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研究生: 孟繁善
Meng, Fan-Shan
論文名稱: 感應加熱電磁鋼之三維熱應力有限元素分析
Three-Dimensional Finite Element Analysis of Thermal Stress in Induction Heating of Electrical Steel
指導教授: 李旺龍
Li, Wong-Long
學位類別: 碩士
Master
系所名稱: 工學院 - 材料科學及工程學系
Department of Materials Science and Engineering
論文出版年: 2020
畢業學年度: 108
語文別: 中文
論文頁數: 125
中文關鍵詞: 感應加熱電磁鋼片數值模擬等效接觸熱阻熱應力
外文關鍵詞: induction heating, electrical steel sheet, numerical simulation, effective, contact thermal resistance, thermal stress
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  • 驅動馬達是電動車中的核心零件,其中驅動馬達鐵芯之主要材料為電磁鋼片,因此電磁鋼片的品質好壞將會直接影響整個馬達鐵芯的輸出效率。在傳統鉚銲接式製程的鐵芯過程中會遇到許多不可避免的問題,如鉚接不佳造成鐵芯脫落而導致驅動馬達的良率不佳,因而促使藉由感應加熱製程之膠合式鐵芯的興起。
    本文將建立感應加熱電磁鋼片之數值計算方法,過程是利用交流電流通過激磁線圈產生變化的磁場而感應出渦電流。當渦電流流經電磁鋼片時,因其電阻而產生出焦耳熱並藉由熱傳導加熱,使電磁鋼片和周圍治具升溫。此外,數值模擬是透過馬克士威方程組、基本熱傳方程式、接觸熱阻模型、本構方程式及等效公式理論,並搭配有限元素分析法以獲得全區域的電磁場分佈、電磁鋼片與治具的溫度分佈及應力分佈。藉由前述之結果再分別進行二維等效模型、三維激磁線圈設計、接觸熱阻及熱應力分析。
    本研究最終結果表明:可利用等效幾何模型代替實際幾何模型;藉由五種影響因子的搭配以獲得較適化之激磁線圈設計;根據接觸熱傳導分析熱接觸對電磁鋼片升溫之影響;透過熱應力分析得知電磁鋼片與治具彼此分離所須施加的力量範圍。因此,藉由本文感應加熱電磁鋼片模型之建立,不僅降低實驗之時間成本,亦能對馬達鐵芯製程的領域提供有價值的參考依據。

    The drive motor is the core of the electric vehicle. The principal component of the drive motor core is electrical steel sheet. Therefore, the quality of the electrical steel sheet will directly affect the output efficiency of the entire motor core. There are lots of inevitable problems in the traditional welding process of the iron core, such as poor welding. So it promotes the glued iron core by the induction heating process.
    This research establishs a finite element method for induction heating of electrical steel sheet. When alternating current flows through the excitation coil, it will make the magnetic field various and then induce eddy current. Eddy current will generate Joule heat due to the electrical resistance of the electrical steel sheet. By heat conduction, Joule heat make the temperature of the electrical steel sheet and surrounding fixtures rise. In addition, the numerical simulation of the research is the combination of Maxwell equation, basic heat transfer equation, contact thermal resistance model, constitutive equation and effective formula theories. Through finite element analysis to obtain the electromagnetic field, temperature and stress distribution in electrical steel sheet and fixtures. Based on the aforementioned results, the two-dimensional effective model, three-dimensional excitation coil design, contact thermal resistance and thermal stress analysis are discussed.
    Therefore, the establishment of the effective geometric model of the induction heating electrical steel sheet model in this article not only reduces the time cost of the experiment, but also provides a valuable reference for the field of motor core manufacturing.

    目錄 摘要 i Extended Abstract ii 誌謝 xiii 目錄 xiv 表目錄 xix 圖目錄 xx 符號表 xxv 第一章、 緒論 1 1.1 前言 1 1.2 文獻回顧 5 1.2.1 感應加熱數值模擬的現況 5 1.2.2 接觸熱阻模型的發展 8 1.2.3 感應加熱之熱應力的研究現況 10 1.3 研究動機與目的 12 1.4 論文架構 13 第二章、 研究理論 15 2.1 簡介 15 2.2 感應加熱基本原理 15 2.2.1 電磁感應定律(Faraday’s Law)和渦流損(Eddy-Current Loss) 16 2.2.2 磁滯效應(Hysteresis Loss) 17 2.2.3 集膚效應(Skin Effect) 18 2.2.4 鄰近效應(Proximity Effect)和圓環效應(Ring Effect) 19 2.3 電磁場的基本理論 23 2.3.1 安培定律(Ampère's Law) 23 2.3.2 法拉第電磁感應定律(Faraday's Law of Electromagnetic Induction) 23 2.3.3 高斯定律(Gauss' law) 24 2.3.4 高斯磁定律(Gauss' Law for Magnetism) 24 2.3.5 磁場統御方程式 25 2.4 溫度場的基本理論 29 2.4.1 熱傳導(Thermal Conduction)定律 29 2.4.2 熱對流(Thermal Convection)定律 30 2.4.3 熱輻射(Thermal Radiation)定律 30 2.4.4 溫度場統御方程式 31 2.4.5 熱接觸模型 33 2.5 力學場的基本理論 36 2.5.1 本構方程式 36 2.5.2 應變-位移的關係 39 2.5.3 熱膨脹方程式 39 2.6 複合材料之等效理論 40 2.6.1 溫度場之材料參數等效方程式 40 2.6.2 電磁場之材料參數等效方程式 42 第三章、 感應加熱數值方法 47 3.1 幾何模型建立 47 3.2 材料參數 51 3.3 邊界條件設定 53 3.3.1 電磁場的邊界條件 53 3.3.2 溫度場的邊界條件 54 3.3.3 力學場的邊界條件 55 3.4 空間大小和網格靈敏度測試 56 3.4.1 空間測試 56 3.4.2 網格靈敏度測試 57 3.5 感應加熱電磁鋼片模型驗證和二維與三維模型間的驗證 65 3.5.1 感應加熱電磁鋼片模型驗證 65 3.5.2 二維與三維模型間的驗證 67 第四章、 結果與討論 71 4.1 等效溫度場和電磁場之二維分析 71 4.1.1 等效溫度場之材料參數 72 4.1.2 等效電磁場之材料參數 73 4.2 電磁鋼片環形鐵芯之三維激磁線圈設計分析 81 4.2.1 激磁線圈電流頻率(f) 81 4.2.2 激磁線圈電流(Ipeak) 82 4.2.3 激磁線圈匝數(Nt) 83 4.2.4 激磁線圈彼此之間距(Dcc) 85 4.2.5 激磁線圈與電磁鋼片之距離(Dsc) 86 4.3 電磁鋼片環形鐵芯之三維熱接觸分析 93 4.3.1 鐵芯內側緊連304不鏽鋼之接觸熱阻分析 93 4.3.2 鐵芯外側緊連二氧化鋯之接觸熱阻分析 95 4.4 電磁鋼片環形鐵芯之三維熱應力分析 102 4.4.1 鐵芯內側緊連304不鏽鋼之熱應力分析 102 4.3.2 鐵芯外側緊連二氧化鋯之熱應力分析 105 第五章、 結論與未來展望 115 5.1 結論 115 5.2 未來展望 117 參考文獻 118

    [1] C. Chaboudez, S. Clain, R. Glardon, D. Mari, J. Rappaz, and M. Swierkosz, Numerical modeling in induction heating for axisymmetric geometries, IEEE Transactions on Magnetics, Vol. 33, No. 1, pp. 739–745, 1997.
    [2] S. Clain, J. Rappaz, M. Swierkosz, and R. Touzani, Numerical modelling of induction heating for two-dimensional geometries, Mathematical Models and Methods, Vol. 3, No. 6, pp. 805–822, 1993.
    [3] J. Rappaz and M. Swierkosz, Mathematical modelling and numerical simulation of induction heating processes, Appl. Math. Comput. Vol. 6, No. 2, pp. 207–221, 1996.
    [4] F. Cajner, B. Smoljan, and D. Landek, Computer simulation of induction hardening, Journal of Materials Processing Technology, Vol. 157, pp. 55-60, 2004.
    [5] S. Wanser, L. Krähenbühl, and A. Nicolas, Computation of 3D induction hardening problems by combined finite and boundary elements methods, IEEE Transactions on Magnetics, Vol. 30, No. 5, pp. 3320-3323, 1994.
    [6] Q.S. Chen, P. Gao, and W.R. Hu, Effects of induction heating on temperature distribution and growth rate in large-size SiC growth system, Journal of Crystal Growth, Vol. 266, No. 1-3, pp. 320-326, 2004.
    [7] O. Klein and P. Philip, Transient numerical investigation of induction heating during sublimation growth of silicon carbide single crystals, Journal of Crystal Growth, Vol. 247, No. 1-2, pp. 219-235, 2003.
    [8] H. Tomita, Industry applications of small induction heater, In Proceedings of the 2012 9th France-Japan and 7th Europe-Asia Congress on and Research and Education in Mechatronics, Paris, France, 21–23, 2012.
    [9] V. Rudnev, D. Loveless, and R.L. Cook, Handbook of Induction Heating, 2nd ed., CRC Press: Boca Raton, FL, USA, 2017.
    [10] B. Drobenko, O. Hachkevych, and T. Kournyts’kyi, A mathematical simulation of high temperature induction heating of electroconductive solids, International Journal of Heat and Mass Transfer, Vol. 50, No. 3-4, pp. 616-624, 2007.
    [11] F. Bay, V. Labbe, Y. Favennec, and J.L. Chenot, A numerical model for induction heating processes coupling electromagnetism and thermomechanics, International Journal For Numerical Methods in Engineering, Vol. 58, No. 6, pp. 839-867, 2003.
    [12] O. Bodart, A.V. Boureau, and R. Touzani, Numerical investigation of optimal control of induction heating processes, Applied Mathematical Modelling, Vol. 25, No. 8, pp. 697-712, 2001.
    [13] C. Marchand and A. Foggia, 2D finite-element program for magnetic induction heating, IEEE Transactions on Magnetics, Vol. 19, No. 6, pp. 2647-2649, 1983.
    [14] S. Wanse, L. Wenbiihl, and A. Nicolas, Computation of 3D induction hardening problems by combined finite and boundary element methods, IEEE Transactions on Magnetics, Vol. 30, No. 5, pp. 3320-3323, 1994.
    [15] K. Sadeghipour, J.A. Dopkin, and K.Li, A computer aided finite element experimental analysis of induction heating process of steel, Computers in Industry, Vol. 28, No. 3, pp. 195-205, 1996.
    [16] C. Chaboudez, S. Clain, R. Glardon, D Mari, J. Rappaz, and M. Swierkosz, Numerical modeling in induction heating for axisymmetric geometries, IEEE Transactions on Magnetics, Vol. 33, No. 1, pp. 739-745, 1997.
    [17] A. Bermúdez, D. Gómez, M.C. Muñiz, and P. Salgado, Transient numerical simulation of a thermoelectrical problem in cylindrical induction heating furnaces, Advances in Computational Mathematics, Vol. 33, No. 1, pp. 739-745, 2007.
    [18] A. Bermúdez, D. Gómez, M.C. Muñiz, P. Salgado, and R. Vázquez, Numerical simulation of a thermo-electromagneto-hydrodynamic problem in an induction heating furnace, Applied Numerical Mathematics, Vol. 59, No. 9, pp. 2082-2104, 2009.
    [19] M. Kranjc, A. Županič, T. Jarm, and D. Miklavčič, Optimization of induction heating using numerical modeling and genetic algorithm, Institute of Electrical and Electronics Engineers, pp. 2104-2108, 2009.
    [20] M.H. Tavakoli, H. Karbaschi, and F. Samavat, Influence of workpiece height on the induction heating process, Mathematical and Computer Modelling, Vol. 54, No. 1-2, pp. 50-58, 2011.
    [21] M.W. Kennedy, S. Akhtar, J.A. Bakken, and R. E. Aune. Analytical and experimental validation of electromagnetic simulations using COMSOL®, re inductance, induction heating and magnetic fields. Submitted to the COMSOL Users Conference, Stuttgart Germany. 2011.
    [22] K. Djellabi and M. E. H. Latreche, Induction heating process design using Comsol® multiphysics software version 4.2a, International Journal of Electrical and Computer Engineering, No. 8, pp. 72-75, 2014.
    [23] H.T. Bui and S.J Hwang, Modeling a working coil coupled with magnetic flux concentrators for barrel induction heating in an injection molding machine, International Journal of Heat and Mass Transfer, No. 86, pp. 16-30, 2015.
    [24] C.G. Kang, P.K. Seo, and H.K. Jung, Numerical analysis by new proposed coil design method in induction heating process for semi-solid forming and its experimental verification with globalization evaluation, Materials Science and Engineering A-Structural Materials Properties Microstructure and Processing, Vol. 341, No. 1-2, pp. 121-138, 2003.
    [25] M.S. Huang and Y.L. Huang, Effect of multi-layered induction coils on efficiency and uniformity of surface heating, International Journal of Heat and Mass Transfer, Vol. 53, No. 11-12, pp. 2414-2423, 2010.
    [26] H. Shen, Z.Q. Yao, Y.J. Shi, and J. Hu, Study on temperature field induced in high frequency induction heating, Acta Metallurgica Sinica, Vol.19, No. 3, pp. 190-196, 2006.
    [27] S.C Nian, C.W. Lien, and M.S. Huang, Experimental rapid surface heating by induction for injection molding of large LCD TV frames, Journal of Polymer Engineering, Vol. 34, No. 2, pp. 173-184, 2014.
    [28] S.C. Nian, S.W. Tsai, M.S. Huang, R.C. Huang, and C.H. Chen, Key parameters and optimal design of a single-layered induction coil for external rapid mold surface heating, International Communications in Heat and Mass Transfer, No. 57, pp. 109-117, 2014.
    [29] S.Y. Shih, S.C. Nian, and M.S. Huang, Comparison between single- and multiple-zone induction heating of largely curved mold surfaces, International Communications in Heat and Mass Transfer, No. 75, pp. 24-35, 2016.
    [30] H.P. Liu, X.H. Wang, L.Y. Si, and J. Gong, Numerical simulation of 3D electromagnetic-thermal phenomena in an induction heated slab, Journal of Iron and Steel Research International, 2020.
    [31] M.G. Cooper, B.B. Mikic, and M.M. Yovanovich, Thermal contact conductance, International Journal in Heat and Mass Transfer, Vol. 12, No. 3, pp. 279-300, 1969.
    [32] M.M. Yovanovich, Thermal contact correlations, Spacecraft Radiative Transfer and Temperature Control, Vol. 83, pp. 83-95, 1981.
    [33] M.M. Yovanovich, A. Hegazy, and J. Devaal, Surface hardness distribution effects upon contact, gap and joint conductances, Materials Science, 1982.
    [34] A.A. H. Hegazy, Thermal Joint Conductance of conforming rough surfaces: effect of surface micro-hardness variation, Waterloo, Ontario, 1985.
    [35] J.A. Greenwood and J.B. Williamson, Contact of nominally flat surfaces, Proceedings of The Royal Society of London Series A-Mathematical and Physical Sciences, Vol. 295, No. 1442, pp. 300-319, 1966.
    [36] B.B. Mikic, Thermal contact conductance; theoretical considerations, International Journal in Heat and Mass Transfer, Vol. 17, pp. 205-214, 1974.
    [37] M.R. Sridhar and M.M. Yovanovich, Review of Elastic and Plastic Contact Conductance Models: Comparison with Experiment, Journal of Thermophysics and Heat Transfer, Vol. 8, No. 4, pp. 633-640, 1994.
    [38] M.R. Sridhar and M. M. Yovanovich, Elastoplastic contact conductance model for isotropic conforming rough surfaces and comparison with experiments, Journal of Heat Transfer-Transactions of The Asme, Vol. 118, No. 1, pp. 3-9, 1996.
    [39] W.B. Kim and S.J. NA, A study on residual-stresses in surface hardening by high-frequency induction-heating, Surface and Coatings Technology, Vol. 52, No. 3, pp. 281-288, 1992.
    [40] F. Bay, V. Labbe, Y. Favennec, and J.L. Chenot, A numerical model for induction heating processes coupling electromagnetism and thermomechanics, International Journal for Numerical Methods in Engineering, Vol. 58, No. 6, pp. 839-867, 2003.
    [41] S.A. Halvorsen, A Model for High Temperature Inductive Heating, Gimlemoen 19, N-4630 Kristiansand, Norway, 2009.
    [42] A.A. Bhatti, Z. Barsoum, H. Murakawa, and I. Barsoum, Influence of thermo-mechanical material properties of different steel grades on welding residual stresses and angular distortion, Materials and Design, No. 65, pp. 878-889, 2015.
    [43] A. Riccioa, A. Russoa, A. Raimondoa, P. Cirillob, and A. Caraviellob, A numerical/experimental study on the induction heating of adhesives forcomposite materials bonding, materials today communications, No. 15, pp. 203-213, 2018.
    [44] V. Rudnev, D. Loveless, R. Cook, and M. Black, Handbook of induction heating, Basel: Marcel Dekker AG, New York, 2003.
    [45] J.C. Maxwell, A dynamical theory of the electromagnetic field, Philos Trans R Soc London, Vol. 155, pp. 459-512, 2006.
    [46] J.M. Jin, The Finite Element Method in Electromagnetics, John Wiley & Sons, 2015.
    [47] A. Holm, A. Johannes, and K. Wolfgang, Mechanics of Composite Structural Elements, Singapore Pte Ltd: Springer Nature, 2018.
    [48] D.L. Deborah, Composite Materials Science and Applications, London Dordrecht Heidelberg New York: Springer, 2010.
    [49] B. Sareni, L. Krahenbuhl, and C. Brosseau, Effective dielectric constant of periodic composite materials, Journal of Applied Physics, Vol. 80, No. 3, pp. 1688-1696, 1996.
    [50] X. Nan and C.R. Sullivan, An Equivalent Complex Permeability Model for Litz-Wire Windings, IEEE Transactions on Industry Applications, Vol. 45, No. 2, pp. 854-860, 2009.
    [51] T. Sasaki, S. Takada, F. Ishibashi, I. Suzuki., S. Noda, and M. Imamura, Magnetostrictive vibration of euclxical steel sheets under a non-sinusoidal magnetizing condition, Ieee Tansactions on Magnetics, Vol. 23, No. 5, pp. 3077-3079, 1987.
    [52] A. Mohammed. Numerical Prediction of Magnetostrictive Behavior in Non-oriented Electrical Steel Sheets, Paper presented at the Proceedings. IEEE SoutheastCon 2001, Clemson, SC, USA, 2001.
    [53] Handbook of Chemistry and Physics, 65th edition. CRC Press:Boca Raton, FL, USA, pp. F114-F120. 1984-1985.
    [54] K. C. Mills, Y. SU, Z. LI, and R. F. Brooks, Equations for the calculation of the thermo-physical properties of stainless steel, Isij International, Vol. 44, No. 10, pp. 1661-1668, 2004.
    [55] L.P. Bendel, F.G. Shellock, and M. Steckel, The effect of mechanical deformation on magnetic properties and MRI artifacts of type 304 and type 316L stainless steel, Jmri-Journal of Magnetic Resonance Imaging, Vol. 7, No. 6, pp. 1170-1173, 1997.
    [56] A. moreau, S.E. Kruger, M. Côté, and P. Bocher, In-Situ Monitoring of Microstructure during Thermomechanical Simulations using Laser-Ultrasonics, Paper presented at the 1st International Symposium on Laser Ultrasonics: Science, Technology and Applications, Montreal, Canada, 2008.
    [57] C. Gautam, J. Joyner, A. Gautam, J. Raoc, and R. Vajtaia, Zirconia based dental ceramics: structure, mechanical properties, biocompatibility and applications, Dalton Transactions, Vol. 45, No. 48, pp. 19194-19215, 2016.
    [58] G. Struzziero, B. Remy, and A.A. Skordos, Measurement of thermal conductivity of epoxy resins during cure, Journal of Applied Polymer Science, Vol. 136, No. 5, pp. 1-10(47015), 2019.
    [59] W. Cui, F. Du, J. Zhao, W. Zhang, Y. Yang, X Xie, and Y. W. Mai, Improving thermal conductivity while retaining high electrical resistivity of epoxy composites by incorporating silica-coated multi-walled carbon nanotubes, Carbon, Vol. 49, No. 2, pp. 495-500, 2011.
    [60] L. Suna, W.J. Booa, A. Clearfieldb, H.J. Suea, and H.Q. Phamc, Barrier properties of model epoxy nanocomposites, Journal of Membrane Science, Vol. 318, No. 1-2, pp. 129-136, 2008.
    [61] M. Kozako, Y. Okazaki, M. Hikita, and T. Tanaka, Preparation and evaluation of epoxy composite insulating materials toward high thermal conductivity, 2010 10th IEEE International Conference on Solid Dielectrics, Potsdam, Germany, 2010.
    [62] S. D. Pawar, P. Murugavel, and D.M. Lal, Effect of relative humidity and sea level pressure on electrical conductivity of air over Indian Ocean, Journal of Geophysical Research-Atmospheres, Vol. 114, 2009.
    [63] B.D. Cullity and C.D. Graham. Introduction to Magnetic Materials, 2nd Edition. John Wiley & Sons:Hoboken, New Jersey, USA, 2008.
    [64] L.G. Hector and H.L. Schultz, The Dielectric Constant of Air at Radiofrequencies, Physics-a Journal of General and Applied Physics, Vol. 7, No. 1-2, pp. 133-136, 1936.
    [65] K.N. Babu. THERMAL CONTACT RESISTANCE: EXPERIMENTS AND SIMULATIONS. Department of Applied Mechanics chalmers university of technology Gothenburg, Sweden, 2015.
    [66] L. Bianchi, A.C. Leger, M. Vardelle, A. Vardelle, and P. Fauchais, Splat formation and cooling of plasma-sprayed zirconia, Thin Solid Films, Vol. 305, No. 1-2, pp. 35-47, 1997.
    [67] F. Borghi, B. Scaparra, C. Paternoster, P. Milani, and A. Podesta, Electrostatic Double-Layer Interaction at the Surface of Rough Cluster-Assembled Films: The Case of Nanostructured Zirconia, Langmuir, Vol. 34, No. 35, pp. 10230-10242, 2018.
    [68] B. Kerkwijk, A.J.A. Winnubst, H. Verweij, E.J. Mulder, H.S.C. Metselaar, and D.J. Schipper, Tribological properties of nanoscale alumina–zirconia composites, Wear, Vol. 225, No. 2, pp. 1293-1302, 1999.

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