鸭舵式双旋弹非线性角运动及其分岔特性

doi:10.12382/bgxb.2022.0426

摘要/Abstract

摘要：

针对鸭舵式双旋弹在飞行过程中可能出现大攻角情况,使原基于小攻角假设获得的稳定性判据等结论难以对这种状况下弹丸的飞行稳定性进行准确判断,为此对该类炮弹的非线性角运动及其分岔特性展开研究。在非滚转系中建立鸭舵式双旋弹改进的6自由度弹道方程,并在考虑几何非线性和气动非线性条件下,推导精确的广义复攻角运动方程及其状态空间模型;应用霍尔维茨方法提出该类炮弹大攻角飞行时的动态稳定性判据,并通过数值仿真计算分析不同因素对系统分岔特性和极限环半径的影响。研究结果表明:升力和马格努斯力矩的非线性项以及飞行速度是影响系统分岔特性的主要因素;舵片控制力和力矩以及空气密度的增大均容易使极限环半径减小;有控飞行时极限环半径可能进一步减小,但其受前体滚转角控制方位的影响不大,即前体滚转角控制方位改变对飞行稳定性影响较小。

关键词: 鸭舵式双旋弹, 非线性角运动, 闭轨线分岔, 不稳定极限环

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

中图分类号:

TJ012.3

赵新新, 史金光, 王中原, 张宁. 鸭舵式双旋弹非线性角运动及其分岔特性[J]. 兵工学报, 2023, 44(10): 3067-3078.

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.

图/表 10

图1 前体结构示意图

Fig.1 The configuration of the forebody

表1 弹丸物理参数

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

图2 空气动力和力矩组合参数

Fig.2 Combination parameters of aerodynamics and moments

图3 弹道顶点处r随τi变化曲线

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

图4 不同初值下的复攻角运动曲线

Fig.4 Complex attack angle motions under different initial values

图5 r随t变化曲线(τi=0)

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

图6 不同弹道点处r随τi变化曲线

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

图7 不同弹道点的复攻角运动曲线

Fig.7 Complex attack angle motion at different ballistic points

图8 不同μ时r随τi(i=1,4,5)变化曲线

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

图9 不同控制方位下的复攻角曲线

Fig.9 Complex attack angle motions under different control directions

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