空气静压支承电主轴动态性能流固耦合分析与实验研究
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摘要
空气静压电主轴是高速精密数控机床的关键部件之一,其动态特性是影响高速数控机床的加工质量和切削能力的重要因素。因此,电主轴的动特性研究,对于进一步提高高速机床的工作性能是有十分重要的现实意义。
当前电主轴的动力学分析中常采用简化法来处理轴承单元的刚度问题,也就是将轴承用假设的弹簧单元来代替,利用有限元法或者传递矩阵法等数值计算法计算主轴的各阶固有频率和振型。该这方法难以解决空气轴承的非线性问题。这种非线性体现在“电机—空气轴承—主轴”耦合系统中的磁场、流体场、固体三场的动态非线性变化。为了寻求解决在这种耦合环境下空气静压电主轴动态问题相应的理论分析方法,本文以高速高精密空气静压电主轴为研究对象,采用磁流固耦合有限元分析方法,对电主轴的动态特性进行了相关的仿真分析、实验研究,主要包括:
1、基于Navier-Stokes(纳维-斯托克斯)运动方程对空气静压轴承的动压效应进行分析,研究主轴在不同转速、不同载荷作用下空气静压轴承气膜动反力及气膜动刚度的非线性变化。其中气膜动反力是通过对气膜压强积分而得,这就减小了传统设计分析中对气膜动反力作弹簧单元处理所带来的误差。
2、为了研究在电主轴回转情况下磁转矩的变化情况,本文采用电磁涡流场模型对电机的磁场分布和感应电流密度的分布进行有限元仿真分析。以此为基础分别从电机的磁固耦合和机械特性这两方面分析电机的磁转矩,并利用数值分析软件MATLAB对电机磁转矩机械特性及启动特性进行仿真分析。
3、在空气静压轴承的流体动力学分析以及电机磁转矩的磁-固耦合分析基础上,本文研究电主轴动态特性进行磁-流-固耦合有限元分析法,建立相关的耦合动力学方程,为后续的仿真分析提供理论依据。
4、以空气静压电主轴磁-流-固耦合动力学方程为基础,对电主轴动态特性进行有限元仿真分析,并采用ANSYS的编程语言APDL开发相应的分析模块。
5、为了验证空气静压电主轴动力学磁流固耦合有限元仿真分析的有效性,本文对主轴静刚度测试、模态实验以及主轴空转特性进行实验研究,实验结果与仿真分析结果具有较好的一致性,这表明磁-流-固耦合动态仿真分析法是可行的。
Aerostatic bearing supported spindle is one of a critical unit of the High Speed Ultra Precise NC machine. Its dynamic performance determines machining qualities and cutting capabilities, and is the important factors influencing the precision of the High-speed NC machine tool. So the study of dynamic performance for High-speed Motorized Spindle makes important and realistic sense.
Currently, in the dynamic analysis of motorized spindle , the simplification way is often used to dealing problem of bear element stiffness, that is exchanging the baer unit with spring unit and then calculating the natural frequency and the vibration type of the spindle by digital arithmetic, like FEM and transfer matrix method。Moreover, it is suitable for dynamic analysis of spindle supported by non-sliding bearing。But it is oversimple to for the nonlinear problem of the aerostatic motorized spindle。In this system, which includes motor、bear and spindle, it is coupled with magnetism-Fluid-solid and its dynamic characteristic is non-linear. So in order to fine the relative way to anslyze this dynamic characteristic, this paper takes works to solve the dynamic problem of The High Speed Ultra Precise Aerostatic Motorized Spindle, such as FEM simulation analysis、experiment research、Structural optimization, which can be seen as follow:
1、Base Navier-Stokes equation, the hydrodynamic action of the aerostatic bear is anslyzed. That is investigating the nonlinear performance of film dynamic anti-force and relative stiffness in different spindle speed and force, which is integrated by film pressure。By this means, it is precise to cut down tolerance from the tradition way to exchange the bear with spring unit.
2、As to the Dynamic Response of magnetism torque and relative physical quantity in the working spindle, according to the mathematical model of whirlpool field, we anslyze the magnetic field and current density of motor by FEM software ANSYS。Then, basing this analyse, the magnetism torque is anslyzed as to magnetism-solid coupled system and mechanical features, and relative simulation is done by MATLAB.
3、The magnetism-Fluid-solid coupled FEM dynamical equation is established baed the previous analyse of aerostatic bear stiffness and motor magnetism torque so that it ground the relative simulation analysis with theory.
4、According to the coupled dynamical equation, this paper use the module ,which is developed by theAPDL of ANSYS, to carry out relatve FEM dynamic simulation analysis of aerostatic motorized spindle.
5、In order to prove the effective of the magnetism-Fluid-solid coupled FEM dynamic simulation analysis of Aerostatic Motorized Spindle, this paper launchs some experimental study, including static stiffness test、mode experiment and characteristic analysis in dry running. And the test data and the result of simulation analysis come to pretty uniform, which certifies the veracity of theory study.
6、For the purpose of raising the spindle stiffness effectively, this paper use the FEM first order method to optimize the aerostatic radial bear. In this process,the hole-throttle number、distribution of hole-throttle、the modes of hole-throttle brought into optimization.
当前电主轴的动力学分析中常采用简化法来处理轴承单元的刚度问题,也就是将轴承用假设的弹簧单元来代替,利用有限元法或者传递矩阵法等数值计算法计算主轴的各阶固有频率和振型。该这方法难以解决空气轴承的非线性问题。这种非线性体现在“电机—空气轴承—主轴”耦合系统中的磁场、流体场、固体三场的动态非线性变化。为了寻求解决在这种耦合环境下空气静压电主轴动态问题相应的理论分析方法,本文以高速高精密空气静压电主轴为研究对象,采用磁流固耦合有限元分析方法,对电主轴的动态特性进行了相关的仿真分析、实验研究,主要包括:
1、基于Navier-Stokes(纳维-斯托克斯)运动方程对空气静压轴承的动压效应进行分析,研究主轴在不同转速、不同载荷作用下空气静压轴承气膜动反力及气膜动刚度的非线性变化。其中气膜动反力是通过对气膜压强积分而得,这就减小了传统设计分析中对气膜动反力作弹簧单元处理所带来的误差。
2、为了研究在电主轴回转情况下磁转矩的变化情况,本文采用电磁涡流场模型对电机的磁场分布和感应电流密度的分布进行有限元仿真分析。以此为基础分别从电机的磁固耦合和机械特性这两方面分析电机的磁转矩,并利用数值分析软件MATLAB对电机磁转矩机械特性及启动特性进行仿真分析。
3、在空气静压轴承的流体动力学分析以及电机磁转矩的磁-固耦合分析基础上,本文研究电主轴动态特性进行磁-流-固耦合有限元分析法,建立相关的耦合动力学方程,为后续的仿真分析提供理论依据。
4、以空气静压电主轴磁-流-固耦合动力学方程为基础,对电主轴动态特性进行有限元仿真分析,并采用ANSYS的编程语言APDL开发相应的分析模块。
5、为了验证空气静压电主轴动力学磁流固耦合有限元仿真分析的有效性,本文对主轴静刚度测试、模态实验以及主轴空转特性进行实验研究,实验结果与仿真分析结果具有较好的一致性,这表明磁-流-固耦合动态仿真分析法是可行的。
Aerostatic bearing supported spindle is one of a critical unit of the High Speed Ultra Precise NC machine. Its dynamic performance determines machining qualities and cutting capabilities, and is the important factors influencing the precision of the High-speed NC machine tool. So the study of dynamic performance for High-speed Motorized Spindle makes important and realistic sense.
Currently, in the dynamic analysis of motorized spindle , the simplification way is often used to dealing problem of bear element stiffness, that is exchanging the baer unit with spring unit and then calculating the natural frequency and the vibration type of the spindle by digital arithmetic, like FEM and transfer matrix method。Moreover, it is suitable for dynamic analysis of spindle supported by non-sliding bearing。But it is oversimple to for the nonlinear problem of the aerostatic motorized spindle。In this system, which includes motor、bear and spindle, it is coupled with magnetism-Fluid-solid and its dynamic characteristic is non-linear. So in order to fine the relative way to anslyze this dynamic characteristic, this paper takes works to solve the dynamic problem of The High Speed Ultra Precise Aerostatic Motorized Spindle, such as FEM simulation analysis、experiment research、Structural optimization, which can be seen as follow:
1、Base Navier-Stokes equation, the hydrodynamic action of the aerostatic bear is anslyzed. That is investigating the nonlinear performance of film dynamic anti-force and relative stiffness in different spindle speed and force, which is integrated by film pressure。By this means, it is precise to cut down tolerance from the tradition way to exchange the bear with spring unit.
2、As to the Dynamic Response of magnetism torque and relative physical quantity in the working spindle, according to the mathematical model of whirlpool field, we anslyze the magnetic field and current density of motor by FEM software ANSYS。Then, basing this analyse, the magnetism torque is anslyzed as to magnetism-solid coupled system and mechanical features, and relative simulation is done by MATLAB.
3、The magnetism-Fluid-solid coupled FEM dynamical equation is established baed the previous analyse of aerostatic bear stiffness and motor magnetism torque so that it ground the relative simulation analysis with theory.
4、According to the coupled dynamical equation, this paper use the module ,which is developed by theAPDL of ANSYS, to carry out relatve FEM dynamic simulation analysis of aerostatic motorized spindle.
5、In order to prove the effective of the magnetism-Fluid-solid coupled FEM dynamic simulation analysis of Aerostatic Motorized Spindle, this paper launchs some experimental study, including static stiffness test、mode experiment and characteristic analysis in dry running. And the test data and the result of simulation analysis come to pretty uniform, which certifies the veracity of theory study.
6、For the purpose of raising the spindle stiffness effectively, this paper use the FEM first order method to optimize the aerostatic radial bear. In this process,the hole-throttle number、distribution of hole-throttle、the modes of hole-throttle brought into optimization.
引文
[1]王云飞.气体润滑理论与气体轴承设计[M]北京:机械工业出版社,1999(2)
[2]盖玉先,董申.超精密加工机床的关键部件技术[J].制造技术与机床.2000年第1期
[3]Kyung Geun Bang et al.design of carbon fiber composite shaft for high speed air spindles.Composite Structures NO.55,2002
[4]Kyung Geun Bang et al.Thrust bearing design for high-speed composite air spindles.Composite Structures NO.57,2002
[5]李树森,刘暾.精密离心机静压气体轴承主轴系统的动力学特性分析[J].机械工程学报,2007,(02)
[6]Marsh,Eric R.;Arneson,David A.;Liebers,Melvin J.;Olson,Mike W.Effects of gas composition on asynchronous error motion in externally pressurized spindles.Precision Engineering.v 32,n 2,April,2008,p 143-147
[7]Couey,Jeremiah A.;Marsh,Eric R.;Knapp,Byron R.;Vallance,R.Ryan.Monitoring force in precision cylindrical grinding.Precision Engineering,.v29,n3,July,2005,p 307-314
[8]Anon.Redefining the boundaries of high precision machining.Aircraft Engineering and Aerospace Technology.v74,n6,2002,p 550-552
[9]Jyh Chyang Renn.Experimental and CFD study on the mass flow-rate characteristic of gas through orifice-type restrictor in aerostatic bearings.Tribology International No.37 2004.-882
[10]Cheng-Ying lo,Cheng—Chi Wang,Yue—Han lee.Performance analysis of high-speed spindle aerostatic bearings.Tribology International 38(2005)5-14
[11]Jerry C.T.Su,K.N.Lie.Rotation effects on hybrid air journal bearings.Tribology International No.36 2003.
[12]K.CzoIczynski.How to obtain stiffness and damping coefficients of gas bearings,wear No.2011996
[13]H.M.Talukder,T.B.Stowell.Pneumatic hammer in an externally pressurized orifice-compensated air journal bearing.Tribology International No.36 2003
[14]杨福兴,董申.超精密空气静压主轴静态性能的数值分析[J].机械设计与研究,2004.4 Vol.20 No.2
[15]边新孝,李谋渭.静压空气轴承的动刚度和阻尼分析[J].轴承,2004,(12).
[16]赵惠英,田世杰,蒋庄德.高精度气体静压轴系刚度分析[J].制造技术与机床,2003,(11).
[17]彭万欢.静压气体径向轴承的静动特性研究[D].中国工程物理研究院,2006年[18]J.J.康纳C.A勃莱皮埃 著 吴望一 译 流体流动的有限元法[M].北京:科学出版社1981年
[18]Moharned Fourka,Marc Bonis.Comparison between externally pressurized gas thrust beatings with different orifice and porous feeding systems.Wear NO.210 1997
[19]梁瑞峰,呼晓青,刘波,张君安.表面节流空气静压润滑轴承性能研究[J].西安工业学院学,2004.3 Vol.24No.1
[20]张君安,张立新,方宗德.空气静压推力轴承压力分布实验台研制[J]西安工业大学学报,2006,(04).
[21]薛龙,张宝生,周灿丰,杨利华,郭德申.真空平衡型气体静压止推轴承的数学模型研究[J].中国机械工程,2001,(08)
[22]Woodson H H.Electromechanical Dynamics[M].New York:John Wilcy and Sons,Inc,1968
[23]Nayfeh A H,Mook D T.Nonlinear Oscillation.New ork:Wilegy-interscience,1979.
[24]Nayfeh A H.An Experimental investigation of complicated responses of a two degree of freedom stmcture[J].JOURNAL OF applied Mechanics,1989,56:960-967.
[25]邱家俊(Qiu Jiajun),汽轮发电机转子由电磁力激发的参数振动规律(The rules of parameters vibration of rotor of steamturbine generator excited by electromagnetic parameters)[J],天津大学学报(Journal of Tianjin University),1981,(4):83-96.
[26]陈贵清,邱家俊(Chen Guiqing,Qiu Jiajun),水轮发电机组转子轴系扭振零阶固有频率的计算和分析(The calculation and analysis of zero-order frequency of hydrogeneration rotor under torsional vibration)[J],商邱师专学报(Joumal of shangQiu teachers college),1999,15(2):18-21.
[27]严登俊,刘瑞芳,胡敏强,李训铭.鼠笼异步电机启动性能的时步有限元计算[J].电机与控制学报,2003,(03)
[28]吴玉厚.数控机床电主轴单元技术[M].北京:机械工业出版社,2006,(03).
[29]濮存德.有限元法在鼠笼式异步电机中的应用——饱和涡流场的分析和启动电流的计算[J].电机技术,1981,(02).
[30]Palit B B.A modle of asynchronous machine with psc stator and rotorcoils,its transformation and its set of equations[J].Ssciential Electrical,1975,21(4).
[31]Peeken H.Torsional vibration during the starting process in driving system with three phase motors[C].The Second of International Conference on Vibration Rotating Machinery,1980.
[32]邱家俊,李文兰(Qiu Jiajun,Li Wenlan),边界约束对水轮发电机定子系统固有频率的影响(The influence of various boundary constraints on the natural frequencies of hydrogenerator stator system)[J],大电机技术(Large Electric Machine and Hydraulic Turbine),1998,(2):1-5.
[33]克利宗,齐曼斯基,雅科夫列夫.转子动力学弹性支承[M].科学出版社,1987(06)
[34]吕浪,熊万里,黄红武,蔡海翔.超高速磨削SPWM电主轴系统机电耦合振动的瞬态特性研究[J].精密制造与自动化,2006,(01)
[35]张力翔,黄文虎.输流管道非线性流固耦合振动的数学建模[J].水动力学研究与进展.2000,15(1):116-128
[29]Edelstein W S,Chen S S,Jendrzejczyk J A.Afinite element computation of the flow-induced oscillations in a cantilevered tube[J].J.Sound ib,1986,107(1):121-129.
[37]Tang D M,Dowell E H.Chaotic oscillations of a cantilevered pipe conveying fluid[J].Journal of Fluids and structures,1988,2:263-283.
[38]TerzaghiK.Theoretical soil mechanics[M].NewYork:Wiley,1943.
[39]BiotMA.General solution of the equation of elasticity and consolida-tion for a porous material[J].J Appl Mech,1956,78:91-96.
[40]郑洽馀 鲁钟琪 流体力学[M].北京:机械工业出版社1979(3)
[41]余鸿钧、王志宏.高速空气静压径向轴承稳定性的试验研究.洛阳轴承研究所,1980
[42]刘墩等著.静压气体润滑.哈尔滨:哈尔滨工业大学出版社,1990
[43]Huang Taiping,The transfer matrix component mode synthesis for rotor-dynamic analysis,ASME Peper No.96-GT-79.
[44]段明亮.空气静压电主轴静态及热态性能的有限元耦合分析与实验研究[D].广州:广东工业大学2006年
[45]张静文,张君安,刘波.空气静压止推轴承性能的数值分析.西安工业学院学报,2002(1):6-10.
[46]Ansys计算流体动力学分析指南[Z].Ansys公司2000年
[47]Crystal A.Heshmat David S.Xu Hooshang Heshmat.Analysis of Gas Lubricated Foil Thrust Bearing Using Coupled Finite Element and Finite Difference Methods[J].Transaciotns of the ASME vol.122,January 2000
[48]Chari M V K,Salon S J.Numerical Methods in Electromagnetism.San Diego:Academic,2000
[49]Binns K J,Lawrenson PJ,Trowbridge C W.The Analytical and Numerical Solution of Electric and Magnetic Fields.New York:John Wiley & Sons,1992.
[50]章文勋.磁场工程中的泛函方法.上海:上海科学技术文献出版社,1985·
[51]章名涛,尚如鸿.电机的磁场.北京:机械工业出版社,1988.
[52]胡敏强,黄学良.电机运行性能数值计算方法及其应用.南京:东南大学出版社,2003(11).
[53]Ho S L,Fu W N,Li H L.The state of art on dynamic mathematical modes of indution machines:Systems,PEDS' 99,1999(1):525-530
[54]盛剑霓.工程磁场数值分析.西安:西安交通大学出版社,1991
[55]汤蕴缪.电机内的电磁场[M]北京:科学出版社1984年
[56]Chang L,Eastham A R,Dawson G E.Permanent magnet synchronous motor:finite element torque calculation.Proc.IEEE Industry Application Society Annual Meeting,San Diego,USA.1989,169(73).
[57]孙玉田,杨明,李北芳.电机动态有限元法中的运动问题.大电机技术,1997(6):15-208
[58]吴宁.电动力学.北京:人民教育出版社,1993.
[59]邱家俊.机电藕联动力学系统的非线性振动.北京:科学出版社,1996.
[60]周鹗.电机学.北京:水利电力出版社,1995
[61]许实章.电机学.北京:机械工业出版社,1987.
[62]Ansys耦合分析指南[Z].Ansys公司2000年
[63]陈祖明.矩阵论引论.北京:北京航空航天大学出版社,1998.
[64]吴望一.流体力学.北京大学出版社,1982
[65]武岳.考虑流固耦合作用的索膜结构风致振动相应研究,哈尔滨工业大学博士学位论文,2003..
[66]黄本才.结构抗风分析原理及应用,上海:同济大学出版社,2001.
[67]王福军.计算流体动力学分析——CFD软件原理与应用,北京:清华大学出版社,2004.
[68]余均鸿.流体静压主轴[M].北京:机械工业出版社1985年12月.
[69]陈世钰.大功率空气静压轴承电主轴[J],中国机械工程,2001年3期
[70]贾启芬,刘习军.机械与结构振动[M]天津:天津大学出版社,2006(7)
[71]阎超,钱翼稷,连祺祥.粘性流体力学[M].北京:北京航空航天大学出版社,2005(8)
[72]李劫科.高速大功率全支承空气静压主轴动静态特性的有限元分析与实验研究[D].广州:广东工业大学2005年.
[73]范云霄,刘桦.测试技术与信号处理[M]北京:中国计量出版社,2003(9).
[74]葛哲学等人.MATLAB6.5辅助优化计算与设计.北京:电子工业出版社,2003(01)
[75]党根茂.气体润滑技术[M].南京:东南大学出版社,1990(6).
[76]J.W.POWELL.空气静压轴承设计.北京:国防工业出版社,1978(12)
[77]Dudgeon,E.H.,and Lowe,I.R.G.'A Theoretical Analysis of Hydrostatic Gas Joumal Bearings'.National Research Council of Canada,Mech.Engineers Report No.MT-54.
[78]杨橚,唐恒龄,廖伯瑜.机床动力学(Ⅱ).北京:机械工业出版社,1983
[79]杨文勇,马平.空气静压轴承动刚度有限元非线性分析[J].机电工程技术,2008,(02).
[80]杨文勇,马平.空气静压轴承静刚度有限元非线性分析[J].润滑与密封,2008,(02).
[81]十合晋一.气体轴承的设计与制造.哈尔滨:黑龙江科学技术出版社,1988(03)
[82]郭彤,李爱群,费庆国,王浩.零阶与一阶优化算法在悬索桥模型修正中的应用对比分析[J].振动与冲击,2007,(04)
[83]王文博.机构和零部件优化设计.北京:机械工业出版社,1990(03)
[84]谢沛霖,陈列,段向阳.一种典型的静压轴承动态特性分析[J].中国机械工程,2005,(19)
[85]阎光萍.超精密空气主轴回转精度的测量与数据处理.航空精密制造技术,1999年第35卷第3期
[86]Mukherjee A.An analytical solution of a finite bearing with an inclined journal.Wear,1974,29.No.1.p.21-29
[87]闻邦椿,顾家柳,夏松波,王正.高等转子动力学——理论、技术与应用究.北京:机械工业出版社,2000(01)
[88]王新月.气体动力学基础[M].陕西:西北工业大学出版社,2006(05)
[89]Brzeski,L.;Kazimierski,Z.;Lech,Y.Experimental investigations of precision spindles equipped with high stiffness gas journal beatings.Precision Engineering Jul,1999,p 155-163.
[90]Kashimura,Y.;Yamasaki,S.;Furutani,K.;Iwamoto,K.A study on air spindle unit for NC milling machine-detection of cutting forces and tool failure using displacement detectors.Journal of the Japan Society of Precision Engineering,.v 56,n 3,March 1990,p 527-32
[2]盖玉先,董申.超精密加工机床的关键部件技术[J].制造技术与机床.2000年第1期
[3]Kyung Geun Bang et al.design of carbon fiber composite shaft for high speed air spindles.Composite Structures NO.55,2002
[4]Kyung Geun Bang et al.Thrust bearing design for high-speed composite air spindles.Composite Structures NO.57,2002
[5]李树森,刘暾.精密离心机静压气体轴承主轴系统的动力学特性分析[J].机械工程学报,2007,(02)
[6]Marsh,Eric R.;Arneson,David A.;Liebers,Melvin J.;Olson,Mike W.Effects of gas composition on asynchronous error motion in externally pressurized spindles.Precision Engineering.v 32,n 2,April,2008,p 143-147
[7]Couey,Jeremiah A.;Marsh,Eric R.;Knapp,Byron R.;Vallance,R.Ryan.Monitoring force in precision cylindrical grinding.Precision Engineering,.v29,n3,July,2005,p 307-314
[8]Anon.Redefining the boundaries of high precision machining.Aircraft Engineering and Aerospace Technology.v74,n6,2002,p 550-552
[9]Jyh Chyang Renn.Experimental and CFD study on the mass flow-rate characteristic of gas through orifice-type restrictor in aerostatic bearings.Tribology International No.37 2004.-882
[10]Cheng-Ying lo,Cheng—Chi Wang,Yue—Han lee.Performance analysis of high-speed spindle aerostatic bearings.Tribology International 38(2005)5-14
[11]Jerry C.T.Su,K.N.Lie.Rotation effects on hybrid air journal bearings.Tribology International No.36 2003.
[12]K.CzoIczynski.How to obtain stiffness and damping coefficients of gas bearings,wear No.2011996
[13]H.M.Talukder,T.B.Stowell.Pneumatic hammer in an externally pressurized orifice-compensated air journal bearing.Tribology International No.36 2003
[14]杨福兴,董申.超精密空气静压主轴静态性能的数值分析[J].机械设计与研究,2004.4 Vol.20 No.2
[15]边新孝,李谋渭.静压空气轴承的动刚度和阻尼分析[J].轴承,2004,(12).
[16]赵惠英,田世杰,蒋庄德.高精度气体静压轴系刚度分析[J].制造技术与机床,2003,(11).
[17]彭万欢.静压气体径向轴承的静动特性研究[D].中国工程物理研究院,2006年[18]J.J.康纳C.A勃莱皮埃 著 吴望一 译 流体流动的有限元法[M].北京:科学出版社1981年
[18]Moharned Fourka,Marc Bonis.Comparison between externally pressurized gas thrust beatings with different orifice and porous feeding systems.Wear NO.210 1997
[19]梁瑞峰,呼晓青,刘波,张君安.表面节流空气静压润滑轴承性能研究[J].西安工业学院学,2004.3 Vol.24No.1
[20]张君安,张立新,方宗德.空气静压推力轴承压力分布实验台研制[J]西安工业大学学报,2006,(04).
[21]薛龙,张宝生,周灿丰,杨利华,郭德申.真空平衡型气体静压止推轴承的数学模型研究[J].中国机械工程,2001,(08)
[22]Woodson H H.Electromechanical Dynamics[M].New York:John Wilcy and Sons,Inc,1968
[23]Nayfeh A H,Mook D T.Nonlinear Oscillation.New ork:Wilegy-interscience,1979.
[24]Nayfeh A H.An Experimental investigation of complicated responses of a two degree of freedom stmcture[J].JOURNAL OF applied Mechanics,1989,56:960-967.
[25]邱家俊(Qiu Jiajun),汽轮发电机转子由电磁力激发的参数振动规律(The rules of parameters vibration of rotor of steamturbine generator excited by electromagnetic parameters)[J],天津大学学报(Journal of Tianjin University),1981,(4):83-96.
[26]陈贵清,邱家俊(Chen Guiqing,Qiu Jiajun),水轮发电机组转子轴系扭振零阶固有频率的计算和分析(The calculation and analysis of zero-order frequency of hydrogeneration rotor under torsional vibration)[J],商邱师专学报(Joumal of shangQiu teachers college),1999,15(2):18-21.
[27]严登俊,刘瑞芳,胡敏强,李训铭.鼠笼异步电机启动性能的时步有限元计算[J].电机与控制学报,2003,(03)
[28]吴玉厚.数控机床电主轴单元技术[M].北京:机械工业出版社,2006,(03).
[29]濮存德.有限元法在鼠笼式异步电机中的应用——饱和涡流场的分析和启动电流的计算[J].电机技术,1981,(02).
[30]Palit B B.A modle of asynchronous machine with psc stator and rotorcoils,its transformation and its set of equations[J].Ssciential Electrical,1975,21(4).
[31]Peeken H.Torsional vibration during the starting process in driving system with three phase motors[C].The Second of International Conference on Vibration Rotating Machinery,1980.
[32]邱家俊,李文兰(Qiu Jiajun,Li Wenlan),边界约束对水轮发电机定子系统固有频率的影响(The influence of various boundary constraints on the natural frequencies of hydrogenerator stator system)[J],大电机技术(Large Electric Machine and Hydraulic Turbine),1998,(2):1-5.
[33]克利宗,齐曼斯基,雅科夫列夫.转子动力学弹性支承[M].科学出版社,1987(06)
[34]吕浪,熊万里,黄红武,蔡海翔.超高速磨削SPWM电主轴系统机电耦合振动的瞬态特性研究[J].精密制造与自动化,2006,(01)
[35]张力翔,黄文虎.输流管道非线性流固耦合振动的数学建模[J].水动力学研究与进展.2000,15(1):116-128
[29]Edelstein W S,Chen S S,Jendrzejczyk J A.Afinite element computation of the flow-induced oscillations in a cantilevered tube[J].J.Sound ib,1986,107(1):121-129.
[37]Tang D M,Dowell E H.Chaotic oscillations of a cantilevered pipe conveying fluid[J].Journal of Fluids and structures,1988,2:263-283.
[38]TerzaghiK.Theoretical soil mechanics[M].NewYork:Wiley,1943.
[39]BiotMA.General solution of the equation of elasticity and consolida-tion for a porous material[J].J Appl Mech,1956,78:91-96.
[40]郑洽馀 鲁钟琪 流体力学[M].北京:机械工业出版社1979(3)
[41]余鸿钧、王志宏.高速空气静压径向轴承稳定性的试验研究.洛阳轴承研究所,1980
[42]刘墩等著.静压气体润滑.哈尔滨:哈尔滨工业大学出版社,1990
[43]Huang Taiping,The transfer matrix component mode synthesis for rotor-dynamic analysis,ASME Peper No.96-GT-79.
[44]段明亮.空气静压电主轴静态及热态性能的有限元耦合分析与实验研究[D].广州:广东工业大学2006年
[45]张静文,张君安,刘波.空气静压止推轴承性能的数值分析.西安工业学院学报,2002(1):6-10.
[46]Ansys计算流体动力学分析指南[Z].Ansys公司2000年
[47]Crystal A.Heshmat David S.Xu Hooshang Heshmat.Analysis of Gas Lubricated Foil Thrust Bearing Using Coupled Finite Element and Finite Difference Methods[J].Transaciotns of the ASME vol.122,January 2000
[48]Chari M V K,Salon S J.Numerical Methods in Electromagnetism.San Diego:Academic,2000
[49]Binns K J,Lawrenson PJ,Trowbridge C W.The Analytical and Numerical Solution of Electric and Magnetic Fields.New York:John Wiley & Sons,1992.
[50]章文勋.磁场工程中的泛函方法.上海:上海科学技术文献出版社,1985·
[51]章名涛,尚如鸿.电机的磁场.北京:机械工业出版社,1988.
[52]胡敏强,黄学良.电机运行性能数值计算方法及其应用.南京:东南大学出版社,2003(11).
[53]Ho S L,Fu W N,Li H L.The state of art on dynamic mathematical modes of indution machines:Systems,PEDS' 99,1999(1):525-530
[54]盛剑霓.工程磁场数值分析.西安:西安交通大学出版社,1991
[55]汤蕴缪.电机内的电磁场[M]北京:科学出版社1984年
[56]Chang L,Eastham A R,Dawson G E.Permanent magnet synchronous motor:finite element torque calculation.Proc.IEEE Industry Application Society Annual Meeting,San Diego,USA.1989,169(73).
[57]孙玉田,杨明,李北芳.电机动态有限元法中的运动问题.大电机技术,1997(6):15-208
[58]吴宁.电动力学.北京:人民教育出版社,1993.
[59]邱家俊.机电藕联动力学系统的非线性振动.北京:科学出版社,1996.
[60]周鹗.电机学.北京:水利电力出版社,1995
[61]许实章.电机学.北京:机械工业出版社,1987.
[62]Ansys耦合分析指南[Z].Ansys公司2000年
[63]陈祖明.矩阵论引论.北京:北京航空航天大学出版社,1998.
[64]吴望一.流体力学.北京大学出版社,1982
[65]武岳.考虑流固耦合作用的索膜结构风致振动相应研究,哈尔滨工业大学博士学位论文,2003..
[66]黄本才.结构抗风分析原理及应用,上海:同济大学出版社,2001.
[67]王福军.计算流体动力学分析——CFD软件原理与应用,北京:清华大学出版社,2004.
[68]余均鸿.流体静压主轴[M].北京:机械工业出版社1985年12月.
[69]陈世钰.大功率空气静压轴承电主轴[J],中国机械工程,2001年3期
[70]贾启芬,刘习军.机械与结构振动[M]天津:天津大学出版社,2006(7)
[71]阎超,钱翼稷,连祺祥.粘性流体力学[M].北京:北京航空航天大学出版社,2005(8)
[72]李劫科.高速大功率全支承空气静压主轴动静态特性的有限元分析与实验研究[D].广州:广东工业大学2005年.
[73]范云霄,刘桦.测试技术与信号处理[M]北京:中国计量出版社,2003(9).
[74]葛哲学等人.MATLAB6.5辅助优化计算与设计.北京:电子工业出版社,2003(01)
[75]党根茂.气体润滑技术[M].南京:东南大学出版社,1990(6).
[76]J.W.POWELL.空气静压轴承设计.北京:国防工业出版社,1978(12)
[77]Dudgeon,E.H.,and Lowe,I.R.G.'A Theoretical Analysis of Hydrostatic Gas Joumal Bearings'.National Research Council of Canada,Mech.Engineers Report No.MT-54.
[78]杨橚,唐恒龄,廖伯瑜.机床动力学(Ⅱ).北京:机械工业出版社,1983
[79]杨文勇,马平.空气静压轴承动刚度有限元非线性分析[J].机电工程技术,2008,(02).
[80]杨文勇,马平.空气静压轴承静刚度有限元非线性分析[J].润滑与密封,2008,(02).
[81]十合晋一.气体轴承的设计与制造.哈尔滨:黑龙江科学技术出版社,1988(03)
[82]郭彤,李爱群,费庆国,王浩.零阶与一阶优化算法在悬索桥模型修正中的应用对比分析[J].振动与冲击,2007,(04)
[83]王文博.机构和零部件优化设计.北京:机械工业出版社,1990(03)
[84]谢沛霖,陈列,段向阳.一种典型的静压轴承动态特性分析[J].中国机械工程,2005,(19)
[85]阎光萍.超精密空气主轴回转精度的测量与数据处理.航空精密制造技术,1999年第35卷第3期
[86]Mukherjee A.An analytical solution of a finite bearing with an inclined journal.Wear,1974,29.No.1.p.21-29
[87]闻邦椿,顾家柳,夏松波,王正.高等转子动力学——理论、技术与应用究.北京:机械工业出版社,2000(01)
[88]王新月.气体动力学基础[M].陕西:西北工业大学出版社,2006(05)
[89]Brzeski,L.;Kazimierski,Z.;Lech,Y.Experimental investigations of precision spindles equipped with high stiffness gas journal beatings.Precision Engineering Jul,1999,p 155-163.
[90]Kashimura,Y.;Yamasaki,S.;Furutani,K.;Iwamoto,K.A study on air spindle unit for NC milling machine-detection of cutting forces and tool failure using displacement detectors.Journal of the Japan Society of Precision Engineering,.v 56,n 3,March 1990,p 527-32
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