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系統識別號 U0026-2609201315465700
論文名稱(中文) 連續退火線鋼帶之三維溫度分佈與縱向翹曲量分析
論文名稱(英文) 3-D Temperature Distribution and Longitudinal Residual Warpage Analysis of Steel Strip in Continuous Annealing Line
校院名稱 成功大學
系所名稱(中) 機械工程學系
系所名稱(英) Department of Mechanical Engineering
學年度 102
學期 1
出版年 102
研究生(中文) 康宗瑋
研究生(英文) Zong-Wei Kang
學號 N18951275
學位類別 博士
語文別 英文
論文頁數 117頁
口試委員 召集委員-陳國聲
口試委員-林震銘
口試委員-屈子正
指導教授-陳鐵城
口試委員-方得華
口試委員-朱清俊
中文關鍵字 連續退火線  有限元素法  能量平衡法  虛擬層法  翹曲 
英文關鍵字 continuous annealing line (CAL)  finite element method (FEM)  energy balance method (EBM)  virtual layer method (VLM)  warpage 
學科別分類
中文摘要 電磁鋼片主要應用於馬達和變壓器,其鐵損值對於電機產品的效率影響極大。根據國際能源機構統計分析,全球發電量約為190000億度,其中馬達就耗了46%,並排放60.4億噸二氧化碳。因此,提高馬達效率是製造業節省能源最有效的方式。
連續退火線(Continuous Annealing Line,簡稱CAL)製造的電磁鋼片於沖製E型和I型鋼片時會有明顯的翹曲現象。此幾何缺陷主要歸咎於鋼帶通過產線內爐輥時產生寬度與厚度方向不均勻塑性變形及溫度分佈所導致的殘留應力有關。且越寬的鋼帶翹曲越嚴重並可能降低產品的品質。本論文研究探討各種不同的輸入參數對鋼帶翹曲的效應。採用三種理論技術,包括有限元素法(Finite Element Method,簡稱FEM)、能量平衡法(Energy Balance Method,簡稱EBM)以及虛擬層法(Virtual Layers Method,簡稱VLM)分別計算鋼帶的應力、溫度以及塑性應變分佈。鋼帶的縱向殘留翹曲量可由此算出。我們發現,通過冷卻區爐輥時的鋼帶橫向溫度分佈與降伏強度對鋼帶的翹曲量最敏感,可能可以藉由適當的冷卻方式將翹曲量控制在可接受的範圍。
英文摘要 Electrical steel (ES) is mainly used for motors and transformers whose iron loss has a great effect on the efficiency of electrical products and may be related to the residual warpage of the strip, generally defined as a deviation from flatness on unloading. According to statistics from the International Energy Agency (IEA), global electricity production was about 19000 TWh, 46% of which is consumed by motors, leading to about 6,040 Megatonnes (Mt) of CO2 emissions. Therefore, improving the efficiency of motors is the most effective way to save energy in industry.
The electrical steel produced by continuous annealing line (CAL) exhibit a significant phenomenon of warpage during punching into the E- and I-type sheets. This geometric defect is mainly attributed to the residual stress induced by the nonuniform temperature and nonuniform plastic deformation along both the width and the thickness of strip when it passes through the rolls in the line. It becomes more serious for the wider strip and may degrade the quality of the products. In the thesis, the effects of various input parameters on the warpage of strip were investigated and discussed. Three theoretical techniques, including finite element method (FEM), energy balance method (EBM), and virtual layers method (VLM), were adopted to evaluate the distributions of stress, temperature, and plastic strain of the strip, respectively. The longitudinal residual warpage of strip can then be calculated accordingly. It was found that the warpage of strip is sensitive to the transverse temperature distributions and the yielding strength of strip as passing through the rolls in CS, which is possibly to be controlled within an accepted range by applying a suitable cooling scheme in this section.
論文目次 摘 要 I
ABSTRACT II
誌 謝 IV
CONTENTS V
LIST OF TABLES VIII
LIST OF FIGURES IX
NOMENCLATURES XII
Chapter 1 INTRODUCTION 1
1.1 Motivation 2
1.2 Literature Review 4
1.3 Objectives 6
1.4 Dissertation Organization 7
Chapter 2 CONTINUOUS ANNEALING LINE 9
2.1 Annealing treatment 10
2.2 Shapes of roll in CAL 13
2.3 Phase transformation 14
2.4 Electrical steel 18
2.5 Measurement of warpage 19
Chapter 3 MATHEMATICAL MODELS 21
3.1 Finite element method 21
3.1.1 Mechanical model of strip 22
3.1.2 Estimation of the emissivity 28
3.1.3 Thermal model of roll 30
3.1.4 Thermal model of strip 33
3.1.5 FEM Computational procedure 35
3.2 Energy balance method 36
3.2.1 Energy balances model 41
3.2.2 EBM Computational procedures 47
3.3 Virtual layers method 49
3.3.1 Virtual layers model 52
3.3.2 Residual stress of elements in straight status on unloading 56
3.3.3 Calculation of strip residual warpage 59
3.3.4 VLM Computational procedures 60
3.4 Computational procedures 61
Chapter 4 NUMERICAL RESULTS AND DISCUSSION 63
4.1 Mechanical model of strip 63
4.1.1 Contact pressure and thermal contact resistance 63
4.1.2 Tangential stress distribution of strip 65
4.2 Temperature of roll surface 66
4.3 Equivalent heat convective coefficient 67
4.4 Thermal model of strip 68
4.4.1 History of strip temperature 68
4.4.2 Effect of phase transformation 70
4.4.3 Distribution of transverse temperature 71
4.5 VLM 73
4.5.1 Reliability test 74
4.5.2 Convergence test 74
4.5.3 Final residual warpage 76
4.5.4 History of warpage 76
4.5.5 Final accumulated plastic strain 78
4.5.6 Final residual stress 79
4.5.7 History of accumulated plastic strain 79
4.5.8 Effect of strip temperature at the outlet of CAL on warpage 80
4.5.9 Effect of cooling condition in CS on warpage 82
4.5.10 Effect of strip tension on warpage 82
4.5.11 Effect of crown and cooling effect in CS on final warpage 83
4.5.12 Effect of Young’s modulus and yielding strength of strip material on warpage 85
Chapter 5 CONCLUSIONS AND FUTURE STUDIES 87
5.1 Conclusions 87
5.2 Future studies 89
REFERENCES 90
APPENDIX 97
A. Simplified finite element models [39] 97
B. Influence of centrifugal force 100
C. Distribution of thermal contact resistances 101
D. Simplification of roll surface temperature [52] 103
D.1 2D model 105
D.2 Comparison with 3-D model 106
E. Emissivities 110
F. Enclosure of sections 111
G. Rolls specification 114
VITA 117
參考文獻 [1] P. Waide, Light’s Labour’s Lost: Policies for Energy‐efficient Lighting: IEA, Paris, 2006.
[2] M. Ellis, Gadgets and Gigawatts: IEA, Paris, 2009.
[3] The Climate Group (on behalf of the Global eSustainability Initiative), Smart 2020: Enabling the Low Carbon Economy in the Information Age: The Climate Group, London, 2008.
[4] A+B International, internal report presented for this work as co‐authors, 2009.
[5] UIC (International Union of Railways), International Railway Statistics 2007, Paris, pp. 176, 2008.
[6] P. Waide and C. U. Brunner, Energy-Efficiency Policy Opportunities for Electric Motor-Driven Systems: IEA, Paris, 2011.
[7] International Energy Agency, newsroom & events, Press Releases & News, News, 2011, May.
Available:http://www.iea.org/newsroomandevents/news/2011/may/name,19833,en.html
[8] China Steel Corporation, Green steel products /ES (Non Grain-Oriented Electrical Steel).
[9] R. E. R. Hill and R. Abbaschian, Physical Metallurgy Principles (3rd Ed.): PWS-Kent Publishing Company, Boston, 1992.
[10] T. Sasaki, T. Hira, H. Abe, F. Yanagishima, Y. Shimoyama and K. Tahara, "Control of strip buckling and snaking in continuous annealing furnace," Kawasaki Steel Technical Report, vol. 9, pp. 36-46, 1984.
[11] T. Z. Chang and Q. D. Zhang, "Analysis and simulation of strip transverse buckling in CAPL," Revue De Metallurgie-Cahiers D Informations Techniques, vol. 106, pp. 257-263, Jun 2009.
[12] J. Yang, D. Tang, L. Su, H. T. Jiang and Q. Yang, "Effect of double taper roll shape on the waved surface of strips in continuous annealing process," Journal of University of Science and Technology Beijing, vol. 32, pp. 1215-1220, 2010 (in Chinese).
[13] J. Yang, D. Tang, L. Su, H. T. Jiang and Q. Yang, "Effect of roller shapes on strip buckling in a continuous annealing furnace," International Journal of Minerals Metallurgy and Materials, vol. 18, pp. 297-302, 2011.
[14] T. Matoba, M. Ataka, I. Aoki and T. Jinma, "Effect of roll crown on heat buckling in continuous annealing and processing lines," Tetsu to Hagane-Journal of the Iron and Steel Institute of Japan, vol. 80, pp. 641-646, 1994.
[15] J. Dai, Q. Zhang and T. Chang, "FEM analysis of large thermo-deflection of strips being processed in a continuous annealing furnace," Journal of University of Science and Technology Beijing, Mineral, Metallurgy, Material, vol. 14, pp. 580-584, 2007.
[16] T. Masui, Y. Kaseda and K. Ando, "Warp control in strip processing plant," Isij International, vol. 31, pp. 262-267, 1991.
[17] N. Jacques, A. Elias, M. Potier-Ferry and H. Zahrouni, "Buckling and wrinkling during strip conveying in processing lines," Journal of Materials Processing Technology, vol. 190, pp. 33-40, 2007.
[18] N. Jacques and M. Potier-Ferry, "On mode localisation in tensile plate buckling," Comptes Rendus Mecanique, vol. 333, pp. 804-809, 2005.
[19] W. D. Morris and J. O. Medwell, "Methodology for designing impingement air jet coolers for continuous annealing of steel strip," Ironmaking & Steelmaking, vol. 23, pp. 438-445, 1996.
[20] W. D. Morris, "A production planning and design model for assessing the thermal behaviour of thick steel strip during continuous heat treatment," Proceedings of the Institution of Mechanical Engineers Part E-Journal of Process Mechanical Engineering, vol. 215, pp. 53-62, 2001.
[21] M. M. Prieto, F. J. Fernandez and J. L. Rendueles, "Development of stepwise thermal model for annealing line heating furnace," Ironmaking & Steelmaking, vol. 32, pp. 165-170, 2005.
[22] M. M. Prieto, F. J. Fernandez and J. L. Rendueles,, "Thermal performance of annealing line heating furnace," Ironmaking & Steelmaking, vol. 32, pp. 171-176, 2005.
[23] C. H. Ho and T. C. Chen, "Two-dimensional Temperature Distribution of Strip in Preheating Furnace of Continuous Annealing Line," Numerical Heat Transfer Part a-Applications, vol. 55, pp. 252-269, 2009.
[24] T. C. Chen, C. H. Ho, J. C. Lin and L. W. Wu, "3-D temperature and stress distributions of strip in preheating furnace of continuous annealing line," Applied Thermal Engineering, vol. 30, pp. 1047-1057, 2010.
[25] S. R. Carvalho, T. H. Ong and G. Guimarães, "A mathematical and computational model of furnaces for continuous steel strip processing," Journal of Materials Processing Technology, vol. 178, pp. 379-387, 2006.
[26] Z. Zhou, P. F. Thomson, Y. C. Lam and D. D. W. Yuen, "Numerical analysis of residual stress in hot-rolled steel strip on the run-out table," Journal of Materials Processing Technology, vol. 132, pp. 184-197, 2003.
[27] R. Colas, L. A. Leduc and M. A. Neri, "Prediction of shape defects during cooling of hot rolled low carbon steel strip," Ironmaking & Steelmaking, vol. 31, pp. 93-96, 2004.
[28] Y. J. Junga, G. T. Lee and C. G. Kang, "Coupled thermal deformation analysis considering strip tension and with/without strip crown in coiling process of cold rolled strip," Journal of Materials Processing Technology, vol. 130, pp. 195-201, 2002.
[29] A. Saboonchi and S. Hassanpour, "Heat transfer analysis of hot-rolled coils in multi-stack storing," Journal of Materials Processing Technology, vol. 182, pp. 101-106, 2006.
[30] M. Imose, "Heating and cooling technology in the continuous annealing," Transactions of the Iron and Steel Institute of Japan, vol. 25, pp. 911-932, 1985.
[31] China Steel Corporation, Steel production flow chart, No.1 Continuous Annealing Line (#1 CAL)
Available: http://www.csc.com.tw/csc_e/pd/prs14.htm
[32] F. H. Milanez, M. M. Yovanovich and M. B. H. Mantelli, "Thermal Contact Conductance at Low Contact Pressures," Journal of Thermophysics and Heat Transfer, vol. 18, pp. 37-44, 2004.
[33] M. R. Sridhar and M. M. Yovanovicht, "Review of Elastic and Plastic Contact Conductance Models- Comparison with Experiment," Journal of Thermophysics and Heat Transfer, vol. 8, pp. 633-640, 1994.
[34] T. R. Tauchert, D. C. Leigh and M. A. Tracy, "Measurements of thermal contact resistance for steel layered vessels," Journal of Pressure Vessel Technology-Transactions of the Asme, vol. 110, pp. 335-337, 1988.
[35] W. D. Callister, Materials Science and Engineering: an Introduction (7th Ed.) Wiley Asia Student Edition: John Wiley & Sons, 2006.
[36] C. l. Chao, C. C. Huang, L. H. Lee and L. W. Chang, "Investigation on the Causes of Bow of Stamped Electrical Steel Sheet," Technology and Training, vol. 25, pp. 97-105, 2000 (in Chinese).
[37] R. Hill, The Mathematical Theory of Plasticity: Oxford University Press, USA, 1998.
[38] J. M. C. Rodrigues and P. A. F. Martins, "Coupled thermo-mechanical analysis of metal-forming processes through a combined finite element boundary element approach," International Journal for Numerical Methods in Engineering, vol. 42, pp. 631-645, 1998.
[39] J. B. Dai, Study on the strip buckling in continuous annealing production line. University of Science and Technology Beijing, 2005 (in Chinese).
[40] B. A. B. Andersson, "Thermal stresses in a submerged-arc welded joint considering phase transformations," Journal of Engineering Materials Technology-Transactions of the ASME, vol. 100, pp. 356-362, 1978.
[41] J. Goldak, M. Bibby, J. Moore, R. House and B. Patel, "Computer modeling of heat-flow in welds," Metallurgical Transactions B-Process Metallurgy, vol. 17, pp. 587-600, 1986.
[42] S. Fukuda, N. Yoshihara, Y. Ohkubo, Y. Fukuoka and S. Takushima, "Heat-transfer analysis of roller quench system in continuous annealing line," Transactions of the Iron and Steel Institute of Japan, vol. 24, pp. 734-741, 1984.
[43] A. A. Tseng, T. C. Chen and F. Z. Zhao, "Direct sensitivity coefficient method for solving two-dimensional inverse heat conduction problems by finite-element scheme," Numerical Heat Transfer, Part B: Fundamentals, vol. 27, pp. 291-307, 1995.
[44] W. H. McAdams, Heat transmission (3rd Ed.): McGraw-Hill, New York, 1954.
[45] R. J. Goldstei, E. M. Sparrow and D. C. Jones, "Natural-convection mass-transfer adjacent to horizontal plates," International Journal of Heat and Mass Transfer, vol. 16, pp. 1025-1035, 1973.
[46] S. W. Churchill and H. H. S. Chu, "Correlating equations for laminar and turbulent free convection from a vertical plate," International Journal of Heat and Mass Transfer, vol. 18, pp. 1323-1329, 1975.
[47] A. J. Chapman, Heat transfer (4th Ed.): Macmillan Publishing Company, New York, 1984.
[48] C. S. Li, H. Liu, G. D. Wang and X. M. He, "Three-dimensional FEM analysis of work roll temperature field in hot strip rolling," Materials Science and Technology, vol. 18, pp. 1147-1150, 2002.
[49] Z. F. Guo, C. S. Li, J. Z. Xu, X. H. Liu and G. D. Wang, "Analysis of temperature field and thermal crown of roll during hot rolling by simplified FEM," Journal of Iron and Steel Research International, vol. 13, pp. 27-30+48, 2006.
[50] A. A. Tseng, S. X. Tong and T. C. Chen, "Thermal expansion and crown evaluations in rolling processes (vol 17, pg 193, 1996)," Materials & Design, vol. 18, pp. 29-41, 1997.
[51] W. B. Lai, T. C. Chen and C. I. Weng, "Transient thermal stresses of work roll by coupled thermoelasticity," Computational Mechanics, vol. 9, pp. 55-71, 1991.
[52] C. H. Ho and T. C. Chen, "Temperature Distribution of Taper Rolls in Preheating Furnace of Cold Rolling Continuous Annealing Line," Heat Transfer Engineering, vol. 31, pp. 880-888, 2010.
[53] C. Zhang and L. J. Li, "A Coupled Thermal-Mechanical Analysis of Ultrasonic Bonding Mechanism," Metallurgical and Materials Transactions B-Process Metallurgy and Materials Processing Science, vol. 40, pp. 196-207, 2009.
[54] U. Gross, K. Spindler and E. Hahne, "Shaperfactor-equations for radiation heat transfer between plane rectangular surfaces of arbitrary position and size with parallel boundaries," Letters in heat and mass transfer, vol. 8, pp. 219-227, 1981.
[55] R. Siegel and J. R. Howell, Thermal radiation heat transfer: Taylor & Francis Group, 2002.
[56] Y. S. Zhao and Y. G. Xu, "Study on influence of the furnace temperature in the heating chamber on the hot waved surface of strip," Journal of East China Institute of Metallurgy, vol. 11, pp. 81-88, 1994 (in Chinese).
[57] P. F. Beer and E. R. Johnston, Mechanics of Materials (4th Ed.): McGraw-Hill Higher Education, Boston, 2006.
[58] Y. Ruan, B. Q. Li and J. C. Liu, "A finite element method for steady-state conduction-advection phase change problems," Finite Elements in Analysis and Design, vol. 19, pp. 153-168, 1995.
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