运转状态下转子不平衡识别方法的研究
摘要
转子动平衡时，常用的方法往往需要通过多次试车才能确定校正质量，费时又
费力，这对大型转子尤为突出。人们一直希望能通过转子运转状态下获得的振动信
息经济、快捷地识别出转子的不平衡量，但尚未有成熟可行的方法。在这种背景下，
本文在前人研究的基础上继续新的探索，以使转子不平衡量的识别可以在线进行，
从而实现无试转的转子现场动平衡。为此，本文对这一领域的近期研究成果进行了
研究学习，并在以下几方面作了进一步的研究工作：
1．基于电磁轴承（AMB）结构，改进了可控电磁激振器（AME）的设计方法
和功率放大器的设计方法，改进了AME磁性材料的选用，使之具有较大的工作电
流、较大的饱和磁感应强度和较小的体积，提出了可供实验室采用的电磁力标定方
法。
2．推导了AME电磁力非线性误差公式，提出了采用数值积分手段进行转子—
激振器系统仿真研究的新方法，解决了不平衡振动与电磁激励振动相互耦合的非线
性系统的仿真分析问题，使得AME/AMB的非线性特性分析更为准确和方便。通过
仿真和实验研究明确了各种因素对AME非线性特性的影响规律，并发现了不同频
率振动对参数识别输入量（相应于激励频率的电磁力分量）的影响，提出了AME
合理的工作参数范围。
3．根据采用达朗伯原理结合利茨法建立的转子动力学方程，提出了基于电磁激
振在线识别转子支承系数的新方法。该方法改变了通常需要改变转速获取振动信息
的做法，避免了支承系数随转速变化带来的识别困难，同时在转子系统建模过程中，
采用了三次多项式作为瑞利函数，将轴作为连续梁处理，比有限元法更为准确。
4．提出了转子支承处无测点时的参数识别方法，这种新的方法改善了通常采用
的用支承附近测点近似代替的方法带来的识别精度低下的问题，仿真和实验表明这
一方法具有较为满意的识别效果。
浙江人学博士学位论文
5．在识别得到转子支承系数的基础上，提出了柔性转子不平衡量识别方法，该
方法以模态平衡为基本思想，识别时不需要改变转子的工作转速。出于一次识别平
衡了主要的低阶不平衡量，因而平衡后即使转速变化了，依然能保持良好的平衡精
度，仿真研究表明当支承系数随转速变化而有较大变化时，识别结果也依然能满足
在感兴趣范围内一次性实现全速动平衡要求。
6．设计研制了转于一可控电磁激振器实验系统，开发了激励一测试工作软件，
提出了数据采集以后的信号整定方法，保证了DFT的准确性。进行了转子支承系数
和不平衡量的实验识别，并通过固有频率和频响曲线实验验证了识别方法的有效性。
In most of the methods of balancing flexible rotors many times of test runs are usually required in order to calculate correction masses, which will cost a large amount of time and motive power (especially in the cast of large scale rotors). Peoples always wish to identify rotor unbalance with the vibration information obtained from the operating rotor, but there are no mature and practicable methods available yet. Therefore, the aim of this thesis is to carry on further study on the basis of the existing achievements in order that rotor unbalance can be identified on-line and rotor balancing without test runs can be completed on-site. Consequently, this thesis develops the following aspects:
1. According to the structure of the active magnetic bearing (AMB) and the characteristic of the active magnetic executor (AME), the design methods of the AME and the power amplifier, and the selection of the magnetic material used in the AME are improved, which make AME have greater working electronic current and saturation magnetic flux density, and smaller volumn. Moreover, this thesis presents calibration methods about the electromagnetic force calibration, which can be used in laboratory conveniently.
2. A nonlinear err formula about the electromagnetic force of AME is derived, and a new method which adopts numerical value integral in the simulate study of the rotor-exciter system is presented, which solves the nonlinear simulate study problem of the rotor-exciter system in which the unbalance excitation vibration and the electromagnetic excitation vibration are mutual coupling and makes the nonlinear characteristic analysis of the AME/AMB even more accurate and convenient. Through simulation and experiment study the various factors that influence the nonlinear characteristic of the AME are cleared, and the effect of the different frequency vibration of rotor on parameters identification input value (the part in the electromagnetic force corresponding excitation frequency) is discovered, and on the basis of the above, the reasonable working parameters extent of the AME is presented.
3. On the basis of the rotor dynamics equation set up by combining d'Alemdert principle with Rize way, a new on-line identification method of dynamic parameters of rotor-bearing system by electromagnetic excitation is presented. The method need not change the rotation speed of the rotor as generally to obtain vibration information of the rotor, and avoid the identification difficulty which will arise when dynamic parameters of rotor-bearing system change with the rotation speed. Meanwhile, by adopting three order polynomial as Rayleigh function and treating rotor shaft as continue beam to set up rotor system mathematical model, the method is more accurate than the finite element method.
4. When there are not measurement sensors at the place where the bearing is installed, the usual method is to substitute the rotor vibration near the bearing for at the
bearing, which often brings about poor identification precision. Therefore, a new parameter identification method used on this condition is presented, and the simulation and experiment study of this thesis indicates that the new method improves the precision of parameter identification effectively.
5. On condition that dynamic parameters of rotor-bearing system have been obtained, the method of flexible rotor unbalance identification is presented, which takes modal dynamic balancing as the criterion of balancing and needs not change the operating speed of the rotor in identification. Because the main low order modal unbalances have been balanced by an identification, even if the rotation speed of the rotor is changed, the rotor can keep up good balance situation. The simulation study indicates that the result of identification and balancing can satisfy the requirement of all speed balancing in very wide extent by an identification without tests run even if dynamic parameters of rotor-bearing system change with rotation speed greatly.
6. An experiment system of the rotor and the
费力，这对大型转子尤为突出。人们一直希望能通过转子运转状态下获得的振动信
息经济、快捷地识别出转子的不平衡量，但尚未有成熟可行的方法。在这种背景下，
本文在前人研究的基础上继续新的探索，以使转子不平衡量的识别可以在线进行，
从而实现无试转的转子现场动平衡。为此，本文对这一领域的近期研究成果进行了
研究学习，并在以下几方面作了进一步的研究工作：
1．基于电磁轴承（AMB）结构，改进了可控电磁激振器（AME）的设计方法
和功率放大器的设计方法，改进了AME磁性材料的选用，使之具有较大的工作电
流、较大的饱和磁感应强度和较小的体积，提出了可供实验室采用的电磁力标定方
法。
2．推导了AME电磁力非线性误差公式，提出了采用数值积分手段进行转子—
激振器系统仿真研究的新方法，解决了不平衡振动与电磁激励振动相互耦合的非线
性系统的仿真分析问题，使得AME/AMB的非线性特性分析更为准确和方便。通过
仿真和实验研究明确了各种因素对AME非线性特性的影响规律，并发现了不同频
率振动对参数识别输入量（相应于激励频率的电磁力分量）的影响，提出了AME
合理的工作参数范围。
3．根据采用达朗伯原理结合利茨法建立的转子动力学方程，提出了基于电磁激
振在线识别转子支承系数的新方法。该方法改变了通常需要改变转速获取振动信息
的做法，避免了支承系数随转速变化带来的识别困难，同时在转子系统建模过程中，
采用了三次多项式作为瑞利函数，将轴作为连续梁处理，比有限元法更为准确。
4．提出了转子支承处无测点时的参数识别方法，这种新的方法改善了通常采用
的用支承附近测点近似代替的方法带来的识别精度低下的问题，仿真和实验表明这
一方法具有较为满意的识别效果。
浙江人学博士学位论文
5．在识别得到转子支承系数的基础上，提出了柔性转子不平衡量识别方法，该
方法以模态平衡为基本思想，识别时不需要改变转子的工作转速。出于一次识别平
衡了主要的低阶不平衡量，因而平衡后即使转速变化了，依然能保持良好的平衡精
度，仿真研究表明当支承系数随转速变化而有较大变化时，识别结果也依然能满足
在感兴趣范围内一次性实现全速动平衡要求。
6．设计研制了转于一可控电磁激振器实验系统，开发了激励一测试工作软件，
提出了数据采集以后的信号整定方法，保证了DFT的准确性。进行了转子支承系数
和不平衡量的实验识别，并通过固有频率和频响曲线实验验证了识别方法的有效性。
In most of the methods of balancing flexible rotors many times of test runs are usually required in order to calculate correction masses, which will cost a large amount of time and motive power (especially in the cast of large scale rotors). Peoples always wish to identify rotor unbalance with the vibration information obtained from the operating rotor, but there are no mature and practicable methods available yet. Therefore, the aim of this thesis is to carry on further study on the basis of the existing achievements in order that rotor unbalance can be identified on-line and rotor balancing without test runs can be completed on-site. Consequently, this thesis develops the following aspects:
1. According to the structure of the active magnetic bearing (AMB) and the characteristic of the active magnetic executor (AME), the design methods of the AME and the power amplifier, and the selection of the magnetic material used in the AME are improved, which make AME have greater working electronic current and saturation magnetic flux density, and smaller volumn. Moreover, this thesis presents calibration methods about the electromagnetic force calibration, which can be used in laboratory conveniently.
2. A nonlinear err formula about the electromagnetic force of AME is derived, and a new method which adopts numerical value integral in the simulate study of the rotor-exciter system is presented, which solves the nonlinear simulate study problem of the rotor-exciter system in which the unbalance excitation vibration and the electromagnetic excitation vibration are mutual coupling and makes the nonlinear characteristic analysis of the AME/AMB even more accurate and convenient. Through simulation and experiment study the various factors that influence the nonlinear characteristic of the AME are cleared, and the effect of the different frequency vibration of rotor on parameters identification input value (the part in the electromagnetic force corresponding excitation frequency) is discovered, and on the basis of the above, the reasonable working parameters extent of the AME is presented.
3. On the basis of the rotor dynamics equation set up by combining d'Alemdert principle with Rize way, a new on-line identification method of dynamic parameters of rotor-bearing system by electromagnetic excitation is presented. The method need not change the rotation speed of the rotor as generally to obtain vibration information of the rotor, and avoid the identification difficulty which will arise when dynamic parameters of rotor-bearing system change with the rotation speed. Meanwhile, by adopting three order polynomial as Rayleigh function and treating rotor shaft as continue beam to set up rotor system mathematical model, the method is more accurate than the finite element method.
4. When there are not measurement sensors at the place where the bearing is installed, the usual method is to substitute the rotor vibration near the bearing for at the
bearing, which often brings about poor identification precision. Therefore, a new parameter identification method used on this condition is presented, and the simulation and experiment study of this thesis indicates that the new method improves the precision of parameter identification effectively.
5. On condition that dynamic parameters of rotor-bearing system have been obtained, the method of flexible rotor unbalance identification is presented, which takes modal dynamic balancing as the criterion of balancing and needs not change the operating speed of the rotor in identification. Because the main low order modal unbalances have been balanced by an identification, even if the rotation speed of the rotor is changed, the rotor can keep up good balance situation. The simulation study indicates that the result of identification and balancing can satisfy the requirement of all speed balancing in very wide extent by an identification without tests run even if dynamic parameters of rotor-bearing system change with rotation speed greatly.
6. An experiment system of the rotor and the
引文
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66． Tonnesen, J., Lund, J., Experimental Techniques for Rotordynamics Anlysis, CISM, Course No.297, Rotordynamics 2Ed. by N. F. Rieger,Springer-Verlag,1988
67． Qiu, z. L. And Tieu, A. K., Identification of sixteen force coefficients of two journal bearings from Impulse responses, Wear 212, 206-212,1997
68． Hiroshi Iida, Application of the Experimental Determination of Character Matrices to the Balancing of a Flexible Rotor, Proc. of 4th Intel. Conf. on Rotordyn., IFTOMN , pp.111-115． Chicago, Sept. 1994
69． Iida, H., Tomita, H., Watanabe, T., Experimental Identification of Mechanical System with Character Matrices, Trans. Jpn. Soc. Mec. Eng., 557c(59) , pp65-72 (Jan, 1993) .
70． Kang, W. And Jin, D., The Application of the Model Reference Adaptive System in the Identification of Dynamic Characteristics of Oil-film Bearings, IME Int. Conf. on Vibration in Rotating Machinery, pp241-246, 1998
71． Stanway, R., Tee, T.K., and Mottershead, J.E., Identification of Squeeze-film
Bearing Dynamics Using a Recursive, Frequency-domain Filter, ASME Vibration Conf., pp167-176, 1989
72．汤炳新，闻邦椿，王占军，一种识别转子在运动状态下模态参数的方法，第四届全国转子动力学年会论文集，214-219，1995。
73. Takeshi Mizuno and Kenji Araki, Application of Dynamic Vibration Absorbers to Rotor Unbalance Measurements, Proceedings of Ninth World Congress on the Theory of Machines and Mechanisms, Milano, Italy, Sept. 1995
74. Kanemitsu, Y., Real Time Balancing of a Flexible Rotor Supported by Magnetic Bearing, Proc. of 3rd Intel. Conf. on Rotordynamics, IFTOMM, PP.263-268, Lyon, Sept., 1990
75．顾家柳，王强，可控挤压油膜轴承主动控制转子系统振动，应用力学学报，1990，7(2)，41-47
76．童水光，转子轴承系统电磁阻尼器控制的研究。浙江大学博士论文，1991
77．汪海航，电磁阻尼器动力特性及转子振动主动控制研究，浙江大学博士学位论文，1994
78. Matsushita, O., Unbalance Resonance Vibration Control for Magnetically Borne Flexible Rotors, Proc. of 4th Intel. Conf. on Rotordyn., IFTOMN, pp.363-370, Chicago, Sept. 1994
79．卢奂采，转子振动主动控制与轴向力在线动态监测研究，浙江大学博士学位论文，1996
80. Nordmaun, R., Matros, M. and Neumer, T., Parameter Identification in Rotating Machinery by means of Magnetic Bearings, Proc. of 4th Intel. Conf. on Rotordyn., IFTOMN , pp. 7-15,Chicago, Sept. 1994
81. Konpf, E., Nordmaun, R., Active Magnetic Bearings for the Parameter Identification of Dynamic Characteristics of Fluid Bearings—Calibration Results, pp.52-61, 1998
82. Gahler, C, and Herzog, R., Identification of Magnetic Bearing Systems, 4th Int. Symp. on Magnetic Bearings, ETH Zurich, Aug. 1993
83. Lottin, J. and Saidi, L., Identification of Physical Parameters in a Active Magnetic Bearing Suspension, 4th Int. Symp. on Magnetic Bearings, ETH Zurich, Aug. 1993
84. Chong-Won Lee, Young-Ho Ha, Cheal-Soon Kim, Identification of Active Magnetic Bearing System Using Magnetic Force Measurement, IV Int. Symposium on Magnetic Bearings, pp.305-309 August. 1994
85. Z Yu L, L T Meng and L M King, Electromagnetic Bearing Actuator for Active
Vibration Control of a Flexible Rotor, Proc. Instn. Mech. Engrs. Vol. 212, Part C, pp.705-716 1998
86． Kreuzinger-Janik,T., Irretier, H., On Modal testing of flexible Rotors for Unbalance Identification, Proceedings of the 16~(th) International Modal Analysis Conference, Part2,pp.l533-1539,1998( 注:此文献仅从EI上查得了文献摘要)
87． Habermann, H., Liard, G., An Active Magnetic Bearing System, Tribology Inter., pp.85-89, April, 1980
88． Habermann, H., Liard, G., Practical magnetic Bearing, IEEE Spectrum, pp.26-30, Sept., 1979
89． Myklestad, N.O., A New Method of Calculating Natural Modes of Uncoupled Bending Vibration of Airplane Wings and Other Types of Beam, J. of Aero. Sci. Vol. 11, pp. 153-162,1944．
90． Prohl, M. A., A General Method for Calculating Critical Speeds of Flexible Rotors, J. of Appl. Mech., Trans. ASME, Vol.12, No.3, pp142-148,1945．
91． Bansal, R. N., and Kirk, R. G., Stability and Damped Critical Speeds of Rotor Bearings Systems, ASME Journal of Engineering for Industry, Vol.98, No.l, pp.71-76,1977．
92． Arther, J.S., Consistent Mass Matrix for Distributed Mass System, J. of the Structural Division, Proceedings of the ASCE, Vol.89, ST4, PP161-164,1963
93． Ruhl, R.L., Dynamics of Distributed Parameter Turborotor Systems: Transfer Matrix and Element Techniques, PhD Thesis, Cornell University, Ithaca N.Y., Jan, 1970．
94． Ruhl, R. L., and Booker, J.F., A Finite Element Model for Distributed Parameter Turborotor System, J. of Engineering for Industry, Trans. ASME,pp.l26-131． 1972
95． Nelson, H.D., and Mc Vaugh, J.M., The Dynamics of Rotor-Bearing Systems Using Finite Elements, J. of Engineering for Industry, Trans. ASME. Vol.98, No.2, pp.593-600． 1976．
96． Zorzi, E.S., and Nelson, H.D., Finite Element Simulation of Rotor Bearing Systems with Internal Damping, J. of Engineering for Power, Trans. ASME, Vol.89, No.l, pp.71-76, 1977．
97． Nelson, H.D., A Finite Rotating Shaft Element Using Timoshenko Beam Theory, ASME Journal of Mechanical Design, Vol.102, pp.793-803． 0ct.1980．
98． Gasch,R., Vibration of Large Turbo-Rotor in Fluid-Film Bearing on an Elastic Foundation, J. of Sound and Vibration, 47(l),pp.53-73,1976．
99. Hashish, E. and Sankar, T. S., Finite Element and Modal Analysis of Rotor-Bearing Systems Under Stochastic Loading Conditions, ASME Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol. 106, pp.80-89, Jan. 1984
100．郑水英，转子机械振动控制的研究—振动分析、气体阻尼器和自学习控制，浙江大学博士后研究工作报告，1996
101 Kirk, R.G. and Gunter, E.J., The Effect of Support Flexibility and Damping on the Synchronous Response of a Single-Mass Flexible Rotor, ASME Journal of Engineering for Industry, pp.221-228, Feb. 1972
102．顾家柳等，转子动力学，国防工业出版社，1985
103．卢文祥，杜润生，机械工程测试 信息 信号分析，华中理工大学出版社，1990
104．曾胜，汪希萱，李元涌，小速差双转子系统不平衡矢量识别方法的研究，振动工程学报，Vol．9 No．4 pp．399-404，Dec．1996
105．钟一谔，何衍宗，王正，李方泽，转子动力学，清华大学出版社，1984
106．傅志方，振动模态分析与参数辩识，机械工业出版社，1990
1．楼向明，郑水英，汪希萱，旋转机械转子不平衡在线识别方法的实验研究，汽轮机技术，1998(4)，PP．222-226
2．楼向明，郑水英，汪希萱，姚滨，一种在线识别转子不平衡的新方法，工程设计，1998(3)，PP．40-43
3．郑水英，楼向明，汪希萱，基于电磁激振在线识别转子不平衡故障的方法，振动工程学报，1998(11)，PP．265-269
4．楼向明，郑水英，汪希萱，电磁激振器电磁力线性度的影响因素研究，机电工程，1999(2)，PP．40-42
2． Gladwell, G.M.L. and Bishop, R.E.D., The vibration of Rotating Shafts Supported in Flexible Bearings, J. of Mech. Engr. Sci., Vol, No.l, p.66, 1959
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4． Bishop, R.E.D. and Parkinson, A.G., On the isolation of modes in the balancing of flexible shafts, Proc. Instn. Mech. Eugrs., Vol. 177, pp.407-426, 1963
5． Lindly, A.G. and Bishop, R.E.D., Some Recent Research of the Balancing of Large Flexible Rotors, Proc. Inst. Mech. Engr., Vol.177, No.30, pp.881, 1963
6． Bishop, R.E.D., Parkinson, A. G., On the Use of Balancing Machines for Flexible Rotors, Trans. ASME Paper No.71-vib-73
7． Kellenberger, W., Balancing Flexible Rotors on Two Generally Flexible Bearings, Brown Boveri Review, Vol.54, No.9, pp.603-619．
8． Kellenberger, W., Should a Flexible Rotor Be Balanced in N or N+2 Planes? Trans. of ASME, J. of Engineering Industry, pp548-569,1972
9． Goodman, TP., A Least-Squares Method for Computing Balance Corrections, Trans, of ASME, J. of Engr. for Industry, Vol.86, No.3, pp.273-279, 1964
10． Lund, J.W., and Tonnesen, J., Analysis and Experiments in Multi-plane Balancing of Flexible Rotors, Trans. of ASME, J. of Engr. for Industry, Vol.94, No.l, 1972
11． Lund, J.W., and Tonnesen, J., Experimental and Analytic Investigation of High-Speed Rotor Balancing-Phase I, Department of Machine Design, Technical University of Denmark, Research Report No. FR-8, Project No.FP-4, 1970
12． Van de Vegte, J. and Lake, R.T., Balancing of Rotating Systems During Operation, J. of Sound and Vibration, 57(2) , pp.225-235, 1978．
13． Bishop, R.E.D., On the Possibility of Balancing Rotating Flexible Shifts, J. of Mechanical Engineering Science, Vol.24 No.4, pp215-220, 1982
14． Borik, P. and Hogfors, C., Autobalancing of Rotors, J. Sound and Vibration, Vol.lll,PP.429-440, 1986．
15． Syouzou Kubo and Yasuka Jinouchi, Automatic Balancer (Pendulum Balancer), Bulletin of JAME., Vol.29, No.249, pp.924-928,1986．
16． Gosiewski, Z., Automatic Balancing of Flexible Rotors, Part I: Theoretical
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18. Smalley, A.J., Spray automated Balancing of rotors: concept and initial feasibility study, J. Eng. Gas, Turbines, Power, Trans. ASME, Vol. 111, n4, pp.659-665, 1989
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22. Parkison, A.G., D.arlow, M.S. and Smalley, A.J., A Theoretical Introduction to the Development of a Unified Approach to Flexible Rotor Balancing, J. of Sound and Vibration; 68(4), pp.489-506, 1980
23. Drechsler, J., A Combination of Modal Balancing and Influence Coefficient Method, Proc. of World Congress on Theory of Machines and Mechanisms, Newcastle-upon-Tyne,pp.81-86,1975.
24. Ibrahim S R., A Time Domain Modal Vibration Test Technique, The Shock and Vibration Bulletin. Vol.43, Part4, June 1973
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26. Ibrahim S R. and Mikulcik E C., A Method for the Direct Identification of Vibration Parameters from the Free Response, The shock and Vibration Bulletin. Vol., 47/4, 183-198. 1977
27. Sullivan, B.J., Application of Modal Superposition in Nonlinear Rotor Dynamic Analysis, Ibid.
28. Black, H.F., Brown, R. D., Modal Dynamic Simulation of Flexible Shafts in Hydrodynamic Bearings. Vibrations in Rotating Machinery, Proc. of Conference, I. Mech. E. C266/80, Cambridge, U.K., 1980
29. Bently, D.E., Muszyuska, A., Oil Whirl Identification by Perturbation Test, Advances in Computer-aided Bearing Design, 82-72978, ASME/ASLE Lubrication Conference, Washington, DC, October 1982
30. Bently, D.E., Muszyuska, A., Perturbation Tests of Bearing/Seal for Evaluation of Dynamic Coefficients, Symposium on Rotor Dynamical Instability, Summer Annual Conference of the ASME Applied Mechanics Division, AMD-Vol.55, Houston, TX, June 1983
31. Bently, D.E., Muszynska, A., Identification of Bearing and Seal Dynamic Stiffness Parameters by steady state Load and Squeeze Film Tests, Proc. of BRDRC Symposium on Instability in Rotating Machinery, Carson City, NV, June 1985
32. Gasch, R. and Drfchasler, J., Modals Auswuchten Elastischer Laufer ohne Testgewichts-Setzungen, VDI Ber, Vol.320, pp.45-54, 1978.
33. Palazzlo, A.B., and Gunter, E.J., Modal Balancing of a Multimass Flexible Rotor Without Trial Weight, Gas Turbine Division of ASME, 82-GT-267,1982.
34. Gnielka, P., Modal Balancing of Flexible Rotors without Test Runs-an Experimental Investigation, J. sound and vibration, Vol.90, pp. 157-172,1983.
35．朱继梅，邵亚声，朱闻，挠性转子动平衡的模态参数识别方法，振动工程学报，1987，1(1)：42-50
36．朱继梅，伍旭强，转子模态动平衡的几种数据处理方法，上海机械学院学报，1990，12(1)：45-50
37. Kanemitsu, Y., Balancing of Flexible Rotor by Modal Parameter Identification, Trans. of the ASME. 1985
38. Bingxin, T. And Bangchum, W., Principle and Application of a High-speed Balancing Technique by Two Runs, Proceedings of Ninth World Congress on the Theory of Machines and Mechanisms, Milano, Italy 1995, pp. 1243-1246
39. Saito, S., and Azuma, T., Balancing of Flexible Rotors by the Complex. Modal Method, Trans. Of the ASME, J. Vibr. Acous. Stress, Relia. Design, Vol. 105, pp.94-101, 1983
40. R. de SILVA, Balancing of Flexible Rotors with one Transient Run-an Experimental and Theoretical Investigation, Intel. Conf. on Vibr. in Rotating Machinery, 4th, Edinburgh, pp. 511-521,1988.
41. Mortan, P.G., Modal Balancing of Flexible shafts Without Trial Weights, Proc. Instn. Mech. Engr., Part c, Vol.199, C1, pp71-77, 1985.
42．汪海良，刘思汉，柔性转子无试重动平衡法的实验研究，振动与冲击，NO．3，pp．57-65，1992。
43. Parkinson, A.G., Balancing of Rotating Machinery, Proc. Instn. Mech. Engr., Vol.205, pp.53-66, 1991
44. Bachschmid, N., Bemante, R., Bruni, S., and Collina, A., Identification with Simple Models of the Mode Shapes and Unbalances of Rotor Systems from Bearing Measurements, Proc. of 4th Intel. Conf. on Rotordyn., IFTOMN , pp.117-122, Chicago, Sept. 1994
45. Bachschmid, N., Bruni, S., and Collina, A., An Application of Unbalance Identification Techniques, Proc. of 9th. World Congress on the theory of Machines and Mechanisms, Milano, pp1257-1261, 1995
46. Song-Ba Xia, A Method of Identifying Bearing Dynamic Coefficients and Unbalances of Turbine Rotor, Proc. of Intel. Conf. Rotor dynamics, Tokyo, pp.69-74, 1986.
47．郑钢铁，黄文虎，邵成勋，利用振动参数识别进行转子的现场动平衡，哈尔滨工业大学学报，3，25-33，1989
48．郑钢铁，黄文虎，转子系统模态参数现场识别技术研究，力学学报，23(5)，634-640，1991
49. Xiao-dong, Z. and Xi-Xuan, W., A Method of Balancing Large-scale Flexible Rotors without Test Runs. 1995.
50．朱晓东，新型动平衡方法研究，浙江大学博士学位论文，1996
51．毕世华，李乃宏，郑钢铁，油膜轴承动态特性参数及转子不平衡的现场识别，航空学报，1998，19(3)，378-383
52. A-C LEE and Y-P SHIH, Identification of the Unbalance Distribution and Dynamic Characteristics of Bearings in Flexible Rotors, Proc. Inst. Mech. Engr. Vol. 210, pp.409-428, 1996
53. YUAN-PIN SHIH and AN-CHEN LEE, Identification of the Unbalance Distribution in Flexible Rotors, Int. J. Mech. Sci. No.7, pp.841-857, 1997
54．郑钢铁，黄文虎，邵成勋，郭泾湘，用于现场条件下识别模态参数的几种时域模型及其比较，振动工程学报，1990，3(3)，67-74
55．饶柱石，周海亭，傅志芳，多跨转子不平衡载荷在线识别的一种新方法，上海交通大学学报，1994，28(4)，26-30
56．段吉安，王世琥，虞烈，谢友柏等，大型汽轮机滑动轴承油膜动特性系数识别的研究，机械工程学报，1997，33(1)，93-98
57．郑铁生，许庆余，滑动轴承油膜动力系数的附加不平衡量辩识方法，西安交通大学学报，1992，26(3)，99-106
58. Tieu, A. K., and Qiu, z. L. Identification of sixteen dynamic coefficients of two journal bearings from experimental unbalance responses, Wear 177,63-67 1994
59． Glienicke,J.,高速轴的滑动轴承的静力和动力特性的实验确定,国外透平(滑动轴承专辑(2) ),东方汽轮机厂, 1977, 109-150
60． Mitchell, J. R., Holmes, R. and von Ballegooyen H., Experimental Determination of a Bearing Oil Film Stiffness, Instn. Mech. Engr. Proc.18/, pt. 3k, pp90-96 (1965-1966)
61． Bently, D.E., and Muszynska, A., Modal Testing and Parameter Identification of Rotating Shaft/Fluid Lubricated Bearing System, Intl. Modal Analysis Conf., Proc. of the 4th, Los Angles, CA, Vol.2, pp.1393-1402, 1986．
62． Morton, P.G. The Derivation of Bearing Characteristics by Means of Transient Excitation Applied Directly to a Rotating Shaft. Dynamics of Rotors, IUTAM Symp., Dynamics of Rotors, Lyngby, Denmark , Springer Verlag, pp350-379(1975)
63． Nordmann, R., Schollhom, K., Identification of stiffness and Damping Coefficients of Journal Bearings by Means of the Impact Method, Second intern. Conference on Vibrations in Rotating Machinery, Cambridge, Sept. 1980
64． Nordmann, R, Schollhom, K., Identification of Modal Parameter of an Elastic Rotor with oil Film Bearing, Journal of Vibration, Acoustics, Stress, and Reliability in Design, Vol.106, 1984
65． Nordmann, R., Massmann, H., Identification of Stiffness, Damping and Mass Coefficients for Annular Seals, Intern. Conference on Vibrations in Rotating Machinery, IMech,C280/84,1984
66． Tonnesen, J., Lund, J., Experimental Techniques for Rotordynamics Anlysis, CISM, Course No.297, Rotordynamics 2Ed. by N. F. Rieger,Springer-Verlag,1988
67． Qiu, z. L. And Tieu, A. K., Identification of sixteen force coefficients of two journal bearings from Impulse responses, Wear 212, 206-212,1997
68． Hiroshi Iida, Application of the Experimental Determination of Character Matrices to the Balancing of a Flexible Rotor, Proc. of 4th Intel. Conf. on Rotordyn., IFTOMN , pp.111-115． Chicago, Sept. 1994
69． Iida, H., Tomita, H., Watanabe, T., Experimental Identification of Mechanical System with Character Matrices, Trans. Jpn. Soc. Mec. Eng., 557c(59) , pp65-72 (Jan, 1993) .
70． Kang, W. And Jin, D., The Application of the Model Reference Adaptive System in the Identification of Dynamic Characteristics of Oil-film Bearings, IME Int. Conf. on Vibration in Rotating Machinery, pp241-246, 1998
71． Stanway, R., Tee, T.K., and Mottershead, J.E., Identification of Squeeze-film
Bearing Dynamics Using a Recursive, Frequency-domain Filter, ASME Vibration Conf., pp167-176, 1989
72．汤炳新，闻邦椿，王占军，一种识别转子在运动状态下模态参数的方法，第四届全国转子动力学年会论文集，214-219，1995。
73. Takeshi Mizuno and Kenji Araki, Application of Dynamic Vibration Absorbers to Rotor Unbalance Measurements, Proceedings of Ninth World Congress on the Theory of Machines and Mechanisms, Milano, Italy, Sept. 1995
74. Kanemitsu, Y., Real Time Balancing of a Flexible Rotor Supported by Magnetic Bearing, Proc. of 3rd Intel. Conf. on Rotordynamics, IFTOMM, PP.263-268, Lyon, Sept., 1990
75．顾家柳，王强，可控挤压油膜轴承主动控制转子系统振动，应用力学学报，1990，7(2)，41-47
76．童水光，转子轴承系统电磁阻尼器控制的研究。浙江大学博士论文，1991
77．汪海航，电磁阻尼器动力特性及转子振动主动控制研究，浙江大学博士学位论文，1994
78. Matsushita, O., Unbalance Resonance Vibration Control for Magnetically Borne Flexible Rotors, Proc. of 4th Intel. Conf. on Rotordyn., IFTOMN, pp.363-370, Chicago, Sept. 1994
79．卢奂采，转子振动主动控制与轴向力在线动态监测研究，浙江大学博士学位论文，1996
80. Nordmaun, R., Matros, M. and Neumer, T., Parameter Identification in Rotating Machinery by means of Magnetic Bearings, Proc. of 4th Intel. Conf. on Rotordyn., IFTOMN , pp. 7-15,Chicago, Sept. 1994
81. Konpf, E., Nordmaun, R., Active Magnetic Bearings for the Parameter Identification of Dynamic Characteristics of Fluid Bearings—Calibration Results, pp.52-61, 1998
82. Gahler, C, and Herzog, R., Identification of Magnetic Bearing Systems, 4th Int. Symp. on Magnetic Bearings, ETH Zurich, Aug. 1993
83. Lottin, J. and Saidi, L., Identification of Physical Parameters in a Active Magnetic Bearing Suspension, 4th Int. Symp. on Magnetic Bearings, ETH Zurich, Aug. 1993
84. Chong-Won Lee, Young-Ho Ha, Cheal-Soon Kim, Identification of Active Magnetic Bearing System Using Magnetic Force Measurement, IV Int. Symposium on Magnetic Bearings, pp.305-309 August. 1994
85. Z Yu L, L T Meng and L M King, Electromagnetic Bearing Actuator for Active
Vibration Control of a Flexible Rotor, Proc. Instn. Mech. Engrs. Vol. 212, Part C, pp.705-716 1998
86． Kreuzinger-Janik,T., Irretier, H., On Modal testing of flexible Rotors for Unbalance Identification, Proceedings of the 16~(th) International Modal Analysis Conference, Part2,pp.l533-1539,1998( 注:此文献仅从EI上查得了文献摘要)
87． Habermann, H., Liard, G., An Active Magnetic Bearing System, Tribology Inter., pp.85-89, April, 1980
88． Habermann, H., Liard, G., Practical magnetic Bearing, IEEE Spectrum, pp.26-30, Sept., 1979
89． Myklestad, N.O., A New Method of Calculating Natural Modes of Uncoupled Bending Vibration of Airplane Wings and Other Types of Beam, J. of Aero. Sci. Vol. 11, pp. 153-162,1944．
90． Prohl, M. A., A General Method for Calculating Critical Speeds of Flexible Rotors, J. of Appl. Mech., Trans. ASME, Vol.12, No.3, pp142-148,1945．
91． Bansal, R. N., and Kirk, R. G., Stability and Damped Critical Speeds of Rotor Bearings Systems, ASME Journal of Engineering for Industry, Vol.98, No.l, pp.71-76,1977．
92． Arther, J.S., Consistent Mass Matrix for Distributed Mass System, J. of the Structural Division, Proceedings of the ASCE, Vol.89, ST4, PP161-164,1963
93． Ruhl, R.L., Dynamics of Distributed Parameter Turborotor Systems: Transfer Matrix and Element Techniques, PhD Thesis, Cornell University, Ithaca N.Y., Jan, 1970．
94． Ruhl, R. L., and Booker, J.F., A Finite Element Model for Distributed Parameter Turborotor System, J. of Engineering for Industry, Trans. ASME,pp.l26-131． 1972
95． Nelson, H.D., and Mc Vaugh, J.M., The Dynamics of Rotor-Bearing Systems Using Finite Elements, J. of Engineering for Industry, Trans. ASME. Vol.98, No.2, pp.593-600． 1976．
96． Zorzi, E.S., and Nelson, H.D., Finite Element Simulation of Rotor Bearing Systems with Internal Damping, J. of Engineering for Power, Trans. ASME, Vol.89, No.l, pp.71-76, 1977．
97． Nelson, H.D., A Finite Rotating Shaft Element Using Timoshenko Beam Theory, ASME Journal of Mechanical Design, Vol.102, pp.793-803． 0ct.1980．
98． Gasch,R., Vibration of Large Turbo-Rotor in Fluid-Film Bearing on an Elastic Foundation, J. of Sound and Vibration, 47(l),pp.53-73,1976．
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