A Mathematical Model of the Reusable Linear
Magnetic Flux Compressor
Ying Wang,Jun Li,Zanji Wang,Min Gao,and Yanjie Cao
Abstract—The reusable linear magnetic flux compressor not only can offer fairly high energy density and work repeatedly, but also can be statically inert prior to firing.Therefore,it can be regarded as an ideal puld power supply for the electric gun. Bad on theoretical studies of this magnetic flux compressor,a mathematical model is developed and described in this paper.This model includes a2-D Hydrodynamic treatment,armature motion, dynamic inductance,dynamic resistance,flux loss,circuit quanti-ties and1-D diffusion for the magnetic field,current and temper-ature inside the conductors.In this model,the gas pressure,which depends on the propellant burn law,propellant mass,armature position and armature velocity,is modeled by2-D homogeneous pha fluid-dynamic equations.The electromagnetic force,which depends on the current and the inductance gradient of the helical winding,is described by electromagnetic parameter equations.The 2-D homogeneous pha fluid-dynamic equations are coupled with electromagnetic parameter equations through the armature mo-tion equation.The simulation results show that the propod model is helpful to the practical design.
Index Terms—Magnetic flux compressor,mathematical model, puld power.
I.I NTRODUCTION
D URING the last20years,a tremendous advance in EML
technology has been achieved becau the military is very interested in its high muzzle velocity that ordinary guns can not provide.For the electric gun itlf,it ems that there will not be any technology issue which can not be resolved.However, the issue of miniature puld power supply(PPS)has not been overcome,which prevents the electric gun from being ud as tactical weapon.
The puld linear flux compressor is a reusable generator.It can not only offer fairly high energy density and work repeat-edly,but also can be statically inert prior to firing,hence it is regarded as an ideal PPS for the electric gun.There are some recent papers concerning this flux compressor[1]–[3],but no systematic mathematical model which can describe the transient phenomenon of burnt gas and electromagnetic field in the com-pressor.In this paper,a systematic mathematical model will be described,and the simulation results will be given bad on the propod model.
Manuscript received December17,1999.
Y.Wang is with Ordnance Engineering College,Shijiazhuang,Hebei050003 P.R.China(e-mail:wangying@oec.edu).
J.Li and Z.Wang are with the Department of Electrical Engineering,Ts-inghua University,Beijing100084,P.R.China(e-mail:jun.li@tsinghua.edu; wzj-dea@mail.tsinghua.edu).
Publisher Item Identifier S0018-9464(01)00226-6.
II.M ATHEMATICAL M ODEL
A.Principle of the Flux Compressor
The primary components of the puld linear flux compressor are illustrated in Fig.1.Prior to firing,the piston(armature) is held at the initial position and the propellant is loaded into the chamber.The firing cycle is initiated by the ignition of the charge,and the pressure within the chamber ris very quickly. Once the pressure reaches a certain value,the piston is free to accelerate to the right by the high pressure if the frictional force and air drag force are small.Before the piston enters the he-lical winding,an initial current in the circuit(formed by the he-lical windings,the sliding piston and coaxial feed rail)is estab-lished by means of a small pul power capacitor or battery,and the initial magnetic flux
(
Fig.1.The primary components of the puld linear flux
compressor.
(4)
and
简单的小幸福
reprents gas
pressure;
and
is the propellant
density;
and
and reprent the relative propellant thickness and
the half of thickness,
respectively;
and
Therefore,the 2-D homogeneous pha fluid-dynamic equa-tions is compod of (5)–(9).
C.Electromagnetic Parameter Equations
The Electromagnetic parameter equations include circuit equations,a magnetic field diffusion equation,a current diffusion equation,a temperature field diffusion equation,an inductance equation,a resistance equation and a flux loss equation.
1)Circuit Equations:Becau the load of the flux com-pressor can be either an ETC gun or a rail gun,there are two kinds of equivalent circuit and two kinds of circuit equations which will be discusd in the following.
The Load is an ETC Gun:The equivalent circuit of the flux compressor is shown in Fig.
2.
童话故事200字the circuit equations should
be
WANG et al.:A MATHEMATICAL MODEL OF THE REUSABLE LINEAR MAGNETIC FLUX COMPRESSOR
比较阅读149
Fig.2.The equivalent circuit of the compressor driving an ETC
load.
Fig.3.Equivalent circuit of generator driving rail
gun.
(11)
where
你在那边还好吗
is the coupling coefficient of the primary winding and the c-ondary winding of the
transformer;
is the armature velocity;both
the inductance
gradient
are negative,which can be determined
by experiment or by theoretical calculation.
The Load is a Rail Gun:When the flux compressor provides electric energy to the rail gun,the equival
ent circuit is shown in Fig.3.All the symbols in this figure are the same as tho in Fig.
2.
什么是矩形
(13)
and
(14)
where is the velocity of projectile
and
带余的成语
is the inductance gradient of rail.
2)Equations of Electromagnetic and Temperature Field Dif-fusion:Suppo the helical winding of the flux compressor is uniform,then the magnetic
intensity ,the magnetic
induction ,the electric
intensity and the temperature of
conductor
.Therefore,the equa-tions that describe the electromagnetic and temperature fields can be described as
follows:
(16)
(17)
and
is constant.
3)Inductance Equation:The inductance of a helical winding with rectangular ction can be calculated using the
equation
is the equivalent inductance,radius and
total number of turns of the helical winding,
respectively;th ction,respectively,
and
(21)
5)Flux Loss Equation:Becau the flux diffus into the winding conductor and the circuit can not recover all of it,the flux loss rate should
be
(24)
150IEEE TRANSACTIONS ON MAGNETICS,VOL.37,NO.1,JANUARY2001
Fig.4.Current and velocity versus time for the chon railgun example.
Fig.5.Current and velocity versus displacement for the chon example.
Similarly,we can get the same result from(12)and(13).
Therefore,during the flux compression stage,the armature mo-
tion equation can be described as:
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WANG et al.:A MATHEMATICAL MODEL OF THE REUSABLE LINEAR MAGNETIC FLUX COMPRESSOR151
IV.C ONCLUSIONS
This paper prents a mathematical model of the reusable puld linear magnetic flux compressor.Bad on this model, the computer code RMFC-1has been developed,which can sim-ulate not only the electromagnetic parameters,but also the burnt gas parameter.The simulation results show that the propod model is helpful to the practical design.
A CKNOWLEDGMENT
The authors would like to thank Dr.E.Goldman for his dis-cussions while this model was being developed.
R EFERENCES
[1] E.Goldman and F.Davies et al.,“Development of a flux compression
power unit for millicond ETC puld power applications,”IEEE Trans.Magn.,Jan.1999.
[2] A.P.Glinov and A.E.Poltanov et al.,“The analysis of linear magnetic
flux compressor pul power supplies,”in6th European Symp.EML Technology,1997.
[3]J.Li,Y.Wang,and M.Gao,“Analysis of combustion driven linear gen-
erator for electric guns applications,”IEEE Trans.Magn.,Jan.1999.
[4] F.W.Grover,Inductance Calculations—Working Formulas and
Tables.New York:Dover Publications,INC.,1962.
[5]J.Li,“The mathematical model of puld linear magnetic flux com-
pressor for electric gun applications,”Ph.D.disrtation(in Chine), Ordinance Engineering College,P.R.China,May1999.
