激磁频率对电磁场及温度场分布影响的研究
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摘要
利用电磁场有限元法分析涡流场在不同电源激励下的分布，进而研究铁磁材料中的温度及其分布可以大大提高对电磁场和对电热场的控制，其中电磁场和其它物理场综合作用理论和计算的研究是相关磁技术应用的理论基础，也是近年来电磁场计算应用的难点课题。本文在深入、系统总结现有文献的基础上，针对课题相关的理论、数值算法，进行了较深入的研究工作。
文中通过对一个空心金属圆筒结构的电磁系统进行分析，以电磁场矢量位有限元法为基础对磁场强度、涡流密度进行了计算求解，采用三角形单元建立了涡流场数学模型，研究了电源频率对涡流密度、透入深度及集肤效应等场量的作用影响。
本文建立了电磁加热系统的涡流场和温度场间接耦合的数学模型，分析了不同频率下涡流和温度的分布情况，并以八节点六面体等参元为例给出了涡流场对应的离散格式，通过计算涡流场获得温度场所需要的内热源强度，加热部件的温度场以轴对称格式进行离散求解，并对瞬态温度场有限单元法的求解特点进行了分析。
最后，本文对编制的软件进行了验证，与理论值相比，结果基本吻合，由此证明了本文提出的论点、算法和程序的正确性。
Use electromagnetic finite element method to analyze the distribution of eddy current field with different power supply, then to research that the temperature and distribution of ferromagnetic material can improve the control of electromagnetic and electrothermal field greatly. There into the research of the theory and computation of electromagnetic field act on other physical field is the foundation of the application of magnetic technology, and it is also one of the hot-spot topics in circles researching electromagnetic field. Base on the embedded and comprehensive summarization of the exiting literature, this article do some embedded researching work to the theory, number arithmetic about the subject.
Through the analyses of electromagnetic system of configuration of hollow metal cylinder by electromagnetic vector potential, an eddy current field math model is built by triangle cell, this article has researched power frequency to eddy current density, permeation depth and the effect of skin effect.
The paper establishes mathematics model of electromagnetic heating system of eddy current field and temperature field, and gives corresponding discrete format with elements as eight nodes, hexahedron equal cell, through calculating eddy-current field to gain the internal heat source that the temperature field needed, to use discrete method to solve the problem of induction-heating part's temperature field by axial symmetrical electromagnetic, and then to analyze the characteristic of instantaneous temperature field.
Finally, the programs are verified through this article, the result accord with theory in substance. All results prove that the theories, algorithm and programs are correct.
文中通过对一个空心金属圆筒结构的电磁系统进行分析，以电磁场矢量位有限元法为基础对磁场强度、涡流密度进行了计算求解，采用三角形单元建立了涡流场数学模型，研究了电源频率对涡流密度、透入深度及集肤效应等场量的作用影响。
本文建立了电磁加热系统的涡流场和温度场间接耦合的数学模型，分析了不同频率下涡流和温度的分布情况，并以八节点六面体等参元为例给出了涡流场对应的离散格式，通过计算涡流场获得温度场所需要的内热源强度，加热部件的温度场以轴对称格式进行离散求解，并对瞬态温度场有限单元法的求解特点进行了分析。
最后，本文对编制的软件进行了验证，与理论值相比，结果基本吻合，由此证明了本文提出的论点、算法和程序的正确性。
Use electromagnetic finite element method to analyze the distribution of eddy current field with different power supply, then to research that the temperature and distribution of ferromagnetic material can improve the control of electromagnetic and electrothermal field greatly. There into the research of the theory and computation of electromagnetic field act on other physical field is the foundation of the application of magnetic technology, and it is also one of the hot-spot topics in circles researching electromagnetic field. Base on the embedded and comprehensive summarization of the exiting literature, this article do some embedded researching work to the theory, number arithmetic about the subject.
Through the analyses of electromagnetic system of configuration of hollow metal cylinder by electromagnetic vector potential, an eddy current field math model is built by triangle cell, this article has researched power frequency to eddy current density, permeation depth and the effect of skin effect.
The paper establishes mathematics model of electromagnetic heating system of eddy current field and temperature field, and gives corresponding discrete format with elements as eight nodes, hexahedron equal cell, through calculating eddy-current field to gain the internal heat source that the temperature field needed, to use discrete method to solve the problem of induction-heating part's temperature field by axial symmetrical electromagnetic, and then to analyze the characteristic of instantaneous temperature field.
Finally, the programs are verified through this article, the result accord with theory in substance. All results prove that the theories, algorithm and programs are correct.
引文
[1]汤景明，“感应电热设备的设计”《工业加热》1997年第一期．
[2]王滨生，梁伟，“横向磁场感应加热的研究”《金属热处理》，1994年第11期．
[3]刘志儒，《金属感应热处理》，机械工业出版社，1987。
[4]张晓明，家用电器原理与维修。北京：电子工业出版社，1991．
[5]感应加热装置，北京，机械工业出版学，1981．
[6]M.Enokizono and T. Todaka "Approximate boundary element formulation for high-frequency eddy current problem",IEEE Trans.on Magn. Vol.29,No.2,March 1993.
[7]A.Muhlbauer, A.Muiznieks and H-J.LeBmann "The calculation of 3D high-frequencye electromagnetic fields during induction heatinusing the BEM" IEEE Trans.on Magn. Vol.29.No.2,march 1993.
[8]李明，李兰“高频电磁场加热流体的方法”，《天然气与石油》，2000年月．
[9]Laurent Krahenbuhl, Olivier Fabregue Sevn Wanser "Surface Impedance,BIEM and FEM coupled with 1D Non Liner solutions to solve 3D high frequency eddy current problems"IEEE,Trans.on. Magn,Vol.33,NO.2 March 1997.
[10]C F Bryant, B Dillon, C R I Emson, J Simkin and C W Trowbridge "Solving high frequency Problems usingthe magnetic vecto potential with Lorentz Gauge" IEEE Trans.On Magn. Vol.28,No.2,March 1992
[11]张文志，“加速器中高频电磁场的计算及应用”中科院电子研究所硕士论文．
[12]孟庆龙，颜威利“电器数值分析”机械工业出版社．
[13]盛剑霓“工程电磁场数值分析”西安交通大学出版社．
[14]P. Hahne and T. Weiland "3D eddy current computation in the frequency domain Regading the displacement current" IEEE Trans.on. Magn. Vol .28,No.2,March 1992.
[15]S.R.H.Hoole and C.J.Carpenter, "Surface impedance models for corners andslots," IEEE Trans. Magn.,Vol 21,pp1841-1843,Sept 1985.
[16]K.Shao and J.D.Lavers, "A skin depth-independent finite element method for eddy current problems,"IEEE Trans.Magn.,Vol.22,pp. 1248-1250 1986.
[17]M.Enokizono,T. Todaka, Y. Uemura and Y. Wada, "Fundamental investigation for flotage-melting problem using the axisymmetric boundary element method "Paper of Combined Techninical Meetings on Rotating Machines and Transformers and Capacitors,IEE of Japan ,RM-91-103, SA-91-34,pp.34-42 1991.
[18]K.R.Shao ,K.D.Zhou and J.D.Lavers, "Boundary element analysis method for 3D multiply conceded eddy current problem based on the second order vector potential formulation" IEEE Trans.
Magn.,vol.28,pp. 1220-1223,March 1992.
[19]W.M.Rucker, K.R.Richter, "A BEM code for 3-D eddy current calculations," IEEE Trans. Magn., vol.26,pp.462-465,March 1990.
[20]M.Enokizono and T. Taka, "Investiongation of high-accurate boundary element analysis on two-dimensional eddy current problem" Trans. IEE of Japan,vol. 109,pp. 133-140,April 1989.
[21]J.Shen and A.Kost, "BEM with mixed specialshape functions for 2D eddy current problems ," IEEE Trans. Magn.,vol.28,pp. 1220-1223,March 1992.
[22]J.P. Webb,G.L.Maile and R.L.Ferrari , "finite-element solution of three-dimension electromagnetic problems," IEE PROC.,vol. 130,Pt.H,No.2, Macrch 1983.
[23]B.M.Dillon,R.I.Ferrari and T.P. Yong, "Hybride FE/BE method for analysis of discontinuities in planar dielectric waveguides ,"Electron. Letts.,Vol.26,No. 1,pp 47-48.
[24]S.R.H.Hoole, "Computer aided analysis and Design of electro-magnetic Devices" Elsevier, NY, 1989
[25]俞勇祥，陈家辉“感应加热电源的发展”浙江大学．
[26]Renota ,Cardoso,Mesquita "3D finite element solution of induction heating problems with efficient time-stepping ", IEEE Trans. Magn,Vol.27,No.5 Setp. 1991
[27]H.H.J.M.Janssen,E.J.W. Termaten, "Simuiation of coupled electromagnetic and heat dissipation problems" IEEE Trans. Magn. 1994
[28]Seven Wanser, Laurent krahenbuhl,Alain Nicolas "Compution of 3D induction hardening problems by combined finite and boundary element methods" IEEE Trans. Magn vol 30 .no.5,Sept. 1994.
[29]Istitutodi Energetica, Universita di,Pperagia "Numerical Modelling of 3-D coupled electromagnetic and heating diffusion problems" IEEE Trans. Magn,vol.30,No.5,Sept 1994.
[30]G. Coatache." finite element method applied to skin effect in strip transmission lines" IEEE. trans 1987.
[31]孔祥谦“有限单元法在传热学中的应用”科学出版社．
[32]A.Sekkak L.Pichon "3-D FEM Magneto-Thermal Analysis in Microwave Ovens" IEEE Trans. Magn, Vol.30,,NO.5,Setp 1994.
[33]P. Viriya S.Sittichok "Analysis of High-Frequency Induction Cooker with Variable Frequency Power Control" IEEE Trans. Magn,2002.
[34]M.S.Milicevic V.M.Milicevic "Impeder for HF inductive welding of steel tubes" IEE Proc.-Sci.Meas.Technol,Vol. 149,No.3,May 2002.
[35]叶永华 肖贤玉“轴对称体温度场有限元程序的编制”武汉汽车工业大学学报1998年．
[36]P.G.Simpson "induction Heating-coil and system design" IEEE Trans. Magn. 1992.
[37]B.Nache“横向感应加热——一种金属板材灵活的加热方法”世界钢铁1996年第1期．
[2]王滨生，梁伟，“横向磁场感应加热的研究”《金属热处理》，1994年第11期．
[3]刘志儒，《金属感应热处理》，机械工业出版社，1987。
[4]张晓明，家用电器原理与维修。北京：电子工业出版社，1991．
[5]感应加热装置，北京，机械工业出版学，1981．
[6]M.Enokizono and T. Todaka "Approximate boundary element formulation for high-frequency eddy current problem",IEEE Trans.on Magn. Vol.29,No.2,March 1993.
[7]A.Muhlbauer, A.Muiznieks and H-J.LeBmann "The calculation of 3D high-frequencye electromagnetic fields during induction heatinusing the BEM" IEEE Trans.on Magn. Vol.29.No.2,march 1993.
[8]李明，李兰“高频电磁场加热流体的方法”，《天然气与石油》，2000年月．
[9]Laurent Krahenbuhl, Olivier Fabregue Sevn Wanser "Surface Impedance,BIEM and FEM coupled with 1D Non Liner solutions to solve 3D high frequency eddy current problems"IEEE,Trans.on. Magn,Vol.33,NO.2 March 1997.
[10]C F Bryant, B Dillon, C R I Emson, J Simkin and C W Trowbridge "Solving high frequency Problems usingthe magnetic vecto potential with Lorentz Gauge" IEEE Trans.On Magn. Vol.28,No.2,March 1992
[11]张文志，“加速器中高频电磁场的计算及应用”中科院电子研究所硕士论文．
[12]孟庆龙，颜威利“电器数值分析”机械工业出版社．
[13]盛剑霓“工程电磁场数值分析”西安交通大学出版社．
[14]P. Hahne and T. Weiland "3D eddy current computation in the frequency domain Regading the displacement current" IEEE Trans.on. Magn. Vol .28,No.2,March 1992.
[15]S.R.H.Hoole and C.J.Carpenter, "Surface impedance models for corners andslots," IEEE Trans. Magn.,Vol 21,pp1841-1843,Sept 1985.
[16]K.Shao and J.D.Lavers, "A skin depth-independent finite element method for eddy current problems,"IEEE Trans.Magn.,Vol.22,pp. 1248-1250 1986.
[17]M.Enokizono,T. Todaka, Y. Uemura and Y. Wada, "Fundamental investigation for flotage-melting problem using the axisymmetric boundary element method "Paper of Combined Techninical Meetings on Rotating Machines and Transformers and Capacitors,IEE of Japan ,RM-91-103, SA-91-34,pp.34-42 1991.
[18]K.R.Shao ,K.D.Zhou and J.D.Lavers, "Boundary element analysis method for 3D multiply conceded eddy current problem based on the second order vector potential formulation" IEEE Trans.
Magn.,vol.28,pp. 1220-1223,March 1992.
[19]W.M.Rucker, K.R.Richter, "A BEM code for 3-D eddy current calculations," IEEE Trans. Magn., vol.26,pp.462-465,March 1990.
[20]M.Enokizono and T. Taka, "Investiongation of high-accurate boundary element analysis on two-dimensional eddy current problem" Trans. IEE of Japan,vol. 109,pp. 133-140,April 1989.
[21]J.Shen and A.Kost, "BEM with mixed specialshape functions for 2D eddy current problems ," IEEE Trans. Magn.,vol.28,pp. 1220-1223,March 1992.
[22]J.P. Webb,G.L.Maile and R.L.Ferrari , "finite-element solution of three-dimension electromagnetic problems," IEE PROC.,vol. 130,Pt.H,No.2, Macrch 1983.
[23]B.M.Dillon,R.I.Ferrari and T.P. Yong, "Hybride FE/BE method for analysis of discontinuities in planar dielectric waveguides ,"Electron. Letts.,Vol.26,No. 1,pp 47-48.
[24]S.R.H.Hoole, "Computer aided analysis and Design of electro-magnetic Devices" Elsevier, NY, 1989
[25]俞勇祥，陈家辉“感应加热电源的发展”浙江大学．
[26]Renota ,Cardoso,Mesquita "3D finite element solution of induction heating problems with efficient time-stepping ", IEEE Trans. Magn,Vol.27,No.5 Setp. 1991
[27]H.H.J.M.Janssen,E.J.W. Termaten, "Simuiation of coupled electromagnetic and heat dissipation problems" IEEE Trans. Magn. 1994
[28]Seven Wanser, Laurent krahenbuhl,Alain Nicolas "Compution of 3D induction hardening problems by combined finite and boundary element methods" IEEE Trans. Magn vol 30 .no.5,Sept. 1994.
[29]Istitutodi Energetica, Universita di,Pperagia "Numerical Modelling of 3-D coupled electromagnetic and heating diffusion problems" IEEE Trans. Magn,vol.30,No.5,Sept 1994.
[30]G. Coatache." finite element method applied to skin effect in strip transmission lines" IEEE. trans 1987.
[31]孔祥谦“有限单元法在传热学中的应用”科学出版社．
[32]A.Sekkak L.Pichon "3-D FEM Magneto-Thermal Analysis in Microwave Ovens" IEEE Trans. Magn, Vol.30,,NO.5,Setp 1994.
[33]P. Viriya S.Sittichok "Analysis of High-Frequency Induction Cooker with Variable Frequency Power Control" IEEE Trans. Magn,2002.
[34]M.S.Milicevic V.M.Milicevic "Impeder for HF inductive welding of steel tubes" IEE Proc.-Sci.Meas.Technol,Vol. 149,No.3,May 2002.
[35]叶永华 肖贤玉“轴对称体温度场有限元程序的编制”武汉汽车工业大学学报1998年．
[36]P.G.Simpson "induction Heating-coil and system design" IEEE Trans. Magn. 1992.
[37]B.Nache“横向感应加热——一种金属板材灵活的加热方法”世界钢铁1996年第1期．
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