不同边界条件下高速旋转带篦齿薄壁短圆柱壳的行波共振特性研究
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摘要
基于传递矩阵法研究了不同边界条件下高速旋转带周向篦齿薄壁短圆柱壳构件的行波共振特性。基于Love壳体理论,考虑离心力、科氏力和惯性力的影响,建立了旋转态薄壁圆柱壳的振动微分方程;引入传递矩阵法,通过壳体子段间的状态向量推导得到了整体结构的传递矩阵关系式;在简支-简支、固支-固支、固支-简支、固支-自由和简支-自由五种边界条件下,通过高精度的精细积分法进行求解,得到了构件的行波共振特性。算例结果表明,在固支-自由边界条件下第1阶模态振动发生在(1,3)阶,而在其它边界条件下第1阶模态振动发生在(1,4)阶,而且边界条件不同时前六阶模态分布规律也不同,但均以周向模态的振动为主;在3×104 r/min转速范围内,随着转速的逐渐增加,由于科氏力作用引起后行波频率大于前行波频率;同时,不同的边界条件对共振特性的影响不同,在工作转速附近行波频率线与激振频率线K=1或K=2相交,出现了共振裕度小于10%的共振转速点,共振裕度数值越小越容易引起对应阶次的共振,应采取措施避免共振现象的发生。
The travelling wave resonance characteristics of a high-speed rotating thin short cylindrical shell component with circumferential sealing teeth were studied in various boundary conditions based on the transfer matrix method. The vibration differential equations of the rotating thin cylindrical shell were set up based on the Love's shell theory,in which centrifugal forces,coriolis forces and inertial forces were involved. Utilizing the continuity of state vectors at the interfaces between sub-segments,the transfer matrix method was introduced to derive the transfer matrix of the overall structure. Then,its resonance characteristics were solved by the high-precise integration method in simply supported-simply supported, clamped-clamped, clamped-simply supported, clamped-free and simply supported-free boundary conditions. The examples ' results show that the first-order modal vibration occurs in the( 1,3) order in clamped-free boundary condition,while the first-order mode vibrations occur in the( 1,4) order in other boundary conditions. The distribution of the first six order modals is also different when the boundary conditions are various,but the vibration modals are mainly presented in circumferential direction in the five boundary conditions. In the speed range of 3× 104 r/min,the backward traveling wave frequencies are greater than the forward ones due to the coriolis force with the gradual increase of rotating speed. The influence of different boundary conditions on the resonant characteristics is different,and the traveling wave frequency lines intersect the excitation frequency lines of K = 1 or K = 2 in the vicinity of the operating speed. At the same time,the resonant speed points with a resonance tolerance of less than 10% appear,and it is easier to cause the corresponding order resonance with a smaller resonant tolerance value,so it is necessary to take measures to avoid the occurrence of resonance phenomenon.
The travelling wave resonance characteristics of a high-speed rotating thin short cylindrical shell component with circumferential sealing teeth were studied in various boundary conditions based on the transfer matrix method. The vibration differential equations of the rotating thin cylindrical shell were set up based on the Love's shell theory,in which centrifugal forces,coriolis forces and inertial forces were involved. Utilizing the continuity of state vectors at the interfaces between sub-segments,the transfer matrix method was introduced to derive the transfer matrix of the overall structure. Then,its resonance characteristics were solved by the high-precise integration method in simply supported-simply supported, clamped-clamped, clamped-simply supported, clamped-free and simply supported-free boundary conditions. The examples ' results show that the first-order modal vibration occurs in the( 1,3) order in clamped-free boundary condition,while the first-order mode vibrations occur in the( 1,4) order in other boundary conditions. The distribution of the first six order modals is also different when the boundary conditions are various,but the vibration modals are mainly presented in circumferential direction in the five boundary conditions. In the speed range of 3× 104 r/min,the backward traveling wave frequencies are greater than the forward ones due to the coriolis force with the gradual increase of rotating speed. The influence of different boundary conditions on the resonant characteristics is different,and the traveling wave frequency lines intersect the excitation frequency lines of K = 1 or K = 2 in the vicinity of the operating speed. At the same time,the resonant speed points with a resonance tolerance of less than 10% appear,and it is easier to cause the corresponding order resonance with a smaller resonant tolerance value,so it is necessary to take measures to avoid the occurrence of resonance phenomenon.
引文
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[17]李波波,宾光富,韩清凯,等.基于有限元的多转子串联轴系扭转振动特性分析[J].湖南科技大学学报(自然科学版),2014,29(2):31-35.LI Bobo,BIN Guangfu,HAN Qingkai,et al.The method of multi-rotor tandem shafting torsional vibration characteristic analysis based on the finite element[J].Journal of Hunan University of Science&Technology(Natural Science Editon),2014,29(2):31-35.
[18]田野,孙岩桦,丁成伟,等.不同支撑和转子装配方式的高速电机临界转速分析[J].振动与冲击,2013,32(8):24-30.TIAN Ye,SUN Yanhua,DING Chengwei,et al.Critical speeds of a high speed motor with different supports and rotor assembly[J].Journal of Vibration and Shock,2013,32(8):24-30.
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[20]王宇.薄壁圆柱壳的振动特性及其篦齿结构影响研究[D].沈阳:东北大学,2014.
[21]LI H,LAM K Y,NG T Y.Rotating shell dynamics[M].Elsevier,2005.
[22]《中国航空材料手册》编辑委员会.中国航空材料手册[M].北京:中国标准出版社,2002.
[2]SUN S,CAO D,CHU S.Free vibration analysis of thin rotating cylindrical shells using wave propagation approach[J].Archive of Applied Mechanics,2013,83(4):521-531.
[3]SUN S,CHU S,CAO D.Vibration characteristics of thin rotating cylindrical shells with various boundary conditions[J].Journal of Sound and Vibration,2012,331(18):4170-4186.
[4]李文达,杜敬涛,杨铁军,等.边界条件对旋转薄壁圆柱壳结构自由振动行波特性的影响分析[J].振动工程学报,2016,29(3):452-464.LI Wenda,DU Jingtao,YANG Tiejun,et al.Influence of boundary conditions on traveling wave characteristics of thin rotating cylindrical shell structure for free vibration[J].Journal of Vibration Engineering,2016,29(3):452-464.
[5]刘彦琦,秦朝烨,褚福磊.不同边界条件下旋转薄壁圆柱壳的振动特性[J].清华大学学报(自然科学版),2012,52(1):5-9.LIU Yanqi,QIN Zhaoye,CHU Fulei.Vibration characteristics of rotating thin cylindrical shells for various boundary conditions[J].Journal of Tsinghua University(Science and Technology),2012,52(1):5-9.
[6]LIU L,CAO D,SUN S.Vibration analysis for rotating ringstiffened cylindrical shells with arbitrary boundary conditions[J].Journal of Vibration&Acoustics,2013,135(6):2627-2637.
[7]曾亮,李琳.用于篦齿封严装置的减振阻尼环设计理论[J].北京航空航天大学学报,2007,33(5):518-522.ZENG Liang,LI Lin.Design of damping-ring for vibration control in labyrinth air seals[J].Journal of Beijing University of Aeronautics and Astronautics,2007,33(5):518-522.
[8]韩清凯,王宇,李学军.旋转薄壁圆柱壳的高节径振动特性以及篦齿结构的影响[J].中国科学:物理学力学天文学,2013,43(4):436-458.HAN Qingkai,WANG Yu,LI Xuejun.High nodal diameter vibration characteristics of rotating shell and the effects of its sealing teeth[J].Scientia Sinica Physica,Mechanica&Astronomica,2013,43(4):436-458.
[9]王宇,韩清鹏,李昌,等.篦齿对悬臂薄壁圆柱壳模态特性的影响研究[J].噪声与振动控制,2015,35(3):82-86.WANG Yu,HAN Qingpeng,LI Chang,et al.Influence of sealing teeth on the modal characteristics of a cantilever thin cylindrical shell[J].Noise and Vibration Control,2015,35(3):82-86.
[10]王洪玉,秦朝烨,褚福磊,等.航空发动机直通型篦齿封严鼓筒气动力分析[J].工程力学,2013,30(12):267-274.WANG Hongyu,QIN Zhaoye,CHU Fulei,et al.Aerodynamic analysis of straight-through labyrinth seal of the drum of an aeroengine[J].Engineering Mechanics,2013,30(12):267-274.
[11]李罡,祝刚,何清军,等.带阻尼套筒的篦齿封严结构振型协调分析[J].机械强度,2007,29(1):124-129.LI Gang,ZHU Gang,HE Qingjun,et al.Vibration mode harmony analysis gas seals with damping sleeve[J].Journal of Mechanical Strength,2007,29(1):124-129.
[12]梁斌,李戎,刘小宛,等.基于波动法的静水压力下环肋圆柱壳耦合振动特性研究[J].振动与冲击,2014,33(21):142-147.LIANG Bin,LI Rong,LIU Xiaowan,et al.Coupled vibration of ring-stiffened cylindrical shells subjected to hydrostatic pressure using wave propagation method[J].Journal of Vibration and Shock,2014,33(21):142-147.
[13]曹雷,马运义,黄玉盈.基于Riccati传递矩阵法分析水下有限长环肋圆柱壳的声辐射性能[J].振动与冲击,2009,28(9):149-154.CAO Lei,MA Yunyi,HUANG Yuying.Analysis of acoustic radiation of a ring-stiffened cylindrical shell with finite length underwater based on Riccati transfer matrix method[J].Journal of Vibration and Shock,2009,28(9):149-154.
[14]李辉,李其汉,晏砺堂.某实际发动机篦齿封严装置振动特性和稳定性分析[J].航空动力学报,2003,18(1):130-133.LI Hui,LI Qihan,YAN Litang.Vibration character and aeroelastic stability analysis of real labyrinth gas seals[J].Journal of Aerospace Power,2003,18(1):130-133.
[15]王宇,谷月,李晖,等.高速旋转薄壁圆柱壳的行波共振特性研究[J].振动与冲击,2016,35(5):222-227.WANG Yu,GU Yue,LI Hui,et al.Travelling wave resonance characteristics of a high-speed rotating thin cylindrical shell[J].Journal of Vibration and Shock,2016,35(5):222-227.
[16]罗忠,王宇,孙宁,等.不同边界条件下旋转薄壁短圆柱壳的强迫振动响应计算[J].机械工程学报,2015,51(9):64-72.LUO Zhong,WANG Yu,SUN Ning,et al.Forced vibration response calculation of rotating short thin cylindrical shells for various boundary conditions[J].Chinese Journal of Mechanical Engineering,2015,51(9):64-72.
[17]李波波,宾光富,韩清凯,等.基于有限元的多转子串联轴系扭转振动特性分析[J].湖南科技大学学报(自然科学版),2014,29(2):31-35.LI Bobo,BIN Guangfu,HAN Qingkai,et al.The method of multi-rotor tandem shafting torsional vibration characteristic analysis based on the finite element[J].Journal of Hunan University of Science&Technology(Natural Science Editon),2014,29(2):31-35.
[18]田野,孙岩桦,丁成伟,等.不同支撑和转子装配方式的高速电机临界转速分析[J].振动与冲击,2013,32(8):24-30.TIAN Ye,SUN Yanhua,DING Chengwei,et al.Critical speeds of a high speed motor with different supports and rotor assembly[J].Journal of Vibration and Shock,2013,32(8):24-30.
[19]王娇.叶片阻尼结构的振动分析方法及其阻尼抑振效果研究[D].沈阳:东北大学,2013.
[20]王宇.薄壁圆柱壳的振动特性及其篦齿结构影响研究[D].沈阳:东北大学,2014.
[21]LI H,LAM K Y,NG T Y.Rotating shell dynamics[M].Elsevier,2005.
[22]《中国航空材料手册》编辑委员会.中国航空材料手册[M].北京:中国标准出版社,2002.