2nd Sino-German Workshop on EPM October 16-19, 2005, Dresden, German Application Of Amplitude-modulated Magnetic Field In Electromagnetic Continuous Casting Zuosheng LEI, Zhongming REN, Kang DENG, Weixuan LI (firstname.lastname@example.org) Shanghai Key Laboratory of Modern Metallurgy & Material Processing, Shanghai University, Shanghai 200072, P.R.China.
Content • IntroductionOscillation marks formationsoft-contact mold EMCCAmplitude-modulated Magnetic Field (AMMF) • Mold Oscillation Coupled with AMMF Electromagnetic Continuous Casting (EMCC ) • Mold Oscillation-less EMCC under AMMF • Conclusion and Outlook
IntroductionOscillation marks formationsoft-contact mold EMCCAmplitude-modulated Magnetic Field (AMMF)
Mold velocity Cast speed Mold flux Rim Molten mold flux Molten steel Oscillation Marks Positive strip Mechanism of Oscillation Marks Formation Mold Flux Initial solidified shell move direction Rim Liquid Mold Flux Liquid Metal Mold Wall Solidified Shell Mold oscillation direction Dynamic pressure of mold flux channel and movement of early solidified shell Negative strip
Tundish Mold I Water-in B Water-out I’ F Coil After cooler Oscillation device Ingot Dummy bar Soft-contact MoldElectromagnetic Continuous Casting (EMCC) • The effects of EMF: • Widen the mold flux channel, promote lubrication • Decrease the dynamic pressure.
EM Field Types Applied in EMCC 1、Continuous, constant amplitude, high frequency 2、Intermittent alternating magnetic field LI 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,surface behavior(Su Zhijian et al . ISIJ Inter. , 1999, 39(12): 1224-1230)
B B Bmin (a) (b) t t T’ τ T’ B B B0 (c) t (d) t T’ T’ 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
Motivation AMMF was applied in order to control the early solidified process precisely during CC, then two Novel EMCC Technologies were proposed: • mold oscillation coupled with AMMF EMCC Balancethe mould flux channel dynamic pressure by AMMF in order to decrease or even eliminate oscillation marks. • Mould Oscillation-less EMCC under AMMFSubstitute the huge mechanical mould oscillation system by AMMF imposing outside the mould.
Coil Mold flux channel be widen Basic Ideal: Balance The Mold Flux Channel Dynamic Pressure By AMMF Molten mold flux Rim Mold oscillation direction Liquid metal Dynamic pressure EM Force Mold wall Early solidified shell AMMF
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.
y 0 Governing equations li (li,hi) P=Pi Silicone oil (x,h(x)) Molten Sn lf (lf,hf) P=Pf boundary conditions x Without EM field: With EM field: h(x) determined by experimental results Mathematical Modelto Calculate the Mold Flux Channel Pressure
Mold Flux Channel Pressure Distribution mold flux channel pressure dynamic pressure of flux channel caused by mold oscillation
Rim Mold Wall Coil ' = = - P P P P ( t ) AMMF em em D Force Equilibrium of Early Solidification Shell Under EM Field Mold oscillation-less, under EM field Mold oscillation, under EM field The meniscus profile change can be neglect, Then, let
Outline of Magnetic Flux Density of AMMF at Different Initial Be (Positive Part)
B τ=1/fm Bmax Bmin t 1/f Dτ 5 6 4 2 7 3 10 13 8 1 9 11 12 Experimental Apparatus 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
Strain Slice Experimental Apparatus: Sketch Map PC with LabVIEW Water-cooling Coil Ⅰ Silicone oil DAQ Card Sn Ⅲ Mold Strain Gauge Salver Fulcrum Strain Gauge Measurement Cantilever DAQ Card Second cooling Ⅱ PC with LabVIEW Oscillation Device
Positive strip The maximum and minimum of withdrawing resistance Billets surface roughness Experimental Results Negative strip No mold flux, no magnetic field outside mold 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. With mold flux, no magnetic field outside mold With mold flux, with magnetic field outside mold. Stead amplitude Be =16.0 mT, 18 kHz
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.
Mold Flux Initial solidified shell move direction Rim Liquid Mold Flux Liquid Metal Solidified Shell Mold Wall Mold oscillation direction Conventional Continuous Casting Why Mold Oscillation Is Necessary In Continuous Casting? • Advantage of Mold oscillation: • Maintain lubrication and reduce the withdraw resistance, • Unlock the billets from the mold , and • Reduce the possibility of breakout and crack formation
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 Basic Ideal: No Mold Oscillation, but EM Field Oscillation Rim Liquid Mold Flux An amplitude varied high frequency alternative current Liquid Metal Mold Wall A varied EM force Coil Solidified Shell Mold oscillation-less EMCC under AMMF A Newly Developed EMCC technology: Mold Oscillation-less Continuous Casting (MOLECC) Process Under High Frequency Amplitude-modulated Magnetic Field
Our Work The 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 • An AMMF power source can generate rectangle, triangle and sine wave AMMF was designed, • the intermittent contacting distance in the mould under AMMF was measured, • MOLECC process under AMMF was examined.
Circuit frame of AMMF power source Specially design IC as a connector and modulator AMMF Power Source Designing
I Imin Imax Dτ 1/f τ=1/fm Be Bemax Bemin t, s t, s t, s a 0 0 0 8 8 8 2 2 2 4 4 4 6 6 6 b c Magnetic Field Inducted in the Mold by the AMMF Power Source • 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.
Digital Camera d PC Liquid Tin Water cooling coil Scale Intermittently Contacting Distance Under Different AMMF Experimental Apparatus Bemin Bemax Bemin 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 Sine wave AMMF，1Hz
Results of Intermittently Contacting Distance Measurements According to the intrinsic frequency of the experimental apparatus is 5.9 Hz. The results shows that d was the largest when fm=5.0Hz under all three wave kinds of AMMF, which indicated that resonance happened between liquid Tin and variation electromagnetic force at 5.0 Hz.
τ=1/fm B Bmax Bmin t 1/f Dτ Experiment system of Mold Oscillation-less Continuous Casting Under High Frequency AMMF 5 6 4 2 7 3 10 13 8 1 9 11 12 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
ExperimentalResults(1)Continuous Cast Friction Force and Billets Surface RoughnessVSModulated Wave Frequency
3.0Hz 4.0Hz 5.0Hz 6.0Hz 7.0Hz 2.0Hz ExperimentalResults (2)Cast Billets Surface Photos Under Sine Wave AMMF At Different Modulated Wave Frequency
Brief Summary of This Part • 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. • 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.
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.
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 Attractor Ergodicity of chaos Never intersect in phase space
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 A Simple Example 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 Bf2can be modulated too. We have much to do…
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. Thank You! 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).