Study on Multibody Dynamics Modeling and Flight Dynamic Characteristics of Combined Aircraft

doi:10.12382/bgxb.2022.0282

Abstract

Abstract:

To precisely and completely describe the location and shape of the combined multibody aircraft, a dynamic modeling method of the 8 DOF combined three-body aircraft reflecting relative rolling motion is proposed using Lagrange’s equations with quasi-coordinates. The aerodynamic database of the combined multibody aircraft system considering the aerodynamic coupling effect is established by the CFD method. The accuracy of the model is verified by comparing the model with ADAMS software through a numerical example. Based on this, the trim scheme and flight dynamic characteristics of the aircraft in different trim states are studied. The stability augmentation control is studied based on the cascade PID control method. The results show that the established model effectively reflects the relative motion of the combined aircraft. With the given trim scheme and flight condition, the aircraft of this configuration has two trim states of "symmetrical lower inverse" and "symmetrical upper inverse", and the static stability of relative rolling motion in the two states is quite different. In addition to the traditional flight mechanics mode, there are 4 new motion modes dominated by relative rolling motion, which can be divided into composite symmetric motion and composite antisymmetric motion according to the motion characteristics. To address the problem that the aircraft with this configuration cannot keep stable flight for a long time without control, the stability augmentation control scheme is reasonable and effective, which can quickly stabilize the divergent flight mechanics system. The proposed modeling method and stabilization control scheme can provide guidance and reference for the design and analysis of multibody aircrafts.

Key words: combined aircraft, multibody dynamics, flight dynamic characteristics, quasi-coordinate, stability augmentation control

CLC Number:

V212.1

DU Wanshan, ZHOU Zhou, BAI Yu, ZHANG Zhilin, WANG Keilei. Study on Multibody Dynamics Modeling and Flight Dynamic Characteristics of Combined Aircraft[J]. Acta Armamentarii, 2023, 44(8): 2245-2262.

Figures/Tables 29

Fig.1 Diagram of combined three-body aircraft

Fig.2 Diagram of coordinate system of combined three-body aircraft

Fig.3 Example model of combined three-body aircraft

Table 1 Basic parameters of single aircraft

参数	数值
质量/kg	3.75
参考展长/m	3.2
平均气动弦长/m	0.3
展弦比	10.6
参考面积/m²	0.87
对轴Ox的惯量I_xx/(kg·m²)	0.734
对轴Oy的惯量I_yy/(kg·m²)	0.41
对轴Oz的惯量I_zz/(kg·m²)	1.1
对轴Oz和Ox的惯性积I_zx/(kg·m²)	-0.01

Fig.4 Model of single aircraft

Table 2 Method of establishing aerodynamic database

CFD仿真内容	气动参数	计算方法
基本气动参数项	CD₀、CL₀等	雷诺平均Navier-Stokes (RANS)方法
气动耦合项	C $D ϕ b a$ 、C $D ϕ c a$ 等
静导数项	CD_α、CL_α等
操纵导数项	C $D δ e$ 、C $Y δ a$ 等
动导数项	CL_q、CY_p等	涡格法

Table 2 Method of establishing aerodynamic database

CFD仿真内容	气动参数	计算方法
基本气动参数项	CD₀、CL₀等	雷诺平均Navier-Stokes (RANS)方法
气动耦合项	C $D ϕ b a$ 、C $D ϕ c a$ 等
静导数项	CD_α、CL_α等
操纵导数项	C $D δ e$ 、C $Y δ a$ 等
动导数项	CL_q、CY_p等	涡格法

Fig.5 Diagram of grid distribution of single aircraft

Fig.6 Diagram of grid distribution of combined three-body aircraft

Fig.7 Curve of aerodynamic parameters of single aircraft varying with attack angle α and sideslip angle β

Fig.8 Curve of aerodynamic parameters of single aircraft varying with relative roll angle ϕba

Fig.9 Diagram of state response of single aircraft a

Table 3 Relative roll angles at different initial states

初始状态	ϕ_ba/(°)	ϕ_ca/(°)
1	10	-10
2	-10	10

Fig.10 Diagram of relative roll angle response in different initial states

Table 4 Result of trim analysis

未知配平量	配平状态1	配平状态2
升降舵偏角/(°)	-0.2622	-0.1347
油门杆操纵量/%	35.5	35.5
方向舵偏角/(°)	0	0
飞行单元a副翼偏角/(°)	0	0
飞行单元b副翼偏角/(°)	1.6809	2.0557
飞行单元c副翼偏角/(°)	-1.6809	2.0557
相对滚转角ϕ_ba/(°)	6.4393	-6.6386
相对滚转角ϕ_ca/(°)	-6.4393	6.6386

Fig.11 Diagram of two trim states

Fig.12 Static stability analysis of relative rolling motion of “symmetrical lower inverse”

Fig.13 Static stability analysis of relative rolling motion of “symmetrical upper inverse”

Table 5 Motion mode analysis of trim states

运动模态	“对称下反”配平点1				“对称上反”配平点2
运动模态	特征根	模态特征	阻尼比	时间常数/s	特征根	模态特征	阻尼比	时间常数/s
短周期模态	-7.1334±5.9653j	收敛	0.7671	1.0533	-7.1254±5.8959j	收敛	0.7704	1.0657
长周期模态	-0.0363±0.9628j	收敛	0.0377	6.5260	-0.0372±0.9639j	收敛	0.0386	6.5185
滚转模态	-56.2923	收敛	1	0.0123	-57.9442	收敛	1	0.0120
螺旋模态	0.1874	发散	1	3.6988	-0.1297	收敛	1	5.3442
荷兰滚模态	-0.6013±0.5190j	收敛	0.7570	12.1063	-0.3580±0.7475j	收敛	0.4319	8.4056
复合对称运动模态1	-17.288	收敛	1	0.0401	-17.8852	收敛	1	0.0388
复合对称运动模态2	-0.1579	收敛	1	4.3898	0.1200	发散	1	5.7762
复合反对称运动模态1	-9.4704	收敛	1	0.0732	-9.6093	收敛	1	0.0721
复合反对称运动模态2	-0.3058	收敛	1	2.2667	0.2888	发散	1	2.4001

Table 6 Feature vector analysis of new motion modes

配平状态	运动模态	Δp_a	Δϕ_a	Δq_a	Δθ_a	Δr_a	Δψ_a	Δω_ba	Δϕ_ba	Δω_ca	Δϕ_ca
“对称下反” 配平点1	复合对称运动模态1	-1.90× 10^-15	1.10× 10^-16	-0.0244	0.0014	2.37× 10^-18	-1.37× 10^-19	0.5766	-0.0334	-0.5766	0.0334
	复合对称运动模态2	1.01× 10^-15	-1.07× 10^-14	-0.0007	0.0043	-3.79× 10^-15	2.39× 10^-14	0.0942	-0.5962	-0.0942	0.5962
	复合反对称运动模态1	-0.7885	0.0833	-1.21× 10^-15	9.12× 10^-17	-0.0488	0.0052	0.4221	-0.0446	0.4221	-0.0446
	复合反对称运动模态2	-0.1118	0.3658	-8.87× 10^-16	1.32× 10^-15	-0.0208	0.0681	0.1840	-0.6018	0.1840	-0.6018
“对称上反” 配平点2	复合对称运动模态1	-1.89× 10^-16	1.39× 10^-18	-0.0261	0.0015	1.10× 10^-16	-6.16× 10^-18	-0.5566	0.0311	0.5566	-0.0311
	复合对称运动模态2	-5.98× 10^-14	-5.05× 10^-13	-0.0026	-0.0216	-1.27× 10^-14	-1.06× 10^-13	0.0755	0.6291	-0.0755	-0.6291
	复合反对称运动模态1	-0.7924	0.0825	1.07× 10^-14	-1.07× 10^-15	-0.0486	0.0051	0.3863	-0.0402	0.3863	-0.0402
	复合反对称运动模态2	0.1039	0.3596	-5.83× 10^-14	-2.06× 10^-13	-0.0345	-0.1195	-0.1795	-0.6214	-0.1795	-0.6214

Table 7 Motion modes of combined two-body aircraft

运动模态	特征根	模态特征
短周期模态	-1.0419±2.1693j	收敛
长周期模态	0.0643±0.0489j	发散
滚转模态	-4.4588	收敛
荷兰滚模态	-0.2048±0.8746j	收敛
复合运动模态1	-0.9696	收敛
复合运动模态2	0.9625	发散

Fig.14 Composite symmetric motion

Fig.15 Composite antisymmetric motion

Fig.16 System free response of “symmetrical lower inverse”

Fig.17 System free response of “symmetrical upper inverse” at trim point 2

Fig.18 System free response under asymmetric disturbance at trim point 1

Fig.19 Diagram of design of stability augmentation control system

Fig.20 Diagram of Simulink simulation

Fig.21 Response under symmetric disturbance at trim point 2 after stability augmentation control

Fig.22 Response under asymmetric disturbance at trim point 1 after stability augmentation control

References 26

[1]	周伟, 马培洋, 郭正, 等. 基于翼尖链翼的组合固定翼无人机研究进展[J]. 航空学报, 2022, 43(9): 325946.
	ZHOU W, MA P Y, GUO Z, et al. Research progress of combined fixed-wing UAV based on wingtip chained[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(9): 325946. (in Chinese)
[2]	杨延平, 张子健, 应培, 等. 集群组合式柔性无人机:创新,机遇及技术挑战[J]. 飞行力学, 2021, 39(2):1-9, 15.
	YANG Y P, ZHANG Z J, YING P, et al. Flexible modular swarming UAV: innovative, opportunities, and technical challenges[J]. Flight Dynamics, 2021, 39(2):1-9, 15. (in Chinese)
[3]	武明建. 变体太阳能无人机设计与能量优化[D]. 南京: 南京航空航天大学, 2018.
	WU M J. Design and energy optimization for morphing wing solar-powered UAV[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2018. (in Chinese)
[4]	WU M J, SHI Z W, XIAO T H, et al. Effect of wingtip connection on the energy and flight endurance performance of solar aircraft[J]. Aerospace Science and Technology, 2021, 108:106404. doi: 10.1016/j.ast.2020.106404 URL
[5]	COOPER J, ROTHHAAR P. Dynamics and control of in-flight wing tip docking[J]. Journal of Guidance Control & Dynamics, 2018, 41(11):2327-2337.
[6]	WLACH S, BALMER G R, HERMANN M, et al. Elaha- elastic aircraft for high altitudes[C]//Proceedings of the 23rd ESA Symposium on European Rocket and Balloon Programmes and Related Research. Visby, Sweden: ESA, 2017.
[7]	SUENAGA Y, SUZUKI K. Preliminary study on aerodynamic design of wing-tip-chained airplanes for mars exploration[C]//Proceedings of Asia Pacific International Symposium on Aerospace Technology. Gold Coast, Australia: Engineers Australia, 2019: 2048-2055.
[8]	MENG Y, AN C, XIE C C, et al. Conceptual design and flight test of two wingtip-docked multi-body aircraft[J]. Chinese Journal of Aeronautics, 2022, 35(12):144-155.
[9]	安朝, 谢长川, 孟杨, 等. 多体组合式无人机飞行力学稳定性分析及增稳控制研究[J]. 工程力学, 2021, 38(11):248-256.
	AN C, XIE C C, MENG Y, et al. Flight dynamics and stable control analyses of multi-body aircraft[J]. Engineering Mechanics, 2021, 38(11):248-256. ) (in Chinese)
[10]	刘东旭, 谢长川, 洪冠新. 翼尖铰接复合飞行器动力学特性研究[J]. 北京航空航天大学学报, 2021, 47(11):2311-2321.
	LIU D X, XIE C C, HONG G X. Dynamic characteristics of wingtip-jointed composite aircraft system[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(11):2311-2321. (in Chinese)
[11]	AN C, XIE C C, MENG Y, et al. Flight mechanical analysis and test of unmanned multi-body aircraft[C]//Proceedings of the 18th International Forum on Aeroelasticity and Structural Dynamics. Savannah, GA, US: Curran Associates, Inc. 2019.
[12]	MONTALVO C. Meta aircraft flight dynamics and controls[D]. Atlanta, GA, US: Geogia Institute of Technology, 2014.
[13]	MONTALVO C, COSTELLO M. Meta aircraft flight dynamics[J]. Journal of Aircraft, 2015, 52(1): 107-115. doi: 10.2514/1.C032634 URL
[14]	KOTHE A, LUCKNER R. Flight mechanical modeling and analysis of multi-body aircraft[C]//Proceedings of the 16th International Forum on Aeroelasticity and Structural Dynamics. Saint Petersburg, Russia: Curran Associates Inc., 2015.
[15]	KOTHE A, BEHRENS A, HAMANN A, et al. Closed-loop flight tests with an unmanned experimental multibody aircraft[C]//Proceedings of the 17th International Forum on Aeroelasticity and Structural Dynamics. Como, Italy: Curran Associates Inc., 2017.
[16]	张青斌, 高峰, 郭锐, 等. 动力翼伞系统拟坐标形式的多体动力学建模[J]. 兵工学报, 2019, 40(9):1935-1942. doi: 10.3969/j.issn.1000-1093.2019.09.019
	ZHANG Q B, GAO F, GUO R, et al. Multibody dynamics modeling of powered parafoil system using equations with quasi-coordinates[J]. Acta Armamentarii, 2019, 40(9):1935-1942. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.09.019
[17]	高峰, 郭锐, 丰志伟, 等. 翼伞系统5段归航轨迹优化研究[J]. 兵工学报, 2020, 41(5):1025-1033. doi: 10.3969/j.issn.1000-1093.2020.05.022
	GAO F, GUO R, FENG Z W, et al. Optimization design of homing trajectory of parafoil system with five segments[J]. Acta Armamentarii, 2020, 41(5):1025-1033. (in Chinese) doi: 10.3969/j.issn.1000-1093.2020.05.022
[18]	蒋国江. 扑翼变形飞行器的动力学建模与飞行仿真[D]. 长沙: 国防科学技术大学, 2015.
	JIANG G J. Dynamic modeling and flight simulation of flapping wing aircraft[D]. Changsha: National University of Defense Technology, 2015. (in Chinese)
[19]	郭锐. 翼伞系统多体动力学与试验[D]. 长沙: 国防科学技术大学, 2017.
	GUO R. Multibody dynamics and experiment of parafoil system[D]. Changsha: National University of Defense Technology, 2017. (in Chinese)
[20]	DARIO H B, LEE D, PENA S, et al. Modeling and control of an aeroelastic morphing vehicle[J]. Journal of Guidance Control & Dynamics, 2008, 31(6):1687-1699.
[21]	YUE T, WANG L X, AI J Q. Gain self-scheduled H_∞ control for morphing aircraft in the wing transition process based on an LPV model[J]. Chinese Journal of Aeronautics, 2013, 26(4): 909-917. doi: 10.1016/j.cja.2013.06.004 URL
[22]	WANG L X, XU Z J, YUE T. Dynamic characteristics analysis and flight control design for oblique wing aircraft[J]. Chinese Journal of Aeronautics, 2016, 29(6):1664-1672. doi: 10.1016/j.cja.2016.10.010 URL
[23]	刘沛清. 空气螺旋桨理论及其应用[M]. 北京: 北京航空航天大学出版社, 2006.
	LIU P Q. Air propeller theory and application[M]. Beijing: Beihang University Press, 2006. (in Chinese)
[24]	班度·N. 帕玛迪. 飞机的性能、稳定性、动力学与控制[M]. 商重阳, 左英桃, 夏露, 等, 译. 第2版. 北京: 航空工业出版社, 2013.
	PAMADI B N. Performance, stability, dynamics, and control of airplanes[M]. SHANG C Y, ZUO Y T, XIA L, et al, translated. 2nd ed. Beijing: Aviation Industry Press, 2013. (in Chinese)
[25]	方振平, 陈万春, 张曙光. 航空飞行器飞行动力学[M]. 北京: 北京航空航天大学出版社, 2012.
	FANG Z P, CHEN W C, ZHANG S G. Flight dynamics of aircraft[M]. Beijing: Beihang University Press, 2012. (in Chinese)
[26]	阙志宏. 线性系统理论[M]. 西安: 西北工业大学出版社, 1995.
	QUE Z H. Linear system theory[M]. Xi’an: Northwestern Polytechnical University Press, 1995. (in Chinese)