An optimization method for passive muzzle arc control devices in augmented railguns

Bo Tng , Qing-hu Lin , Bo-ming Li ,b

a National Key Laboratory of Transient Physics, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu, China

b China Academy of Ordnance,100089, Beijing, China

ABSTRACTIn this paper, a passive muzzle arc control device (PMACD) of the augmented railguns is studied.By discussing its performance at different numbers of extra rails, a parameter optimization model is proposed.Through the calculation model, it is found that the PMACD works well in the simple railgun,which refers to the gun that there is only one pair of rails in the inner bore.The PMACD may decrease the simple railgun’s armature peak current and muzzle arc,but affect its muzzle velocity not much.However,in the augmented railguns it has different characteristics.If the parameters of the PMACD are not selected suitable.It may increase the armature peak current and muzzle arc, but greatly decrease the velocity.The reason for this problem is that the extra rails generate a strong magnetic field in front of the armature, which induces a large current to change the armature current.It is also found that when the resistance and inductance parameters of the PMACD satisfy with the optimization formula, the PMACD can also play a good role in arc suppression in the augmented railguns.Experiments of an augmented railgun with a stainless steel PMACD are carried out to verify this optimization method.Results show that the muzzle arc is obviously controlled.This work may provide a reference for the design of the muzzle arc control device.

Keywords:Augmented railguns Arc suppression Muzzle device Optimization method Shunts

1.Introduction

Electromagnetic gun is a change from traditional gunpowder weapon to electric weapon, while the gunpowder firing cannot avoid burning.In theory, the electromagnetic gun can launch without light or sound, which is a great development of high velocity weapons.However, railguns always produce many muzzle arcs with explosions or flashes at present [1].The reason of producing the muzzle arc is that when the armature leaves the rails,there is still a large current passing through the armature,resulting in the contact interface changes from fine solid contact to arc contact[2].Then the energy in the power supply system continues to be released with the arc, which may raise the arc temperature,produces more metal vapor and plasma.The larger the current density, the greater the arc intensity, and the higher the flash and noise[3].The muzzle arcs may last for a period until the energy in the power system is dissipated [4].In order to control the muzzle arc, we can start from two aspects.One is to avoid a large current passing through the armature when the armature leaves the rail.The other is to avoid the injection of energy into the arc.

Installing a shunt on the muzzle may be an effective way [5].Parker first proposed a muzzle shunt railgun in literature which connected the rails with a conductor on the muzzle[6],so that the magnetic field ahead or behind the armature can both accelerate the armature.Parker further proposed an inductive shunt structure[7],the arc suppression performance was verified by the calculation and experiments.J.S.Bernardes proposed a capacitor-muzzleshunt energy recovery device [8].In which, the remaining energy of the rail circuit was stored,it may also reduce the muzzle energy.A.N.Smith studied the energy distribution in railguns with muzzle arc control device [9], and found the resistance type muzzle arc control device accounted for 29%of the total energy,which would lead to a high temperature rise.However, a high energy consumption rate may reduce the energy of other components,which can be used for thermal management.He Yong used a low impedance trigger switch as an arc control device [10].In this method, when the armature was close to the muzzle, the switch quickly conducted to release the energy.The test results were fine,but the volume of the switch was large.Yang Fan proposed a method of using the additional power supply to decrease the muzzle arc [11].Its principle was when the armature exits, the additional power supply quickly discharged to generate a reverse current,which may decrease the armature current.The calculation and experiment showed that this arc suppression effect was fine,but the system was also too large.

To sum up, the arc control device may mainly be divided into active and passive mode.The active arc control device is using a switch or a reversed power supply to reduce the armature current at muzzle, and the passive arc control device is using the resistor,inductor, or capacitor to connect the muzzle rails.The design method of active arc control device is simple, but it needs the precise measurement of the armature exiting time with a complex system.By comparison, the passive muzzle arc control device(PMACD) is more suitable for the small caliber launcher as its simple structure.In this paper, characteristics of the PMACD in different augmented railguns are analyzed, and the method of parameters optimization is given.

2.Circuit model analysis of the PMACD

The principle of the PMACD is shown in Fig.1, which connects the interior rails by a shunt.The passive muzzle arc control process can be roughly divided into two stages.The first stage is the compressing of the magnetic flux in front of the armature, which may induce a reverse current to reduce the armature current.The second stage is the conducting of the muzzle current with the shunt after the armature is out, with which the energy of the power supply is released.

In the first stage, when the armature moves, both the inductance and resistance are changing in the circuit,as shown in Fig.2.And they are increasing rapidly behind the armature, and decreasing rapidly in the front.The magnetic flux at the front area is also decreasing,inducing a large reverse current in the circuit.The circuit equations of the first stage are as follows.

whereis the breech voltage,is the armature voltage,is the muzzle voltage.andare the induced electromotive force generated by the armature circuit and the shunt circuit.is the total current in the rails.is the armature current,is the shunt current.1’ is the resistance gradient and’ is the inductance gradient of the interior rails.is the mutual inductance gradient.andare the initial resistance and inductance of the railgun.is the contact resistance.andare the resistance and inductance of the PMACD.is the launch range,andis the armature moving length.

Fig.1.Schematic diagram of railgun with arc suppression device.

Fig.2.Equivalent circuit diagram of the first stage.

Fig.3.Equivalent circuit diagram of the second stage.

In the second stage, when the armature is out of the launcher,there still a lot of arcs remaining among the rails,which is seen as a resistor continues to pass the circuit, shown in Fig.3.The circuit equations of the second stage are as follows.

is the arc resistance, the copper plasma conductivity calculated by Marshall [12]is about 20 S/mm.Different from the railgun without the PMACD, the electromagnetic force is affected by the magnetic field on both sides of the armature.The force and motion equations are as follows,whereis the forward force,is the armature mass, andis velocity.

3.Results and discussion

Calculation shows that the influence of PMACD in the augmented railgun is mainly different at the first stage from the simple railgun (in the structure of one pair of rails), the magnetic field in front of the armature is significantly enhanced by the extra rails, which makes a larger reverse current in the armature.At the second stage,the PMACD almost has the same effect with different railguns.Some different features are analyzed below, in which the inductance gradient of the railgun model is 0.45 μH/m for the structure of one pair of rails, 0.75 μH/m for the structure of two pairs of rails, and 1 μH/m for the structure of three pairs of rails.

3.1.Current affected by the extra rails

In the structure of one pair of rails,due to the shunt effect,a part of the current flows through the PMACD, which reduces the armature current from 145.7 kA to 135.5 kA,by about 7%.The total currentis not significantly affected.The current curve is shown in Fig.4(a).Decrease of armature current is beneficial to reduce the erosion and the muzzle arc.Besides,the current in the shunt circuit is always positive, which may increase the propulsion electromagnetic force and the muzzle velocity.So,in the structure of one pair of rails, the PMACD is favorable for arc control and launching.

However, in the structure of two (or more) pairs of rails, the current in armature and shunt have a significant change.The armature current is higher and the shunt current becomes negative.This is due to the current rising in the extra rails, which increases the magnetic field in front of the armature, and induces a strong current in the shunt circuit.In this period,the direction of induced current is consistent with the armature current,which will increase the armature peak current from 145.1 kA to 179.1 ka,increasing by 23.4%of the two pairs of rails,shown in Fig.4(b).And in the three pairs of rails,it increases the armature peak current from 144.5 kA to 215.5 ka, increasing by 49.1%.This huge armature current will erode the rails and insulating materials, which is a big disadvantage.

Fig.4.Currents in different railguns with PMACD.

Fig.5.Calculation model and current curve.

Besides, when the armature moves at a high speed, the area of the shunt circuit is rapidly compressed and the current in extra rails is also decreasing.These changes lead to the decrease of the magnetic flux,and induce a reverse current in the armature,decreasing the armature current to a negative value.When the armature current is negative,there will be a large backward electromagnetic force which will reduce the armature velocity.Therefore, the PMACD is not much suitable for the structure of multi pairs unless its parameters are optimized.

3.2.Muzzle arc current affected by the PMACD

When the armature leaves the muzzle, the residual muzzle arc will continue to conduct the circuit, and the current will further strengthen the arc.If the PMACD is installed, whose resistivity is much less than the arc’s,most of the current will flow through the PMACD instead of the muzzle arc.Using the finite element method,two calculation models are established, one is only rails, and the other is equipped with PMACD.The structure and current waveform are shown in Fig.5.Here, it is assumed that there are conductive arcs at the muzzle.

The calculation results are shown in Fig.6 (a) and (b), with the same current value of 75 kA, the muzzle arc generated by the current almost disappears with the PMACD.This arc suppression effect is the same with simple railgun and augmented railgun.

3.3.Current affected by the PMACD parameters

The impedance of the PMACD has an important influence on the performance of the arc suppression and launcher.If the impedance is too large,the current is difficult to flow through the PMACD,and the arc suppression effect is not well.On the contrary, if the impedance is too small, lots of the currents flow through the PMACD,that makes the armature current to be negative.In order to achieve satisfactory effect, it is necessary to optimize the impedance of the PMACD.

In the structure of one pair of rails,the currents in armature and shunt are shown in Fig.7(a)and(b)with different impedance.The smaller the impedance of the PMACD,the faster the current in the armature drops, and even decreases to negative before the armature exits.Small armature current is beneficial to control the muzzle arc,but when it is negative it may decrease the velocity.The best condition is that when the armature is leaving the muzzle,the armature current reduces to zero,or just slightly greater than zero.

In the structure of multi pairs of rails, the maximum peak current of the armature is higher,and more sensitive to the impedance of the PMACD.The smaller the impedance is, the higher the peak armature current is,and the larger the last negative current value is.In the structure of two pairs of rails, shown in Fig.8 (a) and (b)maximum armature current may achieve 182.8 kA, and the minimum is about -186.9 kA.In the three pairs structure, shown in Fig.9 (a) and (b), maximum armature current may achieve 224.1 kA,and the minimum is about-284.5 kA.Which means more extra rails will lead to a larger variation of current in the armature.However,in some values of the impedance the PMACD works well.Such as 0.3 mΩ and 0.3 μH,the armature current becomes zero,and the launch efficiency is not affected.

It is shown that if the parameters of the PMACD are not designed well,the launch condition may become terrible since the armature current is reversed.On the other hand, if we select suitable parameters,the PMACD can also work well in the augmented railguns.

3.4.Velocity affected by the PMACD parameters

However,the PMACD will reduce the arc at the cost of sacrificing part of the launching efficiency, shown as Fig.10.The velocity will be decreased more in multi pairs of rails, and the smaller the impedance, the more the speed drops.According to Ref.[6], the magnetic flux in front of the armature in the common series augmented railgun is trapped by the rail-to-rail connections and forced to flow back in to the breech region as the projectile moves forward.None of the energy associated with this flux is lost.In contrast, the flux ahead of the projectile in the muzzle shunt railgun, which must decrease as the projectile pushes it out of the railgun,cannot return to the breech region and must be dissipated.Although part of the launch energy is lost,it is better to achieve fine arc suppression performance with minimum loss.Next section,there gives a method to achieve the optimal balance between arc suppression performance and launch efficiency by the selection of the parameters of PMACD.

Fig.6.Muzzle arc effected by the PMACD.

Fig.7.Currents in the structure of one pair of rails.

Fig.8.Currents in the structure of two pairs of rails.

Fig.9.Currents in the structure of three pairs of rails.

Fig.10.Velocity variations affected by the PMACD in different railguns.

4.Parameters optimization method

The purpose of parameters optimization is to make the armature current near zero when the armature leaves the muzzle, in order to decrease the muzzle arc,and not reduce the velocity much.Firstly, we simplify the equations to find out the relationship between the impedanceand.If we assume=0 when armature exits, that is=, and then we get Eq.(5) and Eq.(6).= 0 also indicates=, here we get Eq.(7), which is the optimization formula.

When Eq.(7)is equal to zero,the optimal result can be obtained.When it is greater than zero,the armature current and muzzle arc will increase.When it is less than zero, the armature current may be negative to reduce the velocity,so the formula should be equal to zero, or near zero at the positive side.

To further simplify Eq.(7), assuming that all the armature current will pass the shunt when the armature exits,and here gives an estimated equation as following.

whereis a simplified coefficient,which is approximately taken as inductance gradient multiple between multi pairs structure and one pair structure.△is approximately regarded as the time from peak to exit.

Thus,as Eq.(9),the relationship between the,of the PMACD and the parameters of the launcher is obtained.When the parameters satisfy with this formula, the muzzle arc may be well controlled,and the velocity may not be reduced much.If the left">"the right of the formula, the arc is increasing; If the left "<" the right, the velocity is decreasing.

Taking a two pairs structure railgun as an example,the armature current affected by theandis shown in Fig.11(a),the muzzle velocity result is shown in Fig.11 (b).The dotted line is the optimization result obtained by Eq.(9).Which means the parameters of the PMACD should be selected near the dotted line.On the left side of the dotted line, the armature current will reverse to reduce velocity.On the right side,the residual armature current and muzzle arc is larger.

5.Experimental analysis

We design a PMACD and a two pairs structure railgun for experiments shown in Fig.12, which can be regarded as a combination of resistance and inductance.The PMACD is made of stainless steel,for its high resistivity and intensity.And some holes and ring loops are processed to increase the inductance.This structure is simple like a conventional gun muzzle device.It has small size but high strength, suitable for the small caliber launchers.In Table 1,there are the measured values of the resistance and inductance between the current input terminal and current output terminal of the PMACD, measured by the LCR test instrument set at 200 Hz.Those parameters of the PMACD are optimized according to the calculation method proposed above.

Fig.11.Parameters calculated by the optimization method.

Fig.12.Structure of the PMACD.

Table 1Measured resistance and inductance of the PMACD.

Experiments show that this PMACD has good muzzle arc suppression effect.In test 1 and test 2 there are no PMACD,and in test 3 the PMACD is equipped.The total current waveform is shown in Fig.13(a),with a peak current of about 140 kA,and a pulsed power energy of 200 kJ.The total current of test 3 is a bit larger than that of test 1 and test 2.Breech voltage curves are shown in Fig.13 (b), at the beginning, the induced voltage by the multi rails is large and increase the breech voltage of test 3, but will soon drop below to that of test 1 and test 2.Curves of the muzzle voltage are shown in Fig.14 (a), the shunt current in the PMACD of test 3 is shown in Fig.14(b).At the initial moment,muzzle voltage and shunt current turns into a negative value as the previous calculation.A high resistance voltage divider is installed at the muzzle to measure the voltage, with which the induced voltage is much higher in test 1 and test 2 than that of the PMACD in test 3.At about 1 ms, the muzzle voltage and shunt current become positive with a peak,this may be caused by poor initial electrical contact of the armature and the rails.At this point, some currents pass through the shunt instead of the armature with the effect of PMACD in test 3, which causes the contact voltage much smaller than that in test 1 and test 2.Then, with the increase of electromagnetic force, the contact becomes tighter and the contact resistance drops.The results show that the PMACD can reduce the arc in the bore.When the armature is leaving, the current rapidly increases to 17.5 kA in the PMACD.Which means the current passes through the shunt instead of the armature or the muzzle arc,and the muzzle arc will be decreased.

Fig.13.Total Currents and breech voltage measured of the experiment.

Fig.14.Muzzle voltage and PMACD current measured of the experiment.

Fig.15.High speed video recording of projectile flight without the PMACD in test 1.

Fig.16.High speed video recording of projectile flight without the PMACD in test 2.

Fig.17.High speed video recording of projectile flight with the PMACD in test 3.

The arc suppression effect can be more obvious from the highspeed camera.The high-speed camera is placed about 2 m away from the muzzle, aiming at the trajectory of the projectile.When the PMACD is not installed, lots of arcs are generated and they are wrapping around the projectile,shown in Fig.15 and Fig.16.When the PMACD is installed at the muzzle, it has good arc suppression effect.There is no arc around the projectile,and only the projectile flies,shown in Fig.17,and the weight of the projectile is about 30 g.In the tests,the speed of test3 is about 860 m/s,and the velocity of test1 is 75.6 m/s higher than that of test 3, and test2 is 32.4 m/s higher than that of test3.It seems that the PMACD reduces a little but not much velocity.However, velocity measurement employs on-off current signal,which is greatly disturbed by electromagnetic and arcs.The velocity variation given here is for reference only,further research will be carried out in the next step.In general,from the experiments,we believe that the calculation method proposed in this paper is feasible.This simple and compact passive muzzle arc control device may work well in the small caliber railgun.

6.Conclusions

This paper discusses the performance of the PMACD in the augmented railguns, and derives the optimization formula.Analysis shows that the PMACD has good performance in the structure of one pair of rails,which can reduce the muzzle arc,armature peak current, and not reduce the velocity.However, in the structure of multi pairs of rails,due to the enhancement of the magnetic field in front of the armature, the induced current in the circuit is much larger.When the resistance and inductance of the PMACD are too small.The peak current of armature will increase at initial moment,and then decrease sharply to negative hundreds of kA at exiting moment.

Further analysis shows that by optimizing the parameters of the PMACD,the arc and the launch efficiency may be controlled in the multi pairs.And a formula for the parameter optimization is given.According to this formula, we have designed a stainless steel PMACD, which has small size but high strength.The experiments show that this PMACD has fine arc suppression effect.The PMACD proposed in this paper is suitable for the small caliber launcher.And the optimization method may be useful for the design of the arc control device.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The authors would like to acknowledge the Fundamental Research Funds for the Central Universities (Grants No 309190112102), and the Natural Science Foundation of Jiangsu Province (Grants No BK20200493).