simulation of induction heating device with double inductors

Simulation of Induction Heating Device with Double Inductors forContinuously Heating up Steel Bars

IXiaoguang Yang, Youhua Wang, and Weili Yan

Province-Ministry Joint Key Laboratory of Electromagnetic Field and Electrical Apparatus ReliabilityHebei University of Technology, P.O. Box 359, No.8, Guangrong Road, Tianjin, 300130, China

Fig. 1. The inductors and the steal bars.

equivalent circuit of the induction heatingFig.device.

side ofFig. 2. A simplified equivalent circuit is shown in rightside. The source parameters depend on R, L, C and DCinverter current.

Except for improving the efficiency, there is another

t1

the inductor.For the design of the conductor, the first step is to

determine the exciting current needed, and the correspondingcross-section of the inductor. The current distribution in theconductor is influenced by the skin effect and the proximityeffect. Thus, the virtual area of the cross-section of theinductor must be large enough against overheating of theinductor. The total power losses in the inductor have mainlytwo parts. First, losses are caused by Joule effect of thecarrying current, and the other one caused by the eddycurrents induced by the magnetic flux, associated with skineffect and proximity effect. The power loss in the conductoris very high, and the conductor made ofcopper tubing shouldbe water cooled.

From an electrical network point ofview, the inductors andthe steel bars can be considered as series connectedequivalent resistance R1 and inductance ~, series connected

R2 and L2 and constant parallel compensating capacitance C

connected with nonlinear current source, as shown in the left

II. DEVICE DESIGN

The induction heating device includes the inductors andthe bars. Usually, only a single inductor is used. In order todouble the heating efficiency, two inductors connected inparallel are used in this design, as shown in Fig. 1. The spiralinductor is usually made of fully annealed, high conductivityrectangle copper tubing, which is water-cooled. The heatingeffects are influenced by lots of parameters, such as theexciting current, the working frequency, the shape, the crosssection and thickness of tube, and the diameter and turns of

ICorresponding author

Abstract-The whole design and simulation procedure for aninduction heating device with double inductors is presented. Toobtain a more accuracy solution, a FEM simulation of thecoupled electromagnetic-thermal problem was completed,taking into account the interaction between the inductors, thepower supply source parameters and the resulted loadparameters. The simulation method is validated in the design ofinduction heating equipment and the procedure presented isproven to be efficient in the overall design of induction heatingequipment. The experimental results are discussed, which ishelpful for design of induction heating device.

I. INTRODUCTION

Stabilization rods are used in car industry. To satisfy theirmechanical requirement, the steel bars should be heated

up to 1000°C . Induction heating provides significanttechnological, economic and ecological advantages incomparison with conventional oil-or gas-fired furnace: fastheating rate, instant controllability, high efficient andminimal enviroment pollution. This problem is very complex,because the electromagnetic-thermal coupled problem isinvolved. Conventionally, for the simulation of such aninduction heating process, the energy source is considered asa device supplying constant voltage or constant current at agiven frequency, and the induction heating system is usuallysimplified to the inductor and work piece [1], [2]. This canlead to simulation errors, such as big differences between theheating time and the period ofthe inductor supply source andlow heating efficiency. In order to design an optimalinduction heating device, a detailed analysis ofelectromagnetic-thermal coupled problem as well as thecharacteristic of the load is necessary.

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where J..L is the permeability, u the conductivity, w the

angular frequency and .f..s the excitation current density

(7)

(8)

(6)

(10)

.b IJI2

dVR= U

12

.b B . HdVL=~--

wI2

~ 41de • -1 3 5l(t) = LJ-slnwnt n-, , ...n=l nn

o(c p.9) =V. (A, V .9)+ Pvof

z =R+ j(OJL -OJR2C -alL

2C) (9)

(1- w2LC)2 +w2R2C2

~1JTj(' ~ (~ I .~_~ I

I( )L1 ( R1 <~L2( R2< C-L I(t) L(R:? C::::, r >- <'"' I (I I( \, I LLLJ

Fig. 3. Parallel connected equivalent circuit of the induction heatingdevice.

where c is the specific heat, A the thermal conductivitycoefficient and p the mass density.

The series connected resistance R and the inductance Lare calculated using the following equations

where Q is total volume and I the effective value of thecoil current. For this axisymmetric geometry problem, thevolume integral is the rotation ofthe XY-plane about Y-axis.The impedance ofthe equivalent circuit is

The rectifier and inverter of the induction heater arerepresented by a square waved current source whosemagnitude is equal to DC-link current Ide [3]. Thus, the

current source expanded in a Fourier series is described asfollows

(1)

(3)

source.The requirement of a zero divergence condition of current

density must be fulfilled

consideration for using two inductors in parallel connecteddesign. The inductors and the steel bars can also beconsidered as parallel connected equivalent resistance R1 and

inductance ~, parallel connected R2 and L2 , and constant

parallel compensating capacitance C connected withnonlinear current source, as shown in the left side ofFig. 3. Inthe induction heating process, the equivalent inductance ofthe heating system changes greatly when the steel bar entersinto the inductor, or when the heating temperature is closed toCurie temperature.

According to Fig. 3,

Assumed the mutual inductance' M is zero, we can getdL/d~ < 1 and dL/dL2< 1. It shows that the change of the

inductance ofthe two parallel connected inductors is less thanthat ofone inductor. We can get the similar conclusion for theequivalent resistance. This is helpful for the design ofcontrolsystem for frequency tracking.

III. MATHEMATICAL MODEL

The mathematical model for this sinusoidal quasi-staticeddy current problem results from Maxwell equations and isdescribed by the complex magnetic vector potential ~ andan electrical complex scalar potential ~ with Coulomb

Gauge

The expression for current isThe resonant angular frequency of the RLC circuit is

(4) (11 )

And it determines the heat source distribution

Pv = IL21/0- (5)

and the quality factor is

The temperature field /} is computed based on theFourier's thermal conduction equation

Q= woLR

then

(12)


IZn 1= -;::::::=R==p==

I+Q2(n_~)2n

(13)

inductor.

Copper

Tube

-

n

Fig. 5. Flux

Fig. 6. Eddy current distribution in the steel bars and the inductors.

achieved from the simulation results. A high temperaturewould be caused by the power loss in the inductor, thus, theinductor should be water cooled. Take advantage of theseresults, the thickness and the cross section of the copper tubecan be determined for the exciting current.

In this problem, one ofthe most considerable factors is thedependency of the material properties on temperature. Undersuch high temperature conditions, especially around the Curiepoint, the permeability of steel materials varies abruptly. Inaddition, the electrical conductivity, the thermal conductivityand the specific heat ofthe materials also vary with increasingtemperature. These characteristics can bring about bigchanges the inductance, the resistance and the excitingcurrent ofthe equivalent circuit, which are very important forthe simulation results and circuit design. The inductance,resistance and current as a function ofheating time are shownin Fig. 7, Fig. 8 and Fig. 9, respectively.

Start

IV. RESULIS AND DISCUSSION

The steel bars, 1000mm long, 30mm in diameter arerequired to be heated up to 1000°C. The inductor is made ofafully annealed, high conductivity rectangle (20mmx 1Omm)copper tubing, which is water cooled. The thickness oftube is1mm. There are two identical parallel connected spiralinductors. The inductor's internal diameter is 70mm. Thecapacitor is 160llF with the capacity 2500kVA. The heatingtime is 30s. The time-step size in thermal analysis was chosento be 0.5s.

The flux line distribution is shown in Fig. 5. In Fig. 6, thecurrent distribution in both the steel bar and the inductor areshown in the left side, a magnified eddy current distributionin steel bar shown in the middle part, and a magnified currentdistribution in inductor shown in the right side. It shows thatthe current density at the inner side of the inductor is largerthan that at the outer side, the highest current density locatedat the inner comer, and the eddy current concentrates on thesurface of the steal bar, due to the skin effect and theproximity effect. The power loss of the conductor can be

Fig. 4 Calculation procedure.

current calculation, the load impedance, the frequency andthe supply current are calculated, and the frequency andcurrent are changed at the next eddy current calculation. Thisprocedure is shown in Fig. 4.

Lwhere Rp = - is the equivalent resistance when the circuit

RCis in resonant state. The inverter output wave has thesymmetry property, so, the Fourier series has only odd

harmonics. When Q =10, IZ31 = 0.0375Rp • Therefore, the

real current has been substituted for the first harmonic only.In the coupled problem iteration process, the material

characteristic is updated [4], [5]. At the end of every eddy


20 Tinle(s) }J10

200

400

_ 1200r------~--- __,.__---_~

~'1COJ3EEII)Q),..;::-

E6())r-

20 Time(s) 3010

~1Tiepoint

\'"

5

25 ,..-----...------.....-------

Fig. 7. Inductance as a function of the heating time. Fig. 10. Temperature as a function of heating time.

for an accuracy prediction of the induction heating process,including the current and temperature distribution withsimulation technology, there are two very important points tobe noticed. First, if the internal diameter of the inductor issmaller, the heating efficiency could be improved. But inpractice, it is difficult to start up the device. The other is, thereshould be enough distance between the two inductors. If thedistance were set to be too small, the interaction of the twoinductors would become very high. This device wasdeveloped for an automobile parts factory, and it works verywell to present.

v. CONCLUSION

The design procedure presented in this paper is proven tobe helpful for the design of induction heating device. Thecalculated temperature is in good agreement with themeasurement. For simulation of the coupledelectromagnetic-thermal problem at high temperaturecondition, especially at the Curie point, the interactionbetween the inductors, the power supply source parametersand the resulted load parameters must be taken into accountfor accuracy results. The experimental results show that thearrangement of inductors and the internal diameter of theinductor have some effects on the induction heating device,which should be noticed in practical design.

20 Time(s) 30

Curie point

10

015

035 ~---'-----.....,.......---...............

Fig. 8. Resistance as a function of the heating time.

;:;~. 0.3~~~O.25'ocCJ

~ 0.2

Fig. 9. Current as a function of the heating time.

ACKNOWLEDGMENT

This work was supported by National Natural ScienceFoundation ofChina under Grant No. 50477016.

20 Time(s) 30100'------.....----........------'o

Fig. 10 shows radial temperature in the middle of the steelbar as a function of heating time. Line 1 represents thetemperature of the point at the central line, and line 2represents the temperature of the point at the surface. Theother lines represent the temperature of the points betweenthem, respectively. The calculated temperature and themeasured temperature at the surface of the middle part arel027°C and 993°C, respectively. The error between them isless than 4%.

For practical design ofthe induction heating device, except

REFERENCES

[1] 1. Nerg, K. Tolsa, P. Silventoinen, and 1. Partanen, "A dynamic modelfor the simulation of induction heating devices," IEEE Transactions onMagnetics, vol 35, no.5, pp.3592-3594, Sept. 1999.

[2] 1. Zgraja, "A dynamic model for the simulation of induction heatingdevices," IEEE Transactions on Magnetics, vol 39, no.3, pp.1523-1526,May 2003.

[3] Jung-gi Lee, Sun-kyoung Lim, Kwang-hee Nam, Dong-ik Choi, "Anoptimal selection of induction heater capacitance consideringdissipation loss caused by ESR," APEC '04. Nineteenth Annual Applied


Power Electronics Conference and Exposition, vol 3, pp.1858 - 1863,2004.

[4] Xiaoguang Yang, Youhua Wang, Fugui Liu, Qingxin Yang, and WeiliYan, "The Use of Neural Networks Combined With FEM to Optimizethe Coil Geometry and Structure of Transverse Flux InductionEquipments," IEEE Transactions on Applied Superconductivity,vol14,no.2 pp.1854- 1857, June 2004.

[5] Zanming Wang, Xiaoguang Yang, Youhua Wang and Weili Yan,"Eddy Current and Temperature field Computation in Transverse FluxInduction Heating Equipment," IEEE Transactions on Magnetics, vol.37, no. 5, pp. 3437-3439, Sept. 2001.


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simulation of induction heating device with double inductors