转子挤压油膜阻尼器减振效率的理论研究
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摘要
针对如何有效降低滚动轴承-转子系统振动幅值的问题,将挤压油膜阻尼器-滚动轴承-双盘转子系统作为研究对象,以雷诺方程、动压润滑理论、短轴承假设、油膜力周向边界条件、非线性赫兹接触理论等为基础,建立转子系统动力学方程,运用Newmark-β迭代数值求解方法结合Newton-Raphson迭代来求解转子系统相应节点的激励响应结果,分析该转子系统非线性动力学特性,从轴心轨迹图和时域曲线图两个方面对比有无挤压油膜阻尼器转子系统的位移响应,从理论角度对转轴振动能量被鼠笼支撑及挤压油膜部分有效吸收的程度进行研究,并对转子系统0～10 000 r/min转速区间下不同阻尼器参数情况下的减振效率进行考量,研究发现转子系统在转速相对较低时减振效果不佳,并分析其原因,研究结果可为转子系统挤压油膜阻尼器的结构参数设计提供理论依据。
According to the problem of how to effectively reduce the vibration amplitude of the rotor system supported by rolling bearings, using the squeeze oil film damper-rolling bearing-double disc rotor system as the research object, the dynamic equation of rotor system is established on the basis of the Reynolds equation, hydrodynamic lubrication theory, short bearing assumption,circumferential boundary conditions of oil film force and nonlinear Hertz contact theory. The results of excitation response at corresponding nodes of the rotor system are solved by utilizing the Newmark-β method combined with Newton-Raphson iteration,then the nonlinear dynamics of the rotor system is analyzed. The displacement responses of the rotor system in the case of the presence and absence of the squeeze film damper are compared with the two aspects of the orbit diagram of axle center and the time domain graph. Then whether the vibration energy of the rotating shaft is effectively absorbed by the squirrel cage and squeezed oil film is analyzed in theory. Moreover, the damping efficiency of different damper parameters is also studied in the 0～10 000 r/min speed range and the reasons for the poor damping efficiency when the rotor speed is relatively low are analyzed emphatically. The results of this study can provide theoretical basis for the design of structural parameters of the squeeze film dampers applied to rotor systems with different dynamic characteristics.
According to the problem of how to effectively reduce the vibration amplitude of the rotor system supported by rolling bearings, using the squeeze oil film damper-rolling bearing-double disc rotor system as the research object, the dynamic equation of rotor system is established on the basis of the Reynolds equation, hydrodynamic lubrication theory, short bearing assumption,circumferential boundary conditions of oil film force and nonlinear Hertz contact theory. The results of excitation response at corresponding nodes of the rotor system are solved by utilizing the Newmark-β method combined with Newton-Raphson iteration,then the nonlinear dynamics of the rotor system is analyzed. The displacement responses of the rotor system in the case of the presence and absence of the squeeze film damper are compared with the two aspects of the orbit diagram of axle center and the time domain graph. Then whether the vibration energy of the rotating shaft is effectively absorbed by the squirrel cage and squeezed oil film is analyzed in theory. Moreover, the damping efficiency of different damper parameters is also studied in the 0～10 000 r/min speed range and the reasons for the poor damping efficiency when the rotor speed is relatively low are analyzed emphatically. The results of this study can provide theoretical basis for the design of structural parameters of the squeeze film dampers applied to rotor systems with different dynamic characteristics.
引文
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[14]陈果.带碰摩耦合故障的转子-滚动轴承-机匣耦合动力学模型[J].振动工程学报,2007,20(4):362-368.CHEN Guo.Coupling dynamic model of rotor-rolling-bearing-casing with rubbing coupling fault[J].Journal of Vibration Engineering,2007,20(4):362-368.
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[17]周生通,李鸿光,张龙,等.基于嵌入式谱随机有限元法的转子系统随机不平衡响应特性分析[J].振动与冲击,2016,35(19):45-49.ZHOU Shengtong,LI Hongguang,ZHANG Long,et al.Stochastic unbalance response characteristics of rotor systems based on intrusive spectral stochastic finite element method[J].Jouranl of Vibration and Shock,2016,35(19):45-49.
[18]牛晓东,王维民,李启行,等.一种用于离心压缩机转子稳定性控制的电磁阻尼器设计及应用[J].北京化工大学学报,2016,43(4):109-114.NIU Xiaodong,WANG Weimin,LI Qixing,et al.Design and application of an electromagnetic damper for the stability control of the rotor of a centrifugal compressor[J].Journal of Beijing University of Chemical Technology,2016,43(4):109-114.
[19]DENG Xingqiao,ZHU Weibing,CHEN Yonghong,et al.Optimal design for an end face engagement worm gear with multiple worm-wheel meshing[J].Chinese Journal of Mechanical Engineering,2017,30(2):144-151.
[2]GUNDUZ A,DREYER J T,SINGH R.Effect of bearing preloads on the modal characteristics of a shaft-bearing assembly:Experiments on double row angular contact ball bearings[J].Mechanical Systems and Signal Processing,2012,31:176-195.
[3]CHAVEZ J P,WIERCIGROCH M.Bifurcation analysis of periodic orbits of a non-smooth Jeffcott rotor model[J].Communications in Nonlinear Science and Numerical Simulation,2013,18(9):2571-2580.
[4]EI-SAEIDY F M A.Time-varying total stiffness matrix of a rigid machine spindle-angular contact ball bearings assembly:Theory and analytical/experimental verifications[J].Shock and Vibration,2011,18(5):641-670.
[5]祝长生,汪希萱.新型动静压挤压油膜阻尼器对柔性转子系统振动的控制[J].机械工程学报,1996,32(3):76-83.ZHU Changsheng,WANG Xixuan.Vibration control of a flexible rotor system by a new type of dynamic and static pressure squeeze film damper[J].Chinese Jouranl of Mechanical Engineering,1996,32(3):76-83.
[6]秦卫阳,张劲夫,王宏,等.带弹性支撑的挤压油膜阻尼器转子响应与分叉[J].西北工业大学报,2006,24(2):246-348.QIN Weiyang,ZHANG Jinfu,WANG Hong,et al.Response and bifurcation of the rotor system with Squeeze film dampers and supported by elastic support[J].Journal of Northwestern Polytechnical University,2006,24(2):246-348.
[7]王红瑾,秦卫阳,杨树林,等.带挤压油膜阻尼器双盘转子的参数变化对系统响应的影响[J].航空动力学报,2009,24(11):2546-2550.WANG Hongjin,QIN Weiyang,YANG Shulin,et al.Response of two-disk rotor with squeeze film dampers and its variation with parameters[J].Journal of Aerospace Power,2009,24(11):2546-2550.
[8]桑潇潇,廖明夫,李为.故障转子挤压油膜阻尼器减振特性实验[J].振动、测试与诊断,2015,35(5):978-998.SANG Xiaoxiao,LIAO Mingfu,LI Wei.Damping characteristics test of squeeze film damper with fault rotor[J].Journal of Vibration,Measurement&Diagnosis,2015,35(5):978-998.
[9]刘展翅,廖明夫,丛佩红,等.航空发动机转子挤压油膜阻尼器设计方法[J].航空动力学报,2015,30(11):2763-2770.LIU Zhangchi,LIAO Mingfu,CONG Peihong,et al.Design method of squeeze film damper for aero-engine rotors[J].Journal of Aerospace Power,2015,30(11):2763-2770.
[10]BONELLO P,BRENNAN M J,HOLMES R.Non-linear modelling of rotor dynamic systems with squeeze film dampers-an efficient integrated approch[J].Journal of Sound&Vibration,2002,249(4):743-773.
[11]洪杰,邓吟,张大义.弹性环式挤压油膜阻尼器动力设计方法[J].北京航空航天大学学报,2006,32(6):649-653.HONG Jie,DENG Yin,ZHANG Dayi.Dynamic design method of elastic ring squeeze film damper[J].Journal of Beijing University Aeronautics and Astronautics,2006,32(6):649-653.
[12]徐万孚,温志健,徐礼富,等.带有弹性支承与挤压油膜阻尼器的高速传动试验台[J].机械工程学报,2004,40(9):144-147.XU Wanfu,WEN Zhijian,XU Lifu,et al.High-spped transmission test-bed with elastic support and squeeze film damper[J].Chinese Jouranl of Mechanical Engineering,2004,40(9):144-147.
[13]ZHANG Wei,DING Qian.Elastic ring deformation and pedestal contact status analysis of elastic ring squeeze film damper[J].Journal of Sound&Vibration,2015,346(1):314-327.
[14]陈果.带碰摩耦合故障的转子-滚动轴承-机匣耦合动力学模型[J].振动工程学报,2007,20(4):362-368.CHEN Guo.Coupling dynamic model of rotor-rolling-bearing-casing with rubbing coupling fault[J].Journal of Vibration Engineering,2007,20(4):362-368.
[15]航空发动机设计手册总编委会.航空发动机设计手册.第19册:转子动力学及整机振动[M].北京:航空工业出版社,2000.General editorial board of aero engine design manual.Aero engine design manual.Nineteenth:Rotor dynamics and whole machine vibration[M].Beijing:Aeronautical Industry Press,2000.
[16]韩清凯,于涛,王德友,等.故障转子系统的非线性振动分析与诊断方法[M].北京:科学出版社,2010.HAN Qingkai,YU Tao,WANG Deyou,et al.Nonlinear vibration analysis and diagnosis methods of fault rotor system[M].Beijing:Science Press,2010.
[17]周生通,李鸿光,张龙,等.基于嵌入式谱随机有限元法的转子系统随机不平衡响应特性分析[J].振动与冲击,2016,35(19):45-49.ZHOU Shengtong,LI Hongguang,ZHANG Long,et al.Stochastic unbalance response characteristics of rotor systems based on intrusive spectral stochastic finite element method[J].Jouranl of Vibration and Shock,2016,35(19):45-49.
[18]牛晓东,王维民,李启行,等.一种用于离心压缩机转子稳定性控制的电磁阻尼器设计及应用[J].北京化工大学学报,2016,43(4):109-114.NIU Xiaodong,WANG Weimin,LI Qixing,et al.Design and application of an electromagnetic damper for the stability control of the rotor of a centrifugal compressor[J].Journal of Beijing University of Chemical Technology,2016,43(4):109-114.
[19]DENG Xingqiao,ZHU Weibing,CHEN Yonghong,et al.Optimal design for an end face engagement worm gear with multiple worm-wheel meshing[J].Chinese Journal of Mechanical Engineering,2017,30(2):144-151.