application of amplitude-modulated magnetic field in electromagnetic continuous casting

Application Of Amplitude-modulated Magnetic Field In Electromagnetic Continuous Casti

ng

Zuosheng LEI, Zhongming REN, Kang DENG, Weixuan LI

([email protected])

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


1. Introduction

Oscillation marks formation

soft-contact mold EMCC Amplitude-modulated Magnetic Field (AMMF)


Continuous Casting And Oscillation Marks


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


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.


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 )


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’


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:


2. Mold Oscillation Coupled

With AMMF EMCC


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


Dynamic pressure

Mold flux channel be widen

Coil

EM Force


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.


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


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


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


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


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


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


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


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


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.


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.


3. Mold Oscillation-less EMCC Under AMMF


Why Mold Oscillation Is Necessary In Continuous Casting?

RimLiquid Mold Flux

Mold Flux

Liquid Metal

Solidified Shell

Mol

d W

all

Conventional Continuous Casting


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


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


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.


AMMF Power Source Designing

Circuit frame of AMMF power source

Specially design IC as a connector and modulator


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


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


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.


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


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


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


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.


4. Conclusion and Outlook


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.


-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


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.


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


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.

application of amplitude-modulated magnetic field in electromagnetic continuous casting

Documents

dresden amplitude

ammf emcc

mold flux flow

dresden continuous casting

ammf conclusion

design ammf

kinds of magnetic field

dresden em field types