连铸二次冷却动态模型算法研究及相关软件开发
|
摘要
连铸坯二次冷却在连铸生产中占有非常重要的地位,不但关系到铸坯的质量,而且还与铸机产量密切相关。优化控制二次冷却越来越重要,而计算机数值计算和仿真技术的快速发展为二次冷却制度的制定和优化提供了便利的技术条件。通过建立连铸坯凝固传热模型、确定准确的各计算参数、编写计算程序对影响连铸坯凝固过程的各个阶段和各种工艺因素进行数值模拟,迅速、准确地找出影响连铸坯凝固过程的规律和工艺控制措施,可以提高连铸机生产能力,改善、控制铸坯内部组织结构与质量,取得更好的经济和社会效益。
济南钢铁股份有限公司第一炼钢厂一号方坯连铸机是1989年由德马克设计建成投产的,近来,设备年久以及当初设计的连铸工艺无法满足当今高效连铸技术的发展要求,在质量、产量和生产率方面均存在较大的不足。2005年由重庆大学和济南钢铁公司联合对铸机进行了二次冷却改造,建立了适应该铸机具体结构特点的方坯凝固传热数学模型,对二次冷却制度进行了优化并在此基建上开发了用加权平均速度替换瞬时速度从静态水表调用二次冷却水量进行冷却的方坯动态模型。在拉速突然变化时,方坯动态模型能对防止短时间内二次冷却强度过大或不足起积极作用。
在连铸生产过程中,改善连铸坯的凝固冷却、制定合理的二冷制度,钢种的高温物理性能和高温力学性能均十分重要。课题对广西柳州钢铁公司连铸板坯Q345和AH36两个典型钢种部分高温物理性能及高温力学性能进行了测试。测试结果为确定连铸目标表面温度曲线和其它相关参数进而为开发板坯二冷动态模型提供了重要的基础数据和依据。
为了在不同的浇注条件下对二次冷却进行良好的监测和控制以获得理想的铸坯表面温度分布,建立铸坯凝固传热数学模型仿真计算铸坯温度场分布,并根据铸坯表面温度对二冷冷却喷水量进行在线计算,以便通过控制系统使铸坯表面温度保持沿预先设定的目标表面温度变化,更好地控制铸坯质量。课题根据柳钢板坯连铸机的特点,建立了板坯连铸一维传热模型,根据表面温度计算结果和目标温度差值采用比例、积分、微分算法调整水量。
连铸板坯二次冷却动态模型选用Microsoft的VisualBasic6.0高级语言,编程实现对连铸坯各节片的动态跟踪,实时计算各节点的温度、坯壳厚度和二冷喷淋段的冷却水量,以及实现了各结果的动态显示,模型界面设计友好。
The control of secondary cooling holds very important status during continuous casting. The control of secondary cooling water spraying not only relates to the product quality directly, but also affects caster machine output closely. Perfecting secondary cooling system through optimizing is more and more important, numerical analysis and technique of simulation by computer has provided the convenient engineering facility. Constructing heat transfer of mathematic model, determining accurate computation parameter and compiling computational procedure to analog simulate the cast process, rapidly, accurately discover rule and casting craft in the solidification process of continuous casting blank that can obtain better economy and social efficiency.
NO.1 billet continuous caster in the first steelmaking plant of Jinan Iron and Steel Co. Ltd. was designed by DeMark and putted into production in 1989. Recently, because the year equipment inline is long and the continuous casting craft designed firstly can’t satisfied the high efficient continuous casting that have high requirement on quality, production rate and casting speed.
In 2005, modification works to No.1 continuous cater secondary cooling system was carried by the joint of Chongqing University and the Jinan iron and steel company. Heat transfer mathematic model of billet is built corresponding with casting machine structure of No.1 caster. Dynamic billet secondary cooling system is developed with weighted average velocity replacing actual speed to call secondary water cooling casting blank from static water list. Dynamic billet secondary cooling system can resolve excessively cooling intensity or deficiency in the secondary zone when the casting speed changes abruptly.
Research on mechanical behavior and physical property of steel casting blank under high temperature in order to ameliorate continuous casting blank solidifying process and formulate reasonable secondary cooling systems is significant. Paper select steel Q345 AH36 casting in Liuzhou Iron and Steel Company to test part of high temperature property of steel casting blank. The test result provides basic data for determining surface temperature curve of slab cooling and other calculation parameter for developing slab dynamic model.
In order to monitor and control secondary cooling in a good way under vary casting condition, calculate the amount of secondary cooling water in-line according to
济南钢铁股份有限公司第一炼钢厂一号方坯连铸机是1989年由德马克设计建成投产的,近来,设备年久以及当初设计的连铸工艺无法满足当今高效连铸技术的发展要求,在质量、产量和生产率方面均存在较大的不足。2005年由重庆大学和济南钢铁公司联合对铸机进行了二次冷却改造,建立了适应该铸机具体结构特点的方坯凝固传热数学模型,对二次冷却制度进行了优化并在此基建上开发了用加权平均速度替换瞬时速度从静态水表调用二次冷却水量进行冷却的方坯动态模型。在拉速突然变化时,方坯动态模型能对防止短时间内二次冷却强度过大或不足起积极作用。
在连铸生产过程中,改善连铸坯的凝固冷却、制定合理的二冷制度,钢种的高温物理性能和高温力学性能均十分重要。课题对广西柳州钢铁公司连铸板坯Q345和AH36两个典型钢种部分高温物理性能及高温力学性能进行了测试。测试结果为确定连铸目标表面温度曲线和其它相关参数进而为开发板坯二冷动态模型提供了重要的基础数据和依据。
为了在不同的浇注条件下对二次冷却进行良好的监测和控制以获得理想的铸坯表面温度分布,建立铸坯凝固传热数学模型仿真计算铸坯温度场分布,并根据铸坯表面温度对二冷冷却喷水量进行在线计算,以便通过控制系统使铸坯表面温度保持沿预先设定的目标表面温度变化,更好地控制铸坯质量。课题根据柳钢板坯连铸机的特点,建立了板坯连铸一维传热模型,根据表面温度计算结果和目标温度差值采用比例、积分、微分算法调整水量。
连铸板坯二次冷却动态模型选用Microsoft的VisualBasic6.0高级语言,编程实现对连铸坯各节片的动态跟踪,实时计算各节点的温度、坯壳厚度和二冷喷淋段的冷却水量,以及实现了各结果的动态显示,模型界面设计友好。
The control of secondary cooling holds very important status during continuous casting. The control of secondary cooling water spraying not only relates to the product quality directly, but also affects caster machine output closely. Perfecting secondary cooling system through optimizing is more and more important, numerical analysis and technique of simulation by computer has provided the convenient engineering facility. Constructing heat transfer of mathematic model, determining accurate computation parameter and compiling computational procedure to analog simulate the cast process, rapidly, accurately discover rule and casting craft in the solidification process of continuous casting blank that can obtain better economy and social efficiency.
NO.1 billet continuous caster in the first steelmaking plant of Jinan Iron and Steel Co. Ltd. was designed by DeMark and putted into production in 1989. Recently, because the year equipment inline is long and the continuous casting craft designed firstly can’t satisfied the high efficient continuous casting that have high requirement on quality, production rate and casting speed.
In 2005, modification works to No.1 continuous cater secondary cooling system was carried by the joint of Chongqing University and the Jinan iron and steel company. Heat transfer mathematic model of billet is built corresponding with casting machine structure of No.1 caster. Dynamic billet secondary cooling system is developed with weighted average velocity replacing actual speed to call secondary water cooling casting blank from static water list. Dynamic billet secondary cooling system can resolve excessively cooling intensity or deficiency in the secondary zone when the casting speed changes abruptly.
Research on mechanical behavior and physical property of steel casting blank under high temperature in order to ameliorate continuous casting blank solidifying process and formulate reasonable secondary cooling systems is significant. Paper select steel Q345 AH36 casting in Liuzhou Iron and Steel Company to test part of high temperature property of steel casting blank. The test result provides basic data for determining surface temperature curve of slab cooling and other calculation parameter for developing slab dynamic model.
In order to monitor and control secondary cooling in a good way under vary casting condition, calculate the amount of secondary cooling water in-line according to
引文
[1] Ian Christmas. 钢铁工业面临的挑战. 2005 中国钢铁年会论文集, 北京, 冶金工业出版社, 2005: 1-6
[2] 史宸兴. 实用连铸冶金技术. 北京, 冶金工业出版社, 1998: 5
[3] 蔡开科. 连续铸钢原理与工艺. 北京, 冶金工业出版社, 1994: 5-8
[4] 张兴中. 我国连续铸钢技术的发展状况和趋势. 钢铁研究学报, 2004, 16(6): 1-6
[5] 叶枫. 连铸工艺操作.连铸, 1999, (1): 41-45
[6] 蔡开科. 连铸铸钢. 北京, 科学出版社,1991: 248-255
[7] 潘艳华. 中高碳钢方坯连铸二次冷却技术的研究. 重庆大学硕士论文, 2005 年
[8] 蔡开科. 浇注与凝固. 北京:冶金工业出版社, 1992, 10-16
[9] Laitien E,Neittaanmaki P.On Numerical Solution of the Problem Connected with the Control of the Secondary Cooling in the Continuous Castinuous Casting Process.Control Theory & Advanced Technology, 1988, (4): 285-30
[10] 韩传基, 蔡开科等.板坯连铸二冷区凝固传热过程与控制.北京科技大学学报, 1999, 21(6): 523-525
[11] 刘凤云. 连铸坯凝固计算机模拟计算用数学模型. 连铸通讯, 1985, (5): 1-7
[12] 贾光霖, 齐雅丽等.合金钢连铸坯动态凝固过程数值模拟.东北大学学报(自然科学版), 2004, 25(2): 139-132
[13] 刘坤, 冯亮花等. 板坯连铸机二冷段的动态控制模型.钢铁研究学报, 2005,17(2): 75-78
[14] 韩朋. 连铸坯二次冷却的非稳态控制. 钢铁研究学报, 2002, 14(2): 73-76
[15] K.M rwald. SMART/ASTC 技术的冶金、操作和经济效果. 钢铁, 2003, 38(7): 21-25
[16] 刘旭东, 朱苗勇等. 连铸板坯凝固传热过程的计算机模拟.材料与冶金学报,2002, 1(3): 195-199
[17] I V Samarasekera etc. Application of Mathematical Models for the Improvement of Billet quality, Steelmaking Conference Proceedings. Warrendale, PA, U.S.A. the Iron and Steel Society, Inc, 1991: 91-103
[18] 周筠清. 水平连铸二冷区喷水冷却过程数学模拟. 北京科技大学, 1996, 18(2): 179-182
[19] Flint P J. A Three-dimensional Finite Difference Model of Heat Transfer, Fluid Flow and Solidi-fication in the Continuous Slab. Steelmaking Conference Proceedings, 1991, 73: 481-487
[20] Loubenkilpi S,Laitinen E,Nnermine R. Real-time Simulation of Heat Transfer in Continuous Casting.Metall Trans, 1993, (24): 685-699
[21] 叶枫. 二次冷却的控制. 连铸, 1999, (1): 41-45
[22] 刘青. 连铸二次冷却研究的进展. 钢铁研究学报, 2005, 17(6): 6-9
[23] 文光华. 喷嘴在连铸坯二次冷却过程中的应用和发展. 炼钢, 1998, 5: 49-53
[24] 陈永. 攀钢板坯连铸二冷系统冷却能力标定.四川冶金,1998, (4): 38-40
[25] B.Mintz etc. Hot Ductility of Steels and its Relationship to the Problem of Transverse Cracking during Continuous Casting. International Materials Reviews, 1991, 36(5): 187-215
[26] 李殿明. 高拉速方坯内部裂纹产生原因分析.连铸, 1999, (3): 18-21
[27] 蔡开科. 连铸坯裂纹.钢铁,1982(9): 45-48
[28] 王振民. 小方坯连铸 20MnSi 表面横裂的因素分析及控制. 炼钢, 1998, (6): 48-51
[29] Hiroshi Kametani. Fractal Analysis of the Surface Cracks of Continuously Cast Steel Slabs. Metallurgical and Materials Transactions B, 1998, 29B(6): 1261-1267
[30] 张保师. 小方坯的质量缺陷和控制. 连铸, 1999, (5): 27-30
[31] 曾祖谦. 连铸板坯内裂纹的防止. 炼钢, 1998, (3): 13-15
[32] 袁伟霞. 中碳钢高温力学性能研究及在连铸生产中的应用. 炼钢, 1999, 15(1): 28-31
[33] 李延生. 连铸坯缺陷的成因及防止对策. 炼钢,1998, 3:55-58
[34] B.Mintz, Z.Mohamed. Influence of Manganese and Sulphour on Hot Ductility of Steels Heated directly to Temperature. Materials Science and Technology. 1989, 5(12): 1212-1218
[35] 陈永. 含钒微合金化重轨钢连铸二冷技术的研究. 钢铁, 2003, 38(9): 19-23
[36] 韩志伟. 板坯连铸二冷计算机仿真通用软件的开发及应用. 重庆大学硕士学位论文, 2001
[37] R.Dautov, R.Kadyrov, and E.Laitinen. On 3d Dynamic Control of Secondary Cooling in Continuous Casting Process. Lobachevskii Journal of Mathematics, 2003, 13: 3-13
[38] Osamu Kondo, Katushige Hamaa, and Takashi Kuribayshi. New Dynamic Spray Control System for Secondary Cooling Zone of Continuous Casting Machine. Steelmaking Conference Proceedings, 1993:309-314
[39] F.R.Camisani-Calzolari, I.K.Craig, and P.C.Pistorius. Speed Disturbance Compenation in the Secondary Cooling Zone in Continuous Casting. ISIJ International, 2000, 40(2000): 409-477
[40] Clyne T W.Numerical Modelling of Directional Solidification of Metallic Alloys.Metal Science, 1982, 16: 441-450
[41] Brimacome JK, Cramb AW. Steelmaking, casting and Modelling. In: process Technology Conference Proceedings. Toronto: Iron&Steel Society, 1992, 10: 211-223
[42] 冶金部情报研究总所. 国外连铸新技术(译文集), 1983: 230-250
[43] I V Samarasekera etc. Application of Mathematical Models for the Improvement of Billet quality, Steelmaking Conference Proceedings. Warrendale, PA, U.S.A. the Iron and Steel Society, Inc, 1991: 91-103
[44] 蔡开科, 吴元增.连续铸锭板坯凝固传热数学模型.金属学报,1983,19(1):33-40
[45] 武文斐. 用数值模拟方法研究反向凝固主要工艺参数对母带厚度的影响. 铸造, 2003, 52(2): 105-108
[46] 王宏明. 连铸工艺因素对铸坯凝固过程影响的模型研究. 铸造技术, 2003, 24(5): 385-386
[47] S. K. Choudhary etc. Mathematical modeling of heat transfer phenomena in continuous casting of steel, ISIJ International, 1993, 33 (7): 764-774
[48] 王恩刚. 关于连铸坯凝固传热有限元数值模拟的研究. 钢铁研究, 1996, 8: 30-35
[49] 张建等. 反向凝固 08A/15F 复合钢带凝固传热过程的有限元分析. 连铸技术论文集, 2002: 319-325
[50] Vanaparthy N M. Simulation of Solidification in Continuous Cast Steel Using Finite Element Method. ASME, 1994, (289): 131-138
[51] 陶文铨. 数值传热学.西安:西安交通大学出版社, 1995, 126-130
[52] 冯科. 方坯连铸宏观传输现象复合数值模拟的研究. 重庆大学博士论文, 2004 年
[53] 大中逸雄. 计算机传热凝固解析入门. 机械工业出版社, 1988: 33-53
[54]郭殿锋, 关丽坤. 大方坯连铸凝固传热数学模型的研究.包钢科技, 1999, 1: 36-39
[55] A.K.Tieu, I.S.Kim. Simulation of the Continuous Casting Process by a Mathematical Model. Int.J.Mech.Sci, 1997, 39(2): 185-192
[56] 刘德义. 板坯连铸机二次冷却动态控制数学模型. 冶金自动化,1995, 5:36-38
[57] 马汗超, 姚勇等. 方坯连铸机二冷水动态控制. 炼钢, 1998, 2 :13-15
[58] 刘晓红. 宝钢集团一钢公司不锈钢连铸工艺特点. 上海金属, 2003, 25(6): 22-24
[59] 孙韶元, 李世平等. 连铸二冷控制的智能化方法. 北京科技大学学报, 1997, 19(2): 188-191
[60] 张振山, 柴天佑等. 抚钢合金钢方坯连铸机二次冷却控制. 冶金自动化, 1999, (5): 32-35
[61] Osamu Tsubakihara etc. Development of Secondary Cooling Technology for CC-DR. Transactions ISIJ, 1984, 24: 73-78
[62] 李凤喜,喻承欢等. 板坯连铸机高效化改造及初步生产应用. 炼钢, 004, 6, 20(3): 1-4, 22
[63] 曹晓兵,梁爱生等. 带液芯控制的异型坯连铸二冷区动态控制模型. 太原重型机械学院学报, 2000, 3, 21(1):6-12
[64] 贾光霖,齐雅丽等. 合金钢连铸坯动态凝固过程数值模拟. 东北大学学报, 2004,2, 25(2): 129-132
[65] 刘青, 田乃媛等. 矩形坯连铸机二次冷却的在线控制. 冶金自动化,1997, 2: 9-12.
[66] 李凯玉. 济钢 4#铸机板坯二冷控制模型及应用. 山东冶金,1999, 21(2): 21-22.
[67] 毛汉平, 潘红等. 莱钢 4#矩形坯连铸机二冷水动态控制模型. 冶金自动化,2001, 2: 35-37
[68] 曹广畴. 现代板坯连铸.北京:冶金工业出版社,1994,45-52
[69] Brimacombe J K,Lait J E,Weinberg F.Pool profile,Liquide Mixing and Cast Structure in Steel Continuously Cast in Curved Moulds.Ironmaking and Steelmaking, 1974,1: 35-42
[70] 蔡开科, 吴元增. 连续铸锭板坯凝固传热数学模型.金属学报,1983, 19(1): 33-40.
[71] 陈登福. 薄板连铸坯的温度与应力状态的研究. 重庆大学博士论文, 1995 年
[72] Christian, F.Kurt. D.Dynamic Cooling Models. AISE Conference, Nashville T N/USA, 1999, 25-29 [73 ] 蒋冠路. 连铸板坯传热的计算机模拟. 武钢技术, 1980, (4): 6-18
[74] K.H.Spitzer, K.Harste, and B.Weber. Mathematical Model for Thermal Tracking and On-line Control in Continuous Casting. ISIJ International, 1992, 32(7): 848-856
[75] 王虹洁. 引进二冷动态控制系统提高板坯表面质量. 鞍钢技术, 2005,(5): 36-40
[76] C.A.Santos, J.A.Spim, and A.Garcia. Mathematical Modeling and Optimization Strategies(Genetic Algorithm and Knowledge Base) Applied to the Continuous Casting of Steel. Engineering Applications of Artificial Intelligence, 2003, 16: 511-527
[77] 徐荣军,陈念贻等. 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. 钢铁,2001, 36(2): 25-28
[78] 郭戈, 王伟等. 基于神经网络的铸坯凝固过程自适应控制. 甘肃工业大学学报, 2002, 28(1): 62-64
[79] 孙韶平, 李世平等. 连铸二冷控制的智能化方法. 北京科技大学学报, 1997, 4, 19(2): 188-191
[80] N.Chakraborti, R.Kumar, and D.Jain. A Study of the Continous Casting Mold Using a Pareto-converging genetic Algorithm. Applied Mathematical Modelling, 2001, 25: 287-297
[2] 史宸兴. 实用连铸冶金技术. 北京, 冶金工业出版社, 1998: 5
[3] 蔡开科. 连续铸钢原理与工艺. 北京, 冶金工业出版社, 1994: 5-8
[4] 张兴中. 我国连续铸钢技术的发展状况和趋势. 钢铁研究学报, 2004, 16(6): 1-6
[5] 叶枫. 连铸工艺操作.连铸, 1999, (1): 41-45
[6] 蔡开科. 连铸铸钢. 北京, 科学出版社,1991: 248-255
[7] 潘艳华. 中高碳钢方坯连铸二次冷却技术的研究. 重庆大学硕士论文, 2005 年
[8] 蔡开科. 浇注与凝固. 北京:冶金工业出版社, 1992, 10-16
[9] Laitien E,Neittaanmaki P.On Numerical Solution of the Problem Connected with the Control of the Secondary Cooling in the Continuous Castinuous Casting Process.Control Theory & Advanced Technology, 1988, (4): 285-30
[10] 韩传基, 蔡开科等.板坯连铸二冷区凝固传热过程与控制.北京科技大学学报, 1999, 21(6): 523-525
[11] 刘凤云. 连铸坯凝固计算机模拟计算用数学模型. 连铸通讯, 1985, (5): 1-7
[12] 贾光霖, 齐雅丽等.合金钢连铸坯动态凝固过程数值模拟.东北大学学报(自然科学版), 2004, 25(2): 139-132
[13] 刘坤, 冯亮花等. 板坯连铸机二冷段的动态控制模型.钢铁研究学报, 2005,17(2): 75-78
[14] 韩朋. 连铸坯二次冷却的非稳态控制. 钢铁研究学报, 2002, 14(2): 73-76
[15] K.M rwald. SMART/ASTC 技术的冶金、操作和经济效果. 钢铁, 2003, 38(7): 21-25
[16] 刘旭东, 朱苗勇等. 连铸板坯凝固传热过程的计算机模拟.材料与冶金学报,2002, 1(3): 195-199
[17] I V Samarasekera etc. Application of Mathematical Models for the Improvement of Billet quality, Steelmaking Conference Proceedings. Warrendale, PA, U.S.A. the Iron and Steel Society, Inc, 1991: 91-103
[18] 周筠清. 水平连铸二冷区喷水冷却过程数学模拟. 北京科技大学, 1996, 18(2): 179-182
[19] Flint P J. A Three-dimensional Finite Difference Model of Heat Transfer, Fluid Flow and Solidi-fication in the Continuous Slab. Steelmaking Conference Proceedings, 1991, 73: 481-487
[20] Loubenkilpi S,Laitinen E,Nnermine R. Real-time Simulation of Heat Transfer in Continuous Casting.Metall Trans, 1993, (24): 685-699
[21] 叶枫. 二次冷却的控制. 连铸, 1999, (1): 41-45
[22] 刘青. 连铸二次冷却研究的进展. 钢铁研究学报, 2005, 17(6): 6-9
[23] 文光华. 喷嘴在连铸坯二次冷却过程中的应用和发展. 炼钢, 1998, 5: 49-53
[24] 陈永. 攀钢板坯连铸二冷系统冷却能力标定.四川冶金,1998, (4): 38-40
[25] B.Mintz etc. Hot Ductility of Steels and its Relationship to the Problem of Transverse Cracking during Continuous Casting. International Materials Reviews, 1991, 36(5): 187-215
[26] 李殿明. 高拉速方坯内部裂纹产生原因分析.连铸, 1999, (3): 18-21
[27] 蔡开科. 连铸坯裂纹.钢铁,1982(9): 45-48
[28] 王振民. 小方坯连铸 20MnSi 表面横裂的因素分析及控制. 炼钢, 1998, (6): 48-51
[29] Hiroshi Kametani. Fractal Analysis of the Surface Cracks of Continuously Cast Steel Slabs. Metallurgical and Materials Transactions B, 1998, 29B(6): 1261-1267
[30] 张保师. 小方坯的质量缺陷和控制. 连铸, 1999, (5): 27-30
[31] 曾祖谦. 连铸板坯内裂纹的防止. 炼钢, 1998, (3): 13-15
[32] 袁伟霞. 中碳钢高温力学性能研究及在连铸生产中的应用. 炼钢, 1999, 15(1): 28-31
[33] 李延生. 连铸坯缺陷的成因及防止对策. 炼钢,1998, 3:55-58
[34] B.Mintz, Z.Mohamed. Influence of Manganese and Sulphour on Hot Ductility of Steels Heated directly to Temperature. Materials Science and Technology. 1989, 5(12): 1212-1218
[35] 陈永. 含钒微合金化重轨钢连铸二冷技术的研究. 钢铁, 2003, 38(9): 19-23
[36] 韩志伟. 板坯连铸二冷计算机仿真通用软件的开发及应用. 重庆大学硕士学位论文, 2001
[37] R.Dautov, R.Kadyrov, and E.Laitinen. On 3d Dynamic Control of Secondary Cooling in Continuous Casting Process. Lobachevskii Journal of Mathematics, 2003, 13: 3-13
[38] Osamu Kondo, Katushige Hamaa, and Takashi Kuribayshi. New Dynamic Spray Control System for Secondary Cooling Zone of Continuous Casting Machine. Steelmaking Conference Proceedings, 1993:309-314
[39] F.R.Camisani-Calzolari, I.K.Craig, and P.C.Pistorius. Speed Disturbance Compenation in the Secondary Cooling Zone in Continuous Casting. ISIJ International, 2000, 40(2000): 409-477
[40] Clyne T W.Numerical Modelling of Directional Solidification of Metallic Alloys.Metal Science, 1982, 16: 441-450
[41] Brimacome JK, Cramb AW. Steelmaking, casting and Modelling. In: process Technology Conference Proceedings. Toronto: Iron&Steel Society, 1992, 10: 211-223
[42] 冶金部情报研究总所. 国外连铸新技术(译文集), 1983: 230-250
[43] I V Samarasekera etc. Application of Mathematical Models for the Improvement of Billet quality, Steelmaking Conference Proceedings. Warrendale, PA, U.S.A. the Iron and Steel Society, Inc, 1991: 91-103
[44] 蔡开科, 吴元增.连续铸锭板坯凝固传热数学模型.金属学报,1983,19(1):33-40
[45] 武文斐. 用数值模拟方法研究反向凝固主要工艺参数对母带厚度的影响. 铸造, 2003, 52(2): 105-108
[46] 王宏明. 连铸工艺因素对铸坯凝固过程影响的模型研究. 铸造技术, 2003, 24(5): 385-386
[47] S. K. Choudhary etc. Mathematical modeling of heat transfer phenomena in continuous casting of steel, ISIJ International, 1993, 33 (7): 764-774
[48] 王恩刚. 关于连铸坯凝固传热有限元数值模拟的研究. 钢铁研究, 1996, 8: 30-35
[49] 张建等. 反向凝固 08A/15F 复合钢带凝固传热过程的有限元分析. 连铸技术论文集, 2002: 319-325
[50] Vanaparthy N M. Simulation of Solidification in Continuous Cast Steel Using Finite Element Method. ASME, 1994, (289): 131-138
[51] 陶文铨. 数值传热学.西安:西安交通大学出版社, 1995, 126-130
[52] 冯科. 方坯连铸宏观传输现象复合数值模拟的研究. 重庆大学博士论文, 2004 年
[53] 大中逸雄. 计算机传热凝固解析入门. 机械工业出版社, 1988: 33-53
[54]郭殿锋, 关丽坤. 大方坯连铸凝固传热数学模型的研究.包钢科技, 1999, 1: 36-39
[55] A.K.Tieu, I.S.Kim. Simulation of the Continuous Casting Process by a Mathematical Model. Int.J.Mech.Sci, 1997, 39(2): 185-192
[56] 刘德义. 板坯连铸机二次冷却动态控制数学模型. 冶金自动化,1995, 5:36-38
[57] 马汗超, 姚勇等. 方坯连铸机二冷水动态控制. 炼钢, 1998, 2 :13-15
[58] 刘晓红. 宝钢集团一钢公司不锈钢连铸工艺特点. 上海金属, 2003, 25(6): 22-24
[59] 孙韶元, 李世平等. 连铸二冷控制的智能化方法. 北京科技大学学报, 1997, 19(2): 188-191
[60] 张振山, 柴天佑等. 抚钢合金钢方坯连铸机二次冷却控制. 冶金自动化, 1999, (5): 32-35
[61] Osamu Tsubakihara etc. Development of Secondary Cooling Technology for CC-DR. Transactions ISIJ, 1984, 24: 73-78
[62] 李凤喜,喻承欢等. 板坯连铸机高效化改造及初步生产应用. 炼钢, 004, 6, 20(3): 1-4, 22
[63] 曹晓兵,梁爱生等. 带液芯控制的异型坯连铸二冷区动态控制模型. 太原重型机械学院学报, 2000, 3, 21(1):6-12
[64] 贾光霖,齐雅丽等. 合金钢连铸坯动态凝固过程数值模拟. 东北大学学报, 2004,2, 25(2): 129-132
[65] 刘青, 田乃媛等. 矩形坯连铸机二次冷却的在线控制. 冶金自动化,1997, 2: 9-12.
[66] 李凯玉. 济钢 4#铸机板坯二冷控制模型及应用. 山东冶金,1999, 21(2): 21-22.
[67] 毛汉平, 潘红等. 莱钢 4#矩形坯连铸机二冷水动态控制模型. 冶金自动化,2001, 2: 35-37
[68] 曹广畴. 现代板坯连铸.北京:冶金工业出版社,1994,45-52
[69] Brimacombe J K,Lait J E,Weinberg F.Pool profile,Liquide Mixing and Cast Structure in Steel Continuously Cast in Curved Moulds.Ironmaking and Steelmaking, 1974,1: 35-42
[70] 蔡开科, 吴元增. 连续铸锭板坯凝固传热数学模型.金属学报,1983, 19(1): 33-40.
[71] 陈登福. 薄板连铸坯的温度与应力状态的研究. 重庆大学博士论文, 1995 年
[72] Christian, F.Kurt. D.Dynamic Cooling Models. AISE Conference, Nashville T N/USA, 1999, 25-29 [73 ] 蒋冠路. 连铸板坯传热的计算机模拟. 武钢技术, 1980, (4): 6-18
[74] K.H.Spitzer, K.Harste, and B.Weber. Mathematical Model for Thermal Tracking and On-line Control in Continuous Casting. ISIJ International, 1992, 32(7): 848-856
[75] 王虹洁. 引进二冷动态控制系统提高板坯表面质量. 鞍钢技术, 2005,(5): 36-40
[76] C.A.Santos, J.A.Spim, and A.Garcia. Mathematical Modeling and Optimization Strategies(Genetic Algorithm and Knowledge Base) Applied to the Continuous Casting of Steel. Engineering Applications of Artificial Intelligence, 2003, 16: 511-527
[77] 徐荣军,陈念贻等. 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. 钢铁,2001, 36(2): 25-28
[78] 郭戈, 王伟等. 基于神经网络的铸坯凝固过程自适应控制. 甘肃工业大学学报, 2002, 28(1): 62-64
[79] 孙韶平, 李世平等. 连铸二冷控制的智能化方法. 北京科技大学学报, 1997, 4, 19(2): 188-191
[80] N.Chakraborti, R.Kumar, and D.Jain. A Study of the Continous Casting Mold Using a Pareto-converging genetic Algorithm. Applied Mathematical Modelling, 2001, 25: 287-297