Simulation and analysis of an augmented railgun launching process

Journal of Harbin Instiute of Technology (New Series)，Vol. 19, No. 2, 2012，Simulation and analysis of an augmented railgun launching processWANG Zhen-chun'", u Hui guang' , ZHAN Zaiji'王振春,李惠光，战再吉(1. School of Seience und Technology. Yanshen Univenity, Qinhuangdao 066004 , Chinn, zjzhan@ yan@ y8u. edu.cn;2. Insiule d Eetrical Engneering. Yanshan lUniverity , Qinbuangdao 0660040 China)Abstract: For characterizing a seriea augmented railgun launching process, the simulation and experiment weredone. In the experiment, only observation of muzzle volage, current and armature position were insufcient toanalyze launching process deeply since armature velocity，resistance force and volage drop of armature were al-80 important to the launching process. In the present work, based on MATLAB/ SIMULINK software platform,the simulation model was built, and the dynamic characteristics of system were simulated. Furthermore, thevariations of armature velocity , total resistance foree and voltage drop of armature against time were investigaledbased on the data of B-dot probes (to measure position of amature) , Rogowsky coil ( to monitor curent) andhigh volage probes (to observe muzle volage). The resuls indicated that, the volage drop of amalure andthe total resistance force showed roughly regulartendency. There were obvious stages obeserved in the two tumseries augmented railgun launching process.Key words: armnature; electromagnetic launching; inductance gradient; muzzle voltuge; series augmentedCLC mumber: TP273Document code: AArticle ID: 1005-9113(2012)02-0053-06With the rapid development of moderm pulse powerIn this paper，three important parameters : launch-technology, the electromagnetic launch technology has ing current , armature position and muzzle voltage signalbeen greatly progressed in recent decades. Generalwere investigated in the experiment. Furthermore ,railgun is the simplest electromagnetic launcher config-three features: velocity, resistance force and voltageuration, consisting of two parallel rails and a movabledrop were calculated. The variations of these parame-conducting element. Then, series augmented railgun isters against time were presented. The results from theanother kind of electromagnetic launcher with specialsimulation and experiment showed that the process ofstructure. A pair or more rails are designed and placedaugmented planar railgun appeared regular lendency.around the major rails so that the magnetic fieldstrength can be increased, the rail current decreased1 Model of Launch Systemand the inductance gradient of the rails enlargedMany researchers have focused on augmented rail-1.1 Structure of Augmented Railgungun in recent years4-8. The equivalent inductanceIt has been verified that single turm geometries willgradient at 1.8 uH/m had been obtained by using the require much more energy , while three turn series aug-augmented railgun, which was over 3 times higher thanmented configurations may generate unaceptably hightraditional data of0.5 μH/m 09. And the electromag-breech voltages. This is a selection of two-tum configu-netic force exerted on the amature was also much grea-rations 0. Fig. 1 shows the structure of augmentedter than traditional data at the same current.railgun in the experiment.For clearly demonstrating the launching process,Lorentz force on uhe armature is based on the fol-some parameters should be introduced and simulated.lowing equationMuzzle voltage was always used to analyze the stateF.=号=L'中-+ M'Pchanges. Unlike general railgun launching process, fortwo-tum series augmented railgun the result from analy-where F, is Lorentz force; L,' is efective inductancesis of muzzle vollage was unable to directly reflct thegradient of launcher; L' is inductance gradient of innersituation in the bore because the major part of muzzlerails; M' is mutual inductance gradient belween aug-voltage became induce voltage decided by current andmented and inner rails respectively and I is armatureinductance. Therefore, voltage drop of armalure wascurrent.中国煤化工given to characterize the process of two-tum augmentedplanar railgun launching.MHCNMHGReceived 2011 -04 - 24.●53..Jounal of Harbin Institute of Technology (Nev Series)，Vol. 19，No.2, 2012motive force formed from armature ' S moving in themagnetic field. .Drawn circuit equation is obtained thatU.(t) = R(1)I(t) + [L(t)I(t)] +E(t)(1)Fig 1 Configuration of two-turn augmented planar railgunLorentz force acted on armature is proportional tothe square of curent,1.2 Inductance GradientF.(1) = ma(l) = k(t)r(t) (2)In the finite element electromagnetic field (FEM)where k, (t) is the cofficientanalysis software , the modeling of augmented railgun isThe armature is made into C type. When currentbuilt, as shown in Fig. 2.flows through two sides of C type armature , the electro-magnetic force can act on the two sides of armature.Furthermore, if the rails are not smooth absolutely,friction force between the armature and the rails can begained:F;() =μFN =kj}(I) (3)Armature’s speed，movement distance, cireuit' sresistance and circuit ’s inductance can be expressedasv(t) =Uo+[F.-Fd=mFig.2 FEM modeling of augmented railgun[r(t)dt.(4)nIx(t) =x+Uot +Using finite element numerical simulation and set-ting its solver‘ eddy '，impendence matrix can be a-年一些(c()u)(5)chieved:[L',R' L'r,R'2 L's,R's L'n,R'u47R(t) = R'X。+ R'x(1) +HR' +R(t) (6)L(t) = L'X。+L'x(t) + HL' .IL'n,R'z L',R'22 L'2s,R'3 L'as,R'swhere H is the length of one rail; R' is the resistance ofIL's,R'31 L'z,R'2 L's,R'3 L's,R'uthe unit length of rails; L' is the inductance of the unitL'n,R'4 "'a,R'4 L's,R's L',R'Jlength of rails; xo is the initial location of armature; mwhere L:' is inductance gradient of raili; Ly' is mutualis the quality of armature; Uo is the initial velocity of ar-inductance gradient between rail i and railj.mature; U。is the voltage of capacitor; R. is contact re-So,sistance of rails and armature.L'=L'n +L's-L'x -L's2Because the counter electromotive force is pro-M' =L'21 -L'24 +L'34-L'duced by armature' s cutting magnetic lines, it is ob-1.3 Circuit Model of Launch Systemtained thatThe equivalent circuit is obtained, as shown. inE(t) = k2I(t)V(I)(8Fig. 3.It is obtained by the relationship of storage capaci-tor charge and voltage.R()L(0)1()= cd(U。-U())(9)dtwhere U。is the initial charging voltage of storage capac-u.0E()①itor; C is capacitance.2 Parameters Compute and Model SimulationFig.3 Equivalent circuit of augmented railgun2.1 Analvsis and Simplification of K,中国煤化工. inductions of innerIn Fig.3, U.(t) is capacitor' s voltage; I(t) isandCNMH(iferent, which arecurrent of rails circuit when launching; R(1) is equiva-dHlent resistance in the circuit; L(t) is equivalent induct-Magnetic induction is produced by the inner rail.ance in the circuit; E(t) is inducted counter-electro-●54..Joumnal of Harbin Institute of Technology (New Series), Vol. 19, No. 2, 2012B,.=气Ho(t)x(1)2.3 Analysis of K,When the current lows , the magnetic field is pro-.(0)+(百)duced by rails and armature together here. Then, inMagnetic induction is produced by the augmentedthe magnetie field the electromagnetic force which actsrail.on the two sides of 'C' ( armature) can be given;B2 =404x()+Fn=F.+Fa+F;+Fπl√x(I) + (1/2)*F.=7 LofrL.2π(r +d)H-x(t)μorL((H-x()) + (l/2)P)Fa =z4π(r +c2)Magnetie induction is produced by the rails.14oFL。B=B+B,2π(r +dj)B=uoI(1)2x(1)HoPd.dxπl I2(2) + (12)4πx√x+出H-x(t).where μo is permeability of vacuum; I is electric cur-(H-x(1))+ (Il/2)2rent; L。is the length of‘C' ( armature) side; r is theAs a result, magnetic force which acted on arma-radius of rail; d, - d, is the distance from the one sideture isof armature to the other three rails respectively.F(t) = BlI(r)Compared to Eq. (3), it is obtained thatF(1) ='μol(t) |2x(t)μoL。uoL。√x(1) +(L/2)“= 2m(r+d,) + 4π(r+d2) + 2m(r+d) *.μods(H-x(1)) + (L/2)J4π=dxCompared to Fig.6, it is obtained thatwhere μ is friction coefficient.2.4 Analysis of Contact Electric Resistanceh(x) =(些(2) -x(2)The contact between rail and armature is simpli-fied as two conductors' contact, and the area whereIt is obvious that the value of h depends on thethe current flows through the contract point is far smal-value of x(t)/l and [H - x(t)]/. In generally,ler than the nominal contact area. According to the ex(t)》l, [H-x(I)]》l, the above formula can beletrical conlact theory of Holm, the contact resistancesimplified as :can be expressed as follows.. ρ, +P。h,(1) =4R。='wherep,, Pa are the resistivity of conductors; r。is a2.2 Analysis and Simplification of Kzspots radius.It is known that the counter electromotive force isThe a Spots’radius can be calculated by the for-produced by armature ’s cutting magnetic lines ofmula belowforce, and it can be expressed thatE(1) = Blv(I)T.=NξHπ.E() = 4of(1)whereξ is coefficient; H is rigidity.πl厦+(v2)2.5 Simulation ModelIn this paper, dynamic simulation software SIMU-H-x(1)V(H-x(t)) +(1/2)](1)LINK provided by MATLAB is used to simulate andanalyze the launching process. According to Eqs. (1)Compared to Eq. (12), it is obtained that- (9)，it establishes the simulation models for cur-rent, circuit resistance and circuit inductance andcounth(x)=(2，"二1)中国煤化工builds lhe systemmodelAs the same ask(x), the above formula can be2.6|YHCNMHGsimplified thatAccorung to'Tne simuauon model, the armature '34s launch velocity in bore is obtained in Fig. 5kq(x) =●55.Joumal of Harbin Insiue of Technology (Neu Series), Vol. 19, No. 2.2012(0)Tab.1 Parameters of railgunDerivativePuranelerValue@Power SupplyCapacior modules: max. 6x135 U= 810 J(a) Current Simulation ModelPulse FormingInduclance:17.3 μHSwitchCrowbar-diodes, vacum spurk apsInductance Gradient I' = 0. 48 μH/m;Mutual GradientM' =0.36 μH/mCalibre20 mmx 20 mm[)_ ProductKdnx0.01ltegator Iicgaor GaRailCu aly, 2 tums series mgment (2 m)MechanicalSieel+ GI00.2Aluminum. corpe. 1Sg(b) Reisance Simulation ModelAmature。Tuyget(0.01)-CapectorRosoroki CGHI了B-da 了CHIO“D区J-B-Diyide Ilegator Itgraoda_ R型coiln_ ProduetData aquratiei②广InsulalorE厂Signat .LoLlinearGuin2.2}-FIg.6 Experimental system(e) Inductance Simulation ModelThe system of railgun is shown in Fig. 6, whichwas computer. The position of the armature in the boreE(xEwas measured by B-dot probe, and the current was mo-凹响nitored by Rogowsky coil, and the muzzle voltage wasKProduet Kpm^InlegratorProductobserved by the high voltage probe and the muzzle ve-Dividelocity was measured by light target. All signals weremsent into connected computer by high voltage isolator,(d) Counter Electromotive Force Simulation Modelthen stored and processed.3.2 Experimental Preliminary ResultsB-dot probes were located already, so time (t)一R4)can be obtained according to the probe' s position (x)US)Subaystem 2once the armature passes through. By ftting the data of+ 14)Subsystem 3. L()0-山xt, position curve is shown in Fig. 7. Then, velocitycurve can be obtained by calculating first-order differSubeytem 1气E0)U(0)ential ofx-t, and the result is also shown in Fig. 7Subaystem 4(e) System Simulation Model2.4 rFig.4 The sinulation model of tbe augmented railgun. Velocity20 t" FiltedProbe2:1.6 t.2 tE 0.8).4 I00.20.40.60.81.0.1.2100.2040.60.81.01.21.4t/msig.7 Measured positioo and velocity in experimentFig.5 Velocity during simuatio-measured by Ro-3 Experimental and Results Disposalgowsk中国煤化Iltehe ee fomhigh-f:YHCN M H Gliches do not af-3.1 Experimental Setupfect the increase trend of current against time, so filterExperiments are performned at this railgun systemis used to obtain smooth curve for detailed analysis, awith main parameters listed in Tab.1.shown in Fig. 8.Journal of Harbin Instiute of Technology (New Series), Vol. 19, No. 2, 2012300厂- . - Oniginal datam[(1-x())-- x-v()Fileringdt-I(1) :' do200d/v, =[(1-<())d-I(1)a-v()(11) .where V, is the voltage drop of armature.Obviously, muzzle voltage is insufficient, but the00.2.0.4 0.6 0.8 1.0 1.2 1.4voltage drop can be regarded as the diagnostic tool sim-ilar to muzzle voltage for simple railgun.ig.8 Measured ectric current in experimentOriginal muzzle voltage signals are measured by4 Results and Discussionhigh voltage probe, and the muzzle voltage curve after1.1Processed Results of the Experimentfiltering is presented in Fig. 9. The similar treatmentAccording to Eq. (10), the total resistance forceon muzzle voltage was employed as curent filter.is calculated and the curve is given in Fig. 10, whereinductance gradient can be computed by FEM，and1.0mutual inductance gradient can be calculated too, and06current can be obtained in Fig. 8.0.2700.s50. Onipnal datat 30f0 0.2 0.4 0.6 0.8 1.0 1.2 1.4u/m .10Fig. 9 Measured muzzle voltage in experiment0 0.2 0.40.60.81.01.2 1.43.3 Further Process based on Experimental Resultst/meThe resistance force acted on armature is resultantFig. 10 Processed total resistance forceforce, which includes air resistance force， fricetionforce and viscous drag, and its direction is oppositeAccording to Eq. (11), the voltage drop is cal-from the armature' s movement. The motion control eculaled and shown in Fig. Iquation of the rail launcher can be written asM.d( dx(1) )Fr=E.-F。=上+MIP -迎。(10)80where x is amature position; M. is armature mass; Frois the total resistance on the armature.In electromagnetie launch experiments with solid20armatures, the muzzle voltage is an important diagnos-Wtic means 13-4 , because the muzzle voltage is almost00.20.40.60.81.01.2 1.4voltage drop of armature in the simple railgun.. Howev-er, it is different from the simple railgun that the majorFig.11 Processed voluage droppart of muzzle voltage is induced voltage in series aug-mented railgun.4.2 Results of the SimulationIn augmented railgun, the flux φ in the loop con-After the simulation, some process variables weresisting of the main rails between armature and the muz-recorded，such as electric current, velocity, contact re-zle is given bysistance and so on. According to Eq. (3), the frictionφ = M'(I- x(t) )I(1)force中国煤化ieninFig. 12:where l is the total length of the rail traveled in armature..Imost consisted ofThe muzle voltage is then calculated bythe v0HCNMHGand the body re-_dφsistanco ur auauc. iciciuic, u voltage drop canVn =dt-V,(t) =d[M(T-x(0)(0)I"be given byV,(1) =R(l) x[(t) +R。xI(t) (12)dt●57●Journal of Harbin Institute of Technology (New Series)，Vol. 19, No. 2, 2012where R. is contact electric resistance; R。is body elec-time. Namely, in initial stage ( the velocity is smaller)tric resistance of armature.and final stage ( the velocity is maximum), the totalAccording to Eq. (12), the voltage drop is cal-resistance force and the voltage drop are always in theculated and the curve is shown in Fig. 13.dramatie changing state.20-5 Conclusions80In the paper, the simulation curve is basically图60consistent with the experimental curve in trend, whichillustrates that the process simulation can largely reflecl40actual experiment.20 |The results of simulation and experiment show thatthe launching process of augmented planar railgun ap-pears regular tendency. It also proves that the curve ofvoltage drop and resistance force can reflect the generalFig. 12 Resistance force during simulationstate in bore during the launching process of the aug-mented railgun.0Based on the characteristic curves, the analysis oflaunching process has advantages to target -oriented ad-ojust the waveform of pulse current and offers a refer-g4°ence to judge its repecatability.20/References:[1] Marshall R A, Wang Ying. Railguns: Their Science and0 0.20.4 0.6 0,8 1.0 1.2 1.4Technology. Beijing: China Machine Press, 2004.[2] Fair H D. Electromagneic launch. Internationmal Joumal ofFig, 13 Voltage drop of armature during simulationImpact Engineering, 2003, 29( 2003): 247 -262.[3] Wang Ying, Marshal R A, Cheng Shukang. Physics of E-4.3 Discussionlectrie Launch.Bejing: China Machine Press. 2004.From Fig.10, it is found that the total resistance[4] Fair H D. Advances in electromagnetic launch science andforce curve can be divided into three stages. The firsttechnology and is applications. IEE Trans Magn, 2009 ,45(1): 225 -229.stage is in0.1 -0.6 ms, and the total resistance force[5] Gallant J, Lehmann P. Experiments with brush projectilesincreases firstly with the increase of current rapidly (upin a parallel augmented railgun. IEEE Trans Magn, 2005 ,to 0.3 ms) and then decreases sharply (from0.3 to 0.641(1); 188- 193.ms). It is because the contact friction between the ar-6] Keefer D, Crawford R, Taylor J Inductance gradient scal-mature and rail increases/ decreases, also the electro-ing experiments in an ugmented railgun. IEEE Transmagnetic forces on the wings of C-type armatureMagn, 1995, 31(1): 326-331.strengthens/ weakens to the outside shapely with the in-[7] NeriJ M，Kim Jin Sung. Initial operation, modeling andoptimization of a low velocity augmented railgun. Proceed-crease/ decrease of curent. This shows that the contactings of the IEEE 14th Int Pulsed Power Conf. Dallas;friction is the major part of the total resistance duringIEEE, 2003. 1103 - 1106.0this period. The second stage is from 0.6 ms till 1. 2[8] Crawford R, Taylor J, Keeler D. Solid ring armature exper-ms, and the total resistance force lrends Aat, whichiments in a transaugnented railgun. IEEE Trans Magn,means the armature ran smoothly. The final stage is the1995, 31{1): 138- 143.range greater than 1.2 ms, and sharp increase in the re-[9] Wa T, Crawford M. Experimental resuts from a two-tum 40-sistance force can be observed, and it proves the statemm railgun, IEEE Trans Magn, 2009, 45(1): 490 -494.between the armature and the rail has been changed.[10]Crawford M, Subrnamanian R, Welt T, et al. The deignThe curve in Fig.11 is also divided into three sta-and esting of a large-caliber railgun. IEEE Trans Magn,2009, 45(1): 256 - 260.ges. In the first stage , the curve decreases and then in-[11]Fikse DA, CiesarJ A, Wehri H A, et al. The HARTIcreases rapidly, and it shows that the contact betweenaugmented elctrie gun facility. IEEE Trans Magn, 1991,the wing of C-type armature and the rail is tight and27(1): 176- 180.then becomes loose rapidly under the action of electro-[12]中国煤化I mented rilgam. IEEEmagnetie force. In the second stage the voltage varies ina small range. In the third stage the curve rises abruptly.[13]HC N M H Gemt in muzle volageCompared the results of simulation and experi-races. IEEE 1rans Magn, 200D, 41(1): 214 -219.[14]Dreizin Y A, BarberJ P.0n the origins of murzde voltage.ment, those curves show almost the same trends againstIEE Trans Magn, 1995, 31(1): 582 - 586.●58.