Oblique penetration of elliptical cross-section projectile into metal target
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摘要: 为研究椭圆截面弹体对半无限金属靶体的侵彻弹道规律，基于14.5 mm弹道枪平台，开展了椭圆截面弹体在0°～20°倾角、850～950 m/s撞击速度下对2A12铝合金的斜侵彻试验。基于空腔膨胀理论及局部相互作用模型，建立了椭圆截面弹体侵彻弹道模型，并结合试验数据验证了模型的准确性。在此基础上，进一步分析了椭圆截面弹体长短轴之比、绕弹轴旋转角度、弹体撞击速度对侵彻弹道的影响规律。弹体长短轴之比为1.0时，弹体退化为尖卵形圆截面弹体，且椭圆截面弹体侵彻弹道稳定性随长短轴之比的增大而变弱，最优长短轴之比为1.0，即尖卵形圆截面弹体。椭圆截面弹体绕弹轴旋转一定角度后，侵彻弹道在平面曲线与空间曲线之间变化，当旋转角度为0°、90°时，侵彻弹道为二维平面弹道，当旋转角度在0°～90°之间时，侵彻弹道为三维空间弹道。当弹体撞击速度由800 m/s提升至1000 m/s时，椭圆截面弹体姿态角增量由18.6°降至17.8°。Abstract: In order to study the penetrating trajectories of elliptical cross-section projectiles into semi-infinite metal targets, a penetration trajectory model was established based on the dynamic cavity expansion theory and local interaction model. The shape function of the elliptical cross-section projectile was developed based on the local interaction model, and the resistance model derived from the dynamic cavity expansion theory was used to calculate the forces and moments acting on the elliptical cross-section projectile under the local Cartesian coordinate system. Thus, the factors affecting the projectile penetration trajectory were considered, including the major axis to minor axis ratio of the cross-section, the angle around the projectile axis and the striking velocity. Then, oblique penetrating experiments were carried out at a striking velocity ranging from 850 to950 m/s and an oblique angle ranging from 0° to 20°. Furthermore, the model was validated by experimental results. Finally, the influence of the major axis to minor axis ratio of the cross-section, the angle around the projectile axis and the striking velocity on the penetration trajectory was analyzed. When the major axis to minor axis ratio is 1.0, the projectile is degenerated into an ogive-nosed one. With the increase of this ratio, the stability of the elliptical cross-section projectile reduces. The optimal value of the major axis to minor axis ratio is 1.0, and the penetration trajectory is the most stable at this time. The penetration trajectory will change from a two-dimensional plane curve to a three-dimensional space curve when the angle around the projectile axis varies. When the angle around the projectile axis is 0° or 90°, the penetration trajectory is in a two-dimensional plane. Otherwise, the penetration trajectory is a three-dimensional space curve. The increasement of the attitude angle of the elliptical cross-section projectile decreases from 18.6° to 17.8° when the striking velocity increases from 800 m/s to 1000 m/s.
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图 3 弹体表面微元法向速度分析
Figure 3. Analysis of the outer normal velocity of surface elements of the projectile
图 10 椭圆截面弹体侵彻弹道
Figure 10. Penetration trajectories of the elliptic cross section projectiles
图 11 γ=0°时不同弹体侵彻弹道计算结果
Figure 11. Calculation results of the penetration trajectories of various projectiles while γ is 0°
图 12 γ=0°时不同弹体的姿态角变化
Figure 12. Time histories of the attitude angle αx of various projectiles while γ is 0°
图 13 弹体绕弹轴旋转示意图
Figure 13. Schematic diagraph of the projectile rotating around axis z
图 14 不同γ角下弹体侵彻弹道计算结果
Figure 14. Calculation results of penetration trajectories at different γ
图 15 不同γ角度下弹体姿态角变化
Figure 15. Time histories of the attitude angle of projectiles under different γ
图 16 不同v0下弹体侵彻弹道计算结果
Figure 16. Calculation results of the penetrationtrajectories at different v0
表 1 弹体结构质量参数
Table 1. Parameters of the projectile
弹体 等效曲径比 2ar/mm 2br/mm L/mm m/g HRC硬度 30CrMnSiNi2A 5.6 14.5 9.0 43.5 22.2 42～45 
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表 2 2A12铝合金力学性能参数
Table 2. Parameters of the target material aluminum alloy 2A12
材料 ρt/(kg∙m−3) E/GPa Yt/MPa n 2A12 2730 69.3 326.7 0.069
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表 3 弹体侵彻试验结果
Table 3. Test results of the penetration trajectories
试验 v0/(m∙s−1) α0/(°) γ/(°) θ0/(°) 试验结果 SX/mm SY/mm SZ/mm αend/(°) T2-8 873 5.0 14 –1.0 3.7 14.8 –55.4 22.0 T2-13 898 11.1 –54 1.1 10.0 13.8 –53.3 25.1 T2-12 920 20.8 –7 0.8 5.3 43.5 –57.5 43.3
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表 4 椭圆截面弹体终点坐标对比
Table 4. Comparison of the final coordinates of the elliptic cross section projectiles
试验 v0/(m∙s–1) 试验结果 计算结果 误差 SX/mm SY/mm SZ/mm αend/(°) SX/mm SY/mm SZ/mm αend/(°) ΔSX/mm ΔSY/mm ΔSZ/mm Δαend/(°) T2-8 873 3.7 14.8 –55.4 22.0 0.2 8.5 –60.0 15.4 3.5 6.3 –4.6 6.6 T2-13 898 10.0 13.8 –53.3 25.1 0.9 17.8 –57.5 14.6 9.1 –4.0 –4.2 7.3 T2-12 920 5.3 42.7 –57.5 43.3 1.4 37.2 –59.1 36.1 3.9 5.5 –1.6 –15.8
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表 5 计算弹体结构质量参数
Table 5. Computational parameters of the projectiles
弹体 2ar/mm 2br/mm a rCRH Lp/mm L/mm m/g Jx/(g·mm2) Jy/(g·mm2) Jz/(g·mm2) loc/mm 1# 9.0 9.0 1.0 5.6 20.9 43.5 16.9 1876 1876 158 26.2 2# 10.8 9.0 1.2 5.6 20.9 43.5 17.0 1839 1877 217 24.3 3# 12.6 9.0 1.4 5.6 20.9 43.5 17.0 1847 1930 274 23.1 4# 14.5 9.0 1.6 5.6 20.9 43.5 17.1 1967 2108 344 23.4 5# 16.2 9.0 1.8 5.6 20.9 43.5 17.1 2091 2289 414 22.2 6# 18.0 9.0 2.0 5.6 20.9 43.5 17.0 2010 2266 468 21.2
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