VCR Roll Contour Design and Shape Control Capability Based on Particle Swarm Optimization

doi:10.3901/JME.2025.08.075

Abstract

Abstract: In view of shape control problem of nuclear zirconium alloy strips during the multi-roll and multi-pass cold rolling process. The integrated three-dimensional finite element model of nuclear zirconium alloy strip and roll systems is established. A design method of VCR (varying contact backup rolls) based on particle swarm optimization is proposed. Combining field practice, the automatic optimization iterative design is suitable for the roll contours of the VCR technology during multi pass rolling of nuclear power zirconium alloy strip. Finite element simulation results show that：Compared with the existing industrial scheme of nuclear zirconium alloy strip, the shape control ability of the new scheme is obviously enhanced. The new scheme can effectively eliminate the undesired contact areas between the backup roll and work roll and reduce the length of the undesired contact line length between the rolls by 87.58%, increase the roll gap stiffness of the roll system by 17.55%, and increase the regulating efficiency of the bending force by 15.15%. This provides a theoretical basis for industrial tests aimed at improving the shape quality of nuclear zirconium alloy.

Key words: Zirconium alloy, cold rolling, shape control, finite element modeling, particle swarm optimization

CLC Number:

TG337

CAO Jianguo, WANG Leilei, ZHANG Zhaoxiang, CAO Yuan, WANG Ben, GAO Bo. VCR Roll Contour Design and Shape Control Capability Based on Particle Swarm Optimization[J]. Journal of Mechanical Engineering, 2025, 61(8): 75-84.

References

[1] NOLLE L. SASS applied to optimum work roll profile selection in the hot rolling of wide steel[J]. Knowledge-Based Systems，2007，20(2)：203-208.
[2] NOLLE L，ARMSTRONG A，HOPGOOD A，et al. Optimum work roll profile selection in the hot rolling of wide steel strip using computational intelligence[J]. Computational Intelligence，1999，1625(4)：435-452.
[3] 张䶮，杨荃，何安瑞，等. 连续退火线平整机辊形优化[J]. 北京科技大学学报，2012，34(3)：342-347. ZHANG Yan，YANG Quan，HE Anrui，et al. Roll shape optimization of temper mill for continuous annealing line[J]. Journal of Beijing University of Science and Technology，2012，34(3)：342-347.
[4] 邵健，唐荻，何安瑞，等. 基于多目标满意优化的热轧非对称工作辊设计[J]. 北京科技大学学报，2012，34(9)：1077-1083. SHAO Jian，TANG Di，HE Anrui，et al. Design of asymmetric work roll for hot rolling based on multi-objective satisfactory optimization[J]. Journal of Beijing University of Science and Technology，2012，34(9)：1077-1083.
[5] 戴杰涛，张清东，夏小明，等. 梅钢热轧支持辊辊形遗传算法设计与极限规格板形改善[J]. 钢铁，2009，44(10)：57-60. DAI Jietao，ZHANG Qingdong，XIA Xiaoming，et al. Genetic algorithm design of backup roll shape and improvement of limit gauge flatness of Meisteel[J]. Iron and Steel，2009，44(10)：57-60.
[6] 黄庆学. 高品质钢铁板带轧制关键装备与技术研究进展[J]. 机械工程学报，2023，59(20)：34-63. HUANG Qingxue. Research progress on key equipment and technology for high-quality steel plate and strip rolling[J]. Journal of Mechanical Engineering，2023，59(20)：34-63.
[7] 康永林.“十三五”中国轧钢技术进步及展望[J]. 钢铁，2021，56(10)：1-15. KANG Yonglin. “13th Five-Year” China’s steel rolling technology progress and prospect[J]. Iron & Steel，2021，56(10)：1-15.
[8] 彭艳，石宝东，刘才溢，等. 板带轧制装备-工艺-产品质量综合控制融合发展综述[J]. 机械工程学报，2023，59(20)：96-118. PENG Yan，SHI Baodong，LIU Caiyi，et al. Overview of the integrated development of plate and strip rolling equipment-process-product quality comprehensive control[J]. Journal of Mechanical Engineering，2023，59(20)：96-118.
[9] 杜国强，张清东，刘博，等. 一种六辊CVC平整机的窄边浪控制方法[P]. 中国：CN106269901A，2017-01-04. DU Guoqiang，ZHANG Qingdong，LIU Bo，et al. Narrow edge wave control method for six roller CVC temper mill[P]. China：CN106269901A，2017-01-04.
[10] 周玉川，杨利，王云，等. 热轧宽幅钛薄板板形控制[J]. 热加工工艺，2016，45(1)：134-137. ZHOU Yuchuan，YANG Li，WANG Yun，et al. Shape control of hot rolled wide titanium sheet[J]. Hot Working Process，2016，45(1)：134-137.
[11] 何安瑞，邵健，孙文权. 兼顾热轧不锈钢二次和高次浪形工作辊辊形的设计方法[P]. 中国：CN102641892A，2012-08-22. HE Anrui，SHAO Jian，SUN Wenquan. Design method of roll shape of secondary and high-order wave work roll for hot-rolled stainless steel[P]. China：CN102641892A，2012-08-22.
[12] 徐静霞，王鹏. 装饰铝箔波浪缺陷的影响因素及控制措施[J]. 轻合金加工技术，2011，39(1)：29-30. XU Jingxia，WANG Peng. Influencing factors and control measures of wave defects in decorative aluminum foil[J]. Light Alloy Processing Technology，2011，39(1)：29-30.
[13] 文杰，张清东，饶志雄，等. 四辊冷连轧机高强钢板形控制技术研究[J]. 轧钢，2010，27(6)：28-31. WEN Jie，ZHANG Qingdong，RAO Zhixiong，et al. Research on shape control technology of high strength steel plate for four high tandem cold rolling mill[J]. Steel Rolling，2010，27(6)：28-31.
[14] 王春海，刘学良，苏宝沧，等. 镀锌光整机辊形优化及边浪板形缺陷控制[J]. 中国冶金，2024，34(5)：114-124. WANG Chunhai，LIU Xueliang，SU Baocang，et al. Optimization of roll profile for galvanized temper mill and control of edge wave defect in sheet metal forming[J]. China Metallurgical，2024，34(5)：114-124.
[15] DONG Q，CAO J G，LI H B，et al. Analysis of spalling in roughing mill backup rolls of wide and thin strip hot rolling process[J]. Steel Research International，2015，86(2)：129-136.
[16] 冯夏维，王晓晨，杨荃，等. 六辊轧机工作辊辊形边降调控能力分析[J]. 机械工程学报，2019，55(12)：83-90. FENG Xiawei，WANG Xiaochen，YANG Quan，et al. Analysis of the ability to regulate the profile edge drop of the work roll of a six-high mill[J]. Journal of Mechanical Engineering，2019，55(12)：83-90.
[17] 王仁忠，李文浩，刘广，等. 适用于六辊UCM轧机中间辊侧向横移变凸度的新辊形研发[J]. 中国冶金，2022，32(2)：115-120. WANG Renzhong，LI Wenhao，LIU Guang，et al. Research and development of a new roll shape suitable for lateral lateral displacement of the intermediate roll of a six-high UCM mill to change the crown[J]. China Metallurgy，2022，32(2)：115-120.
[18] 许志强，陈启发，白宇航，等. 电子温控辊形描述方法及其特征调控规律[J]. 塑性工程学报，2024，31(8)：199-207. XU Zhiqiang，CHEN Qifa，BAI Yuhang，et al. Description method and regulation law of characteristics for electronically temperature-controlled roll profile[J]. Journal of Plasticity Engineering，2024，31(8)：199-207.
[19] 张建雷，岳重祥，毛观伟，等. 冷连轧边降控制多机架工作辊端部辊形研究[J]. 钢铁研究学报，2023，35(11)：1375-1383. ZHANG Jianlei，YUE Chongxiang，MAO Guanwei，et al. Research on the end roll profile of multi-stand work rolls for edge drop control in cold continuous rolling[J]. Journal of Iron and Steel Research，2023，35(11)：1375-1383.
[20] 尚飞，李申光，李艳琳. 辊形配置对辊间接触压力与板形调控影响分析[J]. 中国冶金，2022，32(8)：124-135. SHANG Fei，LI Shenguang，LI Yanlin. Analysis of the impact of roll profile configuration on inter-roll contact pressure and plate shape control[J]. China Metallurgical，2022，32(8)：124-135.
[21] 刘宏民，于华鑫，王东城，等. 冷轧带钢板形测控前沿技术的创新方略[J]. 钢铁，2023，58(4)：77-86. LIU Hongmin，YU Huaxin，WANG Dongcheng，et al. Innovative strategy for leading-edge technology in shape measurement and control of cold-rolled steel strip[J]. Iron & Steel，2023，58(4)：77-86.
[22] 曹建国，江军，邱澜，等. 新一代高技术宽带钢冷轧机全机组一体化板形控制[J]. 中南大学学报，2019，50(7)：1584-1591. CAO Jianguo，JIANG Jun，QIU Lan，et al. Integrated plate shape control for the entire high-tech wide strip cold rolling mill of the new generation[J]. Journal of Central South University，2019，50(7)：1584-1591.
[23] 曹建国，宋纯宁，孙磊，等. 新一代高技术宽带钢轧机电工钢高精度板形控制研究进展[J]. 塑性工程学报，2024，31(4)：131-142. CAO Jianguo，SONG Chunning，SUN Lei，et al. Research progress in high-precision plate shape control for electrical steel in the new generation of high-tech wide strip cold rolling mills[J]. Journal of Plasticity Engineering，2024，31(4)：131-142.
[24] 杨庭松，黄敦亮，孙文权，等. 电磁调控轧辊的热力胀形行为及高效控制方法[J]. 东北大学学报，2024，45(5)：660-667. YANG Tingsong，HUANG Dunliang，SUN Wenquan，et al. Thermomechanical bulging behavior and efficient control method of electromagnetic regulation rolls[J]. Journal of Northeastern University(Natural Science)，2024，45(5)：660-667.
[25] 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)：1-4. 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)：1-4.
[26] CHEN X L，ZOU J X. A specialized finite element model for investigating controlling factors affecting behavior of rolls and strip flatness[C/CD]//Proceedings of 4th International Steel Rolling Conference，The Science and Technology of Flat Rolling，Deauville，1987.
[27] 曹建国，黄小海，赵秋芳，等. 板带轧机通用变凸度板形控制技术[J]. 中南大学学报，2020，51(10)：2772-2781. CAO Jianguo，HUANG Xiaohai，ZHAO Qiufang，et al. Profile control technology of strip mill with variable crown[J]. Journal of Central South University，2020，51(10)：2772-2781.
[28] BAI Z H，SI H X，SHI X D，et al. Development of roller ends forced-contact model and cambering technology for UCM temper mill (I)[J]. Engineering，2011，3(7)：743-749.
[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(2)：264-270.
[30] 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. YANG Quan，CHEN Xianlin，XU Yaohuan，et al. Application of variable contact length backup roll to improve comprehensive flatness control capability[J]. Iron and steel，1995，30(2)：48.
[31] KONG N，CAO J G，WANG Y P，et al. Development of smart contact backup rolls in ultra-wide stainless strip rolling process [J]. Materials and Manufacturing Processes，2014，29(2)：129-133.
[32] 曹媛. 核用锆合金板带多轧程多道次热轧板形控制研究[D]. 北京：北京科技大学，2023. CAO Yuan. Research on plate shape control in multi-pass and multi-stand hot rolling of zirconium alloy sheets and strips for nuclear applications[D]. Beijing：University of Science and Technology Beijing，2023.
[33] JIANG Z Y，TIEU A K. Elastic–plastic finite element method simulation of thin strip with tension in cold rolling[J]. Journal of Materials Processing Technology， 2002，130(12)：511-515.
[34] CAO J G，CHAI X T，LI Y L，et al. Integrated design of roll contours for strip edge drop and crown control in tandem cold rolling mills[J]. Journal of Materials Processing Technology，2018，252(2)：432-439.
[35] MORI K，OSAKADA K. Simulation of three-dimensional deformation in rolling by the finite-element method[J]. International Journal of Mechanical Sciences，1984，26(9)：515-525.
[36] CHEN X L，YANG Q，ZHANG Q D，et al. Varying contact back-up roll for improved strip flatness[M]. London：Sterling Publications Limited，1994.
[37] 王国栋. 板形与板凸度控制[M]. 北京：化学工业出版社，2015. WANG Guodong. Shape and crown control[M]. Beijing：Chemical Industry Press，2015.
[38] 刘雪峰，汪凌云. 基于影响函数的轧机辊系变形分析及板形预报[J]. 重庆大学学报2000，23(6)：87-90. LIU Xuefeng，WANG Lingyun. Analysis of elastic deformation of rollers system in rolling mill based on influential function and prediction of plate shape[J]. Journal of Chongqing University，2000，23(6)：87-90.
[39] 丁国龙，邱兆祥，汤明俊，等. 离散化变凸度辊形的自适应设计方法[J]. 机械科学与技术，2020，39(4)：608-614. DING Guolong，QIU Zhaoxiang，TANG Mingjun，et al. Adaptive design method of discrete variable crown roll shape[J]. Mechanical Science and Technology，2020，39(4)：608-614.
[40] 孟静，曹汉民，刘超，等. 1450mm热连轧机支持辊辊形优化设计[J]. 热处理技术与装备，2016，37(4)：58-62. MENG Jing，CAO Hanmin，LIU Chao. et al. Optimization design of backup roll profile of 1450 mm hot strip mill[J]. Heat Treatment Technology and Equipment，2016，37(4)：58-62.
[41] FOURIE P C，GROENWOLD A A. The particle swarm optimization algorithm in size and shape optimization[J]. Structural and Multidiplinary Optimization，2002，23(4)：259-267.
[42] 曹建国，赵秋芳，黄小海，等.基于数据挖掘和有限元集成建模的新一代高技术轧机板形控制创新方法研究进展[C/CD]// 中国机械工程学会机械工业自动化分会&中国自动化学会制造技术专业委员会学术工作进展报告(2019版)，中国威海，2019. CAO Jianguo，ZHAO Qiufang，HUANG Xiaohai，et al. Research progress of new generation high-tech rolling mill shape control innovation method based on data mining and finite element integrated modeling [C/CD]//Academic Work Progress Report of Mechanical Industry Automation Branch of China Society of Mechanical Engineering & AMP；Manufacturing Technology Professional Committee of China Automation Society (2019 Edition)，Weihai，China，August 22-24，2019.
[43] 张华智，孙登月，许石民，等. 5000mm宽厚板轧机支承辊新辊型[J]. 钢铁，2014，49(7)：82-87，93. ZHANG Huazhi，SUN Dengyue，XU Shimin，et al. New backup roll profile of 5000mm wide and heavy plate mill[J]. Iron and Steel，2014，49(7)：82-87，93.
[44] 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]. International Journal of Advanced Manufacturing Technology，2014，74(9)：1733-1745.
[45] GINZBURG V B. High-quality steel rolling theory and practice[M]. Beijing：Metallurgical Industry Press，2000.