Study on similarity law of non-proportionally scaled penetration/perforation test
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摘要: 高速侵彻弹体的弹载部件/关键元器件的生存性与可靠性考核是引战系统研制领域的热点与难点问题，受原型试验的成本限制，利用缩比弹体搭载原型引信部件开展非等比例缩比试验研究是可行途径。针对传统等比例缩比方案无法满足弹体刚体过载相似性要求的情况，研究了非等比例缩比侵彻/贯穿相似规律，提出了非等比例缩比侵彻试验设计方法。数值计算结果表明：侵彻半无限厚混凝土靶条件下，非等比例缩比弹刚体过载的脉宽、幅值均可实现与原型弹刚体过载一致的加载条件；贯穿多层薄靶的条件下，通过调节靶板布置及弹体初速等试验工况，合理设计缩比弹体结构，可使非等比例缩比试验的弹体刚体过载峰值和脉宽覆盖原型试验。通过缩比模型试验得到的刚体过载特性可以为弹体及引信部件抗过载防护设计提供可靠的参考依据。Abstract: Survivability and reliability assessment of components/key components on high-speed penetrating projectiles is a hot and difficult issue in the field of EPW development. Due to the cost limitation of prototype test, it is feasible to carry out non-proportionally scale experimental research by carrying prototype fuze components on scaled projectiles. Through the analysis of the process mechanism of a projectile penetrating concrete target, the analytic solution of rigid-body deceleration when the projectile penetrating the semi-infinite thick concrete target and the multi-layer thin concrete target are discussed respectively. From the point of view of similarity of rigid-body deceleration, the non-proportionally reduced-scale criterion of projectile is proposed when the traditional scaling scheme can not meet the requirements of similarity. The numerical results show that under the condition of penetrating semi-infinite thick concrete target, the rigid-body deceleration of the non-proportionally reduced-scale projectile can achieve the same conditions as which of the prototype projectile from the point of view of pulse width and amplitude; under the condition of penetrating multi-layered thin target, through reasonably setting the scale factor and adjusting the layout of the target plate and the initial velocity of the projectile. The pulse width and amplitude of the rigid-body deceleration in the reduced scale test can cover them in the prototype test. The rigid body deceleration characteristics obtained from scaled model test can provide reliable overload environment reference for missile projectile design.
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图 2 弹体SNL-00-02侵彻23 MPa混凝土时的刚体过载曲线比较
Figure 2. Comparison of rigid-body deceleration curves for projectiles (SNL-00-02) penetrating 23 MPa concrete
图 3 弹径缩比系数
λD 与弹长缩比系数λb 、空腔长度缩比系数λe 的对应关系Figure 3. Corresponding relationships among the diameter scaling coefficient
λD , the length scaling coefficientλb and the cavity length scaling coefficientλe 
图 4 弹体侵彻薄靶的偏转过程示意图
Figure 4. Deflection trajectory of a projectile penetrating into a thin target
图 5 弹身长度缩比系数λb与弹径缩比系数λD、空腔长度缩比系数λe的对应取值
Figure 5. The corresponding range of the length reduction coefficient of projectile body λl, the diameter reduction coefficient λD and the cavity length reduction coefficient λe
图 6 原型试验和缩比弹试验弹体侵深
Figure 6. Penetration depth of prototype projectile and reduced scale projectile for two types projectile
图 7 原型试验和缩比弹试验刚体过载对比
Figure 7. Rigid-body decelerations of prototype projectiles and reduced scale projectiles for two types projectiles
图 8 1 000 kg级原型弹与缩比弹侵彻10层混凝土靶板的刚体过载
Figure 8. Rigid-body decelerations of 1 000 kg prototype projectiles and reduced scale projectiles penetrating ten-layer concrete target
图 9 1 000 kg级原型弹与缩比弹的有限元模型对比
Figure 9. Models of 1 000 kg class prototype projectile and reduced scale projectile
图 10 缩比弹自由状态下初始形状与第12阶拉伸模态振型的位移云图对比
Figure 10. Tensile mode shapes of the 12th order modes of scale projectiles in free state
图 11 弹体侵彻十层靶板1/4有限元模型
Figure 11. 1/4 finite element model of a projectile penetrating a ten-layer target plates
图 12 原型弹和缩比弹贯穿10层薄靶过程刚体过载时程曲线
Figure 12. Rigid-body deceleration curve of a prototype projectile and a scale projectile while penetrating 10 layers of thin target
表 1 模型和原型物理量缩比因子
Table 1. Scaling factors of physical quantities between model and prototype
变量 量纲 原型与模型参量比 缩比因子 特征尺寸 L lp/lm n 时间 T tp/tm n 质量 M Mp/Mm n3 密度 ML−3 ρp/ρm 1 应力 ML−1T−2 σp/σm 1 过载 LT−2 ap/am 1/n 速度 LT−1 Vp/Vm 1 
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表 2 原型弹的弹靶参数
Table 2. Expemrimental parameters of prototype projectiles and targets
弹型 D/mm M/kg l/mm ηCRH v0/(m∙s−1) ρt/(kg∙m-3) fc/MPa Ⅰ 250 500 2 000 3.5 450 2 420 45 Ⅱ 380 1 200 2 500 3.5 850 2 420 45
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表 3 缩比系数表
Table 3. Scaling parameters of prototype projectiles
缩比弹序号 λD λM λb λe 1 1.50 2.25 1.20 1.20 2 2.00 4.00 1.30 1.20 3 2.50 6.25 1.50 1.20 4 3.00 9.00 1.60 1.20
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表 4 Ⅱ型（1 000 kg级）弹原型试验及对应的缩比试验参数
Table 4. Prototype test and corresponding scaling test parameters of type II (1 000 kg) projectile
量 原型试验 缩比试验 相关缩比系数 M/kg 1 200 80 λM=15 l/mm 2 500 890 λl=2.8 D/mm 380 150 λD=2.5 ηCRH 3 3 v0/(m∙s−1) 850 850 λv0=1 θ0/(°) 0/10/15 0/10/15 H/mm 300+180×9 300+140×9 λH=1和1.35 z/mm 3 000 2 900 λz=0.97 σbc/MPa 40 30 λfc=0.75 注：z为靶间距；σbc为靶材料抗压强度。
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表 5 1 000 kg级原型弹及其缩比弹自由状态下前20阶模态频率
Table 5. Top 20 modal frequencies of 1 000 kg class prototype projectile and reduced scale projectile in free state
模态序号 模态频率/Hz 模态序号 模态频率/Hz 原型弹 缩比弹 原型弹 缩比弹 7 335.67 1 159.2 14 1 416.2 4 670.5 8 335.67 1 159.2 15 1 453.2 4 670.5 9 716.72 2 132.5 16 2 012.8 6 291.2 10 833.99 2 708.3 17 2 012.8 6 291.2 11 833.99 2 708.3 18 2 200.1 6 463.9 12 1 085.9 3 196.4 19 2 236.0 7 044.5 13 1 416.2 4 563.3 20 2 633.9 8 244.7
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