IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 41, NO. 5, MAY 2013
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Energy Conversion Efficiency of Electromagnetic Launcher With Capacitor-Based Pulsed Power System Peizhu Liu, Xinjie Yu, Jun Li, and Shizhong Li
Abstract— The stored-to-kinetic energy conversion efficiency of railgun system is investigated by simulation and experiment methods. There are many factors, which might affect the conversion efficiency of the railgun system. These factors include the parameter values of pulsed power supply (PPS), the velocity of armature, the inductance gradient of rail, and so on. To analyze the stored-to-kinetic energy conversion efficiency, a novel electric circuit simulation model for the railgun system is built. The simulation results show that the less resistance, the more inductance of PPS, the more inductance gradient of launcher, and the higher muzzle velocity of armature can improve the energy conversion efficiency of the railgun system. Some experimental results with the 6-MJ railgun system at Beijing Institute of Special Electromechanical Technology are also presented in this paper, which can illustrate the correctness of the analysis and the simulation results. Index Terms— Circuit simulation, energy conversion, pulsed power systems (PPS), railguns.
I. I NTRODUCTION
S
TORED-TO-KINETIC energy conversion efficiency is very important for the development of a railgun launch system [1]. Engel presented a comprehensive theory to conversion efficiency and is applicable to all constant gradient electromagnetic launchers [2]–[4]. The theory not only accounts for the velocity-limit effect, but also predicts a maximum efficiency. Theoretical parameters include the inductance gradient, system resistance, projectile velocity, and sliding contact area. A 6-MJ capacitor-based pulsed power supply (PPS) system is developed to carry out electromagnetic launch experiments at Beijing Institute of Special Electromechanical Technology (BISET) in China and many experiments are done with the 6-MJ railgun launch system. In this paper, the effect of many factors on railgun system performance is investigated
Manuscript received October 30, 2012; revised February 20, 2013; accepted February 26, 2013. Date of current version May 6, 2013. This work was supported in part by the Key Program of National Natural Science Foundation of China under Grant 51237007. P. Liu is with the Department of Electrical Engineering, State Key Lab of Power System, Tsinghua University, Beijing 100084, China, and also with the Science and Technology on Complex Land Systems Simulation Laboratory, Beijing 100012, China (e-mail:
[email protected]). X. Yu is with State Key Lab of Power System, Department of Electrical Engineering, Tsinghua University, Beijing 100084, China (e-mail:
[email protected]). J. Li and S. Li are with the Science and Technology on Complex Land Systems Simulation Laboratory, Beijing 100012, China (e-mail:
[email protected];
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPS.2013.2251367
Fig. 1.
6-MJ PPS system.
by simulation and experiment methods. The factors include some parameters values of PPS, the velocity of armature, the inductance gradient of rail, and so on. To analyze the stored-to-kinetic energy conversion efficiency, a novel electric circuit simulation model for a railgun system is built. Some experimental results with the 6-MJ railgun system of BISET are also presented. II. S IMULATION M ODEL A. PPS System The 6-MJ PPS system consists of 60 modules, each of which stores 100 kJ of energy, and operates at a 10-kV charge voltage (shown in Fig. 1). Each module is composed of two high-energy density capacitors, a solid-state thyristor switch, a crowbar diode, a pulse-shaping inductor, and a coaxial output cable. The entire PPS system can be divided into many segments for asynchronous triggering. Each segment is triggered with a designed delay time to make a proper waveform and each of them can include some modules according to the experimental requirement. B. 6-m Launcher System We increased the length of launcher from 4 to 6 m [5]. The launcher is mainly composed of a pair of parallel rails and the fixture structure of the rails. The rails are two copper bars with a size of 6000 × 40 × 10 mm (length × width × thickness). The fixture structures are used to fix the rails
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TABLE I PARAMETERS OF S YSTEM M ODEL
0
Parameters Resistance of capacitor Resistance of inductor Value of the pulse-shaping inductor Resistance of cable Inductance gradient of rail Resistance gradient of rail Resistance of muzzle-shunt resistor
Value 20 m 10 m 50 μH 2 m/m 0.44 μH/m 0.1 m/m 0.5 m
-1 0 0.5m 1m 1.5m 2m 2.5m 3m 3.5m 4m 1.8k
5m t [s] velocity.VAL
1.5k 1.3k 1.1k 0.9k
and ensure the straightness of the rails over the full length. The fixture structure has six segments whose length is 10-cm made of fiberglass-epoxy slab. Fig. 2 shows the photograph of the launcher. This railgun model also includes a muzzleshunt resistance, to which the current is consumed when the projectile exits the rail.
0.7k 0.5k 0.3k 0.1k -0.1k 0 0.5m 1m 1.5m 2m 2.5m 3m 3.5m 4m
5m t [s]
C. Simulation Model An electric circuit model for the launcher system is built using the software Simplorer to study the influences of the parameters of the system components to the conversion efficiency. Fig. 3 shows the circuit model of the system. The simple launcher model is adopted for numerical simulation according to the 30-mm square bore launcher [1]. The resistance and inductance are assumed to increase linearly along with the rail, with a constant resistance gradient R and a constant inductance gradient L . The acceleration force in the armature is given from the formula F = 1/2 L I 2 , where I is the current flowing into the armature. Table I shows the parameters of the railgun launch system model.
Fig. 5.
Velocity and location of projectile.
III. N UMERICAL R ESULTS AND D ISCUSSION The factors that can affect railgun system conversion efficiency include resistance values of PPS, inductor values of PPS, the velocity of armature, the inductance gradient of rail, and so on. A. Resistance of System Components The resistance of system components, such as module pulse-shaping inductor, capacitors, and the cables, can greatly
LIU et al.: ENERGY CONVERSION EFFICIENCY OF ELECTROMAGNETIC LAUNCHER 0.6Meg
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influence conversion efficiency. According to the design, every PPS module can generate a 50 kA peak current. However, the current of module drops very quickly, which proves that the resistance of the system is high. We made some improvements to increase the conversion efficiency by decreasing the cables resistance [5]. A new cable may be used in the railgun launch system now, the resistance of that is < 0.5 m/m. Initially, the launch processes with different system resistance value is simulated. Figs. 4–7 show the simulation results, including the current, velocity, and the location of projectile over time with different system resistances. For the decrease of the system resistance, the system current duration will increases with a same current peak and the peak current will increases with same current duration. In Figs. 4 and 5, the muzzle velocity of the projectile is ∼1.8 km/s, which means that the kinetic energy is 0.16 MJ with a 100 g projectile. Therefore, the stored-to-kinetic energy efficiency is ∼10%. From Fig. 6, the peak current increased with same current duration for the decrease of the system resistance can be seen. In Fig. 7, it shows that the muzzle velocity is ∼2.1 km/s. The kinetic energy is > 0.22 MJ and the energy conversion efficiency is > 14%. The simulation results show that the improved launch system increases the energy conversion efficiency of the system by 40%.
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C. Velocity of Projectile B. Inductor Values of PPS The pulse-shaping inductor values of PPS can also influence conversion efficiency. Some simulations are carried out to study the launch processes with different inductor values. Based on the railgun launch system that is located in BISET, a 300 g projectile is chosen for this simulation with the 1 MA peak output current. The charging voltage of the capacitors is 8 kV. Figs. 8–11 show the simulation velocity of projectile over time with high and low inductor values, respectively. In Figs. 9 and 11, velocity of projectile varied from 2.2 to 2 km/s. This indicates that the higher inductor value is helpful for the improvement of the system conversion efficiency. It is reasonable that higher inductor means lower output current with the same energy.
According to theoretical analysis of Engel [2]–[4], the velocity of projectile is a key factor for conversion efficiency. To prove this theory, a simulation is done under the same condition as shown in Fig. 8, with the exception of the increasing of the projectile mass from 300 to 500 g. The peak output current is still 1 MA and the charging voltage of capacitors is 8 kV. Fig. 12 shows the simulation current and Fig. 13 shows the simulation velocity of 500 g projectile over time. In Fig. 13, the muzzle velocity of the projectile is ∼1.4 km/s, which means that the kinetic energy is < 0.5 MJ with a 500 g projectile. In Fig. 11, the kinetic energy of the projectile is > 0.6 MJ. The simulation results show that the velocity of projectile increases by 50%, the energy conversion efficiency of the system can be improved by 20%.
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TABLE II E XPERIMENTAL R ESULTS W ITH D IFFERENT V ELOCITY
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Shot #
Mass (g)
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100701 100702 100703
52.4 65.2 96.5
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Velocity (km/s) 2.2 1.92 1.46
Conversion Efficiency 19.8% 19.3% 16.1%
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determined by the larger inductance of these two inductors. Essentially, it is the inductance value of the whole launch system that affects the conversion efficiency. With the same energy, the current waveform of the PPS can also influence conversion efficiency. Higher current means the higher efficiency under the projectile acceleration limit [6].
Velocity of projectile with low PPS inductor.
IV. E XPERIMENTAL R ESULTS D. Other Factors There are few other factors that can affect the conversion efficiency of the railgun system. The inductance gradient of the rail can affect the conversion efficiency as like the pulseshaping inductor values of PPS. The main contribution is
Many experiments are done with the 6-MJ electromagnetic launch system to study the stored-to-kinetic energy conversion efficiency since 2008. Table II shows the experimental results of different launch velocity. It proves that the higher exiting velocity of projectile, the higher energy conversion efficiency.
LIU et al.: ENERGY CONVERSION EFFICIENCY OF ELECTROMAGNETIC LAUNCHER
TABLE III E XPERIMENTAL R ESULTS W ITH D IFFERENT C URRENT WAVEFORM
Shot #
Mass (g)
100709 100710 100714 100715
69.2 69.7 65 52.5
Current Duration (ms) 1.85 1.85 0.55 0.55
Velocity (km/s)
Conversion Efficiency
1.48 1.47 1.67 1.80
12.2% 12.4% 15.7% 14.8%
Table III shows the experimental results of the different output current waveforms. The different currents are generated by triggering the segments of the PPS with different delay times from these results, with the same energy, the less current duration given, the higher velocity of projectile and the better conversion efficiency of the system are obtained.
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[4] T. G. Engel, J. M. Neri, and M. J. Veracka, “The maximum theoretical efficiency of constant inductance gradient electromagnetic launchers,” IEEE Trans. Plasma Sci., vol. 37, no. 4, pp. 608–614, Apr. 2009. [5] P. Liu, J. Li, Y. Gui, S. Li, Q. Zhang, and N. Su, “Analysis of energy conversion efficiency of a capacitor-based pulsed power system for railgun experiments,” IEEE Trans. Plasma Sci., vol. 39, no. 1, pp. 300–303, Jan. 2011. [6] Z. Shi and X. Yu, “Two-objective optimization design for pulsed power supply,” in Proc. 14th Electromagn. Launch Technol. Symp., Jun. 2008, pp. 1–6.
Peizhu Liu was born in Shandong, China, in 1976. He received the B.S. degree in electrical engineering from Qingdao University, Qingdao, China, in 1999, and the M.S. degree from Tsinghua University, Beijing, China, in 2007. He is currently with the Beijing Institute of Special Electromechanical Technology, Beijing. His current research interests include electromagnetic launch technology.
V. C ONCLUSION In this paper, to simulate the influences of the factors to the conversion efficiency, a simple railgun system model and an electric circuit model was built using the software Simplorer based on the BISET railgun launch system. The simulation results showed that the less resistance and the more inductance of PPS, the more inductance gradient of launcher, and the higher muzzle velocity of the projectile can improve the energy conversion efficiency of the railgun system. Some experimental results with the 6-MJ railgun system proved the simulation results.
Xinjie Yu received the B.S. and Ph.D. degrees from the Department of Electrical Engineering, Tsinghua University, Beijing, China, in 1996 and 2001, respectively. He is an Associate Professor with the Department of Electrical Engineering, Tsinghua University. His current research interests include broad aspects of electric-circuit simulation and computational intelligence.
R EFERENCES
Jun Li was born in Sichuan, China, in 1968. He received the B.S., M.S., and Ph.D. degrees from Ordnance Engineering College, Shijiazhuang, China, in 1991, 1994, and 1999, respectively. He was a Post-Doctoral Fellow with the Department of Electrical Engineering, Tsinghua University, Beijing, China, from 1999 to 2001. He is currently with the Beijing Institute of Special Electromechanical Technology, Beijing. His current research interests include electromagnetic launch technology.
[1] R. A. Marshall and W. Ying, Railguns: Their Science and Technology. Beijing, China: China Machine Press, 2004, pp. 7–9. [2] T. G. Engel, W. C. Nunnally, J. M. Gahl, and W. C. Nunnally, “Efficiency and scaling in DC electromagnetic launchers,” in Proc. IEEE Pulsed Power Conf., Jun. 2005, pp. 249–252. [3] T. G. Engel, J. M. Neri, and M. J. Veracka, “The velocity and efficiency limiting effects of magnetic diffusion in railgun sliding contacts,” in Proc. 14th Symp. Electromagn. Launch Technol., Jun. 2008, pp. 417–421.
Shizhong Li was born in Henan, China, in 1980. He received the B.S. and M.S. degrees in electrical engineering from Chongqing University, Chongqing, China, in 2003 and 2006, respectively. He is currently with the Beijing Institute of Special Electromechanical Technology, Beijing. His current research interests include electromagnetic launch technology.
