Application Of Amplitude-modulated Magnetic Field In Electromagnetic Continuous Casti
ng
Zuosheng LEI, Zhongming REN, Kang DENG, Weixuan LI
Shanghai Key Laboratory of Modern Metallurgy & Material Processing, Shanghai
University, Shanghai 200072, P.R.China.
2nd Sino-German Workshop on EPM October 16-19, 2005, Dresden, German
2nd Sino-German Workshop on EPM, (Dresden)
Content1. Introduction
Oscillation marks formationsoft-contact mold EMCC Amplitude-modulated Magnetic Field (AMMF)
2. Mold Oscillation Coupled with AMMF Electromagnetic Continuous Casting (EMCC )
3. Mold Oscillation-less EMCC under AMMF
4. Conclusion and Outlook
2nd Sino-German Workshop on EPM, (Dresden)
1. Introduction
Oscillation marks formation
soft-contact mold EMCC Amplitude-modulated Magnetic Field (AMMF)
2nd Sino-German Workshop on EPM, (Dresden)
Continuous Casting And Oscillation Marks
2nd Sino-German Workshop on EPM, (Dresden)
Mechanism of Oscillation Marks Formation
Mold fluxRim
Molten mold fluxMolten steel
Oscillation Marks
Mold velocity
Cast speed
RimLiquid Mold Flux Mold Flux
Liquid Metal
Solidified Shell
Mol
d W
all
Dynamic pressure of mold flux channel and movement
of early solidified shell
Mold oscillation direction
Initial solidified shell move direction
Negative strip
Positive strip
2nd Sino-German Workshop on EPM, (Dresden)
Soft-contact Mold Electromagnetic Continuous Casting (EMCC)
Tundish
Mold
Water-in
Water-out
Coil
Oscillation device
Dummy bar
Ingot
After cooler
IB
I’F
The effects of EMF:
1. Widen the mold flux channel, promote lubrication
2. Decrease the dynamic pressure.
2nd Sino-German Workshop on EPM, (Dresden)
EM Field Types Applied in EMCC
1 、 Continuous, constant amplitude, high frequency
2 、 Intermittent alternating magnetic fieldLI Tingju et al : surface behavior (Metallurgical
Transaction B: 1995, 353-359)
ZHOU Yueming : surface behavior and mold flux flow.(Tetsu-to-Hagane, 2001, 37(7): 777-780 )
3 、 Half-triangle high frequency magnetic field ( Su Zhijian et al, CAMP-ISIJ. 1998, 11: 132 )
4 、 quasi-sinusoidal magnetic fields : Reaction between slag and molten metal,s
urface behavior (Su Zhijian et al . ISIJ Inter. , 19
99, 39(12): 1224-1230 )
2nd Sino-German Workshop on EPM, (Dresden)
Amplitude-modulated Magnetic Field
All kinds of magnetic field whose amplitude is vary can be named as Amplitude-modulated Magnetic Field(AMMF) 。
Such as : rectangle, sawtooth, sine, triangle Wave modulated MF
And some other tailored wave AMMF
Bmin
B
t(a)
τT’
B
t(b)
T’
B
t(c)
T’
(d)
B0
t
B
T’
2nd Sino-German Workshop on EPM, (Dresden)
Motivation
mold oscillation coupled with AMMF EMCC Balance the mould flux channel dynamic pressure by AMMF in order to decrease or even eliminate oscillation marks.
Mould Oscillation-less EMCC under AMMF Substitute the huge mechanical mould oscillation system by
AMMF imposing outside the mould.
AMMF was applied in order to control the early solidified process precisely during CC, then two Novel EMCC Technologies were proposed:
2nd Sino-German Workshop on EPM, (Dresden)
2. Mold Oscillation Coupled
With AMMF EMCC
2nd Sino-German Workshop on EPM, (Dresden)
Basic Ideal: Balance The Mold Flux Channel Dynamic Pressure By AMMF
AM
MF
Early solidified shell
Mold wallRim Molten mold flux
Liquid metal
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-16
-12
-8
-4
0
4
8
12
16
Mold oscillation direction
Dynamic pressure
Mold flux channel be widen
Coil
EM Force
2nd Sino-German Workshop on EPM, (Dresden)
Our Work
A mathematic model is developed in order to optimize design AMMF .
Mold oscillation coupled with AMMF continuous casting experiments was carried out and the surface of the billet was examined. Withdrawing resistance during CC was measured.
2nd Sino-German Workshop on EPM, (Dresden)
Mathematical Model to Calculate the Mold Flux Channel Pressure
Governing equations g
y
u
dx
dPf
xf
2
2
0)()(
0
xhx
R dyudx
d
dx
dQ
smxfi VVuylxl ,0,
0),(, xfi uxhylxl
iii PPhylx ,0,
fff PPhylx ,0,
boundary conditions
x
y0
li
Molten Sn
Silicone oil
(li,hi)P=Pi
(lf,hf)P=Pf
lf
(x,h(x))
ax
xaaaxaxh 3768.0)
22ln(
2
22)(
222222
Without EM field:
With EM field: h(x) determined by experimental results
2nd Sino-German Workshop on EPM, (Dresden)
Mold Flux Channel Pressure Distribution
)(
)()]()()(6[)()(6)(
fl
xipfpflsVmVffglfxsVmVfgxfipxP
x
l
x
li idx
xhxdx
xhx
)(
1)(,
)(
1)(
32
)(
)()]()()(6[)()(6)(
fl
xipfpflsVmVffglfxsVmVfxPD
mold flux channel pressure
dynamic pressure of flux channel caused by mold oscillation
2nd Sino-German Workshop on EPM, (Dresden)
Force Equilibrium of Early Solidification Shell Under EM Field
Rim
Mold W
all
Coil
metalfluxem PPPP
metalfluxDem PPPtPP '' )(
' PP
Mold oscillation-less, under EM field
Mold oscillation, under EM field
emDem PtPP )('
)(' tPPPP DememAMMF let
The meniscus profile change can be neglect,
Then,
fttPBtB xmDemAMMF 2cos)(22)( 2
2nd Sino-German Workshop on EPM, (Dresden)
An Example of AMMF
0 0.5 1 1.5 2-50
0
50
t, s (two cycles)
Mag
netic
flux
den
sity
of A
MM
F w
ave,
mT
Be=27.3 mT
2nd Sino-German Workshop on EPM, (Dresden)
Outline of Magnetic Flux Density of AMMF at Different Initial Be (Positive Part)
0 0.5 1 1.5 235
40
45
50
55
60
65
70
t, s (two cycles)
Out
line
of A
MM
F, m
T
Be= 46.7 mT
Be= 43.2 mT
Be= 39.9 mT
Be= 36.3 mT
Be= 31.5 mT
Be= 29.8 mT
Be=27.3 mT
2nd Sino-German Workshop on EPM, (Dresden)
Experimental Apparatus
1
35 6 4
7
8
9
1112
13 10
2
t
B Bmax
Bmin
τ=1/fm
Dτ1/f
1. High frequency power source 2. Function generator 3. Converter 4. Coil outside mould
5. Molten metal ladle 6. Tundish and nozzle 7. Cold crucible like mould 8. Oscillation device 9. Continuous casting machine
10. Measurement Cantilever 11. X-Y Recorder 12. Strain Gauge 13. Data acquisition PC
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Experimental Apparatus: Sketch Map
Strain Gauge
DAQ Card
Ⅰ
Ⅱ
Ⅲ
DAQ Card
Strain Gauge
Water-cooling Coil
Mold
Measurement Cantilever
Salver
Fulcrum
Second cooling
Sn
Silicone oil
Strain Slice
Oscillation Device
PC with LabVIEW
PC with LabVIEW
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Experimental Parameters
Table 1 Mould and Coil Dimensions
Inner diameter 60 mm
Outer diameter 76 mm
Length 110 mm
6 slits of width 0.5 mm and length 90 mm from top
Copper mould
Oscillation frequency 1.0 Hz, amplitude ± 5 mm
Coil 2 turns height 25 mm
Inner diameter 85 mm
Outer diameter 105 mm
Location: coil top 20 mm below the mould top
Table 2 Continuous Casting Condition Casting speed 12.5 cm/min
Outside the mould 12 L/min Cooling water density Secondary cooling 13.6 L/min
Metal Tin 300± 5℃
Silicone oil Density 960 kg/m3
Mould flux
Surface tension 0.02 N/m
Viscosity 0.096 Pa.S
Stead amplitude Be =16.0 mT Carrier wave 18 kHz
Modulated wave Rectangle, 1.0 Hz
Magnetic field
Bemax =16.0 mT Bemin=5.3 mT
2nd Sino-German Workshop on EPM, (Dresden)
Experimental Results
- 6. 13
- 2. 4- 2. 79
- 10. 64
1. 05
6. 16
11. 1311. 91
- 15
- 10
- 5
0
5
10
15
condi t i on1
condi t i on2
condi t i on3
condi t i on4
With
draw
ing
resi
stan
ce,N
Max
Mi n
The maximum and minimum of withdrawing resistance
0. 173
0. 2065
0. 08270. 0632
0
0. 05
0. 1
0. 15
0. 2
0. 25
condi t i on 1 condi t i on 2 condi t i on 3 condi t i on 4
Bill
ets
surf
ace
roug
hnes
s,mm
Billets surface roughness
No mold flux, no magnetic field outside mold With mold flux, no magnetic field outside mold With mold flux, with magnetic field outside mold. Stead amplitude Be =16.0 mT, 18 kHz
Posi
tive s
trip
Negati
ve
stri
p
With mold flux, with rectangle wave AMMF. Bemax =16.0 mT during mold oscillation positive strip and Bemin=5.3 mT during negative strip. Carrier wave frequency 18 kHz and modulated wave frequency 1 Hz.
2nd Sino-German Workshop on EPM, (Dresden)
Brief Summary of This Part AMMF is utilized in EMCC in order to
decrease depth of oscillation marks or even to eliminate it. A model to optimize design AMMF is proposed.
Continuous casting experiments results show that imposition of AMMF coupled with mold oscillation can deduce the friction force and improve the billets surface quality.
2nd Sino-German Workshop on EPM, (Dresden)
3. Mold Oscillation-less EMCC Under AMMF
2nd Sino-German Workshop on EPM, (Dresden)
Why Mold Oscillation Is Necessary In Continuous Casting?
RimLiquid Mold Flux
Mold Flux
Liquid Metal
Solidified Shell
Mol
d W
all
Conventional Continuous Casting
Mold oscillation direction
Initial solidified shell move direction
Advantage of Mold oscillation:
1. Maintain lubrication and reduce the withdraw resistance,
2. Unlock the billets from the mold , and
3. Reduce the possibility of breakout and crack formation
2nd Sino-German Workshop on EPM, (Dresden)
Basic Ideal: No Mold Oscillation, but EM Field Oscillation
Rim Liquid Mold Flux
Liquid Metal
Solidified Shell
Mol
d W
all
Coi
l
Mold oscillation-less EMCC under AMMF
An amplitude varied high frequency
alternative current
A varied EM force
EM field can affects metals touch-less by EM force
Together with pressure of liquid metal, a varied EM force can let initial solidified shell moved left and right directly, to maintain the lubrication and unlocking
So we need a varied EM field
outside the mold: AMMF
A Newly Developed EMCC technology:
Mold Oscillation-less Continuous Casting (MOLECC) Process Under High Frequency Amplitude-modulated Magnetic Field
2nd Sino-German Workshop on EPM, (Dresden)
Our WorkThe aim of MOLECC process is to substitute the huge and heavy mechanical
mould oscillation system by a small and light electromagnetic one.
THEN, in our work
1. An AMMF power source can generate rectangle, triangle and sine wave AMMF was designed,
2. the intermittent contacting distance in the mould under AMMF was measured,
3. MOLECC process under AMMF was examined.
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AMMF Power Source Designing
Circuit frame of AMMF power source
Specially design IC as a connector and modulator
2nd Sino-German Workshop on EPM, (Dresden)
Magnetic Field Inducted in the Mold by the AMMF Power Source
(a) rectangle, (b) triangle and (c) sine wave.
The cold crucible like mold: 110mm lengthen, φ76×8mm , near the slits.The coil: 25mm high, φ105×10mm.
f=18kHz, fi=0.5Hz.
t, s2 4 6 80b
t, s2 4 6 80c
at, s2 4 6 80
I
Imax
Imin
BeBemax
τ=1/fm
Dτ 1/f
Bemin
2nd Sino-German Workshop on EPM, (Dresden)
Intermittently Contacting Distance Under Different AMMF Experimental Apparatus
Liquid Tin
Scale
Digital Camera
PC
d
Water cooling
coil
0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1- 1 6
- 1 2
- 8
- 4
0
4
8
1 2
1 6
Time, s
Mag
netic
flu
x de
nsity
, mT
t=0 s t=0.5 s t=1.0 s
Meniscus
Meniscus
Meniscus
5.0
mm
(a) (b) (c)
Sine wave AMMF , 1Hz
Intermittently Contacting Distance affects the mould flux’s behavior of flowing in and out of the mould flux channel between the early-solidified shell and mould wall
Bemin Bemax Bemin
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Results of Intermittently Contacting Distance Measurements
0
2
4
6
8
10
12
0 2 4 6 8 10 12
Modul ated Waves Frequency, Hz
d, m
m
Rectangl e WaveTri angl e WaveSi ne Wave
)(,)tanh()(2
1 3 RkHkkgkf lmlmlmlmlmlm
According to
the intrinsic frequency of the experimental apparatus is 5.9 Hz. The results shows that d was the largest when fm =5.0 Hz under all three wave kinds of AMMF, which indicated that resonance happened between liquid Tin and variation electromagnetic force at 5.0 Hz.
2nd Sino-German Workshop on EPM, (Dresden)
Experiment system of Mold Oscillation-less Continuous Casting Under High Frequency AMMF
1
35 6 4
7
8
9
1112
13 10
2
t
B Bmax
Bmin
τ=1/fm
Dτ1/f
1. High frequency power source 2. Function generator 3. Converter 4. Coil outside mould
5. Molten metal ladle 6. Tundish and nozzle 7. Cold crucible like mould 8. Oscillation device 9. Continuous casting machine
10. Measurement Cantilever 11. X-Y Recorder 12. Strain Gauge 13. Data acquisition PC
2nd Sino-German Workshop on EPM, (Dresden)
Experimental Results(1)Continuous Cast Friction Force and Billets Surface Roughness
VS Modulated Wave Frequency
0
2
4
6
8
10
12
14
16
18
20
1 2 3 4 5 6 7 8
Modul ated Waves Frequency, Hz
Friction Force, N
Rectangl e Wave
Tri angl e Wave
Si ne Wave 0. 1
0. 15
0. 2
0. 25
0. 3
0. 35
0. 4
0 1 2 3 4 5 6 7 8
Modul ated Wave Frequency, HzSurface roughness, mm
Rectangl e Wave
Tri angl e Wave
Si ne Wave
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Experimental Results (2)
Cast Billets Surface Photos Under Sine Wave AMMF At Different Modulated Wave Frequency
4.0Hz 5.0Hz 6.0Hz 7.0Hz2.0Hz 3.0Hz
2nd Sino-German Workshop on EPM, (Dresden)
Brief Summary of This Part
1. During the MOLECC process under rectangle, triangle and sine wave AMMF, an modulated wave frequency a little lower than the intrinsic frequency of the experimental system was the optimum frequency to obtain the greatest intermittent contacting distance, the best mould flux lubricating, the least continuous casting withdrawing resistance, and the best surface quality of billets.
2. Among the three kinds of AMMF, sine wave is the best in increasing the intermittent contacting distance, reducing the withdraw resistance and improving the billets surface quality.
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4. Conclusion and Outlook
2nd Sino-German Workshop on EPM, (Dresden)
Conclusion
In order to improve the continuous casting billets surface quality, AMMF is applied to control the early solidified process. Two technologies were developed. One is mold oscillation coupled with AMMF EMCC, and another is Mold Oscillation-less EMCC under AMMF.
In both the two technologies, AMMF can deduce the friction force during CC and improve the billets surface quality.
2nd Sino-German Workshop on EPM, (Dresden)
-4-2
02
4
-10
-5
0
5
100
50
100
150
200
voltage1,Vvoltage2,V
time,
s
Outlook (1)Problem: What kind of AMMF is the best in continuous casting?We are now trying some special kind of AMMF, for example: chaotic AMMF, which means the amplitude is modulated by a chaotic signal.
Duffing Chaotic AttractorDuffing Chaotic Attractor Ergodicity of chaos
Never intersect in phase space
0 10 20 30 40 50 60 70 80 90 100-4
-3
-2
-1
0
1
2
3
4
t,s
vol
tage
,V
-4 -3 -2 -1 0 1 2 3 4-8
-6
-4
-2
0
2
4
6
8
voltage1,V
voltage2,V
2nd Sino-German Workshop on EPM, (Dresden)
Outlook (2)We know, one magnetic field (both AC and DC) is characterized by three main parameters:
1) Amplitude→Determine the magnetic flux density and EM Force amplitude inside liquid metal
2) Frequency→Determine the EM Force distribution
3) Phase →Determine the EM Force direction
So, by combination adjusting or modulate every two of them we can obtain a kind of complex magnetic field in order to obtain desire volume force in different process, such as EMS, EMBr and EMCC.
2nd Sino-German Workshop on EPM, (Dresden)
An ideal: Frequency adjusted & amplitude modulated magnetic field
Two frequency magnetic field in one coil. All the parameters are adjustable, including f1,f2, T, Tf1, Bf1 and Bf2. The wave of Bf1 and Bf2 can be modulated too.
We have much to do…
A Simple Example
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The author wish to acknowledge the financial support from the National
Natural Science Foundation of China (No. 59734080 and 59974017) and Youth Development Foundation of Shanghai educational committee (NO.04AC87).
Thank you very much, Prof. Gerbeth, for the organization and invitation
to this workshop.
Special thanks go to the Sino-German Science Center
for the funding of this workshop.