Analysis of Complete Period Free Rotational Vibration Motion of a Tail-controlled Dual-spin Projectile

doi:10.12382/bgxb.2024.0782

Abstract

Abstract:

Recently, the guided transformation-based dual-spin configuration has become an effective means to improve the accuracy of ammunition strikes.To study the complete period free disturbance motion of a new type of tail-controlled dual-spin projectile, a 7 degrees of freedom ballistic model is established based on the ideal bearing assumption and non-roll coordinate system.The ballistic equations are linearized using the coefficient freezing method and small disturbance assumption.The complete period free disturbance motion equations are derived and represented in a state space form.A feature point on the ideal trajectory is selected.The motion modal for the complete period free disturbance near the feature point is obtained by numerical calculation method.The forms of free disturbance motion under different initial deviation values are discussed.The results indicate that the dual-spin projectile exhibits strong coupling characteristics in longitudinal and lateral motions.Similar to conventional projectiles, the free disturbance motion of dual-spin projectiles can still be divided into two stages: long period and short period.But the difference lies in the slow convergence of the angle of attack offset, and the modal amplitudes of different angle of attack offsets have different distribution patterns.The research results lay the foundation for further studying the angular motion and designing the guidance law.

Key words: tail-controlled dual-spin projectile, free disturbance motion, coefficient freezing method, linearized trajectory, micro-spoiler

ZHONG Ding, JI Zhentao, YANG Pengxiang, ZHANG Xinye, JIANG Zhihao. Analysis of Complete Period Free Rotational Vibration Motion of a Tail-controlled Dual-spin Projectile[J]. Acta Armamentarii, 2024, 45(S2): 271-282.

Figures/Tables 10

Fig.1 A new type of dual-spin projectile

Fig.2 Ballistic parameters of ideal trajectory and feature point

Table 1 Parameters of coefficient matrix

参数	数值	参数	数值
a₁₁	-0.0237	a₁₂	0.0247
a₁₃	-0.9052	a₁₄	-5.4290
a₂₁	3.3533×10^-5	a₂₂	0.0859
a₂₄	-0.0203	a₂₅	0.0021
a₃₁	3.2666×10^-6	a₃₃	0.0876
a₃₆	0.0021	a₄₁	-0.0069
a₄₂	-13.1608	a₄₃	-363.1512
a₄₆	34.8944	a₄₇	-0.3239
a₄₈	-103.3560	a₅₁	2.9447×10^-5
a₅₂	355.8118	a₅₃	-13.4323
a₅₆	-34.8944	a₅₇	103.3560
a₅₈	-0.3239

Table 2 Motion parameters of different motion modes

模态	振荡周期/s	振幅减小一半的时间/s	周期衰减比例
高频运动	0.0630	3.5630	0.9878
中频运动	1.7437	3.2054	0.6859
低频运动	468.8944	31.5	3.311×10^-5

Fig.3 Two stages of free disturbance motion under given initial conditions

Fig.4 Change relationship between lateral and longitudinal angles of attack

Fig.5 Free disturbance motions under different initial conditions in long period

Fig.6 Free disturbance motions under different initial conditions in short period

Fig.7 Two-circular motions under different initial values

Fig.8 Proportion of amplitude under different initial conditions

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