Analysis of influencing factors on outlet velocity of multi-stage synchronous induction coil gun
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摘要: 多级同步感应线圈炮的电枢出口速度受线圈-电枢发射系统的结构参数、材料参数及线圈激励电路参数等多种因素的综合影响。由于电枢出口速度直接取决于其受到的轴向电磁力，而电磁力与线圈电流和电枢感应涡流等因素正相关，因此增大电枢出口速度的本质是增大电枢所受电磁力或电枢感应涡流。为探究线圈发射中影响出口速度的因素，基于等效电路模型探讨了提高出口速度的理论路径；并以5级线圈驱动32 kg电枢为研究对象，利用有限元软件Ansys Maxwell仿真分析了影响出口速度的因素。主要结论如下：等效电路分析表明，减小回路总电感可提高出口速度；在实际发射系统中，减小单级线圈匝数、降低矩形导线截面形状因子（径向宽/轴向宽）、增大电枢厚度与长度、减小线路电感，均可提高电枢出口速度；其中，线圈匝数由48匝降至24匝时，出口速度提升5.2%；电枢长度由110 mm增大至440 mm时，出口速度提升15.3%。最终仿真实现5级线圈驱动32 kg电枢的出口速度达202.1 m/s，发射效率为33.3%。本文研究结果为设计多级同步感应型线圈发射实验方案提供了一定的理论支撑。Abstract:
Background As an important branch of electromagnetic launch, multi-stage synchronous induction coil gun has become one of the hotspots of launch research because of its non-contact, linear propulsion and high efficiency. Among them, the armature outlet velocity is an important index, which is affected by many factors such as the structural parameters, material parameters and coil circuit parameters. However, the existing research lacks theoretical analysis on various factors.Purpose The purpose of this paper is to analyze theoretical approaches for improving the armature outlet velocity, and to explore the factors affecting it.Methods Based on the equivalent circuit model, this paper derives the analytical formula of armature induced eddy current., and investigates these factors affecting the outlet velocity via finite element simulation.Results Theoretical analysis shows that reducing the total inductance of the coil-armature equivalent circuit can increase the armature outlet velocity. Simulation results show that under the same initial electric energy, reducing the number of turns of coils, reducing the cross-sectional shape factor of rectangular wire, increasing the thickness and length of armature, and reducing the line inductance can improve the armature outlet velocity. Considering various factors, the simulated outlet velocity of 32 kg armature driven by 5-stage coil can reach 202.1 m/s, and the launch efficiency is 33.3%. The influence of various factors on the armature is in line with the theoretical analysis results.Conclusions The research content of this paper provides some theoretical support for the design of multi-stage synchronous induction coil gun scheme. -
图 6 不同线圈匝数的有限元仿真结果
Figure 6. Finite element simulation results with different coil turns
图 9 不同电枢厚度时回路等效电感
Figure 9. Loop equivalent inductance at different thickness of armature
图 10 不同电枢厚度的有限元仿真结果
Figure 10. Finite element simulation results with different thickness of armature
图 11 不同电枢长度时回路等效电感
Figure 11. Loop equivalent inductance at different length of armature
图 12 不同电枢长度的有限元仿真结果
Figure 12. Finite element simulation results with different length of armature
图 13 不同线路电感Ll的有限元仿真结果
Figure 13. Finite element simulation results of different line inductance Ll
图 14 电枢速度和电磁力有限元仿真结果
Figure 14. Finite element simulation results of armature velocity and electromagnetic force
图 16 单级线圈-电枢磁场与范式等效应力仿真（80 kA）
Figure 16. Simulation of single-stage coil-armature magnetic field and von mises stress (80 kA)
表 1 线圈匝数与电枢出口速度、发射效率间的关系
Table 1. The relationship between coil turns and armature outlet velocity, launch efficiency
N armature outlet velocity/m·s−1 launch efficiency 24 192.9 30.4% 30 191.1 29.8% 36 189.0 29.2% 42 186.8 28.5% 48 183.4 27.5% 
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表 2 α与导线截面尺寸的对应关系
Table 2. The corresponding relationship between α and wire section size
α section size(radial width*axial width)/(mm2) 4/3 8×6 1 6.928×6.928 3/4 6×8 12/25 4.8×10
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表 3 α与电枢出口速度、发射效率间的关系
Table 3. The relationship between α and armature outlet velocity, launch efficiency
α armature outlet velocity/m·s−1 launch efficiency 4/3 183.1 27.4% 1 188.7 29.1% 3/4 192.9 30.4% 12/25 197.1 31.7%
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表 4 电枢厚度与电枢出口速度、发射效率间的关系
Table 4. The relationship between the thickness of armature and armature outlet velocity, launch efficiency
D armature outlet velocity/m·s−1 launch efficiency/% 10 188.2 28.9 20 192.9 30.4 30 194.4 30.8 40 194.9 31.0 50 195.2 31.1 60 195.4 31.2
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表 5 电枢长度与电枢出口速度、发射效率间的关系
Table 5. The relationship between the length of armature and armature outlet velocity, launch efficiency
H armature outlet velocity/m·s−1 launch efficiency/% 110 168.9 23.3 220 192.9 30.4 330 194.8 31.0 440 194.8 31.0 550 194.8 31.0 660 194.8 31.0
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表 6 Ll与电枢出口速度、发射效率间的关系
Table 6. The relationship between Ll and armature outlet velocity, launch efficiency
Ll armature outlet velocity/m·s−1 launch efficiency/% 0 194.6 30.9 5 193.2 30.5 12.5 192.9 30.4 20 191.4 29.9 25 189.8 29.4
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表 7 线圈结构参数
Table 7. Coil structure parameters
parameter type N α cross-sectional area of
rectangular wire/mm2optimization parameters 24 12/25 48 initial parameters 36 3/4 48
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表 8 线圈激励电路参数
Table 8. Coil excitation circuit parameters
parameter type storage capacitor/mF voltage of storage capacitor/kV line inductance/μH line resistance/mΩ optimization
parameters16 7 5 8.6 initial
parameters16 7 10 8.6
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表 9 电枢结构参数
Table 9. Armature structure parameters
parameter type D/mm H/mm optimization parameters 20 300 initial parameters 30 220
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