轴对称矢量喷管喷口Lagrange动力学分析
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摘要
以轴对称矢量喷管为研究对象,建立其动力学方程。首先,将轴对称矢量喷管结构简化为等效的3-PRS结构模型,利用等效的3-PRS结构模型建立喷管喷口运动学方程。然后,将气动力等效为动平台虚拟质量,运用Lagrange方法推导出喷管喷口的动力学方程,并分析其动力学特性。通过MATLAB和ADAMS仿真,对比两种仿真结果,验证了建立模型的准确性。结果表明喷口姿态对驱动力影响很大,由此可得出不同姿态下驱动力的变化规律。从而对进一步进行喷管优化设计及控制提供了有效帮助。
The axisymmetric vector nozzle was taken as the research object, and its dynamic equation was established. Firstly, the structure of axisymmetric vector nozzle was simplified to an equivalent 3-PRS structure model, and the kinematics equation of the nozzle was established with the equivalent 3-PRS structure model. Then, the aerodynamic force was settled to be equivalent to the virtual mass of the dynamic platform, and the dynamic model of the nozzle was deduced by Lagrange method, and meanwhile its dynamic features were analyzed. The accuracy of the model was verified by comparing the two simulation results in MATLAB and ADAMS. The results showed that the attitude of nozzle took great influence on driving force. At the same time, the change rule of driving force can be obtained under different attitudes. This study provides effective help for further optimal design and control of nozzles.
The axisymmetric vector nozzle was taken as the research object, and its dynamic equation was established. Firstly, the structure of axisymmetric vector nozzle was simplified to an equivalent 3-PRS structure model, and the kinematics equation of the nozzle was established with the equivalent 3-PRS structure model. Then, the aerodynamic force was settled to be equivalent to the virtual mass of the dynamic platform, and the dynamic model of the nozzle was deduced by Lagrange method, and meanwhile its dynamic features were analyzed. The accuracy of the model was verified by comparing the two simulation results in MATLAB and ADAMS. The results showed that the attitude of nozzle took great influence on driving force. At the same time, the change rule of driving force can be obtained under different attitudes. This study provides effective help for further optimal design and control of nozzles.
引文
[1] Wilson E A,Adler D,Gal-Or B Z,et al.Thrust-vectoring turbofan jet-engine analysis[J].International Journal of Turbo and Jet Engines,1999,16(1):39-48
[2] Williams R G,Vittal B R.Fluidic thrust vectoring and throat control exhaust nozzle[C]//Proceedings of the 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit.Indianapolis,Indiana:AIAA,2002
[3] Capone F,Smereczniak P,Spetnagel D,et al.Comparative investigation of multiplane thrust vectoring nozzles[C]//Proceedings of the 28th Joint Propulsion Conference and Exhibit.Nashville,TN,USA:AIAA,1992
[4] Cler D L,Mason M L,Guthrie A R.Experimental investigation of spherical-convergent-flap thrust-vectoring two-dimensional plug nozzles[C]//Proceedings of the 29th Joint Propulsion Conference and Exhibit.Monterey,CA,USA:AIAA,1993
[5] Deere K A,Berrier B L,Flamm J D,et al.Computational study of fluidic thrust vectoring using separation control in a nozzle[C]//Proceedings of the 21st AIAA Applied Aerodynamics Conference.Orlando,Florida:AIAA,2013
[6] Thayer E B.Gas turbine vectoring exhaust nozzle:US,US5335489A[P].1994-08-09
[7] 王玉新.喷气发动机轴对称推力矢量喷管[M].北京:国防工业出版社,2006Wang Y X.Axian-symmetric vectoring exhaust nozzle for jet-thrust-aircraft[M].Beijing:National Defense Industry Press,2006 (in Chinese)
[8] 王玉新.轴对称推力矢量喷管运动奇异性分析[J].航空动力学报,2009,24(1):162-168Wang Y X.Singularity analysis of axisymmetric vectoring exhaust nozzle[J].Journal of Aerospace Power,2009,24(1):162-168 (in Chinese)
[9] 额日其太,李喜喜,王强.轴对称喷管喉道面积射流控制数值模拟研究[J].推进技术,2010,31(3):361-365Eriqitai,Li X X,Wang Q.Computational investigation on axisymmetric nozzles with fluidic injection for throat area control[J].Journal of Propulsion Technology,2010,31(3):361-365 (in Chinese)
[10] 王玉新,王仪明,李雨桐.轴对称推力矢量喷管载荷变形的控制补偿[J].航空动力学报,2007,22(10):1685-1689Wang Y X,Wang Y M,Li Y T.Load deformation compensation of the axisymmetric vectoring exhaust nozzle[J].Journal of Aerospace Power,2007,22(10):1685-1689 (in Chinese)
[11] 李有德,赵志刚,孟佳东,等.轴对称矢量喷管喉道运动学精确建模研究[J].机械科学与技术,2016,35(11):1785-1790Li Y D,Zhao Z G,Meng J D,et al.Precision kinematic model for throat of axisymmetric Vectorexhaust nozzle[J].Mechanical Science and Technology for Aerospace Engineering,2016,35(11):1785-1790 (in Chinese)
[12] 刘铭达,赵志刚,石广田,等.轴对称矢量喷管A8面运动学分析与求解[J].机械科学与技术,2016,35(6):975-979Liu M D,Zhao Z G,Shi G T,et al.Analysis and solving for kinematics of A8 area of axial-symmetric vectoring exhaust nozzle[J].Mechanical Science and Technology for Aerospace Engineering,2016,35(6):975-979 (in Chinese)
[13] 赵志刚,李建鹏,刘洋,等.三环驱动轴对称推力矢量喷管逆运动学分析[J].航空动力学报,2018,33(1):24-29Zhao Z G,Li J P,Liu Y,et al.Analysis on inverse kinematics of the three rings supporting and driving axial symmetric vectoring exhaust nozzle[J].Journal of Aerospace Power,2018,33(1):24-29 (in Chinese)
[14] 王鑫,武建新.轴对称矢量喷管动力学仿真与分析[J].机械设计与制造,2013,(10):106-109Wang X,Wu J X.Dynamic simulation and analysis of axisymmetric vectoring exhaust nozzle[J].Machinery Design & Manufacture,2013,(10):106-109 (in Chinese)
[15] 赵俊伟,李雪锋,陈国强.基于Lagrange方法的3-PRS并联机构动力学分析[J].机械设计与研究,2015,31(2):1-5Zhao J W,Li X F,Chen G Q.The dynamics equation of a 3-PRS parallel manipulator based on Lagrange method[J].Machine Design and Research,2015,31(2):1-5 (in Chinese)
[2] Williams R G,Vittal B R.Fluidic thrust vectoring and throat control exhaust nozzle[C]//Proceedings of the 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit.Indianapolis,Indiana:AIAA,2002
[3] Capone F,Smereczniak P,Spetnagel D,et al.Comparative investigation of multiplane thrust vectoring nozzles[C]//Proceedings of the 28th Joint Propulsion Conference and Exhibit.Nashville,TN,USA:AIAA,1992
[4] Cler D L,Mason M L,Guthrie A R.Experimental investigation of spherical-convergent-flap thrust-vectoring two-dimensional plug nozzles[C]//Proceedings of the 29th Joint Propulsion Conference and Exhibit.Monterey,CA,USA:AIAA,1993
[5] Deere K A,Berrier B L,Flamm J D,et al.Computational study of fluidic thrust vectoring using separation control in a nozzle[C]//Proceedings of the 21st AIAA Applied Aerodynamics Conference.Orlando,Florida:AIAA,2013
[6] Thayer E B.Gas turbine vectoring exhaust nozzle:US,US5335489A[P].1994-08-09
[7] 王玉新.喷气发动机轴对称推力矢量喷管[M].北京:国防工业出版社,2006Wang Y X.Axian-symmetric vectoring exhaust nozzle for jet-thrust-aircraft[M].Beijing:National Defense Industry Press,2006 (in Chinese)
[8] 王玉新.轴对称推力矢量喷管运动奇异性分析[J].航空动力学报,2009,24(1):162-168Wang Y X.Singularity analysis of axisymmetric vectoring exhaust nozzle[J].Journal of Aerospace Power,2009,24(1):162-168 (in Chinese)
[9] 额日其太,李喜喜,王强.轴对称喷管喉道面积射流控制数值模拟研究[J].推进技术,2010,31(3):361-365Eriqitai,Li X X,Wang Q.Computational investigation on axisymmetric nozzles with fluidic injection for throat area control[J].Journal of Propulsion Technology,2010,31(3):361-365 (in Chinese)
[10] 王玉新,王仪明,李雨桐.轴对称推力矢量喷管载荷变形的控制补偿[J].航空动力学报,2007,22(10):1685-1689Wang Y X,Wang Y M,Li Y T.Load deformation compensation of the axisymmetric vectoring exhaust nozzle[J].Journal of Aerospace Power,2007,22(10):1685-1689 (in Chinese)
[11] 李有德,赵志刚,孟佳东,等.轴对称矢量喷管喉道运动学精确建模研究[J].机械科学与技术,2016,35(11):1785-1790Li Y D,Zhao Z G,Meng J D,et al.Precision kinematic model for throat of axisymmetric Vectorexhaust nozzle[J].Mechanical Science and Technology for Aerospace Engineering,2016,35(11):1785-1790 (in Chinese)
[12] 刘铭达,赵志刚,石广田,等.轴对称矢量喷管A8面运动学分析与求解[J].机械科学与技术,2016,35(6):975-979Liu M D,Zhao Z G,Shi G T,et al.Analysis and solving for kinematics of A8 area of axial-symmetric vectoring exhaust nozzle[J].Mechanical Science and Technology for Aerospace Engineering,2016,35(6):975-979 (in Chinese)
[13] 赵志刚,李建鹏,刘洋,等.三环驱动轴对称推力矢量喷管逆运动学分析[J].航空动力学报,2018,33(1):24-29Zhao Z G,Li J P,Liu Y,et al.Analysis on inverse kinematics of the three rings supporting and driving axial symmetric vectoring exhaust nozzle[J].Journal of Aerospace Power,2018,33(1):24-29 (in Chinese)
[14] 王鑫,武建新.轴对称矢量喷管动力学仿真与分析[J].机械设计与制造,2013,(10):106-109Wang X,Wu J X.Dynamic simulation and analysis of axisymmetric vectoring exhaust nozzle[J].Machinery Design & Manufacture,2013,(10):106-109 (in Chinese)
[15] 赵俊伟,李雪锋,陈国强.基于Lagrange方法的3-PRS并联机构动力学分析[J].机械设计与研究,2015,31(2):1-5Zhao J W,Li X F,Chen G Q.The dynamics equation of a 3-PRS parallel manipulator based on Lagrange method[J].Machine Design and Research,2015,31(2):1-5 (in Chinese)