基于压电纤维复合材料的旋转叶片主动控制

张博; 丁虎; 陈立群

doi:10.6052/0459-1879-20-448

基于压电纤维复合材料的旋转叶片主动控制

doi: 10.6052/0459-1879-20-448

张博^*,†,2), ,,
丁虎^†,
陈立群^**,3), ,

^*长安大学理学院, 西安 710064
^†上海大学力学与工程科学学院, 上海 200444
^**哈尔滨工业大学(深圳)理学院力学系, 广东深圳 518055

基金项目: 1)国家自然科学基金(11702033);国家自然科学基金(11872159);中央高校基本科研业务费专项资金(300102120106);上海市教委创新项目(2017-01-07-00-09-E00019)

详细信息

作者简介:
3)陈立群, 教授, 主要研究方向: 非线性动力学和振动控制. E-mail: chenliqun@hit.edu.cn
2)张博, 讲师, 主要研究方向: 非线性动力学与振动控制. E-mail: zhang_bo@chd.edu.cn;

通讯作者:
张博

陈立群

中图分类号: O322
计量
- 文章访问数: 673
- HTML全文浏览量: 110
- PDF下载量: 219
- 被引次数: 0
出版历程
- 收稿日期: 2020-12-24
- 刊出日期: 2021-04-10

ACTIVE VIBRATION CONTROL OF A ROTATING BLADE BASED ON MACRO FIBER COMPOSITE

Zhang Bo^{*,†,2)
, ,},
Ding Hu^†,
Chen Liqun^{**,3)
, ,}

^*School of Science, Chang'an University, Xi'an 710064, China
^†School of Mechanics and Engineering Sciences, Shanghai University, Shanghai 200444, China
^**School of Science, Harbin Institute of Technology, Shenzhen 518055, Guangdong, China

摘要

摘要: 旋转叶片结构的振动失效占据了航空发动机整机故障的相当比重. 发展针对旋转叶片结构的减振技术对于减轻叶片重量, 提升叶片性能, 延长叶片寿命具有重要意义. 通过引入压电纤维复合材料(macro fiber composite, MFC)传感器和作动器, 研究预变形旋转叶片2:1内共振的主动控制. 建立考虑时滞效应的旋转叶片比例微分闭环控制系统运动方程. 通过摄动分析推导出受控叶片的演化方程, 并结合延拓法揭示速度增益、位移增益、时滞量等系统参数对受控系统稳态响应及稳定性的影响规律. 理论研究结果与数值结果得到相互验证. 研究发现时滞量对系统稳定性影响显著, 当时滞超过某临界值时, 演化方程原有的平衡点失稳, 闭环受控系统将缓慢进入一个大振幅的周期运动, 从而丧失控制效果. 位移增益存在一个范围使得系统出现多值稳态响应, 进而破坏了增益平面内系统稳定区和非稳定区域的直线边界. 不恰当的速度增益和位移增益会给受控系统引入新的共振. 研究结果为叶片结构的减振提供了理论基础.
- 压电纤维复合材料 /
- 预变形旋转叶片 /
- 主动控制 /
- 稳定性 /
- 多尺度法
Abstract: For a long time, blade vibration failure occupies a quite large proportion of the total failure of the complete aeroengine. Developing the vibration reduction technology is of great importance for reducing the weight, improving the performance and extending the life for the rotating blade structure. In the present paper, the active vibration control is investigated in the presence of the 2:1 internal resonance of a pre-deformed rotating blade through introducing the sensors and actuators made of macro fiber composite (MFC). The equations of motion of the proportional-derivative feedback closed-loop control system are established with the effects of the time delay. The evolution equations of the controlled system are derived via the perturbation analysis. The effects of the velocity gain, the displacement gain, the time delay and some other system parameters on the steady-state response and the stabilities of the controlled system are revealed by the application of the continuation method. The analytic solutions are in good agreement with those obtained from the numerical integration. The main findings of the present study are as followings: the time delay has a significant effect on the stabilities of the controlled system. When the time delay exceeds a certain value, the equilibrium points of the evolution equations lose their stability. At the same time, the closed-loop control system enters a new period motion with a large vibration amplitude. There exists a range of displacement gain in which the multi-valued phenomenon appears in the steady-state response of the controlled system. Moreover, the straight borderline between the stable and the unstable regions in the gains plane is destroyed due to this range. Inappropriate assignments of the velocity gain and the displacement gain will cause a new resonance in the close-loop control system. The research results lay the theoretical foundations for the vibration reduction of the blade structure.
- macro fiber composite /
- pre-deformed rotating blade /
- active vibration control /
- stabilities /
- multiple scales method

HTML全文

参考文献(33)

[1]	Yoo HH, Park JH, Park J. Vibration analysis of rotating pre-twisted blades. Computers & Structures, 2001,79(19):1811-1819
[2]	Yoo HH, Shin SH. Vibration analysis of rotating cantilever beams. Journal of Sound and Vibration, 1998,212(5):807-828
[3]	Yao MH, Chen YP, Zhang W. Nonlinear vibrations of blade with varying rotating speed. Nonlinear Dynamics, 2012,68(4):487-504
[4]	Yao MH, Zhang W, Chen YP. Analysis on nonlinear oscillations and resonant responses of a compressor blade. Acta Mechanica, 2014,225(12):3483-3510
[5]	张伟, 冯志青, 曹东兴. 航空发动机叶片非线性动力学分析. 动力学与控制学报, 2012,10(3):213-221 (Zhang Wei, Feng Zhiqing, Cao Dongxing. Analysis on nonlinear dynamics of the aero-engine blade. Journal of Dynamics and Control, 2012,10(3):213-221 (in Chinese))
[6]	王延庆, 郭星辉, 梁宏琨等. 凸肩叶片的非线性振动特性与运动分岔. 力学学报, 2011,43(4):755-764 (Wang Yanqing, Guo Xinghui, Liang Hongkun, et al. Nonlinear vibratory characteristics and bifurcations of shrouded blades. Chinese Journal of Theoretical and Applied Mechanics, 2011,43(4):755-764 (in Chinese))
[7]	Zhang W, Niu Y, Behdinan K. Vibration characteristics of rotating pretwisted composite tapered blade with graphene coating layers. Aerospace Science and Technology, 2020,98:105644
[8]	Takabatake H. Effect of dead loads on natural frequencies of beams. Journal of Structural Engineering-Asce, 1991,117(4):1039-1052
[9]	Zhang B, Li YM. Nonlinear vibration of rotating pre-deformed blade with thermal gradient. Nonlinear Dynamics, 2016,86(1):459-478
[10]	Zhang B, Zhang YL, Yang XD, et al. Saturation and stability in internal resonance of a rotating blade under thermal gradient. Journal of Sound and Vibration, 2019,440(3):34-50
[11]	Zhang B, Ding H, Chen LQ. Super-harmonic resonances of a rotating pre-deformed blade subjected to gas pressure. Nonlinear Dynamics, 2019,98(4):2531-2549
[12]	Zhang B, Ding H, Chen LQ. Subharmonic and combination resonance of rotating pre-deformed blades subjected to high gas pressure. Acta Mechanica Solida Sinica, 2020,33(5):635-649
[13]	Zhang B, Ding H, Chen LQ. Three to one internal resonances of a pre-deformed rotating beam with quadratic and cubic nonlinearities. International Journal of Non-Linear Mechanics, 2020,126:103552
[14]	顾伟, 张博, 丁虎等. 2:1内共振条件下变转速预变形叶片的非线性动力学响应. 力学学报, 2020,52(4):1131-1142 (Gu Wei, Zhang Bo, Ding Hu, et al. Nonlinear dynamic response of pre-deformation blade with variable rotational speed under 2:1 internal resonance. Chinese Journal of Theoretical and Applied Mechanics, 2020,52(4):1131-1142 (in Chinese))
[15]	Geng XF, Ding H, Wei KX, et al. Suppression of multiple modal resonances of a cantilever beam by an impact damper. Applied Mathematics and Mechanics-English Edition, 2020,41(3):383-400
[16]	张红艳, 白长青, 许庆余. 多自由度复杂结构的TMD调谐减震控制研究. 应用力学学报, 2008, 25(4): 583-587, 731-732 (Zhang Hongyan, Bai Changqing, Xu Qingyu. TMD Design for seismic protection of multi-degree of freedom complex structures. Chinese Journal of Applied Mechanics, 2008, 25(4): 583-587, 731-732 (in Chinese))
[17]	徐鉴. 振动控制研究进展综述. 力学季刊, 2015,36(4):547-565 (Xu Jian. Advances of research on vibration contro. Chinese Quarterly of Mechanics, 2015,36(4):547-565 (in Chinese))
[18]	王在华, 胡海岩. 具有采样反馈的力控制系统稳定性. 力学学报, 2016,48(6):1372-1381 (Wang Zaihua, Hu Haiyan. Stability of a force control system with sampled-data feedback. Chinese Journal of Theoretical and Applied Mechanics, 2016,48(6):1372-1381 (in Chinese))
[19]	王强, 梁松, 王在华. 基于采样PD反馈的倒立摆控制系统的稳定性. 动力学与控制学报, 2018,16(4):377-384 (Wang Qiang, Liang Song, Wang Zaihua. Stability of an inverted pendulum with a sampled-data PD feedback control. Journal of Dynamics and Control, 2018,16(4):377-384 (in Chinese))
[20]	Bailey T, Ubbard JE Jr. Distributed piezoelectric-polymer active vibration control of a cantilever beam. Journal of Guidance, Control, and Dynamics, 1985,8(5):605-611
[21]	陶鸿飞, 崔升. 压电智能结构的主动控制及压电执行器布局优化. 动力学与控制学报, 2019,17(3):234-243 (Tao Hongfei, Cui Sheng. Active control of piezoelectric structures and optimal placement of piezoelectric actuators. Journal of Dynamics and Control, 2019,17(3):234-243 (in Chinese))
[22]	涂建维, 张家瑞, 罗威等. 宏纤维复合平板结构的作动方程与试验验证. 武汉大学学报(工学版), 2019,52(4):324-330 (Tu Jianwei, Zhang Jiarui, Luo Wei, et al. Actuating equation and experimental verification of macro-fiber composite coupled-plate structures. Engineering Journal of Wuhan University, 2019,52(4):324-330 (in Chinese))
[23]	李蒙, 李凤明. 采用MFC压电作动器对复合材料悬臂板振动主动控制. 动力学与控制学报, 2017,15(4):342-349 (Li Meng, Li Fengming. Active vibration control of a catilevered laminated plate using MFC actuators. Journal of Dynamics and Control, 2017,15(4):342-349 (in Chinese))
[24]	孙杰, 孙俊, 刘付成等. 含间隙铰接的柔性航天器刚柔耦合动力学与控制研究. 力学学报, 2020,52(6):1569-1580 (Sun Jie, Sun Jun, Liu Fucheng, et al. Dynamics and control of rigid-flexible coupling flexible spacecraft with joint clearance. Chinese Journal of Theoretical and Applied Mechanics, 2020,52(6):1569-1580 (in Chinese))
[25]	Min JB, Duffy KP, Choi BB, et al. Numerical modeling methodology and experimental study for piezoelectric vibration damping control of rotating composite fan blades. Computers and Structures, 2013,128:230-242
[26]	Kandil Ali, El-Gohary Hany A. Suppressing the nonlinear vibrations of a compressor blade via a nonlinear saturation controller. Journal of Vibration and Control, 2018,24(8):1488-1504
[27]	Kandil A, El-Ganaini WA. Investigation of the time delay effect on the control of rotating blade vibrations. European Journal of Mechanics A-Solids, 2018,72:16-40
[28]	Kandil A, El-Gohary H. Investigating the performance of a time delayed proportional-derivative controller for rotating blade vibrations. Nonlinear Dynamics, 2018,91(4):2631-2649
[29]	唐冶, 王涛, 丁千. 主动控制压电旋转悬臂梁的参数振动稳定性分析. 力学学报, 2019,51(6):1872-1881 (Tang Ye, Wang Tao, Ding Qian. Stability analysis on parametric vibration of piezoelectric rotating cantilever beam with active control. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(6):1872-1881 (in Chinese))
[30]	韩江, 乔印虎, 张春燕等. 智能风力机叶片振动主动控制研究综述. 应用力学学报, 2015,32(3):446-453, 449 (Han Jiang, Qiao Yinhu, Zhang Chunyan, et al. The review for elastomer smart active wind turbine blade vibration control. Chinese Journal of Applied Mechanics, 2015,32(3):446-453, 449 (in Chinese))
[31]	姚晓成, 赵程, 曾涛. 压电材料在振动控制领域的研究进展与应用现状. 机械工程材料, 2019,43(6):72-76 (Yao Xiaocheng, Zhao Cheng, Zeng Tao. Research progress and application status of piezoelectric materials for vibration control. Materials for Mechanical Engineering, 2019,43(6):72-76 (in Chinese))
[32]	胡海岩. 线性受控系统的反馈时滞可辨识性. 振动工程学报, 2001(2):41-45 (Hu Haiyan. Identifiability of feedback delays of linear controlled systems. Journal of Vibration Engineering, 2001(2):41-45 (in Chinese))
[33]	Hu HY, Wang ZH. Stability analysis of damped SDOF systems with two time delays in state feedback. Journal of Sound and Vibration, 1998,214(2):213-225