基于Hamilton原理的转子—汽封—轴承系统非线性动力学问题研究
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摘要
汽轮发电机组是电力大系统中的原动机和能源生产的重要环节,随着科学技术的进步,汽轮发电机组的容量和运行参数不断的提高,汽轮机向着多跨度、重载荷的方向发展,汽轮机转子结构变得更加复杂,众多非线性因素成为了危及机组安全运行的隐患,人们也对机组的可靠性、安全性和稳定性提出了更高的要求。
近年来,为了提高能源利用率,我国超超临界汽轮机组和大型核电汽轮机组迅速增多,汽流激振问题也越来越被重视。为了确保机组运行安全,国内外对汽封结构的改进也采取了不少措施,但有效的理论研究和指导尚为欠缺。由于大多转子动力学方面的研究对于非线性激励的作用考虑不全面,具有一定的局限性。
本文在熟悉汽轮机组结构及分析汽流激振引发的事故原因基础上,构建了一个单盘单跨的简单的汽轮机转子模型,在计及转子的弯曲效应、剪切效应以及偏心等因素的同时,综合考虑非线性汽封力、非线性轴承油膜力的综合作用,应用Hamilton原理,并结合有限元方法,推导了转子-汽封-轴承系统的非线性动力学模型。通过数值分析,求得系统的周期响应,根据系统的分岔图、时间历程图、Poincare映射图、频谱图、相位轨迹图等,分析比较了系统在是否考虑汽封力作用下的非线性动力学特性,研究了转速、汽封结构参数、蒸汽参数对系统响应的影响。
本文在建模过程中考虑了多种非线性因素的联合作用,更接近汽轮机组的实际运行状况,具有较好的代表性,为消除汽流激振和提高系统稳定性的研究提供了良好的理论基础。
Steam turbine-generating unit is the original motive and the key link of energy production. With the development in science and technology, the capacity of steam turbine-generator unit, as well as the operating parameters is continuously increasing, and toward the direction of high-speed, multi-span and heavy loads. Since the steam turbine rotor structures are getting more complicated, many nonlinear factors have become the hidden danger of the safe operation of generating units. So people have raised higher requirements toward the reliability, security and stability of the units.
In recent years, in order to raise the energy efficiency, China's ultra-supercritical and large-scale nuclear power steam turbine group are increasing rapidly, and the problem of steam excited vibration are being much accounted of. For the purpose of ensuring the safe operation of generating units, home and abroad have also taken various measures to improve the structures of the seal, but effective theoretical researches and guidance are still lacking. Since most of the researches, which are in the field of rotor dynamics, haven't thoroughly considered the effect of non-linear incentive. There exist some limitations.
This paper, on the basis of getting familiar with turbine steam structure and analyzing the cause of the steam excited vibration-induced accident, constructed a simple single-disc single-spam turbine rotor model. While taking into account the effect rotor bending, shear effect and eccentricity, the author has comprehensively considered the effect of nonlinear seal force and bearing oil-film force, at the same time, applied Hamilton principle, combined the finite element method, and derived the nonlinear dynamic model of rotor-seal-bearing system. By numerical analysis, this paper obtained the periodic response. According to the system's bifurcation diagram, time history diagram, Poincare map, frequency spectrum, phase trajectory maps, the author has investigated the nonlinear dynamic characteristic of rotor-seal-bearing system in some specific rotation speeds, seal structures and steam parameters.
When modeling, this paper has taken the combined effects of several nonlinear factors into account, which is closer to the actual operation condition of the steam turbine and with better representativeness. All these have laid a better theoretical basis for the research of the elimination of steam excited vibration and improvement of systematic stability.
近年来,为了提高能源利用率,我国超超临界汽轮机组和大型核电汽轮机组迅速增多,汽流激振问题也越来越被重视。为了确保机组运行安全,国内外对汽封结构的改进也采取了不少措施,但有效的理论研究和指导尚为欠缺。由于大多转子动力学方面的研究对于非线性激励的作用考虑不全面,具有一定的局限性。
本文在熟悉汽轮机组结构及分析汽流激振引发的事故原因基础上,构建了一个单盘单跨的简单的汽轮机转子模型,在计及转子的弯曲效应、剪切效应以及偏心等因素的同时,综合考虑非线性汽封力、非线性轴承油膜力的综合作用,应用Hamilton原理,并结合有限元方法,推导了转子-汽封-轴承系统的非线性动力学模型。通过数值分析,求得系统的周期响应,根据系统的分岔图、时间历程图、Poincare映射图、频谱图、相位轨迹图等,分析比较了系统在是否考虑汽封力作用下的非线性动力学特性,研究了转速、汽封结构参数、蒸汽参数对系统响应的影响。
本文在建模过程中考虑了多种非线性因素的联合作用,更接近汽轮机组的实际运行状况,具有较好的代表性,为消除汽流激振和提高系统稳定性的研究提供了良好的理论基础。
Steam turbine-generating unit is the original motive and the key link of energy production. With the development in science and technology, the capacity of steam turbine-generator unit, as well as the operating parameters is continuously increasing, and toward the direction of high-speed, multi-span and heavy loads. Since the steam turbine rotor structures are getting more complicated, many nonlinear factors have become the hidden danger of the safe operation of generating units. So people have raised higher requirements toward the reliability, security and stability of the units.
In recent years, in order to raise the energy efficiency, China's ultra-supercritical and large-scale nuclear power steam turbine group are increasing rapidly, and the problem of steam excited vibration are being much accounted of. For the purpose of ensuring the safe operation of generating units, home and abroad have also taken various measures to improve the structures of the seal, but effective theoretical researches and guidance are still lacking. Since most of the researches, which are in the field of rotor dynamics, haven't thoroughly considered the effect of non-linear incentive. There exist some limitations.
This paper, on the basis of getting familiar with turbine steam structure and analyzing the cause of the steam excited vibration-induced accident, constructed a simple single-disc single-spam turbine rotor model. While taking into account the effect rotor bending, shear effect and eccentricity, the author has comprehensively considered the effect of nonlinear seal force and bearing oil-film force, at the same time, applied Hamilton principle, combined the finite element method, and derived the nonlinear dynamic model of rotor-seal-bearing system. By numerical analysis, this paper obtained the periodic response. According to the system's bifurcation diagram, time history diagram, Poincare map, frequency spectrum, phase trajectory maps, the author has investigated the nonlinear dynamic characteristic of rotor-seal-bearing system in some specific rotation speeds, seal structures and steam parameters.
When modeling, this paper has taken the combined effects of several nonlinear factors into account, which is closer to the actual operation condition of the steam turbine and with better representativeness. All these have laid a better theoretical basis for the research of the elimination of steam excited vibration and improvement of systematic stability.
引文
[1]Nelson H D. Rotordynamic modeling and analysis procedures:a review [J]. JSME International Journal, Series C,1998,41(1):1-12.
[2]Jeffcott H H. The lateral vibration of loaded shafts in the neighborhood of a whirling speed-the effect of want of balance [J]. Philosophy Magazine,1919, 6(37):304-314.
[3]Newkirk B L, Taylor H D. Shaft whipping due to oil action in journal bearing [J]. General Electric Review,1925,28:559-568.
[4]Hagg A C. Some dynamic properties of oil film bearings [J]. ASME Journal of Engineers,1956,3:302-306.
[5]Sternlicht B. Elastic and damping properties of cylindrical journal bearing [J]. Journal of Basic Engineering,1959,81:101-108.
[6]Lund J W. The stability of an elastic rotor in journal bearing with flexible damped supports [J]. ASME Journal of Applied Mechanics,1965,32:911-920.
[7]Glienicke J. Experimental investigation of the stiffness and damping coefficients of turbine bearings and their application to instability prediction [J]. Journal Bearings for Reciprocating and Turbo-machinery, IME Symposium in Nottingham,1966.
[8]Ehrich F F. Subharmonic Vibration of Rotors in Bearing Clearance [J]. ASME paper,1966:66-MD-1.
[9]Homles A G. A periodic behavior of a rigid shaft in short bearings [J]. International Journal for Numerical Methods in Engineering,1978,12:695-702.
[10]Myers C J. Bifurcation theory applied to oil whirl in plain cylindrical journal bearings [J]. ASME Journal of Mechanics,1984,51(2):244-250.
[11]Ehrich F F. Some observations of chaotic vibration phenomena in high-speed rotordynamics [J]. ASME Journal of Vibration and Acoustics,1991,113(1): 50-57.
[12]Adiletta G, Guido A R, Rossi C. Chaotic motions of a rigid rotor in short journal bearings [J], Journal of Nonlinear Dynamics,1996,10(6):251-269.
[13]Sundararajan P, Noah S T. Dynamics of forced nonlinear systems using shooting /arc-length continuation method-application to rotor systems [J], Journal of Vibration and Acoustics,1997,119:9-20.
[14]Karlberg M, Aidanpaa J-O. Numerical investigation of an unbalanced rotor system with bearing clearance [J], Chaos, Solitons & Fractals,2003,18(4): 653-664.
[15]Villa C, Sinou J-J, Thouverez F, Stability and vibration analysis of a complex flexible rotor bearing system [J], Communications in Nonlinear Science and Numerical Simulation,2008,13:804-821.
[16]陈予恕,丁千,孟泉.非线性转子的低频振动失稳机理分析[J].应用力学学报,1998,15(1)：113-117.
[17]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.
[18]李晓峰,王立平,史铁林等.考虑非线性油膜力的转子系统稳态响应的研究[J].华中理工大学学报,1999,27(6)：57-58.
[19]何立东,夏松波等.转子-轴承系统非线性振动机理的研究[J],1999,31：88-90.
[20]Zhang W, Zhang H S, Xu X F. Study of general nonlinear formula of oil-film force acting on a journal with unsteady motion [C], Asia-Pacific Vibration Conference, Korea,1997:9-13.
[21]徐小峰,张文.一种非稳态油膜力模型下刚性转子的分岔和混沌特性[J].振动工程学报,2000,13(6)：247-252.
[22]丁千,陈予恕等.转子-轴承系统的非稳态分岔[J].振动工程学报,2003,16：189-193.
[23]Jing J P, Meng G, Sun Y, et al. On the non-linear dynamic behavior of a rotor-bearing system [J]. Journal of Sound and Vibration,2004,274:1031-1044.
[24]吕延军,虞烈,刘恒.非线性轴承-转子系统的稳定性和分岔[J].机械工程学报,2004,40(10)：62-67.
[25]吴其力,荆珂.非线性油膜力作用双跨转子系统动力学特性研究[J].辽宁石 油化工大学学报,2008,28(2)：53-57.
[26]李朝峰,孙伟,马辉等.基于有限元法的非线性转子系统动态特性[J].东北大学学报(自然能科学版),2009,30(5)：716-720.
[27]Thomas H J. Unstable oscillations of turbine rotors due to steam leakage in the sealing glands and the buckets [J]. Bulletin Scientifique, A.J.M,1958,71: 1039-1064.
[28]Alford J S. Protecting turbo-machinery from self-excited rotor whirl [J]. ASME Journal of Engineering for Power,1965,5:335-344.
[29]Urlichsk K. Clearance flow generated transverse of forces at the rotors thermal turbomachines [D]. Dissertation of Technical University of Munich,1975.
[30]Vance J M, Laudadio F J. Experimental measurements of Alford force in axial flow turbo-machinery [J]. ASME Paper,1984:84-GT-140.
[31]Muszynska A, Bently D E. Improvements of lightly loaded rotor bearing and rotor seal models [J]. Journal of Sound and Vibration,1988,110:129-136.
[32]Iwatsubo T. An experimental study of dynamic characteristics of labyrinth seal [C]. NASA cp-3239,1993:219-238.
[33]Kim C H, Lee Y B. Test results for rotor-dynamic coefficients of anti-swirl self injection seals [C]. NASA cp-3239,1993:65-74.
[34]Bently D E, Muszynska A. Role of circumferential flow in the stability of fluid handling machine rotors [C], The 5th Workshop on Rotordynamic Instability Problems in High Performance Turbomachinery, Taxas A &M University,1988: 1-15.
[35]Al-Nahwi A A, Paduano J D, Nayfeh S A. Aerodynamic-rotordynamic interaction in axial compression systems-part Ⅱ:impact of interaction on overall system stability [J], Journal of Turbomachinery,2003,125(7):416-424.
[36]Hua J, Swaddiwudhipong S, Liu Z S, et al. Numerical analysis of nonlinear rotor-seal system [J]. Journal of Sound and Vibration,2005,283:525-542.
[37]Akhmetkhanov R, Banakh L, Nikiforov A. Flow-coupled vibrations of rotor and seal [J]. Journal of Vibration and Control,2005,11(7):887-901.
[38]丁千,陈予恕等.非线性转子-密封系统的稳定性和Hopf分叉研究[J].振动工程学报,1997,10(3)：368-374.
[39]陈佐一.流体激振[M].北京：清华大学出版社,1998.
[40]柴山,张耀明,曲庆文等.汽轮机间隙汽流激振力分析[J].中国工程科学,2001,3(4)：69-72.
[41]孙庆,危奇等.蒸汽激振及其对大机组轴系振动和稳定性影响的计算分析研究[C].透平专委会论文集,2002.
[42]李松涛,许庆余,方万义等.迷宫密封不平衡转子动力系统的稳定性与分岔[J].应用数学与力学,2003,24(11)：1141-1150.
[43]李雪松,黄典贵.迷宫汽封三维非定常场及转子动特性数值仿真[J].机械工程学报,2003,39(4)：136-140.
[44]白长青,许庆余,张小龙.火箭发动机液氢涡轮泵转子-密封系统的非线性动力稳定性[J].西安交通大学学报,2005,39(9)：1016-1020.
[45]骆天舒,王双连,郭乙木.高维动力系统在转子稳定性分析中的应用[J].浙江大学学报(工学版),2007,41(6)：959-962.
[46]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.
[47]Cheng M, Meng G, Jing J P. Numerical analysis of nonlinear rotor-bearing-seal system [J]. Journal of Shanghai Jiaotong University (Science),2008,13(4): 418-425.
[48]李忠刚,孔达,焦映厚等.转子-密封系统非线性动力学特性分析[J].振动与冲击,2009,28(6)：159-163.
[49]Black H F, Jenssen D N. Effects of high-pressure ring seals on pump rotor [J]. ASME paper,1971:71-WA/FF-38.
[50]Childs D W. Testing of turbulent seals for rotor-dynamic coefficients [C]. NASA cp-2133,1980:121-138.
[51]Muszynska A, Bently D E. Frequency-swept rotating input perturbation techniques and identification of the fluid force models in rotor/bearing/seal systems and fluid handling machines [J], Journal of Sound and Vibration,1990, 143(1):103-124.
[52]陈予恕,唐云.非线性动力学中的现代分析方法[M].北京：科学出版社,1992.
[53]刘延柱,陈立群.非线性振动[M].北京：高等教育出版社,2001.
[54]梅凤翔,刘端,罗勇.高等分析力学[M].北京：北京理工大学出版社,1990.
[55]张文.转子动力学基础[M].北京：科学出版社,1990.
[56]曾攀.有限元分析及应用[M].北京：清华大学出版社,2004.
[2]Jeffcott H H. The lateral vibration of loaded shafts in the neighborhood of a whirling speed-the effect of want of balance [J]. Philosophy Magazine,1919, 6(37):304-314.
[3]Newkirk B L, Taylor H D. Shaft whipping due to oil action in journal bearing [J]. General Electric Review,1925,28:559-568.
[4]Hagg A C. Some dynamic properties of oil film bearings [J]. ASME Journal of Engineers,1956,3:302-306.
[5]Sternlicht B. Elastic and damping properties of cylindrical journal bearing [J]. Journal of Basic Engineering,1959,81:101-108.
[6]Lund J W. The stability of an elastic rotor in journal bearing with flexible damped supports [J]. ASME Journal of Applied Mechanics,1965,32:911-920.
[7]Glienicke J. Experimental investigation of the stiffness and damping coefficients of turbine bearings and their application to instability prediction [J]. Journal Bearings for Reciprocating and Turbo-machinery, IME Symposium in Nottingham,1966.
[8]Ehrich F F. Subharmonic Vibration of Rotors in Bearing Clearance [J]. ASME paper,1966:66-MD-1.
[9]Homles A G. A periodic behavior of a rigid shaft in short bearings [J]. International Journal for Numerical Methods in Engineering,1978,12:695-702.
[10]Myers C J. Bifurcation theory applied to oil whirl in plain cylindrical journal bearings [J]. ASME Journal of Mechanics,1984,51(2):244-250.
[11]Ehrich F F. Some observations of chaotic vibration phenomena in high-speed rotordynamics [J]. ASME Journal of Vibration and Acoustics,1991,113(1): 50-57.
[12]Adiletta G, Guido A R, Rossi C. Chaotic motions of a rigid rotor in short journal bearings [J], Journal of Nonlinear Dynamics,1996,10(6):251-269.
[13]Sundararajan P, Noah S T. Dynamics of forced nonlinear systems using shooting /arc-length continuation method-application to rotor systems [J], Journal of Vibration and Acoustics,1997,119:9-20.
[14]Karlberg M, Aidanpaa J-O. Numerical investigation of an unbalanced rotor system with bearing clearance [J], Chaos, Solitons & Fractals,2003,18(4): 653-664.
[15]Villa C, Sinou J-J, Thouverez F, Stability and vibration analysis of a complex flexible rotor bearing system [J], Communications in Nonlinear Science and Numerical Simulation,2008,13:804-821.
[16]陈予恕,丁千,孟泉.非线性转子的低频振动失稳机理分析[J].应用力学学报,1998,15(1)：113-117.
[17]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.
[18]李晓峰,王立平,史铁林等.考虑非线性油膜力的转子系统稳态响应的研究[J].华中理工大学学报,1999,27(6)：57-58.
[19]何立东,夏松波等.转子-轴承系统非线性振动机理的研究[J],1999,31：88-90.
[20]Zhang W, Zhang H S, Xu X F. Study of general nonlinear formula of oil-film force acting on a journal with unsteady motion [C], Asia-Pacific Vibration Conference, Korea,1997:9-13.
[21]徐小峰,张文.一种非稳态油膜力模型下刚性转子的分岔和混沌特性[J].振动工程学报,2000,13(6)：247-252.
[22]丁千,陈予恕等.转子-轴承系统的非稳态分岔[J].振动工程学报,2003,16：189-193.
[23]Jing J P, Meng G, Sun Y, et al. On the non-linear dynamic behavior of a rotor-bearing system [J]. Journal of Sound and Vibration,2004,274:1031-1044.
[24]吕延军,虞烈,刘恒.非线性轴承-转子系统的稳定性和分岔[J].机械工程学报,2004,40(10)：62-67.
[25]吴其力,荆珂.非线性油膜力作用双跨转子系统动力学特性研究[J].辽宁石 油化工大学学报,2008,28(2)：53-57.
[26]李朝峰,孙伟,马辉等.基于有限元法的非线性转子系统动态特性[J].东北大学学报(自然能科学版),2009,30(5)：716-720.
[27]Thomas H J. Unstable oscillations of turbine rotors due to steam leakage in the sealing glands and the buckets [J]. Bulletin Scientifique, A.J.M,1958,71: 1039-1064.
[28]Alford J S. Protecting turbo-machinery from self-excited rotor whirl [J]. ASME Journal of Engineering for Power,1965,5:335-344.
[29]Urlichsk K. Clearance flow generated transverse of forces at the rotors thermal turbomachines [D]. Dissertation of Technical University of Munich,1975.
[30]Vance J M, Laudadio F J. Experimental measurements of Alford force in axial flow turbo-machinery [J]. ASME Paper,1984:84-GT-140.
[31]Muszynska A, Bently D E. Improvements of lightly loaded rotor bearing and rotor seal models [J]. Journal of Sound and Vibration,1988,110:129-136.
[32]Iwatsubo T. An experimental study of dynamic characteristics of labyrinth seal [C]. NASA cp-3239,1993:219-238.
[33]Kim C H, Lee Y B. Test results for rotor-dynamic coefficients of anti-swirl self injection seals [C]. NASA cp-3239,1993:65-74.
[34]Bently D E, Muszynska A. Role of circumferential flow in the stability of fluid handling machine rotors [C], The 5th Workshop on Rotordynamic Instability Problems in High Performance Turbomachinery, Taxas A &M University,1988: 1-15.
[35]Al-Nahwi A A, Paduano J D, Nayfeh S A. Aerodynamic-rotordynamic interaction in axial compression systems-part Ⅱ:impact of interaction on overall system stability [J], Journal of Turbomachinery,2003,125(7):416-424.
[36]Hua J, Swaddiwudhipong S, Liu Z S, et al. Numerical analysis of nonlinear rotor-seal system [J]. Journal of Sound and Vibration,2005,283:525-542.
[37]Akhmetkhanov R, Banakh L, Nikiforov A. Flow-coupled vibrations of rotor and seal [J]. Journal of Vibration and Control,2005,11(7):887-901.
[38]丁千,陈予恕等.非线性转子-密封系统的稳定性和Hopf分叉研究[J].振动工程学报,1997,10(3)：368-374.
[39]陈佐一.流体激振[M].北京：清华大学出版社,1998.
[40]柴山,张耀明,曲庆文等.汽轮机间隙汽流激振力分析[J].中国工程科学,2001,3(4)：69-72.
[41]孙庆,危奇等.蒸汽激振及其对大机组轴系振动和稳定性影响的计算分析研究[C].透平专委会论文集,2002.
[42]李松涛,许庆余,方万义等.迷宫密封不平衡转子动力系统的稳定性与分岔[J].应用数学与力学,2003,24(11)：1141-1150.
[43]李雪松,黄典贵.迷宫汽封三维非定常场及转子动特性数值仿真[J].机械工程学报,2003,39(4)：136-140.
[44]白长青,许庆余,张小龙.火箭发动机液氢涡轮泵转子-密封系统的非线性动力稳定性[J].西安交通大学学报,2005,39(9)：1016-1020.
[45]骆天舒,王双连,郭乙木.高维动力系统在转子稳定性分析中的应用[J].浙江大学学报(工学版),2007,41(6)：959-962.
[46]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.
[47]Cheng M, Meng G, Jing J P. Numerical analysis of nonlinear rotor-bearing-seal system [J]. Journal of Shanghai Jiaotong University (Science),2008,13(4): 418-425.
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