含摩擦与间隙的失谐叶盘系统振动局部化研究
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摘要
针对叶片榫头与轮盘榫槽连接处间隙及摩擦,基于叶盘结构典型集中参数模型,建立含干摩擦、间隙的非线性动力学方程,研究失谐叶盘系统振动局部化。在叶身刚度随机失谐下分析叶盘系统对不同耦合刚度的固有特性及共振响应。结果表明,非线性谐调叶盘系统亦出现振动局部化现象。利用振幅放大系数对线性、非线性失谐叶盘系统振动响应局部化研究,振幅放大系数呈失谐阈值现象,且非线性干摩擦、间隙作用会降低失谐系统振动响应局部化程度。而谐调叶盘系统非线性振动研究表明,随气流激励力频率变化,系统呈非简谐单周期运动、多周期谐波运动、混沌运动等多种动力学行为。失谐因素存在会使非线性失谐叶盘系统动力学行为更复杂。
Based on the lumped parameter model of a bladed disk,the vibration localization of a mistuned bladed disk was investigated in consideration of nonlinear parameters such as dry friction and gap in connections between blade tenton and mortise. For systems with different coupling stiffness,the natural frequencies and resonance responses were discussed under random mistuning of the blades stiffnesses. The results show that the vibration localization would also appear in the tuned system with nonlinear factors. Using the amplitude magnification factor( AMF),the vibration response localization of linear and nonlinear mistuned bladed disks was explored,and the existence of an AMF's threshold was uncovered. The degree of vibration response localization of the mistuned system will reduce because of the participation of nonlinear dry friction and gap. The analysis of nonlinear tuned system under different excitation frequencies turns to reveal the nonlinear dynamics behaviors such as non-harmonic periodic-one motion,multi-period harmonic motion and chaotic motion of the system. Besides,as the mistuning factor exists,the behaviors of nonlinear mistuned disk systems become more complex.
Based on the lumped parameter model of a bladed disk,the vibration localization of a mistuned bladed disk was investigated in consideration of nonlinear parameters such as dry friction and gap in connections between blade tenton and mortise. For systems with different coupling stiffness,the natural frequencies and resonance responses were discussed under random mistuning of the blades stiffnesses. The results show that the vibration localization would also appear in the tuned system with nonlinear factors. Using the amplitude magnification factor( AMF),the vibration response localization of linear and nonlinear mistuned bladed disks was explored,and the existence of an AMF's threshold was uncovered. The degree of vibration response localization of the mistuned system will reduce because of the participation of nonlinear dry friction and gap. The analysis of nonlinear tuned system under different excitation frequencies turns to reveal the nonlinear dynamics behaviors such as non-harmonic periodic-one motion,multi-period harmonic motion and chaotic motion of the system. Besides,as the mistuning factor exists,the behaviors of nonlinear mistuned disk systems become more complex.
引文
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[26]陈广艳,陈国定,李永祥,等.考虑齿侧间隙影响的直齿面齿轮传动动力学分析[J].机械科学与技术,2009,28(9):1244-1251.CHEN Guang-yan,CHEN Guo-ding,LI Yong-xiang,et al.Dynamic analysis of a face-gear drive with spur involute pinion with bachlash considered[J].Mechanical Science and Technology for Aerospace Engineering,2009,28(9):1244-1251.
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[2]臧朝平,兰海强.失谐叶盘结构振动问题研究新进展[J].航空工程进展,2011,2(2):133-142.ZANG Chao-ping,LAN Hai-qiang.Advances in research vibration problem of mistuned blisk assemblies[J].Advances in Aeronautical Science and Engineering,2011,2(2):133-142.
[3]王建军,李其汉.航空发动机失谐叶盘振动减缩模型与应用[M].北京:国防工业出版社,2009.
[4]王红建.复杂耦合失谐叶身-轮盘系统振动局部化问题研究[D].西安:西北工业大学,2006.
[5]Castanier M P,Pierre C.Modeling and analysis of mistuned bladed disk vibration:current status and emerging directions[J].Journal of Propulsion and Power,2006,22(2):384-396.
[6]Castanier M P,Pierre C.Using intentional mistuning in the design of turbomachinery rotors[J].AIAA Journal,2002,40(10):2077-2086.
[7]王建军,于长波,姚建尧,等.失谐叶盘振动模态局部化定量描述方法[J].推进技术,2009,30(4):457-461.WANG Jian-jun,YU Chang-bo,YAO Jian-yao,et al.Vibratory mode localization factors of mistuned bladed disk assemblies[J].Journal of Propulsion Technology,2009,30(4):457-461.
[8]王培屹,李琳.叶盘结构盘片耦合振动特性的参数敏感性[J].航空动力学报,2014,29(1):81-90.WANG Pei-yi,LI Lin.Parametric sensitivity for coupling vibration characteristics of bladed disk[J].Journal of Aerospace Power,2014,29(1):81-90.
[9]Choi B K,Lentz J,Rivas Guerra A J,et al.Optimizations of intentional mistuning patterns for the reduction of the forced response effects of unintentional mistuning[J].Journal of Engineering for Gas Turbines and Power,2003,125(1):131-140.
[10]Wei S T,Pierre C.Statistical analysis of the forced response of mistuned cyclic assemblies[J].AIAA Journal,1990,28(5):861-868.
[11]刘长福,邓明.航空发动机结构分析[M].西安:西北工业大学出版社,2006.
[12]Cierolu E,zgüven H N.Nonlinear vibration analysis of bladed disks with dry friction dampers[J].Journal of Sound and Vibration,2006,295(3):1028-1043.
[13]Sinclair G B,Cormier N G.Contact stresses in dovetail attachments:alleviation via precision crowning[J].Journal of Engineering for Gas Turbines and Power,2003,125(4):1033-1041.
[14]Sinclair G B,Cormier N G.Contact stresses in dovetail attachments physical modeling[J].Journal of Engineering for Gas Turbines and Power,2002,124(2):325-331.
[15]Sinclair G B,Cormier N G,Griffin J H,et al.Contact stresses in dovetail attachments:finite element modeling[J].Journal of Engineering for Gas Turbines and Power,2002,124(1):182-189.
[16]Petrov E P.A method for use of cyclic symmetry properties in analysis of nonlinear multiharmonic vibrations of bladed disks[J].Transactions of the ASME-T-Journal of Turbomachinery,2004,126(1):175-183.
[17]张亮,袁惠群,韩清凯,等.基于微动滑移摩擦模型的失谐叶盘系统振动分析[J].振动工程学报,2012,25(3):289-293.ZHANG Liang,YUAN Hui-qun,HAN Qing-kai,et al.Vibration analysis of mistuned bladed disk system based on microslip friction model[J].Journal of Vibration Engineering,2012,25(3):289-293.
[18]王艾伦,龙清.IHB方法在含强非线性摩擦力失谐叶盘系统响应特性研究中的应用[J].机械强度,2012,34(2):159-164.WANG Ai-lun,LONG Qing.Application of IHB method to study the response characteristics of mistuning bladaded disks with strong non-linear friction[J].Journal of Mechanical Strength,2012,34(2):159-164.
[19]王艾伦,龙清.具有非线性摩擦阻尼随机失谐的叶盘系统响应特性[J].航空动力学报,2011,26(1):178-184.WANG Ai-lun,LONG Qing.Forced response characteristics of bladed disks with random mistuned non-linear friction damping[J].Journal of Aerospace Power,2011,26(1):178-184.
[20]Petrov E P.Analysis of flutter-induced limit cycle oscillations in gas-turbine structures with friction,gap,and other nonlinear contact interfaces[J].Journal of Turbomachinery,2012,134(6):061018-061030.
[21]Berthillier M,Dupont C,Mondal R.Blades forced response analysis with friction dampers[J].Journal of Sound and Vibration,1989,129(3):397-416.
[22]Wei S T,Pierre C.Effect of dry friction damping on the occurrence of localized forced vibration in nearly cyclic structures[J].Journal of Vibration and Acoustics,1998,120:468-474.
[23]Griffin J H,Hoosac T M.Model development and statistical investigation of turbine blade mistuning[J].Journal of Vibration,Acoustics Stress and Reliability in Design,1984,106(2):204-210.
[24]Ghiocel D M,Kirsch U.Combined approximations for efficient probabilistic analysis of structures[J].AIAA Journal,2004,42(7):1321-1330.
[25]Georgiades F,Peeters M,Kerschen G,et al.Modal analysis of a nonlinear periodic structure with cyclic symmetry[J].AIAA Journal,2009,47(4):1014-1025.
[26]陈广艳,陈国定,李永祥,等.考虑齿侧间隙影响的直齿面齿轮传动动力学分析[J].机械科学与技术,2009,28(9):1244-1251.CHEN Guang-yan,CHEN Guo-ding,LI Yong-xiang,et al.Dynamic analysis of a face-gear drive with spur involute pinion with bachlash considered[J].Mechanical Science and Technology for Aerospace Engineering,2009,28(9):1244-1251.
[27]孙智民,季林红,沈允文.2K-H行星齿轮传动非线性动力学[J].清华大学学报:自然科学版,2003,43(5):636-639.SUN Zhi-min,JI Lin-hong,SHEN Yun-wen.Nonlinear dynamics of 2K-H planetary gear train[J].Journal of Tsinghua University:Science and Technology,2003,43(5):636-639.