Modeling and Analysis of Rudder Nonlinear Control Force for Dual-spin Projectile with Canards

doi:10.12382/bgxb.2023.0402

Abstract

Abstract:

A dual-spin projectile with canards is ballistically corrected by adjusting the orientation of the forebody roll angle, and establishing an accurate rudder control force model is the key to an in-depth study of its ballistic characteristics and ballistic design. Taking the interference between projectile and each canard into account, the Fourier series is used in the non-rolling frame to transform the periodic effect arising from the change in the orientation of longitudinal symmetry plane of forebody with respect to the plane of complex attack angle, and an accurate rudder control force model is established for this type of projectile flying at large attack angles. The relationships among the structural parameters of canards, the amplitude and phase of complex attack angle and the orientation of forebody roll angle are revealed. The computational fluid dynamics (CFD) numerical method is used to simulate and analyze the rudder control force at different forebody roll angles and complex attack angles. The results show that the rudder control force has strong non-linearity in magnitude and direction, especially at large attack angles, due to the combined influence of the normal forces of a pair of despinning rudder and steering rudder. The proposed model can accurately describe the rudder non-linear control force of dual-spin projectile with canards and the influence of various factors on it, which provides a theoretical basis for the forebody structure design, ballistic characteristics analysis and ballistic design of the projectile.

Key words: dual-spin projectile with canards, rudder control force, non-linearity, numerical calculation

CLC Number:

TJ011.⁺3

ZHAO Xinxin, SHI Jinguang, WANG Zhongyuan, ZHANG Ning. Modeling and Analysis of Rudder Nonlinear Control Force for Dual-spin Projectile with Canards[J]. Acta Armamentarii, 2024, 45(8): 2607-2616.

Figures/Tables 8

Fig.1 The configuration of dual-spin projectile with canards

Fig.2 Grid of flow area around forebody/afterbody

Table 1 Verification of convergence

N/10⁶	Δt/μs	C_F_x/10^-3	C_F_y/10^-2	C_F_z/10^-3
3.7	5	-5.97	5.41	-9.25
	1	-6.02	5.36	-9.18
5.8	5	-6.17	5.27	-9.07
	1	-6.19	5.24	-9.09
8.4	5	-6.20	5.18	-9.13
	1	-6.20	5.19	-9.13

Fig.3 Variation curves of rudder control force coefficient

Fig.4 CA and ϕ of rudder control force coefficient

Table 2 Fourier coefficients

系数	a_w_,_j_,0	a_w_,_j_,1	b_w_,_j_,1	a_w_,_j_,2	b_w_,_j_,2
F_1,1	1.820	0.044	-0.006	0.003	-0.071
F_1,2	-0.771	-0.199	0.015	0.078	0.039
F_2,0	-0.067	-0.024	-0.002	0	-0.001
F_2,1	1.694	0.211	0.027	0.006	0.013
F_2,2	-0.751	-0.301	-0.020	-0.095	-0.041

Fig.5 Projection of rudder control force coefficient on OyAzA plane

Fig.6 Motion curves of complex disturbance attack angle under different control directions

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