为给出满足直升机地面共振稳定性要求的起落架刚度及阻尼的优化设计方法，首先构造机体无阻尼时其非稳区的模态阻尼比函数，据此给出机体模态非稳区临界转速的计算方法，结合与旋翼摆振后退型模态共振转速下机体模态阻尼比的计算方法，给出了满足地面共振稳定性的机体固有频率及阻尼要求。然后，根据支持在起落架上的机体自由运动模型，建立机体模态频率及阻尼与起落架刚度及阻尼的关系，从而给出满足直升机地面共振稳定性的起落架刚度及阻尼要求。最后，基于上述稳定性要求，在满足着陆缓冲性能要求的起落架刚度及阻尼范围内，以减小起落架需用阻尼且增大机体最小模态阻尼比为优化目标提出了对其刚度及阻尼进行优化设计的方法，并通过对某型直升机4种不同重量重心状态下的起落架刚度及阻尼进行优化验证了该方法的可行性。
To meet the requirement of helicopter ground resonance stability, an optimal design method for landing gear stiffness and damping is proposed. First, a modal damping ratio function in the instable area for the fuselage without damping was constructed. The requirements of fuselage natural frequency and damping for meeting ground resonance stability were given by combining the calculation method of the instable area critical rotate speed with the calculation method of damping ratio at the resonance rotate speed of the fuselage mode. Then, based on the freedom motion model for the fuselage on the landing gear, the relation between landing gear stiffness and damping with fuselage mode frequency and damping was established, and the requirements of landing gear stiffness and damping for meeting ground resonance stability were given. Finally, based on the stability requirements, an optimal design method of landing gear stiffness and damping is proposed to reduce the required damping of landing gear and increase the minimum damping ratio of fuselage mode within the range determined by the buffering property requirements. This method was validated by optimizing the landing gear stiffness and damping of a type of helicopter at 4 states with different weights and gravity centers.
[1] 徐敏. 一种分析轮式起落架直升机舰面共振的方法[J]. 航空学报, 2007, 28(4):886-890. XU M. Analytical method of ship resonance for helicopters with wheel landing gears[J]. Acta Aeronautica et Astronautica Sinica, 2007, 28(4):886-890(in Chinese).
[2] 胡国才, 刘湘一, 刘书岩, 等. 舰面状态直升机机体在起落架上的固有频率分析[J]. 海军航空工程学院学报, 2012, 27(6):639-644. HU G C, LIU X Y, LIU S Y, et al. Analysis of helicopter natural frequencies on landing gear at ship-borne conditions[J]. Journal of Naval Aeronautical and Astronautical University, 2012, 27(6):639-644(in Chinese).
[3] 刘洋, 向锦武. 舰载直升机旋翼/机体耦合动力学稳定性[J]. 北京航空航天大学学报, 2013, 39(4):442-446. LIU Y, XIANG J W. Stability analysis of coupled rotor/fuselage system of shipboard helicopter[J]. Journal of Beijing University of Aeronautics and Astronautics, 2013, 39(4):442-446(in Chinese).
[4] 程金送. 滑橇式起落架装置直升机地面共振初步分析:GF-A0024308N[R]. 景德镇:中国直升机设计研究所, 1998. CHENG J S. The primary analysis of ground resonance for skid landing gear helicopter:GF-A0024308N[R]. Jingdezhen:China Helicopter Research and Development Institute, 1998(in Chinese).
[5] 徐敏, 张晓谷. 一种分析滑橇式起落架直升机地面共振的方法[J]. 南京航空航天大学学报, 2004, 36(4):533-538. XU M, ZHANG X G. Analytical method of ground resonance for helicopters with skid landing gears[J]. Journal of Nanjing University of Aeronautics and Astronautics, 2004, 36(4):533-538(in Chinese).
[6] 刘强, 张晓谷. 直-九直升机地面共振当量模型及稳定性分析[J]. 南京航空航天大学学报, 1996, 26(1):44-53. LIU Q, ZHANG X G. Equivalent model establishment and ground resonance investigation for Z-9 helicopter[J]. Journal of Nanjing University of Aeronautics and Astronautics, 1996, 26(1):44-53(in Chinese).
[7] 陆萌, 费斌军, 任志勇, 等. 共轴(单轴)双桨叶直升机地面共振的数值分析[J]. 航空学报, 1995, 16(3):348-354. LU M, FEI B J, REN Z Y, et al. A numerical analysis for the ground resonance of a two blade helicopter rotor on anisotropic flexible supports[J]. Acta Aeronautica et Astronautica Sinica, 1995, 16(3):348-354(in Chinese).
[8] 胡国才, 崔坤林, 刘湘一. 地面系留对直升机动力响应的影响[J]. 航空学报, 2008, 29(2):387-392. HU G C, CUI K L, LIU X Y. Ground mooring effects on helicopter dynamic response[J]. Acta Aeronautica et Astronautica Sinica, 2008, 29(2):387-392(in Chinese).
[9] TANG D M, DOWELL E H. Effects of nonlinear damping in landing gear on helicopter limit cycle response in ground resonance[J]. Journal of the American Helicopter Society, 1987, 32(1):45-53.
[10] 汤德满. 直升机地面共振的非线性稳定性分析[J]. 航空学报, 1988, 9(7):319-325. TANG D M. Nonlinear stability analysis for helicopter ground resonance[J]. Acta Aeronautica et Astronautica Sinica, 1988, 9(7):319-325(in Chinese).
[11] LEE Y K, KIM K J. Effects of landing gear nonlinearities on ground resonance of helicopter[C]//14th International Congress on Sound and Vibration. Cairns:International Institute of Acoustic and Vibration, 2007.
[12] 董明明, 周长悦, 秦浩, 等. 基于起落架参数设计的某直升机地面共振及参数影响分析[J]. 航空科学技术, 2013(2):45-49. DONG M M, ZHOU C Y, QIN H, et al. A helicopter ground resonance based on design of landing gear parameters and parameters analysis[J]. Aeronautical Science and Technology, 2013(2):45-49(in Chinese).
[13] 张呈林, 张晓谷, 郭士龙, 等. 直升机部件设计[M]. 1版. 南京:航空专业教材编审组, 1986:204-211. ZHANG C L, ZHANG X G, GUO S L, et al. Helicopter parts design[M]. 1st ed. Nanjing:Editing Group of Aviation Textbook, 1986:204-211(in Chinese).
[14] 张晓谷. 直升机动力学设计[M]. 1版. 北京:航空工业出版社, 1995:94-99. ZHANG X G. Helicopter dynamics design[M]. 1st ed. Beijing:Aviation Industry Press, 1995:94-99(in Chinese).
[15] 路录祥. 直升机结构与设计[M]. 1版. 北京:航空工业出版社, 2009:221-222. LU L X. Helicopter structure and design[M]. 1st ed. Beijing:Aviation Industry Press, 2009:221-222(in Chinese).
[16] 米里. 直升机计算和设计, 第二卷:振动和强度[M]. 宁航, 译. 1版. 北京:国防工业出版社, 1976:252-255. MILI. Helicopter calculation and design, Vol. 2:Vibration and strength[M]. NING H, translated. 1st ed. Beijing:National Defence Industry Press, 1976:252-255(in Chinese).
[17] 顾仲权. 抑制直升机地面共振的优化设计[J]. 航空学报:1989, 10(3):113-118. GU Z Q. Optimization design for suppressing ground resonance of helicopter[J]. Acta Aeronautica et Astronautica Sinica, 1989, 10(3):113-118(in Chinese).
[18] COLEMAN R, FEINGOLD A M. Theory of self-excited mechanical oscillation of helicopter rotors with hinged blades:NACA TN 3844[R]. Washington, D.C.:National Advisory Committee for Aeronautics, 1958.
[19] JOHNSON W. Helicopter theory[M]. 1st ed. New York:Princeton University Press, 1994:668-694.
[20] JIM C N, MITHAT Y. Bell 429 main rotor aerodynamic and dynamic development[C]//Proceedings of the American Helicopter Society 66th Annual Forum. Fairfax, VA:American Helicopter Society, 2010.
[21] 胡国才, 魏钢, 吴靖. 滑跑速度对直升机侧向模态频率的影响[J]. 南京航空航天大学学报, 2016, 48(4):516-521. HU G C, WEI G, WU J. Effect of running velocity on helicopter lateral mode frequency[J]. Journal of Nanjing University of Aeronautics and Astronautics, 2016, 48(4):516-521(in Chinese).
[22] HOWLETT J J. UH-60A black hawk engineering simulation program:Volume I-Mathematical model:NASA Contractor Report 166309[R]. Washington, D.C.:Ames Research Center, 1984.
[23] SMILEY R F, HORNE W B. Mechanical properties of pneumatic tires with special reference to modern aircraft tires:NACA TR R-64[R]. Washington, D.C.:NACA, 1958.
CJA