HBM-800T立式斜流泵磁悬浮轴承研究
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摘要
目前,在国内大中型泵站的机组中,导轴承可靠性不高、使用寿命短、维修工作量大是一个普遍性的问题。目前使用广泛的水润滑橡胶轴承以及赛龙轴承在比较复杂的环境中工作时,容易出现轴承损坏或者是主轴损坏等问题,因此寻求一种稳定性高、使用寿命长的高性能导轴承,以保证立式斜流泵可靠运行是很有现实意义的。研究表明,磁轴承应用于立式斜流泵具备无接触、刚度和阻尼可调等传统轴承无法比拟的优势。
课题在调研了国内、外立式斜流泵导轴承及磁悬浮轴承的现状和发展的基础上,以混合磁轴承应用于HBM-800T立式斜流泵进而改善该型立式斜流泵的运行稳定性为研究目标。考虑课题涉及机械学、力学、电磁学、控制理论、电子技术等多学科综合的特性,在不失系统一般性的前提下,突出研究重点,分别研究磁轴承新结构、叶片振动与转子及磁轴承耦合动力学、鲁棒控制等系统核心组成部分。
主要工作及成果如下：
1.提出一种应用于立式斜流泵的新型混合径向磁轴承,这种混合磁轴承是永磁磁轴承和电磁磁轴承的组合。其中永磁磁轴承采用的是斥力型Halbach阵列永磁环堆叠结构,主动磁轴承采用8磁极结构,其中4对磁极径向分布,每对磁极轴向布置,永磁磁路与电磁磁路相互独立。小扰动偏移可以由被动磁轴承消除；扰动较大时,转子的位移由永磁磁轴承和电磁磁轴承共同控制,从而在一定程度上降低主动磁轴承的功耗。研究结果表明,新型混合磁轴承应用于立式斜流泵具备节能及可控的优点。
2.立式斜流泵转子较长,运转过程中,容易产生振动,尤其当泵高速运转时,容易发生叶片与壳体碰摩,非线性振动等有害因素,因此研究转子动力学理论,有利于解决泵的非线性动力学问题。课题建立一个叶片-转子-磁轴承系统的非线性动力学模型来分析叶片、转子和磁轴承之间的相互作用。利用Lagrange方程获得系统的耦合动力学微分方程。采用集中质量法、正交变换及周期变换将具有时变系数的耦合方程转化为常系数微分方程。数值计算结果表明这种系统具有丰富的非线性动力学现象,进入混沌的道路是通过阵发方式实现的。随后混沌运动演化为周期1运动,退出混沌运动状态；通过在较宽的转速范围数值计算表明,系统响应是倍周期运动,说明系统响应在转速大范围内是稳定的。虽然出现局部混沌运动,但转子无量纲位移振幅不大,远小于永磁轴承工作气隙,没有发生碰摩现象。
3.磁悬浮轴承除了无接触外,还有一个很显著的特点就是磁轴承的刚度可通过设计合适的控制系统按控制规律调整。所以研究混合磁轴承系统的组成及相关结构参数与控制系统的承载能力及刚度特性很有必要。课题采用电流分散控制策略,考虑功率放大器、控制电路和位移传感器增益特性,以及位移传感器位置耦合问题,并对系统状态矩阵及输入矩阵进行强制解耦,进而实现新型混合磁轴承的转子系统进行建模。通过以上步骤已经得到单个自由度上的磁轴承-转子系统传递函数,为系统控制器的设计奠定基础。
4.提出一种应用于立式斜流泵磁轴承转子控制系统的L2鲁棒控制器。由于目前磁悬浮轴承系统的动态特性还不能完全被人们掌握,很难得到磁悬浮轴承系统精确的数学模型,即存在模型“不确定性”。这些“不确定性”的主要来源是磁轴承电磁铁与转子之间以及与所处的环境体现出来的多场耦合问题。针对立式斜流泵混合磁轴承工作特点,首先将磁悬浮轴承电流控制器的设计问题转化为标准的L2问题进行设计。其次,基于无源化理论及递推解法求出系统的存储函数,并证明满足耗散不等式及闭环系统在原点全局渐近稳定。最后,用Matlab对L2控制的立式斜流泵磁悬浮轴承系统进行仿真,并与PID控制器的控制效果进行比较研究。结果表明,L2鲁棒控制策略相对PID控制策略更能有效抑制未知外扰动的影响。
5.最后,通过立式斜流泵磁悬浮轴承系统的简化模型实验研究,结果表明,磁悬浮轴承系统中转子能实现稳定悬浮,响应快,相移小以及具备干扰抑制性能。
At present, there is a widespread problem, namely the guide bearing reliability is not high, its life is short,and the large amount of maintenance work in the large and medium-sized pumping station crew of our country.The use of a wide range of water-lubricated rubber bearings and Thordon bearings prone to be damaged its bearing or spindle,when they are working in a extreme environment.Therefore, to find a guide bearing which is high stability, long life, high-performance to ensure the operation of vertical mixed flow pump reliable is significance.The research showed that there are much more advantages with magnetic bearings in vertical mixed flow pump relatively to conventional bearings,such as,no contact stiffness and damping adjustable.
The hybrid magnetic bearings used in HBM-800T vertical mixed flow pump thus improving its operational stability is for the research objectives on the basis of the domestic the outside vertical mixed flow pump guide bearing and magnetic bearing status quo and development.This study,without losing the generality of the foregoing, highlighting research priorities,were to study the key part of the new structure of the magnetic bearing, blade vibration,rotor and magnetic bearing coupling dynamics, robust control system for this topic relates to mechanics,mechanics, electromagnetics,control theory,electronic technology,multi-disciplinary, characterist-ics.
The main actions and results are as follows,
1. A new hybrid radial magnetic bearings used in vertical mixed flow pump has been proposed. This hybrid magnetic bearing is a combination of permanent magnetic bearing and electromagnetic magnetic bearing.Repulsion Halbach array permanent magnet ring stack structure is used in permanent magnetic bearing structure.Active magnetic bearings contains8-poles, with four pairs of magnetic level radial distribution and each pair of magnetic-stage axial arrangement. Permanent magnetic circuit and electromagnetic circuit are independent of each other.Small perturbation offset is controled by the passive magnetic bearing and the displacement of the rotor is jointly controlled by the permanent magnetic bearings and electromagnetic magnetic bearing when the disturbance is large. So this new hybrid radial magnetic bearings could reduce the power consumption of the active magnetic bearing to some extent.The results show that the new hybrid magnetic bearings used in vertical mixed flow pump has the advantages of energy-saving and controllable.
2. The study of rotor dynamics theory help solve the nonlinear dynamics of the vertical mixed flow pump,for its rotor is long and easy to shake.The blade and the housing prone to touch friction and produce other harmful nonlinear vibration factors when the operation speed is high.This study established a nonlinear dynamic model of blade-rotor-magnetic bearing system to analyze the interaction between the blades, rotor and magnetic bearings.The coupling dynamics differential equations of the system has been obtained using the Lagrange equation.Coupled equations with time-varying coefficients have been transformed to constant coefficients by the method of lumped-mass, orthogonal transformation and conversion cycle.The numerical results show that this system has a wealth of nonlinear dynamical phenomena and enters to chaos via burst.Then it exit the chaotic motion by chaotic evolution period-1.And the numerical results show that the system response is periodic motion,which indicates that the system is stable in a wide speed range.Rotor dimensionless displacement amplitude, the local chaotic motion, is far less than the permanent magnet bearing the working air gap and no rub-impact phenomenon.
3. Magnetic levitation bearings have no contact.In addition,there is a very significant feature that is the magnetic bearing stiffness can be adjusted through the design of a suitable control system.Therefore, the hybrid magnetic bearing control system's carrying capacity and stiffness characteristics relation to the composition and structure parameters is necessary to be studied.In this study, the new hybrid magnetic bearing rotor system model is established by current decentralized control strategy, and considering the gain of power amplifier,control circuit and the displacement sensor, and considering the coupling problem of position sensor. And the system state matrix and input matrixby have been decoupled forcibly. A single degree of freedom magnetic bearing-rotor system transfer function is obtained through the above steps that lays the foundation for the the system controller design.
4. A L2robust controller is proposed and applied to the vertical mixed flow pump magnetic bearing rotor control system.Accurate mathematical model of the magnetic bearing system is difficult to be get, due to the dynamic characteristics of the magnetic bearing system can not fully be grasped by people. So there is a problem of model "uncertainty".The main source of the "uncertainty" is coupled magnetic bearing between the electromagnet and the rotor, and the environment.First, the controller design of the magnetic bearing current is converted to a standard L2design considering the hybrid magnetic bearing work characteristics of vertical mixed flow pump.Secondly, the storage function of the system is determined by the passive theory and the recursive solution, and is proved to meet dissipation inequality and the closed-loop system asymptotically stable condition at the origin global.Finally, L2control method of vertical mixed flow pump magnetic bearing system has been simulated by Matlab. And its control effect has been compared with the PID controller.The results showed that the L2robust control strategy relative to PID control strategy is more effective inhibition of the effects of unknown external disturbance.
5.Finally, the simplified model experiment of vertical mixed flow pump magnetic bearing system has been carried out.The results showed that the rotor of the magnetic bearing system can achieve stable levitation, fast response, small phase shift as well as with interference suppression performance.
课题在调研了国内、外立式斜流泵导轴承及磁悬浮轴承的现状和发展的基础上,以混合磁轴承应用于HBM-800T立式斜流泵进而改善该型立式斜流泵的运行稳定性为研究目标。考虑课题涉及机械学、力学、电磁学、控制理论、电子技术等多学科综合的特性,在不失系统一般性的前提下,突出研究重点,分别研究磁轴承新结构、叶片振动与转子及磁轴承耦合动力学、鲁棒控制等系统核心组成部分。
主要工作及成果如下：
1.提出一种应用于立式斜流泵的新型混合径向磁轴承,这种混合磁轴承是永磁磁轴承和电磁磁轴承的组合。其中永磁磁轴承采用的是斥力型Halbach阵列永磁环堆叠结构,主动磁轴承采用8磁极结构,其中4对磁极径向分布,每对磁极轴向布置,永磁磁路与电磁磁路相互独立。小扰动偏移可以由被动磁轴承消除；扰动较大时,转子的位移由永磁磁轴承和电磁磁轴承共同控制,从而在一定程度上降低主动磁轴承的功耗。研究结果表明,新型混合磁轴承应用于立式斜流泵具备节能及可控的优点。
2.立式斜流泵转子较长,运转过程中,容易产生振动,尤其当泵高速运转时,容易发生叶片与壳体碰摩,非线性振动等有害因素,因此研究转子动力学理论,有利于解决泵的非线性动力学问题。课题建立一个叶片-转子-磁轴承系统的非线性动力学模型来分析叶片、转子和磁轴承之间的相互作用。利用Lagrange方程获得系统的耦合动力学微分方程。采用集中质量法、正交变换及周期变换将具有时变系数的耦合方程转化为常系数微分方程。数值计算结果表明这种系统具有丰富的非线性动力学现象,进入混沌的道路是通过阵发方式实现的。随后混沌运动演化为周期1运动,退出混沌运动状态；通过在较宽的转速范围数值计算表明,系统响应是倍周期运动,说明系统响应在转速大范围内是稳定的。虽然出现局部混沌运动,但转子无量纲位移振幅不大,远小于永磁轴承工作气隙,没有发生碰摩现象。
3.磁悬浮轴承除了无接触外,还有一个很显著的特点就是磁轴承的刚度可通过设计合适的控制系统按控制规律调整。所以研究混合磁轴承系统的组成及相关结构参数与控制系统的承载能力及刚度特性很有必要。课题采用电流分散控制策略,考虑功率放大器、控制电路和位移传感器增益特性,以及位移传感器位置耦合问题,并对系统状态矩阵及输入矩阵进行强制解耦,进而实现新型混合磁轴承的转子系统进行建模。通过以上步骤已经得到单个自由度上的磁轴承-转子系统传递函数,为系统控制器的设计奠定基础。
4.提出一种应用于立式斜流泵磁轴承转子控制系统的L2鲁棒控制器。由于目前磁悬浮轴承系统的动态特性还不能完全被人们掌握,很难得到磁悬浮轴承系统精确的数学模型,即存在模型“不确定性”。这些“不确定性”的主要来源是磁轴承电磁铁与转子之间以及与所处的环境体现出来的多场耦合问题。针对立式斜流泵混合磁轴承工作特点,首先将磁悬浮轴承电流控制器的设计问题转化为标准的L2问题进行设计。其次,基于无源化理论及递推解法求出系统的存储函数,并证明满足耗散不等式及闭环系统在原点全局渐近稳定。最后,用Matlab对L2控制的立式斜流泵磁悬浮轴承系统进行仿真,并与PID控制器的控制效果进行比较研究。结果表明,L2鲁棒控制策略相对PID控制策略更能有效抑制未知外扰动的影响。
5.最后,通过立式斜流泵磁悬浮轴承系统的简化模型实验研究,结果表明,磁悬浮轴承系统中转子能实现稳定悬浮,响应快,相移小以及具备干扰抑制性能。
At present, there is a widespread problem, namely the guide bearing reliability is not high, its life is short,and the large amount of maintenance work in the large and medium-sized pumping station crew of our country.The use of a wide range of water-lubricated rubber bearings and Thordon bearings prone to be damaged its bearing or spindle,when they are working in a extreme environment.Therefore, to find a guide bearing which is high stability, long life, high-performance to ensure the operation of vertical mixed flow pump reliable is significance.The research showed that there are much more advantages with magnetic bearings in vertical mixed flow pump relatively to conventional bearings,such as,no contact stiffness and damping adjustable.
The hybrid magnetic bearings used in HBM-800T vertical mixed flow pump thus improving its operational stability is for the research objectives on the basis of the domestic the outside vertical mixed flow pump guide bearing and magnetic bearing status quo and development.This study,without losing the generality of the foregoing, highlighting research priorities,were to study the key part of the new structure of the magnetic bearing, blade vibration,rotor and magnetic bearing coupling dynamics, robust control system for this topic relates to mechanics,mechanics, electromagnetics,control theory,electronic technology,multi-disciplinary, characterist-ics.
The main actions and results are as follows,
1. A new hybrid radial magnetic bearings used in vertical mixed flow pump has been proposed. This hybrid magnetic bearing is a combination of permanent magnetic bearing and electromagnetic magnetic bearing.Repulsion Halbach array permanent magnet ring stack structure is used in permanent magnetic bearing structure.Active magnetic bearings contains8-poles, with four pairs of magnetic level radial distribution and each pair of magnetic-stage axial arrangement. Permanent magnetic circuit and electromagnetic circuit are independent of each other.Small perturbation offset is controled by the passive magnetic bearing and the displacement of the rotor is jointly controlled by the permanent magnetic bearings and electromagnetic magnetic bearing when the disturbance is large. So this new hybrid radial magnetic bearings could reduce the power consumption of the active magnetic bearing to some extent.The results show that the new hybrid magnetic bearings used in vertical mixed flow pump has the advantages of energy-saving and controllable.
2. The study of rotor dynamics theory help solve the nonlinear dynamics of the vertical mixed flow pump,for its rotor is long and easy to shake.The blade and the housing prone to touch friction and produce other harmful nonlinear vibration factors when the operation speed is high.This study established a nonlinear dynamic model of blade-rotor-magnetic bearing system to analyze the interaction between the blades, rotor and magnetic bearings.The coupling dynamics differential equations of the system has been obtained using the Lagrange equation.Coupled equations with time-varying coefficients have been transformed to constant coefficients by the method of lumped-mass, orthogonal transformation and conversion cycle.The numerical results show that this system has a wealth of nonlinear dynamical phenomena and enters to chaos via burst.Then it exit the chaotic motion by chaotic evolution period-1.And the numerical results show that the system response is periodic motion,which indicates that the system is stable in a wide speed range.Rotor dimensionless displacement amplitude, the local chaotic motion, is far less than the permanent magnet bearing the working air gap and no rub-impact phenomenon.
3. Magnetic levitation bearings have no contact.In addition,there is a very significant feature that is the magnetic bearing stiffness can be adjusted through the design of a suitable control system.Therefore, the hybrid magnetic bearing control system's carrying capacity and stiffness characteristics relation to the composition and structure parameters is necessary to be studied.In this study, the new hybrid magnetic bearing rotor system model is established by current decentralized control strategy, and considering the gain of power amplifier,control circuit and the displacement sensor, and considering the coupling problem of position sensor. And the system state matrix and input matrixby have been decoupled forcibly. A single degree of freedom magnetic bearing-rotor system transfer function is obtained through the above steps that lays the foundation for the the system controller design.
4. A L2robust controller is proposed and applied to the vertical mixed flow pump magnetic bearing rotor control system.Accurate mathematical model of the magnetic bearing system is difficult to be get, due to the dynamic characteristics of the magnetic bearing system can not fully be grasped by people. So there is a problem of model "uncertainty".The main source of the "uncertainty" is coupled magnetic bearing between the electromagnet and the rotor, and the environment.First, the controller design of the magnetic bearing current is converted to a standard L2design considering the hybrid magnetic bearing work characteristics of vertical mixed flow pump.Secondly, the storage function of the system is determined by the passive theory and the recursive solution, and is proved to meet dissipation inequality and the closed-loop system asymptotically stable condition at the origin global.Finally, L2control method of vertical mixed flow pump magnetic bearing system has been simulated by Matlab. And its control effect has been compared with the PID controller.The results showed that the L2robust control strategy relative to PID control strategy is more effective inhibition of the effects of unknown external disturbance.
5.Finally, the simplified model experiment of vertical mixed flow pump magnetic bearing system has been carried out.The results showed that the rotor of the magnetic bearing system can achieve stable levitation, fast response, small phase shift as well as with interference suppression performance.
引文
[1]仇宝云,汤正军,黄海田等.黄海田等大型水泵机组大修与大修周期分析.水泵技术,1998.,24(1)：40-42
[2]孙文丽,王优强,时高伟.赛龙轴承材料摩擦学性能的试验研究.润滑与密封,2011,36(5)：36-39
[3]林海江,仇宝云,汤正军.大中型水泵导轴承材料比较选用研究.水泵技术,2005,6：22-26
[4]杨树雄.大型卧式轴流泵水导轴承研究.排灌机械,2003,21(1)：15-17
[5]曹海红,仇宝云,邓东升.水泵水润滑导轴承耐久性研究.排灌机械,2009,29(3)：277-282
[6]杨洪群.吴玲玲.泵站机组水导轴承的研究.排灌机械,2004,22(3)：22-24
[7]黄毅.斜轴伸水泵的导轴承材料应用分析.水利水电科技进展,2003,23(6)：47-48
[8]杨成仁,苏逢荃,王优强.八纵向沟水润滑橡胶轴承润滑机理的实验研究.青岛建筑工程学院学报,1995,16(4)：51-58
[9]王优强,李鸿琦.水润滑赛龙轴承及其润滑性能综述.润滑与密封,2003,(1)：101-104
[10]周泽华,王家序.陶瓷在水润滑轴承中的应用.陶瓷工程,2000,(12)：29-31
[11]吴仁荣.水润滑滑动轴承设计计算.机电设备,1997,(6)：30-32,35
[12]仇宝云,黄海田,魏强林等.大型立式水泵油轴承改水轴承的应用研究.流体机械,2000,28(1)：35-37
[13]Howard Smitb. Is the Writing on the Wall for Oil Lubricated Bearings in Pumps. World Pumps,1995,12:38-41
[14]Robin Kyte. Advanced Bearing Technology Improves Pump Performance. World Pumps,2002,7:42-45
[15]Rick Bruggeman. Innovative Ceramic Sliding Bearings. World Pumps, October, 2002,10:30-32
[16]Zhao Xusheng, Deng Zhiquan, Wang Xiaolin, et al. Research status and development of permanent magnet biased magnetic bearings. Diangong Jishu Xuebao/Transactions of China Electrotechnical Society.2009,24 (9):9-20
[17]苏义鑫,王提峰.磁力轴承技术研究进展.仪器仪表用户,2007,14(5)：2-4
[18]蒋启龙,连级三.电磁轴承及其应用研究综述.重庆大学学报,2004,27(7)：146-151
[19]Gerhard Schweitzer, Hanner Bleuler, Matthew Cole, et al.磁悬浮轴承-理论、设计及旋转机械应用.北京：机械工业出版社,2012：1-16
[20]S.Earnshaw.On the nature of the molecular forces which regulate the constitution of the luminiferous ether. Trans. Camb. Phil. Soc.,1842,7:97-112
[21]Kemper H. Overhead suspension railway with wheelless vehicles employing magnetic suspension from iron rails.Germ.Pat.Nos.643316 and 644302,1937
[22]Kemper H. Suspension by electromagnetic forces:a possibility for a radically new method of transportation. ETZ,1938,59:391-395
[23]董宏涛.磁力轴承功率放大器的设计与仿真：[武汉理工大学硕士学位论文].武汉：武汉理工大学,2006
[24]Toumier P.L. Magnetic suspension for model in wind tunnel. La recherche aeronautique No.59, July-August,1957, Paris
[25]Toumier P.L.Totally active magnetic suspension system.French Pat.Nos.1186527, 1957
[26]宗鸣.永磁偏置混合式磁轴承及其控制方法的研究：[沈阳工业大学博士学位论文].沈阳：沈阳工业大学,2007
[27]陈龙.磁力轴承结构参数化设计：[武汉理工大学硕士学位论文].武汉：武汉理工大学,2005
[28]全定策.磁力轴承结构设计及其转子结构特性分析：[武汉理工大学硕士学位论文].武汉：武汉理工大学,2004
[29]邓坚强.电磁轴承有限元分析、结构设计及控制：[浙江大学硕士学位论文].杭州：浙江大学,2004
[30]钟毅.磁悬浮嵌入式控制系统基础理论和关键技术研究：[武汉理工大学博士学位论文].武汉：武汉理工大学,2007
[31]张敬.混合式磁悬浮轴承及其控制系统的研究：[沈阳工业大学硕士学位论文].沈阳：沈阳工业大学,2005
[32]仇志坚.永磁型无轴承电机的基础研究：[南京航空航天大学博士学位论文].南京：南京航空航天大学,2009
[33]虞烈.可控磁悬浮转子系统.北京：科学出版社,2003
[34]Lee An-Chen, Hsiao Foam-Zone, Ko Dennil.Analysis and testing of magnetic bearing with permanent magnets for bias.JSME International Journal,Series C, 1994,37(4):774-782
[35]Silva I D, Horikawa O.An 1-D.o.f.Controlled attraction type magnetic bearing, electric machines and drives.International Conference IEMD'99,1999:481-483
[36]Fang J.R., Lin, L.Z., Yan L.G., et al. A new flywheel energy storage system using hybrid superconducting magnetic bearings. Applied Superconductivity. 2001,11 (1):1657-1660
[37]Peng Wu, Tseng, K.J. A self-bearing centrifugal blood pump based on induction motor with active and passive magnetic bearings. In:The Fifth International Conference on Power Electronics and Drive Systems. Singapore,2003: 1642-1646
[38]Onuma Hiroyuki, Murakami Michiko, Masuzawa Toru. Novel maglev pump with a combined magnetic bearing. ASAIO Journal.2005,51 (1):50-55
[39]方家荣,林良真,夏平畴,严陆光.超导混合磁力轴承的发展现状和前景.电工电能新技术,2000,(1)：27-31
[40]Dun Yueqin, Wang Xiuhe, Kong Yu. Analysis of hybrid magnetic bearing with a permanent magnet in the rotor by FEM.IEEE Transactions on Magnetics,2006, 42 (4):1363-1366
[41]肖林京,孙传余,李鹏,等.一种永磁上吸下斥结构的低功耗混合式磁轴承.中国专利.201010110709.9,2010-1-26
[42]钟一锷,何衍宗,王正,等.转子动力学.北京：清华大学出版社,1987
[43]张文.转子动力学理论基础.北京：科学出版社,1990
[44]闻邦椿,顾家柳,夏松波,等.高等转子动力学理论、技术与应用.北京：机械工业出版社,1999
[45]黄文虎,夏新波,焦映厚,等.旋转机械非线性动力学的理论与试验.北京：科学出版社,2006
[46]Carta FO. Coupled blade-disk-shroud flutter instabilities in turbojet engine rotors.ASME Journal of Engineering for Power,1967,89:419-427
[47]D.R.Chivens, H.D.Nelson.The natural frequencies and critical speeds of a rotating, flexible shaft-disk system. ASME Jou(?)nal of Engineering for Industry, 1975,97:881-886
[48]L.E.E1-Bayoumy, A.V. Srinivasan.Influence of mistuning on rotor-blade vibrations. AIA A Journal,1975,13:460-464
[49]A.V.Srinivasan. Vibrations of bladed-disk assemblies-A selected survey. ASME, Transactions, Journal of Vibration, Acoustics, Stress and Reliability in Design,1984,106:165-168
[50]E.F.Crawley, D.R.Mokadam.Stagger angle dependence of inertial and elastic coupling in bladed disks. Journal of vibration, acoustics, stress, and reliability in design,1984,106:181-188
[51]M. Sakata, K. Kimura, S.K. Park, et al. Vibration of bladed flexible rotor due to gyroscopic moment. Journal of Sound and Vibration,1989,113(3):417-430
[52]J. Padovan, F.K. choy. Nonlinear dynamics of rotor/blade/casing rub interactions. Journal of Turbomachinery,1987,109:527-534
[53]N. Lesaffre, J.J. Sinou, F. Thouverez. Contact analysis of a flexible bladed-rotor. european Journal of Mechanics A/Solids,2007,26:541-557
[54]S.B. Chun, C.W. Lee.Vibration analysis of shaft-bladed disk system by using substructure synthesis and assumed modes method. Journal of Sound and Vibration,1996,189 (5):587-608
[55]S.K. Sinha. Dynamic characteristics of a flexible bladed-rotor with Coulomb damping due to tip-rub. Journal of Sound and Vibration,2004,273(4-5):875-919
[56]C.H. Yang, S.C. Huang.The influence of disk's flexibility on coupling vibration of shaft-disk-blades systems.Journal of sound and vibration,2007,301 (1-2): 1-17
[57]ivlizuno Takeshil, Hara Yusuke.Active stabilization of a repulsive magnetic bearing using the motion control of permanent magnets.JSME International Journal, Series C:Mechanical Systems, Machine Elements and Manufacturing, 2000,43 (3):632-637
[58]Demachi Kazuyuki, Miura Akiral, Sawada Akihiko, et al. Numerical simulation of dynamics of radial type superconducting magnetic bearing. International Journal of Applied Electromagnetics and Mechanics,2001, 1491-4):127-132
[59]Sim Hyun-Sik, Kim Ha-Yong, Lee Chong-Won, et al. Stabilization of active magnetic bearing system subject to base motion.In:19th Biennial Conference on Mechanical Vibration and Noise, Chicago,2003:2007-2013
[60]Jiang Shuyun, Ju Lihua. Study on electromechanical coupling nonlinear vibration of flywheel energy storage system.Science in China, Series E:Technological Sciences,2006,49 (1):61-77
[61]Cansiz, Ahmet. Static and dynamic analysis of a diamagnetic bearing system. Journal of Applied Physics,2008,103 (3):034510
[62]Kang Kyungdae,Palazzolo Alan. Dynamical and experimental researches of active magnetic bearing rotor systems for high-speed PM machines.IEEE Transactions on Magnetics,2012,48 (6):1984-1994
[63]田拥胜,孙岩桦,虞烈.高速永磁电机电磁轴承转子系统的动力学及实验研究.中国电机工程学报,2012,32(9)：116-123
[64]Morii Y., Sukedai M., Ohashi S..Rotational characteristics in the resonance state of the HTSC-permanent magnet hybrid magnetic bearing. C:Superconductivity and its Applications,2011,471 (21-22):1483-1486
[65]Li Songsheng, Mao Huawei, Chen Ping, et al.Dynamic performance of the bearing-rotor system in the ultra-high speed electric spindle with a additional supporting system make up of the permanent magnetic bearings. Advanced Materials Research,2011,295-297:2294-2299
[66]吴刚.混合磁轴承飞轮系统设计与控制方法研究：[国防科技大学博士学位论文].长沙：国防科技大学研究生院,2006
[67]张凯.磁悬浮动量轮系统研究：[清华大学博士学位论文].北京：清华大学工程物理系,2004
[68]董淑成,房建成,俞文伯.基于PID控制的主动磁轴承一飞轮转子系统运动稳定性研究.宇航学报,2005,26(3)：296-306
[69]孙玉坤,朱烷秋,蔡兰.三自由度混合磁悬浮轴承耦合特性.江苏大学学报(自然科学版),2006,27(4)：342-346
[70]P.D. Timothy, V.B. Gerald, P.D. Kirsten, et al. Modeling and development of a magnetic bearing controller for a high speed flywheel system.In:2nd International Energy Conversion Engineering Conference, Rhode island,2004,16-19
[71]B. Polajzer, J. Ritonja, G. Stumberger. Decentralized PI/PD Position Control for Active Magnetic Bearings. Electrical Engineering,2006,89:53-59
[72]Albert F K, Gerald V B, Ralph H. Jansen, et al. Dever. Stability limits of a PD controller for a flywheel supported on rigid rotor and magnetic bearings. AIAA Guidance, Navigation and Control Conference and Exhibition,2005,8:AIAA 2005-5956
[73]Z Kai, Z Xiaozhang, Z Lei, et al. Structure Eigen Vibration Control of Flywheel Suspended by Active Magnetic Bearings.Chinese Journal of Mechanical Engineering,2007,43 (6):220-225
[74]苏义鑫.主动磁力轴承模糊控制的相关理论与技术研究：[华中科技大学博士学位论文].武汉：华中科技大学研究生学院,2006
[75]楼晓春,吴国庆.主动磁轴承系统的自适应滑模控制.电工技术学报,2012,27(1)：142-147
[76]F.H. Nagi, J.I. Inayat-Hussain, S.K. Ahmed. Fuzzy bang-bang relay control of a single-axis active magnetic bearing system. Simulation modelling practice and theory,2009, (17):1734-1747
[77]Kai Z, Heng L, Lie Y. Robust Fuzzy Control of a Nonlinear Magnetic Bearing System with Computing Time Delay. In:Proceedings of IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Xi' an,2008:839-894
[78]Kai Z, Heng L, Lie Y.Fuzzy Modelling and Output Feedback Stabilization of Nonlinear Magnetic Bearing with Delayed Feedback. In:Proceedings of the Twelfth International Symposium on Magnetic Bearings, Wuhan,2010:525-536
[79]Hung-Cheng C.Optimal fuzzy PID controller design of an active magnetic bearing system based on adaptive genetic algorithms. In:Proceedings of the Seventh International Conference on Machine Learning and Cybernetics, Kunming, 2008:2054-2060
[80]ChaoLin K, TzuuHseng S L, Nairen G. Design of a novel fuzzy sliding-mode control for magnetic ball levitation system. Journal of Intelligent and Robotic Systems,2005, (42):295-316
[81]T Ye, S Yanhua, Y Lie.LQG Control of Hybrid Foil-Magneitc Bearing. In:Proceedings of the Twelfth International Symposium on Magnetic Bearings, Wuhan,2010:579-58
[82]曹建荣,虞烈,谢友柏.磁悬浮电动机的状态反馈线性化控制.中国电机工程学报,2001,21(9)：22-26
[83]朱熀秋,徐龙祥.径向四自由度主动磁悬浮轴承控制器研究与探讨.应用科学学报,2002,209(1)：55-60
[84]吴刚,张育林,刘昆.两轴型混合磁悬浮轴承变结构控制与仿真研究.系统仿真学报,2006,18(1)：251-253
[85]魏彤,房建成.磁悬浮控制力矩陀螺磁轴承的变工作点线性化自适应控制方法.机械工程学报,2007,43(6)：110-115
[86]Y. Kanemitsu, M. Ohsawa, E. Marui. Comparison of control laws for magnetic levitation. in Fourth International Symposium on Magnetic Bearings, ETH Zuerich.,1994:13-18.
[87]曹广忠,孟欣.基于Hβ和PID混合控制的点磁轴承控制器性能分析.In：Proceedings of the 6th World Congress on Intelligent Control and Automation, Dalian,2006:2403-2407
[88]Zdzislaw G,Arkadiusz M. Robust Control of Active Magnetic Suspension: Analytical and Experimental Results.Mechanical Systems and Signal Processing, 2008, (22):1297-1303
[89]M Arkadiusz, G Zdzislaw.Energy Save Robust Control of Active Magnetic Bearings in Flywheel.In:Proceedings of the Twelfth International Symposium on Magnetic Bearings, Wuhan,2010,8:497-502
[90]Zdzislaw G, Arkadiusz M.Sliding Mode Control for Active Magnetic Bearings. In:Proceedings of the 10th International Symposium on Magnetic Bearings, Martigny,2006
[91]J T Sawicki, E H Maslen, K R Bischof. AMB Controller Design for a Machining Spindle using μ-synthesis. In:Proceedings of the 10th International Symposium on Magnetic Bearings, Martigny,2006
[92]P H Rocha, H C Ferreira, M C Porsch, et al. Fixed-point DSP Implementation of Nonlinear H-Controller for Large Gap Electromagnetic Suspension System. Control Engineering Practice,2009,17(10):1148-1156
[93]Jeffrey D L, Carl R K.Feedback Linearization of an Active Magnetic Bearing with Voltage Control. IEEE Transactions on Control Systems Technology,2002,10 (1):21-32
[94]A A Emadzadeh, T D Lorentz, T C Tsao. Experiment and Comparison of Robust Linear and Sliding Mode Controllers for Regulation of a Magnetic Bearing System. In:Proceedings of the ASME Dynamic Systems and Control Conference, Cambridge,2010
[95]梅生伟,申铁龙,刘康志.现代鲁棒控制理论与应用.北京：清华大学出版社,2003,120
[96]蓝益鹏.永磁直线电机伺服系统鲁棒性控制的研究：[沈阳工业大学博士论文].沈阳：沈阳工业大学研究生院,2007,42
[97]张凤阁,金石.无刷双馈风力发电系统的L2鲁棒控制.电机与控制学报,2010,14(8)：70-74
[98]刘海涛,张铁.基于时延估计和鲁棒Hβ控制的工业机器人跟踪控制.华南理工大学学报(自然科学版),2012,40(1)：77-81
[99]陈娇英,李啸骢,李文涛,等.基于自适应Backstepping的SVC鲁棒L2性能控制设计.电力系统保护与控制,2011,39(17)：40-44
[100]Zhu Ziqiang. Recent development of Halbach permanent magnet machines and applications.Fourth Power Conversion Conference-NAGOYA, PCC-NAGOYA 2007-Conference Proceedings,2007, k9-k16
[101]Choi Jaeseok, Yoo Jeonghoon.Design of a Halbach magnet array based on optimization techniques. IEEE Transactions on Magnetics,2008,44 (10): 2361-2366
[102]Yonnet Jeanpierre.Passive magnetic bearings with permanent magnets. IEEE Transactions on Magnetics,1978,14(5):803-805
[103]王洪昌,蒋书运,梁玉飞.基于分子电流法轴向永磁轴承轴向刚度的分析.机械工程学报,2009,45(5)：102-107
[104]陈君辉.永磁轴承应用于立式轴流泵的设计.[兰州理工大学硕士学位论文].兰州：兰州理工大学,2010
[105]胡业发,周祖德,江征风.磁力轴承的基础理论与应用.北京：机械工业出版社,2006,14-19
[106]严密,彭晓领.磁学基础与磁性材料.杭州：浙江大学出版社,2006,10-17
[107]Allag. Hicham, Yonnet.J-P, et al.3D analytical calculation of interactions between perpendicularly magnetized magnets-application to any magnetization direction. American Scientific Publishers.2009,7(3):486-491
[108]Akoun.G, Yonnet.J-P,3D analytical calculation of the forces exerted between two cuboidal magnets.IEEE Transactions on Magnetics,1984,20(5):1962-1964
[109]J-P.Yonnet, Rare Earth Iron Permanent Magnets, Oxford University Press,1996
[110]孙立军,张涛等.永磁磁轴承数学模型的研究.机械工程学报,2005,41(4)：69-74
[111]H.Allag,J-P.Yonnet,M.E.H.Latreche.3D analytical calculation of forces between linear halbach-type permanent magnet arrays.ELECTROMOTION 2009.8th International Symposium on.2009:1-6
[112]田录林,李言,田琦,等.径向磁化的多环嵌套永磁轴承轴向磁力解析模型.计算力学学报,2010,(2)：379-384
[113]田录林,李言,田琦等.大外径多环嵌套永磁轴承轴向磁力模型.电机与控制学报,2009,(3)：349-355
[114]成玉卫.基于Halbach结构的永磁电动悬浮技术研究.[国防科学技术大学研究生院硕士学位论文].长沙：国防科学技术大学,2009
[115]贺光.基于Halbach结构的永磁电动与电磁混合悬浮技术研究.[国防科学技术大学研究生院硕士学位论文].长沙：国防科学技术大学,2010
[116]Yonnet J P.Permanent magnet bearings and couplings.IEEE Transactions on Magnetics,1981,17 (1):1169-1173
[117]李春生,王武等,直线型Halbach磁体和导体板构成的电动式悬浮系统的实验装置设计.工程设计学报,2008,15(1)：33-36
[118]李春生,杜玉梅等,磁浮列车工程中的Halbach永久磁体结构的优化.工程设计学报,2007,14(4)：334-337
[119]张锦,刘晓平.叶轮机振动模态分析理论及数值方法.北京：国防工业出版社.2001
[120]G.Genta.On the Stability of Rotating Blade Arrays.Journal of Sound and Vibration.2004, (273):805-836
[121]S.B.Chun, C.W.Lee.Vibration Analysis of Shaft-bladed Disc System by Using Substructure Synthesis and Assumed Modes Method. Journal of Sound and Vibration.1996, (189):587-60
[122]王立刚.叶片-转子-轴承耦合系统的非线性动力学特性研究.[哈尔滨工业大学博士学位论文].哈尔滨：哈尔滨工业大学,2009
[123]焦晓红,关兴平.非线性系统分析与设计.北京：电子工业出版社,2008,158-197
[2]孙文丽,王优强,时高伟.赛龙轴承材料摩擦学性能的试验研究.润滑与密封,2011,36(5)：36-39
[3]林海江,仇宝云,汤正军.大中型水泵导轴承材料比较选用研究.水泵技术,2005,6：22-26
[4]杨树雄.大型卧式轴流泵水导轴承研究.排灌机械,2003,21(1)：15-17
[5]曹海红,仇宝云,邓东升.水泵水润滑导轴承耐久性研究.排灌机械,2009,29(3)：277-282
[6]杨洪群.吴玲玲.泵站机组水导轴承的研究.排灌机械,2004,22(3)：22-24
[7]黄毅.斜轴伸水泵的导轴承材料应用分析.水利水电科技进展,2003,23(6)：47-48
[8]杨成仁,苏逢荃,王优强.八纵向沟水润滑橡胶轴承润滑机理的实验研究.青岛建筑工程学院学报,1995,16(4)：51-58
[9]王优强,李鸿琦.水润滑赛龙轴承及其润滑性能综述.润滑与密封,2003,(1)：101-104
[10]周泽华,王家序.陶瓷在水润滑轴承中的应用.陶瓷工程,2000,(12)：29-31
[11]吴仁荣.水润滑滑动轴承设计计算.机电设备,1997,(6)：30-32,35
[12]仇宝云,黄海田,魏强林等.大型立式水泵油轴承改水轴承的应用研究.流体机械,2000,28(1)：35-37
[13]Howard Smitb. Is the Writing on the Wall for Oil Lubricated Bearings in Pumps. World Pumps,1995,12:38-41
[14]Robin Kyte. Advanced Bearing Technology Improves Pump Performance. World Pumps,2002,7:42-45
[15]Rick Bruggeman. Innovative Ceramic Sliding Bearings. World Pumps, October, 2002,10:30-32
[16]Zhao Xusheng, Deng Zhiquan, Wang Xiaolin, et al. Research status and development of permanent magnet biased magnetic bearings. Diangong Jishu Xuebao/Transactions of China Electrotechnical Society.2009,24 (9):9-20
[17]苏义鑫,王提峰.磁力轴承技术研究进展.仪器仪表用户,2007,14(5)：2-4
[18]蒋启龙,连级三.电磁轴承及其应用研究综述.重庆大学学报,2004,27(7)：146-151
[19]Gerhard Schweitzer, Hanner Bleuler, Matthew Cole, et al.磁悬浮轴承-理论、设计及旋转机械应用.北京：机械工业出版社,2012：1-16
[20]S.Earnshaw.On the nature of the molecular forces which regulate the constitution of the luminiferous ether. Trans. Camb. Phil. Soc.,1842,7:97-112
[21]Kemper H. Overhead suspension railway with wheelless vehicles employing magnetic suspension from iron rails.Germ.Pat.Nos.643316 and 644302,1937
[22]Kemper H. Suspension by electromagnetic forces:a possibility for a radically new method of transportation. ETZ,1938,59:391-395
[23]董宏涛.磁力轴承功率放大器的设计与仿真：[武汉理工大学硕士学位论文].武汉：武汉理工大学,2006
[24]Toumier P.L. Magnetic suspension for model in wind tunnel. La recherche aeronautique No.59, July-August,1957, Paris
[25]Toumier P.L.Totally active magnetic suspension system.French Pat.Nos.1186527, 1957
[26]宗鸣.永磁偏置混合式磁轴承及其控制方法的研究：[沈阳工业大学博士学位论文].沈阳：沈阳工业大学,2007
[27]陈龙.磁力轴承结构参数化设计：[武汉理工大学硕士学位论文].武汉：武汉理工大学,2005
[28]全定策.磁力轴承结构设计及其转子结构特性分析：[武汉理工大学硕士学位论文].武汉：武汉理工大学,2004
[29]邓坚强.电磁轴承有限元分析、结构设计及控制：[浙江大学硕士学位论文].杭州：浙江大学,2004
[30]钟毅.磁悬浮嵌入式控制系统基础理论和关键技术研究：[武汉理工大学博士学位论文].武汉：武汉理工大学,2007
[31]张敬.混合式磁悬浮轴承及其控制系统的研究：[沈阳工业大学硕士学位论文].沈阳：沈阳工业大学,2005
[32]仇志坚.永磁型无轴承电机的基础研究：[南京航空航天大学博士学位论文].南京：南京航空航天大学,2009
[33]虞烈.可控磁悬浮转子系统.北京：科学出版社,2003
[34]Lee An-Chen, Hsiao Foam-Zone, Ko Dennil.Analysis and testing of magnetic bearing with permanent magnets for bias.JSME International Journal,Series C, 1994,37(4):774-782
[35]Silva I D, Horikawa O.An 1-D.o.f.Controlled attraction type magnetic bearing, electric machines and drives.International Conference IEMD'99,1999:481-483
[36]Fang J.R., Lin, L.Z., Yan L.G., et al. A new flywheel energy storage system using hybrid superconducting magnetic bearings. Applied Superconductivity. 2001,11 (1):1657-1660
[37]Peng Wu, Tseng, K.J. A self-bearing centrifugal blood pump based on induction motor with active and passive magnetic bearings. In:The Fifth International Conference on Power Electronics and Drive Systems. Singapore,2003: 1642-1646
[38]Onuma Hiroyuki, Murakami Michiko, Masuzawa Toru. Novel maglev pump with a combined magnetic bearing. ASAIO Journal.2005,51 (1):50-55
[39]方家荣,林良真,夏平畴,严陆光.超导混合磁力轴承的发展现状和前景.电工电能新技术,2000,(1)：27-31
[40]Dun Yueqin, Wang Xiuhe, Kong Yu. Analysis of hybrid magnetic bearing with a permanent magnet in the rotor by FEM.IEEE Transactions on Magnetics,2006, 42 (4):1363-1366
[41]肖林京,孙传余,李鹏,等.一种永磁上吸下斥结构的低功耗混合式磁轴承.中国专利.201010110709.9,2010-1-26
[42]钟一锷,何衍宗,王正,等.转子动力学.北京：清华大学出版社,1987
[43]张文.转子动力学理论基础.北京：科学出版社,1990
[44]闻邦椿,顾家柳,夏松波,等.高等转子动力学理论、技术与应用.北京：机械工业出版社,1999
[45]黄文虎,夏新波,焦映厚,等.旋转机械非线性动力学的理论与试验.北京：科学出版社,2006
[46]Carta FO. Coupled blade-disk-shroud flutter instabilities in turbojet engine rotors.ASME Journal of Engineering for Power,1967,89:419-427
[47]D.R.Chivens, H.D.Nelson.The natural frequencies and critical speeds of a rotating, flexible shaft-disk system. ASME Jou(?)nal of Engineering for Industry, 1975,97:881-886
[48]L.E.E1-Bayoumy, A.V. Srinivasan.Influence of mistuning on rotor-blade vibrations. AIA A Journal,1975,13:460-464
[49]A.V.Srinivasan. Vibrations of bladed-disk assemblies-A selected survey. ASME, Transactions, Journal of Vibration, Acoustics, Stress and Reliability in Design,1984,106:165-168
[50]E.F.Crawley, D.R.Mokadam.Stagger angle dependence of inertial and elastic coupling in bladed disks. Journal of vibration, acoustics, stress, and reliability in design,1984,106:181-188
[51]M. Sakata, K. Kimura, S.K. Park, et al. Vibration of bladed flexible rotor due to gyroscopic moment. Journal of Sound and Vibration,1989,113(3):417-430
[52]J. Padovan, F.K. choy. Nonlinear dynamics of rotor/blade/casing rub interactions. Journal of Turbomachinery,1987,109:527-534
[53]N. Lesaffre, J.J. Sinou, F. Thouverez. Contact analysis of a flexible bladed-rotor. european Journal of Mechanics A/Solids,2007,26:541-557
[54]S.B. Chun, C.W. Lee.Vibration analysis of shaft-bladed disk system by using substructure synthesis and assumed modes method. Journal of Sound and Vibration,1996,189 (5):587-608
[55]S.K. Sinha. Dynamic characteristics of a flexible bladed-rotor with Coulomb damping due to tip-rub. Journal of Sound and Vibration,2004,273(4-5):875-919
[56]C.H. Yang, S.C. Huang.The influence of disk's flexibility on coupling vibration of shaft-disk-blades systems.Journal of sound and vibration,2007,301 (1-2): 1-17
[57]ivlizuno Takeshil, Hara Yusuke.Active stabilization of a repulsive magnetic bearing using the motion control of permanent magnets.JSME International Journal, Series C:Mechanical Systems, Machine Elements and Manufacturing, 2000,43 (3):632-637
[58]Demachi Kazuyuki, Miura Akiral, Sawada Akihiko, et al. Numerical simulation of dynamics of radial type superconducting magnetic bearing. International Journal of Applied Electromagnetics and Mechanics,2001, 1491-4):127-132
[59]Sim Hyun-Sik, Kim Ha-Yong, Lee Chong-Won, et al. Stabilization of active magnetic bearing system subject to base motion.In:19th Biennial Conference on Mechanical Vibration and Noise, Chicago,2003:2007-2013
[60]Jiang Shuyun, Ju Lihua. Study on electromechanical coupling nonlinear vibration of flywheel energy storage system.Science in China, Series E:Technological Sciences,2006,49 (1):61-77
[61]Cansiz, Ahmet. Static and dynamic analysis of a diamagnetic bearing system. Journal of Applied Physics,2008,103 (3):034510
[62]Kang Kyungdae,Palazzolo Alan. Dynamical and experimental researches of active magnetic bearing rotor systems for high-speed PM machines.IEEE Transactions on Magnetics,2012,48 (6):1984-1994
[63]田拥胜,孙岩桦,虞烈.高速永磁电机电磁轴承转子系统的动力学及实验研究.中国电机工程学报,2012,32(9)：116-123
[64]Morii Y., Sukedai M., Ohashi S..Rotational characteristics in the resonance state of the HTSC-permanent magnet hybrid magnetic bearing. C:Superconductivity and its Applications,2011,471 (21-22):1483-1486
[65]Li Songsheng, Mao Huawei, Chen Ping, et al.Dynamic performance of the bearing-rotor system in the ultra-high speed electric spindle with a additional supporting system make up of the permanent magnetic bearings. Advanced Materials Research,2011,295-297:2294-2299
[66]吴刚.混合磁轴承飞轮系统设计与控制方法研究：[国防科技大学博士学位论文].长沙：国防科技大学研究生院,2006
[67]张凯.磁悬浮动量轮系统研究：[清华大学博士学位论文].北京：清华大学工程物理系,2004
[68]董淑成,房建成,俞文伯.基于PID控制的主动磁轴承一飞轮转子系统运动稳定性研究.宇航学报,2005,26(3)：296-306
[69]孙玉坤,朱烷秋,蔡兰.三自由度混合磁悬浮轴承耦合特性.江苏大学学报(自然科学版),2006,27(4)：342-346
[70]P.D. Timothy, V.B. Gerald, P.D. Kirsten, et al. Modeling and development of a magnetic bearing controller for a high speed flywheel system.In:2nd International Energy Conversion Engineering Conference, Rhode island,2004,16-19
[71]B. Polajzer, J. Ritonja, G. Stumberger. Decentralized PI/PD Position Control for Active Magnetic Bearings. Electrical Engineering,2006,89:53-59
[72]Albert F K, Gerald V B, Ralph H. Jansen, et al. Dever. Stability limits of a PD controller for a flywheel supported on rigid rotor and magnetic bearings. AIAA Guidance, Navigation and Control Conference and Exhibition,2005,8:AIAA 2005-5956
[73]Z Kai, Z Xiaozhang, Z Lei, et al. Structure Eigen Vibration Control of Flywheel Suspended by Active Magnetic Bearings.Chinese Journal of Mechanical Engineering,2007,43 (6):220-225
[74]苏义鑫.主动磁力轴承模糊控制的相关理论与技术研究：[华中科技大学博士学位论文].武汉：华中科技大学研究生学院,2006
[75]楼晓春,吴国庆.主动磁轴承系统的自适应滑模控制.电工技术学报,2012,27(1)：142-147
[76]F.H. Nagi, J.I. Inayat-Hussain, S.K. Ahmed. Fuzzy bang-bang relay control of a single-axis active magnetic bearing system. Simulation modelling practice and theory,2009, (17):1734-1747
[77]Kai Z, Heng L, Lie Y. Robust Fuzzy Control of a Nonlinear Magnetic Bearing System with Computing Time Delay. In:Proceedings of IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Xi' an,2008:839-894
[78]Kai Z, Heng L, Lie Y.Fuzzy Modelling and Output Feedback Stabilization of Nonlinear Magnetic Bearing with Delayed Feedback. In:Proceedings of the Twelfth International Symposium on Magnetic Bearings, Wuhan,2010:525-536
[79]Hung-Cheng C.Optimal fuzzy PID controller design of an active magnetic bearing system based on adaptive genetic algorithms. In:Proceedings of the Seventh International Conference on Machine Learning and Cybernetics, Kunming, 2008:2054-2060
[80]ChaoLin K, TzuuHseng S L, Nairen G. Design of a novel fuzzy sliding-mode control for magnetic ball levitation system. Journal of Intelligent and Robotic Systems,2005, (42):295-316
[81]T Ye, S Yanhua, Y Lie.LQG Control of Hybrid Foil-Magneitc Bearing. In:Proceedings of the Twelfth International Symposium on Magnetic Bearings, Wuhan,2010:579-58
[82]曹建荣,虞烈,谢友柏.磁悬浮电动机的状态反馈线性化控制.中国电机工程学报,2001,21(9)：22-26
[83]朱熀秋,徐龙祥.径向四自由度主动磁悬浮轴承控制器研究与探讨.应用科学学报,2002,209(1)：55-60
[84]吴刚,张育林,刘昆.两轴型混合磁悬浮轴承变结构控制与仿真研究.系统仿真学报,2006,18(1)：251-253
[85]魏彤,房建成.磁悬浮控制力矩陀螺磁轴承的变工作点线性化自适应控制方法.机械工程学报,2007,43(6)：110-115
[86]Y. Kanemitsu, M. Ohsawa, E. Marui. Comparison of control laws for magnetic levitation. in Fourth International Symposium on Magnetic Bearings, ETH Zuerich.,1994:13-18.
[87]曹广忠,孟欣.基于Hβ和PID混合控制的点磁轴承控制器性能分析.In：Proceedings of the 6th World Congress on Intelligent Control and Automation, Dalian,2006:2403-2407
[88]Zdzislaw G,Arkadiusz M. Robust Control of Active Magnetic Suspension: Analytical and Experimental Results.Mechanical Systems and Signal Processing, 2008, (22):1297-1303
[89]M Arkadiusz, G Zdzislaw.Energy Save Robust Control of Active Magnetic Bearings in Flywheel.In:Proceedings of the Twelfth International Symposium on Magnetic Bearings, Wuhan,2010,8:497-502
[90]Zdzislaw G, Arkadiusz M.Sliding Mode Control for Active Magnetic Bearings. In:Proceedings of the 10th International Symposium on Magnetic Bearings, Martigny,2006
[91]J T Sawicki, E H Maslen, K R Bischof. AMB Controller Design for a Machining Spindle using μ-synthesis. In:Proceedings of the 10th International Symposium on Magnetic Bearings, Martigny,2006
[92]P H Rocha, H C Ferreira, M C Porsch, et al. Fixed-point DSP Implementation of Nonlinear H-Controller for Large Gap Electromagnetic Suspension System. Control Engineering Practice,2009,17(10):1148-1156
[93]Jeffrey D L, Carl R K.Feedback Linearization of an Active Magnetic Bearing with Voltage Control. IEEE Transactions on Control Systems Technology,2002,10 (1):21-32
[94]A A Emadzadeh, T D Lorentz, T C Tsao. Experiment and Comparison of Robust Linear and Sliding Mode Controllers for Regulation of a Magnetic Bearing System. In:Proceedings of the ASME Dynamic Systems and Control Conference, Cambridge,2010
[95]梅生伟,申铁龙,刘康志.现代鲁棒控制理论与应用.北京：清华大学出版社,2003,120
[96]蓝益鹏.永磁直线电机伺服系统鲁棒性控制的研究：[沈阳工业大学博士论文].沈阳：沈阳工业大学研究生院,2007,42
[97]张凤阁,金石.无刷双馈风力发电系统的L2鲁棒控制.电机与控制学报,2010,14(8)：70-74
[98]刘海涛,张铁.基于时延估计和鲁棒Hβ控制的工业机器人跟踪控制.华南理工大学学报(自然科学版),2012,40(1)：77-81
[99]陈娇英,李啸骢,李文涛,等.基于自适应Backstepping的SVC鲁棒L2性能控制设计.电力系统保护与控制,2011,39(17)：40-44
[100]Zhu Ziqiang. Recent development of Halbach permanent magnet machines and applications.Fourth Power Conversion Conference-NAGOYA, PCC-NAGOYA 2007-Conference Proceedings,2007, k9-k16
[101]Choi Jaeseok, Yoo Jeonghoon.Design of a Halbach magnet array based on optimization techniques. IEEE Transactions on Magnetics,2008,44 (10): 2361-2366
[102]Yonnet Jeanpierre.Passive magnetic bearings with permanent magnets. IEEE Transactions on Magnetics,1978,14(5):803-805
[103]王洪昌,蒋书运,梁玉飞.基于分子电流法轴向永磁轴承轴向刚度的分析.机械工程学报,2009,45(5)：102-107
[104]陈君辉.永磁轴承应用于立式轴流泵的设计.[兰州理工大学硕士学位论文].兰州：兰州理工大学,2010
[105]胡业发,周祖德,江征风.磁力轴承的基础理论与应用.北京：机械工业出版社,2006,14-19
[106]严密,彭晓领.磁学基础与磁性材料.杭州：浙江大学出版社,2006,10-17
[107]Allag. Hicham, Yonnet.J-P, et al.3D analytical calculation of interactions between perpendicularly magnetized magnets-application to any magnetization direction. American Scientific Publishers.2009,7(3):486-491
[108]Akoun.G, Yonnet.J-P,3D analytical calculation of the forces exerted between two cuboidal magnets.IEEE Transactions on Magnetics,1984,20(5):1962-1964
[109]J-P.Yonnet, Rare Earth Iron Permanent Magnets, Oxford University Press,1996
[110]孙立军,张涛等.永磁磁轴承数学模型的研究.机械工程学报,2005,41(4)：69-74
[111]H.Allag,J-P.Yonnet,M.E.H.Latreche.3D analytical calculation of forces between linear halbach-type permanent magnet arrays.ELECTROMOTION 2009.8th International Symposium on.2009:1-6
[112]田录林,李言,田琦,等.径向磁化的多环嵌套永磁轴承轴向磁力解析模型.计算力学学报,2010,(2)：379-384
[113]田录林,李言,田琦等.大外径多环嵌套永磁轴承轴向磁力模型.电机与控制学报,2009,(3)：349-355
[114]成玉卫.基于Halbach结构的永磁电动悬浮技术研究.[国防科学技术大学研究生院硕士学位论文].长沙：国防科学技术大学,2009
[115]贺光.基于Halbach结构的永磁电动与电磁混合悬浮技术研究.[国防科学技术大学研究生院硕士学位论文].长沙：国防科学技术大学,2010
[116]Yonnet J P.Permanent magnet bearings and couplings.IEEE Transactions on Magnetics,1981,17 (1):1169-1173
[117]李春生,王武等,直线型Halbach磁体和导体板构成的电动式悬浮系统的实验装置设计.工程设计学报,2008,15(1)：33-36
[118]李春生,杜玉梅等,磁浮列车工程中的Halbach永久磁体结构的优化.工程设计学报,2007,14(4)：334-337
[119]张锦,刘晓平.叶轮机振动模态分析理论及数值方法.北京：国防工业出版社.2001
[120]G.Genta.On the Stability of Rotating Blade Arrays.Journal of Sound and Vibration.2004, (273):805-836
[121]S.B.Chun, C.W.Lee.Vibration Analysis of Shaft-bladed Disc System by Using Substructure Synthesis and Assumed Modes Method. Journal of Sound and Vibration.1996, (189):587-60
[122]王立刚.叶片-转子-轴承耦合系统的非线性动力学特性研究.[哈尔滨工业大学博士学位论文].哈尔滨：哈尔滨工业大学,2009
[123]焦晓红,关兴平.非线性系统分析与设计.北京：电子工业出版社,2008,158-197
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