磁悬浮转子系统动态特性研究
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摘要
磁力轴承作为目前可应用于工程实际、且能够实施主动控制的支承部件之一,具有一般传统轴承和支承技术所无法比拟的优点,目前己在各个领域的高速旋转机械中开始应用。虽然磁力轴承的基础理论已经取得了丰硕的成果,也有成功实例,但样机在实验时实际稳定转速达不到设计工作转速,且在高速运行状态下稳定性差等问题,已经严重制约了该技术的推广应用。磁悬浮转子系统的动力学特性就成为其进入应用基础研究阶段后,研究者普遍关注的诸多实际问题之一。本文的主要工作内容就是针对这些问题和现象,解决在磁力轴承支承条件下高速转子系统的临界转速分析和计算问题。
本文首先引述和概括了传统转子动力学的研究方法及有关理论,并以此作为磁悬浮轴承转子动力学的研究基础,接着,以单自由度等效刚度阻尼系数计算方法为基础,详细分析了完整的磁力轴承动力特性系数的计算方法。然后,本文分别对磁悬浮刚性转子系统和磁悬浮柔性转子系统进行了数学建模,并用Riccati传递矩阵法结合磁力轴承的有关特点,建立了磁悬浮柔性转子系统的动力学计算和分析方法。最后,对一实际的磁悬浮柔性转子系统进行了理论计算和实验验证。
通过本文的研究,得到以下主要结论:磁力轴承的动力特性系数可以由八个等效的刚度阻尼系数来表示,这八个等效的动力特性系数和轴承的结构参数和控制器的控制参数密切相关;磁悬浮转子系统的低阶临界转速主要由磁力轴承支承刚度决定,其大小与磁力轴承和控制器的参数有关,可以通过改变磁力轴承的结构参数和控制器的控制参数来改变低阶临界转速的值;而高阶临界转速受磁力轴承支承刚度的影响很小,很难通过改变支承刚度来改变它们的大小,只能通过改变转子的几何尺寸或结构来调整。
As one of the supporting components, which can be controlled actively, active magnetic bearing (AMB) has been widely used in many machines with high rotation speed in all kinds of field because of its high performances beyond other traditional bearings. The basic research of the AMB has been achieved, but there are still many problems to be solved before putting them into industrial applications. One of them is bearing-rotor system dynamics and its stability. This paper will deal with these problems, and mainly focus on the critical speeds of the high speed rotating machinery supported AMB.First, some useful methods and theories in traditional bearing-rotor dynamics are summarized as the basis of study on dynamics of active magnetic bearing-rotor system. Next, basic on the analysis and calculation formulas of stiffness and dampness of one-degree-of-freedom, calculation formulas of stiffness and dampness of five-degree-of-freedom is given. Secondly, the mathematical model and mechanic models have been established using traditional dynamics combined with the characteristics of AMB. Then, by considering the characteristics of AMB and adapting the traditional Riccati transfer matrix method to active magnetic suspension rotor system, a method is established for calculating and analyzing dynamics. Finally, an actual active magnetic bearing-rotor system is calculated and validated by using above method and experiment.Some conclusions are formed by analyzing the results of the calculations: Like traditional bearings, the dynamic characteristic coefficient can be described by eight equivalent stiffness and dampness coefficients. The stiffness and dampness coefficients relate with not only parameters of bearing itself but those of controller as well and thus stiffness and dampness coefficients can be adjusted by changing those parameters. Low critical speed of magnetic suspension rotor system is mainly determined by bearing structure and parameters of controller on AMB, while high critical speed is mainly affected by rotor structure.
本文首先引述和概括了传统转子动力学的研究方法及有关理论,并以此作为磁悬浮轴承转子动力学的研究基础,接着,以单自由度等效刚度阻尼系数计算方法为基础,详细分析了完整的磁力轴承动力特性系数的计算方法。然后,本文分别对磁悬浮刚性转子系统和磁悬浮柔性转子系统进行了数学建模,并用Riccati传递矩阵法结合磁力轴承的有关特点,建立了磁悬浮柔性转子系统的动力学计算和分析方法。最后,对一实际的磁悬浮柔性转子系统进行了理论计算和实验验证。
通过本文的研究,得到以下主要结论:磁力轴承的动力特性系数可以由八个等效的刚度阻尼系数来表示,这八个等效的动力特性系数和轴承的结构参数和控制器的控制参数密切相关;磁悬浮转子系统的低阶临界转速主要由磁力轴承支承刚度决定,其大小与磁力轴承和控制器的参数有关,可以通过改变磁力轴承的结构参数和控制器的控制参数来改变低阶临界转速的值;而高阶临界转速受磁力轴承支承刚度的影响很小,很难通过改变支承刚度来改变它们的大小,只能通过改变转子的几何尺寸或结构来调整。
As one of the supporting components, which can be controlled actively, active magnetic bearing (AMB) has been widely used in many machines with high rotation speed in all kinds of field because of its high performances beyond other traditional bearings. The basic research of the AMB has been achieved, but there are still many problems to be solved before putting them into industrial applications. One of them is bearing-rotor system dynamics and its stability. This paper will deal with these problems, and mainly focus on the critical speeds of the high speed rotating machinery supported AMB.First, some useful methods and theories in traditional bearing-rotor dynamics are summarized as the basis of study on dynamics of active magnetic bearing-rotor system. Next, basic on the analysis and calculation formulas of stiffness and dampness of one-degree-of-freedom, calculation formulas of stiffness and dampness of five-degree-of-freedom is given. Secondly, the mathematical model and mechanic models have been established using traditional dynamics combined with the characteristics of AMB. Then, by considering the characteristics of AMB and adapting the traditional Riccati transfer matrix method to active magnetic suspension rotor system, a method is established for calculating and analyzing dynamics. Finally, an actual active magnetic bearing-rotor system is calculated and validated by using above method and experiment.Some conclusions are formed by analyzing the results of the calculations: Like traditional bearings, the dynamic characteristic coefficient can be described by eight equivalent stiffness and dampness coefficients. The stiffness and dampness coefficients relate with not only parameters of bearing itself but those of controller as well and thus stiffness and dampness coefficients can be adjusted by changing those parameters. Low critical speed of magnetic suspension rotor system is mainly determined by bearing structure and parameters of controller on AMB, while high critical speed is mainly affected by rotor structure.
引文
[1] G.施韦策、H.布鲁勒、A.特拉克斯勒著,虞烈、袁崇军译.主动磁轴承基础、性能及应用.北京:新时代出版社,1997
[2] R. Sindlinger, Magnetic bearing momentum wheels with vernier gimballing capability for 3-axis active attitude control and energy storage. Ⅶ IFAC Symp. on Automatic control in space, Rottach-Egem, May, 1986
[3] J.A. Kirk, D.K. Anand, P. Dachen, Performance of a Magnetically Suspended Flywheel Energy Storage System, Proceedings of the Fourth International Symposium on Magnetic Bearings, ETH Zurich, Switzerland, August 23-26,1994
[4] V. Gondhalekar, G Schweitzer. Dynamics and magnetic control of a micro-gravity platform. Rep. Inst. ETH Zurich, 1994
[5] 朱秋,吴鹏,曾励,徐龙祥,刘正埙.磁轴承控制器的设计及仿真研究.南京航空航天大学党报1999.03
[6] 胡业发,江征风,郭顺生,刘小英,沈顺成.单自由度磁力轴承的数字控制.武汉汽车工业大学党报1996.06
[7] 胡业发,郭顺生,余先涛,杨明忠.数控制磁悬浮智能转子系统的研究.武汉汽车工业大学党报1996.06
[8] 刘迎澍.高速磁悬浮机床主轴的离散变结构控制.控制理论与应用.2002.04
[9] 李俊.机床磁悬浮主轴的变结构控制.机床与液压.2000.02
[10] 景敏卿,郝金平,谢友柏.基于DSP的电磁轴承控制器硬件设计.机械工程学报.1999.07
[11] 陈立群,张艳鸣,张钢,谢友柏.电磁轴承的力学特性.西北轻工业学院学报.1997.09
[12] Atthew O. T. Cole, Patrick S. Keogh, Clifford R. Burrows. Tuneable H_8 Vibration Control in Rotor/Magnetic Bearing Systems Using Parameter Dependent Shaping Functions. Proceedings of the 7~(th) International Symposium on Magnetic Bearings. ETH Zurich, Switzerland, August 23-25,2000.
[13] Ichuan Li, Paul E. Allaire, Sensorless Sliding Mode Control of Magnetic Bearing Actuators Using Implicit Switching Surfaces. Proceedings of the 7~(th) International Symposium on Magnetic Bearings. ETH Zurich, Switzerland, August 23-25,2000.
[14] Lrich Schonhoff, Jihao Luo, Guoxin Li, etc. Implementation Result of μ-synthesis Control for an Engergy Storage Flywheel Test Rig. Proceedings of the 7~(th) International Symposium on Magnetic Bearings. ETH Zurich, Switzerland, August 23-25,2000.
[15] Kosaki Takahiro, Sao Manabu, Tanaka Kazuo. Model-based Fuzzy Control System Design for Magnetic Bearings. IEEE International Conference on Fuzzy Systems v2 Jul 1-5 1997 1997:895-899.
[16] Hong Sung-Kyung, Langari Reza. Robust Fuzzy Control of a Magnetic Bearings System Subject to Harmonic Disturbances. IEEE Transactions on Control Systems Technology 8 2 2000 IEEE:366-371.
[17] Shi Yang, Yah Weisheng, Ren Zhang, Xu Demin. Neural Network PID Control Scheme for the Active Magnetic Bearing. Jixie Kexue Yu Jishu/Mechanical Science and Technology 17 2 Mar 1998:337-338
[18] Fittro Roger L, Anand Davinder K. Neural Network Controller Design for a Magnetic Bearing Flywheel Energy Storage System. Proceedings of the Intersociety Energy Conversion Engineering Conference v4 Aug 3-7 1992
[19] 赵雷,张德魁,杨作兴等.电磁轴承最优刚度与系统结构参数关系的研究.机械工程学报.2000.12
[20] 胡业发,余先涛,郭顺生,杨明忠 基于结构动态特性的磁力轴承转子系统的设计.机械工程学报2000.02
[21] 龙志强,王水泉,杨泉林.径向磁轴承电磁参数的计算.磁性材料及器件2000.10
[22] 杨静,林治强,何钦象.径向电磁轴承优化设计2001.06
[23] 沈钺,虞烈.电磁轴承及控制系统的设计原理及参数选择.机械工程学报2000.11
[24] D. Fermental, E.A. Townsend. Stability of Magnetic Bearing-Rotor Systems and the Effects of Gravity and Damping. AIAA Journal. Vol. 32, No. 7 July 1998:1492
[25] Andrea Asgodizza, S. Carabelli, A. Tonoli. Finite Element Model Reduction for Rotating System. Proceedings of the 7~(th) International Symposium on Magnetic Bearings. ETH Zurich, Switzerland, August 23-25,2000. ETH Zurich.
[26] Russell D. Smith, William F. Weldon. Nonlinear Control of a Rigid Rotor Magnetic Bearing System: Modeling and Simulation with Full State Feedback. IEEE Transactions on Magnetic Vol. 31, No. 2. March 1995:973-980
[27] H. Ming Chen. Magnetic Bearings and Flexible Rotor Dynamics. Tribology Transactions, Vol. 32(1996)1:9-15
[28] 谢振宇,徐龙祥,李迎,丘大谋,虞烈.磁悬浮轴承转子系统的稳定性及动态特性分析[J],机械科学与技术,2004,7
[29] 谢振宇,徐龙祥,李迎,丘大谋,虞烈.磁悬浮轴承转子系统动态特性的实验研究.航空动力学报,2004年01期
[30] 朱礼进,汪希平,王文等.磁悬浮支承转子系统动力学特性的实验研究.上海大学学报(自然科学版),2002.6
[31] 汪希平,朱礼进,于良,王文,王小静,张直明,万金贵.主动磁轴承转子系统动力学特性的研究[J],机械工程学报,2001,11
[32] 孙首群,虞烈.磁轴承柔性转子系统动力特性建模与优化仿真[J],系统仿真学报,2003.3
[33] G.J. Shu, S,M. Yang, C.D. Yang. Design of Experiments for the Controller of Rotor Systems With a Magnetic Bearing. Transactions of the ASME, Journal of Vibration and Acoustics. 200/vol. 119. April 1997
[34] 孟光.转子动力学研究的回顾与展望.振动工程学报,2002.3
[35] 虞烈,刘恒等.轴承—转子系统动力学.中国机械工程,1999.11.
[36] 钟一谔,何衍宗.转子动力学.清华大学出版社,1987.11.
[37] 徐龙祥.高速旋转机械轴系动力学设计.北京:国防工业出版社:1994.6
[38] 顾家柳等编著,转子动力学,国防工业出版社,1985.
[39] 唐克伦.多盘柔性转子系统的磁轴承刚度和阻尼设计.四川轻化工学院学报,2003.09
[40] 杨国军,耿文骥,李红伟.10MW高温气冷堆磁轴承转子结构与固有频率的关系研究.高技术通讯,2003.04
[41] 胡超,王岩,王立国等.机械化数学在转子动力学研究中的应用.应用数学和力学,第23卷第9期(2002.9)
[42] 高小冲,李运华.基于电液可控挤压油膜阻尼器的转子系统振动的主动控制研究.机床与液压,2002.05
[43] Shinji Shinnaka. Characteristic-varying systems in the D-Module: Their properties of existence, realization, and stability. Electrical Engineering in Japan, Volume 145, Issue 1, Date: October 2003, Pages: 39-51
[44] Zhu, Changsheng, Robb, D.A. Ewins, D.J. The dynamics of a cracked rotor with an active magnetic bearing. Journal of Sound and Vibration Volume: 265, Issue: 3, August 14, 2003, pp. 469-487
[45] Hsu, Chan-Tang; Chen, Shyh-Leh. Nonlinear control of a 3-pole active magnetic bearing system. Automatica Volume: 39, Issue: 2, February, 2003, pp. 291-298
[46] Aenis, Knopf, E, Nordmann, R. Active magnetic bearings for the identification and fault diagnosis in turbo machinery. Mechatronics Volume: 12, Issue: 8, October, 2002, pp. 1011-1021
[47] Skricka, Norbert, Markert, Richard. Improvements of the integration of active magnetic bearings. Mechatronics Volume: 12, Issue: 8, October, 2002, pp. 1059-1068
[48] Skricka, Norbert, Markert, Richard. Improvements in the integration of active magnetic bearings. Control Engineering Practice Volume: 10, Issue: 8, August, 2002, pp. 917-922
[49] 李松生,王兵华等.高速电主轴轴系转子动力学特性分析.轴承,2002.2
[50] 胡业发.基于结构动态特性的磁悬浮转子系统研究.武汉理工大学博士学位论文,2001
[51] 张钢,虞烈,谢友柏.推力轴承的力学特性及其对径向轴承的影响.机械工程学报,2000.12
[52] 宋曦,赵荣珍,转子—轴承系统固有频率对设计参数的灵敏度.甘肃工业大学学报,1999.2
[53] 祝长生.基础横向振动对电磁轴承转子系统动力特性影响的实验研究.航空学报,2004.02
[2] R. Sindlinger, Magnetic bearing momentum wheels with vernier gimballing capability for 3-axis active attitude control and energy storage. Ⅶ IFAC Symp. on Automatic control in space, Rottach-Egem, May, 1986
[3] J.A. Kirk, D.K. Anand, P. Dachen, Performance of a Magnetically Suspended Flywheel Energy Storage System, Proceedings of the Fourth International Symposium on Magnetic Bearings, ETH Zurich, Switzerland, August 23-26,1994
[4] V. Gondhalekar, G Schweitzer. Dynamics and magnetic control of a micro-gravity platform. Rep. Inst. ETH Zurich, 1994
[5] 朱秋,吴鹏,曾励,徐龙祥,刘正埙.磁轴承控制器的设计及仿真研究.南京航空航天大学党报1999.03
[6] 胡业发,江征风,郭顺生,刘小英,沈顺成.单自由度磁力轴承的数字控制.武汉汽车工业大学党报1996.06
[7] 胡业发,郭顺生,余先涛,杨明忠.数控制磁悬浮智能转子系统的研究.武汉汽车工业大学党报1996.06
[8] 刘迎澍.高速磁悬浮机床主轴的离散变结构控制.控制理论与应用.2002.04
[9] 李俊.机床磁悬浮主轴的变结构控制.机床与液压.2000.02
[10] 景敏卿,郝金平,谢友柏.基于DSP的电磁轴承控制器硬件设计.机械工程学报.1999.07
[11] 陈立群,张艳鸣,张钢,谢友柏.电磁轴承的力学特性.西北轻工业学院学报.1997.09
[12] Atthew O. T. Cole, Patrick S. Keogh, Clifford R. Burrows. Tuneable H_8 Vibration Control in Rotor/Magnetic Bearing Systems Using Parameter Dependent Shaping Functions. Proceedings of the 7~(th) International Symposium on Magnetic Bearings. ETH Zurich, Switzerland, August 23-25,2000.
[13] Ichuan Li, Paul E. Allaire, Sensorless Sliding Mode Control of Magnetic Bearing Actuators Using Implicit Switching Surfaces. Proceedings of the 7~(th) International Symposium on Magnetic Bearings. ETH Zurich, Switzerland, August 23-25,2000.
[14] Lrich Schonhoff, Jihao Luo, Guoxin Li, etc. Implementation Result of μ-synthesis Control for an Engergy Storage Flywheel Test Rig. Proceedings of the 7~(th) International Symposium on Magnetic Bearings. ETH Zurich, Switzerland, August 23-25,2000.
[15] Kosaki Takahiro, Sao Manabu, Tanaka Kazuo. Model-based Fuzzy Control System Design for Magnetic Bearings. IEEE International Conference on Fuzzy Systems v2 Jul 1-5 1997 1997:895-899.
[16] Hong Sung-Kyung, Langari Reza. Robust Fuzzy Control of a Magnetic Bearings System Subject to Harmonic Disturbances. IEEE Transactions on Control Systems Technology 8 2 2000 IEEE:366-371.
[17] Shi Yang, Yah Weisheng, Ren Zhang, Xu Demin. Neural Network PID Control Scheme for the Active Magnetic Bearing. Jixie Kexue Yu Jishu/Mechanical Science and Technology 17 2 Mar 1998:337-338
[18] Fittro Roger L, Anand Davinder K. Neural Network Controller Design for a Magnetic Bearing Flywheel Energy Storage System. Proceedings of the Intersociety Energy Conversion Engineering Conference v4 Aug 3-7 1992
[19] 赵雷,张德魁,杨作兴等.电磁轴承最优刚度与系统结构参数关系的研究.机械工程学报.2000.12
[20] 胡业发,余先涛,郭顺生,杨明忠 基于结构动态特性的磁力轴承转子系统的设计.机械工程学报2000.02
[21] 龙志强,王水泉,杨泉林.径向磁轴承电磁参数的计算.磁性材料及器件2000.10
[22] 杨静,林治强,何钦象.径向电磁轴承优化设计2001.06
[23] 沈钺,虞烈.电磁轴承及控制系统的设计原理及参数选择.机械工程学报2000.11
[24] D. Fermental, E.A. Townsend. Stability of Magnetic Bearing-Rotor Systems and the Effects of Gravity and Damping. AIAA Journal. Vol. 32, No. 7 July 1998:1492
[25] Andrea Asgodizza, S. Carabelli, A. Tonoli. Finite Element Model Reduction for Rotating System. Proceedings of the 7~(th) International Symposium on Magnetic Bearings. ETH Zurich, Switzerland, August 23-25,2000. ETH Zurich.
[26] Russell D. Smith, William F. Weldon. Nonlinear Control of a Rigid Rotor Magnetic Bearing System: Modeling and Simulation with Full State Feedback. IEEE Transactions on Magnetic Vol. 31, No. 2. March 1995:973-980
[27] H. Ming Chen. Magnetic Bearings and Flexible Rotor Dynamics. Tribology Transactions, Vol. 32(1996)1:9-15
[28] 谢振宇,徐龙祥,李迎,丘大谋,虞烈.磁悬浮轴承转子系统的稳定性及动态特性分析[J],机械科学与技术,2004,7
[29] 谢振宇,徐龙祥,李迎,丘大谋,虞烈.磁悬浮轴承转子系统动态特性的实验研究.航空动力学报,2004年01期
[30] 朱礼进,汪希平,王文等.磁悬浮支承转子系统动力学特性的实验研究.上海大学学报(自然科学版),2002.6
[31] 汪希平,朱礼进,于良,王文,王小静,张直明,万金贵.主动磁轴承转子系统动力学特性的研究[J],机械工程学报,2001,11
[32] 孙首群,虞烈.磁轴承柔性转子系统动力特性建模与优化仿真[J],系统仿真学报,2003.3
[33] G.J. Shu, S,M. Yang, C.D. Yang. Design of Experiments for the Controller of Rotor Systems With a Magnetic Bearing. Transactions of the ASME, Journal of Vibration and Acoustics. 200/vol. 119. April 1997
[34] 孟光.转子动力学研究的回顾与展望.振动工程学报,2002.3
[35] 虞烈,刘恒等.轴承—转子系统动力学.中国机械工程,1999.11.
[36] 钟一谔,何衍宗.转子动力学.清华大学出版社,1987.11.
[37] 徐龙祥.高速旋转机械轴系动力学设计.北京:国防工业出版社:1994.6
[38] 顾家柳等编著,转子动力学,国防工业出版社,1985.
[39] 唐克伦.多盘柔性转子系统的磁轴承刚度和阻尼设计.四川轻化工学院学报,2003.09
[40] 杨国军,耿文骥,李红伟.10MW高温气冷堆磁轴承转子结构与固有频率的关系研究.高技术通讯,2003.04
[41] 胡超,王岩,王立国等.机械化数学在转子动力学研究中的应用.应用数学和力学,第23卷第9期(2002.9)
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