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IEEE REGION 8 SIBIRCON 2008
Analysis of Induction Heating Eddy Current Distribution Based on 3D FEM Wang Youhua, Wang Junhua, Li Jiangui, Li Haohua (Province-Ministry Joint Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability, Hebei University of Technology, Tianjin, China, email: junhuawang08@yahoo.com.cn ) Abstract— In some applications, travelling wave induction heating (TWIH) could make this kind of heating more profitable in comparison with other known systems. In this paper a three-dimensional single-coil model of transverse flux induction heating inductors (TFIH) and TWIH has been simulated by ANSYS. The different eddy current densities in the metal strip also have been analyzed when the circle loop lies in the internal or external of the
Fig. 1. 3D induction heating theoretical model
projector.
I. INTRODUCTION II. THEORETICAL ANALYSIS OF EDDY CURRENT
The fundamental principles of the Travelling Wave Induction Heating (TWIH) are known for many years
DISTRIBUTION
[1-3]. Travelling Wave Induction Heating, as one of the
some heating and melting processes in industry. Among
Suppose that there is a piece of big enough metal strip, parallels to it is a circular C1 with a radius of r1, and the projection of C1 on the strip is circular C2 with a radius of r2. Draw a concentric circle which shares the same center with C2 and its radius is ar as show in Fig.
the advantages we can mention the possibility to heat
2.
multiphase induction heating systems, has particular features which make them attractive for application to
quite uniformly thin strips or regions of a body without moving the inductor above its surface, to reduce the vibrations of inductor and load due to the electro-dynamic forces and also the noise provoked by them, to obtain nearly balanced distributions of power and temperature [4]. Fig. 1 shows a
simplified three-dimensional
single-coil model of TFIH and TWIH induction heating.
Fig. 2. The relationship between eddy current distribution and the
It is much simpler than the experimental and practical
projection of the coil geometry
applications, but it is enough for the preliminary analysis
Then feed circular C1 with an alternating current.
of traveling wave and three-dimensional transverse flux
Because the distance between the coil and the metal strip
system. ANSYS modeling and simulation are executed
is far smaller than the area that the coil surrounded, the
based on this model to find the characteristic of eddy
magnetic flux density approximately remains constant
current distribution.
between the projection and the internal coil. According to the Faraday law, the induction electric
Manuscript received Feb. 29, 2008. This work was supported in part by the National Natural Science Foundation of China (50477016) and Natural Science Foundation of Hebei Province (No. E2005000019).
978-1-4244-2134-3/08/$25.00 ©2008 IEEE
potential in the circle loop is
ϕ
1
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(1)
YOUHUA WANG, JUNHUA WANG, JIANGUI LI AND HAOHUA LI: ANALYSIS OF INDUCTION HEATING
Where,
ϕ
is the chain magnetic flux induced by
the coil current, and
and obviously B parallels to n. S is the area that is
W is the time.
surrounded by the circuit loop. The magnetic flux Φ that passes projection area can
When exciting current changes, the magnetic flux
be expressed as
density changes accordingly. So we get
Φ = ΦM sinωt And ΦM is the amplitude of
, and
¡
(2)
¼ is the angular
Where,
ρ is
ρ
l S
ρ
G BaM π r22 sin(ωt ) (8) GW Where, BaM is the amplitude of Ba when Ba has H
2π ar dr h
(3)
sinusoidal changes. According to (4), eddy current in the loop is
length, h is the thickness of metal strip, and S is the cross-section area of the circuit. The current density distribution is discussed under two circumstances:
i=
The eddy current is
e ωd h Φ i = = - r × M cosωt R 2πρ ar
ar increases, BaM ar also increases. So, when the circle (4)
current density is more intensive from the center along
ωd h - r is a constant. With 2πρ
the radius direction. The eddy current density in the metal strip is
ar radius of the circle, ΦM declines
continuous. Based on Conclusions 1 and Conclusion 2 we
because the projector's internal and external magnetic flux are in the contrary direction. Therefore, when circle loop lies in the external of
can know: Conclusion 3: The eddy current density attains its maximum value around the coil projection. Outside the
projector C2, we can get the following conclusion:
projection coil, the eddy current density is less intensive
Conclusions 1: Outside the projection coil, the eddy
from the center along the radius direction, and inside the
current density is less intensive from the center along the
projection coil, the change is reversed.
radius direction.
All of the conclusions are based on a simple
B. Coil Lies in Internal of the Projection C2 The magnetic flux expressed as
(9)
loop lies in C2, the eddy current distribution is as following: Conclusion 2: Inside the projection coil, the eddy
For metal strip with given thickness, resistivity and
the increasing
e ωd h Φ = - r × M cosωt R 2ρ ar
For the metal strip with given thickness, resistivity and frequency, K 2 - d r h is a constant. As the radius 2
A. Coil Lies in External of the Projection C2
K1
(7)
(7)
the resistivity of the metal strip, l is loop
operational frequency,
B π r22
Therefore, we get equation (8) through (1), (5), and
frequency. The resistance of circle loop is
R
239
theoretical model. It should be added that eddy current distributions are not the only problems for in the use of
that passes area S can be
∫
n
these systems and for this reason the comparison must be studied further. The electromagnetic problem must be
(5)
coupled with the thermal and the mechanical ones in
Because the metal strip in the magnetic flux density B is continuous, according to the integral median formula there must be a Ba , which satisfies the flowing
order to have a more accurate understanding of the different
S
distributions,
mechanical
deformations and noises.
equation
∫
temperature
However, it is difficult to get a specific mathematical
% dsn = Ba S
(6)
equation due to the complication of eddy current distribution and its characteristics [5-9]. So we can only
Where, n is the right law Plane Circle Line direction, 2
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IEEE REGION 8 SIBIRCON 2008
use Finite Element Numerical analysis or other modern methods to analyze this problem. III. ANSYS MODELING AND SIMULATION Both analytical and numerical techniques can be used for the study of these heating systems. Analytical methods are more convenient for the integral parameters determination
and
analysis,
while
the
numerical
techniques are more universal and particularly useful for investigating the induced current and power distributions, taking into account the inductor edge-effects and the slots effects which are usually well pronounced in TWIH Fig. 5. Coil with loading current
systems. The analytical methods which make use of Fourier
The boundary conditions are shown in figure 6. For
integral transformation or series are effective for the
the purpose of simplifying calculation, meshing rate is set
simulation of lD, 2D and even 3D multiphase devices, but
to 6, which can greatly curtail the computation time
some simplifications and assumptions must be made.
without affecting the solution.
Since in this paper the analysis has been performed by FEM software ANSYS, in which the FEM code is called as an external subroutine. Fig. 4 shows the ANSYS theoretical model. The element type is solid117; air is the 1st material, coil the 2nd material and metal strip the 3rd material. We assume that these parameters do not change as the temperature flux. The value of current in the coil is 60 Amp, and the frequency is 60 Hz. All physical quantities are analyzed under the frequency-domain. Fig. 6. ANSYS model after loading parameters
Fig. 7 and Fig. 8 show the cloud diagram of magnetic density and the curve of eddy current density respectively.
Fig. 4. 3D induction heating ANSYS model
After the material definition and the unit dimension, specify current density to the coil, then couple VOLT constraint on the strip, and finally add parallel flux and normal flux boundary condition respectively. Fig. 5 Fig. 7. The magnetic flux density distribution in the strip of TWIH
shows the mesh results and current density.
systems
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YOUHUA WANG, JUNHUA WANG, JIANGUI LI AND HAOHUA LI: ANALYSIS OF INDUCTION HEATING
[5]
241
A.Ali, V.Bukanin, F.Dughiero, et al. “Simulation of multiphase induction heating systems,” IEE Conference Publication, 1994, vol.38, no.4, pp.211-214.
[6]
V.V.Vadher, I.R.Smith. "Travelling Wave Induction Heaters with Compensating Windings", ISEF"93, Warsaw (Poland). 16-18 Sept. 1993, pp. 211-217.
[7] Yang Xiaoguang, Wang Youhua, “The Effect of Coil Geometry on the Distributions of Eddy Current and Temperature in Transverse Flux Induction Heating Equipment,” Heat Treatment of Metals. 2003, vol.28, no.7, pp.49-54. [8] Yang Xiaoguang, Wang Youhua, “New Method for
Fig. 8. The eddy current density distribution in the strip of TWIH
Coupled Field Analysis in Transverse Flux Induction
systems
Heating of Continuously Moving Sheet,” Heat Treatment
From the results we can see that theoretical analysis
of Metals, 2004, vol.29, no.4, pp.53-57.
of eddy current distribution in section 1 accords with the
[9] S.Lupi, M.Forzan, F.Dughiero, et al. “Comparison of
simulation results. When the distance from the center
edge-effects of transverse flux and travelling wave
increases, eddy current intensity weakens in the internal
induction heating inductors,” IEEE Transactions on
coil projection; on the opposite, it becomes more
Magnetics, 1999, vol.35, no5, pp.3556 -3558.
intensive in the external coil projection. IV. CONCLUSIONS Through ANSYS simulation, the different eddy current density distribution has been analyzed, and the simulation results certified the theoretical conclusions. The trend of the eddy current distribution in the internal or external of the projection coil is different as the distance from the center becomes larger. REFERENCES [1]
A.L.Bowden, E.J.Davies, “Travelling Wave induction Heaters Design Considerations,” BNCE-UIE Electroheat for Metals Conference, 11.5.2, Cambridge (England), 21-23 Sept. 1982
[2] S.Lupi, M.Forzan, F.Dughiero, et al. “In the corresponding TWIH system this problem is reduced since less and not sharp peaks are present with their highest,” IEEE Transactions on Magnetics, 1999, vol35, no.5, pp.3556-3558. [3]
F.Dughiero, S.Lupi, P.Siega, “Analytical Calculation of Traveling Wave Induction Heating Systems,” International Symposium on Electromagnetic Fields in Electrical Engineering 1993, 16-18 September 1993, Warsaw-Poland, 207-210.
[4] F.Dughiero, S.Lupi, V.Nemkov, et al.
“Travelling wave
inductors for the continuous induction heating of metal strips,” Proceedings of the Mediterranean Electrotechnical Conference MELECON .1994, vol.3 , no.3, pp.1154-1157.
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