Trajectory characteristics of elliptical cross-section projectile penetrating multi-layer spaced steel targets
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摘要: 为了研究椭圆类截面弹体侵彻多层间隔钢靶的弹道特性，开展了典型弹体侵彻多层间隔Q355B钢靶试验，基于LS-DYNA软件开展有限元仿真研究，得到了弹体在侵彻过程中的姿态偏转和弹道参数，分析了弹体的偏转机制，获得了截面形状、截面压缩系数、初速、滚转角和着角等弹靶参数对椭圆类截面弹体侵彻弹道特性和姿态偏转特性的影响规律。研究结果表明：滚转角为0°时，圆截面弹体侵彻弹道稳定性优于椭圆类截面弹体；弹体截面压缩系数越大，弹体侵彻弹道稳定性越好；弹体初速越大，弹体姿态偏转越小，侵彻弹道越平稳；滚转角为90°时，椭圆截面和非对称椭圆截面弹体在入射平面内的侵彻弹道最稳定，并且两种弹体在水平面内的弹道偏移量分别在滚转角为45°和90°时达到最大，非对称椭圆截面弹体在滚转角为钝角时的侵彻弹道稳定性优于锐角时的情况；弹体着角在[0°，50°]范围内时，侵彻弹道稳定性随着角的增大先减弱后增强，着角在30°左右时姿态偏转和弹道失稳最严重；弹体以较正姿态贯穿薄钢靶时，在弹头部侵彻阶段就已经与靶体分离；弹体以较大攻角贯穿薄钢靶时，弹靶接触主要发生在弹体的上表面。Abstract: An experimental investigation of typical projectiles penetrating multi-layer spaced Q355B steel targets was conducted to study the trajectory characteristics of elliptical cross-section projectiles penetrating multi-layer spaced steel targets. Numerical simulations were performed on LS-DYNA finite element software and typical results obtained were validated by experimental results. The attitude and trajectory parameters in the penetration process and the deflection mechanism of the projectile were obtained. The influence of cross-section shape, the minor-to-major axis length ratio of the projectile cross-section, initial velocity, rotation angle, and incident angle on the penetration trajectories and attitude deflection was investigated. The research results show that the penetration trajectory stability of the circular cross-section projectile is better than the elliptical and asymmetric elliptical cross-section projectiles when the rotation angle is 0°. As the minor-to-major axis length ratio increases, the trajectory is more stable. The trajectory deflection reduces with a higher initial velocity. When the rotation angle is 90°, the penetration trajectory of both symmetric and asymmetric elliptical cross-section projectiles in the incident plane is the most stable, and the trajectory deflection of the two projectiles in the horizontal plane reaches its maximum at rotation angles of 45° and 90°, respectively. The trajectory stability of an asymmetric elliptical projectile, when the rotation angle is obtuse, is better than that at the acute angle. When the incident angle is in the range of [0°, 50°], the trajectory instability and attitude deflection of the projectile increase with the increase of incident angle and then decrease, and both reach the largest when the incident angle is about 30°. It is also found that the projectile will separate from the target during the penetration stage of the projectile nose when penetrating a thin steel target in a stable attitude. When the projectile penetrates a thin steel target at a large attack angle, the attachment of the projectile and target mainly occurs on the upper surface of the projectile.
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图 3 弹体侵彻条件示意图
Figure 3. Schematic representation of conditions of projectile penetration
图 5 不同初始条件下的侵彻弹道偏转
Figure 5. Penetration trajectory deflection under different initial conditions
图 7 回收到的4发弹体（左1～4）和原始弹体（右1）
Figure 7. The recovered four residual projectiles (1st to 4th from left) and original projectile (1st from right)
图 10 姿态角、攻角变化试验与仿真结果的对比
Figure 10. Comparison between simulations and experiments for trajectory angle and attack angle
图 11 侵彻弹道试验与仿真结果的对比
Figure 11. Comparison between simulations and experiments for penetration trajectory
图 12 弹体偏转角加速度曲线和对应侵彻过程
Figure 12. Rotation acceleration curve and corresponding penetration process
图 14 不同截面压缩比下弹体侵彻弹道的仿真结果
Figure 14. Penetration trajectory simulation results of projectiles under different λ
图 15 不同截面压缩系数弹体偏转角速度和角加速度时程曲线
Figure 15. Time history curves of angular velocity and angular acceleration under different λ
图 16 不同截面压缩系数弹体攻角和姿态角时程曲线
Figure 16. Time history curves of attack angle and trajectory angle under different λ
图 18 不同滚转角下E1弹体侵彻弹道仿真结果
Figure 18. Penetration trajectory simulation results of E1 projectile under different rotation angles
图 19 不同滚转角下NE1弹体侵彻弹道仿真结果
Figure 19. Penetration trajectory simulation results of NE1 projectile under different rotation angles
图 20 不同滚转角下E1和NE1弹体攻角变化
Figure 20. Changes in the attack angle of E1 and NE1 projectiles under different rotation angles
图 21 不同滚转角下E1和NE1弹体在水平面和入射平面内的姿态角变化
Figure 21. Changes in the trajectory angle of E1 and NE1 projectiles under different rotation angles
图 22 不同滚转角下E1弹体在2个平面的侵彻弹道轨迹
Figure 22. Penetration trajectories of E1 projectile in different rotation angles (horizontal plane and incidence plane)
图 23 不同滚转角下NE1弹体在2个平面内的弹道轨迹
Figure 23. Penetration trajectories of E1 projectile in different rotation angles (horizontal plane and incidence plane)
图 24 不同着角下E1弹体侵彻弹道仿真结果
Figure 24. Penetration trajectory simulation results of E1 projectile with different incident angles
图 25 不同着角下E1弹体攻角和姿态角时程曲线
Figure 25. The time history curves of attack angle and trajectory angle at different incident angles
表 1 4种弹体的主要几何参数
Table 1. Main geometry parameters of the four projectiles
弹体类型 λ a/mm b/mm CRH m/g C1 1.0 12.5 12.5 4.19 389 E1 0.7 15.0 10.5 3.00 389 NE1 0.8/0.6 15.0 12.0/9.0 3.00 389 NE2 0.9/0.5 15.0 13.5/7.5 3.00 389 
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表 2 弹体侵彻每层钢靶前后的弹道参数
Table 2. Trajectory parameters of the projectile before and after penetrating each steel plate
试验
编号v0/
(m·s−1)β0/
(°)β1/
(°)β2/
(°)β3/
(°)β4/
(°)ϕ0/(°) ϕ1/(°) ϕ2/(°) ϕ3/(°) ϕ4/(°) 水平面 入射平面 水平面 入射平面 水平面 入射平面 水平面 入射平面 水平面 入射平面 E1-1 809.1 1.6 — 2.5 — 10.6 1.8 2.0 — — 0.9 4.0 — — 11.5 13.4 E1-2 790.6 2.4 −2.8 −3.3 −9.3 −22.8 0 16.1 0 14.8 0.9 11.9 3.0 −2.0 4.3 −19.4 E1-3 610.5 0 −0.8 −7.9 −20.6 −44.2 −0.9 30 −2.5 27 — 14.0 — −1.1 −6.5 −34.3 E1-4 799.7 1.5 −1.1 −5.4 −13.8 −31.5 0 31.5 0 28.7 0 21.2 0 7.3 0 −7.9 E1-5 1000.0 0.9 −0.4 −4.3 — −14.4 0.2 30.9 1.0 30.0 1.9 27.5 — — 4.0 12.5 E1-6 807.3 −0.8 −1.6 −6.3 −10.2 −24.6 −1.5 29.2 −1.3 27.2 0 23.9 0 16.9 4.8 2.1 E1-7 802.4 0 −0.2 −0.3 −0.3 −3.7 0 30.0 0 29.0 0 27.9 0 27.6 0 25.6 C1-1 796.3 0 0 −0.3 −2.4 −10.4 0 30.0 0 30.0 0 28.8 0 25.9 0 16.9 NE1-1 807.2 0.5 — — — −46.7 — 29.5 — — — — — −2.1 — −24.9 NE2-1 798.7 0 −2.9 −12.6 −33.3 −53.2 5.3 30.0 6.6 26.4 9.8 9.1 22.4 −9.0 51.3 −38.3
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表 3 材料参数
Table 3. Material parameters
材料 ρ/(g·cm−3) E/GPa μ A/MPa B/MPa n c m D1 D2 D3 D4 35CrMnSiA 7.85 210 0.30 Q355B[20] 7.85 210 0.28 339.5 620.0 0.403 0.02 0 0.820 6.047 −7.09 −0.003
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表 4 部分典型工况弹体剩余速度试验与仿真结果的对比
Table 4. Comparison between simulations and experiments for residual velocity of projectiles
试验编号 靶板层数 剩余速度/（m·s−1） 误差/% 试验结果 仿真结果 E1-4 1 794.2 795.4 0.15 2 782.5 789.2 0.86 3 762.7 779.2 2.16 4 737.9 754.1 2.19 E1-6 1 801.0 802.2 0.14 2 789.9 794.5 0.58 3 780.8 783.1 0.29 4 764.6 760.1 −0.59 NE2-1 1 792.7 793.6 0.11 2 783.4 783.6 0.02 3 751.5 759.5 1.06 4 681.4 689.9 1.24
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