,2010,41(3):294-299
[110]王维强,牛振东,曹玉娟等.基于ARMA-TS-GARCH有限混合模型的交通数据分析.中南大学学报:自然科学版,2010,41(5):1860-1864
[111]李永祥,杨建国,郭前建等.数控机床热误差的混合预测模型及应用.上海交通大学学报,2006,40(12):2030-2034
[112]曾勇红,王锡凡,冯宗建.基于混合自回归滑动平均潜周期模型的短期电价预测.西安交通大学学报,2008,42(2):184-188
[113]闫嘉钰,杨建国.数控机床热误差的最优线性组合建模.上海交通大学学报,2009,43(4):633-637
[114] Hatamura Y, Nagao T, Mitsuishi M, et al. Development of an intelligent machin-ing center incorporating active compensation for thermal distortion. CIRPAnnals-Manufacturing Technology,1993,42(1):549-552
[115] Chen J S, Hsu W Y. Characterizations and models for the thermal growth of amotorized high speed spindle. International Journal of Machine Tools andManufacture,2003(43):1163-1170
[116] Chen J S, Chen K W. Bearing load analysis and control of a motorized highspeed spindle. International Journal of Machine Tools and Manufacture,2005,3(45):1487-1493
[117] Li S H, Zhang Y Q, Zhang G X. A study of pre-compensation for thermal errorsof NC machine tools. International Journal of Machine Tools and Manufacture,1997,37(12):1715-1719
[118]张奕群,李书和,刘安伟等.基于主轴转速的机床热误差状态方程模型.仪器仪表学报,1998,19(5):460-463
[119]李书和,张奕群,王东升等.数控机床热误差的建模与预补偿.计量学报,1999,20(1):49-52
[120] Gull M. Contouring accuracy assessment of CNC machine tools-a user’s view. In:Proc Int Conf on Laser Metrology and Machine Performance.1997,401-412
[121] Attia M H, Kops L. Thermometric design considerations for temperature moni-toring in machine tools and CMM structures．The International Journal ofAdvanced Manufacturing Technology1993,8:311-319
[122] Statham A, Martin D, Blackshaw M S. Assessing the thermal distortion causedby spindle rotation of a machining centre using the draft standard ISO/DIS230-3.In: Proc3rd Int Conf on Laser Metrology and Machine Performance.1997:101-111
[123] Ni J. Study on online identification and forecasting compensatory control ofvolumetric errors for multiple axis machine tools:[dissertation]. Madison: Uni-versity of Wisconsin,1987,23-34
[124] Chen J S. Computer-aided accuracy enhancement for multi-axis CNC machinetool. International Journal of Machine Tools and Manufacture,1995,35(4):593-605
[125] Srinivasa N, Ziegert J C, Mize C D. Spindle thermal drift measurement using thelaser ball bar. Precision Engineering,1996,18:118-28
[126] Jywe W Y, Chen C J. The development of a high-speed spindle measurement sys-tem using a laser diode and a quadrants sensor. International Journal of MachineTools and Manufacture,2005,45:1162-1170
[127] Chang C F, Chen J J, Chen T R. A theory thermal growth control techniques ofhigh speed spindles. In: Proc of Int Conf on Advances in Electronics and Micro-electronics. Washington,2008,96-101
[128]高赛,曾理江,殷纯永等.基于单光束干涉仪的机床主轴热误差实时测量.计量学报,2001,22(1):1-6
[129]商鹏.基于球杆仪的高速五轴数控机床综合误差建模与检测方法:[天津大学博士学位论文].天津:天津大学,2008,45-55
[130] Wang K C,Tseng P C,Lin K M.Thermal error modeling of a machining centerusing grey system theory and adaptive network-based fuzzy inference system.Trans JSME C,2006,49(4):1179-1187
[131] Kurtoglu A. The accuracy improvement of machine tools. CIRP Annals-Manu-facturing Technology,1990,39(1):417-419
[132] Chen J. Fast calibration and modeling of thermally-induced machine tool errorsin real machining. International Journal of Machine Tools and Manufacture,1996,37(2):159-169
[133]张德贤,刘筱连,师汉民等.神经网络在数控机床热变形控制中的应用.制造技术与机床,1995,1:8-11
[134]张奕群,李书和,张国雄. Kalman滤波器在机床热误差建模中的应用．航空精密制造技术,1997,33(1):16-18
[135]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.中国机械工程,2004,15(6):478-451
[136]邓卫国,杨建国,任永强等.精密车削中心热误差测试和优化建模.机械制造,2004,42(7):22-26
[137]林伟清,傅建中,许亚洲等.基于LS-SVM与遗传算法的数控机床热误差辨识温度传感器优化策略.光学精密工程,2008,16(9):1682-1687
[138] Zhao C L, Wang Y Q. Optimization of Measuring Points Based on the GreySystem Theory for Spindle of CNC Machine Tool. Proc of the IEEE Int Conf onMechatronics and Automation, Changchun, China,2009:686-690
[139]郭军.基于热接触分析的电主轴热态特性研究:[广东工业大学硕士学位论文].广州:广东工业大学,2005,36-41
[140] YASDA Precison Tools K.K.支撑YADSA的核心技术. www.yasda.co.jp,2007
[141] Avallone E A, Baumeister T. Marks’standard handbook for mechanical engineers,9thed, New York: McGraw Hill,1987,56-81
[142] Jordan H E. Engergy-efficient electric motors and their applications. New York:2ndEd, Plenum Press,1994,85-98
[143] Boglietti A, Ferraris P, Lazzari M. Power derating for inverter fed inductionmotors.In: Proc of Industry Applications Society Annual Meeting. Piscataway,1994,1:55-61.
[144] Palmgren A. Ball and Roller Bearing Engineering,3rded. Philadelphia: Burbank,1959,87-106
[145] Burton R A，Staph H E.Thermally Activated Seizure of Angular Contact Bearillg.Trans ASJE,1967,10(4):408-417
[146] Ni J. CNC Machine accuracy enhancement through real-time error compensation.Journal of Manufacturing Science and Engineering,1997,119(4B):717-725.
[147]高新波.模糊聚类分析及其应用.西安：西安电子科技大学出版社,2004,2-6
[148]杨纶标.模糊数学原理及应用.广州:华南理工大学出版社,2005,3-32
[149] Zadeh L A. Fuzzy sets. Information and Control,1965,8(3):338-353
[150]刘思峰,郭天榜,党耀国等.灰色系统理论及其应用.北京:科学出版社,1999(第二版),50-76
[151]罗佑新,张龙庭,李敏等.灰色系统理论及其在机械工程中的应用.长沙:国防科技大学出版社,2001,20-31
[152] Anderson R T, Choudhary G, Johnson E N. Comparison of RBF and SHL NeuralNetwork Based Adaptive Control. Journal of Intelligent and Robotic Systems,2009,54:183-199.
[153]姜绍飞.基于神经网络的结构优化与损伤检测.北京:科学出版社,2002,32-34
[154] Guo Z X, Wong W K, Leung S Y S, et al. A genetic-algorithm-based ptimizationmodel for scheduling flexible assembly lines. The International Journal of Ad-vanced Manufacturing Technology,2008,36:156-168
[155] Sahoo G B, Ray C. Predicting flux decline in crossflow membranes using artifi-cial neural networks and genetic algorithms. Journal of Membrane Science,2006,283:147-157.
[156]佟德纯,张黛华.时序分析与工程应用.上海:上海交通大学出版社,1990,5-13
[157]杨叔子.时间序列分析的工程应用(上册).武汉:华中科技大学出版社,2007,255-268
[158]傅立.灰色系统理论及其应用.北京:科学技术文献出版社,1992,21-28
[159] Chen C T. Extensions of the TOPSIS for group decision-making under fuzzyenvironment. Fuzzy sets and Systems,2000,114:1-9
[160]陈耀茂.模糊理论.台北:五南图书出版有限公司,2002,89-102
[161] Visioli A. Fuzzy logic based set-point weight tuning of PID controllers. IEEETrans. on Systems, Man and Cybernetics, Pt.A.1999,29(6):587-592.
[162] Lee J H, Lee J H, Yang S H. Thermal error modeling of a horizontal machiningcenter using fuzzy logic strategy. Journal of Manufacturing Processes,2001,3(2):120-127