Simulation of Induction Heating Device with Double Inductors for Continuously Heating up Steel Bars IXiaoguang Yang, Youhua Wang, and Weili Yan Province-Ministry Joint Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability Hebei University of Technology, P.O. Box 359, No.8, Guangrong Road, Tianjin, 300130, China
Abstract-The whole design and simulation procedure for an induction heating device with double inductors is presented. To obtain a more accuracy solution, a FEM simulation of the coupled electromagnetic-thermal problem was completed, taking into account the interaction between the inductors, the power supply source parameters and the resulted load parameters. The simulation method is validated in the design of induction heating equipment and the procedure presented is proven to be efficient in the overall design of induction heating equipment. The experimental results are discussed, which is helpful for design of induction heating device.
I. INTRODUCTION
S
tabilization rods are used in car industry. To satisfy their mechanical requirement, the steel bars should be heated up to 1000째C . Induction heating provides significant technological, economic and ecological advantages in comparison with conventional oil-or gas-fired furnace: fast heating rate, instant controllability, high efficient and minimal enviroment pollution. This problem is very complex, because the electromagnetic-thermal coupled problem is involved. Conventionally, for the simulation of such an induction heating process, the energy source is considered as a device supplying constant voltage or constant current at a given frequency, and the induction heating system is usually simplified to the inductor and work piece [1], [2]. This can lead to simulation errors, such as big differences between the heating time and the period of the inductor supply source and low heating efficiency. In order to design an optimal induction heating device, a detailed analysis of electromagnetic-thermal coupled problem as well as the characteristic of the load is necessary.
Fig. 1. The inductors and the steal bars.
the inductor. For the design of the conductor, the first step is to determine the exciting current needed, and the corresponding cross-section of the inductor. The current distribution in the conductor is influenced by the skin effect and the proximity effect. Thus, the virtual area of the cross-section of the inductor must be large enough against overheating of the inductor. The total power losses in the inductor have mainly two parts. First, losses are caused by Joule effect of the carrying current, and the other one caused by the eddy currents induced by the magnetic flux, associated with skin effect and proximity effect. The power loss in the conductor is very high, and the conductor made of copper tubing should be water cooled. From an electrical network point ofview, the inductors and the steel bars can be considered as series connected equivalent 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 and the bars. Usually, only a single inductor is used. In order to double the heating efficiency, two inductors connected in parallel are used in this design, as shown in Fig. 1. The spiral inductor is usually made of fully annealed, high conductivity rectangle copper tubing, which is water-cooled. The heating effects are influenced by lots of parameters, such as the exciting current, the working frequency, the shape, the cross section and thickness of tube, and the diameter and turns of ICorresponding author
t1
Fig. device.
equivalent circuit of the induction heating
side ofFig. 2. A simplified equivalent circuit is shown in right side. The source parameters depend on R, L, C and DC inverter current. Except for improving the efficiency, there is another
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consideration for using two inductors in parallel connected design. The inductors and the steel bars can also be considered as parallel connected equivalent resistance R1 and inductance ~, parallel connected R 2 and L 2 , and constant parallel compensating capacitance C connected with nonlinear current source, as shown in the left side ofFig. 3. In the induction heating process, the equivalent inductance of the heating system changes greatly when the steel bar enters into the inductor, or when the heating temperature is closed to Curie temperature. According to Fig. 3, (1)
Assumed the mutual inductance' M is zero, we can get dL/d~ < 1 and dL/dL 2 < 1. It shows that the change of the inductance ofthe two parallel connected inductors is less than that ofone inductor. We can get the similar conclusion for the equivalent resistance. This is helpful for the design of control system for frequency tracking.
o(c p.9) = V. (A, V .9)+ Pv of
(6)
where c is the specific heat, A the thermal conductivity coefficient and p the mass density. The series connected resistance R and the inductance L are calculated using the following equations
~1JTj
(' ~ (~ I .~_~ I( )L1 ( R1 <~L2( R2< C-L I(t) L(R:? >- <'"' I (I ( \, I ,
I
LLLJ
r
C::::
I
Fig. 3. Parallel connected equivalent circuit of the induction heating device.
.b IJI R=
2
dV (7)
U
12
.b B . HdV
(8)
L=~--Â
III.
wI 2
MATHEMATICAL MODEL
The mathematical model for this sinusoidal quasi-static eddy current problem results from Maxwell equations and is described by the complex magnetic vector potential ~ and an electrical complex scalar potential ~ with Coulomb
where Q is total volume and I the effective value of the coil current. For this axisymmetric geometry problem, the volume integral is the rotation ofthe XY-plane about Y-axis. The impedance ofthe equivalent circuit is
Gauge
z = R + j(OJL -OJR C -al L C) 2
2
(1- w 2LC)2 + w 2R2C 2
where
J..L
is the permeability, u the conductivity, w the
angular frequency and .f..s the excitation current density source. The requirement of a zero divergence condition of current density must be fulfilled
The rectifier and inverter of the induction heater are represented by a square waved current source whose magnitude is equal to DC-link current Ide [3]. Thus, the current source expanded in a Fourier series is described as follows 41de â&#x20AC;˘ -1 3, 5 ... l(t) = ~ LJ-slnwnt n-,
(3)
n=l
nn
(10)
The resonant angular frequency of the RLC circuit is
The expression for current is (4)
And it determines the heat source distribution Pv =
(9)
IL
2
1/0-
(5)
The temperature field /} is computed based on the Fourier's thermal conduction equation
(11 )
and the quality factor is Q= woL R
then
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(12)
IZn 1= -;::::::=R==p= =
(13)
I+Q2(n_~)2 n
L where Rp = is the equivalent resistance when the circuit RC is in resonant state. The inverter output wave has the symmetry property, so, the Fourier series has only odd harmonics. When Q = 10, IZ31 = 0.0375R p â&#x20AC;˘ 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 Start
inductor.
Fig. 5. Flux
Copper Tube
Fig. 4 Calculation procedure.
current calculation, the load impedance, the frequency and the supply current are calculated, and the frequency and current are changed at the next eddy current calculation. This procedure is shown in Fig. 4. IV. RESULIS AND DISCUSSION The steel bars, 1000mm long, 30mm in diameter are required to be heated up to 1000°C. The inductor is made of a fully annealed, high conductivity rectangle (20mm x 1Omm) copper tubing, which is water cooled. The thickness oftube is 1mm. There are two identical parallel connected spiral inductors. The inductor's internal diameter is 70mm. The capacitor is 160llF with the capacity 2500kVA. The heating time is 30s. The time-step size in thermal analysis was chosen to be 0.5s. The flux line distribution is shown in Fig. 5. In Fig. 6, the current distribution in both the steel bar and the inductor are shown in the left side, a magnified eddy current distribution in steel bar shown in the middle part, and a magnified current distribution in inductor shown in the right side. It shows that the current density at the inner side of the inductor is larger than that at the outer side, the highest current density located at the inner comer, and the eddy current concentrates on the surface of the steal bar, due to the skin effect and the proximity effect. The power loss of the conductor can be
n
Fig. 6. Eddy current distribution in the steel bars and the inductors.
achieved from the simulation results. A high temperature would be caused by the power loss in the inductor, thus, the inductor should be water cooled. Take advantage of these results, the thickness and the cross section of the copper tube can be determined for the exciting current. In this problem, one of the most considerable factors is the dependency of the material properties on temperature. Under such high temperature conditions, especially around the Curie point, the permeability of steel materials varies abruptly. In addition, the electrical conductivity, the thermal conductivity and the specific heat ofthe materials also vary with increasing temperature. These characteristics can bring about big changes the inductance, the resistance and the exciting current ofthe equivalent circuit, which are very important for the simulation results and circuit design. The inductance, resistance and current as a function of heating time are shown in Fig. 7, Fig. 8 and Fig. 9, respectively.
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_ 1200 r------~---
25 ,..-----...------.....-------
__,.__---_
~
~1Tiepoint
~'1COJ 3
EEII) Q) ,..
\'"
;::-
E6())
r-
400 5
200 10
20 Time(s) 30
10
Fig. 7. Inductance as a function of the heating time.
;:;
035 ~---'-----.....,.......--........
~. 0.3 ~ ~
~O.25
'oCJc
~ 0.2
015
10
for an accuracy prediction of the induction heating process, including the current and temperature distribution with simulation technology, there are two very important points to be noticed. First, if the internal diameter of the inductor is smaller, the heating efficiency could be improved. But in practice, it is difficult to start up the device. The other is, there should be enough distance between the two inductors. If the distance were set to be too small, the interaction of the two inductors would become very high. This device was developed for an automobile parts factory, and it works very well to present.
20 Time(s) 30
0'------.....----........------' 20 Time(s) 30 o 10 Fig. 9. Current as a function of the heating time.
Fig. 10 shows radial temperature in the middle of the steel bar as a function of heating time. Line 1 represents the temperature of the point at the central line, and line 2 represents the temperature of the point at the surface. The other lines represent the temperature of the points between them, respectively. The calculated temperature and the measured temperature at the surface of the middle part are l027째C and 993째C, respectively. The error between them is less than 4%. For practical design ofthe induction heating device, except
}J
Fig. 10. Temperature as a function of heating time.
v.
Fig. 8. Resistance as a function of the heating time.
Curie point
20 Tinle(s)
CONCLUSION
The design procedure presented in this paper is proven to be helpful for the design of induction heating device. The calculated temperature is in good agreement with the measurement. For simulation of the coupled electromagnetic-thermal problem at high temperature condition, especially at the Curie point, the interaction between the inductors, the power supply source parameters and the resulted load parameters must be taken into account for accuracy results. The experimental results show that the arrangement of inductors and the internal diameter of the inductor have some effects on the induction heating device, which should be noticed in practical design. ACKNOWLEDGMENT
This work was supported by National Natural Science Foundation of China under Grant No. 50477016. REFERENCES [1] [2] [3]
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May 2003. Jung-gi Lee, Sun-kyoung Lim, Kwang-hee Nam, Dong-ik Choi, "An optimal selection of induction heater capacitance considering dissipation loss caused by ESR," APEC '04. Nineteenth Annual Applied
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[4]
[5]
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