Analysis of Angular Motion and Swerving Response Characteristics of Dual-spinning Two-dimensional Correction Projectile with Canard Layout

doi:10.12382/bgxb.2023.0057

Abstract

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

CLC Number:

TJ012.3

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.

Figures/Tables 19

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Fig.11 Variation curves of Q at different elevation angles

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

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

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

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

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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