A simplified theoretical model for attack angle change of a hemispherically-nosed projectile while penetrating the stiffener of a ship plate frame
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摘要: 舰船板架结构加强筋对于弹体侵彻着角与攻角变化有较大影响，而目前对此尚无理论模型。本文开展板架加强筋对弹体攻角变化的理论研究。针对刚性球头弹体侵彻舰船板架结构加强筋问题，将加强筋简化为刚塑性梁模型，建立了侵彻过程力学模型，给出了弹体剩余速度、着角和攻角变化的求解公式。公式表明弹体攻角与着角的变化与弹体初始速度、初始着角、初始攻角以及加强筋极限弯矩有关。通过编程求解理论公式，发现初始着角对于侵彻结束攻角和着角变化的影响大于初始攻角；初始着角超过某一值后，攻角改变会急剧增大，而当初始着角超过另一极限值后会发生弹体跳飞；初始速度越高，弹体侵彻结束后着角和攻角变化越小；加强筋的极限弯矩对弹体攻角改变有较大影响。Abstract: At present, there is no theoretical model for the influence of stiffeners on the impact angle and attack angle of a projectile penetrating a ship plate frame. In this paper, the problem of the rigid hemispherical nosed projectile penetrating the stiffener of the ship's plate frame is studied to give theoretical solution of the change of the attack angle. The stiffener is simplified as a rigid-plastic beam, the motion of which is controlled by plasto-dynamic equations of small deformation. By solving the coupled kinetic equations of the projectile and the beam, the deflection of the beam and the motion of the plastic hinges are obtained. The fracture of the beam is assumed to occur when the maximum tensile strain of the beam reaches the fracture strain of the material. By the above methods, the mechanical model of the penetration process is established. The formulas for the residual velocity, the change of impact angle, and the change of attack angle of the projectile are given. The formulas show that the change of impact angle and attack angle is related to the initial velocity, initial impact angle, initial attack angle, and the ultimate moment of the stiffener. By programming the theoretical formula, it is found that the influence of initial impact angle on the change of impact angle and attack angle at the end of penetration is greater than that of the initial attack angle. When the initial impact angle exceeds a certain value, the change of attack angle will increase dramatically. When the initial impact angle exceeds another limit value, the projectile will ricochet. A higher initial velocity corresponds to a smaller change of the impact angle and the attack angle. The ultimate moment of the stiffener has an important influence on the change of the attack angle.
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Key words:
- penetration /
- plate frame /
- attack angle /
- impact angle /
- residual velocity
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图 2 弹体侵彻板架结构示意图与简化模型
Figure 2. The diagrammatic sketch and simplified model for a projectile penetrating a ship plate frame
图 8 侵彻结束时转角改变Δαm与初始攻角的关系
Figure 8. Relationship between the change of rotation angle and the initial attack angle
图 9 侵彻结束时着角改变Δβm与初始攻角的关系
Figure 9. Relationship between the change of impact angle and the initial attack angle
图 10 飞行至下层甲板时攻角变化Δφ与初始攻角的关系
Figure 10. Relationship between the change of attack angle Δφ at the next deck and the initial attack angle
图 12 侵彻结束时转角改变Δαm与初始着角的关系
Figure 12. Relationship between the change of rotation angle and the initial impact angle
图 13 飞行至下层甲板时攻角变化Δφ与初始着角的关系
Figure 13. Relationship between the change of attack angle Δφ at the next deck and the initial impact angle
图 14 初始速度对着角改变的影响
Figure 14. The influence of initial velocity on the change of impact angle
图 15 初始速度对飞行至下层甲板时攻角变化Δφ的影响
Figure 15. The influence of initial velocity on the change of attack angle Δφ at the next deck
图 16 梁的极限弯矩M0对着角和攻角改变的影响
Figure 16. The influence of the ultimate moment of the beam on the changes of impact angle and attack angle
表 1 板架结构与弹体材料参数
Table 1. Material parameters of the plate frame and the projectile
材料型号 密度/（kg·m−3） 弹性模量/GPa 泊松比 屈服应力/MPa 硬化模量/GPa D p 921A 7 850 202 0.30 685 1.060 8 000 0.8 30CrMnSiNi2A 7 850 517 0.28 1 600 0.594 4 322 0.2 
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表 2 板架结构参数表
Table 2. Structural parameters of the plate frame
板厚/mm 纵骨 横梁 尺寸/mm 间距/m 尺寸/mm 间距/m 8 $\bot \dfrac{ { {\rm{115} } \times 1{\rm{5} } } }{ {1{\rm{00} } \times {\rm{15} } } }$ 0.6 $\bot \dfrac{ {200 \times 6} }{ {80 \times 8} }$ 1.2
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表 3 数值与理论剩余速度结果比对
Table 3. Comparison of the numerical and theoretical results of the residual velocity
v0/（m∙s−1） β0/（°） φ0/（°） Δv/（m∙s−1） 理论 数值 误差/% 750 10 5 14.64 16.59 11.8 750 20 5 14.78 16.88 12.4 750 30 5 14.98 17.52 14.5 750 40 5 15.34 18.83 18.5 750 50 5 16.11 19.13 15.8 750 40 10 15.42 17.99 14.3 650 40 10 18.35 20.79 11.7 550 40 10 23.04 25.59 10.0
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表 4 数值与理论着角结果比对
Table 4. Comparison of the numerical and theoretical results of the impact angle
v0/(m∙s−1) β0/（°） φ0/（°） Δβm/（°） 理论 数值 误差/% 750 10 5 0.23 0.20 15.0 750 20 5 0.44 0.39 12.8 750 30 5 0.75 0.70 7.2 750 40 5 1.07 0.98 9.2 750 50 5 1.51 1.31 15.3 750 40 10 1.02 0.97 5.2 650 40 10 1.43 1.32 8.3 550 40 10 2.14 2.01 6.5 450 40 10 2.51 2.39 5.0
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表 5 数值与理论攻角结果比对
Table 5. Comparison of the numerical and theoretical results of the attack angle
v0/(m∙s−1) β0/（°） φ0/（°） Δφ/（°） 理论 数值 误差/% 750 10 5 0.08 0.07 14.3 750 20 5 0.17 0.16 6.3 750 30 5 0.19 0.18 5.6 750 40 5 0.23 0.20 15.0 750 50 5 2.01 1.92 4.7 750 40 10 0.43 0.4 7.5 650 40 10 1.21 1.15 5.2 550 40 10 4.98 4.56 9.2 450 40 10 5.35 5.21 2.7
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靶板 材料 板厚 纵骨截面积 横梁截面积 纵骨间距 横梁间距 第1层 907A t 34.4t2 91.9t2 δl 3.65δl 第2层 921A 2t 34.4t2 91.9t2 δl 3.65δl 第3层 907A t 34.4t2 91.9t2 δl 3.65δl 第4层 907A t 34.4t2 91.9t2 δl 3.65δl
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