大型水轮发电机组轴系动力学建模与仿真分析
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摘要
振动是影响水轮发电机组安全、稳定运行的最重要因素之一。过大的振动会导致材料的疲劳损坏,缩短设备的使用寿命,甚至可能引发严重的机组毁坏事故,造成重大的经济损失。随着水轮发电机组单机装机容量和水头的不断提高,机组的振动问题日益突出,已经成为水电行业亟待解决的关键课题之一。建立一个合适的水轮发电机组轴系动力学模型对于振动机理的阐明、振动故障的诊断以及状态检修技术的实现都具有重要的研究意义。
本文以葛洲坝电厂125MW机组为例,深入研究了大型水轮发电机组轴系的动力学建模与仿真。为了建立更准确的轴系动力学模型,详细分析了机组的结构特性。针对机组的结构特性,将机组轴系的动力学相关因素按逻辑分为轴系本体、边界条件、外部激励、运行工况四个模块。轴系本体指机组的旋转部分,为主要的研究对象。边界条件和外部激励是影响轴系动力响应的重要因素,而运行工况参数如转速、励磁电流及负荷等对边界条件和外部激励都具有重要的影响。
在认真总结转子动力学建模理论的基础上,选用了有限元方法建立机组轴系本体模型。详细讨论了利用转子动力学有限元方法建立轴系本体转子模型的过程,以及实际机组建模过程中的问题及解决办法。在此基础上,分别详细论述了对机组轴系动力响应具有重要影响的边界条件和外部激励。其中边界条件主要包括导轴承、推力轴承及密封等,与轴系的动力响应密切相关,同时对轴系的动力特性具有重要影响。数值计算的方法可以较精确地求解轴承动力特性系数,但是因为过大的计算量而无法在轴系响应分析时实时更新系数。为了解决这一问题,提出了简洁而实用的基于动力特性系数数据库的轴承分析方法。既解决数值计算方法计算量过大而无法实用的问题,又改进了传统的轴系响应分析时轴承分析过于简化的缺陷。该轴承分析方法还可以考虑转速及轴承间隙对轴承力的影响,使模型能够仿真分析轴承参数对轴系动力响应的影响。外部激励指质量不平衡力、水力、不平衡磁拉力及故障因素引起的受力等。水轮发电机组在运行中表现出的一些“个性”较强的特征,往往是由运行环境所引起的外部激励所造成。轴系所受的水力及不平衡磁拉力分别由流固耦合作用及电磁场作用引起,通过有限元等数值计算方法能够计算得到较精确的受力。但是,同样存在计算量过大而无法适用于以轴系响应分析为目的的模型的问题。为此,提出了利用发电机空载特性曲线分析计算不平衡磁拉力的方法。该分析方法考虑了励磁电流及其饱和效应对不平衡磁拉力的影响,改进了以往轴系响应分析中用一个负刚度系数简化不平衡磁拉力作用的做法。提出了施加不平衡力矩于轴系转角自由度的方法模拟水力不平衡。
通过对机组轴系各模块的系统分析,得到一个描述机组轴系动力学特性的仿真模型。仿真模型是一个只在若干结点自由度上具有局部非线性因素的线性动力系统,由一个高维二阶微分方程组描述。利用数值积分方法求解该系统运动方程,可在合理的时间内得到轴系的动力响应。利用动力学模型仿真分析了机组在变转速试验、变励磁试验、工况变化以及轮叶和导叶开口不均下的振动特性。与葛洲坝水电站最优维护信息系统(HOMIS)采集到的振动监测信息进行对比分析,得到一些有意义的振动故障机理推断知识。分析结果显示,仿真模型在振动机理的阐明、振动故障的诊断方面已显示出其应用价值。在该轴系仿真模型框架下,不断完善相应结点下各种影响因素的考虑,可发展成为更加成熟的仿真模型。模型精度将更高,应用范围将更广,应用价值也将更大。
Vibration is one of the most important factors affecting the safety and stable operation of hydro-turbine generators. Excessive vibration can cause fatigue damage to the unit equipment and shorten the life of units, and may even lead to a serious damage accident, resulting in significant economic losses. With the continuous improvement in water head and single-machine capacity, vibration problems of the hydro-turbine generator units are increasingly prominent and have become key issues to be solved in the hydropower industry. An appropriate dynamic model of the shaft system of a hydro-turbine generator unit is of great significance for the clarification of vibration mechanism, the diagnosis of vibration failure and for the implementation of technology of the condition based maintenance.
Taking 125 MW hydroelectric units in Gezhouba as example, a comprehensive rotordynamic modeling and simulation of the shaft system of a large hydro-turbine generator unit is investigated in this study. The dynamic model is built up taking full account of the structural characteristics of the unit to ensure its feasibility.In accordance with the structural characteristics, dynamic relevant factors are divided into four modules of shaft, boundary conditions, exciting forces and operating conditions logically. While Shaft is the essential part of a shaft system including all the rotating part of the unit. Both boundary conditions and exciting forces, which are affected by the operating conditions like rotating speed, field current and load etc., are important factors affecting the dynamic response of the shaft system.
Finite element (FE) method is selected to model the shaft system. The modeling process of the shaft system by FE method is discussed in detail along with the solutions to the problems encountered in the process of modeling. The boundary conditions and the exciting forces are discussed in detail respectively, both of which are very important factors affecting the dynamic response of shaft system. The boundary conditions, including guide bearing, thrust bearing and seal etc., are closely related to the dynamic response of the shaft system, and meanwhile, have important influence on the dynamic response. Numerical method could be useful to obtain accurate bearing coefficients, but coefficients could not be updated with the operating conditions due to the oversized computational cost. To overcome this problem, a simplified and practical coefficient database method is proposed. The database method takes much less computational cost than numerical method and the accuracy could be guaranteed by a suitable database. Effect of the rotating speed and bearing clearance on dynamic response could also be considered by the method. The exciting forces, like unbalanced force due to mass eccentricity, hydraulic force, unbalanced magnetic pull (UMP) and exciting forces induced by the failure etc., are another type of important factors affecting the dynamic response of shaft system. Some strong individuality features, behaved in the operation of hydro-turbine generator unit, are probably caused by the exciting forces due to operating environment. Hydraulic force and UMP are induced by the fluid-structure interaction around runner and electromagnetic field around rotor respectively. Numerical method such as FE method could be useful to obtain proper solution for the induced force. However, problems due to oversized computational cost also exist. Therefore, an analytical method for unbalanced magnetic pull taking advantages of the no load characteristic curve of a generator is proposed. The method takes account of field current and its saturation effect on UMP, which would be more suitable than treating the UMP as a negative stiffness coefficient. To simulate the hydraulic imbalance on the runner, unbalanced moments are exerted on the rotational coordinates.
Finally, a simulation model describing dynamic characteristics of the shaft system is established by systematically analyzing the factors mentioned above. The simulation model, which is described by high dimensional second order differential equations, is a linear dynamic system with local nonlinearity only at several nodes. The dynamic response of the model can be obtained within a reasonable time by a numerical integration method. Taking the advantage of the model, dynamic response of the unit are calculated under rotating speed test, excitation test, variation of operating conditions and opening uneven of the runner blades and the guide vanes. Comparative analysis between the simulation with the the vibration monitoring information acquired by the Optimal Maintenance Information System for Hydropower plants (HOMIS), many meaningful results about vibration fault mechanism are obtained. Although not all the factors are considered, the current simulation model still shows its application value for illustrating the fault mechanism and diagnosis. If all the factors are considered properly, a more applicable simulation model could be obtained. And higher accuracy, wider application range and greater application value of the model would be obtained.
本文以葛洲坝电厂125MW机组为例,深入研究了大型水轮发电机组轴系的动力学建模与仿真。为了建立更准确的轴系动力学模型,详细分析了机组的结构特性。针对机组的结构特性,将机组轴系的动力学相关因素按逻辑分为轴系本体、边界条件、外部激励、运行工况四个模块。轴系本体指机组的旋转部分,为主要的研究对象。边界条件和外部激励是影响轴系动力响应的重要因素,而运行工况参数如转速、励磁电流及负荷等对边界条件和外部激励都具有重要的影响。
在认真总结转子动力学建模理论的基础上,选用了有限元方法建立机组轴系本体模型。详细讨论了利用转子动力学有限元方法建立轴系本体转子模型的过程,以及实际机组建模过程中的问题及解决办法。在此基础上,分别详细论述了对机组轴系动力响应具有重要影响的边界条件和外部激励。其中边界条件主要包括导轴承、推力轴承及密封等,与轴系的动力响应密切相关,同时对轴系的动力特性具有重要影响。数值计算的方法可以较精确地求解轴承动力特性系数,但是因为过大的计算量而无法在轴系响应分析时实时更新系数。为了解决这一问题,提出了简洁而实用的基于动力特性系数数据库的轴承分析方法。既解决数值计算方法计算量过大而无法实用的问题,又改进了传统的轴系响应分析时轴承分析过于简化的缺陷。该轴承分析方法还可以考虑转速及轴承间隙对轴承力的影响,使模型能够仿真分析轴承参数对轴系动力响应的影响。外部激励指质量不平衡力、水力、不平衡磁拉力及故障因素引起的受力等。水轮发电机组在运行中表现出的一些“个性”较强的特征,往往是由运行环境所引起的外部激励所造成。轴系所受的水力及不平衡磁拉力分别由流固耦合作用及电磁场作用引起,通过有限元等数值计算方法能够计算得到较精确的受力。但是,同样存在计算量过大而无法适用于以轴系响应分析为目的的模型的问题。为此,提出了利用发电机空载特性曲线分析计算不平衡磁拉力的方法。该分析方法考虑了励磁电流及其饱和效应对不平衡磁拉力的影响,改进了以往轴系响应分析中用一个负刚度系数简化不平衡磁拉力作用的做法。提出了施加不平衡力矩于轴系转角自由度的方法模拟水力不平衡。
通过对机组轴系各模块的系统分析,得到一个描述机组轴系动力学特性的仿真模型。仿真模型是一个只在若干结点自由度上具有局部非线性因素的线性动力系统,由一个高维二阶微分方程组描述。利用数值积分方法求解该系统运动方程,可在合理的时间内得到轴系的动力响应。利用动力学模型仿真分析了机组在变转速试验、变励磁试验、工况变化以及轮叶和导叶开口不均下的振动特性。与葛洲坝水电站最优维护信息系统(HOMIS)采集到的振动监测信息进行对比分析,得到一些有意义的振动故障机理推断知识。分析结果显示,仿真模型在振动机理的阐明、振动故障的诊断方面已显示出其应用价值。在该轴系仿真模型框架下,不断完善相应结点下各种影响因素的考虑,可发展成为更加成熟的仿真模型。模型精度将更高,应用范围将更广,应用价值也将更大。
Vibration is one of the most important factors affecting the safety and stable operation of hydro-turbine generators. Excessive vibration can cause fatigue damage to the unit equipment and shorten the life of units, and may even lead to a serious damage accident, resulting in significant economic losses. With the continuous improvement in water head and single-machine capacity, vibration problems of the hydro-turbine generator units are increasingly prominent and have become key issues to be solved in the hydropower industry. An appropriate dynamic model of the shaft system of a hydro-turbine generator unit is of great significance for the clarification of vibration mechanism, the diagnosis of vibration failure and for the implementation of technology of the condition based maintenance.
Taking 125 MW hydroelectric units in Gezhouba as example, a comprehensive rotordynamic modeling and simulation of the shaft system of a large hydro-turbine generator unit is investigated in this study. The dynamic model is built up taking full account of the structural characteristics of the unit to ensure its feasibility.In accordance with the structural characteristics, dynamic relevant factors are divided into four modules of shaft, boundary conditions, exciting forces and operating conditions logically. While Shaft is the essential part of a shaft system including all the rotating part of the unit. Both boundary conditions and exciting forces, which are affected by the operating conditions like rotating speed, field current and load etc., are important factors affecting the dynamic response of the shaft system.
Finite element (FE) method is selected to model the shaft system. The modeling process of the shaft system by FE method is discussed in detail along with the solutions to the problems encountered in the process of modeling. The boundary conditions and the exciting forces are discussed in detail respectively, both of which are very important factors affecting the dynamic response of shaft system. The boundary conditions, including guide bearing, thrust bearing and seal etc., are closely related to the dynamic response of the shaft system, and meanwhile, have important influence on the dynamic response. Numerical method could be useful to obtain accurate bearing coefficients, but coefficients could not be updated with the operating conditions due to the oversized computational cost. To overcome this problem, a simplified and practical coefficient database method is proposed. The database method takes much less computational cost than numerical method and the accuracy could be guaranteed by a suitable database. Effect of the rotating speed and bearing clearance on dynamic response could also be considered by the method. The exciting forces, like unbalanced force due to mass eccentricity, hydraulic force, unbalanced magnetic pull (UMP) and exciting forces induced by the failure etc., are another type of important factors affecting the dynamic response of shaft system. Some strong individuality features, behaved in the operation of hydro-turbine generator unit, are probably caused by the exciting forces due to operating environment. Hydraulic force and UMP are induced by the fluid-structure interaction around runner and electromagnetic field around rotor respectively. Numerical method such as FE method could be useful to obtain proper solution for the induced force. However, problems due to oversized computational cost also exist. Therefore, an analytical method for unbalanced magnetic pull taking advantages of the no load characteristic curve of a generator is proposed. The method takes account of field current and its saturation effect on UMP, which would be more suitable than treating the UMP as a negative stiffness coefficient. To simulate the hydraulic imbalance on the runner, unbalanced moments are exerted on the rotational coordinates.
Finally, a simulation model describing dynamic characteristics of the shaft system is established by systematically analyzing the factors mentioned above. The simulation model, which is described by high dimensional second order differential equations, is a linear dynamic system with local nonlinearity only at several nodes. The dynamic response of the model can be obtained within a reasonable time by a numerical integration method. Taking the advantage of the model, dynamic response of the unit are calculated under rotating speed test, excitation test, variation of operating conditions and opening uneven of the runner blades and the guide vanes. Comparative analysis between the simulation with the the vibration monitoring information acquired by the Optimal Maintenance Information System for Hydropower plants (HOMIS), many meaningful results about vibration fault mechanism are obtained. Although not all the factors are considered, the current simulation model still shows its application value for illustrating the fault mechanism and diagnosis. If all the factors are considered properly, a more applicable simulation model could be obtained. And higher accuracy, wider application range and greater application value of the model would be obtained.
引文
[1]周大兵.抓住机遇开拓进取为促进水电建设事业更大发展而努力[J].水力发电学报,2000,1：Ⅰ-Ⅻ.
[2]张国宝.科学发展：电力工业赢得挑战的根本路径[J].中国水能及电气化,2009(5)：58-60.
[3]沈东.水力机组故障分析[M].北京：中国水利水电出版社,1996.
[4]Harris CM, Piersol AG. Harris Shock and Vibration Handbook[M].5th. New York: McGraw-Hill Professional,2002.
[5]沈东,褚福涛.水轮发电组振动故障诊断与识别[J].水动力学研究与进展：A辑,2000,15(1)：129-133.
[6]师汉民.机械振动系统—分析测试建模对策[M].第2版.武汉：华中科技大学出版社,2004.
[7]Tanaka M. The Diagnostic Technologies in Power Plants in Japan[C].In:Diagnostics of Rotating Machines in Power Plants:Proceedings of the CISM/IFToMM Symposium. Udine:Springer, 1993.199-210.
[8]严可国,魏克严,李植.大型旋转机械监测保护故障诊断系统[M].北京：北京英华达电力电子工程科技有限公司,1994.
[9]刘万景.水电厂机组的状态监测[J].水力发电,1999(9)：55-57.
[10]付元初,熊海华.《水轮发电机组状态在线监测系统技术导则》(国家标准)编写中有关问题的研究和讨论[J].水电站机电技术,2009,32(2)：1-5.
[11]Li ZH, Ai YZ, Shi HX. Optimal Maintenance Information System of Gezhouba Hydro Power Plant[C]. In:Power Engineering Society General Meeting.Florida:IEEE,2007.1-5.
[12]万元.大型发电机局部放电在线监测与分析方法研究：[博士学位论文].武汉：华中科技大学,2009.
[13]陈杰.葛洲坝水电机组稳定性数据分析及应用：[硕士学位论文].武汉：华中科技大学,2009.
[14]李初辉.水电机组集成监测系统中稳定性单元研究与开发：[硕士学位论文].武汉：华中科技大学,2009.
[15]李亮.基于DSP的水电机组稳定性监测平台的设计与开发：[硕士学位论文].武汉：华中科技大学,2009.
[16]刘明军.变压器局放超高频监测与基于知识的分析方法研究：[博士学位论文].武汉：华中科技大学,2011.
[17]史会轩.大型水轮机空化在线监测与分析——方法及应用研究：[博士学位论文].武汉： 华中科技大学,2008.
[18]孙监湖.水轮发电机温度状态分析与特性辨识方法研究：[硕士学位论文].武汉：华中科技大学,2009.
[19]Thomas G. Rotordynamic Modelling for Turbogenerator Defect Diagnosis[C]. In:IEE Colloquium on Advanced Condition Monitoring Systems for Power Generation. London:IET, 1991.6/1-6/4.
[20]徐敏.设备故障诊断手册—机械设备状态监测和故障诊断[M].西安：西安交通大学出版社,1998.
[21]乔卫东.水轮发电机组轴系动力特性分析及轴线精度检测方法研究：[博士学位论文]：西安理工大学,2006.
[22]张景绘.动力学系统建模[M].北京：国防工业出版社,2000.
[23]Edwards S, Lees A, Friswell M. Fault Diagnosis of Rotating Machinery[J]. Shock and Vibration Digest,1998,30(1):4-13.
[24]钟一谔,何衍宗,王正等.转子动力学[M].北京：清华大学出版社,1987.
[25]张文.转子动力学理论基础[M].北京：科学出版社,1990.
[26]闻邦椿,顾家柳,夏松波等.高等转子动力学[M].北京：机械工业出版社,1999.
[27]顾家柳,丁奎元,刘启洲.转子动力学[M].北京：国防工业出版社,1985.
[28]Rao JS. Rotor dynamics[M]. New Delhi:New Age International,1996.
[29]Muszynska A. Rotordynamics[M]. Boca Raton:Taylor & Francis Group, LLC,2005.
[30]孟光.转子动力学研究的回顾与展望[J].振动工程学报,2002,15(1)：1-9.
[31]Jeffcott H. ⅩⅩⅦ. The Lateral Vibration of Loaded Shafts in the Neighbourhood of a Whirling Speed.-The Effect of Want of Balance[J]. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science,1919,37(219):304-314.
[32]陆颂元.论国内旋转动力机械非线性振动理论研究的现状和发展[J].汽轮机技术,2006,48(2)：85-87.
[33]Prohl M. A General Method for Calculating Critical Speeds of Flexible Rotors [J]. Journal of Applied Mechanics,1945,12(3):142-148.
[34]Myklestad NO. A New Method of Calculating Natural Modes of Uncoupled Bending Vibration of Airplane Wings and Other Types of Beams[J]. Journal of the aeronautical sciences,1944, 11(4):153-162.
[35]Lund JW. Stability and Damped Critical Speeds of a Flexible Rotor in Fluid-film B earings [J]. Rotating machinery dynamics,1987:1-9.
[36]李郁侠,段凌剑.基于传递矩阵法的大型水轮发电机组主轴系统非线性瞬态响应数学模型[J].水利水电技术,2002,33(7)：21-23.
[37]冯辅周,李承军.大型抽水蓄能机组轴系的动特性研究[J].振动.测试与诊断,1999,19(4)：313-319.
[38]Zorzi ES, Nelson HD. Finite Element Simulation of Rotor-bearing Systems with Internal Damping[C]. In:American Society of Mechanical Engineers, Gas Turbine Conference and Products Show. New Orleans, La:ProQuest,1976.1976.
[39]Nelson HD. A Finite Rotating Shaft Element Using Timoshenko Beam Theory[J]. Journal of Mechanical Design,1980,102(10):793-803.
[40]Thomas DL, Wilson JM, Wilson RR. Timoshenko Beam Finite Elements[J]. Journal of Sound and Vibration,1973,31(3):315-330.
[41]Rastogi V, Kumar C. Bond Graph Modeling of a Cracked Rotor[C]. In:Proceedings of the 2010 Spring Simulation Multiconference. Orlando, Florida:ACM,2010.1-7.
[42]Pedersen E. Rotordynamics and Bond Graphs:Basic Models[J]. Mathematical and Computer Modelling of Dynamical Systems,2009,15(4):337-352.
[43]Campos J, Crawford M, Longoria R. Rotordynamic Modeling Using Bond Graphs:Modeling the Jeffcott Rotor[J]. IEEE Transactions on Magnetics,2005,41(1):274-280.
[44]Batlle C,Doria-Cerezo A. Bond Graph Models of Electromechanical Systems. The AC Generator Case[C]. In:IEEE International Symposium on Industrial Electronics. Cambridge:IEEE, 2008.1064-1069.
[45]夏松波,武新华,汪光明等.热套转子力学模型研究[J].航空学报,1987,8(9)：A449-A455.
[46]谭善光,汪希宣.热套轮盘对轴段弯曲刚度的影响系数计算[J].应用力学学报,1990,7(1)：93-97.
[47]Newkirk BL, Taylor HD. Shaft Whipping Due to Oil Action in Journal Bearings[J]. General Electric Review,1925,28(8):559-568.
[48]Lund JW. Spring and Damping Coefficients for the Tilting-Pad Journal Bearing[J]. ASLE transactions,1964,7:342-352.
[49]Muszynska A. Rotordynamics[M]. Boca Raton:Taylor & Francis Group, LLC,2005.
[50]Ohashi H. Vibration and Oscillation of Hydraulic Machinery[M]. Brookfield:Avebury Technical,1991.
[51]Bettig BP, Han RPS. Modeling the Lateral Vibration of Hydraulic Turbine-generator Rotors[J].Journal of Vibration and Acoustics-Transactions of the ASME,1999,121(3): 322-327.
[52]马震岳,董毓新.水轮发电机组轴系统的动力反应[J].大电机技术,1988,5：6-13.
[53]李苹,窦海波,王正.水轮发电机组主轴系统的建模及其非线性瞬态响应[J].清华大学学报：自然科学版,1998,38(6)：123-128.
[54]Feng FZ, Chu FL. Dynamic Analysis of a Hydraulic Turbine Unit[J]. Mechanics of Structures and Machines,2001,29(4):505-531.
[55]Ma LF, Zhang XZ. Numerical Simulation of Nonlinear Oil Film Forces of Tilting-Pad Guide Bearing in Large Hydro-unit[J]. International Journal of Rotating Machinery,2000,6(5): 345-353.
[56]Cardinali R. Dynamic Simulation of Non-linear Models of Hydroelectric Machinery[J]. Mechanical Systems and Signal Processing,1993,7(1):29-44.
[57]王文,张直明.油叶型轴承非线性油膜力数据库[J].上海工业大学学报,1993,14(4)：299-305.
[58]孟志强,徐华,朱均.基于Poincare变换的滑动轴承非线性油膜力数据库方法[J].摩擦学学报,2001,21(3)：223-227.
[59]杨晓明,马震岳,黄军义.导轴承与推力轴承耦合作用下水电机组的横向振动研究[J].水力发电学报,2007,26(6)：132-136.
[60]陈贵清.推力轴承油膜刚度对发电机转子轴系固有频率的影响[J].河北理工学院学报,2000,22(4)：48-53.
[61]Mittwollen N, Hegel T, Glienicke J. Effect of Hydrodynamic Thrust Bearings on Lateral Shaft Vibrations[J]. Journal of Tribology,1991,113(4):811-817.
[62]Lie Y, Bhat RB. Coupled Dynamics of a Rotor-Journal Bearing System Equipped with Thrust Bearings[J]. Shock and Vibration,1995,2(1):1-14.
[63]Jiang PL, Yu L. Dynamics of a Rotor-bearing System Equipped with a Hydrodynamic Thrust Bearing[J]. Journal of Sound and Vibration,1999,227(4):833-872.
[64]张雷克,马震岳,宋兵伟.水轮发电机组在不平衡磁拉力及密封力下振动特性分析[J].水电能源科学,2010,28(9)：117-120.
[65]杨晓明,马震岳,张振国.水轮机迷宫密封系统非线性动力稳定性研究[J].大连理工大学学报,2007,47(1)：95-100.
[66]肖忠会.转子—轴承—密封系统动力学建模及其特性研究：[博士学位论文].上海：复旦大学,2006.
[67]马震岳,杨晓明.非线性水轮机密封系统自激振动分析[C].第十六次中国水电设备学术讨论会论文集,2007.
[68]马震岳,董毓新.水轮机转轮密封处水流的动力特性及其对机组自振特性的影响[J].大电机技术,1987,6：43-50.
[69]李松涛,许庆余,万方义.迷宫密封转子系统非线性动力稳定性的研究[J].应用力学学报,2002,19(2)：27-30.
[70]成玫,孟光,荆建平.非线性“转子-轴承-密封”系统动力分析[J].振动工程学报,2006, 19(4)：519-524.
[71]Schwirzer T. Dynamic Stressing of Hydroelectric Units by Stochastic Hydraulic Forces on the Turbine Runner[J]. Water Power & Dam Construction,1977:39-44.
[72]马震岳,董毓新.水力荷载作用下水电机组的动力响应[J].水力发电学报,1990(2)：31-40.
[73]Kramer E. Determining the Hydraulic Lateral Force of Pump-turbines [J]. Water Power and Dam Construction,1981,33:50-54.
[74]Chamieh DS, Acosta AJ, Brennen CE et al. Experimental Measurements of Hydrodynamic Radial Forces and Stiffness Matrices for a Centrifugal Pump-Impeller[J]. Journal of Fluids Engineering,1985,107(3):307-315.
[75]马震岳,董毓新.水轮发电机组动力学[M].大连：大连理工大学出版社,2003.
[76]邢景棠,周盛,崔尔杰.流固耦合力学概述[J].力学进展,1997,27(1)：19-38.
[77]刘德民,刘小兵,李娟.基于流固藕合的水轮机振动分析[J].流体传动与控制,2008(1)：21-25.
[78]谷朝红,姚熊亮,陈起富.水轮机部件流固耦合振动特性研究[J].大电机技术,2001(6)：47-52.
[79]Behrend B. On the Mechanical Forces in Dynamos Caused by Magnetic Attraction[J]. American Institute of Electrical Engineers, Transactions of the,1900,17:613-633.
[80]白晖宇,荆建平,孟光.电机不平衡磁拉力研究现状与展望[J].噪声与振动控制,2009,29(6)：5-7.
[81]Talas P, Toom P. Dynamic Measurement and Analysis of Air Gap Variations in Large Hydroelectric Generators [J]. IEEE Transactions on Power Apparatus and Systems,1983, PAS-102(9):3098-3106.
[82]邱家俊.机电耦联动力系统的非线性振动[M].北京：科学出版社,1996.
[83]白延年.水轮发电机设计与计算[M].北京：机械工业出版社,1982.
[84]Rosenberg E. Magnetic Pull in Electric Machines[J].Transactions of the American Institute of Electrical Engineers,1918,37(2):1425-1469.
[85]Covo A. Unbalanced Magnetic Pull in Induction Motors with Eccentric Rotors[J]. Power Apparatus and Systems, Part III. Transactions of the American Institute of Electrical Engineers, 1954,73(2):1421-1425.
[86]Ohishi H, Sakabe S, Tsumagari K et al. Radial Magnetic Pull in Salient Pole Machines with Eccentric Rotors[J]. IEEE Transactions on Energy Conversion,1987, EC-2(3):439-443.
[87]Perers R, Lundin U, Leijon M. Saturation Effects on Unbalanced Magnetic Pull in a Hydroelectric Generator with an Eccentric Rotor[J]. IEEE Transactions on Magnetics,2007, 43(10):3884-3890.
[88]Guo D, Chu F, Chen D. The Unbalanced Magnetic Pull and Its Effects on Vibration in a Three-phase Generator with Eccentric Rotor[J]. Journal of Sound and Vibration,2002,254(2): 297-312.
[89]姜培林,虞烈.电机不平衡磁拉力及其刚度的计算[J].大电机技术,1998(4)：32-34.
[90]Wang L, Cheung RW, Ma ZY et al. Finite-element Analysis of Unbalanced Magnetic Pull in a Large Hydro-generator under Practical Operations[J]. IEEE Transactions on Magnetics,2008, 44(6):1558-1561.
[91]Lundin U, Wolfbrandt A. Method for Modeling Time-Dependent Nonuniform Rotor/Stator Configurations in Electrical Machines[J]. IEEE Transactions on Magnetics,2009,45(7): 2976-2980.
[92]曲凤波,孙玉田,曲大庄.水轮发电机不平衡磁拉力[J].大电机技术,1997(4)：1-3.
[93]Lundstrom L, Gustavsson Rk, Aidanpaa JO et al. Influence on the Stability of Generator Rotors due to Radial and Tangential Magnetic Pull Force[J]. IET Electric Power Applications,2007, 1(1):1-8.
[94]Karisson M, Aidanpaa JO, Perers R et al. Rotor Dynamic Analysis of an Eccentric Hydropower Generator with Damper, Winding for Reactive Load[J]. Journal of Applied Mechanics Transactions of the ASME,2007,74(6):1178-1186.
[95]Gustavsson RK, Aidanpaa JO. The Influence of Nonlinear Magnetic Pull on Hydropower Generator Rotors [J].Journal of Sound and Vibration,2006,297(3-5):551-562.
[96]Pennacchi P. Computational Model for Calculating the Dynamical Behaviour of Generators Caused by Unbalanced Magnetic Pull and Experimental Validation[J]. Journal of Sound and Vibration,2008,312(1-2):332-353.
[97]夏松波,张新江,刘占生等.旋转机械不对中故障研究综述[J].振动、测试与诊断,1998,18(3)：157-161.
[98]Lees AW. Misalignment in Rigidly Coupled Rotors[J].Journal of Sound and Vibration,2007, 305(1-2):261-271.
[99]Sekhar AS, Prabhu BS. Effects of Coupling Misalignment on Vibrations of Rotating Machinery[J].Journal of Sound and Vibration,1995,185(4):655-671.
[100]Muszynska A, Goldman P. Chaotic Responses of Unbalanced Rotor/Bearing/Stator Systems with Looseness or Rubs[J]. Chaos, Solitons & Fractals,1995,5(9):1683-1704.
[101]李振平,罗跃纲,姚红良等.转子系统支承松动的非线性动力学及故障特征[J].东北大学学报(自然科学版),2002,23(11)：1048-1051.
[102]Chu F, Tang Y. Stability and Non-linear Responses of a Rotor-bearing System with Pedestal Looseness[J]. Journal of Sound and Vibration,2001,241(5):879-893.
[103]Lu WX, Chu FL. Experimental Investigation of Pedestal Looseness in a Rotor-bearing System[J]. Damage Assessment of Structures Viii,2009,413-414:599-605,824.
[104]马震岳,董毓新.有限元法分析水电机组轴系的临界转速[J].水电站机电技术,1991(4)：5-10.
[105]马震岳,董毓新.基础、导轴承刚度和磁拉力等对机组自振特性的影响[J].大电机技术,1986,6：46-53.
[106]荣吉利,李志和.水电机组轴系横向自振特性的有限元计算方法与结果分析[J].中国电机工程学报,1997,17(1)：33-36.
[107]杨晓明,马震岳.水轮发电机组横向振动的敏感性分析[J].振动工程学报,2004,17(S)：206-209.
[108]Nagafuji T. Lateral Vibration Analysis of Generator-Turbine Shaft System[J]. International Water Power and Dam Construction,1975,27(11):418-423.
[109]李苹,王正.大型水泵一水轮机组轴系的动力特性[J].清华大学学报：自然科学版,1996,36(7)：24-29.
[110]刘保国,张信志.水轮发电机组主轴系统非线性动力学问题的计算分析[J].中国机械工程,2001,12(8)：939-942.
[111]Brito G, Weber H, Fuerst A. Dynamics of Large Hydrogenerators[C]. In:Proceedings of the XVIII IAHR Symposium on Hydraulic Machinery and Cavitation. Netherlands:Kluwer Academic Pub,1996.464-473.
[112]于振威.水轮发电机组转轴临界转速和强迫振动的精确计算[J].大电机技术,1984,4：5-12.
[113]曲大庄.水轮发电机组轴系临界转速及弯曲变形计算的解析法[J].大电机技术,1986,1：6-13.
[114]Ma ZY, Song ZQ. Nonlinear Dynamic Characteristic Analysis of the Shaft System in Water Turbine Generator Set[J]. Chinese Journal of Mechanical Engineering,2009,22(1):124-131.
[115]杨晓明.水电站机组振动及其与厂房的耦联振动研究：[博士学位论文]：大连理工大学,2006.
[116]宋志强,马震岳,张运良等.考虑厂房基础耦联作用的水轮发电机组轴系统动力反应分析[J].振动与冲击,2008,27(6)：158-161.
[117]沈克昌,钟梓辉.葛洲坝工程丛书9-水轮发电机组[M].北京：水利电力出版社,1991.
[118]张正松.旋转机械振动监测及故障诊断[M].北京：机械工业出版社,1991.
[119]中华人民共和国国家标准,水轮机基本技术条件[S],GB/T 15468-2006,2006.
[120]辜承林,陈乔夫,熊永前.电机学[M].武汉：华中科技大学出版社,2001.
[121]王勖成,邵敏.有限单元法基本原理和数值方法[M].第2版.北京：清华大学出版社,1997.
[122]虞烈,刘恒.轴承一转子系统动力学[M].西安：西安交通大学出版社,2000.
[123]Villa C, Sinou JJ, Thouverez F. Stability and Vibration Analysis of a Complex Flexible Rotor Bearing System[J]. Communications in Nonlinear Science and Numerical Simulation,2008, 13(4):804-821.
[124]Hutchinson JR. Shear Coefficients for Timoshenko Beam theory[J]. Journal of Applied Mechanics-Transactions of the ASME,2001,68(1):87-92.
[125]Bettig BP, Han RPS. Predictive Maintenance Using the Rotordynamic Model of a Hydraulic Turbine-generator Rotor[J]. Journal of Vibration and Acoustics-Transactions of the ASME, 1998,120(2):441-448.
[126]刘禄臣.无轴结构转子支架的扭矩分配[J].大电机技术,1983,3：10-16.
[127]王珂仑.水力机组振动[M].北京：水利电力出版社,1986.
[128]水利部第二工程局.水轮发电机试验[M].北京：电力工业出版社,1980.
[129]东北水利水电学校.水轮机[M].北京：电力工业出版社,1980.
[130]Ma H, Zhao XY, Teng YN et al. Analysis of Dynamic Characteristics for a Rotor System with Pedestal Looseness[J]. Shock and Vibration,2011,18:13-27.
[131]Si XH, Lu WX, Chu FL. Lateral Vibration of Hydroelectric Generating Set with Different Supporting Condition of Thrust Pad[J]. Shock and Vibration,2011,18:317-331.
[132]马南任,涂阳文.转桨式水轮机水导轴承的运行经验[J].华中电力,1990(2)：22-26.
[133]曹鹍,姚志民.水轮机原理及水力设计[M].北京：清华大学出版社,1991.
[134]Bachschmid N, Pennacchi P, Vania A. Identification of Multiple Faults in Rotor Systems[J].Journal of Sound and Vibration,2002,254(2):327-366.
[135]Sekhar A. Model-based Identification of Two Cracks in a Rotor System[J]. Mechanical Systems and Signal Processing,2004,18(4):977-983.
[136]Pennacchi P, Bachschmid N, Vania A et al. Use of Modal Representation for the Supporting Structure in Model-based Fault Identification of Large Rotating Machinery, part 1--Theoretical Remarks[J]. Mechanical Systems and Signal Processing,2006,20(3):662-681.
[137]Lees A, Sinha J, Friswell M. Model-based Identification of Rotating Machines [J]. Mechanical Systems and Signal Processing,2009,23(6):1884-1893.
[138]Jalan AK, Mohanty A. Model Based Fault Diagnosis of a Rotor-bearing System for Misalignment and Unbalance under Steady-state Condition[J]. Journal of Sound and Vibration, 2009,327(3-5):604-622.
[139]Bachschmid N, Pennacchi P. Accuracy of Fault Detection in Real Rotating Machinery using Model Based Diagnostic Techniques [J]. JSME International Journal Series C,2003,46(3): 1026-1034.
[140]Pennacchi P, Bachschmid N, Vania A et al.Use of Modal Representation for the Supporting Structure in Model-based Fault Identification of Large Rotating Machinery:Part 2-Application to a Real Machine [J]. Mechanical Systems and Signal Processing,2006,20(3):682-701.
[141]Jardine AKS, Lin D, Banjevic D. A Review on Machinery Diagnostics and Prognostics Implementing Condition-based Maintenance [J]. Mechanical Systems and Signal Processing, 2006,20(7):1483-1510.
[2]张国宝.科学发展：电力工业赢得挑战的根本路径[J].中国水能及电气化,2009(5)：58-60.
[3]沈东.水力机组故障分析[M].北京：中国水利水电出版社,1996.
[4]Harris CM, Piersol AG. Harris Shock and Vibration Handbook[M].5th. New York: McGraw-Hill Professional,2002.
[5]沈东,褚福涛.水轮发电组振动故障诊断与识别[J].水动力学研究与进展：A辑,2000,15(1)：129-133.
[6]师汉民.机械振动系统—分析测试建模对策[M].第2版.武汉：华中科技大学出版社,2004.
[7]Tanaka M. The Diagnostic Technologies in Power Plants in Japan[C].In:Diagnostics of Rotating Machines in Power Plants:Proceedings of the CISM/IFToMM Symposium. Udine:Springer, 1993.199-210.
[8]严可国,魏克严,李植.大型旋转机械监测保护故障诊断系统[M].北京：北京英华达电力电子工程科技有限公司,1994.
[9]刘万景.水电厂机组的状态监测[J].水力发电,1999(9)：55-57.
[10]付元初,熊海华.《水轮发电机组状态在线监测系统技术导则》(国家标准)编写中有关问题的研究和讨论[J].水电站机电技术,2009,32(2)：1-5.
[11]Li ZH, Ai YZ, Shi HX. Optimal Maintenance Information System of Gezhouba Hydro Power Plant[C]. In:Power Engineering Society General Meeting.Florida:IEEE,2007.1-5.
[12]万元.大型发电机局部放电在线监测与分析方法研究：[博士学位论文].武汉：华中科技大学,2009.
[13]陈杰.葛洲坝水电机组稳定性数据分析及应用：[硕士学位论文].武汉：华中科技大学,2009.
[14]李初辉.水电机组集成监测系统中稳定性单元研究与开发：[硕士学位论文].武汉：华中科技大学,2009.
[15]李亮.基于DSP的水电机组稳定性监测平台的设计与开发：[硕士学位论文].武汉：华中科技大学,2009.
[16]刘明军.变压器局放超高频监测与基于知识的分析方法研究：[博士学位论文].武汉：华中科技大学,2011.
[17]史会轩.大型水轮机空化在线监测与分析——方法及应用研究：[博士学位论文].武汉： 华中科技大学,2008.
[18]孙监湖.水轮发电机温度状态分析与特性辨识方法研究：[硕士学位论文].武汉：华中科技大学,2009.
[19]Thomas G. Rotordynamic Modelling for Turbogenerator Defect Diagnosis[C]. In:IEE Colloquium on Advanced Condition Monitoring Systems for Power Generation. London:IET, 1991.6/1-6/4.
[20]徐敏.设备故障诊断手册—机械设备状态监测和故障诊断[M].西安：西安交通大学出版社,1998.
[21]乔卫东.水轮发电机组轴系动力特性分析及轴线精度检测方法研究：[博士学位论文]：西安理工大学,2006.
[22]张景绘.动力学系统建模[M].北京：国防工业出版社,2000.
[23]Edwards S, Lees A, Friswell M. Fault Diagnosis of Rotating Machinery[J]. Shock and Vibration Digest,1998,30(1):4-13.
[24]钟一谔,何衍宗,王正等.转子动力学[M].北京：清华大学出版社,1987.
[25]张文.转子动力学理论基础[M].北京：科学出版社,1990.
[26]闻邦椿,顾家柳,夏松波等.高等转子动力学[M].北京：机械工业出版社,1999.
[27]顾家柳,丁奎元,刘启洲.转子动力学[M].北京：国防工业出版社,1985.
[28]Rao JS. Rotor dynamics[M]. New Delhi:New Age International,1996.
[29]Muszynska A. Rotordynamics[M]. Boca Raton:Taylor & Francis Group, LLC,2005.
[30]孟光.转子动力学研究的回顾与展望[J].振动工程学报,2002,15(1)：1-9.
[31]Jeffcott H. ⅩⅩⅦ. The Lateral Vibration of Loaded Shafts in the Neighbourhood of a Whirling Speed.-The Effect of Want of Balance[J]. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science,1919,37(219):304-314.
[32]陆颂元.论国内旋转动力机械非线性振动理论研究的现状和发展[J].汽轮机技术,2006,48(2)：85-87.
[33]Prohl M. A General Method for Calculating Critical Speeds of Flexible Rotors [J]. Journal of Applied Mechanics,1945,12(3):142-148.
[34]Myklestad NO. A New Method of Calculating Natural Modes of Uncoupled Bending Vibration of Airplane Wings and Other Types of Beams[J]. Journal of the aeronautical sciences,1944, 11(4):153-162.
[35]Lund JW. Stability and Damped Critical Speeds of a Flexible Rotor in Fluid-film B earings [J]. Rotating machinery dynamics,1987:1-9.
[36]李郁侠,段凌剑.基于传递矩阵法的大型水轮发电机组主轴系统非线性瞬态响应数学模型[J].水利水电技术,2002,33(7)：21-23.
[37]冯辅周,李承军.大型抽水蓄能机组轴系的动特性研究[J].振动.测试与诊断,1999,19(4)：313-319.
[38]Zorzi ES, Nelson HD. Finite Element Simulation of Rotor-bearing Systems with Internal Damping[C]. In:American Society of Mechanical Engineers, Gas Turbine Conference and Products Show. New Orleans, La:ProQuest,1976.1976.
[39]Nelson HD. A Finite Rotating Shaft Element Using Timoshenko Beam Theory[J]. Journal of Mechanical Design,1980,102(10):793-803.
[40]Thomas DL, Wilson JM, Wilson RR. Timoshenko Beam Finite Elements[J]. Journal of Sound and Vibration,1973,31(3):315-330.
[41]Rastogi V, Kumar C. Bond Graph Modeling of a Cracked Rotor[C]. In:Proceedings of the 2010 Spring Simulation Multiconference. Orlando, Florida:ACM,2010.1-7.
[42]Pedersen E. Rotordynamics and Bond Graphs:Basic Models[J]. Mathematical and Computer Modelling of Dynamical Systems,2009,15(4):337-352.
[43]Campos J, Crawford M, Longoria R. Rotordynamic Modeling Using Bond Graphs:Modeling the Jeffcott Rotor[J]. IEEE Transactions on Magnetics,2005,41(1):274-280.
[44]Batlle C,Doria-Cerezo A. Bond Graph Models of Electromechanical Systems. The AC Generator Case[C]. In:IEEE International Symposium on Industrial Electronics. Cambridge:IEEE, 2008.1064-1069.
[45]夏松波,武新华,汪光明等.热套转子力学模型研究[J].航空学报,1987,8(9)：A449-A455.
[46]谭善光,汪希宣.热套轮盘对轴段弯曲刚度的影响系数计算[J].应用力学学报,1990,7(1)：93-97.
[47]Newkirk BL, Taylor HD. Shaft Whipping Due to Oil Action in Journal Bearings[J]. General Electric Review,1925,28(8):559-568.
[48]Lund JW. Spring and Damping Coefficients for the Tilting-Pad Journal Bearing[J]. ASLE transactions,1964,7:342-352.
[49]Muszynska A. Rotordynamics[M]. Boca Raton:Taylor & Francis Group, LLC,2005.
[50]Ohashi H. Vibration and Oscillation of Hydraulic Machinery[M]. Brookfield:Avebury Technical,1991.
[51]Bettig BP, Han RPS. Modeling the Lateral Vibration of Hydraulic Turbine-generator Rotors[J].Journal of Vibration and Acoustics-Transactions of the ASME,1999,121(3): 322-327.
[52]马震岳,董毓新.水轮发电机组轴系统的动力反应[J].大电机技术,1988,5：6-13.
[53]李苹,窦海波,王正.水轮发电机组主轴系统的建模及其非线性瞬态响应[J].清华大学学报：自然科学版,1998,38(6)：123-128.
[54]Feng FZ, Chu FL. Dynamic Analysis of a Hydraulic Turbine Unit[J]. Mechanics of Structures and Machines,2001,29(4):505-531.
[55]Ma LF, Zhang XZ. Numerical Simulation of Nonlinear Oil Film Forces of Tilting-Pad Guide Bearing in Large Hydro-unit[J]. International Journal of Rotating Machinery,2000,6(5): 345-353.
[56]Cardinali R. Dynamic Simulation of Non-linear Models of Hydroelectric Machinery[J]. Mechanical Systems and Signal Processing,1993,7(1):29-44.
[57]王文,张直明.油叶型轴承非线性油膜力数据库[J].上海工业大学学报,1993,14(4)：299-305.
[58]孟志强,徐华,朱均.基于Poincare变换的滑动轴承非线性油膜力数据库方法[J].摩擦学学报,2001,21(3)：223-227.
[59]杨晓明,马震岳,黄军义.导轴承与推力轴承耦合作用下水电机组的横向振动研究[J].水力发电学报,2007,26(6)：132-136.
[60]陈贵清.推力轴承油膜刚度对发电机转子轴系固有频率的影响[J].河北理工学院学报,2000,22(4)：48-53.
[61]Mittwollen N, Hegel T, Glienicke J. Effect of Hydrodynamic Thrust Bearings on Lateral Shaft Vibrations[J]. Journal of Tribology,1991,113(4):811-817.
[62]Lie Y, Bhat RB. Coupled Dynamics of a Rotor-Journal Bearing System Equipped with Thrust Bearings[J]. Shock and Vibration,1995,2(1):1-14.
[63]Jiang PL, Yu L. Dynamics of a Rotor-bearing System Equipped with a Hydrodynamic Thrust Bearing[J]. Journal of Sound and Vibration,1999,227(4):833-872.
[64]张雷克,马震岳,宋兵伟.水轮发电机组在不平衡磁拉力及密封力下振动特性分析[J].水电能源科学,2010,28(9)：117-120.
[65]杨晓明,马震岳,张振国.水轮机迷宫密封系统非线性动力稳定性研究[J].大连理工大学学报,2007,47(1)：95-100.
[66]肖忠会.转子—轴承—密封系统动力学建模及其特性研究：[博士学位论文].上海：复旦大学,2006.
[67]马震岳,杨晓明.非线性水轮机密封系统自激振动分析[C].第十六次中国水电设备学术讨论会论文集,2007.
[68]马震岳,董毓新.水轮机转轮密封处水流的动力特性及其对机组自振特性的影响[J].大电机技术,1987,6：43-50.
[69]李松涛,许庆余,万方义.迷宫密封转子系统非线性动力稳定性的研究[J].应用力学学报,2002,19(2)：27-30.
[70]成玫,孟光,荆建平.非线性“转子-轴承-密封”系统动力分析[J].振动工程学报,2006, 19(4)：519-524.
[71]Schwirzer T. Dynamic Stressing of Hydroelectric Units by Stochastic Hydraulic Forces on the Turbine Runner[J]. Water Power & Dam Construction,1977:39-44.
[72]马震岳,董毓新.水力荷载作用下水电机组的动力响应[J].水力发电学报,1990(2)：31-40.
[73]Kramer E. Determining the Hydraulic Lateral Force of Pump-turbines [J]. Water Power and Dam Construction,1981,33:50-54.
[74]Chamieh DS, Acosta AJ, Brennen CE et al. Experimental Measurements of Hydrodynamic Radial Forces and Stiffness Matrices for a Centrifugal Pump-Impeller[J]. Journal of Fluids Engineering,1985,107(3):307-315.
[75]马震岳,董毓新.水轮发电机组动力学[M].大连：大连理工大学出版社,2003.
[76]邢景棠,周盛,崔尔杰.流固耦合力学概述[J].力学进展,1997,27(1)：19-38.
[77]刘德民,刘小兵,李娟.基于流固藕合的水轮机振动分析[J].流体传动与控制,2008(1)：21-25.
[78]谷朝红,姚熊亮,陈起富.水轮机部件流固耦合振动特性研究[J].大电机技术,2001(6)：47-52.
[79]Behrend B. On the Mechanical Forces in Dynamos Caused by Magnetic Attraction[J]. American Institute of Electrical Engineers, Transactions of the,1900,17:613-633.
[80]白晖宇,荆建平,孟光.电机不平衡磁拉力研究现状与展望[J].噪声与振动控制,2009,29(6)：5-7.
[81]Talas P, Toom P. Dynamic Measurement and Analysis of Air Gap Variations in Large Hydroelectric Generators [J]. IEEE Transactions on Power Apparatus and Systems,1983, PAS-102(9):3098-3106.
[82]邱家俊.机电耦联动力系统的非线性振动[M].北京：科学出版社,1996.
[83]白延年.水轮发电机设计与计算[M].北京：机械工业出版社,1982.
[84]Rosenberg E. Magnetic Pull in Electric Machines[J].Transactions of the American Institute of Electrical Engineers,1918,37(2):1425-1469.
[85]Covo A. Unbalanced Magnetic Pull in Induction Motors with Eccentric Rotors[J]. Power Apparatus and Systems, Part III. Transactions of the American Institute of Electrical Engineers, 1954,73(2):1421-1425.
[86]Ohishi H, Sakabe S, Tsumagari K et al. Radial Magnetic Pull in Salient Pole Machines with Eccentric Rotors[J]. IEEE Transactions on Energy Conversion,1987, EC-2(3):439-443.
[87]Perers R, Lundin U, Leijon M. Saturation Effects on Unbalanced Magnetic Pull in a Hydroelectric Generator with an Eccentric Rotor[J]. IEEE Transactions on Magnetics,2007, 43(10):3884-3890.
[88]Guo D, Chu F, Chen D. The Unbalanced Magnetic Pull and Its Effects on Vibration in a Three-phase Generator with Eccentric Rotor[J]. Journal of Sound and Vibration,2002,254(2): 297-312.
[89]姜培林,虞烈.电机不平衡磁拉力及其刚度的计算[J].大电机技术,1998(4)：32-34.
[90]Wang L, Cheung RW, Ma ZY et al. Finite-element Analysis of Unbalanced Magnetic Pull in a Large Hydro-generator under Practical Operations[J]. IEEE Transactions on Magnetics,2008, 44(6):1558-1561.
[91]Lundin U, Wolfbrandt A. Method for Modeling Time-Dependent Nonuniform Rotor/Stator Configurations in Electrical Machines[J]. IEEE Transactions on Magnetics,2009,45(7): 2976-2980.
[92]曲凤波,孙玉田,曲大庄.水轮发电机不平衡磁拉力[J].大电机技术,1997(4)：1-3.
[93]Lundstrom L, Gustavsson Rk, Aidanpaa JO et al. Influence on the Stability of Generator Rotors due to Radial and Tangential Magnetic Pull Force[J]. IET Electric Power Applications,2007, 1(1):1-8.
[94]Karisson M, Aidanpaa JO, Perers R et al. Rotor Dynamic Analysis of an Eccentric Hydropower Generator with Damper, Winding for Reactive Load[J]. Journal of Applied Mechanics Transactions of the ASME,2007,74(6):1178-1186.
[95]Gustavsson RK, Aidanpaa JO. The Influence of Nonlinear Magnetic Pull on Hydropower Generator Rotors [J].Journal of Sound and Vibration,2006,297(3-5):551-562.
[96]Pennacchi P. Computational Model for Calculating the Dynamical Behaviour of Generators Caused by Unbalanced Magnetic Pull and Experimental Validation[J]. Journal of Sound and Vibration,2008,312(1-2):332-353.
[97]夏松波,张新江,刘占生等.旋转机械不对中故障研究综述[J].振动、测试与诊断,1998,18(3)：157-161.
[98]Lees AW. Misalignment in Rigidly Coupled Rotors[J].Journal of Sound and Vibration,2007, 305(1-2):261-271.
[99]Sekhar AS, Prabhu BS. Effects of Coupling Misalignment on Vibrations of Rotating Machinery[J].Journal of Sound and Vibration,1995,185(4):655-671.
[100]Muszynska A, Goldman P. Chaotic Responses of Unbalanced Rotor/Bearing/Stator Systems with Looseness or Rubs[J]. Chaos, Solitons & Fractals,1995,5(9):1683-1704.
[101]李振平,罗跃纲,姚红良等.转子系统支承松动的非线性动力学及故障特征[J].东北大学学报(自然科学版),2002,23(11)：1048-1051.
[102]Chu F, Tang Y. Stability and Non-linear Responses of a Rotor-bearing System with Pedestal Looseness[J]. Journal of Sound and Vibration,2001,241(5):879-893.
[103]Lu WX, Chu FL. Experimental Investigation of Pedestal Looseness in a Rotor-bearing System[J]. Damage Assessment of Structures Viii,2009,413-414:599-605,824.
[104]马震岳,董毓新.有限元法分析水电机组轴系的临界转速[J].水电站机电技术,1991(4)：5-10.
[105]马震岳,董毓新.基础、导轴承刚度和磁拉力等对机组自振特性的影响[J].大电机技术,1986,6：46-53.
[106]荣吉利,李志和.水电机组轴系横向自振特性的有限元计算方法与结果分析[J].中国电机工程学报,1997,17(1)：33-36.
[107]杨晓明,马震岳.水轮发电机组横向振动的敏感性分析[J].振动工程学报,2004,17(S)：206-209.
[108]Nagafuji T. Lateral Vibration Analysis of Generator-Turbine Shaft System[J]. International Water Power and Dam Construction,1975,27(11):418-423.
[109]李苹,王正.大型水泵一水轮机组轴系的动力特性[J].清华大学学报：自然科学版,1996,36(7)：24-29.
[110]刘保国,张信志.水轮发电机组主轴系统非线性动力学问题的计算分析[J].中国机械工程,2001,12(8)：939-942.
[111]Brito G, Weber H, Fuerst A. Dynamics of Large Hydrogenerators[C]. In:Proceedings of the XVIII IAHR Symposium on Hydraulic Machinery and Cavitation. Netherlands:Kluwer Academic Pub,1996.464-473.
[112]于振威.水轮发电机组转轴临界转速和强迫振动的精确计算[J].大电机技术,1984,4：5-12.
[113]曲大庄.水轮发电机组轴系临界转速及弯曲变形计算的解析法[J].大电机技术,1986,1：6-13.
[114]Ma ZY, Song ZQ. Nonlinear Dynamic Characteristic Analysis of the Shaft System in Water Turbine Generator Set[J]. Chinese Journal of Mechanical Engineering,2009,22(1):124-131.
[115]杨晓明.水电站机组振动及其与厂房的耦联振动研究：[博士学位论文]：大连理工大学,2006.
[116]宋志强,马震岳,张运良等.考虑厂房基础耦联作用的水轮发电机组轴系统动力反应分析[J].振动与冲击,2008,27(6)：158-161.
[117]沈克昌,钟梓辉.葛洲坝工程丛书9-水轮发电机组[M].北京：水利电力出版社,1991.
[118]张正松.旋转机械振动监测及故障诊断[M].北京：机械工业出版社,1991.
[119]中华人民共和国国家标准,水轮机基本技术条件[S],GB/T 15468-2006,2006.
[120]辜承林,陈乔夫,熊永前.电机学[M].武汉：华中科技大学出版社,2001.
[121]王勖成,邵敏.有限单元法基本原理和数值方法[M].第2版.北京：清华大学出版社,1997.
[122]虞烈,刘恒.轴承一转子系统动力学[M].西安：西安交通大学出版社,2000.
[123]Villa C, Sinou JJ, Thouverez F. Stability and Vibration Analysis of a Complex Flexible Rotor Bearing System[J]. Communications in Nonlinear Science and Numerical Simulation,2008, 13(4):804-821.
[124]Hutchinson JR. Shear Coefficients for Timoshenko Beam theory[J]. Journal of Applied Mechanics-Transactions of the ASME,2001,68(1):87-92.
[125]Bettig BP, Han RPS. Predictive Maintenance Using the Rotordynamic Model of a Hydraulic Turbine-generator Rotor[J]. Journal of Vibration and Acoustics-Transactions of the ASME, 1998,120(2):441-448.
[126]刘禄臣.无轴结构转子支架的扭矩分配[J].大电机技术,1983,3：10-16.
[127]王珂仑.水力机组振动[M].北京：水利电力出版社,1986.
[128]水利部第二工程局.水轮发电机试验[M].北京：电力工业出版社,1980.
[129]东北水利水电学校.水轮机[M].北京：电力工业出版社,1980.
[130]Ma H, Zhao XY, Teng YN et al. Analysis of Dynamic Characteristics for a Rotor System with Pedestal Looseness[J]. Shock and Vibration,2011,18:13-27.
[131]Si XH, Lu WX, Chu FL. Lateral Vibration of Hydroelectric Generating Set with Different Supporting Condition of Thrust Pad[J]. Shock and Vibration,2011,18:317-331.
[132]马南任,涂阳文.转桨式水轮机水导轴承的运行经验[J].华中电力,1990(2)：22-26.
[133]曹鹍,姚志民.水轮机原理及水力设计[M].北京：清华大学出版社,1991.
[134]Bachschmid N, Pennacchi P, Vania A. Identification of Multiple Faults in Rotor Systems[J].Journal of Sound and Vibration,2002,254(2):327-366.
[135]Sekhar A. Model-based Identification of Two Cracks in a Rotor System[J]. Mechanical Systems and Signal Processing,2004,18(4):977-983.
[136]Pennacchi P, Bachschmid N, Vania A et al. Use of Modal Representation for the Supporting Structure in Model-based Fault Identification of Large Rotating Machinery, part 1--Theoretical Remarks[J]. Mechanical Systems and Signal Processing,2006,20(3):662-681.
[137]Lees A, Sinha J, Friswell M. Model-based Identification of Rotating Machines [J]. Mechanical Systems and Signal Processing,2009,23(6):1884-1893.
[138]Jalan AK, Mohanty A. Model Based Fault Diagnosis of a Rotor-bearing System for Misalignment and Unbalance under Steady-state Condition[J]. Journal of Sound and Vibration, 2009,327(3-5):604-622.
[139]Bachschmid N, Pennacchi P. Accuracy of Fault Detection in Real Rotating Machinery using Model Based Diagnostic Techniques [J]. JSME International Journal Series C,2003,46(3): 1026-1034.
[140]Pennacchi P, Bachschmid N, Vania A et al.Use of Modal Representation for the Supporting Structure in Model-based Fault Identification of Large Rotating Machinery:Part 2-Application to a Real Machine [J]. Mechanical Systems and Signal Processing,2006,20(3):682-701.
[141]Jardine AKS, Lin D, Banjevic D. A Review on Machinery Diagnostics and Prognostics Implementing Condition-based Maintenance [J]. Mechanical Systems and Signal Processing, 2006,20(7):1483-1510.