﻿ 轨道炮动力学特性仿真分析
 舰船科学技术  2017, Vol. 39 Issue (8): 133-137 PDF

1. 中国船舶重工集团公司 第七一三研究所，河南 郑州 450015;
2. 洛阳舒诚机械有限公司，河南 洛阳 471000

Simulation analysis on the dynamics characteristics of railgun
GAO Bo1, QIU Qun-xian1, WU Li-zhou1, MA Xin-ke1, QIE Wen-jing1, CUI Hai-li2
1. The 713 Research Insitute of CSIC, Zhengzhou 450015, China;
2. Luoyang Shucheng Mechanical Equipment Co.,Ltd., Luoyang 471000, China
Abstract: Based on the general dynamic model of railgun, with the focus on the expression of the dynamic response of rail, conduct the sensitivity analysis of the influence factors of critical speed, seek the maximum influence factors of critical speed of the rail gun, provide the support for the structural design of the rail gun. With the regard to the launch device of certain rail gun, use the software of Ansys to conduct the numerical simulation of aerodynamics, and compare the simulation analysis with the result of theoretical calculation methods, provide the reference accordance for the further research on the characteristics of the rail gun and the optimization design for the railgun.
Key words: railgun     critical speed     susceptibility     structural design
0 引 言

1 轨道炮临界速度分析 1.1 轨道炮简化模型

 图 1 轨道炮简化模型示意图 Fig. 1 Simplified model diagram for the railgun
1.2 轨道炮临界速度计算

 $m\frac{{{\partial ^2}\omega }}{{\partial {t^2}}} + E{I_x}\frac{{{\partial ^4}\omega }}{{\partial {x^4}}} + {K_f}\omega = q[1 - H(x - Vt)]\text{，}$ (1)

 $q[1 - H(x - Vt)] = \left\{ \begin{array}{l}0,\quad(x > Vt),\\q,\quad(x \leqslant Vt),\end{array} \right.$ (2)

 ${V_{cr}} = \sqrt[4]{{4\frac{{E{I_x} \cdot {K_f}}}{{{m^2}}}}} = \sqrt[4]{{\frac{1}{3}\frac{h}{B}\frac{{E{K_f}}}{{{\rho ^2}}}}},$ (3)

 $w(x,t) = \frac{2}{L}\sum\limits_{n = 1}^\infty {W(n,t)\sin \left( {\frac{{n\pi x}}{L}} \right)} \text{。}$ (4)
1.3 临界速度敏感度分析

 图 2 弹性模量E不同时轨道中点变形图 Fig. 2 Maximum displacement of the mid pointof the rail versus E with different velocity

 图 3 截面惯性矩Ix不同时轨道中点变形图 Fig. 3 Maximum displacement of the mid point of the rail versus Ix with different velocity

 图 4 轨道密度ρ不同时轨道中点变形图 Fig. 4 Maximum displacement of the mid point of the rail versus ρ with different velocity

 图 5 支撑弹性系数Kf不同时轨道中点变形图 Fig. 5 Maximum displacement of the mid point of the rail versus Kf with different velocity

1）由图2图3可知，随着轨道的弹性模量E、截面惯性矩Ix增加，其临界速度亦增加，但轨道最大变形量变化小于5%；

2）由图4可知，随着轨道的密度ρ增加其临界速度降低，但轨道的最大变形量变化不大于10%；

3）由图5可知，随着支撑弹性系数Kf增加，轨道炮临界速度增加，导轨的最大变形量减小40%。

2 某轨道炮动力学仿真 2.1 有限元模型建立

 图 6 某轨道炮实体模型 Fig. 6 Solid model of certain rail gun

 图 7 某轨道炮有限元模型 Fig. 7 Finite element model of certain rail gun
2.2 理论临界速度计算

 图 8 在轨道上施加均布荷载 Fig. 8 Application of even load on the rail

 $\Delta x = 0.2099{\rm E} - 3\;{\rm m},$

 $\Delta F = P*A = 100{\rm E}6 \times 3 \times 0.06 = 1.8{\rm E}7{\rm N}\text{，}$

 ${K_f} = \Delta F/\Delta x = 8.57{\rm E}10{\rm N}/{\rm m}\text{，}$

 ${V_{cr}} = \sqrt[4]{{\frac{1}{3}\frac{h}{B}\frac{{E{K_f}}}{{{\rho ^2}}}}} = 2265\;{\rm m}/{\rm s}\text{。}$
2.3 不同移动载荷速度下轨道典型节点位移响应的计算

 图 9 载荷移动速度为2 500 m/s时炮尾节点位移随时间的变化曲线 Fig. 9 When the load moving speed is 2 500 m/s, the deformation curve for the displacement of the joints of the gun tail with time

 图 10 载荷移动速度为2 500 m/s时中间节点位移随时间的变化曲线 Fig. 10 When the load moving speed is 2 500 m/s, the deformation curve for the displacement of the joints of the middle with time

 图 11 载荷移动速度为2 500 m/s时炮口节点位移随时间的变化曲线 Fig. 11 When the load moving speed is 2 500 m/s, the deformation curve for the displacement of the joints of the gun mouth with time

 图 12 炮尾节点位移响应随速度变化值 Fig. 12 Deformation value of the displacement response of joints in the gun tail with the speed

 图 13 中间节点位移响应随速度变化值 Fig. 13 Deformation value of the displacement response of joints in the middle with the speed

 图 14 炮口节点位移响应随速度变化值 Fig. 14 Deformation value of the displacement response of joints in the gun mouth with the speed

3 结 语

1）轨道炮结构设计过程中一方面要充分考虑临界速度对轨道变形的影响，设计时要尽可能的通过优化轨道炮系统中的各个参数，以提高轨道炮的临界速度，至少要使轨道炮的临界速度大于所预定的炮口初速，从而减少对导轨的烧蚀影响。

2）支撑材料的弹性系数作为影响轨道炮临界速度主要因子，设计时要在其他条件允许的情况下应尽可能地提高该参数数值，从而以最快的方式提高轨道炮的临界速度，得到合理的结构形式。

3）本文的研究成果可为轨道炮结构特性研究奠定基础，为身管优化设计提供参考依据。

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