Nonlinear Angular Motionand Bifurcation Characteristics of Canard Dual-Spin Projectiles

doi:10.12382/bgxb.2022.0426

Abstract

Abstract:

Canard dual-spin projectiles may exhibit a significant angle of attack during flight, challenging the original stability criteria derived under the assumption of small attack angles. Thus, it is difficult to accurately judge the flight stability of projectiles under such conditions. In this paper, the nonlinear angular motion and bifurcation characteristics of such projectiles are studied. An improved six-degree-of-freedom ballistic equation of canard dual-spin projectiles is established with the geometric nonlinearity and aerodynamic nonlinearity considered, and the accurate generalized motion equation of complex attack angle and its corresponding state space model are deduced. Accordingly, numerical methods are used to analyze the influence of different factors on the bifurcation characteristics and limit cycle radius of the system. The results show that the nonlinear of lift and Magnus moment and the flight velocity are the main factors affecting the bifurcation characteristics of the system. The increase of the control force and moment of canards and air density tend to reduce the limit cycle radius. The radius of the limit cycle may be reduced in controlled flight compared with that in uncontrolled flight, but it is approximately independent of the control orientation of the front body roll angle, that is, the change of front body roll angle has little impact on flight stability.

Key words: canard dual-spin projectiles, nonlinear angular motion, closed track bifurcation, unstable limit cycle

CLC Number:

TJ012.3

ZHAO Xinxin, SHI Jinguang, WANG Zhongyuan, ZHANG Ning. Nonlinear Angular Motionand Bifurcation Characteristics of Canard Dual-Spin Projectiles[J]. Acta Armamentarii, 2023, 44(10): 3067-3078.

Figures/Tables 10

Fig.1 The configuration of the forebody

Table 1 Physical parameters of the projectile

参数	数值	参数	数值
m/kg	45.50	d/m	0.155
l/m	0.902	L/m	0.495
A/(kg·m²)	1.792	δ_f/(°)	4
C/(kg·m²)	0.163	δ_d/(°)	6

Fig.2 Combination parameters of aerodynamics and moments

Fig.3 Variation curves of r with τi at ballistic apex

Fig.4 Complex attack angle motions under different initial values

Fig.5 Variation curve of r with t (τi=0)

Fig.6 Variation curves of r with τi at different ballistic points

Fig.7 Complex attack angle motion at different ballistic points

Fig.8 Variation curve of r with τi(i=1,4,5) under different μ values

Fig.9 Complex attack angle motions under different control directions

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