基于时滞半主动控制的起落架摆振反共振峰优化

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (8) : 341-350.

论文

李非凡，赵艳影

作者信息 +

Anti-resonance optimization of landing gear shimmy based on time-delay semi-active control

LI Feifan, ZHAO Yanying

Author information +

文章历史 +

摘要

考虑在飞机起落架上加装磁流变减摆器并考虑摆振过程中存在的时滞问题，利用时滞半主动控制来达到降幅优化的目的。首先，为了排除量纲的影响使得到的结果更能描述客观普遍规律，对摆振方程组无量纲化处理后分析了无量纲磁流变阻尼器阻尼系数对摆振振幅的影响。然后，为了进一步降低幅值，设计优化准则将反共振峰幅值限制在足够小的范围内。在摆振方程组中引入时滞半主动控制项，提出了一种求解时滞动力学方程的特征方程的数学方法，利用时滞半主动控制可将反共振峰幅值控制在较低水平且几乎消除了第二个共振峰。最后，在频域和时域上做了验证与对比分析，证明了计算的正确性和时滞半主动控制减振效果的优越性。

Abstract

Considering the installation of MR damper on the aircraft landing gear and the time-delay issue in the process of shimmy, the time-delay semi-active control is used to achieve the purpose of amplitude reduction optimization. Firstly, in order to eliminate the influence of dimensionality and make the results better describe the objective universal law, after dimensionless treatment of the shimmy equations, the influence of dimensionless MR damper damping coefficient on the shimmy amplitude is analyzed. Then, in order to further reduce the amplitude, the design optimization criterion limits the anti-resonance amplitude in a small enough range. The time-delay semi-active control term is introduced into the shimmy equations, and a mathematical method for solving the characteristic equation of the time-delay dynamic equation is proposed. The anti-resonance amplitude can be controlled at a low level by using the time-delay semi-active control, and the second resonance can be almost eliminated. Lastly, it is verified and compared in the frequency domain and time domain, the correctness of the calculation and the superiority of time-delay semi-active control are proved.

导出引用

李非凡，赵艳影. 基于时滞半主动控制的起落架摆振反共振峰优化[J]. 振动与冲击, 2023, 42(8): 341-350

LI Feifan, ZHAO Yanying. Anti-resonance optimization of landing gear shimmy based on time-delay semi-active control[J]. Journal of Vibration and Shock, 2023, 42(8): 341-350

参考文献

[1] KANTROWITZ A. Stability of castering wheels for aircraft landing gears[R]. No. NACA-TR-686, Washington: NACA, 1940.
[2] HOWARD J. A full-scale investigation of the effect of several factors on the shimmy of cantering wheels[R]. No. NACA-TN-760, Washington: NACA, 1940.
[3] CHRISTIAN B. Analytical study of shimmy of airplane wheels[R]. No. NACA-TM-1337, Washington: NACA, 1952.
[4] MORELAND W J. Landing-gear vibration[R]. AF Technical Report No. 6590, London: Wright Air Development Center, 1951.
[5] SMILEY R F. Correlation, evaluation, and extension of linearized theories for tire motion and wheel shimmy[J]. Technical Report Archive & Image Library, 1956, 241(1):136-51.
[6] BOECKH. Determination of the elastic constants of airplane tires[J]. Technical Report Archive & Image Library, 1954, 14(1):1-40.
[7] VON SCHLIPPE B, DIETRICH R. Shimmying of a Pneumatic Wheel [R]. Washington: NACA, 1954.
[8] GAMON M T. Active Shimmy Control System[R]. California: Lockheed-California Company, 1975.
[9] BANDARU S, MAITI D K. Lateral stability of a typical nose landing gear using torsional magneto-rheological (MR) damper[C]// India Conference. IEEE, 2009.
[10] SURA N K, SURYANARAYAN S. Lateral Stability of Aircraft Nose Wheel Landing Gear with Closed-Loop Shimmy Damper[J]. Journal of Aircraft, 2009, 46(2):505-509.
[11] POULY G, HUYNH T H, LAUFFENBURGER J P, et al. State Feedback Fuzzy Adaptive Control for Active Shimmy Damping[J]. European Journal of Control, 2011, 17(4):370-393.
[12] HAJILOO A, XIE W F. The Stochastic Robust Model Predictive Control of Shimmy Vibration in Aircraft Landing Gears[J]. Asian Journal of Control, 2015, 17(2):476-485.
[13] ATABAY E, OZKOL I. Application of a magnetorheological damper modeled using the current-dependent Bouc-Wen model for shimmy suppression in a torsional nose landing gear with and without freeplay[J]. Journal of Vibration and Control , 2014 , 20(11) :1622-1644.
[14] ORLANDO C, ALAIMO A. A robust active control system for shimmy damping in the presence of free play and uncertainties[J]. Mechanical Systems and Signal Processing, 2017, 84(1): 551-569.
[15] BEREGI S, TAKACS D, GYEBROSZKI G, et al. Theoretical and experimental study on the nonlinear dynamics of wheel-shimmy[J]. Nonlinear Dynamics, 2019, 98(4): 2581-2593.
[16] LAPORTE D J, LOPES V, BUENO D D. An approach to reduce vibration and avoid shimmy on landing gears based on an adapted eigenstructure assignment theory[J]. Meccanica, 2020, 55(1):7-17.
[17] MUSTASHIN M S, RAHMANI M, BEHDINAN K. Experimental characterization of a novel nose landing gear shimmy damper using a small-scale test rig[J]. Aerospace Science and Technology, 2021, 112:106625.
[18] 诸德培. 摆振理论及防摆措施[M]. 北京：国防工业出版社，1984.
[19] 杨国柱, 余仿春. 前轮摆振问题的数值方法[J]. 航空学报, 1989,10(4):78-81.                                   YANG Guozhu, YU Fangchun. Numerical method for nose wheel shimmy of landing gear[J]. Journal of Aeronautics, 1989, 10(4) :78-81.
[20] 顾虞. 考虑转向系间隙的汽车前轮摆振系统研究[D]. 合肥工业大学, 2007.
[21] 陈大伟, 顾宏斌, 吴东苏. 基于磁流变阻尼器的起落架摆振半主动控制[J]. 中国机械工程, 2010,021(012):1401-1405.                                                                  CHEN Dawei, GU Hongbin, WU Dongsu. Semi-active control of landing gear shimmy based on MR damper[J]. China Mechanical Engineering, 2010, 021(012):1401-1405.
[22] 李莹, 王博, 祝世兴. 起落架磁流变减摆器模糊PID控制算法的研究[J]. 计算机测量与控制, 2016,24(2):80-83.                                                                        LI Ying, WANG Bo, ZHU Shixing. Research on Fuzzy PID control algorithm of landing gear magnetorheological damper[J]. Computer measurement and control, 2016,24(2):80-83.
[23] 祝世兴, 刘秀. 飞机前起落架磁流变液减摆器设计与性能分析[J]. 机床与液压, 2019, 47(02):75-78+108.                    ZHU Shixing, LIU Xiu. Design and performance analysis of MR fluid damper for aircraft nose gear[J]. Machine tools and hydraulic pressure, 2019, 47(02):75-78+108.
[24] 田静, 王恕浩. 飞机前轮摆振影响因素分析[J]. 机械设计, 2019(7):52-57.                                 TIAN Jing, WANG Shuhao. Analysis of factors affecting aircraft front wheel shimmy[J]. Machine design, 2019(7):52-57.
[25] MENG Q H, QIAN C J. Active steering wheel shimmy control for electric vehicle by sampled-data output feedback[J]. ISA Transactions, 2019, 84:262-270.
[26] 郝新琛. 基于磁流变原理的前起落架摆振特性研究[D]. 中国民航大学, 2020.
[27] OLGAC N, HOLM B T. A Novel Active Vibration Absorption Technique: Delayed Resonator[J]. Journal of Sound and Vibration, 1994, 176(1):93-104.
[28] 董成, 赵艳影. 高速列车非线性减振系统联合时滞反馈控制[J]. 科学技术与工程, 2019, 19(32): 24-30.                DONG Cheng, ZHAO Yanying. Joint time delay feedback control for nonlinear vibration damping system of high-speed train[J]. Science Technology and Engineering, 2019, 19(32): 24-30.
[29] MENG H, SUN X, XU J, et al. Establishment of the equal-peak principle for a multiple-DOF nonlinear system with multiple time-delayed vibration absorbers[J]. Nonlinear Dynamics, 2021, 104(5): 241-266.
[30] POWELL A L, CHOI Y T, HU W, et al. Nonlinear modeling of adaptive magnetorheological landing gear dampers under impact conditions[J]. Smart Materials and Structures, 2016, 25(11):115011.
[31] CHOI Y T, WERELEY N M. Vibration Control of a Landing Gear System Feature Electrorheological/Magnetorheological Fluids[J]. Journal of Aircraft, 2003, 40(3):432-439.
[32] THOTA P, KRAUSKOPF B, LOWENBERG M. Interaction of torsion and lateral bending in aircraft nose landing gear shimmy[J]. Nonlinear Dynamics, 2009, 57(3):455-467.
[33] VYHLÍDAL T, LAFAY J F, SIPAHI R. QPmR Quasi Polynomial Root-Finder: Algorithm Update and Examples[J]. Springer International Publishing, 2014, 22(5):299-312.
[34] DIXON A L. The Eliminant of Three Quantics in two Independent Variables: (Second Paper.)[J]. Proceedings of the London Mathematical Society, 2016, 31(2):87-91.