长杆弹侵彻流体动力学模型的精确解及其分析

Discussion and Derivation on Solutions of Long-Rod Penetration Erosion Equations

Alekseevskii-Tate模型(简称为AT模型)是目前长杆弹侵彻理论模型中最经典且应用最广泛的改进的流体动力学模型。在AT模型基础上,指出并完善了其推导过程的存在不足之处。推导出了一般情况下AT模型中关键参数如瞬时侵彻深度与最大侵彻深度的解析解,并对几种具体情况下的具体精确解进行了讨论分析。从理论上,论述分析了长杆弹垂直侵彻半无限靶板侵彻主要过程中的弹体速度的"不稳定"特性,并就弹靶材料密度比、弹靶流变强度比对弹体侵彻过程中弹体的瞬时侵彻深度、弹体的最大侵彻深度、弹体的瞬时速度等主要特性的影响规律进行了理论分析。

The Alekseevskii-Tate model is the most important and most widely used model in the modified hydrodynamic theory of penetration model over 50 years. The problem in the derivation on the long rod penetration equations first formulated by Tate in 1967 was solved. The analytical solutions of the instanta- neous penetration depth and maximal penetration depth were deduced. And the exact solutions of them in some special cases were presented and discussed. Based on the solutions, the ＂non-steady＂ behavior of the velocity of the penetrator in the process of penetration was analyzed and then the influences of the den- sity ratio and resistance ratio of the penetrator to target on the instantaneous penetration depth, the instan- taneous velocity of the penetrator and maximal penetration depth were investigated theoretically.