Ù 46 ¾ Ù 8 «Vol.46 No.8 21 8 Ù 118 124 ACTA METALLURGICA SINICA Aug. 21 pp.118 124»³ ¾ Æ À ÃÅÄ ÇÂÁ (Đ Î ÌÝÈ ³ÏÚÆ, 11819) ÛÕ½Û Sn 32%Pb 52%Bi Ä Ù ÐÞ É, Ç Ê É ÛÓ ÄÉ ( É + ³É ) Ù ± ÚÒ ÓÆ ÐÃ. Ç, Á ÞÉ Ä, ÒÝ Ã Ý, Ð É É±», Ò ÖÍ Ð ÛÀ ÀÀÒ ; Ä Ò À, ËÄÒ Ë ¾ÛÃ. É É±», Ë Ûû. É Ñ ³É ( 1.44 T) Á Ü ÞÆ É Ù ± ÀÒ Ð Ã ;» ³É ɱ, Ò. ³É Û ÞÆÒ,» ³É, ½Ô«, ³É Ù ±, Ò ¹¹. ÇÞ Ë ÔºÄÀ ³É ɱ, ËÄÒ Ð, Ò À. Æ, É, ³É, Ò ± «TF777 µ¹þ A µ Ü 412 1961(21)8 118 7 EXPERIMENTAL RESEARCH ON MELTING SURFACE BEHAVIOR IN MOLD UNDER COMPOUND MAGNETIC FIELD DENG Anyuan, WANG Engang, XU Yongyi, ZHANG Xingwu, HE Jicheng Key Laboratory of Electromagnetic Processing of Materials, Ministry of Education, Northeastern University, Shenyang 11819 Correspondent: DENG Anyuan, associate professor, Tel: (24)83681716, E-mail: dengay@epm.neu.edu.cn Supported by National High Technology Research and Development Program of China (No.27AA3Z519), National Natural Science Foundation of China (Nos.5645 and 58341) and the Program of Introducing Talents of Discipline to Universities (No.B715) Manuscript received 21 2 2, in revised form 21 3 19 ABSTRACT In order to control stability of molten metal surface during electromagnetic continuous casting, the stabilities of melting surface under applications of an alternating magnetic field and a compound magnetic field were investigated experimentally. The melting surface behavior of the Sn 32%Pb 52%Bi alloy with low melting point was measured by using a laser displacement sensor and visualized by using a high speed video camera. The Fourier analysis method was introduced to reveal the fluctuation characteristics of free surface. It is experimentally found that when only alternating field is applied, the free surface keeps fluctuating. However, with increasing the alternating magnetic flux density, two statuses of the free surface, the stable camber deformation and the swinging phenomenon, can be observed orderly, and during swinging, the square like or triangular prism like deformations appear stochastically. The Fourier analysis indicates that the dominant fluctuation frequency at free surface center increases with increasing the alternating magnetic flux density. After simultaneously superposing a transverse static magnetic field within 1.44 T, the unstable swinging behavior of free surface can be remarkably controlled. Increase of static magnetic flux density can make the swinging amplitude reduce. Also the static magnetic field can effectively * Ð Ö Ú Ô 27AA3Z519, ÐÔ Ï Ô 5645 À 58341, ÛÓ ÑÏ Ï Æ ĐÈÚ Ô B715 Ò º : 21 2 2, Ç º : 21 3 19 Ù : Ô, Ø, 1971 Ð,, Î DOI: 1.3724/SP.J.137.21.66
Ù 8 «Ó Ð : ÃÈ¾Ø Ñ Â Æ 119 damp the free surface fluctuation. The stretch phenomenon was observed due to application of high static magnetic field in compound field, also a series of regular surface fluctuations appeared on free surface. There is an appropriate range of the static magnetic flux density to obtain more stable free surface, lower fluctuation amplitude and dominant fluctuation frequency. KEY WORDS continuous casting, alternating magnetic field, static magnetic field, free surface fluctuation µµ Ç ½Ì, µ ºÁÇÒ º, µîë Ç É Ì Ä Á Ò, ݼĐË ½, ÖË ½. Âе Ä Æ Ê Ù½ ßÊÅÝÉ Ó Á Á, Ï«ÖÅ, ÇÁ Đ ÊÉ. ÃÅ Æ ßÊÅ ÚÅ, ßÊÇ Ú µç Al ÁÇ Cu ¾ÐÌ Ë Å. Õ 1989 Vives [1] Đ µßê ÂÇ Î, ßÊÇ µç ÌÜĐ ÊÉ. µ ÆÌ, ¼ ¹ Á [2,3] Ê ² [4,5] Á [6 8] Ò ÄË É Á Á¾Ý Æ. Æ Ê ÁÆ ß ÚŽ ßÊÅ Ý µó, Ó,»ÇËßÊ Á ÊÉ Đ. Ì Ó Á Æ ßÊÇ Ñ. Õ, ¼ Ú ßÊÅ ÎÐ ÚÅ ÄË [9 11], µåå ¾Ý Ò Ë Đ Ó Æ [2,12], Áݵջ Û Ó. Ê Ý ßÇ, µå Ö¾Ü Sn 32%Pb 52%Bi(ÊÉ ) Å, È Ë Æ Ê ÚŲ ¾ ÆÁ Ä, ÅÂĐ Ê, Ë ÅÊ ÚŲ Ó Ä, µ ÅÁ ÇÓ Ä ¾Ý Đ º. 1 Å È Å 1 ÙÍ. Sn 32%Pb 52%Bi Å ß ¾ÜÁ Ê 95 kg/cm 3, 1.11 1 6 S/m, 94 Á 1, À¾ÜÆ, µó Æ ( ß ¾ÜÁ Ê 72 kg/m 3,.7 1 6 S/m, 15 Á 1), ̵ Å Sn 32%Pb 52%Bi Ö¾ÜÅ ÑßµÓ, Å µ¾¼ Þ² Ûµ 46 mm à Ì. µã Æ ²ÅÒ Cu Dz ½², f=23 khz Æ ß Ç, ½ Æ Ê. ² ½² 5 ±, 66 mm. ½² Ì ¾ ÊÓ. ßʲ, Æ Ê µ¾ Û½ Æ ß, ÚÅ µ¾ Æ Ò ºÛ½ Ç ¾ Æ À Ó ßÊÅ, ÉÓ Á Á, µ¾ ÛÁ ² 2» [13]. Á 2 ÙÍ. Ú ßÊ Å Å ÅÁ Ž Å Þ Ë. Ó Å Ë ( 1 (ρ s ρ f )g z = γ + 1 ) + p d + B2 a R 1 R 2 4µ (1) ËÌ, ρ s Á ρ f ÓÁÆ ¾, g Å ĐÔ, z, γ µóáóþæ ¾ Å, R 1 Á R 2 µ, p d Å, B a ÅÄ Ê². Ì Ü Å 2 ÙÍ ÓÁÆ ¾ Æ Ü. Ü ÜÄ Ê² B a Ú ÍÆ Ê. ÜÄ Ê² Å ½², È Ì Ü Ê² ǵ.6 T. µå LK 2 Ð Ó Ø ÉÓÞ ¼ Ü, Ë ¾ Ü Ó 1/2 µ ÅÁÓ Ì ÜÒ Å ( 2) Ä, µ 1 ms. Å FASTCAM ultima APX Ô Ü µæ Ê Ì» ÁÁ Æ, µò 25 frames/s. ÅÊ È Å 3 ÙÍ. Ú µæ ² ² 1 Ç ÄÌЫFig.1 Schematic of experimental apparatus ² 2 ÌЫFig.2 Schematic of meniscus
12 Í Ù 46 ¾ ² 3 ÄÉ Ç ÄÌЫFig.3 Schematic of experimental setup with compound magnetic field ƳÂĐÕ» Ê, Ê ÊÑÌ ² Ì ¾ ÊÓ 3. Ê ² ½² ß Ç. Å Ü 1 Ä ( 3) Ê Ê² Ú B Í Ê, B µ 1.44 T. 2 Æ 2.1 Ý Đ ½ Æ ßÊÅ Ù, µ È ², ÑßÛÕËÆ Ê ² ÜÄ Ê² Á ßÊÅØÅ, 4 ÙÍ., ʲ ÁßÊÅÕ Ä Þ. Ë (1), µßêå ÚŲ, Ó ÅÆ Á, ØÆ Ê Ê² ¼Đ, Ó ÁÁ Ó ¼. Ó Á ßÊ Å Å ÅÁ Å Þ Ë, Ì ßÊÅ ÁßÊÅ «ÚÅ Á, Å ÃÓ. 5 ÙÍ, Ó Æ ÙÂĐÆ Ê Ê². Æ Ê Ê².44 T Å, Å Ó Á ( 5a). Æ Ê Ê².53 T Å, ÓÆ Á ( 5b). µ Å, Ó Ê².44 T Å ÊÍÆ Á, «Ä Þ Á Þ, ÔÓÖ µ Á ½ ¾ Ì, Õ, ²ÕÅ Æ Ë Å Ï, Ý µ¾ Ì,  ÏÕ, «Ê, ¹ËÓ Ø Å, Å ØÑ Ì. 5b,.44 T Å Ü Á, ÌÅ ¹ 2 ÎÁË, Ô Á Á Á, Ø ¹. Ó Å É Æ Æ Â, Ï«Đ ÊÉ,»ÇËßÊÇ. È, Øʲ ¼Đ, Ç ¹Ï,  À, Î Ï [14]. Ó Æ Øʲ ¼Đ«¼ Ó, ¹ Ó ½ÍØÅ. Ó, Æ ÅÆ Ê Ê² ǵŠÛ, µßêç ÌÆ µ± ÚÓ ÇÁ Â. Ίƹ ßÊÅ Æ. 4, ßÊÅ ÊÍÀ Ó, µ, ÓÕÅ Â ¹. Ó Å Ë, ßÊÅ Å, Ó Æ Á, Ï«Ó ½Ì, Õ ½². ½²Û ʲ µ Ø ½² ¼ ¼ «, Ì ½²Õ Ó Ê ¼, ßÊ Å¼, Ì ½²Õ Ó ßÊ Å, ż»ÆÉÓ Ì Å Ï. Æ, Óµ Ì Ì «ÏÕ, Ï«Å,» Î Å. Æ Ê Å, ºÓ Á, Ó Ö. Õ Ýż, ÏÕ ßÊÅ, Ì., Æ Ê ¼, º ¹ Æ. 2.2 Ý Đ ß ½ 6 Ó Ì ÜÁ 1/2 µä Ó B x, T.15. -.15 (a) B z, T.6 (b).3. -.3 -.6 F x, 1 5 N/m 3 8 4-2..1.2.3.4..1.2.3.4 Time, 1-3 s Time, 1-3 s ² 4 ¾Ûà ɱ ÀÞÉÄ Fig.4 Changes of x components (a) and z components (b) of alternating magnetic flux density (B x, B z ) and induced Lorentz force (F x, F z ) at triple phase point with time F z, 1 5 N/m 3-1
Ù 8 «Ó Ð : ÃÈ¾Ø Ñ Â Æ 121 ² 5 É É± ± Ò ÐÅ Fig.5 Photos of the swinging instability of free surface under alternating magnetic fields with B a =.44 T (a) and.55 T (b) with frequency f=23 khz Vibrating amplitude, mm 4 3 2 1-1 T.51 T.51 T.51 T -2 Triple-phase Half position Center point of radius -3 1 2 3 1 2 3 1 2 3 1 2 3 Time, s ² 6 ÄÃ Ò Fig.6 Fluctuations of melt surface at triple phase point, half position of radius and center of free surface under B a =.51 T, f=23 khz ½., ßÊÅ Ð ÚÅ, Õ Ó µßê ÚÅ²Õ Ä Þ. È Æ¹, µæ Ê Ê².43 T Å, Ó Ì Ä, µ ÜÄ. 6 ÙÍ, ʲ.51 T Å, ÓÆ Å, Ó Ì Ä «, 1.9 3.19 mm, «µ ÜÄ, 2.3 1.9 mm. Î ß ÊÅ Ó ÚÅÁÓ Æ. Æà ¾ ²Á Đ. µ Ç Ì, Đ Ç ÊÉ, ÅÓ Çµ ±3 mm ÜÛ,, Æ Ý Ó Á Æ, ¾, Ã Đ ÊÉ [15,16]. Ì,»Ç Ë Ê Ê², «Ç Ë Á Đ. 7 ½º 6 Ì ½, Å Ô Fourier Ì ÜÁ ÜÄ Å ², Power spectrum density, mm 2 /s Power spectrum density, mm 2 /s 1-2 1-4 1-6 1-8 1-1 (a) 1-12 1 2 3 4 5 Frequency, Hz 1-4 1-6 1-8 (b) 1-1 1 2 3 4 5 Frequency, Hz ² 7 Ò Ë À ¾Ûà ± Fig.7 Power spectrum densities at the center of free surface (a) and triple phase point (b) obtained by Fourier transformation of Fig.6 Ë ÝÉ ². 7 ÙÍ, µó Ì, 2.12 Hz; µ ÜÄ, Ò Ìµ 5.8 Hz, ŵ 19.92 Hz µõ»î., µ ÅÄ, Æ ßÊÅ Ó»Æ. Å, È Æ¹, Æ Ê, Ó. µê²
122 Í Ù 46 ¾.29,.36 Á.43 T Å, Ó Ì Ä 1.17, 1.17 Á 5.7 Hz. ØÊ ² ¼Đ, Ì ÜÄ ¼. µê² Ï.43 T ¼Đ.51 T Å, Æ Õ»Å. Ð Ó Ï Á Þ Å Þ. 2.3 Đ ½ º ÅÁ ÇÓ Á Ä ( 3), µ Æ ßÊ Ó ÅÂĐÕ»Ê Ê. 8 µ Ê Ê².65 Á 1.44 T Å Å Ó Å. ÙÍ, ÂĐ Ê Î, Æ Ê ÚŲ Ó Æ, Ó Æƹ Ì, Áµ Ê ÊÅ½Ç Æ Å. Ê Ê², Ó Å. Ê Ý ßÇÆ Ê ÚŲ ÁÓ Ä. 2.4 Đ ß ¼ º 9 Ê Ê² ² Ó., ÅÂĐÒ Ê Î, Ó»Æ Æ, ÊŽ, Ó. È, ÌÅ Ê ÊŽ Ä Ì Á ÊÅ½Ç Á. Ê.65 T Å, Ú ¹ËßÊÇ ¹, Ê, Ä ¹Ë º ². Ê.81 T Å, ßÊÇ, ÌÅ Ó. Ê.97, 1.2 Á 1.44 T Å, Ø Ê Ê ² ¼Đ, Ó ¹Ë ºº. Ê Ê².97 T Å, º Áµ Ü ¹, µ ¾ Ì º, µó Ì ÕÏ» º, Ø Ê Ê² ¼Đ, º Ó Ì Å, Ê Ê² 1.44 T Å, Ó Ì ¹º, «. ι µ ¾ Û µê ² ² ß Á ¹ÊŽ ½ ² ß, Ê ÚŽ 2 ÎßÊÅ, ßÇ Á, Î º Ó. Ê Ê² ÖÅ, ßÇ ßÊÅ Ø, Ø Ê Ê² ¼ Đ, Î ¼, Ì ÃÓ Æ¼ Ï, µ ÚŲ Ý ¹ º. 1 Ê ²Ó Ì Ü ½., Ø Ê Ê² ¼Đ,, µ Ê Ê².97 T Å, Ó Ì ÜÄ Ö ±1 mm Û; ß˼ Ê Ê², Ì Ü Ä ¼. Ó Ê Æ ß ÊÅ Ó ÆÈ ßÇÚÅ, µõ»å Ê Ê², µåì ßÇ. Ù, Ó Ì Ä Ø Ê Ê² Ó ½ º Æ. ̵µÅ Ê ÇÆ Ê Ó Ä ÅßÊÇ Ì, Æ µå Ù Ê Ê². 11 Å Ô Fourier 1 Ì Ê Ê² ²Ì Ü ½ ². ² 8 ³É ɱ ± Ò ÐÅ Fig.8 Photos of the swinging instability of free surface under application of compound field with static magnetic flux densities B =.65 T (a), 1.44 T (b) and f=23 khz, B a =.55 T
Ù 8 «Ó Ð : ÃÈ¾Ø Ñ Â Æ 123 ² 9 ³É ɱ ± Ò Fig.9 Photos of the fluctuation behavior of the melt surface under compound field with different static magnetic flux densities (f=23 khz, B a =.55 T) (a) T (b).65 T (c).81 T (d).97 T (e) 1.2 T (f) 1.44 T Vibrating amplitude, mm 2-2 T.65 T.81 T.97 T 1.2 T 1.44 T 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 Time, s ² 1 ³É ɱ ± Ò ¼ Fig.1 Fluctuations of the melt surface at its center position under different static magnetic flux densities (f= 23 khz, B a =.55 T) 1 Ì Ø Ê Ê² Õ Ã, Ó Ì Ø Ê Ê² ¼Đ Î ¼, µ B =.97 T Å, Æ., µ B =.97 T Å, Ó, Ü. Å Ó ÁÞÁ, Æ Ê.55 T Å Ó, Æ Ê Ê² µ.8 1. T. Frequency, Hz 6 4 2..4.8 1.2 B, T ² 11 ÄÉ Ù ±Ò Ë ± 3 Fig.11 Curve of main fluctuation frequency vs static magnetic flux density obtained by Fourier transformation of Fig.1 (1) µæ Ê ÚŲ, ØÆ Ê Ê² ¼Đ, Ó Î ¹ Ü ÁÁØ Å Á¹, µ Å Ì ØÆ Ì. (2) Æ Ê É Õ Ó Õ Ä Þ, Ó Ì Ä ÜÄ. ØÆ Ê Ê² ¼Đ, Ì ÜÄ ¼.
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