耦合故障转子系统非线性动力学若干问题
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摘要
随着现代工业的快速发展,旋转机械的作用日益明显,转子-轴承系统作为旋转机械的关键部件,时常出现各种形式的故障,最常见的故障有裂纹、碰摩和基座松动等。由于非线性气膜力、裂纹和碰摩等因素的作用,在振动剧烈时会发生重大事故。因此应用现代非线性动力学理论和转子动力学理论研究故障转子系统成为当今国内外的热门研究课题之一。
本文以现代非线性动力学理论为基础,采用气浮短轴承模型,将打靶法思想与四阶龙格库塔法结合起来,对转子系统由于气膜力和裂纹导致的非线性动力学行为进行数值模拟,借助分岔图、相图、Poincare映射和频谱分析了转子系统的运动形态。研究结果表明,随着转速增加,系统响应出现了丰富的非线性现象;随着偏心量增大,系统动力学行为更加复杂并出现混沌运动,周期五窗口明显加宽;随着深度的加深,在超高速区出现周期六窗口,并且逐步变宽。
其次,建立了考虑气膜力的裂纹与碰摩转子-轴承系统的模型,研究了系统随转速、定子刚度以及偏心量等参数变化的非线性动力学特性,发现裂纹-碰摩耦合故障转子在临界转速时与单一碰摩故障转子有相似的动力学行为,在高转速时,由于碰摩力的作用,系统响应的稳定性下降,动力学行为比单一裂纹故障时更加复杂。系统具有裂纹-碰摩耦合故障时,随着裂纹的扩展,周期4窗口变窄,概周期和混沌区域增加,系统响应由高倍周期直接进入混沌运动。结果显示耦合故障的非线性动力学行为比单一裂纹故障时更加复杂突出。
第三,基于时域的时间有限元法,将描述转子系统动力学特征的非线性微分方程组离散成一组非线性代数方程,然后应用吴消去法的特征列思想对所得到的非线性代数方程组进行降维求解,进而分析了定子刚度和摩擦系数对含有气膜力的碰摩转子响应的影响。
最后,总结了本文所做的主要工作,指出了存在的问题和今后的发展趋势。
With the rapid development of modern industry, the role of the rotating machinery is becoming important. As a key component of the rotating machinery, the rotor system emerges all kinds of faults frequently, such as crack, rub, looseness of pedestal and so on. Because of the influence of nonlinear gas film force, crack, rub and many other reasons, great tragedy may occur if the vibration is violent enough. So studying rotor system with multi-faults with modern nonlinear dynamic theory and rotor dynamic theory becomes one of the most popular research problems at home and abroad.
This paper based on modern nonlinear dynamic theory and gas film force of the short journal bearing, Nonlinear dynamical behaviors of rotor system caused by gas film force and crack fault were studied through numerical simulations based on the combination of thought of Shooting method and Runge-Kutta method. The motion characteristics are analyzed by bifurcation diagram, phase diagram, Poincare maps and spectrum analysis. The results show that many abundant nonlinear phenomena appear in the response of the system along with the increase of rotor speed; system dynamic behaviors are more complex and appear chaos motions, and period-5 window becomes wilder along with the increase of eccentric quantum; system has emerge period-5 window in high-speed zone and becomes wider gradually with the deepening of the crack.
Secondly, built the dynamic model of rotor system with the coupling faults of cracking and rub-impact and provided the equations of motion. In this model, the nonlinear gas film force, the crack and the rub impacting are considered. See about the nonlinear dynamic characteristics along with the change of rotation speed, stator stiffness and eccentric mass, and find that rotor-bearing system with coupling faults of crack and rub-impact has the similar dynamic behavior with the rotor with a single rub impacting fault at the critical speed, as a result of the force of colliding and rubbing, the stability of the system response drops, and dynamic behaviors are more abundant than those singular crack fault at the high rotation speed. When the system has coupling faults of crack and rub-impact, with crack expanding ,period-4 window becomes narrow, almost periodic and chaos region increase, system response from multi-periodic enter chaos move directly. Results show that dynamic behaviors induced by coupled faults are more complex than those singular fault, and nonlinear questions are more serious.
Thirdly, based on a finite element formulation in the time domain, this method transforms the non- linear differential equations governing the dynamic behavior of rotor-bearing system into a set of non- linear algebraic equations that can be reduced and calculated by the characteristic set of Wu elimination method. The effect of stator stiffness and friction coefficient on response for rub-impact rotor system with gas film force is comprehensively analyzed.
Finally, the primary work of this text has been concluded, and the problem existed and the development trend of future work has been pointed out.
本文以现代非线性动力学理论为基础,采用气浮短轴承模型,将打靶法思想与四阶龙格库塔法结合起来,对转子系统由于气膜力和裂纹导致的非线性动力学行为进行数值模拟,借助分岔图、相图、Poincare映射和频谱分析了转子系统的运动形态。研究结果表明,随着转速增加,系统响应出现了丰富的非线性现象;随着偏心量增大,系统动力学行为更加复杂并出现混沌运动,周期五窗口明显加宽;随着深度的加深,在超高速区出现周期六窗口,并且逐步变宽。
其次,建立了考虑气膜力的裂纹与碰摩转子-轴承系统的模型,研究了系统随转速、定子刚度以及偏心量等参数变化的非线性动力学特性,发现裂纹-碰摩耦合故障转子在临界转速时与单一碰摩故障转子有相似的动力学行为,在高转速时,由于碰摩力的作用,系统响应的稳定性下降,动力学行为比单一裂纹故障时更加复杂。系统具有裂纹-碰摩耦合故障时,随着裂纹的扩展,周期4窗口变窄,概周期和混沌区域增加,系统响应由高倍周期直接进入混沌运动。结果显示耦合故障的非线性动力学行为比单一裂纹故障时更加复杂突出。
第三,基于时域的时间有限元法,将描述转子系统动力学特征的非线性微分方程组离散成一组非线性代数方程,然后应用吴消去法的特征列思想对所得到的非线性代数方程组进行降维求解,进而分析了定子刚度和摩擦系数对含有气膜力的碰摩转子响应的影响。
最后,总结了本文所做的主要工作,指出了存在的问题和今后的发展趋势。
With the rapid development of modern industry, the role of the rotating machinery is becoming important. As a key component of the rotating machinery, the rotor system emerges all kinds of faults frequently, such as crack, rub, looseness of pedestal and so on. Because of the influence of nonlinear gas film force, crack, rub and many other reasons, great tragedy may occur if the vibration is violent enough. So studying rotor system with multi-faults with modern nonlinear dynamic theory and rotor dynamic theory becomes one of the most popular research problems at home and abroad.
This paper based on modern nonlinear dynamic theory and gas film force of the short journal bearing, Nonlinear dynamical behaviors of rotor system caused by gas film force and crack fault were studied through numerical simulations based on the combination of thought of Shooting method and Runge-Kutta method. The motion characteristics are analyzed by bifurcation diagram, phase diagram, Poincare maps and spectrum analysis. The results show that many abundant nonlinear phenomena appear in the response of the system along with the increase of rotor speed; system dynamic behaviors are more complex and appear chaos motions, and period-5 window becomes wilder along with the increase of eccentric quantum; system has emerge period-5 window in high-speed zone and becomes wider gradually with the deepening of the crack.
Secondly, built the dynamic model of rotor system with the coupling faults of cracking and rub-impact and provided the equations of motion. In this model, the nonlinear gas film force, the crack and the rub impacting are considered. See about the nonlinear dynamic characteristics along with the change of rotation speed, stator stiffness and eccentric mass, and find that rotor-bearing system with coupling faults of crack and rub-impact has the similar dynamic behavior with the rotor with a single rub impacting fault at the critical speed, as a result of the force of colliding and rubbing, the stability of the system response drops, and dynamic behaviors are more abundant than those singular crack fault at the high rotation speed. When the system has coupling faults of crack and rub-impact, with crack expanding ,period-4 window becomes narrow, almost periodic and chaos region increase, system response from multi-periodic enter chaos move directly. Results show that dynamic behaviors induced by coupled faults are more complex than those singular fault, and nonlinear questions are more serious.
Thirdly, based on a finite element formulation in the time domain, this method transforms the non- linear differential equations governing the dynamic behavior of rotor-bearing system into a set of non- linear algebraic equations that can be reduced and calculated by the characteristic set of Wu elimination method. The effect of stator stiffness and friction coefficient on response for rub-impact rotor system with gas film force is comprehensively analyzed.
Finally, the primary work of this text has been concluded, and the problem existed and the development trend of future work has been pointed out.
引文
[1]胡海岩.应用非线性动力学[M].第一版.北京:航空工业出版社,2000
[2]刘延柱,陈立群.非线性振动[M].第一版.北京:高等教育出版社,2001
[3]陈予恕.非线性振动系统的分叉和混沌理论[M].第一版.北京:高等教育出版社,1993
[4]焦映厚等.非线性转子动力学的研究现状与展望[J].哈尔滨工业大学学报.1999(3):1-4
[5]黄文虎,武新华,焦映厚等[J].非线性转子动力学研究综述.振动工程学报.2000(4):479-509
[6]苏少锦,谢元广,龙新峰.汽轮机发电机组动静碰摩故障的诊断与处理[J].电力设备,2006,(09):75-78
[7]钟一谔等.转子动力学[M].北京:清华大学出版社,1987
[8]张文.转子动力学理论基础[M].北京:科学出版社,1990
[9]闻邦椿等.离等转子动力学[M].北京:机械工业出版社,2000
[10]杨志永.高速静电喷漆涡轮系统稳定性理论及结构动态特性研究[D].天津:天津大学,2000
[11]李振平.多故障转子系统若干非线性问题的研究[D].沈阳:东北大学,2002
[12]Mayes I W etal.Analysis of the response of a multi-rotor-bearing system containing a transverse crack in a rotor[J].ASME.Journal of Vibration,Acoustics,Stress,and Reliability in Design,1984,106:139-145
[13]Meng Guang.The nonlinear influences of whirl speed on the stability and response of a cracked rotor[J].Journal of Machine Viration,1992,4:216-230
[14]高建民等.转轴上裂纹开闭模型的研究[J].应用力学学报.1992,9(1):108-112
[15]Nelson H D etal.The dynamic of a rotor system with a cracked shaft[J].ASME Journal of Vibration,Acoustics,Stress,and Reliability in Design,1986,108:189-196
[16]Davies W G R etal.Analysis of the response of a multi-shaft-beating System containing a transverse crack in a rotor.ASME[J].Journal of Vibration and Acoustics;1984,106:139-145
[17]薛璞.具有横向裂纹转子系统的振动特性研究.第五届全国一般力学学术会议论文集[C].北京:北京大学出版社学学报
[18]朱晓梅,高建民.含裂纹转子在变速过程中的瞬态振动[J].固体力学学报.1996,16(1):65-69
[19]Tsai.T.C,Wang Y Z.The vibration of a multi-crack rotor[J].Int.Journal of Mechanical Science,1997,39(9):1037-1053
[20]Muszsynska A.Partial lateral rotor to stator rubs[C].Proc.of Third International Conference on Vibration in Rotation Machinery,C281/84,Mech,Yorkshire,UK,1984,327-335
[21]Szczygieiski W M,Schweltzer G..Dynamics of a high speed rotor touching a boundary[J].Proc.Dynam.of Multibody Systems IUTAM/AFTOMM Symp.Udlne,Italy,1986,287-298
[22]Newkirt B L.Shaft rubbing relative freedom of rotor shafts form sensitiveness to rubbing contact when running above their critical speeds[J].Mech.Eng,1996,48(8):830-832
[23]Muszynska A.Rub-an important malfunction in rotating machinery[J].Proc Senoir Mech.EngrgSem,NV,1983
[24]Kascak A F and Tomko J J.Effects of different rub models on simulated rotor dynamics[J].NASA Technical Paper 2220 ASME Appl.Mech.1983,1-9
[25]Choy F K,Padovan J.Investigation of rub effects of rotor-bearing-Casting system response[J].Proc.of the 40~(th) Mechanical Failures Prevention Group Symposium,National Bureau of Standards,Gaithersburg,Maryland,April,1985
[26]袁惠群.转子系统的若干非线性动力学问题及分岔与混沌研究研究[D].沈阳:东北大学,2000
[27]袁惠群,闻邦椿,李鸿光.非线性转子局部碰摩故障的分叉与混沌行为[J].东北大学学报.2000,21(6):610-613
[28]褚福磊,张正松.转子-轴承系统发生动静件碰摩时的混沌路径[J].应用力学报.1998,15(2):81-86
[29]张宇,陈予恕.转子碰摩非线性动力学特征分析[J].天津大学学报.1998,31(3)
王德友.发电机转静件碰磨振动特征的提取与理论研究[D].北京:北京航空航天大学,1995
[30]刘元峰,赵枚,朱厚军.转子有碰摩和支承松动故障时的混沌特性研究[J].振动与冲击.2002,21(4):36-38
[31]李振平,罗跃纲,姚红良等.具有裂纹-碰摩耦合故障转子-轴承的动力学研究fJ].应用力学学报.2003,20(3):136-140
[32]李振平,闻邦椿等.考虑油膜力的弹性转子系统碰摩故障研究[J].东北大学学报.2002,23(10):980-983
[33]罗跃纲,李振平等.非线性刚度转子松动与碰摩耦合故障动力学特性研究[J].中国机械工程.2003,14(14):1224-1227
[34]刘长利,闻邦椿等.碰摩转子轴承系统非线性振动特征的实验研究[J].东北大学学 报,200324(10):970-973
[35]吴文俊.吴文俊论数学机械化[M].济南:山东科学技术出版社.1996
[36]郭良斌.静压气体轴承静态特征的理论研究综述[J].武汉科技大学学报.2006,29(1):37-40
[37]陈育华,陈世杰.静压气体润滑[M].哈尔滨:工业大学出版社.1990
[38]荣吉利,李瑞英.水轮发电机轴系横向振动响应的时间有限元法[J].北京理工大学学报.2001,21(5):553-557
[39]于开平,邹经湘等.用于求解结果动力响应的不协调时间有限元法[J].振动工程学报.1998,11(1):85-90
[40]周建房,卓家寿等.基于Hamilton有限元法方法[J].河南大学常州分校学报.2000,14(3):1-6
[2]刘延柱,陈立群.非线性振动[M].第一版.北京:高等教育出版社,2001
[3]陈予恕.非线性振动系统的分叉和混沌理论[M].第一版.北京:高等教育出版社,1993
[4]焦映厚等.非线性转子动力学的研究现状与展望[J].哈尔滨工业大学学报.1999(3):1-4
[5]黄文虎,武新华,焦映厚等[J].非线性转子动力学研究综述.振动工程学报.2000(4):479-509
[6]苏少锦,谢元广,龙新峰.汽轮机发电机组动静碰摩故障的诊断与处理[J].电力设备,2006,(09):75-78
[7]钟一谔等.转子动力学[M].北京:清华大学出版社,1987
[8]张文.转子动力学理论基础[M].北京:科学出版社,1990
[9]闻邦椿等.离等转子动力学[M].北京:机械工业出版社,2000
[10]杨志永.高速静电喷漆涡轮系统稳定性理论及结构动态特性研究[D].天津:天津大学,2000
[11]李振平.多故障转子系统若干非线性问题的研究[D].沈阳:东北大学,2002
[12]Mayes I W etal.Analysis of the response of a multi-rotor-bearing system containing a transverse crack in a rotor[J].ASME.Journal of Vibration,Acoustics,Stress,and Reliability in Design,1984,106:139-145
[13]Meng Guang.The nonlinear influences of whirl speed on the stability and response of a cracked rotor[J].Journal of Machine Viration,1992,4:216-230
[14]高建民等.转轴上裂纹开闭模型的研究[J].应用力学学报.1992,9(1):108-112
[15]Nelson H D etal.The dynamic of a rotor system with a cracked shaft[J].ASME Journal of Vibration,Acoustics,Stress,and Reliability in Design,1986,108:189-196
[16]Davies W G R etal.Analysis of the response of a multi-shaft-beating System containing a transverse crack in a rotor.ASME[J].Journal of Vibration and Acoustics;1984,106:139-145
[17]薛璞.具有横向裂纹转子系统的振动特性研究.第五届全国一般力学学术会议论文集[C].北京:北京大学出版社学学报
[18]朱晓梅,高建民.含裂纹转子在变速过程中的瞬态振动[J].固体力学学报.1996,16(1):65-69
[19]Tsai.T.C,Wang Y Z.The vibration of a multi-crack rotor[J].Int.Journal of Mechanical Science,1997,39(9):1037-1053
[20]Muszsynska A.Partial lateral rotor to stator rubs[C].Proc.of Third International Conference on Vibration in Rotation Machinery,C281/84,Mech,Yorkshire,UK,1984,327-335
[21]Szczygieiski W M,Schweltzer G..Dynamics of a high speed rotor touching a boundary[J].Proc.Dynam.of Multibody Systems IUTAM/AFTOMM Symp.Udlne,Italy,1986,287-298
[22]Newkirt B L.Shaft rubbing relative freedom of rotor shafts form sensitiveness to rubbing contact when running above their critical speeds[J].Mech.Eng,1996,48(8):830-832
[23]Muszynska A.Rub-an important malfunction in rotating machinery[J].Proc Senoir Mech.EngrgSem,NV,1983
[24]Kascak A F and Tomko J J.Effects of different rub models on simulated rotor dynamics[J].NASA Technical Paper 2220 ASME Appl.Mech.1983,1-9
[25]Choy F K,Padovan J.Investigation of rub effects of rotor-bearing-Casting system response[J].Proc.of the 40~(th) Mechanical Failures Prevention Group Symposium,National Bureau of Standards,Gaithersburg,Maryland,April,1985
[26]袁惠群.转子系统的若干非线性动力学问题及分岔与混沌研究研究[D].沈阳:东北大学,2000
[27]袁惠群,闻邦椿,李鸿光.非线性转子局部碰摩故障的分叉与混沌行为[J].东北大学学报.2000,21(6):610-613
[28]褚福磊,张正松.转子-轴承系统发生动静件碰摩时的混沌路径[J].应用力学报.1998,15(2):81-86
[29]张宇,陈予恕.转子碰摩非线性动力学特征分析[J].天津大学学报.1998,31(3)
王德友.发电机转静件碰磨振动特征的提取与理论研究[D].北京:北京航空航天大学,1995
[30]刘元峰,赵枚,朱厚军.转子有碰摩和支承松动故障时的混沌特性研究[J].振动与冲击.2002,21(4):36-38
[31]李振平,罗跃纲,姚红良等.具有裂纹-碰摩耦合故障转子-轴承的动力学研究fJ].应用力学学报.2003,20(3):136-140
[32]李振平,闻邦椿等.考虑油膜力的弹性转子系统碰摩故障研究[J].东北大学学报.2002,23(10):980-983
[33]罗跃纲,李振平等.非线性刚度转子松动与碰摩耦合故障动力学特性研究[J].中国机械工程.2003,14(14):1224-1227
[34]刘长利,闻邦椿等.碰摩转子轴承系统非线性振动特征的实验研究[J].东北大学学 报,200324(10):970-973
[35]吴文俊.吴文俊论数学机械化[M].济南:山东科学技术出版社.1996
[36]郭良斌.静压气体轴承静态特征的理论研究综述[J].武汉科技大学学报.2006,29(1):37-40
[37]陈育华,陈世杰.静压气体润滑[M].哈尔滨:工业大学出版社.1990
[38]荣吉利,李瑞英.水轮发电机轴系横向振动响应的时间有限元法[J].北京理工大学学报.2001,21(5):553-557
[39]于开平,邹经湘等.用于求解结果动力响应的不协调时间有限元法[J].振动工程学报.1998,11(1):85-90
[40]周建房,卓家寿等.基于Hamilton有限元法方法[J].河南大学常州分校学报.2000,14(3):1-6
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