PENG Yan , NIU Shan . Review on Assessment Methods for Shape Control Performance of#br# Strip Rolling Mills[J]. Journal of Mechanical Engineering, 2017 , 53(6) : 26 -44 . DOI: 10.3901/JME.2017.06.026

 [1] 中国金属学会，中国钢铁工业协会. 2011—2020年中国钢铁工业科学与技术发展指南[M]. 北京：冶金工业出版社，2012.
 The Chinese Society for Metals，China Iron & Steel Association. Technology roadmap on Chinese steel industry 2011—2020[M]. Beijing：Metallurgical Industry Press，2012.
 [2] 王国栋. 板形控制和板形理论[M]. 北京：冶金工业出版社，1986.
 WANG Guodong. Shape control and shape theory[M]. Beijing：Metallurgical Industry Press，1986.
 [3] 连家创，刘宏民. 板厚板形控制[M]. 北京：兵器工业出版社，1996.
 LIAN Jiachuang，LIU Hongmin. Flatness and gauge control of strips[M]. Beijing：Weapon Industry Press，1996.
 [4] 曹建国，张杰，张少军，等. 轧钢设备及自动控制[M]. 北京：化学工业出版社，2010.
 CAO Jianguo，ZHANG Jie，ZHANG Shaojun，et al. Rolling equipment and automatic control[M]. Beijing：Chemical Industry Press，2010.
 [5] 刘宏民. 三维轧制理论及其应用[M]. 北京：科学出版社，1999.
 LIU Hongmin. Three dimensional rolling theory and its application[M]. Beijing：Science Press，1999.
 [6] 刘宏民，郑振忠，彭艳，等. 六辊CVC宽带轧机轧辊接触压力横向分布特性的计算机仿真[J]. 机械工程学报，2000，36(8)：69-73.
 LIU Hongmin，ZHENG Zhenzhong，PENG Yan，et al. Computer simulation of the roll contact pressure characteristic for 6-high CVC wide strip mill[J]. Chinese Journal of Mechanical Engineering，2000，36(8)：69-73.
 [7] LIU H M，ZHENG Z Z，PENG Y. Streamline strip element method for analysis of the three-dimensional stresses and deformations of strip rolling[J]. International Journal for Numerical Methods in Engineering，2001，50(5)：1059-1076.
 [8] 曹建国，张杰，陈先霖，等. 宽带钢热连轧机选型配置与板形控制[J]. 钢铁，2005，40(6)：40-43.
 CAO Jianguo，ZHANG Jie，CHEN Xianlin，et al. Selection of strip mill conf iguration and shape control[J]. Iron & Steel，2005，40(6)：40-43.
 [9]  LI Y L，CAO J G，YANG G H，et al. ASR bending force mathematical model for the same width strip rolling campaigns in hot rolling[J]. Steel Research International，2015，86(5)：567-575.
[10] CAO J G，ZHANG J，YANG G H，et al. Comprehensive edge drop control technology of non-oriented electrical steel strip in 4-high ECC tandem cold rolling mills[C]//Proceedings of the 10th ICSR. Beijing：Metallurgical Industry Press，2010：1065-1073.
[11] YU Q B，LIU X H，TANG D L. Extreme extensibility of copper foil under compound forming conditions.[J]. Scientific Reports，2013，3(8)：3556-3556.
[12] 刘玉礼，连家创，段振勇，等. 新型四辊DC轧机的研究[J]. 重型机械，1989(3)：51-56.
 LIU Yuli，LIAN Jiachuang，DUAN Zhenyong，et al. Research into a new 4-high DC rolling mill[J]. Heavy Machinery，1989(3)：51-56.
[13] 白振华，常金梁，郭乾勇，等. AS-UCM 机型的开发及其板形控制技术[J]. 中国机械工程，2015，26(10)：1390-1394.
 BAI Zhenhua，CHANG Jinliang，GUO Qianyong，et al. Development of AS-UCM temper mill and its shape control technology[J]. China Mechanical Engineering，2015，26(10)：1390-1394.
[14] 王仁忠，杨荃，何安瑞，等. 宽带钢热连轧轧机弯辊控制性能研究[J]. 冶金自动化，2006(S1)：584-587.
 WANG Renzhong，YANG Quan，HE Anrui，et al. Study on the control performance of roller bending of wide strip hot continuous rolling mills[J]. Metallurgical Industry Automation，2006(S1)：584-587.
[15] 杨荃，杜晓钟. 六辊精密冷连轧机带钢截面和边缘降调控性能研究[J]. 鞍钢技术，2007(5)：1-4.
 YANG Quan，DU Xiaozhong. Study on control property of strip steel profile and wedge drop in 6-high precision cold tandem mill[J]. Angang Technology，2007(5)：1-4.
[16]  MASUI T，YAMADA J，NAGAI T，et al. Strip shape and profile control with a new type of the variable crown roll system[J]. Transactions ISIJ，1983，23(10)：846-853.
[17]  NISHIOKA K，MIZUTANI Y，HORI Y，et al. High reduction rolling technology on pair cross mill[J]. Nippon Steel Technical Report，1997(75)：9-19.
[18]  NAKAJIMA K，ASAMURA T，KIKUMA T，et al. Hot strip crown control by six-high mill[J]. Transactions ISIJ，1984，24(4)：284-291.
[19]  FUKUDA N. Progress of rolling technologies in Japan[J]. Transactions ISIJ，1981，21(4)：221-234.
[20]  HE A R，KONG F F，SHAO J. Novel curved roll contour technology for profile control in hot strip mills[J]. Ironmaking & Steelmaking，2015，42(1)：55-62.
[21]  何安瑞，张清东，杨荃，等. 现代化冷连轧机的最佳机型配置[J]. 钢铁，2004，39(5)：43-46.
 HE Anrui，ZHANG Qingdong，YANG Quan，et al. Optimum configuration of modern tandem cold rolling mill[J]. Iron & Steel，2004，39(5)：43-46.
[22]  陈先霖. 新一代高技术薄带冷轧机的发展趋向[J]. 上海金属，1995，17(4)：1-8.
 CHEN Xianlin. Development trend of the new generation of high-tech thin strip cold rolling mills[J]. Shanghai Metals，1995，17(4)：1-8.
[23] PENG Y，LIU H M，WANG D C. Simulation of type selection for 6-high cold tandem mill based on shape control ability[J]. Journal of Central South University of Technology，2007，14(2)：278-284.
[24] 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.
 ZHU Dongkui，ZHANG Qingdong，WEI Gangcheng，et al. Shape equation of hot strip mills[J]. Journal of University of Science and Technology Beijing，2001，23(1)：71-74.
[25] 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.
[26] SEILINGER A，MAYRHOFER A，KAINZ A. SmartCrown—a new system for improved profile and flatness control in strip mills[J]. Steel Times International，2002(11)：11-13.
[27] 杨光辉，曹建国，张杰，等．SmartCrown四辊冷连轧机工作辊辊形[J]．北京科技大学学报，2006，28(7)：669-671.
 YANG Guanghui，CAO Jianguo，ZHANG Jie，et al. SmartCrown work roll contour of a 4-hi tandem cold rolling mill[J]. Journal of University of Science and Technology Beijing，2006，28(7)：669-671.
[28] LI H B，ZHANG J，CAO J G，et al. Analysis of crown control characteristics for SmartCrown work roll [C]//Advanced Materials Research. Trans. Tech. Publications，2011，156-157：1261-1265.
[29] CAO J G，WEI G C，ZHANG J，et al. VCR and ASR technology for profile and flatness control in hot strip mills[J]. Journal of Central South University of Technology，2008，15：264-270.
[30] 臧元国，张霖，张艳艳，等. HVC辊形在莱钢1500热连轧机组的应用[J]. 山东科学，2009，22(3)：80-82.
 ZANG Yuanguo，ZHANG Lin，ZHANG Yanyan，et al. The application of HVC roll in Laiwu Steel’s 1500 hot strip mill[J]. Shandong Science，2009，22(3)：80-82.
[31] 连家创. 一种轴向移动改变辊缝凸度并可变辊缝形状的轧辊辊型：95117449.5[P]. 1997-05-21.
 LIAN Jiachuang. A roll profile for variable roll gap crown and shape with axial movement：95117449.5[P]. 1997-05-21.
[32] 王鹏飞，刘宏民，彭艳，等. 1450mm冷连轧机多变量最优板形闭环控制策略研究与应用[J]. 燕山大学学报，2014，38(2)：122-126.
 WANG Pengfei，LIU Hongmin，PENG Yan，et al. Strategy and application of flatness control system based on multi-variable optimal control of 1450mm cold strip mill [J]. Journal of Yanshan University，2014，38(2)：122-126.
[33] 常铁柱，张清东，姜正连，等. 连续热镀锌线板形控制技术研究[J]. 中国机械工程，2008，19(2)：231-235.
 CHANG Tiezhu，ZHANG Qingdong，JIANG Zhenglian，et al. Research on strip shape control technology on continuous galvanizing line[J]. China Mechanical Engineering，2008，19(2)：231-235.
[34] 段婷婷，黄彦峰，张晓伟. 冷轧机板形调控能力评价指标研究[J]. 一重技术，2012(6)：13-17.
 DUAN Tingting，HUANG Yanfeng，ZHANG Xiaowei. Indexes to evaluate plate shape control ability of cold mills[J]. CFHI Technology，2012(6)：13-17.
[35] 许健勇，姜正连，阙月海. 热轧来料及冷轧工艺对连轧机出口板形的影响[J]. 宝钢技术，2003(5)：60-64.
 XU Jianyong，JIANG Zhenglian，QUE Yuehai. Effect of HR coil and CR technology on strip shape at the exit of the mill[J]. Baosteel Technology，2003(5)：60-64.
[36] 王晓晨，杨荃，孙友昭. 六辊冷轧机的弯辊力组合板形控制策略[J]. 北京科技大学学报，2014，36(6)：824-829.
 WANG Xiaochen，YANG Quan，SUN Youzhao. Shape control strategy by bending force combination adjustment for 6-hi cold rolling mill[J]. Journal of University of Science and Technology Beijing，2014，36(6)：824-829.
[37] 戚向东. 宝钢新建板带轧机轧制规程及机型选择的研究[D]. 秦皇岛：燕山大学，2002.
 QI Xiangdong. Study on pass schedule and mill types selection for new plate and strip mill in Baosteel[D]. Qinhuangdao：Yanshan University，2002.
[38] 戚向东，连家创，李山青. 新建冷带连轧机机型选择和配置方案研究[J]. 重型机械，2005(1)：1-4.
 QI Xiangdong，LIAN Jiachuang，LI Shanqing. Study on type selection for new cold strip tandem mill[J]. Heavy Machinery，2005(1)：1-4.
[39] 张清东，代畅，文杰，等. 二十辊森吉米尔轧机板形调控性能仿真研究[J]. 轧钢，2013，30(3)：1-6.
 ZHANG Qingdong，DAI Chang，WEN Jie，et al. Simulation and analysis on shape control behavior of 20-h Sendzimir mill[J]. Steel Rolling，2013，30(3)：1-6.
[40] 曾尚武，李激光. 热轧板凸度控制实践分析[J]. 轧钢，2011，28(6)：8-11.
 ZENG Shangwu，LI Jiguang. Analysis about crown control of hot rolled plate[J]. Steel Rolling，2011，28(6)：8-11.
[41] 李洪波，张杰，曹建国，等. 热轧带钢横截面多参数表示及高精度板形控制[J]. 北京科技大学学报，2009，31(4)：487-491.
 LI Hongbo，ZHANG Jie，CAO Jianguo，et al. Strip profile multi-factor description and high-quality steel rolling control in hot rolling[J]. Journal of University of Science and Technology Beijing，2009，31(4)：487-491.
[42] 刘洋，王晓晨，杨荃，等. 基于预测函数算法的冷连轧边降滞后控制研究[J]. 机械工程学报，2015，51(18)：64-70.
 LIU Yang，WANG Xiaochen，YANG Quan，et al. Research on time-delay of the edge drop control in tandem cold mill based on the predictive functional control algorithm[J]. Journal of Mechanical Engineering，2015，51(18)：64-70.
[43] KAMADA S，LYAMA S，HAMADA R，et al. Edge profile control using pair cross mill in cold rolling[J]. Iron & Steel Engineer，1996，73(6)：20-26.
[44] 何安瑞，邵健，孙文权，等. 冷轧无取向硅钢横向厚差控制[J]. 机械工程学报，2011，47(10)：25-30.
 HE Anrui，SHAO Jian，SUN Wenquan，et al. Transverse thickness deviation control of non-oriented silicon steel during cold rolling[J]. Journal of Mechanical Engineering，2011，47(10)：25-30.
[45] LINGHU K Z，JIANG Z Y，ZHAO J W，et al. 3D FEM analysis of strip shape during multi-pass rolling in a 6-high CVC cold rolling mill[J]. The International Journal of Advanced Manufacturing Technology，2014，74(9)：1733-1745.
[46] HARTUNG H G，HOLZ R，PAWELSKI H. Kaltband-Ertragssteigerung durch das EDC-System[J]. Metall，2000，54(10)：581-585.
 HARTUNG H G，HOLZ R，PAWELSKI H. Increased yield of cold strip through the EDC system[J]. Metall，2000，54(10)：581-585.
[47] 孙铁铠，赵永和. WRS轧机板形控制特性的研究[J]. 东北重型机械学院学报，1991，15(2)：139-146.
 SUN Tiekai，ZHAO Yonghe. On profile controlling characteristics of WRS mill[J]. Journal of Northeast Institute of Heavy Machinery，1991，15(2)：139-146.
[48] 郭新宇，何安瑞，邵健，等. 铝热连轧分段冷却系统建模与仿真[J]. 机械工程学报，2013，49(4)：70-74.
 GUO Xinyu，HE Anrui，SHAO Jian，et al. Modeling and simulation of subsectional cooling system during hot aluminum rolling[J]. Journal of Mechanical Engineering，2013，49(4)：70-74.
[49] 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(2)：48-51.
 YANG Quan，CHEN Xianlin，XU Yaohuan，et al. Applying VCL back-up roll to raise the control level of strip shape[J]. Iron & Steel，1995，30(2)：48-51.
[50] 周晓敏，张清东，王长松，等. UCMW轧机的边缘降控制性能和影响因素分析[J]. 北京科技大学学报，2007，29(4)：417-420.
 ZHOU Xiaomin，ZHANG Qingdong，WANG Changsong，et al. Edge drop control performance and influence factor analysis of a UCMW cold mill[J]. Journal of University of Science and Technology Beijing，2007，29(4)：417-420.
[51] 吴海淼，董建荣，赵立新，等. 冷轧带钢边部减薄影响因素的分析[J]. 重型机械，2009(3)：30-34.
 WU Haimiao，DONG Jianrong，ZHAO Lixin，et al. Analysis on edge-drop and its influencing factors in cold strip rolling[J]. Heavy Machinery，2009(3)：30-34.
[52] 王军生，赵启林，矫志杰，等. 宝钢益昌冷连轧机组改造新技术[J]. 材料与冶金学报，2002，1(2)：136-141.
 WANG Junsheng，ZHAO Qilin，JIAO Zhijie，et al. New technology for Baosteel Yichang tandem cold mill modernization[J]. Journal of Materials and Metallurgy，2002，1(2)：136-141.
[53] 章晓辉，成小军，赵检罗，等. 冷轧平整边皱产生原因及解决措施[J]. 钢铁，2008，43(2)：65-67.
 ZHANG Xiaohui，CHENG Xiaojun，ZHAO Jianluo，et al. Courses of edge wrinkling in cold temper rolling and countermeasures[J]. Iron & Steel，2008，43(2)：65-67.
[54] KITAMURA K，NAKANISHI T，YARITA I，et al. Edge-drop control of hot and cold rolled strip by tapered-crown work roll shifting mill[J]. Iron & Steel Engineer，1995，72(2)：27-32.
[55] 曹建国，毛娜，张杰，等. 冷连轧机边降控制窜辊数学模型研究[J]. 钢铁，2008，43(8)：57-60.
 CAO Jianguo，MAO Na，ZHANG Jie，et al. Study on shifting mathematical model of edge drop control in tandem cold rolling mill[J]. Iron & Steel，2008，43(8)：57-60.
[56] 贾广顺. SMS-EDC轧机边降控制能力特性研究[D]. 秦皇岛：燕山大学，2010.
 JIA Guangshun. Special properties analysis of the edge drop control ability for SMS-EDC mill[D]. Qinhuangdao：Yanshan University，2010.
[57] 彭艳，贾广顺. 一种SMS-EDC轧机轧制带材边部减薄量的预报方法：201010220590.0[P]. 2010-12-01.
 PENG Yan，JIA Guangshun. An edge drop forecast method of SMS-EDC rolling mill：201010220590.0[P]. 2010-12-01.
[58] 张云鹏，吴庆海，王长松. 六辊CVC冷轧机板形控制性能研究[J]. 冶金设备，1998(6)：8-10.
 ZHANG Yunpeng，WU Qinghai，WANG Changsong. Study of flatness control on 6-h CVC mill[J]. Metallurgical Equipment，1998(6)：8-10.
[59] HAJDUK D，BERNARDES F G. Models for flatness of hot rolled strips and sheets[C/OL]. [2016-01-08]. http://www.ita-tech.cz/cs/produkty-a-sluzby/konference-vybrane-prispevky.
[60] 魏钢城，张清东，陈先霖. 2250mm带钢热连轧机板形调控性能改善与提高[J]. 钢铁，2007，42(4)：46-49.
 WEI Gangcheng，ZHANG Qingdong，CHEN Xianlin. Improvement on shape control performance on finishing train of 2250 mm hot steel strip mill[J]. Iron & Steel，2007，42(4)：46-49.
[61] 彭艳，刘宏民，张守刚，等. HC轧机板形板凸度控制策略的研究[J]. 钢铁，2002，37(4)：35-38.
 PENG Yan，LIU Hongmin，ZHANG Chougang，et al. Shape and profile control strategy for HC mill[J]. Iron & Steel，2002，37(4)：35-38.
[62] 上郡龍馬，御厨尚，加地孝行，ほか. クラスターミルの自動形状制御：12段クラスター圧延機の実機特性 III[J]. 鐵と鋼，1986，72(4)：373.
 KAMIGORI R，MIKURIYA T，KAJI T，et al. Automatic flatness control-system of cluster mill：characteristics of 12-hi cluster mill III[J]. Tetsu-to-Hagane，1986，72(4)：373.
[63] ALJABRI A，JIANG Z Y，WEI D B. Analysis of thin strip profile by work roll crossing and shifting in asymmetrical cold rolling[J]. International Journal of Modern Physics B，2015，29(10-11)：1540032.
[64] YU H L，LIU X H，LEE G T. Contact element method with two relative coordinates and its application to prediction of strip profile of a Sendzimir mill[J]. ISIJ International，2007，47(7)：996-1005.
[65] 陆小武，彭艳，刘宏民. DC轧机板厚板形控制策略[J]. 中南大学学报，2011，42(8)：2309-2317.
 LU Xiaowu，PENG Yan，LIU Hongmin. Gauge and shape control strategy for DC mill[J]. Journal of Central South University，2011，42(8)：2309-2317.
[66] CAO J G，ZHANG J，KONG N，et al. Finite element analysis of strip and rolling mills[M]//MORTAL D，Finite Element Analysis，Rijeka：Sciyo，2010：561-587.
[67] 张清东，白剑，徐乐江，等. 宝钢1550UCMW冷连轧机组机型研究与改善[J]. 钢铁，2009，44(11)：67-70.
 ZHANG Qingdong，BAI Jian，XU Lejiang，et al. Study and improvement of mill type of 1550 tandem cold mill in Baosteel[J]. Iron & Steel，2009，44(11)：67-70.
[68] LIU H M，LIAN J C，PENG Y. Third-power spline function strip element method and its simulation of the three-dimensional stresses and deformations of cold strip rolling[J]. Journal of Materials Processing Technology，2001，116(2-3)：235-243.
[69] 孙静娜，薛涛，杜凤山，等. 基于刚度特性分析的UCM冷轧机板形板厚综合设定模型[J]. 钢铁，2014，49(8)：64-69.
 SUN Jingna，XUE Tao，DU Fengshan，et al. Strip shape and gauge integrated set model of UCM cold mill based on rigidity characteristics analysis[J]. Iron & Steel，2014，49(8)：64-69.
[70] 彭艳，刘宏民，胡建平，等. 冷轧带钢板形控制仿真分析软件(FCEACSR)[J]. 冶金设备，2003(3)：13-16.
 PENG Yan，LIU Hongmin，HU Jianping，et al. Software of flatness control emulation analysis of cold strip rolling(FCEACSR)[J]. Metallurgical Equipment，2003(3)：13-16.
[71] 王志勇. 基于模糊混沌的板形识别与控制技术的研究[D]. 秦皇岛：燕山大学，2006.
 WANG Zhiyong. Research on flatness recognition based on fuzzy chaotic and control technique[D]. Qinhuangdao：Yanshan University，2006.
[72] LIU H M，PENG Y，CHU Y P，et al. Strip element method for shape discrimination of strip rolling[J]. Communications in Numerical Methods in Engineering，2004，20(9)：709-720.
[73] OGAWA S，HAMAUZU S，MATSUMOTO H，et al. Prediction of flatness of fine gauge strip rolled by 12-high cluster mill[J]. ISIJ International，1991，31(6)：599-606.
[74] KIHARA J. Application of boundary element method to rolling technology with special respect to flatness and crown of plate and sheet[J]. ISIJ International，1991，31(6)：543-549.
[75] HARA K，YAMADA T，TAKAGI K. Shape controllability for quarter buckles of strip in 20-high Sendzimir mills[J]. ISIJ International，1991，31(6)：607-613.
[76] ZHANG X L，ZHAO L，ZANG J Y，et al. Flatness intelligent control based on T-S cloud inference neural network[J]. ISIJ International，2014，54(11)：2608-2617.
[77] 彭艳，刘宏民. 冷轧带钢板形检测信号模式识别方法的进展[J]. 燕山大学学报，2003，27(2)：142-145.
 PENG Yan，LIU Hongmin. Pattern recognition method progress of measured signals of shape in cold rolling[J]. Journal of Yanshan University，2003，27(2)：142-145.
[78] 陈丽杰. 基于IGA-RBF网络的板形智能识别与控制[D]. 秦皇岛：燕山大学，2009.
 CHEN Lijie. IGA-RBF-based strip shape intelligence recognition and control research[D]. Qinhuangdao：Yanshan University，2009.
[79] 彭艳，刘宏民. 基于机理模型的HC冷轧机板形预设定控制模型的工业应用[C]//中国金属学会. 2001中国钢铁年会论文集. 北京：冶金工业出版社，2001：96-99.
 PENG Yan，LIU Hongmin. Industry application of shape preset control model for HC mill based on mechanism model[C]//The Chinese Society for Metals. CSM 2001 Annual Meeting Proceedings. Beijing：Metallurgical Industry Press，2001：96-99.
[80] 彭艳. 基于条元法的HC冷轧机板形预设定控制理论研究及工业应用[D]. 秦皇岛：燕山大学，2000.
 PENG Yan. Theoretical studies and engineering application of shape preset control for HC cold mill based on strip element method[D]. Qinhuangdao：Yanshan University，2000.
[81] 刘建，王益群，孙福，等. 基于粒子群理论的板形模糊模式识别方法[J]. 机械工程学报，2008，44(1)：173-178.
 LIU Jian，WANG Yiqun，SUN Fu，et al. Fuzzy pattern recognition method of flatness based on particle swarm theory[J]. Journal of Mechanical Engineering，2008，44(1)：173-178.
[82] WANG P F，PENG Y，LIU H M，et al. Actuator efficiency adaptive flatness control model and its application in 1250 mm reversible cold strip mill[J]. Journal of Iron and Steel Research，International，2013，20(6)：13-20.
[83] 张云鹏，王长松，张清东. 基于效应函数的冷轧机板形闭环控制策略[J]. 北京科技大学学报，1999(2)：195-197.
 ZHANG Yunpeng，WANG Changsong，ZHANG Qingdong. Flatness control strategy on cold mill based on efficiency function[J]. Journal of University of Science and Technology Beijing，1999(2)：195-197.
[84] 王鹏飞，张殿华，刘佳伟，等. 冷轧板形测量值计算模型的研究与应用[J]. 机械工程学报，2011，47(4)：58-65.
 WANG Pengfei，ZHANG Dianhua，LIU Jiawei，et al. Research and application of the flatness measurement calculation model on cold rolling mill[J]. Journal of Mechanical Engineering，2011，47(4)：58-65.
[85] WANG X C，YANG Q，LIANG Z G，et al. Research on generalized overall shape setting control models with asymmetric shape control function for UCM mill[C]//Advanced Materials Research. Trans Tech Publications，2012，415：478-486.
[86] 高山凤，刘鸿飞，郗安民，等. 热轧铝板带分段冷却闭环控制策略[J]. 机械工程学报，2016，52(8)：207-212.
 GAO Shanfeng，LIU Hongfei，XI Anmin，et al. Closed-loop control strategy of segmented cooling in hot rolling of aluminum alloys[J]. Journal of Mechanical Engineering，2016，52(8)：207-212.
[87] 刘宏民，于丙强，杨利坡，等. 整辊镶块智能型冷轧带钢板形仪的研制与工业应用[J]. 钢铁，2011，46(12)：86-89.
 LIU Hongmin，YU Bingqiang，YANG Lipo，et al. Development of cold strip shape meter with entire roller inlayed block intelligence and its industrial application[J]. Iron & Steel，2011，46(12)：86-89.
[88] 刘宏民，于丙强，杨利坡，等. 整辊无缝无线式板形仪：2009100757909[P]. 2010-04-14.
 LIU Hongmin，YU Bingqiang，YANG Lipo，et al. Seamless wireless type flatness meter：2009100757909[P]. 2010-04-14.
[89] 郝亮，邸洪双，龚殿尧，等. 带钢冷轧闭环反馈控制最优化算法程序开发[J]. 机械工程学报，2012，48(6)：39-43.
 HAO Liang，DI Hongshuang，GONG Dianyao，et al. Development of optimization algorithm for closed-loop feedback control in cold strip rolling[J]. Journal of Mechanical Engineering，2012，48(6)：39-43.
[90] 闫沁太，张杰，贾生晖，等. 冷轧机板形调节能力分析方法的研究与应用[J]. 机械工程学报，2011，47(4)：77-81.
 YAN Qintai，ZHANG Jie，JIA Shenghui，et al. Research on analyzing the flatness adjusting capacity for cold mill and its application[J]. Journal of Mechanical Engineering，2011，47(4)：77-81.
[91]  JIANG Z L，WANG G D，ZHANG Q，et al. Shifting-roll profile and control characteristics[J]. Journal of Materials Processing Technology，1993，37(1-4)：53-60.
[92] 张连军，张清东，于孟. 20辊森吉米尔轧机板形调控性能研究[J]. 冶金设备，2008(1)：40-43.
 ZHANG Lianjun，ZHANG Qingdong，YU Meng. Analysis on shape control behavior of 20h Sendzimir mill by finite element method[J]. Metallurgical Equipment，2008(1)：40-43.
[93] 严洪凯，杜素周，张清东. CVC工作辊磨损和热凸度对轧机板形控制性能的影响[J]. 冶金设备，2000(3)：1-4.
 YAN Hongkai，DU Suzhou，ZHANG Qingdong. Influence of wear and hot crown of CVC work roll on the behaviors of strip shape control[J]. Metallurgical Equipment，2000(3)：1-4.
[94] 黄华贵，史英钦，任新意，等. 工作辊凸度对超宽六辊CVC轧机板形调控性能的影响[J]. 钢铁，2014，49(7)：88-93.
 HUANG Huagui，SHI Yingqin，REN Xinyi，et al. Influence of initial crown of work roll on strip shape adjusting performance of ultra-wide 6-h CVC mill[J]. Iron & Steel，2014，49(7)：88-93.
[95] YASUDA K，NARITA K，SHIDA S，et al. Rolling of dead flat strip using UC mill with small diameter work rolls[C]//Proceedings of the 4th International Steel Rolling Conference：the Science and Technology of Flat Rolling. 1987，2：E22.1-E22.12.
[96] 李洪波，张杰，曹建国，等. CSP热连轧机板形的调控特性[J]. 中南大学学报，2009，40(2)：422-428.
 LI Hongbo，ZHANG Jie，CAO Jianguo，et al. Characteristics of profile control on CSP hot strip mill[J]. Journal of Central South University，2009，40(2)：422-428.
[97] 刘玉礼，胡锡增，孙铁铠. HC轧机板形控制机能的理论与实验研究[J]. 河北机电学院学报，1989(3)：83-86.
 LIU Yuli，HU Xizeng，SUN Tiekai. Theoretical and experimental research on shape control function of HC rolling mill[J]. Journal of Hebei Institute of Mechano-Electric Engineering，1989(3)：83-86.
[98] 王骏飞. 宝钢2030冷连轧机CVC和DSR板形控制技术比较研究[C]//中国金属学会第八届轧钢年会论文集. 北京，2004：190-196.
 WANG Junfei. Comparisons between CVC and DSR technology in Baosteel’s 2030 cold tandem mill[C]//The 8th Annual Rolling Conference Symposium of the Chinese Society for Metals. Beijing，2004：190-196.
 [99] 林秉敬. 六辊可逆冷轧板形分析模型研究[D]. 重庆：重庆大学，2008.
 LIN Bingjing. Research in reversible six-high cluster mill profile model[D]. Chongqing：Chongqing University，2008.
[100] 陈曦，张小平，刘光明，等. 四辊板带轧机全宽度辊缝横向刚度分析[J]. 锻压技术，2015，40(9)：111-116.
 CHEN Xi，ZHANG Xiaoping，LIU Guangming，et al. Analysis on transverse rigidity along entire roll gap width of four-roller strip mill[J]. Forging and Stamping Technology，2015，40(9)：111-116.
[101] 陈先霖. 新一代高技术宽带钢轧机的板形控制[J]. 北京科技大学学报，1997，19(S1)：1-5.
 CHEN Xianlin. Flatness control in new generation high-tech mills for wide strip rolling[J]. Journal of University of Science and Technology Beijing，1997，19(S1)：1-5.
[102] YANG G H，CAO J G，ZHANG J，et al. Backup roll contour of a SmartCrown tandem cold rolling mill[J]. Journal of University of Science and Technology Beijing，2008，15(3)：357-361.
[103] 孙林，张清东，陈先霖，等. 2800四辊轧机“逆宽”轧制中的凸度控制[J]. 北京科技大学学报，2001，23(3)：278-280.
 SUN Lin，ZHANG Qingdong，CHEN Xianlin，et al. Plate crown control on RPWIS for 2800 four-high mill[J]. Journal of University of Science and Technology Beijing，2001，23(3)：278-280.
[104] 魏立群，戴志方，肖壮，等. 高速冷连轧机组的振动与对策研究[J]. 机械工程学报，2016，52(11)：88-94.
 WEI Liqun，DAI Zhifang，XIAO Zhuang，et al. Research of vibration and strategy in high speed cold-rolling mill[J]. Journal of Mechanical Engineering，2016，52(11)：88-94.
[105] 李振兴，刘相华. 热轧宽带钢精轧机组机架振动分析及抑制措施[J]. 钢铁，2009，44(12)：50-53.
 LI Zhenxing，LIU Xianghua. Vibration of finishing stands in hot strip mill and suppression measure[J]. Iron & Steel，2009，44(12)：50-53.
[106] YUN I S，WILSON W R D，EHMANN K F. Review of chatter studies in cold rolling[J]. International Journal of Machine Tools and Manufacture，1998，38(12)：1499-1530.
[107] 郜志英，臧勇，曾令强. 轧机颤振建模及理论研究进展[J]. 机械工程学报，2015，51(16)：87-105.
 GAO Zhiying，ZANG Yong，ZENG Lingqiang. Review of modelling and theoretical studies on chatter in the rolling mills[J]. Journal of Mechanical Engineering，2015，51(16)：87-105.
[108] 高亚南，彭艳，孙建亮，等. 1580热连轧机F2精轧机振动综合测试与分析[J]. 钢铁，2013，48(1)：52-58.
 GAO Yanan，PENG Yan，SUN Jianliang，et al. Vibration comprehensive test and analysis on finisher 2 of 1580 hot strip mill[J]. Iron & Steel，2013，48(1)：52-58.
[109] 孙建亮，彭艳，高亚南，等. 热连轧机水平振动仿真与实验研究[J]. 中南大学学报，2015，46(12)：1-7.
 SUN Jianliang，PENG Yan，GAO Yanan，et al. Simulation and experiment of horizontal vibration of hot tandem rolling mill[J]. Journal of Central South University，2015，46(12)：1-7.
[110] SUN Jianliang，PENG Yan，LIU Hongmin. Coupled dynamic modeling of rolls model and metal model for four high mills based on strip crown control[J]. Chinese Journal of Mechanical Engineering，2013，26(1)：144-150.
[111] 孙建亮，张明，彭艳. 六辊轧机扭振动态建模及与板带钢质量关系研究[J]. 工程力学，2014，34(4)：239-244.
 SUN Jianliang，ZHANG Ming，PENG Yan. Torsional vibration of 6-h rolling mill based on continuum dynamics and its relationship with strip quality[J]. Engineering Mechanics，2014，34(4)：239-244.
[112] PENG Yan，ZHANG Yang，SUN Jianliang，et al. Tandem strip mill’s multi-parameter coupling dynamic modeling based on the thickness control[J]. Chinese Journal of Mechanical Engineering，2015，28(2)：353-362.
[113] 曹建国，陈先霖，张清东，等. 宽带钢热轧机轧辊磨损与辊形评价[J]. 北京科技大学学报，1999，21(2)：188-190.
 CAO Jianguo，CHEN Xianlin，ZHANG Qingdong，et al. Roll wear pattern and appraisal of roll contour in hot wide strip mill[J]. Journal of University of Science and Technology Beijing，1999，21(2)：188-190.
[114] 张清东，黄纶伟，周晓敏. 宽带钢轧机板形控制技术比较研究[J]. 北京科技大学学报，2000，22(2)：177-181.
 ZHANG Qingdong，HUANG Lunwei，ZHOU Xiaomin. Comparative study on shape control technologies for wide strip mills[J]. Journal of University of Science and Technology Beijing，2000，22(2)：177-181.
[115] 何安瑞，张清东，曹建国，等. 宽带钢热轧支持辊辊形变化对板形的影响[J]. 北京科技大学学报，1999，21(6)：565-567.
 HE Anrui，ZHANG Qingdong，CAO Jianguo，et al. Effect of back-up roll profile in hot wide strip mill on the strip profile and flatness[J]. Journal of University of Science and Technology Beijing，1999，21(6)：565-567.
[116] WANG X D，LI F，LI B H，et al. VCR back-up roll and negative work roll contour design for solving roll spalling and transfer bar profile problems in hot strip mill[J]. Ironmaking & Steelmaking，2010，37(8)：633-640.
[117] PENG K X，ZHONG H，ZHAO L，et al. Strip shape modeling and its setup strategy in hot strip mill process[J]. The International Journal of Advanced Manufacturing Technology，2014，72(5-8)：589-605.
[118] 王静. 基于遗传算法的板形缺陷识别的研究[D]. 鞍山：辽宁科技大学，2012.
 WANG Jing. Research on defects recognition of flatness shape based on genetic algorithms[D]. Anshan：University of Science and Technology Liaoning，2012.
[119] 张清东，张晓峰，文杰. 薄带钢冷连轧横向厚差控制理论及DI材横向厚差控制技术研究[J]. 机械工程学报，2013，49(24)：30-38.
 ZHANG Qingdong，ZHANG Xiaofeng，WEN Jie. Theory and technology of transverse thickness deviation control for DI tinplate during tandem cold rolling[J]. Journal of Mechanical Engineering，2013，49(24)：30-38.
[120] GUO R M. Cascade effect of crown and shape control devices in tandem rolling mills[J]. Iron & Steel Engineer，1988，65(7)：29-38.
[121] CHIEN W Y，HWU Y J，CHEN L H. An online setup strategy of strip shape control for tandem hot rolling mills[J]. Chinese Steel Technical Report，2010(23)：21-24.
[122] 彭艳，刘宏民，胡建平，等. 冷轧带材板形分析及预设定控制软件(FAPCSR)及其应用[J]. 钢铁，2003，38(2)：34-37.
 PENG Yan，LIU Hongmin，HU Jianping，et al. Software for flatness analysis and presetting control of cold strip rolling(FAPCSR) and application[J]. Iron & Steel，2003，38(2)：34-37.
[123] 张清东，吴越，瞿标，等. 1220冷连轧机板形控制性能综合改善[J]. 上海金属，2005，27(3)：23-25.
 ZHANG Qingdong，WU Yue，QU Biao，et al. Improving on the flatness control performance of 1220mm cold tandem mill[J]. Shanghai Metals，2005，27(3)：23-25.
[124] BAO R R，ZHANG J，LI H B，et al. Flatness assessment system of ultra-wide tandem cold rolling mill[C] //AKTAS M. Applied Mechanics and Materials. 2014，529：415-419.
[125] 郝亮，邸洪双，龚殿尧，等. 平直度离线显示和板形识别统计软件开发[J]. 东北大学学报，2010，31(10)：1414-1416.
 HAO Liang，DI Hongshuang，GONG Dianyao，et al. Software development of strip flatness off-line display and pattern recognition[J]. Journal of Northeastern University，2010，31(10)：1414-1416.
[126] 王骏飞，魏春生，张清东. 板带钢冷轧动态板形辊(DSR)技术的机理与实践[C]//2001中国钢铁年会论文集. 北京：冶金工业出版社，2001：126-129.
 WANG Junfei，WEI Chunsheng，ZHANG Qingdong. Theory and practice of the DSR for cold rolling steel strips[C]//2001 CSM Annual Meeting Proceedings. Beijing：Metallurgical Industry Press，2001：126-129.
[127] 王晓东，李飞，李本海，等. 变接触支持辊辊形及辊形配置技术在宽带钢热连轧粗轧机组的应用[J]. 首钢科技，2010(4)：41-46.
 WANG Xiaodong，LI Fei，LI Benhai，et al. Application of variable contact backup roll contour and configuration technology on roughing mills of a hot wide strip mill[J]. Shougang Science and Technology，2010(4)：41-46.
[128] 康永林，周明伟，刘旭辉，等. 半无头轧制薄规格带钢的组织性能与板形[J]. 钢铁，2012，47(1)：44-50.
 KANG Yonglin，ZHOU Mingwei，LIU Xuhui，et al. Microstructure-properties and profile of thin strip by semi-endless rolling[J]. Iron & Steel，2012，47(1)：44-50.
[129] 何安瑞，杨荃，陈先霖，等. 热带钢轧机线性变凸度工作辊的研制及应用[J]. 机械工程学报，2008，44(11)：255-259.
 HE Anrui，YANG Quan，CHEN Xianlin，et al. Development and application of linearly variable crown work roll in hot strip mills[J]. Journal of Mechanical Engineering，2008，44(11)：255-259.
[130] SHAO J，HE A R，SUN W Q，et al. Research and application of VCR plus technology in hot strip mills[C]//Proceedings of 2011 Second International Conference on MACE. IEEE，2011：5120-5123.