考虑附加力影响的弹性体远程火箭弹弹道分析
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摘要
远程火箭弹具有长细比大、射程远的特点,为提高弹道分析精度,有必要充分考虑气动弹性和其它附加力的影响。以远程火箭弹非线性运动方程为基础,考虑气动弹性效应,分别采用细长体理论和气动导数法计算弹身和弹翼舵面产生的非定常气动力,并考虑地球自转和发动机燃料变化所引起的附加力以及地球曲率的影响,建立弹性体远程火箭弹六自由度运动模型。通过弹道仿真,对比分析气动弹性、附加力和结构刚度对远程火箭弹脱靶量的影响。仿真对比结果表明,气动弹性和附加力都对远程火箭弹脱靶量产生影响,且附加力与气动弹性高度耦合,在考虑气动弹性效应的前提下,附加力对远程火箭弹脱靶量的影响被显著放大,因此在全弹道仿真分析中必须同时考虑气动弹性和附加力的耦合影响;弹体结构刚度越小,远程火箭弹的脱靶量越大,在远程火箭弹初步设计中,应保证弹体结构刚度以确保命中精度。
Long-range rockets have the characteristics of large slenderness ratio and long range. To improve the accuracy of trajectory simulation, it is necessary to consider aeroelasticity and subsidiary load effect. Based on the nonlinear motion equation of the rockets, the effect of aeroelasticity is is incorporated in the trajectory simulations. The unsteady aerodynamic loads of the body, wings and rudders are calculated by slender body theory and aerodynamic derivative method, respectively. Besides, the six-degree-of-freedom flight dynamics model considering the curvature and the subsidiary loads generated by Earth rotation and fuel mass change is built. Then, the effect of aeroelasticity, subsidiary loads and structural stiffness on rocket miss distance is analyzed through the trajectory simulations. Simulation results show that aeroelasticity and subsidiary loads have a great impact on the miss distance of the rocket. In addition, the subsidiary loads are highly coupled with aeroelasticity and the effect of the subsidiary loads on miss distance of the rocket is significantly amplified with the consideration of aeroelasticity effect. Thus, it is necessary to consider the coupling effect of aeroelasticity and subsidiary loads simultaneously in whole trajectory simulation analysis. Furthermore, when the rocket structural stiffness becomes insufficient, the miss distance of the rocket increases greatly. Therefore, sufficient structural stiffness is essential for improving the hit precision in rocket preliminary design.
Long-range rockets have the characteristics of large slenderness ratio and long range. To improve the accuracy of trajectory simulation, it is necessary to consider aeroelasticity and subsidiary load effect. Based on the nonlinear motion equation of the rockets, the effect of aeroelasticity is is incorporated in the trajectory simulations. The unsteady aerodynamic loads of the body, wings and rudders are calculated by slender body theory and aerodynamic derivative method, respectively. Besides, the six-degree-of-freedom flight dynamics model considering the curvature and the subsidiary loads generated by Earth rotation and fuel mass change is built. Then, the effect of aeroelasticity, subsidiary loads and structural stiffness on rocket miss distance is analyzed through the trajectory simulations. Simulation results show that aeroelasticity and subsidiary loads have a great impact on the miss distance of the rocket. In addition, the subsidiary loads are highly coupled with aeroelasticity and the effect of the subsidiary loads on miss distance of the rocket is significantly amplified with the consideration of aeroelasticity effect. Thus, it is necessary to consider the coupling effect of aeroelasticity and subsidiary loads simultaneously in whole trajectory simulation analysis. Furthermore, when the rocket structural stiffness becomes insufficient, the miss distance of the rocket increases greatly. Therefore, sufficient structural stiffness is essential for improving the hit precision in rocket preliminary design.
引文
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[2]ZHAO L Y,PARK G J,LEE K S,et al.Conceptual design of wrap-around-fin rockets using the MDOmethodology[J].Canadian Aeronautics and Space Journal,2010,56(1):17-30.
[3]杨超,黄超,吴志刚,等.气动伺服弹性研究的进展与挑战[J].航空学报,2015,36(4):1011-1033.YANG Chao,HUANG Chao,WU Zhigang,et al.Progress and challenges for aeroservoelasticity research[J].Acta Aeronautica et Astronautica Sinica,2015,36(4):1011-1033.
[4]魏琼,焦宗夏,吴帅,等.气动伺服加载系统的非线性复合控制[J].机械工程学报,2017,53(14):217-224.WEI Qiong,JIAO Zongxia,WU Shuai,et al.Nonlinear compound control of pneumatic servo loading system[J].Journal of Mechanical Engineering,2017,53(14):217-224.
[5]VIDANOVI?N,RA?UO B,KASTRATOVI?G,et al.Aerodynamic-structural missile fin optimization[J].Aerospace Science and Technology,2017,65:26-45.
[6]VERHAEGEN A,?BIKOWSKI R.Aeroservoelastic modelling and control of a slender anti-air missile for active damping of longitudinal bending vibrations[J].Aerospace Science and Technology,2017,66:20-27.
[7]刘鹏云,薛晓中,孙瑞胜,等.曲面地表对远程火箭弹弹道影响的计算方法[J].火力与指挥控制,2012,37(8):44-46.LIU Pengyun,XUE Xiaozhong,SUN Ruisheng,et al.Acalculation method for influence of curved earth surface on far range rocket projectile calculating trajectory[J].Fire Control and Command Control,2012,37(8):44-46.
[8]杨艳明,唐胜景.基于Simulink的子导弹全弹道仿真[J].系统仿真学报,2006,18(6):1442-1444.YANG Yanming,TANG Shengjing.Trajectory simulation of submunitions based on simulink[J].Journal of System Simulation,2006,18(6):1442-1444.
[9]杨希祥,张为华.小型固体运载火箭六自由度弹道仿真[J].航空学报,2010,31(1):41-47.YANG Xixiang,ZHANG Weihua.Six-degree-of-freedom trajectory simulation of small solid launch vehicles[J].Acta Aeronautica et Astronautica Sinica,2010,31(1):41-47.
[10]刘莉,王岩松,周思达,等.考虑弹体弹性的导弹半物理仿真方法与影响分析[J].北京航空航天大学学报,2016,42(4):639-645.LIU Li,WANG Yansong,ZHOU Sida,et al.Hardware-in-the-loop simulation method and influence analysis of missiles considering body elasticity[J].Journal of Beijing University of Aeronautics and Astronautics,2016,42(4):639-645.
[11]YAO S,WU Z G,YANG C.Trajectory simulation of flexible missiles and the effect of flexibility on hit precision[C]//AIAA Atmospheric Flight Mechanics Conference.National Harbor,Maryland,US:AIAA,2014.
[12]SCHMIDT D K,RANEY D L.Modeling and simulation of flexible flight vehicles[J].Journal of Guidance,Control,and Dynamics,2001,24(3):539-546.
[13]DU W,WIE B,WHORTON M.Dynamic modeling and flight control simulation of a large flexible launch vehicle[C]//AIAA Guidance,Navigation and Control Conference and Exhibit.Honolulu,Hawaii,US:AIAA,2008.
[14]董严,付小燕,张怀宇.弹体结构变形对发射起始扰动影响研究[J].弹箭与制导学报,2016,36(6):75-77.DONG Yan,FU Xiaoyan,ZHANG Huaiyu.Study on effect of the projectile body’s structural deformation to launching initial disturbance[J].Journal of Projectile,Rockets,Missile and Guidance,2016,36(6):75-77.
[15]RUSSKIKH S V.Vibrations of an elastic guide beam with a missile moving along it[J].Russian Aeronautics,2014,57(1):107-110.
[16]杨超,吴志刚.导弹气动伺服弹性稳定性分析[J].飞行力学,2000,18(4):1-5.YANG Chao,WU Zhigang.Aeroservoelastic stability of missile[J].Flight Dynamics,2000,18(4):1-5.
[17]WASZAK M,SCHMIDT D.Flight dynamics of aeroelastic vehicles[J].Journal of Aircraft,1988,25(6):563-571.
[18]徐劲祥.弹道修正弹六自由度弹道仿真研究[J].兵工学报,2007,28(4):411-413.XU Jinxiang.Study on 6-DOF trajectory simulation of course correction projectiles[J].Acta Armamentarii,2007,28(4):411-413.
[19]HUA R H,ZHAO C X,YE Z Y,et al.Effect of elastic deformation on the trajectory of aerial separation[J].Aerospace Science and Technology,2015,45:128-139.
[20]陈克俊,刘鲁华,孟云鹤.远程火箭飞行动力学与制导[M].北京:国防工业出版社,2014.CHEN Kejun,LIU Luhua,MENG Yunhe.Launch vehicle flight dynamics and control[M].Beijing:National Defense Industry Press,2014.
[21]CAO R D,ZHANG X B.Multi-objective optimization of the aerodynamic shape of a long-range guided rocket[J].Structural and Multidisciplinary Optimization,2018,57(4):1779-1792.
[22]GHOSH S,YAKIMENKO O A,DAVIS D T,et al.Unmanned aerial vehicle guidance for an all-aspect approach to a stationary point[J].Journal of Guidance,Control,and Dynamics,2017,40(11):1-19.