旋转导弹结构细长，具有较大弹性，结构低频振动易与刚体运动相互耦合。为更好地研究旋转导弹的动力学特性，对考虑刚体运动与弹体变形耦合效应的旋转导弹动力学建模问题展开研究。引入瞬态坐标系，在该坐标系下利用拉格朗日方程建立弹性旋转导弹的惯性耦合完整模型。该模型考虑了弹性变形对质量特性的影响，能够完整描述刚体运动和弹性变形间的耦合效应。在不同假设下，将惯性耦合完整模型简化后可得到弹性耦合简化模型和非惯性耦合模型。仿真分析结果表明：相对于其他两种简化模型，惯性耦合完整模型能够更全面地描述旋转导弹的运动，而刚体运动与弹体变形耦合效应在旋转导弹建模和分析中不可忽略，需要加以考虑；在旋转导弹运动稳定情况下，3种模型的差别主要体现在姿态运动上，而在弹性变形上的差别可以忽略。
Abstract
Considering the interaction between flexible and rigid modes caused by the increased aspect ratio and elasticity of spinning missile, the nonlinear equations of motion for elastic spinning missile are developed. The transient coordinate system, in which vibration mode is used to describe the missile’s elastic deformation, is introduced. The slice theory is used to establish an aerodynamics model. Lagrangian equation is used to derive the complete inertial coupling model of elastic spinning missiles. In the model, the influence of elastic deformation on the mass property is considered, and the coupling effect between flexible and rigid modes are fully described. Under different assumptions, the complete inertial coupling model can be simplified to obtain the simplified inertial and non-inertial coupling models. Numerical simulationsdemonstrate that the main difference on the attitude motion is not negligible, while the difference on the flexible mode is negligible. The influence of inertial coupling must be considered in the modeling and analysis of elastic spinning missile. Key
关键词
旋转导弹 /
刚体运动与弹体变形耦合效应 /
弹性变形 /
惯性耦合 /
动力学建模 /
飞行动力学 /
锥形运动
{{custom_keyword}} /
Key words
spinningmissile /
rigid-elasticcouplingeffect /
elasticitydeformation /
inertialcoupling /
dynamicsmodeling /
flightdynamics /
conicalmotion
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
［1］张龙，赵志勤，范斌宁，等. 基于弹载地磁测试的高速旋转稳定弹锥形运动分析[J]．兵工学报，2016，37(12)：2235-2241.
ZHANG Long, ZHAO Zhi-qin, FAN Bin-ning, et al. Analysis on coning motion of high-speed spin-stabilized projectile base on on-board magnetic test[J].Acta Armamentarii, 2016, 37(12): 2235- 2241. (in Chinese)
[2］杨树兴，赵良玉，闫晓勇. 旋转弹动态稳定性理论[M].北京：国防工业出版社，2014：1-27.
YANG Shu-xing, ZHAO Liang-yu, YAN Xiao-yong. Dynamics stability of spinning missiles[M]. Beijing: National Defense Industry Press, 2014: 1-27. (in Chinese)
[3］闫晓勇，杨树兴，张成. 基于章动运动理论的火箭弹锥形运动稳定性分析[J]．兵工学报，2009，30(10)：1291-1296.
YAN Xiao-yong, YANG Shu-xing, ZHANG Cheng. Analysis of stability for coning motion of rockets based on theory of nutation movement[J]. Acta Armamentarii, 2009, 30(10): 1291-1296. (in Chinese)
[4］崔垚，李顺利，计佳俊，等. 空空导弹高抛弹道作战效能研究[J].飞行力学，2012，30(4)：376-384.
CUI Yao, LI Shun-li, JI Jia-jun, et al. Study on the operational effectiveness of high parabola trajectory of air-to-air missile[J]. Flight Dynamics, 2012, 30(4): 376-384. (in Chinese)
[5］Li M J, Rui X T, Abbas L K. Elastic dynamic effects on the trajectory of a flexible launch vehicle[J]. Journal of Spacecraft and Rockets, 2015, 52(6): 1586-1602.
[6］Shi Z J, Zhao L Y. Effects of aeroelasticity on coning motion of a spinning missile[J]. Proceedings of the Institution of Mechanical Engineers Part G: Journal ofAerospace Engineering, 2016, 230(14):2581-2591.
[7］黄程德，郑冠男，杨国伟，等. 基于CFD/CSD耦合间隙三维全动舵面气动弹性研究[J]．应用力学学报，2018，35(1)：1-8.
HUANG Cheng-de, ZHENG Guan-nan, YANG Guo-wei,et al. Aeroelastic study of a three dimensional all-movable wing with free play using CFD/CSD coupling[J]. Chinese Journal of Applied Mechanics, 2018, 35(1): 1-8. (in Chinese)
[8］郭东，徐敏，陈士橹. 弹性飞行器飞行动力学建模研究[J].空气动力学学报，2013，31(4)：413-419.
GUO Dong, XU Min, CHEN Shi-lu. Research on flight dynamic modeling of highly flexible aircrafts[J]. Acta Aerodynamica Sinica, 2013, 31(4): 413-419. (in Chinese)
[9］Platus D H. Aeroelastic stability of slender, spinning missiles[J]. Journal of Guidance, Control and Dynamics, 1992, 15(1): 144-151.
[10］Murphy C H, Mermagen W H. Flight mechanics of an elastic symmetric missile[J]. Journal of Guidance, Control and Dyna- mics,2001, 24(6): 1125-1132.
[11］Canavin J R, Likins P W. Floating reference frames for flexible spacecraft[J]. Journal of Spacecraft, 1977, 14(12): 724-732.
[12］赵贺伟，杨秀霞，沈如松，等. 弹性高超声速飞行器预设性能精细姿态控制[J]．兵工学报，2017，38(3)：501-511.
ZHAO He-wei, YANG Xiu-xia, SHEN Ru-song, et al. Prescribed performance fine attitude control for aeroelastic hypersonic vehicle[J]. Acta Armamentarii, 2017, 38(3): 501-511. (in Chinese)
[13］张希彬，宗群，曾凡琳. 考虑气动—推进—弹性耦合的高超声速飞行器面向控制建模与分析[J]．宇航学报，2014，35(5)：528-536.
ZHANG Xi-bin, ZONG Qun, ZENG Fan-lin.Control-oriented modeling and analysis of a hypersonic vehicle with coupled aerodynamic-propulsion-elastic[J]. Journal of Astronautics, 2014, 35(5): 528-536. (in Chinese)
[14］Waszak M R, Schmidt D K. Flight dynamics of aeroelastic vehicles[J]. Journal of Aircraft, 1988, 25(6): 563-571.
[15］Xu T F, Rong J L, Xiang D L, et al. Dynamic modeling and stability analysis of a flexible spinning missile under thrust[J]. International Journal of Mechanical Sciences, 2016, 119: 144-154.
[16］Zhang Z, Li S L. Two-degree controller design for flexible missile based on H-inf interference suppression[C]∥Proceedings of the 2nd International Conference on Instrumentation & Measurement, Computer, Communication and Control.Harbin, China: IEEE, 2012: 1653-1656.
[17］李惠峰. 高超声速飞行器制导与控制技术[M]．北京：中国宇航出版社，2012：84-100.
LI Hui-feng. Guidance and control technology of hypersonic vehicle[M]. Beijing: China Astronautic Publishing House, 2012: 84-100. (in Chinese)
[18］Hu Q L, Meng Y, Wang C L, et al. Adaptive backstepping control for air-breathing hypersonic vehicles with input nonlinearities[J]. Aerospace Science and Technology, 2018, 73(2): 289-299.
[19］Meirovitch L, Tuzcu I. The lure of the mean axis[J]. Journal of Applied Mechanics, 2007, 74(3): 497-504.
[20］Meirovitch L, Tuzcu I. Unified theory for the dynamics and control of maneuvering flexible aircraft[J]. AIAA Journal, 2004, 42(4): 714-727.
第39卷
第11期2018年11月兵工学报ACTA
ARMAMENTARIIVol.39No.11Nov.2018
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
