利用高频磁场去除铝合金中的非金属夹杂
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摘要
电磁净化技术作为材料电磁加工技术的一个分支，已经逐渐发展成为具有广
阔应用前景的新型金属熔体净化工艺。在各种电磁力施加方式中，外加高频交变
磁场方式有其特有的优点：只需通过提高电磁力密度就可以去除熔体中微米级的
夹杂，而无需添加任何净化介质，熔体流经置于磁场中的分离器就可以达到分离
的目的，因此不会对合金造成污染，而且夹杂的去除效率受夹杂物颗粒粒径的影
响小，比较适合于微小夹杂物的去除。
针对高频线圈感生磁场作用下分离铝熔体中非金属夹杂的特点，本文在已有
的相关研究基础上，进一步研究了，静止状态下，铝熔体中非金属夹杂物的运动
和分离规律，推导得到了实心圆柱熔体中球形夹杂物颗粒在高频磁场中所受电磁
排斥力的计算公式。并就实心圆柱状熔体在静止状态下的各工艺参数对电磁净化
效率进行了分析和讨论，结果表明，在熔体静止状态下，rl／6值对分离效率的影
响与频率有关，频率高，则rl／6的取值范围也宽，一般的在r1／6=2．6左右可得
到分离效率的最大值。
在现有的实验设备条件下分别以TM(电气石)、SiC、A1203和Si作为铝合
金中的夹杂物进行了实验，结果表明，在频率为30～40kI-Hz、电流强度为4A时，
分离效果比较好；但是TM颗粒的分离效果比较差，由于结晶水的存在，试样的
表面存在很多气孔。分离器中初生Si相的迁移行为与电磁作用时间、分离器管
径、磁场频率等参数有关；对SiC来说，颗粒尺寸的影响非常明显；另外，对
A1203的分离也取得了一定的效果，而且感应线圈内不同径向位置分离通道内夹
杂物颗粒的电磁分离效果差别很小，不同轴向位置的电磁分离效果差别则比较明
显。
理想的有限长螺线管线圈通电流后会产生中心对称的磁场，磁场在线圈端
部、特别是靠近线圈内壁处会产生急剧变化，增大长径比b／a可使磁场强度在轴
向和径向分布得更均匀些。用小线圈法测定的实际线圈中磁场强度的分布比理论
计算结果稍微偏小。
As an offset of the electromagnetic processing technology, electromagnetic separation technology was rapidly developed and became a novel melt cleaning method with much prospect in application. Among various methods with different way to exert electromagnetic force, the method of applied high frequency alternating magnetic field posses such special advantages as easily removing micron-grade inclusion from metal melt by enhanced electromagnetic force density, and no addition of cleaning media , thus without pollution to the environment, the least dependence of the inclusion removal efficiency on the inclusion size, hence being most favorable for the removal of micro inclusions.
Based on the former study of this method, the thesis furthered the theoretical study on the principle of separating nonmetallic inclusions in the aluminum melt using high frequency magnetic field. The electromagnetic repulsive force exerted on the a spherical particle in the solid cylinder-like melt was deduced. The influence of various processing parameters on the electromagnetic removal efficiency under different condition of solid cylinder-like melt, quiescent flowing condition, were analyzed and discussed. The results show that the effect of r\l 8 on removal efficiency is related with the frequency in the case of quiescent melt, and namely wider value range of r\l 8 can be obtained with higher frequency. Normally the value of T\/ 8 about at 2.6 leads to the best removal efficiency.
On the experiment condition, melts were respectively performed to investigate the migrating behavior of TM particle, the primary Si phase, carborundum particles and alumina particles in the quiescent melt by using high frequency magnetic field. Results showed while the frequency is in the range from thirty to forty kHz and the current intensity is 4A, the separation efficiency is better; Due to the exist of crystal water, however there are many holes on the surface of sample for the melt with TM particles. The migrating behavior of the primary Si phase in segregator relates to imposing time, pipe diameter of the separator, frequency and so on. In terms of carborundum particles, particles size has more influence; At the same time, the method can separate the alumina particles too, furthermore the electromagnetic removal efficiency has tiny difference along the radial, but has clear difference.
When the electric current was exerted on the ideal solenoid with finite length, it
can bring a center symmetry magnetic field, the end side of the coil direction, especially the area approaching the inside wall, is among the area where great change of the magnetic field occurs. Enlarged ratio of the length to diameter can lead to more homogeneous distribution of the magnetic flux density in the coil.
阔应用前景的新型金属熔体净化工艺。在各种电磁力施加方式中，外加高频交变
磁场方式有其特有的优点：只需通过提高电磁力密度就可以去除熔体中微米级的
夹杂，而无需添加任何净化介质，熔体流经置于磁场中的分离器就可以达到分离
的目的，因此不会对合金造成污染，而且夹杂的去除效率受夹杂物颗粒粒径的影
响小，比较适合于微小夹杂物的去除。
针对高频线圈感生磁场作用下分离铝熔体中非金属夹杂的特点，本文在已有
的相关研究基础上，进一步研究了，静止状态下，铝熔体中非金属夹杂物的运动
和分离规律，推导得到了实心圆柱熔体中球形夹杂物颗粒在高频磁场中所受电磁
排斥力的计算公式。并就实心圆柱状熔体在静止状态下的各工艺参数对电磁净化
效率进行了分析和讨论，结果表明，在熔体静止状态下，rl／6值对分离效率的影
响与频率有关，频率高，则rl／6的取值范围也宽，一般的在r1／6=2．6左右可得
到分离效率的最大值。
在现有的实验设备条件下分别以TM(电气石)、SiC、A1203和Si作为铝合
金中的夹杂物进行了实验，结果表明，在频率为30～40kI-Hz、电流强度为4A时，
分离效果比较好；但是TM颗粒的分离效果比较差，由于结晶水的存在，试样的
表面存在很多气孔。分离器中初生Si相的迁移行为与电磁作用时间、分离器管
径、磁场频率等参数有关；对SiC来说，颗粒尺寸的影响非常明显；另外，对
A1203的分离也取得了一定的效果，而且感应线圈内不同径向位置分离通道内夹
杂物颗粒的电磁分离效果差别很小，不同轴向位置的电磁分离效果差别则比较明
显。
理想的有限长螺线管线圈通电流后会产生中心对称的磁场，磁场在线圈端
部、特别是靠近线圈内壁处会产生急剧变化，增大长径比b／a可使磁场强度在轴
向和径向分布得更均匀些。用小线圈法测定的实际线圈中磁场强度的分布比理论
计算结果稍微偏小。
As an offset of the electromagnetic processing technology, electromagnetic separation technology was rapidly developed and became a novel melt cleaning method with much prospect in application. Among various methods with different way to exert electromagnetic force, the method of applied high frequency alternating magnetic field posses such special advantages as easily removing micron-grade inclusion from metal melt by enhanced electromagnetic force density, and no addition of cleaning media , thus without pollution to the environment, the least dependence of the inclusion removal efficiency on the inclusion size, hence being most favorable for the removal of micro inclusions.
Based on the former study of this method, the thesis furthered the theoretical study on the principle of separating nonmetallic inclusions in the aluminum melt using high frequency magnetic field. The electromagnetic repulsive force exerted on the a spherical particle in the solid cylinder-like melt was deduced. The influence of various processing parameters on the electromagnetic removal efficiency under different condition of solid cylinder-like melt, quiescent flowing condition, were analyzed and discussed. The results show that the effect of r\l 8 on removal efficiency is related with the frequency in the case of quiescent melt, and namely wider value range of r\l 8 can be obtained with higher frequency. Normally the value of T\/ 8 about at 2.6 leads to the best removal efficiency.
On the experiment condition, melts were respectively performed to investigate the migrating behavior of TM particle, the primary Si phase, carborundum particles and alumina particles in the quiescent melt by using high frequency magnetic field. Results showed while the frequency is in the range from thirty to forty kHz and the current intensity is 4A, the separation efficiency is better; Due to the exist of crystal water, however there are many holes on the surface of sample for the melt with TM particles. The migrating behavior of the primary Si phase in segregator relates to imposing time, pipe diameter of the separator, frequency and so on. In terms of carborundum particles, particles size has more influence; At the same time, the method can separate the alumina particles too, furthermore the electromagnetic removal efficiency has tiny difference along the radial, but has clear difference.
When the electric current was exerted on the ideal solenoid with finite length, it
can bring a center symmetry magnetic field, the end side of the coil direction, especially the area approaching the inside wall, is among the area where great change of the magnetic field occurs. Enlarged ratio of the length to diameter can lead to more homogeneous distribution of the magnetic flux density in the coil.
引文
[1] 越武壮,段德炳,郝晓华。2001年我国铝工业的生产经营情况分析.世界有色金属,2002,2: 10
[2]王建华。我国铝及铝材消费预测.世界有色金属,1998,1: 37-41
[3] 我国铝材产能现状与分布.铝加工。2001,24(4): 24
[4] Sutton T L. Aluminum casting-A step forward into the next century. Foundryman, 1997(6) : 217~229
[5] 余东梅，国内外废铝回收及再生利用概况。世界有色金属，1998（11）：7~10，15
[6] 郭连杰，日本废铝再生利用简介。世界有色金属，1996（11）：43~45
[7] Apelian D, New developments in Aluminum Processing, Proceedings of the 2nd International Symposium, Light Metals Committee, USA, 1982: 423~456
[8] 周明诘，周宏，梁涛等，压铸铝合金中金属间化合物，特种铸造及有色合金，1999 增刊（1）：117~119
[9] 康积行，傅高升，铝熔体中夹杂物和气体的行为，特种铸造及有色合金，1995（5）：5-8
[10] 闫海，陈鹏，丁传富等，LY12CZ铝合金短裂纹行为的微观扩展机制的研究，材料工程，1999（4）：13~15
[11] Shivkumar S, Wang L, Apelian D, Molten metal processing of advanced cast aluminum alloys, Journal of Metals, 1991(1): 26~32
[12] 叶荣茂，常庆明，王惠光，过滤器过滤效率的评价，铸造，1992（12），1~6
[13] Clement Guillaume, The pechiney deep bed filter: Technology and performance , Light Metals 1995, In: J. W. Evans, The Minerals, Metals & Materials Society, 1995: 1253~1262
[14] Kakimoto K, Shiraishi Y, Filtration of molten aluminum by ceramic rigid tube filters, Light Metals 1994, In: Euel R. Cutshall, The Minerals, Metals & Materials Society, 1994: 1099~1106
[15] 贾天敏，李军文，江度，安阁英，泡沫陶瓷过滤器净化原理及含过滤器浇注系统的设计，铸造，1998，5：22~26
[16] Brett Sirrell, John Campbell, Experiment shows filters reduce melt turbulence defects, Moden Casting, 1998, June, 39~41
[17] C Tian and R I L Guthrie, Fundamentals of liquid metal filtration, Recent Developments in Light Metals, 415~430
[18] Wuilloud E, Implementing metal treatment technologies: A step ahead or just a remedy, Light Metals 1994, in: U. Mannweiler, The Minerals, Metals & Materials Society, 1994 : 1079~1082
[19] Johansen S T, Graadahl S, Tetile P M et al., Can rotor-based refining units be developed and optimized based on water model experiments, Light Metals 1998, In: Barry Welch, The Minerals, Metals & Materials Society, 1998: 805~810
[20] Beland G, Dupuis C, Martin J P, Improving fluxing of aluminum alloys, Light Metals 1995, In J. W Evans, The Minerals, Metals & Materials Society, 1995 : 1189~1195
[21] Chesonis D C, Yu H, Scherbak M, In-line fluxing with high speed multiple rotor dispersers, Light Metals 1997, In: Reidar Huglen, The Minerals, Metals & Materials Society, 1997: 843~846
[22] Gates E., Diamagnetic separation, U.S. Patent, 653344,1900
[23] Leenov D, Kolin A. Theory of electromagnetophoresis. I. Magnetohydrodynamic forces experienced by spherical and symmetrically oriented cylindrical particles. J Chem Phys, 1954, 22(4): 683-688
[24] Kolin A. An electromagnetokinetics phenomenom involving migration of neutral particals. Sciences, 1953, 117(6): 134-137
[25] L A Verte, Process of treating a liquid metal, Author Certificate No.141592, Class 31c,13, Byull, Izqbret, No 19,1961
[26] Marty P, Alemany A. Theoretical and experimental aspects of electromagnetic separation. Proceedings of Symposium of IUTAM. London: The Metals Society, 1982. 245~259
[27] 张国志，辛启斌，张辉，贾光霖，高允彦.关于液态金属电磁净化的讨论。 材料与冶金学报,2002,1(1): 31-35
[28] 姚若琼，王义海，曹志强。铝合金电磁净化现状与前景。铸造，2002，4
[29] Park J P,Morihira A,Sassa K, et al. Elimination of nonmetallic inclusions using electromagnetic force . Tetsu-to-Hagane, 1994, 80(5): 31-36
[30] 朴俊杓，浅井滋生．电磁力しメン熔融金属中の非金属介在物の除去．铁と钢，1994，80(25): 251
[31] Park J P, Sassa K, Asai S. Improvement of wear resistance in hypereutectic Al-Si alloy by surface concentration of primary silicon using electromagnetic force. J Japan Inst Metals, 1995, 59(7): 733-739
[32] Alemany A, Argous J P, Barber J, et al. Procedes et dispositifs electromagnetique de separation condimued’ inclusions solides ou liquids continues dans un metal liquide. France: 804004430, 1980
[33] 金俊泽，张永安，曹志强。电磁搅拌自生表面复合材料的组织与性能，材料研究学报，1998，Vol.12, (4)：446~448
[34] Yamao F, Sassa K, Iwai K, et al.Separation of inclusions in liquid metal using fixed alternating magnetic field. Tetsu-to-Hagane, 1997, 83(1)：30-35
[35] El-Kaddah N, Pater A D, Natarajan T T. The electromagnetic filtration of molten aluminium using an induced-current separator. JOM,1995, 47(5): 46-49
[36] 仁忠鸣，周月明，张春源，蒋国昌。 水平电磁连铸中金属磁悬浮行为，金属学报，1996，vol.32, No.6: 642~646
[37] 山尾文孝，佐タ健介，岩井一彦。固定交流磁场を利用した熔融金属の非金属介在物除去. 钢と铁，1997，83（1）：30~35
[38] 杨桂香，钱熔，倪红军．利用高频磁场连续分离铝熔体中夹杂物的理论分析．铝加工，2002，25(3): 1-4
[39] Taniguchi S, Brimacombe J K. Application of pinch force to the separation of inclusion particles from liquid steel. Iron Steel Inst Jpn Int, 1994,34(9): 722-731
[40] Patel A D, EL-Kaddah N. On the theory of electromagnetic separation in alternating electromagnetic fields. Proceedings of International Symposium on Electromagnetic Processing of
Materials. Nagoya: ISIJ, 1994. 115-120
[41] 谷口尚司，Keith Brimacpmbe J.ビンチカよにゐ圆管内溶钢流からの介在物除去にする理论的研究.铁と钢，1994,80(1): 24-28
[42] 钟云波，任忠鸣，邓康，俞迅捷，蒋国昌，徐匡迪.行波磁场净化液体金属的电磁力参数.中国有色金属学报，1999，9（3）: 482-487
[43] 钟云波，仁忠鸣，邓康，杨森龙，蒋国昌，徐匡迪，行波磁场净化液态金属时矩形管及三角形管内夹杂去除效率的理论解析，金属学报，1999，35（5），503~508
[44] Barglik J, Sajdak C, Purification of liquid aluminum from non-metallic inclusions in the electromagnetic-field, Elektrowarme International,1985, vol.43(B2): 77~80
[45] Miki Y, Kitaoka H, Sakuraya T, et al., Mechanism for separating inclusions from molten steel stirred with a rotating electro-magnetic field, ISIJ International, 1992, vol.32(1): 142~149
[46] 翟秀静，范立志，孙中祺，姚广春。电磁分离铝熔体中不同粒径夹杂颗粒的研究。分子科学学报，2001，17（1）：23~26
[47] 李克，孙宝德，疏达，李天晓，丁文江，周尧和。利用交变磁场分离空心圆柱状金属熔体中非金属夹杂. 上海交通大学学报，2001，35（3）：375~379
[48] 许永兴，电磁场理论及计算，上海：同济大学出版社，1994
[49] 徐永斌，何国瑜，卢才成等，工程电磁场基础。北京：北京航空航天大学出版社，1992
[50] 奚定平，贝塞尔函数。北京：高等教育出版社，德国：施普林格出版社，1998
[51] Li Tian-xiao, Shu Da, Xu Zhen-ming, Sun Bao-de, Zhou Yao-he. ?Physical simulation and theoretical analysis of migrating rate of inclusions in aluminum melt in electromagnetic field. Transactions of Nonferrous Metals Society of China, 2001(1): 30~34
[52] 许振明,李天晓,周尧和.电磁过滤钢液中非金属夹杂物的运动速度和去除效率的理论分析.金属学报,2001,37(4): 423-428
[53] 李克，孙宝德，李天晓，丁文江，周尧和．利用高频磁场分离Al熔体中的非金属夹杂．金属学报，2001，37(4): 405-410
[54] 曹志强，张秋明，贾非，金俊泽。铝熔体中非金属夹杂物电磁分离效率研究。大连理工大学学报，2002，42（4），441~445
[55] 雷银照，轴对称线圈磁场计算，北京：中国计量出版社，1991
[56] 雷银照，时谐电磁场解析方法，北京：科学出版社，2000
[57] 焦其祥，王道东，电磁场理论，北京：北京邮电出版社，1997
[58] 秦曾煌.电工学(上册).高等教育出版社，1999：231
[59] Flemings M C. 凝固过程.北京:冶金工业出版社,1982 202
[2]王建华。我国铝及铝材消费预测.世界有色金属,1998,1: 37-41
[3] 我国铝材产能现状与分布.铝加工。2001,24(4): 24
[4] Sutton T L. Aluminum casting-A step forward into the next century. Foundryman, 1997(6) : 217~229
[5] 余东梅，国内外废铝回收及再生利用概况。世界有色金属，1998（11）：7~10，15
[6] 郭连杰，日本废铝再生利用简介。世界有色金属，1996（11）：43~45
[7] Apelian D, New developments in Aluminum Processing, Proceedings of the 2nd International Symposium, Light Metals Committee, USA, 1982: 423~456
[8] 周明诘，周宏，梁涛等，压铸铝合金中金属间化合物，特种铸造及有色合金，1999 增刊（1）：117~119
[9] 康积行，傅高升，铝熔体中夹杂物和气体的行为，特种铸造及有色合金，1995（5）：5-8
[10] 闫海，陈鹏，丁传富等，LY12CZ铝合金短裂纹行为的微观扩展机制的研究，材料工程，1999（4）：13~15
[11] Shivkumar S, Wang L, Apelian D, Molten metal processing of advanced cast aluminum alloys, Journal of Metals, 1991(1): 26~32
[12] 叶荣茂，常庆明，王惠光，过滤器过滤效率的评价，铸造，1992（12），1~6
[13] Clement Guillaume, The pechiney deep bed filter: Technology and performance , Light Metals 1995, In: J. W. Evans, The Minerals, Metals & Materials Society, 1995: 1253~1262
[14] Kakimoto K, Shiraishi Y, Filtration of molten aluminum by ceramic rigid tube filters, Light Metals 1994, In: Euel R. Cutshall, The Minerals, Metals & Materials Society, 1994: 1099~1106
[15] 贾天敏，李军文，江度，安阁英，泡沫陶瓷过滤器净化原理及含过滤器浇注系统的设计，铸造，1998，5：22~26
[16] Brett Sirrell, John Campbell, Experiment shows filters reduce melt turbulence defects, Moden Casting, 1998, June, 39~41
[17] C Tian and R I L Guthrie, Fundamentals of liquid metal filtration, Recent Developments in Light Metals, 415~430
[18] Wuilloud E, Implementing metal treatment technologies: A step ahead or just a remedy, Light Metals 1994, in: U. Mannweiler, The Minerals, Metals & Materials Society, 1994 : 1079~1082
[19] Johansen S T, Graadahl S, Tetile P M et al., Can rotor-based refining units be developed and optimized based on water model experiments, Light Metals 1998, In: Barry Welch, The Minerals, Metals & Materials Society, 1998: 805~810
[20] Beland G, Dupuis C, Martin J P, Improving fluxing of aluminum alloys, Light Metals 1995, In J. W Evans, The Minerals, Metals & Materials Society, 1995 : 1189~1195
[21] Chesonis D C, Yu H, Scherbak M, In-line fluxing with high speed multiple rotor dispersers, Light Metals 1997, In: Reidar Huglen, The Minerals, Metals & Materials Society, 1997: 843~846
[22] Gates E., Diamagnetic separation, U.S. Patent, 653344,1900
[23] Leenov D, Kolin A. Theory of electromagnetophoresis. I. Magnetohydrodynamic forces experienced by spherical and symmetrically oriented cylindrical particles. J Chem Phys, 1954, 22(4): 683-688
[24] Kolin A. An electromagnetokinetics phenomenom involving migration of neutral particals. Sciences, 1953, 117(6): 134-137
[25] L A Verte, Process of treating a liquid metal, Author Certificate No.141592, Class 31c,13, Byull, Izqbret, No 19,1961
[26] Marty P, Alemany A. Theoretical and experimental aspects of electromagnetic separation. Proceedings of Symposium of IUTAM. London: The Metals Society, 1982. 245~259
[27] 张国志，辛启斌，张辉，贾光霖，高允彦.关于液态金属电磁净化的讨论。 材料与冶金学报,2002,1(1): 31-35
[28] 姚若琼，王义海，曹志强。铝合金电磁净化现状与前景。铸造，2002，4
[29] Park J P,Morihira A,Sassa K, et al. Elimination of nonmetallic inclusions using electromagnetic force . Tetsu-to-Hagane, 1994, 80(5): 31-36
[30] 朴俊杓，浅井滋生．电磁力しメン熔融金属中の非金属介在物の除去．铁と钢，1994，80(25): 251
[31] Park J P, Sassa K, Asai S. Improvement of wear resistance in hypereutectic Al-Si alloy by surface concentration of primary silicon using electromagnetic force. J Japan Inst Metals, 1995, 59(7): 733-739
[32] Alemany A, Argous J P, Barber J, et al. Procedes et dispositifs electromagnetique de separation condimued’ inclusions solides ou liquids continues dans un metal liquide. France: 804004430, 1980
[33] 金俊泽，张永安，曹志强。电磁搅拌自生表面复合材料的组织与性能，材料研究学报，1998，Vol.12, (4)：446~448
[34] Yamao F, Sassa K, Iwai K, et al.Separation of inclusions in liquid metal using fixed alternating magnetic field. Tetsu-to-Hagane, 1997, 83(1)：30-35
[35] El-Kaddah N, Pater A D, Natarajan T T. The electromagnetic filtration of molten aluminium using an induced-current separator. JOM,1995, 47(5): 46-49
[36] 仁忠鸣，周月明，张春源，蒋国昌。 水平电磁连铸中金属磁悬浮行为，金属学报，1996，vol.32, No.6: 642~646
[37] 山尾文孝，佐タ健介，岩井一彦。固定交流磁场を利用した熔融金属の非金属介在物除去. 钢と铁，1997，83（1）：30~35
[38] 杨桂香，钱熔，倪红军．利用高频磁场连续分离铝熔体中夹杂物的理论分析．铝加工，2002，25(3): 1-4
[39] Taniguchi S, Brimacombe J K. Application of pinch force to the separation of inclusion particles from liquid steel. Iron Steel Inst Jpn Int, 1994,34(9): 722-731
[40] Patel A D, EL-Kaddah N. On the theory of electromagnetic separation in alternating electromagnetic fields. Proceedings of International Symposium on Electromagnetic Processing of
Materials. Nagoya: ISIJ, 1994. 115-120
[41] 谷口尚司，Keith Brimacpmbe J.ビンチカよにゐ圆管内溶钢流からの介在物除去にする理论的研究.铁と钢，1994,80(1): 24-28
[42] 钟云波，任忠鸣，邓康，俞迅捷，蒋国昌，徐匡迪.行波磁场净化液体金属的电磁力参数.中国有色金属学报，1999，9（3）: 482-487
[43] 钟云波，仁忠鸣，邓康，杨森龙，蒋国昌，徐匡迪，行波磁场净化液态金属时矩形管及三角形管内夹杂去除效率的理论解析，金属学报，1999，35（5），503~508
[44] Barglik J, Sajdak C, Purification of liquid aluminum from non-metallic inclusions in the electromagnetic-field, Elektrowarme International,1985, vol.43(B2): 77~80
[45] Miki Y, Kitaoka H, Sakuraya T, et al., Mechanism for separating inclusions from molten steel stirred with a rotating electro-magnetic field, ISIJ International, 1992, vol.32(1): 142~149
[46] 翟秀静，范立志，孙中祺，姚广春。电磁分离铝熔体中不同粒径夹杂颗粒的研究。分子科学学报，2001，17（1）：23~26
[47] 李克，孙宝德，疏达，李天晓，丁文江，周尧和。利用交变磁场分离空心圆柱状金属熔体中非金属夹杂. 上海交通大学学报，2001，35（3）：375~379
[48] 许永兴，电磁场理论及计算，上海：同济大学出版社，1994
[49] 徐永斌，何国瑜，卢才成等，工程电磁场基础。北京：北京航空航天大学出版社，1992
[50] 奚定平，贝塞尔函数。北京：高等教育出版社，德国：施普林格出版社，1998
[51] Li Tian-xiao, Shu Da, Xu Zhen-ming, Sun Bao-de, Zhou Yao-he. ?Physical simulation and theoretical analysis of migrating rate of inclusions in aluminum melt in electromagnetic field. Transactions of Nonferrous Metals Society of China, 2001(1): 30~34
[52] 许振明,李天晓,周尧和.电磁过滤钢液中非金属夹杂物的运动速度和去除效率的理论分析.金属学报,2001,37(4): 423-428
[53] 李克，孙宝德，李天晓，丁文江，周尧和．利用高频磁场分离Al熔体中的非金属夹杂．金属学报，2001，37(4): 405-410
[54] 曹志强，张秋明，贾非，金俊泽。铝熔体中非金属夹杂物电磁分离效率研究。大连理工大学学报，2002，42（4），441~445
[55] 雷银照，轴对称线圈磁场计算，北京：中国计量出版社，1991
[56] 雷银照，时谐电磁场解析方法，北京：科学出版社，2000
[57] 焦其祥，王道东，电磁场理论，北京：北京邮电出版社，1997
[58] 秦曾煌.电工学(上册).高等教育出版社，1999：231
[59] Flemings M C. 凝固过程.北京:冶金工业出版社,1982 202