六辊轧机工作辊辊形边降调控能力分析
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摘要
使用带有辊形的工作辊是六辊轧机减小带刚边降的有效手段之一,然而目前对于辊形设计规律的研究仍显不足。首先在分析各种轧机辊系弹性变形计算算法优缺点的基础上,提出分割矩阵求解方法:针对六辊轧机建立影响函数线性方程组,将方程组系数矩阵分割后,把矩阵条件数最小的系数矩阵作为最终迭代环节,同有限元法对比显示其精度合格、速度更快,适用于承担大规模辊系弹性变形预设定分析时的高强度计算任务。其次利用分割矩阵影响函数法,针对工作辊辊形曲线段高度、锥度段斜率对边降调控能力的影响进行研究。结果表明,工作辊辊形高度越大,边降调控能力越强,同凸度控制耦合作用越强;斜线段斜率对边降调控能力影响不大,斜率越小,越有利于同平坦度控制解耦。最后根据以上规律,为工业现场设计了新式辊形曲线,进一步提高5mm边降合格率。研究结果表明,通过分割矩阵迭代法,辊系弹性变形计算更为精确,同时大的曲线段高度与小的直线段斜率是提高工作辊辊形边降控制能力的有效方案。
Tapered work roll is an effective measure of six-high roll mill to reduce edge drop but its design criterion is not adequately investigated. Firstly, Based on analysis of previous roll stack's elastic deformation theories, the influence function method based on the partitioned matrix iteration scheme is proposed: Influence Function matrix solution for the six-high roll stack is founded, and by partitioning the matrix solution, the coefficient matrix with the smallest condition number is proposed as the outermost iteration. By this iteration scheme, the results are in better agreement with Finite Element Method, which makes it an optimal tool for intensive presetting analysis. Secondly, the proposed method is used to analyze the differences in control properties between different curve heights and tapered slopes of work roll contour. Results show that a higher curve height is beneficial for the edge drop control ability, but strongly coupled with crown control. The tapered slope has limited influence on the edge drop control effect, but a smaller slope is beneficial to decouple edge drop control and crown control. Finally, based on these laws, a new contour is designed and utilized into industrial line, and percentage of edge drop smaller than 5 mm is further improved. The results show that through partitioned matrix iteration scheme, elastic deformation of rolls stack can be accurately calculated. The results also suggest that a large curve height and a small tangent slope is effective to improve the edge drop control performance of work roll contour.
Tapered work roll is an effective measure of six-high roll mill to reduce edge drop but its design criterion is not adequately investigated. Firstly, Based on analysis of previous roll stack's elastic deformation theories, the influence function method based on the partitioned matrix iteration scheme is proposed: Influence Function matrix solution for the six-high roll stack is founded, and by partitioning the matrix solution, the coefficient matrix with the smallest condition number is proposed as the outermost iteration. By this iteration scheme, the results are in better agreement with Finite Element Method, which makes it an optimal tool for intensive presetting analysis. Secondly, the proposed method is used to analyze the differences in control properties between different curve heights and tapered slopes of work roll contour. Results show that a higher curve height is beneficial for the edge drop control ability, but strongly coupled with crown control. The tapered slope has limited influence on the edge drop control effect, but a smaller slope is beneficial to decouple edge drop control and crown control. Finally, based on these laws, a new contour is designed and utilized into industrial line, and percentage of edge drop smaller than 5 mm is further improved. The results show that through partitioned matrix iteration scheme, elastic deformation of rolls stack can be accurately calculated. The results also suggest that a large curve height and a small tangent slope is effective to improve the edge drop control performance of work roll contour.
引文
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[16]WANG Tao,HUANG Qingxue,XIAO Hong,et al.Modification of roll flattening analytical model based on the plane assumption[J].Chinese Journal of Mechanical Engineering,2018,31(1):46-53.
[17]员征文,肖宏,谢红飙.基于边界积分方程法的六辊轧机辊系变形分析[J].机械工程学报,2013,49(18):125-131.YUAN Zhengwen,XIAO Hong,XIE Hongbiao.6-Hi mill deformation analysis based on boundary integral equation method[J].Journal of Mechanical Engineering,2013,49(18):125-131.
[18]YUAN Zhengwen,XIAO Hong,XIE Hongbiao,et al.Practice of improving roll deformation theory in strip rolling process based on boundary integral equation method[J].Metallurgical and Materials Transactions A-physical Metallurgy and Materials Science,2014,45(2):1019-1026.
[19]HACQUIN A,MONTMITONNET P,GUILLERAULT J.A three-dimensional semi-analytical model of rolling stand deformation with finite element validation[J].European Journal of Mechanics A-solids,1998,17(1):79-106.
[20]孔繁甫,何安瑞,邵健.快速辊系变形在线计算方法研究[J].机械工程学报,2012,48(2):121-126.KONG Fanfu,HE Anrui,SHAO Jian.Research on rapid online calculation methods of roll stack deformation[J].Journal of Mechanical Engineering,2012,48(2):121-126.
[21]BERGER B,PAWELSKI O,FUNKE P.Die elastische verformung der walzen von vierwalzengerüsten[J].Archiv Für Dassenhüttenwesen,1976,47(6):351-356.BERGER B,PAWELSKI O,FUNKE P.Elastic deformation of rolls in four-high rolling stands[J].Archiv Für Dassenhüttenwesen,1976,47(6):351-356.
[22]GOLUB G,VAN LOAN C.Matrix computations[M].Baltimore:Johns Hopkins University Press,1996.
[23]LE H,SUTCLIFFE M.A robust model for rolling of thin strip and foil[J].International Journal of Mechanical Sciences,2001,43(6):1405-1419.
[2]胡强,王晓晨,杨荃.六辊冷连轧机边降自动控制系统设计及应用[J].冶金自动化,2016,40(1):34-39.HU Qiang,WANG Xiaochen,YANG Quan.Design and application of automatic edge drop control system for6-high tandem cold rolling mill[J].Metallurgical Industry Automation,2016,40(1):34-39.
[3]张岩,高健,吴鲲魁,等.单锥度辊冷轧机边部减薄控制应用研究[J].冶金自动化,2016,40(1):45-49.ZHANG Yan,GAO Jian,WU Kunkui,et al.Application research for edge drop control on cold mill of single taper roll[J].Metallurgical Industry Automation,2016,40(1):45-49.
[4]CAO Jianguo,CHAI Xueting,LI Yanlin,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,2018,252:432-439.
[5]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.
[6]张赟,杨荃,邵健,等.UCMW轧机正弦函数形单锥度工作辊边降控制[J].工程科学学报,2009,31(12):1611-1615.ZHANG Yun,YANG Quan,SHAO Jian,et al.Edge drop control using sinusoidal tapered work roll on a UCMWmill[J].Chinese Journal of Engineering,2009,31(12):1611-1615.
[7]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 roll mill in Baosteel[J].Iron and Stell,2009,44(11):67-70.
[8]WANG Qinglong,SUN Jie,LIU Yuanming,et al.Analysis of symmetrical flatness actuator efficiencies for UCM cold rolling mill by 3D elastic-plastic FEM[J].International Journal of Advanced Manufacturing Technology,2017,92(10):1-19.
[9]PARK H,HWANG S.3-D Coupled analysis of deformation of the strip and rolls in flat rolling by FEM[J].Steel Research International,2017,88(12):1700227-1700240.
[10]LINGHU Kezhi,JIANG Zhengyi,ZHAO Jingwei,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(9-12):1733-1745.
[11]LIU Chao,HE Anrui,QIANG Yi,et al.Effect of volume changes on hot rolling deformation behavior of non-oriented electrical steel[J].ISIJ International,2017,57(9):1595-1602.
[12]LIU Chao,HE Anrui,QIANG Yi,et al.Effect of phase transformation and latent heat on hot rolling deformation behavior of non-oriented electrical steel[J].ISIJInternational,2017,57(5):857-865.
[13]NAKHOUL R,MONTMITONNET P,LEGRAND N.Manifested flatness defect prediction in cold rolling of thin strips[J].International Journal of Material Forming,2015,8(2):283-292.
[14]ABDELKHALEK S,MONTMITONNET P,LEGRANDN,et al.Coupled approach for flatness prediction in cold rolling of thin strip[J].International Journal of Mechanical Sciences,2011,53(9):661-675.
[15]MONTMITONNET P.Hot and cold strip rolling processes[J].Computer Methods in Applied Mechanics and Engineering,2006,195(48):6604-6625.
[16]WANG Tao,HUANG Qingxue,XIAO Hong,et al.Modification of roll flattening analytical model based on the plane assumption[J].Chinese Journal of Mechanical Engineering,2018,31(1):46-53.
[17]员征文,肖宏,谢红飙.基于边界积分方程法的六辊轧机辊系变形分析[J].机械工程学报,2013,49(18):125-131.YUAN Zhengwen,XIAO Hong,XIE Hongbiao.6-Hi mill deformation analysis based on boundary integral equation method[J].Journal of Mechanical Engineering,2013,49(18):125-131.
[18]YUAN Zhengwen,XIAO Hong,XIE Hongbiao,et al.Practice of improving roll deformation theory in strip rolling process based on boundary integral equation method[J].Metallurgical and Materials Transactions A-physical Metallurgy and Materials Science,2014,45(2):1019-1026.
[19]HACQUIN A,MONTMITONNET P,GUILLERAULT J.A three-dimensional semi-analytical model of rolling stand deformation with finite element validation[J].European Journal of Mechanics A-solids,1998,17(1):79-106.
[20]孔繁甫,何安瑞,邵健.快速辊系变形在线计算方法研究[J].机械工程学报,2012,48(2):121-126.KONG Fanfu,HE Anrui,SHAO Jian.Research on rapid online calculation methods of roll stack deformation[J].Journal of Mechanical Engineering,2012,48(2):121-126.
[21]BERGER B,PAWELSKI O,FUNKE P.Die elastische verformung der walzen von vierwalzengerüsten[J].Archiv Für Dassenhüttenwesen,1976,47(6):351-356.BERGER B,PAWELSKI O,FUNKE P.Elastic deformation of rolls in four-high rolling stands[J].Archiv Für Dassenhüttenwesen,1976,47(6):351-356.
[22]GOLUB G,VAN LOAN C.Matrix computations[M].Baltimore:Johns Hopkins University Press,1996.
[23]LE H,SUTCLIFFE M.A robust model for rolling of thin strip and foil[J].International Journal of Mechanical Sciences,2001,43(6):1405-1419.
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