感应加热温度场的数值模拟
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摘要
本文主要研究感应加热器内被加热钢坯温度分布的数值模拟。感应加热是利用工件中涡流的焦耳效应将工件加热,这种加热方式具有效率高、控制精确、污染少等特点,在工业生产中得到了广泛的应用。如何设置加热过程的参数使之满足被加热工件中各项性能要求是普遍关注的问题。工件的诸多性能指标与热处理过程中的温度分布是密切相关的,然而基于实验的系统设计方法却耗时费力,并且温度测量成本高,传感器的引入还会影响本来的温度分布。因此,数值模拟技术对于这类系统的设计和研究具有重要意义。
本文从感应加热的有关原理和电磁一热耦合场计算的有限元方法着手,以电磁学和传热学为基础,对感应加热电磁场和温度场分布进行了理论推导,给出了电磁场、温度场分布的数学模型及相应的有限元分析模型。其中,电磁场的数学模型由A ?φ法建立,电磁场和温度场的有限元离散化方程组由伽辽金加权余量法导出。
根据数值模拟的基本理论,本文在比较ANSYS有限元软件中两种耦合场分析方法的基础上,选择了顺序耦合方法。并对圆柱形45号钢样件建立了相应的电磁一热耦合分析的数学、物理有限元模型;对加热过程的温度场分布进行模拟,得到感应加热温度场的分布图。并分析了感应加热参数对模拟结果的影响,得出了一些具有工程借鉴意义的结论,为合理选择加热参数提供理论依据。
通过数值模拟的结果与实验测试所得的结果相比较,证明数值数拟的结果达到了工艺上的准确性,可应用于生产实际。
This paper mainly do research for the numerical simulation of temperature distribution of metal billet in induction heating. The induction heating process generates heat by means of Joule effect resulting from an eddy current , it is widely used in industrial operations due to its high efficiency,precise control and low pollution properties .It is an impotrant problem to control each parameters of the induction heating system to ensure that every properties of metal billet are reasonable.In fact,some properties are linked to temperature distribution in heat treatment process,However,the design of an induction heating system based on experiments would be tedious and time-consuming.Furthermore,temperature measurements are expensive and the induction of sensors often results in perturbing the phenomena. Therefore, numerical simulation seems a well-adapted tool for the design and the investigation of induction heating system.
Based on the Electromagnetics theory and Thermal theory,it constructed the mathematic analysis models of electromagnetic field and temperature field. The mathematical model of electromagnetic field are established by A ?φmethod.Then it deduced the finite element discretization equations of electromagnetic field and temperature field by Galarkin weighted residual method.
According to the basic principle of numerical simulation, the sequential anlaysis method is selected as the main method to solve the problem of the Electromagnetic-Thermal coupled field by comparing and analysing two coupled field methods offered by ANSYS. The uniform EFM model of eddy current field and temperature field is set on 45# steel .The induction magnetic field and the transient temperature distribution is obtained by means of calculation for heating process. The influence of the technical parameters on the induction heating simulation result is analyzed.,and some referential conclusions are drawed.On the basis of these conclusions, induction heating parameter will be chosen correctly in the design of the induction heating system.
At last,it proved that the result of simulation is correct by means of comparing with the result of experiment, numerical simulation seems a well-adapted tool for the design and the investigation of induction heating system.
本文从感应加热的有关原理和电磁一热耦合场计算的有限元方法着手,以电磁学和传热学为基础,对感应加热电磁场和温度场分布进行了理论推导,给出了电磁场、温度场分布的数学模型及相应的有限元分析模型。其中,电磁场的数学模型由A ?φ法建立,电磁场和温度场的有限元离散化方程组由伽辽金加权余量法导出。
根据数值模拟的基本理论,本文在比较ANSYS有限元软件中两种耦合场分析方法的基础上,选择了顺序耦合方法。并对圆柱形45号钢样件建立了相应的电磁一热耦合分析的数学、物理有限元模型;对加热过程的温度场分布进行模拟,得到感应加热温度场的分布图。并分析了感应加热参数对模拟结果的影响,得出了一些具有工程借鉴意义的结论,为合理选择加热参数提供理论依据。
通过数值模拟的结果与实验测试所得的结果相比较,证明数值数拟的结果达到了工艺上的准确性,可应用于生产实际。
This paper mainly do research for the numerical simulation of temperature distribution of metal billet in induction heating. The induction heating process generates heat by means of Joule effect resulting from an eddy current , it is widely used in industrial operations due to its high efficiency,precise control and low pollution properties .It is an impotrant problem to control each parameters of the induction heating system to ensure that every properties of metal billet are reasonable.In fact,some properties are linked to temperature distribution in heat treatment process,However,the design of an induction heating system based on experiments would be tedious and time-consuming.Furthermore,temperature measurements are expensive and the induction of sensors often results in perturbing the phenomena. Therefore, numerical simulation seems a well-adapted tool for the design and the investigation of induction heating system.
Based on the Electromagnetics theory and Thermal theory,it constructed the mathematic analysis models of electromagnetic field and temperature field. The mathematical model of electromagnetic field are established by A ?φmethod.Then it deduced the finite element discretization equations of electromagnetic field and temperature field by Galarkin weighted residual method.
According to the basic principle of numerical simulation, the sequential anlaysis method is selected as the main method to solve the problem of the Electromagnetic-Thermal coupled field by comparing and analysing two coupled field methods offered by ANSYS. The uniform EFM model of eddy current field and temperature field is set on 45# steel .The induction magnetic field and the transient temperature distribution is obtained by means of calculation for heating process. The influence of the technical parameters on the induction heating simulation result is analyzed.,and some referential conclusions are drawed.On the basis of these conclusions, induction heating parameter will be chosen correctly in the design of the induction heating system.
At last,it proved that the result of simulation is correct by means of comparing with the result of experiment, numerical simulation seems a well-adapted tool for the design and the investigation of induction heating system.
引文
1.刘庄.热处理过程的数值模拟[M].北京:科学出版社,1996.283
2.沈锦飞,惠晶,吴雷.2MHz/1KW超高频感应加热电源[J].电子电力技术,2002,36(6):13-15
3.沈锦飞,颜文旭,惠晶,吴雷.PSM高频逆变电源在金属针布热处理中的应用[J].电子电力技术,2005,39(5):75-77
4.沈锦飞,单广伟,颜文旭,惠晶.PSM功率控制大功率感应加热电源及应用[J].电子电力技术,2006,40(2):84-92
5.惠晶,蔡爱军,沈锦飞.基于感应加热电流的温度控制模型研究[J].金属热处理,2006,31(2):70-74
6.吴雷,沈锦飞,惠晶.VD-MOS高频感应加热装置的研究[J].江南学院学报,2000,15(4):38-41
7.沈锦飞,颜文旭,惠晶,吴雷.钢丝热处理用大功率高频感应电源的研制[J].电子电力技术,2003,37(6):56-58
8.姜士林,赵长汉.感应加热原理与应用[M].天津:天津科技翻译出版公司,1993:10-26
9.刘志儒,卢锦宝.金属感应热处理(上册)[M].北京:机械工业出版社,1985
10.K.Kurpisz. Numerical Solution of One Case of Inverse Heat Conduction Problems[J]. Heat Conduction Problems, Trans. ASME, J.Neat Transfer, 1990,18(5):23-45
11.J V Beck, B Blackwell,Ch R C1air.Inverse Heat Conduction Problems[M]. New York: A Wiley-Intersc. Publ.,1985.134-200
12.Jeske U. Eddy current calculation in 3-D using the finite element method[J].IEEE Transactions on Magnetics,1982,18(2):426-430
13.Chaei M,Konrad A. Finite element computation of 3-Delectrostatic and magnetostatic field problems[J].IEEE Transactions on Magnetics,1983,19(6):2321-2324
14.Hyun-Kyo,Gi-shik Lee,Song-yop Hahn.3-D magnetic field computations using finite-element approach with localized functional[J].IEEE Transactions on Magnetics,1985,21(6):2129-2198
15.Fireteanu V, Tudorache T. Electromagntic forces in transverse flux induction heating[J].IEEE Transactions on Magnetics.2000, 36(4): 1792-1795
16.Adam Bokota, Slawomir Iskierka.Numerical analysis of phase transformations and residual stresses in steel cone-shaped elements hardened by induction and flame method[J].Int. J Mesh,1998,(40):617-629
17.Wang KF, Chandrasekar S, Yang HTY. Finite-element simulation of induction heat-treatment[J].Journal of Materials Engineering and Performance,1996, 118 (4):571-575
18.Wang KF, Chandrasekar S, Yang HTY. Finite-element simulation of moving induction heat treatment[J].Journal of Materials Engineering and Performance, 1995, 4(4): 460-473
19.Chaboudez C,Clain S,Glardon R,Rappaz J,Swierkosz M.Numerical modeling of induction heating for axisymmetric geometries[J].IEEE Transactions onMagnetics,1997,33(1):739-745
20.Fuhrmann J , Homberg D.Numerical simulation of induction hardening of steel [J].International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 1999, 18(3): 482-493
21.Fuhrmann J, Homberg D.Numerical simulation of the surface hardening of steel[J].International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 1999, 9(5-6): 705-724
22.Pokrovskii AM, Leshkovtsev VG.Computational determination of the structure and hardness of rolls after induction hardening[J].Metal Science and Heat Treatment,1997, 39(9):327-334
23.Di Barba P, Dughiero F,Trevisan F.Optimal design of windings for the continuous induction hardening process of steel bars[J].International Journal of Applied Electronmagnetics and Mechanics, 1998, 9(l): 53-63
24.Krahenbuhl L, Fabregue O, Wanser S.BIEM and FEM coupled with ID nonlinear solutions to solve 3D high frequency eddy current problems [J].IEEE Transactions on Magnetics,1997, 33(2): 1167-1172
25.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.
26.Bukanin V, Dughiero F. 3D-FEM simulation of transverse-flux induction heaters[J]. IEEE Transactions on Magnetics,1995,31(3 ):2174-2177
27.Karol A, Adam S. A New Concept for Finite Element Simulation of Induction Heating of Steel Cylinders[J]. IEEE transactions on industry applications,1997,33(4):893-897
28.Wang Z,Huang,W,ect.3D multifields FEM computation of transverse flux induction heating for moving-strips[J].IEEE Transactions on Magnetics,1999,35(3):1642-1645
29.刘继全.感应加热的热计算模型[J] .大型铸锻件, 2003(3):16-20
30.金晓昌.感应加热技术中的趋肤效应[J].武汉化工学院学报,1995,17(4):65-68
31.金晓昌.感应线圈中电磁场分析[J].武汉化工学院学报,1996,18(2):76-78
32.肖新棉.感应加热线圈中的电磁场[J].武汉水利电力大学学报,1996,29(6):23-27
33.肖国春.圆管感应加热工件内电参数计算[J].工业加热,1993,(4):19-26
34.帅克刚.高频感应加热弯板成型温度场的有限元分析[J]锅炉技术,2004,35(3):52-54
35.王璋奇,范孝良,张文建.管道感应加热过程的计算机模拟[J].华北电力大学学报,1999,26(4):67-70
36.戴挺,吴炳尧.半固态坯料感应三次加热的模拟分析[J].中国压铸、挤压铸造、半固态加工学术年会论文集,2001:158-161
37.郭景杰,王同敏,苏彦庆.钦的水冷铜增锅感应熔炼温度场数值模拟[J].铸造.1997(9): 1-4
38.鄢波,程先华,赵萍.减振器连杆高频感应淬火工艺的温度场有限元模拟[J].上海交通大学学报,2003,37(1):111-114
39.徐东辉,匡震邦,骆竞希.抽油杆表面感应淬火引起的残余应力[J].应用力学学报.1995,(3): 26-32
40.Biro,K.preis.On the use of the magnetic vector potential in the finite element analysls of Three-dimensional eddy currents[J].IEEE Transations on Magnetics,1989,25(4):3145-3159
41.刘乐昌感应加热过程的数值模拟与感应线圈的优化设计[D]:[硕士学位论文].哈尔滨:哈尔滨工业大学,2002
42.唐兴伦,范群波,张朝晖.ANSYS工程应用教程(热学、电磁学篇) [M]:第一版.北京:中国铁道出版社,2003.222-249
43.刘高腆.温度场的数值模拟[M].重庆:重庆大学出版社,1990.211-248
44.徐祖耀.相变原理[M].北京:机械工业出版社,1998.49-78
45.梁克中.金相原理与应用[M].北京:机械工业出版社,1983.126-160
46.徐霖,张恒华,邵光杰.半固态铝合金感应加热工艺参数的模拟研究[J].上海金属,2002,24(6):56-59
47.徐祖耀.相变原理[M].北京:机械工业出版社,1998.134-158
48.林信智.淬火感应器的选用,设计与制造[M].北京:机械工业出版社,1991.41-57
49.美国Raytek公司.Marathon系列高性能的红外测温仪,www, raytek. com. Cn.
50.王宏.曲轴感应加热淬火仿真研究[D]:[硕士学位论文] .吉林:吉林大学,2003
2.沈锦飞,惠晶,吴雷.2MHz/1KW超高频感应加热电源[J].电子电力技术,2002,36(6):13-15
3.沈锦飞,颜文旭,惠晶,吴雷.PSM高频逆变电源在金属针布热处理中的应用[J].电子电力技术,2005,39(5):75-77
4.沈锦飞,单广伟,颜文旭,惠晶.PSM功率控制大功率感应加热电源及应用[J].电子电力技术,2006,40(2):84-92
5.惠晶,蔡爱军,沈锦飞.基于感应加热电流的温度控制模型研究[J].金属热处理,2006,31(2):70-74
6.吴雷,沈锦飞,惠晶.VD-MOS高频感应加热装置的研究[J].江南学院学报,2000,15(4):38-41
7.沈锦飞,颜文旭,惠晶,吴雷.钢丝热处理用大功率高频感应电源的研制[J].电子电力技术,2003,37(6):56-58
8.姜士林,赵长汉.感应加热原理与应用[M].天津:天津科技翻译出版公司,1993:10-26
9.刘志儒,卢锦宝.金属感应热处理(上册)[M].北京:机械工业出版社,1985
10.K.Kurpisz. Numerical Solution of One Case of Inverse Heat Conduction Problems[J]. Heat Conduction Problems, Trans. ASME, J.Neat Transfer, 1990,18(5):23-45
11.J V Beck, B Blackwell,Ch R C1air.Inverse Heat Conduction Problems[M]. New York: A Wiley-Intersc. Publ.,1985.134-200
12.Jeske U. Eddy current calculation in 3-D using the finite element method[J].IEEE Transactions on Magnetics,1982,18(2):426-430
13.Chaei M,Konrad A. Finite element computation of 3-Delectrostatic and magnetostatic field problems[J].IEEE Transactions on Magnetics,1983,19(6):2321-2324
14.Hyun-Kyo,Gi-shik Lee,Song-yop Hahn.3-D magnetic field computations using finite-element approach with localized functional[J].IEEE Transactions on Magnetics,1985,21(6):2129-2198
15.Fireteanu V, Tudorache T. Electromagntic forces in transverse flux induction heating[J].IEEE Transactions on Magnetics.2000, 36(4): 1792-1795
16.Adam Bokota, Slawomir Iskierka.Numerical analysis of phase transformations and residual stresses in steel cone-shaped elements hardened by induction and flame method[J].Int. J Mesh,1998,(40):617-629
17.Wang KF, Chandrasekar S, Yang HTY. Finite-element simulation of induction heat-treatment[J].Journal of Materials Engineering and Performance,1996, 118 (4):571-575
18.Wang KF, Chandrasekar S, Yang HTY. Finite-element simulation of moving induction heat treatment[J].Journal of Materials Engineering and Performance, 1995, 4(4): 460-473
19.Chaboudez C,Clain S,Glardon R,Rappaz J,Swierkosz M.Numerical modeling of induction heating for axisymmetric geometries[J].IEEE Transactions onMagnetics,1997,33(1):739-745
20.Fuhrmann J , Homberg D.Numerical simulation of induction hardening of steel [J].International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 1999, 18(3): 482-493
21.Fuhrmann J, Homberg D.Numerical simulation of the surface hardening of steel[J].International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 1999, 9(5-6): 705-724
22.Pokrovskii AM, Leshkovtsev VG.Computational determination of the structure and hardness of rolls after induction hardening[J].Metal Science and Heat Treatment,1997, 39(9):327-334
23.Di Barba P, Dughiero F,Trevisan F.Optimal design of windings for the continuous induction hardening process of steel bars[J].International Journal of Applied Electronmagnetics and Mechanics, 1998, 9(l): 53-63
24.Krahenbuhl L, Fabregue O, Wanser S.BIEM and FEM coupled with ID nonlinear solutions to solve 3D high frequency eddy current problems [J].IEEE Transactions on Magnetics,1997, 33(2): 1167-1172
25.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.
26.Bukanin V, Dughiero F. 3D-FEM simulation of transverse-flux induction heaters[J]. IEEE Transactions on Magnetics,1995,31(3 ):2174-2177
27.Karol A, Adam S. A New Concept for Finite Element Simulation of Induction Heating of Steel Cylinders[J]. IEEE transactions on industry applications,1997,33(4):893-897
28.Wang Z,Huang,W,ect.3D multifields FEM computation of transverse flux induction heating for moving-strips[J].IEEE Transactions on Magnetics,1999,35(3):1642-1645
29.刘继全.感应加热的热计算模型[J] .大型铸锻件, 2003(3):16-20
30.金晓昌.感应加热技术中的趋肤效应[J].武汉化工学院学报,1995,17(4):65-68
31.金晓昌.感应线圈中电磁场分析[J].武汉化工学院学报,1996,18(2):76-78
32.肖新棉.感应加热线圈中的电磁场[J].武汉水利电力大学学报,1996,29(6):23-27
33.肖国春.圆管感应加热工件内电参数计算[J].工业加热,1993,(4):19-26
34.帅克刚.高频感应加热弯板成型温度场的有限元分析[J]锅炉技术,2004,35(3):52-54
35.王璋奇,范孝良,张文建.管道感应加热过程的计算机模拟[J].华北电力大学学报,1999,26(4):67-70
36.戴挺,吴炳尧.半固态坯料感应三次加热的模拟分析[J].中国压铸、挤压铸造、半固态加工学术年会论文集,2001:158-161
37.郭景杰,王同敏,苏彦庆.钦的水冷铜增锅感应熔炼温度场数值模拟[J].铸造.1997(9): 1-4
38.鄢波,程先华,赵萍.减振器连杆高频感应淬火工艺的温度场有限元模拟[J].上海交通大学学报,2003,37(1):111-114
39.徐东辉,匡震邦,骆竞希.抽油杆表面感应淬火引起的残余应力[J].应用力学学报.1995,(3): 26-32
40.Biro,K.preis.On the use of the magnetic vector potential in the finite element analysls of Three-dimensional eddy currents[J].IEEE Transations on Magnetics,1989,25(4):3145-3159
41.刘乐昌感应加热过程的数值模拟与感应线圈的优化设计[D]:[硕士学位论文].哈尔滨:哈尔滨工业大学,2002
42.唐兴伦,范群波,张朝晖.ANSYS工程应用教程(热学、电磁学篇) [M]:第一版.北京:中国铁道出版社,2003.222-249
43.刘高腆.温度场的数值模拟[M].重庆:重庆大学出版社,1990.211-248
44.徐祖耀.相变原理[M].北京:机械工业出版社,1998.49-78
45.梁克中.金相原理与应用[M].北京:机械工业出版社,1983.126-160
46.徐霖,张恒华,邵光杰.半固态铝合金感应加热工艺参数的模拟研究[J].上海金属,2002,24(6):56-59
47.徐祖耀.相变原理[M].北京:机械工业出版社,1998.134-158
48.林信智.淬火感应器的选用,设计与制造[M].北京:机械工业出版社,1991.41-57
49.美国Raytek公司.Marathon系列高性能的红外测温仪,www, raytek. com. Cn.
50.王宏.曲轴感应加热淬火仿真研究[D]:[硕士学位论文] .吉林:吉林大学,2003