行波感应加热中涡流场问题分析
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摘要
电磁感应加热利用工件中涡流产生的焦耳热将工件加热，这种方法具有加热速度快、率高、控制精确、污染少等特点，在工业生产中具有广泛的应用前景。行波感应加热Traveling Wave Induction Heating，TWIH)除具有其他一些感应加热方式同样的优点外，能产生更均匀的温度分布，而且具有振动和工业噪音低、边缘效应好、加热均匀和三相载平衡、对电网影响小的显著优点，在加热非铁磁性带材时，因为电磁力的显著增加和热参数的变化，这一优点显得非常重要。
简要介绍了感应加热技术的原理、特点、和发展现状，对行波磁场感应加热的基本原进行了说明，给出了二维和三维模型，并简要介绍了本课题的研究意义和主要研究内容。次，对电磁场数值计算有限元方法作了介绍，推导了感应加热工件内电磁场与涡流场分的理论公式以及涡流场方程的离散，建立了感应加热的有限元数学模型。介绍了ANSYS件中计算电磁场、涡流场的矢量磁位法，并介绍了感应加热技术的数值仿真方法。对行波感应加热二维模型进行合理简化，给出ANSYS中进行二维有限元分析的单元类，边界条件设置；根据行波磁场感应加热的特点，建立分析模型，确定了边界条件、网划分、材料特性等问题的处理方法。利用ANSYS软件对行波磁场感应加热进行二维研究，细计算分析了相同条件下行波感应加热系统与横向磁通感应加热系统中磁力线、磁感应度和涡流场以及功率密度的分布情况。此外，简要计算了在不同电源、不同气隙大小、同初级位置以及不同线圈结构下带材中的功率密度分布情况。
以单线圈理论模型进行三维初步研究，推导线圈结构及其排布对带材中涡流分布的影；给出等效电路及ANSYS仿真模型，得出了影响涡流分布的初步规律。同时，对全文行总结，提出有待进一步研究和解决的问题。
Traveling Wave Induction Heating (TWIH), involving three-dimensional non-liner coupled problem of eddy current field and temperature field for continuously moving strip, has particular features which make them attractive for application to some heating and melting processes in industry. Among the advantages we can mention the possibility to heat quite uniformly thin strips or regions of a body without moving the inductor above its surface, to reduce the vibrations of inductor and load due to the electro-dynamic forces and also the noise provoked by them, to obtain nearly balanced distributions of power and temperature
The characteristic, development and present research situation of induction heating are briefly introduced. The background of this project, the main contents and the significance of this paper are mentioned. And the electromagnetic field value computational method is introduced. A mathematical model is developed to describe the distribution of electromagnetic field and eddy current density in the strip. The mathematical modal of electromagnetic fields is presented by a magnetic vector potential, which is also applied to solve eddy current field in ANSYS. And the analytical simulating methods for induction heating are represented.
Mathematical model is offered for solving the coupled problem for TWIH. To improve the efficiency of eddy current field calculation, necessary simplification is applied and boundary conditions are accurately analyzed. The magnetic force and the final eddy current distribution demonstrated and analyzed. And the computation of power density distribution in the strip has analyzed under different power source frequency, different air gap size, different primary position as well as different coil structure, which is based on ANSYS software. Comparison of edge-effects of traveling wave and transverse flux induction heating is done.
A single-coil model is applied to do basic three-dimensional study, and deduce the effect of coil structure and arrangement for the eddy current distributions. With the results, as well as the equivalent circuit and ANSYS simulation model, we get some rules about what mainly influences the distribution of inducting eddy current.
简要介绍了感应加热技术的原理、特点、和发展现状，对行波磁场感应加热的基本原进行了说明，给出了二维和三维模型，并简要介绍了本课题的研究意义和主要研究内容。次，对电磁场数值计算有限元方法作了介绍，推导了感应加热工件内电磁场与涡流场分的理论公式以及涡流场方程的离散，建立了感应加热的有限元数学模型。介绍了ANSYS件中计算电磁场、涡流场的矢量磁位法，并介绍了感应加热技术的数值仿真方法。对行波感应加热二维模型进行合理简化，给出ANSYS中进行二维有限元分析的单元类，边界条件设置；根据行波磁场感应加热的特点，建立分析模型，确定了边界条件、网划分、材料特性等问题的处理方法。利用ANSYS软件对行波磁场感应加热进行二维研究，细计算分析了相同条件下行波感应加热系统与横向磁通感应加热系统中磁力线、磁感应度和涡流场以及功率密度的分布情况。此外，简要计算了在不同电源、不同气隙大小、同初级位置以及不同线圈结构下带材中的功率密度分布情况。
以单线圈理论模型进行三维初步研究，推导线圈结构及其排布对带材中涡流分布的影；给出等效电路及ANSYS仿真模型，得出了影响涡流分布的初步规律。同时，对全文行总结，提出有待进一步研究和解决的问题。
Traveling Wave Induction Heating (TWIH), involving three-dimensional non-liner coupled problem of eddy current field and temperature field for continuously moving strip, has particular features which make them attractive for application to some heating and melting processes in industry. Among the advantages we can mention the possibility to heat quite uniformly thin strips or regions of a body without moving the inductor above its surface, to reduce the vibrations of inductor and load due to the electro-dynamic forces and also the noise provoked by them, to obtain nearly balanced distributions of power and temperature
The characteristic, development and present research situation of induction heating are briefly introduced. The background of this project, the main contents and the significance of this paper are mentioned. And the electromagnetic field value computational method is introduced. A mathematical model is developed to describe the distribution of electromagnetic field and eddy current density in the strip. The mathematical modal of electromagnetic fields is presented by a magnetic vector potential, which is also applied to solve eddy current field in ANSYS. And the analytical simulating methods for induction heating are represented.
Mathematical model is offered for solving the coupled problem for TWIH. To improve the efficiency of eddy current field calculation, necessary simplification is applied and boundary conditions are accurately analyzed. The magnetic force and the final eddy current distribution demonstrated and analyzed. And the computation of power density distribution in the strip has analyzed under different power source frequency, different air gap size, different primary position as well as different coil structure, which is based on ANSYS software. Comparison of edge-effects of traveling wave and transverse flux induction heating is done.
A single-coil model is applied to do basic three-dimensional study, and deduce the effect of coil structure and arrangement for the eddy current distributions. With the results, as well as the equivalent circuit and ANSYS simulation model, we get some rules about what mainly influences the distribution of inducting eddy current.
引文
[1] Barbosa Joaquim, et al. Zr bearing r-TiAl Induction Melted. Key Engineering Materials. 2000, 188,45-54.
[2] Nakajima Tadahito, Morimoto Yukitoshi, Seiichi, et al. Purification of Ti-Al alloys by Induction-HeatingFloating-Zone Melting and Cold-crucible Melting in Ultra-high Vacuum. Materials Transactions, JIM.2000, 41(1): 22-27.
[3]刘志儒.金属感应热处理[M].北京:机械工业出版社，1985
[4]王军华,汪友华,李建贵.行波感应加热器与横向磁通感应加热器磁场均匀度比较研究.理论与新技术全国电工2007年学术年会(CTATEE’07), 2007.8.11-16,张家界. 150-153.
[5] Yang Xiaoguang, Wang Youhua. New Method for Coupled Field Analysis in Transverse Flux InductionHeating of Continuously Moving Sheet. Heat Treatment of Metals, 2004, vol.29, no.4, pp.53-57.
[6] Yang Xiaoguang, Wang Youhua. The Effect of Coil Geometry on the Distributions of Eddy Current andTemperature in Transverse Flux Induction Heating Equipment. Heat Treatment of Metals. 2003, vol.28,no.7, pp.49-54.
[7] A.L.Bowden, E.J.Davies. Travelling Wave induction Heaters Design Considerations. BNCE-UIEElectroheat for Metals Conference, 11.5.2, Cambridge (England), 21-23 Sept. 1982.
[8] S.Lupi, M.Forzan, F.Dughiero, et al. In the corresponding TWIH system this problem is reduced sinceless and not sharp peaks are present with their highest. IEEE Transactions on Magnetics, 1999, vol.35,no.5, pp.3556-3558.
[9] S.Lupi, M.Forzan, F.Dughiero, et al. Comparison of edge-effects of transverse flux and travelling waveinduction heating inductors. IEEE Transactions on Magnetics, 1999, vol.35, no5, pp.3556 -3558.
[10] F.Dughiero, S.Lupi, V.Nemkov, et al. Travelling wave inductors for the continuous induction heating ofmetal strips. Proceedings of the Mediterranean Electrotechnical Conference-MELECON.1994, vol.3,no.3, pp.1154-1157.
[11] A.Ali, V.Bukanin, F.Dughiero, et al. Simulation of multiphase induction heating systems. IEEConference Publication, 1994, vol.38, no.4, pp.211-214.
[12] Dolezel L, Barglik 1., Sajdak C. Modelling of W duction Heating and Consequent Hardening of LongPrismatic Bodies. COMPEL-The International Journal for Computation and Mathematics in Electricaland Electronic Engineering. 2003, vol.22, no.1, pp. 79-87.
[13] Jeske U. Eddy current calculation in 3-D using the finite element method[J].IEEE Transactions onMagnetics,1982, vol.18, no.2, pp.426-430.
[14] Chaei M. Finite element computation of 3-D electrostatic and Magnetostatic field problems[J].IEEETransactions on Magnetics,1983, vol.19, no.6, pp.2321-2324.
[15] Hyun-Kyo，Gi-shik Lee，Song-yop Hahn. 3-D magnetic field computations using finite-elementapproach with localized functional. IEEE Transactions on Magnetics, 1985, vol.21, no.6, pp. 2129-2198.
[16] Kawase Yoshihiro, Miyatake Tsutomu, Hirata Katsuhiro. Thermal Analysis of Steel Blade Quenching byInduction Heating. IEEE Transactions on Magnetics. 2000, vol.36, no.4, pp.1788-1791.
[17]孔祥谦.有限单元法在传热学中的应用[M].北京:科学出版社，1986.
[18]约翰.戴维斯[英]著.感应加热手册[M].张淑芳译.北京:国防工业出版社，1985.
[19]杨晓光.横向磁通感应加热及其优化问题的研究,河北工业大学博士学位论文.
[20] Krahenbuhl L，Fabregue O，Wanser S.BIEM and FEM coupled with ID non linear solutions to solve 3Dhigh frequency eddy current problems[J].IEEE Transactions on Magnetics.1997，vol.33, no2, pp.1167-1172.
[21]王军华,汪友华,李建贵.行波感应加热器与横向磁通感应加热器磁场均匀度比较.天津市程学会电机工2007年学术年会, 2007,天津. pp.168-171.
[22] Dolezel L, Barglik 1., Sajdak C. Modelling of W Induction Heating and Consequent Hardening of LongPrismatic Bodies. COMPEL-The International Journal for Computation and Mathematics in Electricaland Electronic Engineering. 2003, vol22, no.1, pp. 79-87.
[23] Kawase Yoshihiro, Miyatake Tsutomu, Hirata Katsuhiro. Thermal Analysis of Steel Blade Quenching byInduction Heating. IEEE Transactions on Magnetics. 2000, 36(4): 1788-1791.
[24]美国ANSYS公司.ANSYS耦合场分析指南.1998
[25]美国ANSYS公司.ANSYS软件帮助文档.1998
[26] Hiraoka Masahiro, et al. Development of RF and Microwave Heating Equipment and ClinicalApplications to Cancer Treatment in Japan. IEEE Transactions on Microwave Theory andTechniques,2000,48 (11):1789-1799.
[27] Fuhrmann J，Homberg D. Numerical simulation of the surface hardening of steel[J].International Journalfor Computation and Mathematics in Electrical and Electronic Engineering.1999，9(5-6): 705-724
[28] Razavi, S.H. Szpunar J., Arabi H. Improvement of Age-Hardening Process of a Nickel-Base Super-alloy,IN738LC, by Induction Aging. Journal of Materials Science. 2002, 37 (7):1461-1471.
[29] Grum Janez. Measuring and Analysis of Residual Stresses after Induction Hardening and Grinding.Materials Science Forum. 2000, 347: 453-458.
[30] Zgraja, Jerzy. Computer Simulation of Induction Hardening of Moving Flat Charge. IEEE Transactionson Magnetics.2003,39 (3):1523-1526.
[31] Lee Houston, Khersonsky Anatoly. Induction Heating for Efficient Laser Applications. AdvancedMaterials and Processes.2000,157(4):39-41.
[32] Dughiero F, Battistetti M. Optimization procedures in the design of continuous induction hardening andtempering installations for magnetic steel bars[J].IEEE Transactions on Magnetics.1998， 34(5):2865-2868
[33] Pokrovskii AM，Leshkovtsev VG. Computational determination of the structure and hardness of rollsafter induction hardening[J].Metal Science and Heat Treatment.1997，39(9-10): 396-400.
[34] Di Barba P，Dughiero F，Trevisan F. Optimal design of windings for the continuous induction hardeningprocess of steel bars[J].International Journal of Applied Electroromagnetics and Mechanics.1998，9(1):53-63.
[35]张恒华，许洛萍等. A356铝合金半固态重熔温度场的有限元模拟.材料热处理学报.2002,23(2):37-42.
[36]崔成林，毛卫民.感应加热对半固态AISi7Mg合金连铸坯温度场和组织的影响.中国有色金属学报.2000,10(6):809-814.
[37] Acero J., Artigas J. LPower, Burdio, J. M., Barragan, L. A., Llorente S. Measuring in Two-OutputResonant Inverters for Induction Cooking Appliances. PESO Record-IEEE Annual Power ElectronicsSpecialists Conference.2002,3:1161-1166.
[38] Byun Jin-kyu, Choi Kyung, Roh Hee-Succ. Optimal Design Procedure For a Practical Induction HeatingCooker. IEEE Transactions on Magnetics.2000, 36(4):1390-1393.
[39] Xu DH, Kuang ZB.A study on the distribution of residual stress due to surface induction hardening[J].Journal of Engineering Materials and Technology-Transactions of the ASME.1996,118(4):571-575.
[2] Nakajima Tadahito, Morimoto Yukitoshi, Seiichi, et al. Purification of Ti-Al alloys by Induction-HeatingFloating-Zone Melting and Cold-crucible Melting in Ultra-high Vacuum. Materials Transactions, JIM.2000, 41(1): 22-27.
[3]刘志儒.金属感应热处理[M].北京:机械工业出版社，1985
[4]王军华,汪友华,李建贵.行波感应加热器与横向磁通感应加热器磁场均匀度比较研究.理论与新技术全国电工2007年学术年会(CTATEE’07), 2007.8.11-16,张家界. 150-153.
[5] Yang Xiaoguang, Wang Youhua. New Method for Coupled Field Analysis in Transverse Flux InductionHeating of Continuously Moving Sheet. Heat Treatment of Metals, 2004, vol.29, no.4, pp.53-57.
[6] Yang Xiaoguang, Wang Youhua. The Effect of Coil Geometry on the Distributions of Eddy Current andTemperature in Transverse Flux Induction Heating Equipment. Heat Treatment of Metals. 2003, vol.28,no.7, pp.49-54.
[7] A.L.Bowden, E.J.Davies. Travelling Wave induction Heaters Design Considerations. BNCE-UIEElectroheat for Metals Conference, 11.5.2, Cambridge (England), 21-23 Sept. 1982.
[8] S.Lupi, M.Forzan, F.Dughiero, et al. In the corresponding TWIH system this problem is reduced sinceless and not sharp peaks are present with their highest. IEEE Transactions on Magnetics, 1999, vol.35,no.5, pp.3556-3558.
[9] S.Lupi, M.Forzan, F.Dughiero, et al. Comparison of edge-effects of transverse flux and travelling waveinduction heating inductors. IEEE Transactions on Magnetics, 1999, vol.35, no5, pp.3556 -3558.
[10] F.Dughiero, S.Lupi, V.Nemkov, et al. Travelling wave inductors for the continuous induction heating ofmetal strips. Proceedings of the Mediterranean Electrotechnical Conference-MELECON.1994, vol.3,no.3, pp.1154-1157.
[11] A.Ali, V.Bukanin, F.Dughiero, et al. Simulation of multiphase induction heating systems. IEEConference Publication, 1994, vol.38, no.4, pp.211-214.
[12] Dolezel L, Barglik 1., Sajdak C. Modelling of W duction Heating and Consequent Hardening of LongPrismatic Bodies. COMPEL-The International Journal for Computation and Mathematics in Electricaland Electronic Engineering. 2003, vol.22, no.1, pp. 79-87.
[13] Jeske U. Eddy current calculation in 3-D using the finite element method[J].IEEE Transactions onMagnetics,1982, vol.18, no.2, pp.426-430.
[14] Chaei M. Finite element computation of 3-D electrostatic and Magnetostatic field problems[J].IEEETransactions on Magnetics,1983, vol.19, no.6, pp.2321-2324.
[15] Hyun-Kyo，Gi-shik Lee，Song-yop Hahn. 3-D magnetic field computations using finite-elementapproach with localized functional. IEEE Transactions on Magnetics, 1985, vol.21, no.6, pp. 2129-2198.
[16] Kawase Yoshihiro, Miyatake Tsutomu, Hirata Katsuhiro. Thermal Analysis of Steel Blade Quenching byInduction Heating. IEEE Transactions on Magnetics. 2000, vol.36, no.4, pp.1788-1791.
[17]孔祥谦.有限单元法在传热学中的应用[M].北京:科学出版社，1986.
[18]约翰.戴维斯[英]著.感应加热手册[M].张淑芳译.北京:国防工业出版社，1985.
[19]杨晓光.横向磁通感应加热及其优化问题的研究,河北工业大学博士学位论文.
[20] Krahenbuhl L，Fabregue O，Wanser S.BIEM and FEM coupled with ID non linear solutions to solve 3Dhigh frequency eddy current problems[J].IEEE Transactions on Magnetics.1997，vol.33, no2, pp.1167-1172.
[21]王军华,汪友华,李建贵.行波感应加热器与横向磁通感应加热器磁场均匀度比较.天津市程学会电机工2007年学术年会, 2007,天津. pp.168-171.
[22] Dolezel L, Barglik 1., Sajdak C. Modelling of W Induction Heating and Consequent Hardening of LongPrismatic Bodies. COMPEL-The International Journal for Computation and Mathematics in Electricaland Electronic Engineering. 2003, vol22, no.1, pp. 79-87.
[23] Kawase Yoshihiro, Miyatake Tsutomu, Hirata Katsuhiro. Thermal Analysis of Steel Blade Quenching byInduction Heating. IEEE Transactions on Magnetics. 2000, 36(4): 1788-1791.
[24]美国ANSYS公司.ANSYS耦合场分析指南.1998
[25]美国ANSYS公司.ANSYS软件帮助文档.1998
[26] Hiraoka Masahiro, et al. Development of RF and Microwave Heating Equipment and ClinicalApplications to Cancer Treatment in Japan. IEEE Transactions on Microwave Theory andTechniques,2000,48 (11):1789-1799.
[27] Fuhrmann J，Homberg D. Numerical simulation of the surface hardening of steel[J].International Journalfor Computation and Mathematics in Electrical and Electronic Engineering.1999，9(5-6): 705-724
[28] Razavi, S.H. Szpunar J., Arabi H. Improvement of Age-Hardening Process of a Nickel-Base Super-alloy,IN738LC, by Induction Aging. Journal of Materials Science. 2002, 37 (7):1461-1471.
[29] Grum Janez. Measuring and Analysis of Residual Stresses after Induction Hardening and Grinding.Materials Science Forum. 2000, 347: 453-458.
[30] Zgraja, Jerzy. Computer Simulation of Induction Hardening of Moving Flat Charge. IEEE Transactionson Magnetics.2003,39 (3):1523-1526.
[31] Lee Houston, Khersonsky Anatoly. Induction Heating for Efficient Laser Applications. AdvancedMaterials and Processes.2000,157(4):39-41.
[32] Dughiero F, Battistetti M. Optimization procedures in the design of continuous induction hardening andtempering installations for magnetic steel bars[J].IEEE Transactions on Magnetics.1998， 34(5):2865-2868
[33] Pokrovskii AM，Leshkovtsev VG. Computational determination of the structure and hardness of rollsafter induction hardening[J].Metal Science and Heat Treatment.1997，39(9-10): 396-400.
[34] Di Barba P，Dughiero F，Trevisan F. Optimal design of windings for the continuous induction hardeningprocess of steel bars[J].International Journal of Applied Electroromagnetics and Mechanics.1998，9(1):53-63.
[35]张恒华，许洛萍等. A356铝合金半固态重熔温度场的有限元模拟.材料热处理学报.2002,23(2):37-42.
[36]崔成林，毛卫民.感应加热对半固态AISi7Mg合金连铸坯温度场和组织的影响.中国有色金属学报.2000,10(6):809-814.
[37] Acero J., Artigas J. LPower, Burdio, J. M., Barragan, L. A., Llorente S. Measuring in Two-OutputResonant Inverters for Induction Cooking Appliances. PESO Record-IEEE Annual Power ElectronicsSpecialists Conference.2002,3:1161-1166.
[38] Byun Jin-kyu, Choi Kyung, Roh Hee-Succ. Optimal Design Procedure For a Practical Induction HeatingCooker. IEEE Transactions on Magnetics.2000, 36(4):1390-1393.
[39] Xu DH, Kuang ZB.A study on the distribution of residual stress due to surface induction hardening[J].Journal of Engineering Materials and Technology-Transactions of the ASME.1996,118(4):571-575.
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