热轧带钢板形控制技术的研究与应用
|
摘要
本文以本钢热轧厂的“提高1700mm热轧带钢板形控制精度的研究”项目、唐山港陆的“港陆1250mm板形控制系统开发”项目以及首钢迁钢的“迁钢2160mm热轧控制系统的消化吸收”项目为背景,系统研究了板形控制系统的理论、数学模型、控制策略以及辊型曲线优化设计。主要研究内容如下：
(1)研究了板形控制理论中的辊系变形理论。采用影响函数法建立了辊系弹性变形数学模型,完善了辊间压扁和工作辊压扁的影响函数,编制了辊系弹性变形解析软件。在考虑轧辊磨损主要影响因素的前提下,建立了轧辊磨损预报模型,编制了轧辊磨损预报软件。建立了轧辊热膨胀计算的二维有限差分数学模型,采用热平衡法处理了边界条件,编制了轧辊热凸度预报软件。
(2)建立了物理意义清晰的板形控制数学模型。采用空载辊缝凸度模型将影响辊缝的辊型因素综合为工作辊间辊缝凸度和支撑辊与工作辊间辊缝凸度,简化了板形控制模型结构；建立了描述单位宽轧制力、弯辊力、带钢宽度、轧辊弹性模量、轧辊直径以及空载辊缝凸度等影响因素和辊系弹性变形之间关系的均载辊缝凸度模型,给出了模型系数的确定方法；基于体积不变条件推导了考虑横向流动和二次变形影响的带钢板形预报模型；建立了考虑机架间张力和来料潜在板形不良影响的板形判别模型。
(3)研究了板形控制系统的控制策略。指出传统凸度分配策略忽略了潜在板形不良的影响,且下游机架未参与凸度控制降低了轧机板凸度的命中率。提出了一种新型的板形控制策略,该策略在保证带钢板形良好的前提下,提高了目标板凸度的命中率,有利于最大程度发挥轧机的板形控制能力。建立了各板形控制手段设定计算的数学模型。根据工作辊横移位置与工作辊间辊缝凸度的关系,建立了一种确定工作辊横移位置的迭代计算方法。
(4)开发了适用于常规轧机、CVC轧机和PC轧机的在线板形控制系统。为消除传统平直度反馈控制中存在的时间滞后和速度波动的影响,将Smith预估控制方法引入到平直度反馈控制中,选取调节器为积分形式,且采用带钢样本长度跟踪作为事件触发中断进行反馈控制。
(5)研究了热带轧机CVC-plus工作辊和支撑辊辊型曲线的优化设计方法。根据CVC-plus辊型曲线的特点,以轴向力最小为目标函数,推导了其辊型曲线的设计方法,编制了CVC-plus工作辊辊型曲线优化设计软件。研究了支撑辊辊型曲线及轧辊热磨损对辊间压力分布和带钢出口凸度的影响。在对带钢凸度在机架间进行合理分配的前提下,建立了以辊间压力均匀化和保证机架间板形良好为目标的支撑辊辊型曲线优化设计算法。
本文的研究内容面向热轧带钢在线控制,改进了平直度反馈控制系统,建立了包括物理意义清晰数学模型和新型控制策略的板形控制系统,提出了CVC-plus工作辊和支撑辊辊型曲线优化设计方法,具有很高的实际应用价值。支撑辊辊型曲线优化设计和板形控制系统已应用于唐山港陆1250mm热带轧机：辊型曲线优化后,支撑辊的轧制重量得到了提高；板形控制系统投入后,轧辊磨损和热凸度预报精度较高,板形质量有了较大的提高。
Based on the project of "Research on Improving Shape Control Accuracy of 1700mm Hot Rolling Mill" in Ben Steel Hot Rolling Plant, the project of "Development of Strip Shape Control System for Ganglu 1250mm Hot Rolling Mill" and the project of "Digestion and Absorption of Control System for Shougang 2160mm Hot Rolling Mill", the theory, mathematical model, control strategy of the strip shape control system and the roll contour optimization were researched systematically in the paper. The main works are shown as follows:
(1) The roll deformation theory of the shape control was studied. The mathematical model of roll elastic deformation was set up by the influence function method, the influence functions of work roll flattening and flattening between rolls were improved, and the analytical software on roll elastic deformation was developed. The roll wear model was established by taking into account the main influential factors, and the forecast program of roll wear was complied. The roll thermal expansion model was set up by the two-dimensional finite-difference method, the boundary condition was handled by the heat balance method, and the forecast software of roll thermal crown was complied.
(2) The shape control mathematical model of specific physical meaning was set up. Roll contour factors which impacting the roll gap were summarized into two parameters through the unload roll gap crown model to simplify the shape control model structure. The uniform load gap crown was influenced by rolling force, roll bending force, strip width, elastic modulus of the roll, roll diameter and unload roll gap crown. The uniform load distribution roll gap model was developed to describe the relationship between the roll elastic deformation and the influencing factors. The method was provided for determining the uniform load distribution roll gap model coefficient. Based on the volume conservation, the strip shape forecast model was deduced by considering the material transverse flow and secondary deformation between mills. The shape discriminant model was set up by considering the effect of the potential shape defect and the tension.
(3) The control strategy of the shape control system was researched. Due to ignoring of the potential shape defect and the absence of strip crown control by the downstream stands, the traditional crown strategy had reduced the hit rate of the strip crown. A new kind of shape control strategy was proposed to enhance the hit rate of the target strip crown under the condition of guaranteeing the strip flatness quality. The new strategy can increase the shape control capability to utmost extent. The setup calculation mathematical model of each shape control actuator was established. According to the relationship between the shifting position of the work roll and the roll gap crown, the iterative calculation method was established to determine the shifting position of the work roll.
(4) The on-line shape control system was developed. Smith prediction control method, whose regulator employs the integral form, was introduced to the flatness feedback control in order to eliminate the influence of time lag and velocity fluctuation in traditional flatness feedback control; the sample length tracking of the strip was acted as the event-triggered interruption in the feedback control.
(5) The optimum design methods of the CVC-plus work roll shape curve and the backup roll contour were studied. Taking the minimum of the axial force as the objective function, the design method of the CVC-plus roll shape curve was deduced, and the optimum design software was developed. The effect of the backup roll contour and the roll thermal wear on the load distribution between rolls and the exit strip crown was studied. Taking the uniform load distribution between the rolls and the fine shape between the stands as the target, the optimum design method of the backup roll contour was developed by distributing the strip crown reasonably in every stand.
The main research content of the paper, which was of great practical application value, was focused on the online control of hot strip mill. The flatness feedback control system was improved; the shape control system, which contained the mathematical model of specific physical meaning and the new kind of control strategy, was established; and the optimum design methods of the CVC-plus shape curve and the backup roll contour were introduced. The backup roll contour optimum design method and the shape control system have been employed in Tangshan Ganglu 1250mm hot strip mill. The application results show that the rolling weight was increased, and the shape quality was enhanced.
(1)研究了板形控制理论中的辊系变形理论。采用影响函数法建立了辊系弹性变形数学模型,完善了辊间压扁和工作辊压扁的影响函数,编制了辊系弹性变形解析软件。在考虑轧辊磨损主要影响因素的前提下,建立了轧辊磨损预报模型,编制了轧辊磨损预报软件。建立了轧辊热膨胀计算的二维有限差分数学模型,采用热平衡法处理了边界条件,编制了轧辊热凸度预报软件。
(2)建立了物理意义清晰的板形控制数学模型。采用空载辊缝凸度模型将影响辊缝的辊型因素综合为工作辊间辊缝凸度和支撑辊与工作辊间辊缝凸度,简化了板形控制模型结构；建立了描述单位宽轧制力、弯辊力、带钢宽度、轧辊弹性模量、轧辊直径以及空载辊缝凸度等影响因素和辊系弹性变形之间关系的均载辊缝凸度模型,给出了模型系数的确定方法；基于体积不变条件推导了考虑横向流动和二次变形影响的带钢板形预报模型；建立了考虑机架间张力和来料潜在板形不良影响的板形判别模型。
(3)研究了板形控制系统的控制策略。指出传统凸度分配策略忽略了潜在板形不良的影响,且下游机架未参与凸度控制降低了轧机板凸度的命中率。提出了一种新型的板形控制策略,该策略在保证带钢板形良好的前提下,提高了目标板凸度的命中率,有利于最大程度发挥轧机的板形控制能力。建立了各板形控制手段设定计算的数学模型。根据工作辊横移位置与工作辊间辊缝凸度的关系,建立了一种确定工作辊横移位置的迭代计算方法。
(4)开发了适用于常规轧机、CVC轧机和PC轧机的在线板形控制系统。为消除传统平直度反馈控制中存在的时间滞后和速度波动的影响,将Smith预估控制方法引入到平直度反馈控制中,选取调节器为积分形式,且采用带钢样本长度跟踪作为事件触发中断进行反馈控制。
(5)研究了热带轧机CVC-plus工作辊和支撑辊辊型曲线的优化设计方法。根据CVC-plus辊型曲线的特点,以轴向力最小为目标函数,推导了其辊型曲线的设计方法,编制了CVC-plus工作辊辊型曲线优化设计软件。研究了支撑辊辊型曲线及轧辊热磨损对辊间压力分布和带钢出口凸度的影响。在对带钢凸度在机架间进行合理分配的前提下,建立了以辊间压力均匀化和保证机架间板形良好为目标的支撑辊辊型曲线优化设计算法。
本文的研究内容面向热轧带钢在线控制,改进了平直度反馈控制系统,建立了包括物理意义清晰数学模型和新型控制策略的板形控制系统,提出了CVC-plus工作辊和支撑辊辊型曲线优化设计方法,具有很高的实际应用价值。支撑辊辊型曲线优化设计和板形控制系统已应用于唐山港陆1250mm热带轧机：辊型曲线优化后,支撑辊的轧制重量得到了提高；板形控制系统投入后,轧辊磨损和热凸度预报精度较高,板形质量有了较大的提高。
Based on the project of "Research on Improving Shape Control Accuracy of 1700mm Hot Rolling Mill" in Ben Steel Hot Rolling Plant, the project of "Development of Strip Shape Control System for Ganglu 1250mm Hot Rolling Mill" and the project of "Digestion and Absorption of Control System for Shougang 2160mm Hot Rolling Mill", the theory, mathematical model, control strategy of the strip shape control system and the roll contour optimization were researched systematically in the paper. The main works are shown as follows:
(1) The roll deformation theory of the shape control was studied. The mathematical model of roll elastic deformation was set up by the influence function method, the influence functions of work roll flattening and flattening between rolls were improved, and the analytical software on roll elastic deformation was developed. The roll wear model was established by taking into account the main influential factors, and the forecast program of roll wear was complied. The roll thermal expansion model was set up by the two-dimensional finite-difference method, the boundary condition was handled by the heat balance method, and the forecast software of roll thermal crown was complied.
(2) The shape control mathematical model of specific physical meaning was set up. Roll contour factors which impacting the roll gap were summarized into two parameters through the unload roll gap crown model to simplify the shape control model structure. The uniform load gap crown was influenced by rolling force, roll bending force, strip width, elastic modulus of the roll, roll diameter and unload roll gap crown. The uniform load distribution roll gap model was developed to describe the relationship between the roll elastic deformation and the influencing factors. The method was provided for determining the uniform load distribution roll gap model coefficient. Based on the volume conservation, the strip shape forecast model was deduced by considering the material transverse flow and secondary deformation between mills. The shape discriminant model was set up by considering the effect of the potential shape defect and the tension.
(3) The control strategy of the shape control system was researched. Due to ignoring of the potential shape defect and the absence of strip crown control by the downstream stands, the traditional crown strategy had reduced the hit rate of the strip crown. A new kind of shape control strategy was proposed to enhance the hit rate of the target strip crown under the condition of guaranteeing the strip flatness quality. The new strategy can increase the shape control capability to utmost extent. The setup calculation mathematical model of each shape control actuator was established. According to the relationship between the shifting position of the work roll and the roll gap crown, the iterative calculation method was established to determine the shifting position of the work roll.
(4) The on-line shape control system was developed. Smith prediction control method, whose regulator employs the integral form, was introduced to the flatness feedback control in order to eliminate the influence of time lag and velocity fluctuation in traditional flatness feedback control; the sample length tracking of the strip was acted as the event-triggered interruption in the feedback control.
(5) The optimum design methods of the CVC-plus work roll shape curve and the backup roll contour were studied. Taking the minimum of the axial force as the objective function, the design method of the CVC-plus roll shape curve was deduced, and the optimum design software was developed. The effect of the backup roll contour and the roll thermal wear on the load distribution between rolls and the exit strip crown was studied. Taking the uniform load distribution between the rolls and the fine shape between the stands as the target, the optimum design method of the backup roll contour was developed by distributing the strip crown reasonably in every stand.
The main research content of the paper, which was of great practical application value, was focused on the online control of hot strip mill. The flatness feedback control system was improved; the shape control system, which contained the mathematical model of specific physical meaning and the new kind of control strategy, was established; and the optimum design methods of the CVC-plus shape curve and the backup roll contour were introduced. The backup roll contour optimum design method and the shape control system have been employed in Tangshan Ganglu 1250mm hot strip mill. The application results show that the rolling weight was increased, and the shape quality was enhanced.
引文
[1]张殿华,李旭,张浩,等.辊缝型监控AGC纯滞后补偿控制器的算法设计及应用[J],钢铁,2008,43(6)：52-55.
[2]刘相华,王国栋.热轧带钢新技术的发展[J],钢铁研究,2000,(5)：1-3.
[3]Johns R L, Reiner V R, Mengel J D. Hydraulic AGC at Bethlehemis Burns Harbor 160 in plate mill[J], Iron and Steel Engineer,1994,71(8):52-57.
[4]张进之,张宇.板形板厚的数学理论[J],冶金设备,2002,(3)：4-8.
[5]赵勐.2150mm热连轧板形控制数学模型的研究与应用[D],沈阳,东北大学硕士论文,2007.
[6]王国栋.板形控制和板形理论[M],北京：冶金工业出版社,1986,6-8.
[7]王国栋.板形控制和板形理论[M],北京：冶金工业出版社,1986,11-13.
[8]何安瑞,张清东,曹建国,等.宽带钢热轧支持辊辊型变化对板形的影响[J]，北京科技大学学报,1999,21(6)：565-567.
[9]华建新,周泽雁.冷轧带钢板形缺陷的多项式回归及数学模型[J],钢铁,1992,27(3)：27-31.
[10]Jiang Z Y, Tieu A K, Lu C. A FEM modelling of the elastic deformation zones in flat rolling[J], Journal of Materials Processing Technology,2004,146(2):167-174.
[11]王国栋.板形控制和板形理论[M],北京：冶金工业出版社,1986,239-289.
[12]Stone M D, Gray R. Theory and Practical Aspects in Crown Control[J], Iron and Steel Engineer, 1965,42(8):73-77.
[13]Shohet K N, Townsend N A. Roll bending methods of crown control in four-high plate mills[J], Journal of Iron and Steel Institute,1969, (11):1088-1098.
[14]Ewards W J, Spooner P D. Automation of tandem mills[M], London, Iron Steel Institute,1973: 34-45.
[15]Tozawa Y, Ishikawa T. Study on stress distribution in strip rolling - rolling pressure and stresses at the upper stream side of roll gap[J], Memories of the Faculty of Engineering Nagoya University,1984,36(2):81-91.
[16]Salganik V. Mathematical modeling of roll load and deformation in a four-high strip mill[J], Journal of Materials Processing Technology,2002,125-126(9):695-699.
[17]王国栋,张树堂.四辊轧机轧辊弹性变形的矩阵计算法[J]，重型机械,1982,2(8)：9-18.
[18]王国栋,张树堂.轧辊弹性变形和板形理论的研究[J],钢铁研究总院学报,1983,3(3)：461-470.
[19]徐建忠,龚殿尧,王国栋,等.轧辊直径对热轧带钢凸度的影响规律[J],东北大学学报：自然科学版,2002,23(12)：1170-1173.
[20]徐建忠,孔祥伟,王国栋,等.大凸度支撑辊带钢凸度的控制能力[J],东北大学学报：自然科学版,2003,24(02)：151-154.
[21]徐建忠,龚殿尧,刘相华,等.单位宽度轧制力对热轧带钢凸度的影响规律[J],东北大学学报：自然科学版,2003,24(03)：280-283.
[22]龚殿尧,徐建忠,张凤琴,等.轧辊凸度及直径对热轧带钢凸度的影响[J],钢铁研究学报,2003,15(03)：17-20.
[23]常安,邸洪双,白金兰,等.影响冷轧边部减薄的因素[J],钢铁,2007,42(10)：51-55.
[24]Chen X L, Zhou J X. A specialized finite element model for investigating controlling affecting behavior of rolls and strip flatness [A], Proc. of the 4th International Steel Rolling conf., Deauvillle-France,1987,2(E4):1-7.
[25]Kihara J. Application of BEM to calculation of the roll profile in flat rolling[A], Proc. of the 4th International Steel Rolling Conf., Deauvillle-France,1987,2(E1):1-12.
[26]Knapinski M. The numerical analysis of roll deflection during plate rolling[J], Journal of Materials Processing Technology,2006,175(1):257-265.
[27]Shi X, Liu X H, Wang G D, et al. FEM analysis for roll flattening in thin strip rolling[A], Second International Conference on Advanced Structural Steels, ShangHai, China,2004:1037-1041.
[28]周顺新,钟掘,刘光连.轧机辊系弹性变形的有限元计算[J],中南工业大学学报(自然科学版),1994,25(6)：733-737.
[29]VB金兹伯格.高精度板带材轧制理论与实践[M],北京：冶金工业出版社,2000,328.
[30]Somers R R, Pallone G T, McDermott J F, et al. Verification and applications of a model for predicting hot strip profile crown and flatness[J], Iron and Steel Engineer,1984,61 (9):441-450.
[31]George S, James V L. Roll wear in finishing trains of hot strip mills[J], Iron and Steel Engineer, 1961,38(12):71-92.
[32]Uijtdebroeks H, Franssen R, Sonck G, et al. On-line analysis of the work roll surface deterioration in a hot strip mill[J], Revue de Metallurgie. Cahiers D'Informations Techniques, 1998,95(6):789-799.
[33]John S, Sikdar S, Mukhopadhyay A, et al. Roll wear prediction model for finishing stands of hot strip mill[J], Iron making and Steel making, 2006, 33(2):169-175
[34]邹家祥.轧辊磨损预报计算[J],钢铁,1986,21(7)：23-27.
[35]何安瑞,张清东,张杰,等.板带钢热轧支持辊不均匀磨损及其解决措施[J],上海金属,2000,22(2)：19-22.
[36]连家创,黄传清,陈连生.2050CVC热连轧机精轧机组轧辊磨损的研究[J],钢铁,2002,37(3)：24-27.
[37]令狐克志,何安瑞,杨荃,等.宽带钢热连轧支承辊磨损模型研究[J],钢铁,2006,41(12)：45-48.
[38]郭忠峰,龚殿尧,荆涛,等.1700热连轧机CVC轧辊的磨损[J],钢铁研究学报,2008,20(1)：21-24.
[39]Chang D F. Thermal stress in work rolls during the rolling of metal strip[J], Journal of Materials Processing Technology,1999,94(1):45-51.
[40]Campos A M, Carcia D F, Deabajo N, et al. Real-time rule-based control of the thermal crown of work rolls installed in hot strip mills[J], IEEE Transactions on Industry Applications,2004, 40(2):642-649.
[41]徐乐江.板带冷轧机板形控制与机型选择[M],北京：冶金工业出版社,2007,74.
[42]Tseng A A, Tong S X, Chen T C. Thermal expansion and crown evaluations in rolling processes[J], Steel Research,1996,67(5):188-199.
[43]Devadas C, Samarasekera I V. Heat transfer during hot rolling of steel strip[J], Ironmaking Steelmaking,1986,13(6):311-321.
[44]Pallone G T. Transient temperature distribution in work rolls during hot rolling of sheet and strip[J], Iron and Steel Engineer,1983,60(12):21-26.
[45]Galantucci L M, Tricarico L. Thermo-mechanical simulation of a rolling process with an FEM approach[J], Journal of Materials Processing Technology,1999,92-93(8):494-501.
[46]Ginzburg V B, Bakhtar F A, Issa R J. Application of coolflex model for analysis of work roll thermal conditions in hot strip mills[J], Iron and Steel Engineer,1997,74(11):38-45.
[47]Corral R L, Colas R, Perez A. Modeling the thermal and thermoelastic responses of work rolls used for hot rolling steel strip[J], Journal of Materials Processing Technology,2004,153(11): 886-893.
[48]Abbaspour M, Saboonchi A. Work roll thermal expansion control in hot strip mill[J], Applied Mathematical Modelling,2008,32(12):2652-2669.
[49]Zhang X M, Jiang Z Y, Tieu A K, et al. Numerical modelling of the thermal deformation of CVC roll in hot strip rolling[J], Journal of Materials Processing Technology,2002,131(12):219-223.
[50]杨利坡,彭艳,刘宏民.热连轧工作辊三维瞬态温度场数值模拟[J],燕山大学学报,2004,28(5)：380-383.
[51]徐光,张黄强,刘显军,等.CVC轧辊热凸度模型研究[J],冶金设备,2006,(5)：35-37.
[52]郭忠峰,徐建忠,李长生,等.1700热连轧机轧辊温度场及热凸度研究[J],东北大学学报(自然科学版),2008,29(4)：517-520.
[53]Aratani H, Ozono R, Nakano T. Expansion of pair cross (PC) mill applications to hot and cold rolling mills[J], Iron and Steel Engineer,1993,70(3):32-37.
[54]Nakajima K, Kikuma T, Matsumoto H, et al. Research on crown control for hot strip mills[J], Nippon Steel Technical Report,1980, (15):110-126.
[55]Yamada J, Ono H, Takigawa T, et al. Development of sumitomo VC (Variable Crown) roll system[J], Iron and Steel Maker,1982,9(6):37-42.
[57]Nagai T, Yamada J, Masui T, et al. Strip Shape and Profile Control with Sumitomo Variable Crown Roll System[J], Iron and Steel Engineer,1983,60(1):56-63.
[58]Kono T. Study of Crown Control Technologies in Hot and Cold Strip Mills[J], Sumitomo Metals, 1990,42(4):190-200.
[59]Hiruta T, Nakata N, Kitahama M, et al. Influence of rolling mill type on rigidity characteristics in hot and cold strip rolling[J], Iron and Steel Engineer,1996,73(3):32-37.
[60]#12
[61]#12
[62]Ono H, Watanabe I, Yoshimoto K, et al. Industrial Application of the HCX-MILL to Hot Strip Mills[J], Hitachi Review,1996,45(6):271-278.
[64]Bolte. CVC-technologies ein neues kaltwalzverfahren zur erzeugung planer stablbaednder[J], Stahl und Eisen,1986,106(9):59-64.
[65]Bald W, Beisemann G, Feldmann H, et al. Continuously variable crown(CVC) rolling[J], Iron and Steel Engineer,1987,64(3):32-41.
[66]Tsukamoto H, Matsumoto H. Shape and Crown Control Mill-Crossed Roll System [J], Iron and Steel Engineer,1984,61(10):26-37.
[67]Nakajima K, Kawamoto T, Hatae S, et al. Basic Characteristics of Pair Cross Mill[J], Technical Review-Mitsubishi Heavy Industries,1985,22(2):143-148.
[68]Kuroda A, Hayash K, Ayano T. Development of On-Line Roll Grinder[J], Iron and Steel Engineer,1993,70(3):38-44.
[69]Garcia D F, Garcia M, Obseo F, et al. Real-time flatness inspection system for steel strip production lines[J], Real-Time Imaging,1999,5(1):35-47.
[70]Henze M, Nilsson H. Stressometer systems with microcomputer-based electronics[J], ASEA Journal,1977,50(5):109-114.
[71]Garcia D P, Garcia M, Obeso F, et al. Real-time Flatness Inspection System for Steel Strip Production Lines[J], Real-Time Imaging,1999,5(1):35-47.
[72]Shaw D A, Burns T I. Hochkeppel T P, et al. Strip profile control technology and economic impact of target profiles[J], Iron and Steel Engineer,1995,72(9):22-30.
[73]Roey J V, Vergote H, Mielke R. Accurate profile and flatness control on a modernized hot strip mill[J], Iron and Steel Engineer,1996,73(2):29-33.
[74]Tellman G M, Heesen G J. Improving crown performance of a hot strip mill[J], Iron and Steel Engineer,1995,72(12):21-26.
[75]陈先霖,张杰,张清东,等.宽带钢热连轧机板形控制系统的开发[J],钢铁,2000,35(7)：28-33.
[76]钟恬,何安瑞,杨荃,等.热连轧自动板形控制系统的研究与应用[J],冶金自动化,2007,(4)：28-31.
[77]Cresdee R B, Edwards W J, Thomas P J. An advanced model for flatness and profile prediction in hot rolling[J], Iron and Steel Engineer,1991,68(10):41-51.
[78]段春华.新的板形理论[J],钢铁(增刊),1999,34(10)：809-811.
[79]Nilsson A. FE simulations of camber in hot strip rolling[J], Journal of Materials Processing Technology,1998,80-81(8):325-329.
[80]John S, Mukhopadhyay A, Sikdar S. Optimisation of work roll shifting and bending to roll thinner gauge HR coils using genetic algorithm[J], Ironmakong and SteelMaking,2006,33(1): 67-73.
[81]Salimi M, Forouzan M R. Determination of bending actuators set points to control crown and flatness in hot rolling of strip[J], Journal of Materials Processing Technology,2002,125-126[9]: 670-677.
[82]张进之,张宇.板形板厚的数学理论[J],冶金设备,2002,(3)：4-8.
[83]刘宏民.板形理论的研究现状与发展方向[J],钢铁,1993,28(2)：75-78.
[84]刘宏民,F.Sanfilippo,F.Dolci,等.热带钢连轧机板形设定控制数学模型[J],钢铁,1996,31(10)：30-34.
[85]王宏伟,陈先霖,张清东,等.宽带钢热连轧机多机架板形控制模型的探讨[J],冶金设备,2000,(1)：1-3.
[86]祝东奎,张清东,魏钢城,等.宽带钢热连轧机组的板形方程[J],北京科技大学学报,2001,23(1)：71-74.
[87]Liu H M, Zhang X L, Wang Y R. Transfer matrix method of flatness control for strip mills[J], Journal of Materials Processing Technology,2005,166(2):237-242.
[88]Zhang G M, Xiao H, Wang C H. Three-dimensional model for strip hot rolling[J], Journal of Iron and Steel Research,2006,13(1):23-26.
[89]Berger S, Hoen K, Hof H, et al. Evolution of CVC plus(?) technology in hot rolling mills[J], Revue de Metallurgie,2008,105(1):44-49.
[90]Lu C, Tieu A K, Jiang ZY. A design of a third-order CVC roll profile[J], Journal of Materials Processing Technology,2002,125-126:645-648.
[91]Xu G, Liu X J, Zhao J R, et al. Analysis of CVC roll contour and determination of roll crown[J], Journal of University of Science and Technology Beijing,2007,14(4):378-380.
[92]郭忠锋,徐建忠,李长生,等.几类典型轧辊横移变凸度辊型的比较与分析[J],东北大学学报(自然科学版),2008,29(6)：830-833.
[93]李洪波,张杰,曹建国,等.五次CVC辊型曲线的分析与设计[J,机械设计与制造,2008, (12)：41-43.
[94]刘光明,邸洪双,常安,等.CVC轧机辊型曲线设计及等效凸度探讨[J],东北大学学报(自然科学版),2008,29(10)：1443-1446.
[95]何伟,邸洪双,夏晓明,等.五次CVC辊型曲线的设计[J],轧钢,2006,23(2)：12-15.
[96]Auzinger D, Djumlija G, Nihuis T, et al. Application of advanced technology packages for improved strip profile and flatness in hot strip mills[J], Iron and Steel maker.2003,30(9):17-21.
[97]王云,宁晓霞.支撑辊边部导角数学模型的建立及其磨削工艺[J],本系冶金高等专科学校校报,2003,5(3)：29-31.
[98]常安,自金兰,邸洪双,等.首钢3500mm中板轧机辊型研究与应用[J],钢铁,2006,41(8)：41-45.
[99]田勇,胡贤磊,王昭东,等.2500mm中厚板精轧机支承辊辊型优化设计[J],2006,18(10)：23-25.
[100]窦鹏,李友国,梁开明,等.CVC热轧机支承辊接触应力有限元分析[J],清华大学学报(自然科学版),2005,45(12)：1668-1671.
[101]何安瑞,杨荃,陈先霖,等.变接触轧制技术在热带钢轧机上的应用[J],钢铁,2007,42(2)：31-34.
[102]杨荃,陈先霖,徐耀寰,等.应用变接触长度支承辊提高板形综合调控能力[J],钢铁,1995,30(3)：48-51.
[103]何安瑞,曹建国,吴庆海,等.热轧精轧机组变接触支持辊综合性能研究[J],上海金属,2001,23(])：14-17.
[104]何安瑞.宽带钢热轧精轧机组辊型的研究[D],北京科技大学博士论文,北京,2000.
[105]郝建伟,曹建国,张杰,等.2250 CVC热连轧机支持辊辊型研究[J],中南大学学报(自然科学版),2007,38(4)：734-738.
[106]李洪波,张杰,曹建国,等.CSP热连轧机支撑辊辊型研究[J]，钢铁,2008,43(3)：61-64.
[107]连家创,戚向东,岳晓丽,等.最优辊型技术的开发和应用[J],钢铁,2007,42(10)：60-63.
[108]岳晓丽,连家创,李汉良,等.1580PC热连轧机支承辊辊型优化曲线的研究[J]，中国机械工程,2001,12(7)：747-749.
[109]赵旭亮,王淑君,徐建忠,等.四辊轧机轧辊弹性变形的研究[J],东北大学学报(自然科学版),2008,29(6)：834-837.
[110]王国栋.板形控制和板形理论[M],北京：冶金工业出版社,1986,289.
[111]Guo R M. Development of a mathematical model for strip thickness profile[J], Iron and Steel Engineer,1990,67(9):32-39.
[112]Timoshenko S P, Good J N. Theory of Elasticity[M], New York:McGraw Hill,1951.
[113]Liu H M, Lian J C. Transverse distributions of front and back tension stresses in cold strip rolling[J], Chinese Journal of Metal Science and Technology,1992,8(6):427-434.
[115]孔祥伟.工作辊横移及自由程序轧制技术的研究[D]，东北大学博士论文,沈阳,2003.
[116]Sims R B. The calculation of roll force and torque in hot rolling mills[J], Proc. Inst. Mech. Engrs.,1954, (168):191-207.
[117]徐建忠,张凤琴,龚殿尧,等.四辊轧机轧辊弹性变形解析模块的开发[J],轧钢,2003,20(2)：8-11.
[118]Colas R, Ramirez J, Sandoval I, et al. Damage in hot rolling work rolls[J], Wear,1999,230(1): 56-60.
[119]Tseng A A, Lin F H. Roll cooling and its relationship to roll life[J], Metallurgical Transaction, 1989,20A(11):2305-2320.
[120]Guo R M.轧辊磨损统计模型的开发、验证和应用[A],第六界国际轧钢会议译文集,1994,70-75.
[121]Wang X D, Yang Q, He A R, et al. Comprehensive contour prediction model of work rolls in hot wide strip mill[J]. Journal of University of Science and Technology Beijing,2007,14(3): 240-245.
[122]孙一康.带钢热连轧的模型与控制[M],北京：冶金工业出版社,2002,38.
[123]Somers R R, Pallone G T, Mcdermott J F, et al. Verificationand applications of a model for predicting hot strip profile crown and flatness[J], Iron and Steel Engineer,1984,61(9):35-44.
[124]Guo R M. Optimal profile and shape control of flat sheet metal using multiple control devices[J], IEEE Transaction on Industry Applications,1996,32(2):449-457.
[125]孙一康.带钢热连轧的模型与控制[M],北京：冶金工业出版社,2002,171-173.
[126]Younes MA, Shahtout M, Damir M N. A parameters design approach to improve product quality and equipment performance in hot rolling[J], Journal of Materials Processing Technology,2006, 171(1):83-92.
[127]丁修堑.轧制过程自动化[M],北京：冶金工业出版社,2005,207.
[128]Fapiano D J, Steeper D E. Control of strip thickness in hot rolling[J], Iron and Steel Engineer, 1985,62(11):34-43.
[129]叶红卫.宝钢2050热轧过程厚度控制技术[J],宝钢技术,2003,(1)：23-27.
[130]Lawrence W J, MacAlister A F, Reever P J. On line modelling and control of strip cooling[J], Ironmaking and Steelmaking,1996,23(1):74-78.
[131]王萍,黄贞益,尹桂全,等.热轧带钢层流冷却温度控制模型的应用分析[J],钢铁研究学报,2007,19(4)：31-34.
[132]Hong W K, Kim P H, Moon Y H, et al. Hot strip width control method by using looper tension measuring system in finishing mill[J], Journal of Materials Processing Technology,2001,111(3): 74-78.
[133]吕程,王国栋,刘相华,等.热连轧精轧宽度自动控制[J],钢铁研究,1997,(5)：52-56.
[134]孙一康.带钢热连轧的模型与控制[M],北京：冶金工业出版社,2002,13.
[135]Shimoda N, Okamoto K, Wang H L, et al. Process control technology for thin strip production in Tangshan China[J], Iron and Steel Technology,2005,2(1):33-41.
[136]孙一康.带钢热连轧的模型与控制[M],北京：冶金工业出版社,2002,14.
[137]Zhang D H, Zhang H, Sun T, et al. Monitor automatic gauge control strategy with a Smith predictor for steel strip rolling[J], Journal of University of Science and Technology Beijing, 2008,15(6):827-832.
[138]Nolle L. SASS applied to optimum wok roll profile selection in the hot rolling of wide steel[J], Knowledge-Based Systems,2007,20(2):203-208.
[139]郭忠峰.热连轧带钢板形控制与辊型优化设计[D],东北大学博士论文,2008.
[2]刘相华,王国栋.热轧带钢新技术的发展[J],钢铁研究,2000,(5)：1-3.
[3]Johns R L, Reiner V R, Mengel J D. Hydraulic AGC at Bethlehemis Burns Harbor 160 in plate mill[J], Iron and Steel Engineer,1994,71(8):52-57.
[4]张进之,张宇.板形板厚的数学理论[J],冶金设备,2002,(3)：4-8.
[5]赵勐.2150mm热连轧板形控制数学模型的研究与应用[D],沈阳,东北大学硕士论文,2007.
[6]王国栋.板形控制和板形理论[M],北京：冶金工业出版社,1986,6-8.
[7]王国栋.板形控制和板形理论[M],北京：冶金工业出版社,1986,11-13.
[8]何安瑞,张清东,曹建国,等.宽带钢热轧支持辊辊型变化对板形的影响[J]，北京科技大学学报,1999,21(6)：565-567.
[9]华建新,周泽雁.冷轧带钢板形缺陷的多项式回归及数学模型[J],钢铁,1992,27(3)：27-31.
[10]Jiang Z Y, Tieu A K, Lu C. A FEM modelling of the elastic deformation zones in flat rolling[J], Journal of Materials Processing Technology,2004,146(2):167-174.
[11]王国栋.板形控制和板形理论[M],北京：冶金工业出版社,1986,239-289.
[12]Stone M D, Gray R. Theory and Practical Aspects in Crown Control[J], Iron and Steel Engineer, 1965,42(8):73-77.
[13]Shohet K N, Townsend N A. Roll bending methods of crown control in four-high plate mills[J], Journal of Iron and Steel Institute,1969, (11):1088-1098.
[14]Ewards W J, Spooner P D. Automation of tandem mills[M], London, Iron Steel Institute,1973: 34-45.
[15]Tozawa Y, Ishikawa T. Study on stress distribution in strip rolling - rolling pressure and stresses at the upper stream side of roll gap[J], Memories of the Faculty of Engineering Nagoya University,1984,36(2):81-91.
[16]Salganik V. Mathematical modeling of roll load and deformation in a four-high strip mill[J], Journal of Materials Processing Technology,2002,125-126(9):695-699.
[17]王国栋,张树堂.四辊轧机轧辊弹性变形的矩阵计算法[J]，重型机械,1982,2(8)：9-18.
[18]王国栋,张树堂.轧辊弹性变形和板形理论的研究[J],钢铁研究总院学报,1983,3(3)：461-470.
[19]徐建忠,龚殿尧,王国栋,等.轧辊直径对热轧带钢凸度的影响规律[J],东北大学学报：自然科学版,2002,23(12)：1170-1173.
[20]徐建忠,孔祥伟,王国栋,等.大凸度支撑辊带钢凸度的控制能力[J],东北大学学报：自然科学版,2003,24(02)：151-154.
[21]徐建忠,龚殿尧,刘相华,等.单位宽度轧制力对热轧带钢凸度的影响规律[J],东北大学学报：自然科学版,2003,24(03)：280-283.
[22]龚殿尧,徐建忠,张凤琴,等.轧辊凸度及直径对热轧带钢凸度的影响[J],钢铁研究学报,2003,15(03)：17-20.
[23]常安,邸洪双,白金兰,等.影响冷轧边部减薄的因素[J],钢铁,2007,42(10)：51-55.
[24]Chen X L, Zhou J X. A specialized finite element model for investigating controlling affecting behavior of rolls and strip flatness [A], Proc. of the 4th International Steel Rolling conf., Deauvillle-France,1987,2(E4):1-7.
[25]Kihara J. Application of BEM to calculation of the roll profile in flat rolling[A], Proc. of the 4th International Steel Rolling Conf., Deauvillle-France,1987,2(E1):1-12.
[26]Knapinski M. The numerical analysis of roll deflection during plate rolling[J], Journal of Materials Processing Technology,2006,175(1):257-265.
[27]Shi X, Liu X H, Wang G D, et al. FEM analysis for roll flattening in thin strip rolling[A], Second International Conference on Advanced Structural Steels, ShangHai, China,2004:1037-1041.
[28]周顺新,钟掘,刘光连.轧机辊系弹性变形的有限元计算[J],中南工业大学学报(自然科学版),1994,25(6)：733-737.
[29]VB金兹伯格.高精度板带材轧制理论与实践[M],北京：冶金工业出版社,2000,328.
[30]Somers R R, Pallone G T, McDermott J F, et al. Verification and applications of a model for predicting hot strip profile crown and flatness[J], Iron and Steel Engineer,1984,61 (9):441-450.
[31]George S, James V L. Roll wear in finishing trains of hot strip mills[J], Iron and Steel Engineer, 1961,38(12):71-92.
[32]Uijtdebroeks H, Franssen R, Sonck G, et al. On-line analysis of the work roll surface deterioration in a hot strip mill[J], Revue de Metallurgie. Cahiers D'Informations Techniques, 1998,95(6):789-799.
[33]John S, Sikdar S, Mukhopadhyay A, et al. Roll wear prediction model for finishing stands of hot strip mill[J], Iron making and Steel making, 2006, 33(2):169-175
[34]邹家祥.轧辊磨损预报计算[J],钢铁,1986,21(7)：23-27.
[35]何安瑞,张清东,张杰,等.板带钢热轧支持辊不均匀磨损及其解决措施[J],上海金属,2000,22(2)：19-22.
[36]连家创,黄传清,陈连生.2050CVC热连轧机精轧机组轧辊磨损的研究[J],钢铁,2002,37(3)：24-27.
[37]令狐克志,何安瑞,杨荃,等.宽带钢热连轧支承辊磨损模型研究[J],钢铁,2006,41(12)：45-48.
[38]郭忠峰,龚殿尧,荆涛,等.1700热连轧机CVC轧辊的磨损[J],钢铁研究学报,2008,20(1)：21-24.
[39]Chang D F. Thermal stress in work rolls during the rolling of metal strip[J], Journal of Materials Processing Technology,1999,94(1):45-51.
[40]Campos A M, Carcia D F, Deabajo N, et al. Real-time rule-based control of the thermal crown of work rolls installed in hot strip mills[J], IEEE Transactions on Industry Applications,2004, 40(2):642-649.
[41]徐乐江.板带冷轧机板形控制与机型选择[M],北京：冶金工业出版社,2007,74.
[42]Tseng A A, Tong S X, Chen T C. Thermal expansion and crown evaluations in rolling processes[J], Steel Research,1996,67(5):188-199.
[43]Devadas C, Samarasekera I V. Heat transfer during hot rolling of steel strip[J], Ironmaking Steelmaking,1986,13(6):311-321.
[44]Pallone G T. Transient temperature distribution in work rolls during hot rolling of sheet and strip[J], Iron and Steel Engineer,1983,60(12):21-26.
[45]Galantucci L M, Tricarico L. Thermo-mechanical simulation of a rolling process with an FEM approach[J], Journal of Materials Processing Technology,1999,92-93(8):494-501.
[46]Ginzburg V B, Bakhtar F A, Issa R J. Application of coolflex model for analysis of work roll thermal conditions in hot strip mills[J], Iron and Steel Engineer,1997,74(11):38-45.
[47]Corral R L, Colas R, Perez A. Modeling the thermal and thermoelastic responses of work rolls used for hot rolling steel strip[J], Journal of Materials Processing Technology,2004,153(11): 886-893.
[48]Abbaspour M, Saboonchi A. Work roll thermal expansion control in hot strip mill[J], Applied Mathematical Modelling,2008,32(12):2652-2669.
[49]Zhang X M, Jiang Z Y, Tieu A K, et al. Numerical modelling of the thermal deformation of CVC roll in hot strip rolling[J], Journal of Materials Processing Technology,2002,131(12):219-223.
[50]杨利坡,彭艳,刘宏民.热连轧工作辊三维瞬态温度场数值模拟[J],燕山大学学报,2004,28(5)：380-383.
[51]徐光,张黄强,刘显军,等.CVC轧辊热凸度模型研究[J],冶金设备,2006,(5)：35-37.
[52]郭忠峰,徐建忠,李长生,等.1700热连轧机轧辊温度场及热凸度研究[J],东北大学学报(自然科学版),2008,29(4)：517-520.
[53]Aratani H, Ozono R, Nakano T. Expansion of pair cross (PC) mill applications to hot and cold rolling mills[J], Iron and Steel Engineer,1993,70(3):32-37.
[54]Nakajima K, Kikuma T, Matsumoto H, et al. Research on crown control for hot strip mills[J], Nippon Steel Technical Report,1980, (15):110-126.
[55]Yamada J, Ono H, Takigawa T, et al. Development of sumitomo VC (Variable Crown) roll system[J], Iron and Steel Maker,1982,9(6):37-42.
[57]Nagai T, Yamada J, Masui T, et al. Strip Shape and Profile Control with Sumitomo Variable Crown Roll System[J], Iron and Steel Engineer,1983,60(1):56-63.
[58]Kono T. Study of Crown Control Technologies in Hot and Cold Strip Mills[J], Sumitomo Metals, 1990,42(4):190-200.
[59]Hiruta T, Nakata N, Kitahama M, et al. Influence of rolling mill type on rigidity characteristics in hot and cold strip rolling[J], Iron and Steel Engineer,1996,73(3):32-37.
[60]#12
[61]#12
[62]Ono H, Watanabe I, Yoshimoto K, et al. Industrial Application of the HCX-MILL to Hot Strip Mills[J], Hitachi Review,1996,45(6):271-278.
[64]Bolte. CVC-technologies ein neues kaltwalzverfahren zur erzeugung planer stablbaednder[J], Stahl und Eisen,1986,106(9):59-64.
[65]Bald W, Beisemann G, Feldmann H, et al. Continuously variable crown(CVC) rolling[J], Iron and Steel Engineer,1987,64(3):32-41.
[66]Tsukamoto H, Matsumoto H. Shape and Crown Control Mill-Crossed Roll System [J], Iron and Steel Engineer,1984,61(10):26-37.
[67]Nakajima K, Kawamoto T, Hatae S, et al. Basic Characteristics of Pair Cross Mill[J], Technical Review-Mitsubishi Heavy Industries,1985,22(2):143-148.
[68]Kuroda A, Hayash K, Ayano T. Development of On-Line Roll Grinder[J], Iron and Steel Engineer,1993,70(3):38-44.
[69]Garcia D F, Garcia M, Obseo F, et al. Real-time flatness inspection system for steel strip production lines[J], Real-Time Imaging,1999,5(1):35-47.
[70]Henze M, Nilsson H. Stressometer systems with microcomputer-based electronics[J], ASEA Journal,1977,50(5):109-114.
[71]Garcia D P, Garcia M, Obeso F, et al. Real-time Flatness Inspection System for Steel Strip Production Lines[J], Real-Time Imaging,1999,5(1):35-47.
[72]Shaw D A, Burns T I. Hochkeppel T P, et al. Strip profile control technology and economic impact of target profiles[J], Iron and Steel Engineer,1995,72(9):22-30.
[73]Roey J V, Vergote H, Mielke R. Accurate profile and flatness control on a modernized hot strip mill[J], Iron and Steel Engineer,1996,73(2):29-33.
[74]Tellman G M, Heesen G J. Improving crown performance of a hot strip mill[J], Iron and Steel Engineer,1995,72(12):21-26.
[75]陈先霖,张杰,张清东,等.宽带钢热连轧机板形控制系统的开发[J],钢铁,2000,35(7)：28-33.
[76]钟恬,何安瑞,杨荃,等.热连轧自动板形控制系统的研究与应用[J],冶金自动化,2007,(4)：28-31.
[77]Cresdee R B, Edwards W J, Thomas P J. An advanced model for flatness and profile prediction in hot rolling[J], Iron and Steel Engineer,1991,68(10):41-51.
[78]段春华.新的板形理论[J],钢铁(增刊),1999,34(10)：809-811.
[79]Nilsson A. FE simulations of camber in hot strip rolling[J], Journal of Materials Processing Technology,1998,80-81(8):325-329.
[80]John S, Mukhopadhyay A, Sikdar S. Optimisation of work roll shifting and bending to roll thinner gauge HR coils using genetic algorithm[J], Ironmakong and SteelMaking,2006,33(1): 67-73.
[81]Salimi M, Forouzan M R. Determination of bending actuators set points to control crown and flatness in hot rolling of strip[J], Journal of Materials Processing Technology,2002,125-126[9]: 670-677.
[82]张进之,张宇.板形板厚的数学理论[J],冶金设备,2002,(3)：4-8.
[83]刘宏民.板形理论的研究现状与发展方向[J],钢铁,1993,28(2)：75-78.
[84]刘宏民,F.Sanfilippo,F.Dolci,等.热带钢连轧机板形设定控制数学模型[J],钢铁,1996,31(10)：30-34.
[85]王宏伟,陈先霖,张清东,等.宽带钢热连轧机多机架板形控制模型的探讨[J],冶金设备,2000,(1)：1-3.
[86]祝东奎,张清东,魏钢城,等.宽带钢热连轧机组的板形方程[J],北京科技大学学报,2001,23(1)：71-74.
[87]Liu H M, Zhang X L, Wang Y R. Transfer matrix method of flatness control for strip mills[J], Journal of Materials Processing Technology,2005,166(2):237-242.
[88]Zhang G M, Xiao H, Wang C H. Three-dimensional model for strip hot rolling[J], Journal of Iron and Steel Research,2006,13(1):23-26.
[89]Berger S, Hoen K, Hof H, et al. Evolution of CVC plus(?) technology in hot rolling mills[J], Revue de Metallurgie,2008,105(1):44-49.
[90]Lu C, Tieu A K, Jiang ZY. A design of a third-order CVC roll profile[J], Journal of Materials Processing Technology,2002,125-126:645-648.
[91]Xu G, Liu X J, Zhao J R, et al. Analysis of CVC roll contour and determination of roll crown[J], Journal of University of Science and Technology Beijing,2007,14(4):378-380.
[92]郭忠锋,徐建忠,李长生,等.几类典型轧辊横移变凸度辊型的比较与分析[J],东北大学学报(自然科学版),2008,29(6)：830-833.
[93]李洪波,张杰,曹建国,等.五次CVC辊型曲线的分析与设计[J,机械设计与制造,2008, (12)：41-43.
[94]刘光明,邸洪双,常安,等.CVC轧机辊型曲线设计及等效凸度探讨[J],东北大学学报(自然科学版),2008,29(10)：1443-1446.
[95]何伟,邸洪双,夏晓明,等.五次CVC辊型曲线的设计[J],轧钢,2006,23(2)：12-15.
[96]Auzinger D, Djumlija G, Nihuis T, et al. Application of advanced technology packages for improved strip profile and flatness in hot strip mills[J], Iron and Steel maker.2003,30(9):17-21.
[97]王云,宁晓霞.支撑辊边部导角数学模型的建立及其磨削工艺[J],本系冶金高等专科学校校报,2003,5(3)：29-31.
[98]常安,自金兰,邸洪双,等.首钢3500mm中板轧机辊型研究与应用[J],钢铁,2006,41(8)：41-45.
[99]田勇,胡贤磊,王昭东,等.2500mm中厚板精轧机支承辊辊型优化设计[J],2006,18(10)：23-25.
[100]窦鹏,李友国,梁开明,等.CVC热轧机支承辊接触应力有限元分析[J],清华大学学报(自然科学版),2005,45(12)：1668-1671.
[101]何安瑞,杨荃,陈先霖,等.变接触轧制技术在热带钢轧机上的应用[J],钢铁,2007,42(2)：31-34.
[102]杨荃,陈先霖,徐耀寰,等.应用变接触长度支承辊提高板形综合调控能力[J],钢铁,1995,30(3)：48-51.
[103]何安瑞,曹建国,吴庆海,等.热轧精轧机组变接触支持辊综合性能研究[J],上海金属,2001,23(])：14-17.
[104]何安瑞.宽带钢热轧精轧机组辊型的研究[D],北京科技大学博士论文,北京,2000.
[105]郝建伟,曹建国,张杰,等.2250 CVC热连轧机支持辊辊型研究[J],中南大学学报(自然科学版),2007,38(4)：734-738.
[106]李洪波,张杰,曹建国,等.CSP热连轧机支撑辊辊型研究[J]，钢铁,2008,43(3)：61-64.
[107]连家创,戚向东,岳晓丽,等.最优辊型技术的开发和应用[J],钢铁,2007,42(10)：60-63.
[108]岳晓丽,连家创,李汉良,等.1580PC热连轧机支承辊辊型优化曲线的研究[J]，中国机械工程,2001,12(7)：747-749.
[109]赵旭亮,王淑君,徐建忠,等.四辊轧机轧辊弹性变形的研究[J],东北大学学报(自然科学版),2008,29(6)：834-837.
[110]王国栋.板形控制和板形理论[M],北京：冶金工业出版社,1986,289.
[111]Guo R M. Development of a mathematical model for strip thickness profile[J], Iron and Steel Engineer,1990,67(9):32-39.
[112]Timoshenko S P, Good J N. Theory of Elasticity[M], New York:McGraw Hill,1951.
[113]Liu H M, Lian J C. Transverse distributions of front and back tension stresses in cold strip rolling[J], Chinese Journal of Metal Science and Technology,1992,8(6):427-434.
[115]孔祥伟.工作辊横移及自由程序轧制技术的研究[D]，东北大学博士论文,沈阳,2003.
[116]Sims R B. The calculation of roll force and torque in hot rolling mills[J], Proc. Inst. Mech. Engrs.,1954, (168):191-207.
[117]徐建忠,张凤琴,龚殿尧,等.四辊轧机轧辊弹性变形解析模块的开发[J],轧钢,2003,20(2)：8-11.
[118]Colas R, Ramirez J, Sandoval I, et al. Damage in hot rolling work rolls[J], Wear,1999,230(1): 56-60.
[119]Tseng A A, Lin F H. Roll cooling and its relationship to roll life[J], Metallurgical Transaction, 1989,20A(11):2305-2320.
[120]Guo R M.轧辊磨损统计模型的开发、验证和应用[A],第六界国际轧钢会议译文集,1994,70-75.
[121]Wang X D, Yang Q, He A R, et al. Comprehensive contour prediction model of work rolls in hot wide strip mill[J]. Journal of University of Science and Technology Beijing,2007,14(3): 240-245.
[122]孙一康.带钢热连轧的模型与控制[M],北京：冶金工业出版社,2002,38.
[123]Somers R R, Pallone G T, Mcdermott J F, et al. Verificationand applications of a model for predicting hot strip profile crown and flatness[J], Iron and Steel Engineer,1984,61(9):35-44.
[124]Guo R M. Optimal profile and shape control of flat sheet metal using multiple control devices[J], IEEE Transaction on Industry Applications,1996,32(2):449-457.
[125]孙一康.带钢热连轧的模型与控制[M],北京：冶金工业出版社,2002,171-173.
[126]Younes MA, Shahtout M, Damir M N. A parameters design approach to improve product quality and equipment performance in hot rolling[J], Journal of Materials Processing Technology,2006, 171(1):83-92.
[127]丁修堑.轧制过程自动化[M],北京：冶金工业出版社,2005,207.
[128]Fapiano D J, Steeper D E. Control of strip thickness in hot rolling[J], Iron and Steel Engineer, 1985,62(11):34-43.
[129]叶红卫.宝钢2050热轧过程厚度控制技术[J],宝钢技术,2003,(1)：23-27.
[130]Lawrence W J, MacAlister A F, Reever P J. On line modelling and control of strip cooling[J], Ironmaking and Steelmaking,1996,23(1):74-78.
[131]王萍,黄贞益,尹桂全,等.热轧带钢层流冷却温度控制模型的应用分析[J],钢铁研究学报,2007,19(4)：31-34.
[132]Hong W K, Kim P H, Moon Y H, et al. Hot strip width control method by using looper tension measuring system in finishing mill[J], Journal of Materials Processing Technology,2001,111(3): 74-78.
[133]吕程,王国栋,刘相华,等.热连轧精轧宽度自动控制[J],钢铁研究,1997,(5)：52-56.
[134]孙一康.带钢热连轧的模型与控制[M],北京：冶金工业出版社,2002,13.
[135]Shimoda N, Okamoto K, Wang H L, et al. Process control technology for thin strip production in Tangshan China[J], Iron and Steel Technology,2005,2(1):33-41.
[136]孙一康.带钢热连轧的模型与控制[M],北京：冶金工业出版社,2002,14.
[137]Zhang D H, Zhang H, Sun T, et al. Monitor automatic gauge control strategy with a Smith predictor for steel strip rolling[J], Journal of University of Science and Technology Beijing, 2008,15(6):827-832.
[138]Nolle L. SASS applied to optimum wok roll profile selection in the hot rolling of wide steel[J], Knowledge-Based Systems,2007,20(2):203-208.
[139]郭忠峰.热连轧带钢板形控制与辊型优化设计[D],东北大学博士论文,2008.