连铸坯凝固过程传热模型与热应力场模型的研究及应用
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摘要
连铸生产中,常常由于不合理的浇注工艺和二冷配水制度导致铸坯内部产生质量缺陷,特别是以中间裂纹和中心裂纹为代表的铸坯裂纹缺陷占总质量缺陷的50%以上。为了消除铸坯内部裂纹缺陷,必须对内部裂纹产生的机理进行研究,并对其凝固过程进行控制。在实际生产过程中,由于受设备、流程和突发事情等因素的影响,过热度和拉速等工艺参数经常发生变化,使得基于稳定条件下建立的凝固传热模型在应用过程中往往满足不了生产高品质钢的要求;另一方面,为了消除铸坯内部裂纹等缺陷,必须对裂纹源和裂纹扩展的机理进行分析,从而为提出预防裂纹产生的措施,并为优化二冷水量改善铸坯质量提供理论依据。因此,热弹塑性应力场模型和实时凝固传热模型的研究对铸坯内部质量的提高具有实际意义。
     本文以方坯凝固过程中出现的内部裂纹为研究对象,以减少乃至消除内部裂纹缺陷为主要目标。为了消除铸坯内部裂纹,就必须对产生内部裂纹的原因进行研究,这就要求对铸坯截面热应力分布及影响因素进行分析,为此必须建立铸坯热弹塑性应力场模型。由于传热模型是热应力场模型的基础,因此对传热模型也进行了深入的研究,并将应力场模型和传热模型在现场进行了应用研究。主要研究内容与创新工作如下:
     (1)二维热弹塑性应力场模型的建立及内部裂纹产生的机理研究
     针对以中间裂纹和中心裂纹为表征的内部裂纹是各现场存在的主要内部缺陷,建立二维热弹塑性应力场模型对裂纹产生的机理进行了研究。
     通过应力场模型对铸坯应力分布和裂纹产生的原因进行了分析,提出了裂纹是由于铸坯表面温度回温过高导致铸坯凝固前沿过大的拉应力和凝固前沿凝固速率的不均造成的,并指出裂纹源是发生在补缩边界与固相边界之内,向着固相扩展。而过热度偏高和拉速波动频繁加剧了柱状晶生长速度不均从而加剧内部裂纹产生和扩展。通过钢种的性能和模型的分析,提出在二冷区最好使铸坯表面温度减少波动,减少各段回温的二冷优化目标。
     (2)方坯实时凝固传热模型建立及动态特性分析
     针对连铸二次冷却是影响铸坯内部质量的关键环节,因此必须对二次冷却凝固过程加以控制,也就是对铸坯温度场加以控制。由于连铸二冷区高温、水汽及铸坯表面的水膜、氧化铁皮等的影响,难以准确地测量铸坯表面温度,特别是铸坯内部温度难以测量,因此在分析连铸生产过程中浇注工艺条件频繁变化特性的基础上,建立了方坯实时凝固传热模型。
     对建立的实时凝固传热模型,利用铸坯表面温度测量和射钉测厚对其进行了校正和验证。在此基础上,分析了网格划分对模型可靠性的影响,并在实际浇注过程中,通过变化浇注条件对模型的动态特性进行了分析,通过模型的在线运行和铸坯表面温度的测量对比,模型计算和实测值最大偏差在10℃范围内,为实时传热模型的在线应用和热应力场模型奠定了基础。
     (3)连铸热应力场模型和实时传热模型的应用研究
     对某钢厂Q235普碳钢和HRB400低合金钢进行了应用研究。从现场低倍数据和模型计算分析指出,铸坯内部裂纹主要是因为不合理的二冷配水导致二冷区的高回温在凝固前沿产生较大的拉应力;同时由于过热度偏高和拉速波动频繁加剧了柱状晶生长速度不均从而加剧内部裂纹产生和扩展。通过优化二冷各段水量,并对水量优化前后铸坯截面应力分布以及现场试验相结合,确定拉速和过热度的配水系数,同时把有效拉速和过热度引入到二冷动态配水控制系统中消除了因拉速突变引起的温度大幅波动。
     该系统应用现场后,对六个月的铸坯低倍抽样检验,结果表明:Q235钢中间裂纹基本消除,中心裂纹的级别由原来大于1.0级占10.3%降低到4.7%,铸坯等轴晶区直径由优化前的φ28~32mm提高到优化后的φ35~42mm,其他缺陷的级别也在允许范围之内且比优化之前有所降低;HRB400钢中心裂纹基本消除,中间裂纹由原来大于1.0级占12.7%降低到7.4%,铸坯质量得到明显提高。
In the continuous casting process, the internal defects which can be formed in cast material are due to inappropriate casting operation and improper secondary cooling water distribution, especially the defects of cracks represented by the midway crack and centreline crack which cover over 50% of total quality problems. In order to avoid internal cracks and other defects, it is necessary to make studies on the formation mechanism of internal cracks and control the process of solidification. The casting conditions such as pouring temperature and casting speed fluctuate frequently caused by change of equipments, process and rhythm etc, so that the heat transfer model which is built based on the static conditions cannot meet the requirements of making high-quality billet. On the other hand, the formation mechanism of internal cracks should be studied in order to avoid internal cracks, which will offer theoretical grounds for the preventing of the occurrence of internal cracks and the optimization of secondary cooling water flow to improve the strand quality. Thus, it is of practical significance to study the real-time heat transfer model and thermal stress model to improve the billet quality.
     With the internal crack of solidification process as the research object, and eliminating the internal crack as the final target, this dissertation was formed. In order to avoid the internal crack, the reason of internal crack generation was studied. The stress model was established to analyse the stress distribution and influence factors. The heat transfer model was systemically studied because it is the basis of the thermal stress model. The heat transfer model and thermal stress model were applied to the industrial caster. The main content and innovations are as follows:
     (1) Establishing two-dimensional thermal elasto-plastic stress model and researching the formation mechanism of internal cracks
     The internal cracks such as midway crack and centreline crack are the main internal defect. A two-dimensional thermal elasto-plastic stress model was established to analyze the formation mechanism of internal cracks.
     The billet thermal stress distribution and the formation mechanism of internal cracks were analyzed by the model. It was presented that the internal cracks were caused by excessive surface reheating and solidification velocity disproportionation. The cracks occur between shrinkage boundary and solidoid boundary and spread to the solidoid boundary. Meanwhile, the high superheat and frequent casting speed fluctuation aggravated the expansion of cracks. By means of analysis of mechanical properties of steel and model, the surface temperature fluctuation should be reduced and the reheating should be decresased in each section of secondary cooling zones.
     (2) Establishing the real-time heat transfer and solidification model and analysing the dynamic performance of billet temperature field
     Secondary cooling control is one of the key techniques of influencing the quality of billet. The solidification process in the secondary cooling should be controlled, which is equal to control the temperature field of billet.Owing to the influence of high-temperature, water vapor, water film and scales on the strand surface, etc in the secondary cooling zone, it is difficult to measure the billet surface temperature accurately, let alone the internal temperature. According to the frequent changes of casting processes in the continuous casting production, a two-dimensional real-time heat transfer and solidification model was established.
     In order to correct and test the real-time heat transfer and solidification model, the surface temperature and shell thicknesses were measured by the thermal imager and nail shooting respectively. The the influence of the grid division to the reliability of the model was analyzed. The dynamic performance and response to operation conditions were tested by changing casting conditions. The maximum deviation between the calculated surface temperature and measued ones were below 10°C at measured point by changing operation conditions, the foundation which the real-time model was on-line application and the thermal stress model was established.
     (3) Application research of thermal stress model and real-time heat transfer model for the control system of billet continuous casting
     The application research of steel grade Q235 and HRB400 were performed in a steel plant. On the basis of model calculation and the results of experimentation, the improper secondary cooling water distribution which leads to high reheating between sections in secondary cooling zone was the major cause of internal cracks. Meanwhile, the high superheat and frequent casting speed fluctuation aggravated the expansion of cracks. The secondary cooling water was optimized, and the stress distribution was calculated before and after the optimization of secondary cooling water. The water distribution coefficients of casting speed and superheat were obtained. The fluctuation of surface temperature was reduced greatly during casting speed abrupt changing beacuse the superheat and effective casting speed were imported in the dynamic secondary cooling control system
     After the system was applied to the field, the analysis of macrostructure random specimens of six months showed that the Grade Q235 centreline cracks were basically eliminated and the midway cracks above 1.0 degree has been dropped from 10.3%o 4.7%. The equiaxed grains diameter has risen up from 28~32mm to 35~42mm, and other defect grades have been reduced; the Grade HRB400 centreline cracks were basically eliminated and the midway cracks above 1.0 degree has dropped from 12.7%to 7.4%. The quality of products has been improved obviously
引文
1.蔡开科,程士富.连续铸钢原理与工艺[M],北京:冶金出版社,1994,302-358
    2.卢盛意等.连铸坯质量[M],北京:冶金工业出版社,1994,10-17.
    3.周尧和,胡壮麟,介万奇.凝固技术[M],北京:机械工业出版社,1998.
    4.熊毅刚.板坯连铸[M],北京:冶金工业出版社,1994.
    5.蔡开科.连铸坯裂纹[J],钢铁,1982,(9),45-49.
    6.大桥彻郎.连铸坯内部裂纹与表面裂纹的形成机理[J],钢铁,1982,17(3):674-691
    7.C.M.Chimani,H.Resch,K.Morwald,O.Kolednik.Precipitation and phase transformation modelling to predict surface cracks and slab quality[J],Ironmaking and Steelmaking,2005,Vol 32,No.1,75-79.
    8.Toru KATO,Yoshiki ITO,Masayuki KAWAMOTO,Akihiro YAMANAKA,Tadao WATANABE.Prevention of Slab Surface Transverse Cracking by Microstructure Control[J],ISIJ International,2003,Vol.43,No.11,1742-1750.
    9.T.Nozaki,J.I.Matsuno,K.Murata,H.Ooi,and M.Kodama,A Secondary Cooling Pattern for Preventing Surface Cracks of Continuous Casting Slab[J],Trans.Iron Steel Inst.Jpn,1978,Vol.18(6),pp.330-338.
    10.Brian G.Thomas.Continuous Casting of Steel[M],O.Yu,editor,Marcel Dekker,New York,NY,2001:499-540.
    11.朱立光,周建宏,王硕明,王迎春,李建新,刘战玲.基于目标温度的方坯连铸二冷配水方案优化,炼钢,2006,Vol.22,No.2,34-38.
    12.蔡开科.连铸二冷区凝固传热及冷却控制[J],河南冶金,2003,Vol.11(1):3-7
    13.Karl M(o|¨)rwald,Kurt Dittenberger.,Gerald Hohenbichler.Improvement of Secondary Cooling Control by On-line Temperature Calculation[J],Steelmaking conference proceedings[C],1997:583-590.
    14.山中章裕,冈村一男,金泽敬.连铸坯内裂产生的机理[J],铁と钢,1996,Vol 82(12):35-40.
    15.李金,谭连兵.小方坯内部裂纹成因研究[J],湖南冶金,2002,No.5:24-27
    16.李殿明,张明祥,陶金波.高拉速方坯内部裂纹产生原因分析[J],山东冶金,1999,Vol2(1):40-43
    17.陈伟庆,南晓东,张克强.高碳钢连铸小方坯缩孔及中心偏析的研究[J],河南冶金,2003,11(1):8-11.
    18.Fernando camisani-calzolari,Ian Craig,Chris pistorius.Mould Temperature Control in Continuous Casting for the Reduction of Surface Defects[J].ISIJ International.Vol.44(2004) No.8.1393-1402.
    19.Noriko KUBO,Jun KUBOTA1) and Toshio ISHII.Simulation of Sliding Nozzle Gate Movements for Steel Continuous Casting[J],ISIJ International,2001,Vol.41,No.10,1221-1228.
    20.史宸兴.实用连铸冶金技术[M],北京:冶金工业出版社,1998,29-49,262-272
    21.A.Grill,K.Schwerdtfeger.Finite-element analysis of bulging produced by creep in continuously cast steel slabs[J],Ironmaking and Steelmaking,1979,No.3,131-135.
    22.Bernardin J.D.,I.Mudawar I.A Cavity Activation and Bubble Growth Model of the Leidenfrost Point[J],Journal of the ASME,2002,Vol.124:864-887.
    23.干勇,仇圣桃,萧泽强.连铸铸钢过程数学物理模拟[M].北京:冶金工业出版社,2001.249-277.
    24.熊守美,许庆彦,康进武.铸造过程模拟仿真技术[M].北京:机械工业出版社,2004.278-325.
    25.B.C.鲁捷斯等.连续铸钢原理[M],上海:上海人民出版社,1977.
    26.J.K.Brimacombe,I.V.Samarasekera,J.E.Lait.Continuous Casting-Heat Flow,Solidification and Crack Formation[J].Iron and Steel Society,AIME,New York,(1984),26.
    27.A.Grill,J.K.Brimacombe,F.Weinberg.Mathematical analysis of stresses in continuous casting of steel[J].Ironmaking and Steelmaking,1976.No.1,38-47.
    28.J.K.BRIMACOMBE,K.SORIMACHI.Crack formation in the continuous casting of steel [J],Metallurgical transactions B,1977,Vol.SB:489-505.
    29.K.Sorimachi,J.K.Brimacombe.Improvements in mathematical modeling of stresses in continuous casting of steel[J].Ironmaking and Steelmaking,1977,No.4,240-245.
    30.Sorimachi K,Brimacobe J K.Improvements in mathematical modeling of stress in Continuous casting of steel[J],Ironmaking and Steelmaking,1977,4(4):240-245.
    31.G.Van Drunen,J.K.Brimacombe,and F.Weinberg.Internal cracks in strand-cast billets [J],Ironmaking and Steelmaking,2(1975),125.
    32.A.A.I.Manesh,Fayetteville and L.J.Segerlind,East Lansing.Simulation of heat transfer and stress analysis of continuous casting[J],Archive of Applied Mechanics 6i (1991) 393-403.
    33.CHUNSHENG LI,BRIAN G.THOMAS.Thermomechanical Finite-Element Model of Shell Behavior in Continuous Casting of Steel[J],Metallurgical transactions B,2004,35B,1151-1172.
    34.En-Gang Wang,Ji-Cheng He.Finite element numerical simulation on thermo-mechanical behavior of steel billet in continuous casting mold [J], Science and Technology of Advanced Materials, 2001, 2, 257-263.
    
    35. T.C. Tszeng, S. Kobayashi. Stress analysis in solidification processes application to continuous casting [J]. Int. J. Mach. Tools Manufact. 1989,29(1): 121-140
    
    36. Klaus Schwerdtfeger, Mitsuru Sato, Karl-Hermann Tacke. Stress Formation in Solidifying Bodies. Solidification in a Round Continuous Casting Mold [J], Metallurgical transactions B, 1998, 29B, 1057-1068.
    
    37. A.A.I.Manesh, Fayetteville, L.J.Segerlind, East Lansing, Simulation of heat transfer and stress analysis of continuous casting [J]. Archive of applied mechanics, 1991, 61, 393-403.
    
    38. Michel BELLET and Alban HEINRICH. A Two-dimensional Finite Element Thermomechanical Approach to a Global Stress-Strain Analysis of Steel Continuous Casting [J]. ISIJ International, Vol.44(2004), pp.1686-1695.
    
    39. M.Janik, H.Dyja, S.Berski and GBanaszek. Two-dimensional thermomechanical analysis of continuous casting process [J]. Journal of Materials processing Technology, 153-154(2004), 578-582.
    
    40. J. M. Risso, A. E. Huespe and A. Cardona. Thermal stress evaluation in the steel continuous casting process [J], Int. J. Numer. Meth. Engng 2006, 65:1355-1377.
    
    41. M. Uehara, I.V.Samarasekera, J.K.Brimacombe, Mathematical modeling of unbending of continuously cast steel slabs [J], Ironmaking and Steelmaking, 1986, Vol.13, No.3, 138-153.
    
    42. J.H.Hattel, P.N.Hansen. A control volume-based finite difference method for solving the equilibrium equations in terms of sidplacements [J]. Appl. Math. Modeling 1995, Vol.19, 219-238.
    
    43. Jung-Eui LEE, Heung Nam HAN, Kyu Hwan OH, Jong-Kyu YOON. A fully coupled analysis of fluid flow, heat transfer and stress in continuous round billet casting [J], ISIJ International, Vol. 39(1999), No.5, 435-444.
    
    44. A.A.I.Manesh. Thermo-elastic stress analysis to predict design parameters of continuous casting [J], Journal of materials science, 1992, 27, 4097-4106.
    
    45. F. Pascon, S. Cescotto, A. M. Habraken. A 2.5D finite element model for bending and straightening in continuous casting of steel slabs [J], Int. J. Numer. Meth. Engng 2006, 68:125-149.
    
    46. J.Konishi, M.Miltzer, J.K.Brimacombe, I.V.Samarasekera. Modeling the Formation of Longitudinal Facial Cracks during Continuous Casting of Hypoperitectic Steel [J], Metallurgical transactions B, 2002, 33B, 413-423.
    
    47. L.G.Zhu, R.V.Kumar, Modelling of steel shrinkage and optimization of mould taper for high speed continuous casting[J],Ironmaking and Steelmaking,2007,Vol 34,No.1,76-82.
    48.Van Drunen.G.,Brimacombe.J.K.,Weinberg.F.Internal cracks in strand-cast billets[J],Ironmaking and Steelmaking(Quarterly),1975,No.2:125-133.
    49.G.Van Drunen,J.K.Brimacombe etal.Interal cracks in strand-cast billets[J],Ironmaking and Steelmaking,1975,(2):125-132.
    50.J.K.Brimaconbe,E.B.Hawbolt,etal.Formation of off-corner internal cracks in continuously-cast billets[J].Canadian metallurgical quarterly,1980,19:215-227.
    51.Barber B,Lewis B A,Leckenby B M.Finite element analysis of strand deformation and strain distribution in solidifying shell during continuous slab casting[J],Ironmaking and Steelmaking,1985,12(4):131-135.
    52.Royzman Seinyon E.板坯凝固过程中的热应力[J],武钢技术,1998,36(12):29-33
    53.Kozlowski P F,Thomas B G,Azzli J A et al.Simple constitutive equations for steel at high temperature[J],Metal.Trans.1992,23A(3):903-917
    54.荆德君,蔡开科.连铸结晶器内铸坯温度场和应力场耦合过程数值模拟[J],北京科技大学学报,2000,22(5):417-421
    55.张克强,李永东.方坯高碳钢连铸中心缩孔模型及其应用[J],北京科技大学学报,2001,Vol.23,No.6,511-513.
    56.Ren J,Wang Z.Analysis of bulging and strain for continuously cast slab as thermoelastic continuously beam[J],Ironmaking and Steelmaking,1998,25(5):394-397
    57.蔡开科,党紫九.连铸钢高温力学性能专辑[J],北京科技大学学报,1993.Vol.15增刊(2),19-23.
    58.赖朝彬,黄庆芳.连铸坯高温力学性能研究[J],江西冶金,1997,Vol.17(6):7-9
    59.蔡开科.连铸坯裂纹与钢的高温性能[J],连铸,1994,No.4:421-429
    60.蔡开科.碳钢凝固的包晶转变与连铸坯裂纹[J],连铸,1994,No.3:391-398
    61.马竹梧.钢铁工业自动化进展与展望[J],中国冶金,196,No.6:27-36
    62.陶文铨等.数值传热学[M],西安:西安交通大学出版社,2001,78-104.
    63.V.R.Voller.Advances in Numerical Heat Transfer[M],W.J.Minkowycz and E.M.Sparrow,1997,345-352.
    64.陈雷等.连续铸钢[M],北京:冶金工业出版社,1994,16-19.
    65.J.Savage and W.H.Pritchard,The problem of rupture of the billet in the continuous casting of steel[J],J.Iron Steel Inst.,178(1954),267.
    66.J.E.Lait,J.K.Brimacombe,and F.Weinberg.Mathematical modeling of heat flow in the continuous casting of steel[J],lronmaking and Steelmaking,1974,1(No.2),90.
    67. Mizikar, E.A. Spray Cooling Investigation for Continuous Casting of Billets and Blooms [J], Iron and Steel Engineer, 47(1970), 53.
    
    68. Takaho Kawawa, Hideki Sato, etal. Determination of solidifying shell thickness of continuously cast slab by rivet pin shooting [J], 1974, (2):206-216.
    
    69. J.K.Brimacombe. Design of continuous casting machines based on a heat-flow analysis: state-of-the-art review [J]. Canadian metallurgical quarterly, 1976, Vol.15 (2), 163-175.
    
    70. M.Salcudean, Z.Abdullah. On the numerical modeling of heat transfer during solidification processes [J], International journal for numerical methods in engineering, 1988, Vol.25, 445-473.
    
    71. M.Salcudean, Z.Abdullah, Mackenbrock, A.Tacke, K. H. Generalized enthalpy method for multi-component phase change [J], Metallurgical and Materials Transactions B, 1996, Vol.27(5): 871-882.
    
    72. Bo Rogberg. Testing and Application of a Computer Program for Simulating the Solidification Process of a Continuously Cast Strand [J], Scandinvian Journal Metallurgy 12(1983), 13-21.
    
    73. V.R.Voller, C.Prakash. A Fixed Numerical Modeling Methodology for Convection-Diffusion Mushy Region Phase-Change Problems [J], Int. J. Heat Mass Transfer. 1987,30:1709-1719.
    
    74. E. Laitinen, P. Neittaanm¨aki. On Numerical Simulation of the Continuous Casting Process [J], J. Engrg. Math., 1988, Vol.22 (5), 335-354.
    
    75. Louhenkilpi, Seppo. Study of heat transfer in a continuous billet casting machine[J], Scandinavian Journal of Metallurgy, 1994, Vol.23 (1):9-17
    
    76. M.El-Bealy, N. Leskinen, H. Fredriksson. Simulation of cooling conditions in secondary cooling zone in continous casting process [J], Ironmaking and Steelmaking, 1995, Vol.22(3):169-184.
    
    77. Raithby G D, Chui E H. A Finite-volume Method for Predicting a Radiant Heat Transfer in Enclosures with Participating Media [J], ASME Journal of Heat Transfer, 1990,112(5):415-423
    
    78. HONGLIANG YANG, LIANG ZHAO, XINGZHANG, KAIWEN DENG. Mathematical Simulation on Coupled Flow, Heat, and Solute Transport in Slab Continuous Casting Process [J], Metallurgical transactions B, Vol. 29B, 1998, 1345-1356.
    
    79. A. K. TIEU and I. S. KIM. Simulation of the continuous casting process by a mathematical model [J], Int. J. Mech. Sci. 1997, Vol. 39, No. 2, 185-192.
    
    80. B.Q. Li. Numerical simulation of flow and temperature evolution during the initial phase of steady-state solidification [J], Journal of Materials Processing Technology, 1997, 71, 402-413.
    81. Sang-Min LEE, Suk-YongJANG. Problems in Using the Air-mist Spray cooling and Its Solving Methods at Pohang No.4 Continuous Casting Machine [J], ISIJ International, 1996, Vol. 36, Supplement, S208-S210.
    
    82. Ian Stewart, John D. Massingham, etal. Heat transfer coefficient effects on spray cooling, Iron and steel engineer [J], 1996, (17):17-23.
    
    83. B.LALLY, L.BIEGLER, H.HENEIN. Finite Difference Heat-Transfer Modelling for Continuous Casting [J], Metallurgical and Materials Transactions B, Vol.21B, (1990), 761-770.
    
    84. Dmity Sediako, Olga Sediako, Kuan Ju Lin. Some aspects of thermal analysis and technology upgrading in steel continuous casting [J], Candian metallurgical quaterly, 1999, 38(5):377-385.
    
    85. S.K.CHOUDHARY, DMAZUMDAR, HOSH. Mathematical Modelling of Heat Transfer Phenomena in Continuous Casting of Steel [J], ISIJ international, 1993, Vol.33, No.7.
    
    86. Seppo Louhenkilpi, Mika Makinen, Sami Vapahti, Tuomo Raisanen, Jukka Laine. 3D steady state and transient simulation tools for heat transfer and solidification in continuous casting [J], Materials Science and Engineering A, 413-414 (2005), 135-138.
    
    87. M.Janik, H.Dyja. Modelling of three-dimensional temperature field inside the mould continuous casting of steel [J], Journal of Materials Processing Technology, 157-158 (2004), 177-182.
    
    88. Yao MAN, Yin HEBI and Fang DACHENG. Real-time analysis on non-uniform heat transfer and solidification in mould of continuous casting round billets [J], ISIJ International, Vol. 44(2004), No 10, 1696-1704.
    
    89. K.Morward, K. Dittenberger, K.D.Ives. Dynamic Cooling System-Features and Operational Results [J], Ironmaking and Steelmaking, 1998, Vol.25 (4):323-327.
    
    90. K H SPITZER, K HARSTE, B.WEBER, MONHEIM, K.SCHWERDTFEGER. Mathematical Model for Thermal Tracking and On-line Control in Continuous Casting [J], ISIJ International, 1992, Vol. 32, No. 7, 848-856.
    
    91. Richard A. Hardin, Kai Liu, Atul Kapoor, Christoph Beckermain. A Transient Simulation and Dynamic Spray Control Model for Continuous Steel Casting[J], Metallurgical and Materials Transactions B, 2003, Vol.34 (3): 297-306.
    
    92. R.Dautov, R.Kadyrov, E.Laitinen. On 3D dynamic control of secondary cooling in continuous casting process [J]. Lobachevskii Journal of mathematics, Vol.13, 2003, 3-13.
    
    93. Jiang G S, Boyle J R. Computer Dynamic Control of the Secondary Cooling During Continuous Casting [J], Metallurgical Press. 1993:567-570.
    
    94. Brian G. Thomas. Modeling of the continuous casting of steel past, present and future [J], Electric Furnace Conf. Proa, 2001,59: 3-30
    95.M.M.Makela,T.Mannikko.Numerical Solution of Non-smooth Optimal Control Problems with an Application to the Continuous Casting Process[J],Adv.Math.Sci.Appl.,1994,Vol.4.(5):491-515.
    96.J.Kronl,M.Bellet,A.Ludwig,B.Pustal,J.Wendt,H.Fredriksson,Comparison of numerical simulation models for predicting temperature in solidification analysis with reference to air gap formation[J],International Journal of CastMetals Research,2004Vol.17,No.5,295-310.
    97.Carlos A.Santos,Amauri Garcia,Carlos R.Frick,Jaime A.Spim.Evaluation of heat transfer coefficients along the secondary cooling zones in the continuous casting of steel billets[J],Inverse problems,Design and Optimization Symposium,2004.
    98.David A.Sinton.Computational modeling of solid-liquid phase change with application to continuous casting[D].Quebec:the degree of master of engineering McGill University,2000.
    99.王地君.硫印技术在铸机诊断上的应用[J],四川冶金,1998,No.5:60-62.
    100.张克强,蔡开科.连铸二冷区水冷喷嘴的结构与冷却特性[J],连铸通讯,1982,No.2:47-52
    101.徐荣军,陈念贻,刘洪霖.基于模式识别和人工神经网络建立的板坯连铸二冷水模型[J],钢铁,2001,Vol.36(2):26-28.
    102.Stefane Bazozzl,Piergiorgio Fontana etal.Computer control and optimization of secondary cooling during continuous casting[J].Iron and Steel Engineer.1986,(12):21-26
    103.Kelgo Okuno,Takashi Kurlbayash etal.Dynamic spray cooling control system for continuous casting[J],Iron and Steel Engineer.1987,(4):34-38
    104.Laitinen Erkki,Rekkil(a|¨) Mika etal.Control of steel solidification in continuous casting process[J],Ironmaking Conference Proceedings.1997:647-653
    105.张克强,林宪,高海,林剑平,吕森强.方坯连铸二级配水技术研究[J],钢铁,2006,Vol.41,No.1,39-42.
    106.郭戈.连铸过程建模与控制方法的研究[D],沈阳:东北大学,1998.
    107.陈家祥.连续铸钢手册[M],北京:冶金工业出版社,1991,191-194
    108.J.Savage et al.,Improvement in centre segregation of high carbon steel continuous casting[J],ISIJ,.1954,Vol.178,269-275.
    109.J.E.Lait et la.,New techniques in EAP Steel making Process[J],Ironmaking ans steelmaking,1974,Vol.1,No.2,90-95.
    110.E1-Bealy.M.On the mechanism of halfway cracks and macro-segregation in continuously cast steel slabs.(Ⅱ).Macro-segregation.Source[J],Scandinavian Journal of Metallurgy,1995,Vol.24(3):106-120.
    111.王成,邵敏.有限单元法基本原理和数值方法[M],北京:清华大学出版社,1997,90-98
    112.颜云辉,谢里阳,韩清凯.结构分析中的有限单元法及其应用[M],沈阳:东北大学出版社,2000:113-127.
    113.C.A.Santos,J.A.Spim,A.Garia,Mathematical modeling and optimization strategies (genetic algorithm,and knowledge base) applied to the continuous casting of steel[J],Engineering Apphcations of Artificial Intelligence,16(2003) 511-527.
    114.C.A.Santos,Jaime A.The use of artificial intelligence technique for the optimization of process parameters used in the continuous casting of steel[J].Applied Mathematical Modelling,2002,26:1077-1092.
    115.Wu Rongyang,Mei Guohui,Meng Hongji,Ci Ying,Xie Zhi.Optimization of the water rate in secondary cooling zone of continuous casting billet by using particle swarm optimization algorithm[J].Conference proceedings of Materials Science and Technology 2004,211-216.
    116.B.Lally,L.T.Biegler,H.Henein.Optimization and continuous casting:Part Ⅰ.Problem formulation and solution strategy[J].Metallurgical transactions B,1991,Vol 22B,641-569.
    117.Lally.B.,Biegler.L.T.,Henein,H.,Henein.Optimization and Continuous Casting:Part Ⅱ.Application to Industrial Caster[J],Metallurgical Transactions B,1991,Vol.22(7):649-659
    118.Santos.C.A,Spim Jr.J.A.,Ierardi.M.C.F,Garcia,A.The Use of Artificial Intelligence Technique for the Optimization of Process Parameters Used in the Continuous Casting of Steel[J],Applied Mathematical Modeling,2002,Vol.26(11):1077-1092.
    119.J.Kennedy and R.C.Eberhart.Particle Swarm Optimization[J].Proc.IEEE International Conference on Neural Netwks,Piscataway[M],N J,Ⅳ,1995:1942-1948
    120.Y.H.Shi and R.C.Eberhart.A Modified Particle Swarm Optimizer[J],Proc.IEEE International Conference on Evolutionary Computation[C],Anchorage,Alaska.1998:69-73
    121.Y.Shi and R.C.Eberhart.Parameter Selection in Particle Swarm Optimization[M],Evolutionary Programming Ⅶ,1998:591-600
    122.Eberhart,R.C.,and Shi,Y.Comparing Inertia Weights and Constriction Factors in Particle Swarm Optimization[J],Proceedings of the 2000 International Congress on Evolutionary Computation[C],IEEE Service Center,Piscataway,N J,2000:84-88
    123.T.Mannikko and M.M.Makela.Nonsmooth Penalty Techniques in Control of the Continuous Casting Process [J], In Proceedings of the Conference on Numerical Methods for Free Boundary Problems [C], P. Neittaanmaki Birkhauser Verlag, Basel, 1991: 297-307.
    124.Ferdinando Roux Camisani-calzolari, Lan Keith Craig and Petrus Christiaan Pistorius. Specification Framework for Control of the Secondary Cooling Zone in Continuous Casting [J], ISIJ, Vol. 38(1998), No.5, 447-453.
    125.Ferdinando Roux Camisani-calzolari, I. K. CRAIG and Petrus Christiaan pistorius.Speed Disturbance Compenation in the Secondary Cooling Zone in Continuous Casting [J], ISIJ International, Vol. 40 (2000), No. 5, 469-477.
    126.D.Constales, J.Kacur, R.Van Keer. On the Optimal Cooling Strategy for Variable-Speed Continuous Casting [J]. International journal for numerical methods in engineering, 2002, 53, 539-565.
    127.Alexander V. Lotov, George K. Kamenev, Vadim E. Berezkin, Kaisa Miettinen. Optimal control of cooling process in continuous casting of steel using a visualization-based multi-criteria approach [J]. Applied Mathematical Modelling, 29 (2005): 653-672.
    128.X.HUANG, B.G.Thomas, F.M.Najjar. Modeling Superheat Removal during Continuous Casting of Steel Slabs [J], Metallurgical Transactions B, 1992, Vol.23 (4): 339-356.