鸭式布局二维修正双旋弹角运动及转向响应特性分析

doi:10.12382/bgxb.2023.0057

摘要/Abstract

摘要：

为研究鸭式布局双旋弹受控状态下的动态响应规律,对弹丸角运动特性及转向响应特性进行理论分析。基于7自由度刚体弹道模型,求解弹丸受控状态下的攻角瞬态及稳态解析解,并推导弹丸瞬态及稳态转向响应解析表达式。研究控制指令更新周期、射角、转速及初速对转向响应特性的影响。研究结果表明:输入控制力方向对转向响应相移角影响较小;控制指令更新周期较短时,在弹道顶点相移角瞬态解与稳态解相差较大,采用瞬态解修正后弹丸横纵向耦合程度较低,随着指令更新周期的增大,转向响应相移角瞬态解逐渐趋于稳态解;相移角稳态解随转速增加而减小,随初速增加而增加。通过实验数据验证了理论的正确性。研究结果可为鸭式布局双旋弹二维修正控制系统分析设计提供理论依据。

关键词: 二维弹道修正弹, 鸭式布局, 角运动特性, 转向响应特性, 瞬态响应

Abstract:

In order to study the dynamic response law of dual-spinning projectile with canard layout in the state of control, the angular motion and swerving response characteristics of it are analyzed theoretically. Based on the seven degrees of freedom rigid body ballistic model, the transient-state and steady-state analytical solutions of the angle of attack of projectile are solved, and the analytical expressions of projectile’s transient-state and steady-state swerving responses are derived. The effects of control command update period, elevation angle, spin rate and initial velocity on swerving response characteristics are explored. The results show that the direction of control force has little influence on the phase shift angle of swerving response. When the update period of control command is short, the transient-state and steady-state solutions of phase shift angle differ greatly at the ballistic apex, and the transverse-longitudinal coupling of projectile is low after using the transient solution correction. With the increase in update period, the transient-state solution of phase shift angle of swerving response gradually approaches to the steady-state solution. In addition, the steady-state solution of phase shift angle decreases with the increase in rotational speed and increases with the increase in projectile velocity. The correctness of the theory is verified by experimental data. This research provides some theoretical basis for the design and analysis of two-dimensional correction control system of dual-spinning projectile with canard layout.

Key words: two-dimensional trajectory correction projectile, canard layout, angular motion characteristics, swerving response characteristics, transient-state response

中图分类号:

TJ012.3

李红云, 申强, 邓子龙. 鸭式布局二维修正双旋弹角运动及转向响应特性分析[J]. 兵工学报, 2024, 45(6): 1866-1876.

LI Hongyun, SHEN Qiang, DENG Zilong. Analysis of Angular Motion and Swerving Response Characteristics of Dual-spinning Two-dimensional Correction Projectile with Canard Layout[J]. Acta Armamentarii, 2024, 45(6): 1866-1876.

图/表 19

图1 鸭式布局双旋弹及鸭舵修正组件

Fig.1 Dual-spinning projectile with canard layout and correction part

表1 弹丸主要参数

Table 1 Main parameters of projectile

参数	数值	参数	数值
m/kg	45.50	d/m	0.155
l/m	0.952	l_f/m	0.560
$I a x$ /(kg·m²)	0.163	$I a y$ /(kg·m²)	1.814

表1 弹丸主要参数

Table 1 Main parameters of projectile

参数	数值	参数	数值
m/kg	45.50	d/m	0.155
l/m	0.952	l_f/m	0.560
$I a x$ /(kg·m²)	0.163	$I a y$ /(kg·m²)	1.814

表2 弹丸起控点的主要弹道参数

Table 2 Main ballistic parameters of projectile starting control point

θ₀/(°)	t_c/s	v/(m·s^-1)	$γ ·$ /(r·s^-1)	γ_c/(°)
29	10	588.3	255.7	0,90
	29	340.1	214.1	0,90
51	10	590.2	260.3	0,90
	45	274.5	221.4	0,90

表2 弹丸起控点的主要弹道参数

Table 2 Main ballistic parameters of projectile starting control point

θ₀/(°)	t_c/s	v/(m·s^-1)	$γ ·$ /(r·s^-1)	γ_c/(°)
29	10	588.3	255.7	0,90
	29	340.1	214.1	0,90
51	10	590.2	260.3	0,90
	45	274.5	221.4	0,90

图2 攻角解析解和数值解变化曲线(θ0=29°, tc=10s)

Fig.2 Variation curves of analytical solution and numerical solution of angle of attack(θ0=29°,tc=10s)

图3 攻角解析解和数值解变化曲线(θ0=29°,tc=29s)

Fig.3 Variation curves of analytical solution and numerical solution of angle of attack(θ0=29°,tc=29s)

图4 攻角解析解和数值解变化曲线(θ0=51°,tc=10s)

Fig.4 Variation curves of analytical solution and numerical solution of angle of attack(θ0=51°,tc=10s)

图5 攻角解析解和数值解变化曲线(θ0=51°,tc=45s)

Fig.5 Variation curves of analytical solution and numerical solution of angle of attack(θ0=51°,tc=45s)

图6 转向响应相移角随起控时间变化曲线(θ0=29°)

Fig.6 Variation curves of swerve response phase shift angle over starting control time(θ0=29 °)

图7 转向响应相移角随起控时间变化曲线(θ0=51°)

Fig.7 Variation curves of swerve response phase shift angle over starting time (θ0=51°)

图8 不同射角时转向响应相移角随控制指令更新周期的变化曲线(θ0=29°)

Fig.8 Variation curves of swerve response phase shift angle with control command update cycle (θ0=29 °)

图9 不同射角时转向响应相移角随控制指令更新周期的变化曲线(θ0=51°)

Fig.9 Variation curves of swerve response phase shift angle with control command update cycle (θ0=51°)

表3 不同控制周期下的弹丸耦合比

Table 3 Projectile coupling ratio at different control cycles

射角/(°)	周期/s	$ζ s c o u p l e$ /%	$ζ t c o u p l e$ /%
	5	26.1	4.6
29	10	11.5	1.3
	15	6.6	0.4
	12	33.0	1.4
51	18	17.1	3.4
	25	7.4	5.3

表3 不同控制周期下的弹丸耦合比

Table 3 Projectile coupling ratio at different control cycles

射角/(°)	周期/s	$ζ s c o u p l e$ /%	$ζ t c o u p l e$ /%
	5	26.1	4.6
29	10	11.5	1.3
	15	6.6	0.4
	12	33.0	1.4
51	18	17.1	3.4
	25	7.4	5.3

图10 不同射角下的稳态转向响应相移角变化曲线

Fig.10 Variation curves of steady-state swerve response phase shift angle at different elevation angles

图11 不同射角下的Q值变化曲线

Fig.11 Variation curves of Q at different elevation angles

图12 不同射角下的 γ ·/v变化曲线

Fig.12 Variation curves of γ ·/v at different elevation angles

图13 不同初速下的稳态转向响应相移角变化曲线

Fig.13 Variation curves of steady-state swerve response phase shift angle at different initial velocities

图14 不同转速下的稳态转向响应相移角变化曲线

Fig.14 Variation curves of steady-state swerve response phase shift angle at different spin rates

表4 实验初始条件

Table 4 Experimental initial conditions

参数	数值	参数	数值
初速/(m·s^-1)	917	实际起控时间/s	29
射角/(°)	29	落点射程/m	24620
滚转角/(°)	270	落点横偏/m	912

表5 理论与实验结果对比

Table 5 Comparison of theoretical and experimental results

时间间隔/s	相移角/(°)		相对误差/%
时间间隔/s	实验值	理论值	相对误差/%
5	123.3	131.2	6.4
10	134.7	140.4	4.2
15	136.9	141.7	3.5
20	132.3	142.9	8.0

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