碰摩双转子系统弯扭耦合振动分析与实验
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摘要
针对航空发动机双转子系统,利用拉格朗日方程建立了含碰摩力的弯扭耦合动力学方程,采用龙格-库塔法进行数值计算,结合瀑布图、频谱图、分岔图、庞加莱截面图、幅频曲线分析了弯曲振动和扭转振动的频谱特征和分岔特性;利用增量式编码器对转子实验台进行了扭转振动测量,验证了数值计算得到的频率特征。研究结果表明:弯扭振动具有相似的特征频率,包括倍频、分数倍频、工作频率与倍频/分数倍频的组合频率,但扭转振动的特征频率更加明显;两者还具有相似的分岔过程和相同的分岔点,在每个分岔点处都存在幅值跳跃现象。
For a dual-rotor system of aero-engine,the coupled bending and torsional dynamic equations with rub-impact force were first established using the Lagrange equation.The Runge-Kutta method was used for numerical calculation.Combined with waterfall map,spectrum diagram,bifurcation diagram,Poincarémap and amplitude-frequency curve,the spectral characteristics and bifurcation characteristics of the bending vibration and torsional vibration were analyzed.The torsional vibration of the rotor experimental platform was measured by incremental encoders to verify the spectral characteristics obtained from the simulation analysis.The research results show that the torsional vibration exhibits characteristic frequencies similar to bending vibration,including multiple frequency,fractional frequency,and the combined frequency of working frequency and multiple/fractional frequency,but these are more obvious in the torsional vibrations;bending and torsional vibrations have similar bifurcation process and same bifurcation point,and there are jump phenomena of amplitude at each bifurcation point.
For a dual-rotor system of aero-engine,the coupled bending and torsional dynamic equations with rub-impact force were first established using the Lagrange equation.The Runge-Kutta method was used for numerical calculation.Combined with waterfall map,spectrum diagram,bifurcation diagram,Poincarémap and amplitude-frequency curve,the spectral characteristics and bifurcation characteristics of the bending vibration and torsional vibration were analyzed.The torsional vibration of the rotor experimental platform was measured by incremental encoders to verify the spectral characteristics obtained from the simulation analysis.The research results show that the torsional vibration exhibits characteristic frequencies similar to bending vibration,including multiple frequency,fractional frequency,and the combined frequency of working frequency and multiple/fractional frequency,but these are more obvious in the torsional vibrations;bending and torsional vibrations have similar bifurcation process and same bifurcation point,and there are jump phenomena of amplitude at each bifurcation point.
引文
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[10]LU Wenxiu,CHU Fulei.Radial and torsional vibration characteristics of a rub rotor[J].Nonlinear Dynamics,2014,76(1):529-549.
[11]李朝峰,周世华,刘文明,等.齿轮-转子-滚动轴承传动系统的弯扭耦合振动[J].航空动力学报,2014,29(7):1543-1555.LI Chaofeng,ZHOU Shihua,LIU Wenming,et al.Vibration of bending-torsion coupling gear-rotor-rolling bearing transmission system[J].Journal of Aerospace Power,2014,29(7):1543-1555.(in Chinese)
[12]廖明夫,宋明波,张霞妹.转子/机匣碰摩引起的转子弯扭耦合振动[J].振动、测试与诊断,2016,36(5):1009-1017.LIAO Mingfu,SONG Mingbo,ZHANG Xiamei.Coupled bending and torsional vibration due to rotor-casing contact[J].Journal of Vibration,Measurement and Diagnosis,2016,36(5):1009-1017.(in Chinese)
[13]HUA Chunli,CAO Guohua,RAO Zhushi,et al.Coupled bending and torsional vibration of a rotor system with nonlinear friction[J].Journal of Mechanical Science and Technology,2017,31(6):2679-2689.
[14]洪杰,马艳红,张大义.航空燃气轮机总体结构设计与动力学分析[M].北京:北京航空航天大学出版社,2014.
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[16]李杰,曹树谦,郭虎伦,等.机动飞行条件下双转子系统动力学建模与响应分析[J].航空动力学报,2017,32(4):835-849.LI Jie,CAO Shuqian,GUO Hulun,et al.Modeling and response analysis of dual-rotor system under maneuvering flight[J].Journal of Aerospace Power,2017,32(4):835-849.(in Chinese)
[17]晏砺堂,王德友.航空双转子发动机动静件碰摩振动特征研究[J].航空动力学报,1998,13(2):173-176.YAN Litang,WANG Deyou.Vibration features from rubbing between rotor and casing for a dual-shaft aeroengine[J].Journal of Aerospace Power,1998,13(2):173-176.(in Chinese)
[18]周海仑,陈果.航空发动机双转子-滚动轴承-机匣耦合系统动力学分析[J].航空动力学报,2009,24(6):1284-1291.ZHOU Hailun,CHEN Guo.Dynamic response analysis of dual rotor-ball bearing-stator coupling system for aero-engine[J].Journal of Aerospace Power,2009,24(6):1284-1291.(in Chinese)
[19]YANG Yang,CAO Dengqing,YU Tianhu,et al.Prediction of dynamic characteristics of a dual-rotor system with fixed point rubbing:theoretical analysis and experimental study[J].International Journal of Mechanical Sciences,2016,115/116:253-261.
[20]陈会征.挤压油膜阻尼器-滚动轴承-转子系统非线性动力学研究[D].哈尔滨:哈尔滨工业大学,2017.CHEN Huizheng.Study on nonlinear dynamics of squeeze film damper-rolling bearing-rotor systems[D].Harbin:Harbin Institute of Technology,2017.(in Chinese)
[2]陈予恕,李军.汽轮发电机组轴系弯扭耦合振动问题研究综述[J].汽轮机技术,2012,54(3):161-164.CHEN Yushu,LI Jun.Research on bending-torsion coupling vibration of shaft system of turbine generator[J].Turbine Technology,2012,54(3):161-164.(in Chinese)
[3]邓小文,廖明夫,LIMBACH R,等.双盘转子碰摩的弯曲和扭转振动实验研究[J].航空动力学报,2002,17(2):205-211.DENG Xiaowen,LIAO Mingfu,LIMBACH R,et al.Experimental research of bending and torsional vibrations of a double disc rotor due to rotor-to-stator contacts[J].Journal of Aerospace Power,2002,17(2):205-211.(in Chinese)
[4]邓小文,廖明夫,LIMBACH R,等.碰摩转子的弯曲和扭转振动分析[J].航空动力学报,2002,17(1):97-104.DENG Xiaowen,LIAO Mingfu,LIMBACH R,et al.Coupled bending and torsional vibrations due to rotor-to-stator contacts[J].Journal of Aerospace Power,2002,17(1):97-104.(in Chinese)
[5]何成兵,顾煜炯,杨坤.一种新的转子碰摩故障诊断特征的研究[J].机械强度,2003,25(4):355-359.HE Chengbing,GU Yujiong,YANG Kun.Research of a new characteristic for fault diagnosis of rub-impact rotor[J].Journal of Mechanical Strength,2003,25(4):355-359.(in Chinese)
[6]何成兵,顾煜炯,李猛.Jeffcott转子碰摩的弯扭耦合振动特性分析[J].振动与冲击,2006,25(2):59-69.HE Chengbing,GU Yujiong,LI Meng.Characteristic analysis on coupled bending and torsional vibrations of Jeffcott rubbing rotor system[J].Journal of Vibration and Shock,2006,25(2):59-69.(in Chinese)
[7]SUN Zhengce,XU Jianxue,ZHOU Tong,et al.Study on influence of bending-torsion coupling in an impacting-rub rotor system[J].Applied Mathematics and Mechanics,2003,24(11):1316-1323.
[8]ZHANG Kunpeng,DING Qian.Lateral and torsional vibrations of a two-disk rotor-stator system with axial contact/rubs[J].International Journal of Applied Mechanics,2009,1(2):305-326.
[9]TEJAS H P,ZUO Mingjian,ZHAO Xiaomin.Nonlinear lateral-torsional coupled motion of a rotor contacting a viscoelastically suspended stator[J].Nonlinear Dynamics,2012,69(1/2):325-339.
[10]LU Wenxiu,CHU Fulei.Radial and torsional vibration characteristics of a rub rotor[J].Nonlinear Dynamics,2014,76(1):529-549.
[11]李朝峰,周世华,刘文明,等.齿轮-转子-滚动轴承传动系统的弯扭耦合振动[J].航空动力学报,2014,29(7):1543-1555.LI Chaofeng,ZHOU Shihua,LIU Wenming,et al.Vibration of bending-torsion coupling gear-rotor-rolling bearing transmission system[J].Journal of Aerospace Power,2014,29(7):1543-1555.(in Chinese)
[12]廖明夫,宋明波,张霞妹.转子/机匣碰摩引起的转子弯扭耦合振动[J].振动、测试与诊断,2016,36(5):1009-1017.LIAO Mingfu,SONG Mingbo,ZHANG Xiamei.Coupled bending and torsional vibration due to rotor-casing contact[J].Journal of Vibration,Measurement and Diagnosis,2016,36(5):1009-1017.(in Chinese)
[13]HUA Chunli,CAO Guohua,RAO Zhushi,et al.Coupled bending and torsional vibration of a rotor system with nonlinear friction[J].Journal of Mechanical Science and Technology,2017,31(6):2679-2689.
[14]洪杰,马艳红,张大义.航空燃气轮机总体结构设计与动力学分析[M].北京:北京航空航天大学出版社,2014.
[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.
[16]李杰,曹树谦,郭虎伦,等.机动飞行条件下双转子系统动力学建模与响应分析[J].航空动力学报,2017,32(4):835-849.LI Jie,CAO Shuqian,GUO Hulun,et al.Modeling and response analysis of dual-rotor system under maneuvering flight[J].Journal of Aerospace Power,2017,32(4):835-849.(in Chinese)
[17]晏砺堂,王德友.航空双转子发动机动静件碰摩振动特征研究[J].航空动力学报,1998,13(2):173-176.YAN Litang,WANG Deyou.Vibration features from rubbing between rotor and casing for a dual-shaft aeroengine[J].Journal of Aerospace Power,1998,13(2):173-176.(in Chinese)
[18]周海仑,陈果.航空发动机双转子-滚动轴承-机匣耦合系统动力学分析[J].航空动力学报,2009,24(6):1284-1291.ZHOU Hailun,CHEN Guo.Dynamic response analysis of dual rotor-ball bearing-stator coupling system for aero-engine[J].Journal of Aerospace Power,2009,24(6):1284-1291.(in Chinese)
[19]YANG Yang,CAO Dengqing,YU Tianhu,et al.Prediction of dynamic characteristics of a dual-rotor system with fixed point rubbing:theoretical analysis and experimental study[J].International Journal of Mechanical Sciences,2016,115/116:253-261.
[20]陈会征.挤压油膜阻尼器-滚动轴承-转子系统非线性动力学研究[D].哈尔滨:哈尔滨工业大学,2017.CHEN Huizheng.Study on nonlinear dynamics of squeeze film damper-rolling bearing-rotor systems[D].Harbin:Harbin Institute of Technology,2017.(in Chinese)