磁力轴承支承的多盘柔性转子系统主动控制
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摘要
转子动力学设计是旋转机械设计的一个重要环节，其中转子运行的稳定性是旋转机械设计首要考虑的内容。随着现代化工业的发展，各种旋转机械除了向高速、细长、高效的方向发展，同时还要求机器的噪声及振动更小，寿命更长，工作更可靠。传统的轴承—转子系统设计已逐渐不能满足现代工业发展的需要。
本文从现代工业发展的需要出发，讨论了磁轴承支承的转子系统的主动控制设计。首先，本文讨论了磁轴承支承的转子系统的力学模型，其次给出了计算转子系统固有频率的常用方法—有限元法和传递矩阵法的推导，接着再从转子系统稳定性出发，讨论了系统控制规律的设计，最后给出了一个磁轴承支承的转子系统的主动控制设计的例子以及其计算机仿真模型及仿真结果。
从计算方法上，本文对有限元法和传递矩阵法作了比较。由于有限元法计算精度高，易于同其它控制方法相联系，所以选择了有限元法作为本文的基本方法。同时，也对其稍加改进，使得编程更为简单。对于临界转速的计算方法，本文采用迭代法代替传统的作图法，结果表明，该法收敛速度快、精度高。
在控制规律上，本文从转子系统稳定性要求和磁轴承控制的特性出发探寻一个优化目标函数，最后给出了该目标函数的解法。与包含许多人为因素的最优二次型控制规律设计比较，该方法直观。
从轴承选型上，本文采用了先进的磁悬浮轴承，同传统的轴承相比，它有着其它轴承所没有的独特的优点。磁悬浮轴承必将是今后轴承技术发展的方向。
Rotor dynamic design is one of the most important aspects of rotating machinery design. And the stability of running rotor system is of first importance in rotating machinery design. With the development of the modem industry civilization, all kinds of rotating machinery not only demand rapid speed, long and thin, high efficiency, but also demands lower noise and vibration, long life, and more reliability. The custom rotor-bearing system design is gradually unfit for the demand of development of modern industry.
This paper discusses the active control design of rotor system mounted on the magnetic bearing in detail. Firstly, this paper discusses the mechanic model of rotor system mounted on the magnetic bearing. Secondly, this paper also discusses the most common methods of computing critical speed of rotor system that include the finite method and transfer method. Fourthly, this paper discusses the active control design according to the stability of running rotor system. Finally, this paper gives an example of active control design of rotor system mounted on the magnetic bearing and its simulated result.
From calculating methods, this paper give a comparison between the finite method and the transfer method and choose the finite method as the basic computing method due to its higher precision and its more apt to connect with other control methods. Meanwhile, this paper slightly improves on the finite method that result in easier programming. As to the critical speed computing method, there is also an improvement. Compare to the charting, the method of iteration is a rapid and high precision method.
From control method, this paper seeks for a majorized function according to the stability of running rotor system and properties of magnetic bearing in the first instance and then work out it. Against the optimal linear quadratic control, this method has its advantages.
From the selection of bearing types, this paper chooses an advanced magnetic bearing. This kind of bearing has its peculiarity and will be the future direction of development of bearing technology.
本文从现代工业发展的需要出发，讨论了磁轴承支承的转子系统的主动控制设计。首先，本文讨论了磁轴承支承的转子系统的力学模型，其次给出了计算转子系统固有频率的常用方法—有限元法和传递矩阵法的推导，接着再从转子系统稳定性出发，讨论了系统控制规律的设计，最后给出了一个磁轴承支承的转子系统的主动控制设计的例子以及其计算机仿真模型及仿真结果。
从计算方法上，本文对有限元法和传递矩阵法作了比较。由于有限元法计算精度高，易于同其它控制方法相联系，所以选择了有限元法作为本文的基本方法。同时，也对其稍加改进，使得编程更为简单。对于临界转速的计算方法，本文采用迭代法代替传统的作图法，结果表明，该法收敛速度快、精度高。
在控制规律上，本文从转子系统稳定性要求和磁轴承控制的特性出发探寻一个优化目标函数，最后给出了该目标函数的解法。与包含许多人为因素的最优二次型控制规律设计比较，该方法直观。
从轴承选型上，本文采用了先进的磁悬浮轴承，同传统的轴承相比，它有着其它轴承所没有的独特的优点。磁悬浮轴承必将是今后轴承技术发展的方向。
Rotor dynamic design is one of the most important aspects of rotating machinery design. And the stability of running rotor system is of first importance in rotating machinery design. With the development of the modem industry civilization, all kinds of rotating machinery not only demand rapid speed, long and thin, high efficiency, but also demands lower noise and vibration, long life, and more reliability. The custom rotor-bearing system design is gradually unfit for the demand of development of modern industry.
This paper discusses the active control design of rotor system mounted on the magnetic bearing in detail. Firstly, this paper discusses the mechanic model of rotor system mounted on the magnetic bearing. Secondly, this paper also discusses the most common methods of computing critical speed of rotor system that include the finite method and transfer method. Fourthly, this paper discusses the active control design according to the stability of running rotor system. Finally, this paper gives an example of active control design of rotor system mounted on the magnetic bearing and its simulated result.
From calculating methods, this paper give a comparison between the finite method and the transfer method and choose the finite method as the basic computing method due to its higher precision and its more apt to connect with other control methods. Meanwhile, this paper slightly improves on the finite method that result in easier programming. As to the critical speed computing method, there is also an improvement. Compare to the charting, the method of iteration is a rapid and high precision method.
From control method, this paper seeks for a majorized function according to the stability of running rotor system and properties of magnetic bearing in the first instance and then work out it. Against the optimal linear quadratic control, this method has its advantages.
From the selection of bearing types, this paper chooses an advanced magnetic bearing. This kind of bearing has its peculiarity and will be the future direction of development of bearing technology.
引文
1．钟一谔 等．转子动力学．清华大学出版社，1987
2. M.S. Darlow, B.T. Murphy, J.A. Elder, G.N. Sandor. Extensions of the Transfer Matrix Method for Rotordynamic Analysis to Include a Direct Representation of Conical Sections and Trunnions. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1980, Vol. 102: 122～129
3. H. Diken I.G Tadjbakhoh. Unbalance Response of Flexible Rotors Coupled with Torsion. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1980, Vol. 111: 179～186
4. F.H. Chu, W.D. Pilkey. A Direct Integration Technique for the Transient Analysis of Rotating Shaft. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1982, Vol. 104:384～388
5. G.T. Flowers. Modelling of an Elastic Disk with Finite Hub Motions and Small Vibrations with Application to RotorDynamics. Transactions of the ASME .Journal of Vibration and Acoustics 1996 v116/10-15
6．十合晋一著，韩焕臣 译．气体轴承设计、制作与应用．宇航出版社，1988
7．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
8．祝长生 汪希萱 新型动静压挤压油膜阻尼器对柔性转子系统振动的控制．机械工程学报．1996 vol(32)76-83
9．骆志明，冯庚斌，顾家柳．转子动力系统时滞H~∞控制．振动工程学报，1998，v11/317-321。
10．郭银朝，孟光．挤压油膜阻尼器支承的柔性转子的双稳态响应特性．振动工程学报，1997，v10/65-70
11. D. Dhar L.E. Barrett. Design of Magnetic Bearings for Rotor Systems With Harmonic Excitations. Transactions of the ASME .Journal of Vibration and Acoustics 1993 v115 359-366
12．徐龙样．高速旋转机械轴系动力学设计．国防工业出版社，1994
13. Y. Okada B. Nagai T. Shimane. Cross-Feedback Stabilization of the Digitally controlled Magnetic Bearing. Transactions of the ASME .Journal of Vibration and Acoustics 1992 v114 54-59
14. Kai-Yew Lum. Vincent T. Coppola Dennis S. Bernstein Adaptive
Virtual Autobalancing for a Rigid Rotor With unknown Mass Imbalance Supported by Magnetic Bearings. Transactions of the ASME .Journal of Vibration and Acoustics 1998 v120 557-570
15. Chyuan-Yow. Tseng, Pi-Cheng. Tung. Dynamics of a Flexible Beam with Active Nonlinear Magnetic Force. Transactions of the ASME .Journal of Vibration and Acoustics 1998 v120/39-46
16．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．机械工业出版社，2000
17．虞烈，刘恒．轴承转子系统动力学．西安交通大学出版社，2001
18．梅凤翔，刘端，罗勇．高等分析力学．北京理工大学出版社，1991
19．黄安基，理论力学。中国铁道出版社，1991
20. E.S. Zorzi,H.D. Nelson. The dynamics of Rotor-Bearing systems With Axial Torque-A Finite Element Approach. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1980, Vol. 102: 158～161
21．张文．转子动力学理论基础．科学出版社，1990
22. Shinshu Saito, Tsuneo Someya. Study of Damped Critical Speeds and Damping Ratios of Flexible Rotors. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1984 Vol. 106: 62～73
23. S. Donghty. Eigenvalue Derivatives for Damped Torsional Vibrations. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1982, Vol. 104: 463～465
24. K.E Rouch, J.S Kao. Dynamic Reduction in Rotor Dynmaics by the Finite Element Method. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1980, Vol. 102: 360～368
25. Ting Nung Shiau, Jon Li Hwang. A New Approach to the Dynamic Characteritic of Undamped Rotor-Bearing System. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1980, Vol. 111: 279～385
26．顾家柳．转子动力学．国防工业出版社，1985
27．唐克伦 高淑英 梁智权 计算转子系统固有频率的有限元法之改进。四川轻化工学院学报．2002，Vol．15 No．2．
28. DuhlR, L Dynamics of Distrubuted parameter tutoror systems: Transfer Matrix and Finite Element Techniques, ph.D. Thesis Cornell University, 1970
29. H.D. Nclson, J.M. Mc Vaugh: the Dynamics of Rotor-Bearing systems Using Finite Elements, J. of Eng. for Indus. Trans. ASME 1976 vol. 98 No. 2 593-600
30．何衍宗 计算多跨轴的频率与振型中，传递矩阵的改进．清华大学学报，1979 Vol．1 No．1，77～90．
31. G.C. Horner and W.D. Pilkey: The Riccati Transfer Matrix Method, J. of Mech. Des. Trans ASME 1978. vol.100, 297-302
32．王正Riccati传递矩阵法在转子动力学中的应用，清华大学工程力学系理论力学教研组，1982
33．顾仲权，马扣根，陈卫东．振动主动控制．北京：国防工业出版社，1997
34．张阿舟，姚起杭 振动控制工程。北京航空工业出版社。1989
35．丁文镜 减振理论 北京清华大学出版社．1988
36．顾仲权，朱德懋．振动控制评述．噪声与振动控制．1988(1)，5-13
37．谢友柏，袁崇君，虞烈．主动控制电磁轴承在混合方剂中的应用．摩擦学设计——案例分析及论述．周仲荣，谢友柏，2000
38．刘淑琴，虞烈．电磁轴承转速与控制精度相互影响的研究．振动工程学报，1999，12(1)
39．李自新，景敏树，罗岷，虞烈．非线性电磁力作用下的转子不平衡响应和界限碰摩转速．振动工程学报，2001，v14/76-80
40．薛定宇．反馈系统控制设计与分析——MATLAB语言应用．清华大学出版社，2000
41．吴沧浦．最优控制的理论与方法．国防工业出版社，2000
42．程云鹏．矩阵论．西北工业大学出版社，2000
43．陈祖明．矩阵论引论．北京航空航天出版社，1998
44．宋玉亭，薛豪，蓝信悌．基础物理学手册．江苏科学技术出版社，1988
45．邢郁甫，杨天民．新编电工实用手册．人民邮电出版社，1998
46．电工手册编写组．电工手册．上海科学技术出版社，1990
47．《新编实用电工手册》编写组．新编实用电工手册．北京：海洋出版社，1990
48．尉迟斌，徐德胜．制冷工程技术．上海交通大学出版社，1987
49．中国电子学会．1999/2000传感器与执行器大全．电子工业出版社，2000
50．杜润祥．测试与传感技术．华南理工大学出版社，1991
51．集成电路编委会．标准集成电路数据手册—运算放大器．电子工业出版社，1998
52．杨钰，何旭洪，赵昊彤．Mathematica应用指南．人民邮电出版社，1999
53．张志涌，徐彦琴．MATLAB教程．北京航空航天大学出版社，2001
54．陈卫国，冯峰，姚东等．MATLAB5.3应用指南．人民邮电出版社，1999
55．薛定宇．反馈系统控制设计与分析——MATLAB语言应用．清华大学出版社，2000
2. M.S. Darlow, B.T. Murphy, J.A. Elder, G.N. Sandor. Extensions of the Transfer Matrix Method for Rotordynamic Analysis to Include a Direct Representation of Conical Sections and Trunnions. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1980, Vol. 102: 122～129
3. H. Diken I.G Tadjbakhoh. Unbalance Response of Flexible Rotors Coupled with Torsion. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1980, Vol. 111: 179～186
4. F.H. Chu, W.D. Pilkey. A Direct Integration Technique for the Transient Analysis of Rotating Shaft. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1982, Vol. 104:384～388
5. G.T. Flowers. Modelling of an Elastic Disk with Finite Hub Motions and Small Vibrations with Application to RotorDynamics. Transactions of the ASME .Journal of Vibration and Acoustics 1996 v116/10-15
6．十合晋一著，韩焕臣 译．气体轴承设计、制作与应用．宇航出版社，1988
7．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
8．祝长生 汪希萱 新型动静压挤压油膜阻尼器对柔性转子系统振动的控制．机械工程学报．1996 vol(32)76-83
9．骆志明，冯庚斌，顾家柳．转子动力系统时滞H~∞控制．振动工程学报，1998，v11/317-321。
10．郭银朝，孟光．挤压油膜阻尼器支承的柔性转子的双稳态响应特性．振动工程学报，1997，v10/65-70
11. D. Dhar L.E. Barrett. Design of Magnetic Bearings for Rotor Systems With Harmonic Excitations. Transactions of the ASME .Journal of Vibration and Acoustics 1993 v115 359-366
12．徐龙样．高速旋转机械轴系动力学设计．国防工业出版社，1994
13. Y. Okada B. Nagai T. Shimane. Cross-Feedback Stabilization of the Digitally controlled Magnetic Bearing. Transactions of the ASME .Journal of Vibration and Acoustics 1992 v114 54-59
14. Kai-Yew Lum. Vincent T. Coppola Dennis S. Bernstein Adaptive
Virtual Autobalancing for a Rigid Rotor With unknown Mass Imbalance Supported by Magnetic Bearings. Transactions of the ASME .Journal of Vibration and Acoustics 1998 v120 557-570
15. Chyuan-Yow. Tseng, Pi-Cheng. Tung. Dynamics of a Flexible Beam with Active Nonlinear Magnetic Force. Transactions of the ASME .Journal of Vibration and Acoustics 1998 v120/39-46
16．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．机械工业出版社，2000
17．虞烈，刘恒．轴承转子系统动力学．西安交通大学出版社，2001
18．梅凤翔，刘端，罗勇．高等分析力学．北京理工大学出版社，1991
19．黄安基，理论力学。中国铁道出版社，1991
20. E.S. Zorzi,H.D. Nelson. The dynamics of Rotor-Bearing systems With Axial Torque-A Finite Element Approach. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1980, Vol. 102: 158～161
21．张文．转子动力学理论基础．科学出版社，1990
22. Shinshu Saito, Tsuneo Someya. Study of Damped Critical Speeds and Damping Ratios of Flexible Rotors. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1984 Vol. 106: 62～73
23. S. Donghty. Eigenvalue Derivatives for Damped Torsional Vibrations. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1982, Vol. 104: 463～465
24. K.E Rouch, J.S Kao. Dynamic Reduction in Rotor Dynmaics by the Finite Element Method. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1980, Vol. 102: 360～368
25. Ting Nung Shiau, Jon Li Hwang. A New Approach to the Dynamic Characteritic of Undamped Rotor-Bearing System. Journal of Vibration, Acoustics, Stress and Reliability in Design, 1980, Vol. 111: 279～385
26．顾家柳．转子动力学．国防工业出版社，1985
27．唐克伦 高淑英 梁智权 计算转子系统固有频率的有限元法之改进。四川轻化工学院学报．2002，Vol．15 No．2．
28. DuhlR, L Dynamics of Distrubuted parameter tutoror systems: Transfer Matrix and Finite Element Techniques, ph.D. Thesis Cornell University, 1970
29. H.D. Nclson, J.M. Mc Vaugh: the Dynamics of Rotor-Bearing systems Using Finite Elements, J. of Eng. for Indus. Trans. ASME 1976 vol. 98 No. 2 593-600
30．何衍宗 计算多跨轴的频率与振型中，传递矩阵的改进．清华大学学报，1979 Vol．1 No．1，77～90．
31. G.C. Horner and W.D. Pilkey: The Riccati Transfer Matrix Method, J. of Mech. Des. Trans ASME 1978. vol.100, 297-302
32．王正Riccati传递矩阵法在转子动力学中的应用，清华大学工程力学系理论力学教研组，1982
33．顾仲权，马扣根，陈卫东．振动主动控制．北京：国防工业出版社，1997
34．张阿舟，姚起杭 振动控制工程。北京航空工业出版社。1989
35．丁文镜 减振理论 北京清华大学出版社．1988
36．顾仲权，朱德懋．振动控制评述．噪声与振动控制．1988(1)，5-13
37．谢友柏，袁崇君，虞烈．主动控制电磁轴承在混合方剂中的应用．摩擦学设计——案例分析及论述．周仲荣，谢友柏，2000
38．刘淑琴，虞烈．电磁轴承转速与控制精度相互影响的研究．振动工程学报，1999，12(1)
39．李自新，景敏树，罗岷，虞烈．非线性电磁力作用下的转子不平衡响应和界限碰摩转速．振动工程学报，2001，v14/76-80
40．薛定宇．反馈系统控制设计与分析——MATLAB语言应用．清华大学出版社，2000
41．吴沧浦．最优控制的理论与方法．国防工业出版社，2000
42．程云鹏．矩阵论．西北工业大学出版社，2000
43．陈祖明．矩阵论引论．北京航空航天出版社，1998
44．宋玉亭，薛豪，蓝信悌．基础物理学手册．江苏科学技术出版社，1988
45．邢郁甫，杨天民．新编电工实用手册．人民邮电出版社，1998
46．电工手册编写组．电工手册．上海科学技术出版社，1990
47．《新编实用电工手册》编写组．新编实用电工手册．北京：海洋出版社，1990
48．尉迟斌，徐德胜．制冷工程技术．上海交通大学出版社，1987
49．中国电子学会．1999/2000传感器与执行器大全．电子工业出版社，2000
50．杜润祥．测试与传感技术．华南理工大学出版社，1991
51．集成电路编委会．标准集成电路数据手册—运算放大器．电子工业出版社，1998
52．杨钰，何旭洪，赵昊彤．Mathematica应用指南．人民邮电出版社，1999
53．张志涌，徐彦琴．MATLAB教程．北京航空航天大学出版社，2001
54．陈卫国，冯峰，姚东等．MATLAB5.3应用指南．人民邮电出版社，1999
55．薛定宇．反馈系统控制设计与分析——MATLAB语言应用．清华大学出版社，2000
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