Structural optimization design and structural response of elliptical-section penetration projectiles
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摘要: 针对异型截面侵彻弹体的工程应用需求，围绕椭圆截面侵彻弹体结构响应及优化设计问题开展研究。引入无量纲壁厚系数，改进了椭圆截面弹体参数化表达式；以提高短轴惯性矩和静矩、降低短轴方向结构响应为目标，开展了椭圆截面弹体抗弯优化设计。基于152 mm口径轻气炮开展了椭圆截面弹体反弹道侵彻试验研究，获得了软回收试验弹体的弯曲挠度结果；开展了试验工况的数值模拟研究，提取了数值模拟中弹体的变形结果；建立了椭圆截面侵彻弹体弯曲结构响应计算模型，利用此模型对试验弹体变形情况进行了计算。与原椭圆截面弹体相比，优化后截面短轴惯性矩、静矩提高比例约为16%，试验弹体弯曲挠度降低比例约为25.3%，数值模拟及理论模型计算结果与试验结果较为相符，验证了本文优化设计方法的有效性，可为工程设计提供参考。Abstract: According to the engineering application requirements of special-shaped section penetrating projectiles, the structural response and optimal design of elliptical-section penetration projectiles were studied. From this point of view, an improved general design method of elliptical-section projectiles was developed by introducing a dimensionless cartridge thickness coefficient of the elliptical projectile. In order to improve the inertia moment and static moment to the short axis of the cross-section, a bending optimization design method of the elliptical-section projectile was proposed by reducing the cartridge thickness of the projectile to a certain extent and redistributing the reduced materials. Based on a 152-mm-diameter light gas gun test device, the reverse tests of three kinds of elliptical-section hollow projectiles with the long axis of 1.8 cm and the short axis of 1.2 cm penetrating a 2024-O aluminum target were carried out, and the responses of the projectiles in the penetration process were obtained. The projectiles after tests were collected by the soft recovery method, and the deformation of the central axes of the projectile was obtained by the gray processing method. Numerical simulations of the tests were carried out by LS-DYNA. The stress, strain, and penetration load of the projectiles during the penetration process were obtained, and the equivalence of the normal ballistic test and reverse ballistic test was verified. Based on the free-free beam theory, a bending response calculation model of the elliptical-section projectile was established. Through the optimized design, the inertia moment to the short axis of the elliptical section increases by 16.44%, and the static moment increases by 15.95%. Under the test conditions, the bending deflection of the projectile decreases by 25.25%. The structural response model was used to calculate the projectile deformation under the test conditions. The calculation results of the theoretical model are in good agreement with the test results, which shows that the calculation method of the model has a certain accuracy and can provide a reference for engineering design.
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图 2 圆形截面弹体、现有椭圆截面弹体与改进的椭圆截面弹体截面设计方法
Figure 2. Cross-section designs of circular-section, existing elliptical-section, and improved elliptical-section projectiles
图 4 椭圆异型侵彻体截面优化设计方法
Figure 4. Optimal design method for bending resistance of elliptical-section projectiles
图 5 优化截面内腔翼缘形状尺寸示意图
Figure 5. Schematic diagram of the shape and size of the upper edge of an optimized section inner cavity
图 7 椭圆截面弹体反弹道侵彻试验结果
Figure 7. Reverse ballistic penetration test results of elliptical-section projectiles
图 9 不同结构弹体试验结果中轴线的对比
Figure 9. Comparison of the central axes of the projectiles with different structures after tests
图 11 ξ=0.15的弹体形变模拟结果与试验结果的对比
Figure 11. Comparisons between simulation and test results for deformation of the projectiles of ξ=0.15
图 12 ξ=0.15弹体模拟形变中轴线与试验形变中轴线对比
Figure 12. Comparison of simulation and test results of the central axes of the projectiles of ξ=0.15
图 13 0.15-0.15弹体正反弹道模拟结果对比 (t=115 μs)
Figure 13. Simulated results of normal ballistic and reverse ballistic of the 0.15-0.15 projectile (t=115 μs)
图 14 0.15-0.15弹体正反弹道z向接触载荷对比
Figure 14. Comparison of z-directional contact loads between normal ballistic and reverse ballistic of the 0.15-0.15 projectile
图 15 反弹道撞击过程中弹体所受到的接触载荷
Figure 15. Contact loads on the projectile during reverse ballistic impact
图 17 ξ=0.15弹体理论计算中轴线与试验形变中轴线对比(Mp1)
Figure 17. Comparison of calculation and test results of the central axes of the projectiles of ξ=0.15 (Mp1)
图 18 弹体理论计算中轴线与试验形变中轴线对比(Mp2)
Figure 18. Comparison of calculation and test results of the central axes of the projectiles of ξ=0.15 (Mp2)
表 1 试验弹体截面几何特征
Table 1. Geometric characteristics of test projectile sections
弹体结构 截面形状 短轴惯性矩/mm4 短轴静矩/mm3 长轴惯性矩/mm4 长轴静矩/mm3 0.15-0.15 
1159.45 141.91 5870.66 212.86 0.15-0.10 
1257.49 151.20 4704.62 182.68 0.15-0.05 
1350.02 164.55 3274.32 166.59 
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表 2 试验撞击条件与弹体挠度结果
Table 2. Test conditions and deflections obtained
弹体编号 弹体截面形状 弹体着靶速度/（m·s−1） 挠度结果/mm 实际攻角/（°） 0.15-0.15(1) 
198.22 4.62 6.54 0.15-0.15(2) 
216.48 4.79 5.84 0.15-0.10(1) 
215.01 4.08 6.07 0.15-0.05(1) 
209.42 3.58 6.42
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表 3 数值模拟中弹靶材料参数
Table 3. Material parameters in numerical simulation
材料 ρ/（g·cm−3） E/GPa ν Y/MPa EH/MPa K/MPa n 双线性硬化30CrMnSiNi2A 7.83 201.0 0.33 1 650.0 300 指数硬化2024-O 2.70 67.2 0.34 134.4 273 0.114
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表 4 弹体中轴线挠度结果试验、计算与模拟结果对比
Table 4. Comparison of test, calculation, and simulation results of projectile central axis deflection
弹体结构 挠度/cm 与试验结果的相对误差/% 试验 理论 模拟 理论 模拟 0.15-0.05 0.358 0.364 0.355 1.7 0.9 0.15-0.10 0.408 0.417 0.411 2.2 0.7 0.15-0.15 0.479 0.477 0.492 0.4 2.6
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