四辊轧机辊系弹性变形高效计算方法
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摘要
为解决普通影响函数法计算速度慢的缺点,在分析普通影响函数法计算精度与计算速度主要影响因素的基础上,提出了一种新型四辊轧机辊系弹性变形高效计算方法。该方法采用高次多项式描述辊间压力与轧制压力的横向分布,减少了轧辊挠度的计算量;与普通影响函数法相比,求解辊间压力的线性方程组阶数显著降低,大大降低了计算时间。采用该方法后,四辊轧机辊系弹性变形的单次计算时间不超过1 ms,计算精度与划分单元数为100的普通影响函数法计算精度相差很小,为板形在线设定提供了理想的必要条件,并可推广应用于其他机型。
The calculation speed of the general influence function method is slow. To solve the problem, a new high-efficiency calculation method of roll stack elastic deformation for four- high mill was proposed based on the analysis of the main factors affecting the calculation precision and speed of general influence function method. In this method,the transverse distribution of the pressure between rolls and rolling pressure were described by high-order polynomial,reducing the calculated amount of roll deflection. Compared with the general influence function method,the order of linear equations to solve the pressure between rolls was significantly reduced,thus greatly saving the computing time. With this method,the single computing time of roll stack elastic deformation for four-high mill was less than 1 ms. Meanwhile,the computing accuracy matched well with that obtained by general influence function when dividing into 100 elements. It provided the ideal necessary condition for the on-line setting of flatness,and it could be applied to other mill types.
The calculation speed of the general influence function method is slow. To solve the problem, a new high-efficiency calculation method of roll stack elastic deformation for four- high mill was proposed based on the analysis of the main factors affecting the calculation precision and speed of general influence function method. In this method,the transverse distribution of the pressure between rolls and rolling pressure were described by high-order polynomial,reducing the calculated amount of roll deflection. Compared with the general influence function method,the order of linear equations to solve the pressure between rolls was significantly reduced,thus greatly saving the computing time. With this method,the single computing time of roll stack elastic deformation for four-high mill was less than 1 ms. Meanwhile,the computing accuracy matched well with that obtained by general influence function when dividing into 100 elements. It provided the ideal necessary condition for the on-line setting of flatness,and it could be applied to other mill types.
引文
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[16]于斌,王义栋,杨旭,等.面向局部高点控制的工作辊同宽轧制公里数[J].钢铁,2013,48(4):40.(YU Bin,WANG Yi-dong,YANG Xu,et al.Research of work roll same width rolling kilometer for local high point control[J].Iron and Steel,2013,48(4):40.)
[17]刘光明,邸洪双,郝亮.四辊CVC冷轧机辊间压力影响因素分析[J].中国冶金,2010,20(2):11.(LIU Guang-ming,DI Hongshuang,HAO Liang.Analyses on contact pressure between rolls of 4-high CVC cold rolling mill[J].China Metallurgy,2010,20(2):11.)
[18]董立杰,何安瑞,宋勇,等.热带钢轧机辊系纵向刚度在线计算模型[J].北京科技大学学报,2009,31(11):1452.(DONG Lijie,HE An-rui,SONG Yong,et al.Online calculation model of roll vertical stiffness in a hot rolling-mill[J].Journal of University of Science and Technology Beijing,2009,31(11):1452.)
[19]秦剑,缪谦.基于影响函数法的多辊轧机辊系变形矩阵迭代法[J].工程力学,2013,30(5):271.(QIN Jian,MIAO Qian.The matrix iteration method for elastic deformation of multi-roll mill based on influence function method[J].Engineering Mechanics,2013,30(5):271.)
[20]刘宏民.三维轧制理论及其应用[M].北京:科学出版社,1999.(LIU Hong-min.Three Dimensional Rolling Theory and Its Application[M].Beijing:Science Press,1999.)
[2]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.(KONG Fan-fu,HE An-rui,SHAO Jian.Research on rapid online calculation methods of roll stack deformation[J].Journal of Mechanical Engineering,2012,48(2):121.)
[3]王东城,赵章献,刘宏民.冷轧带钢板形高效分析与设定软件及其应用[J].钢铁,2015,50(7):54.(WANG Dong-cheng,ZHAO Zhang-xian,LIU Hong-min.High-efficiency software and its application for shape analysis and presetting of cold rolling strip[J].Iron and Steel,2015,50(7):54.)
[4]王国栋.板形控制和板形理论[M].北京:冶金工业出版社,1986.(WANG Guo-dong.Shape Control and Shape Theory[M].Beijing:Metallurgical Industry Press,1986.
[5]龚寄,王艾伦,骆拓.四辊轧机有载辊缝解析模型研究[J].中国机械工程,2007,18(22):2752.(GONG Ji,WANG Ai-un,LUO Tuo.Study on modeling of the roll gap with load for 4-h mill[J].China Mechanical Engineering,2007,18(22):2752.)
[6]陈杰,钟掘,周鸿章,等.CVC四辊轧机有载辊缝解析模型[J].重型机械,1998(6):42.(CHEN Jie,ZHONG Jun,ZHOU Hongzhang,et al.Analytical model of the roll gap with load for CVC4-h mill[J].Heavy Machinery,1998(6):42.)
[7]张清东,孙向明,白剑.六辊CVC轧机辊系变形的有限元分析[J].中国机械工程,2007,18(7):789.(ZHANG Qing-dong,SUN Xiang-ming,BAI Jian.Analysis of rolls'elastic deformation on CVC 6-h mill by FEM[J].China Mechanical Engineering,2007,18(7):789.)
[8]魏娟,杨荃,何安瑞.六辊轧机辊系变形的有限元分析[J].冶金设备,2006(4):5.(WEI Juan,YANG Quan,HE An-rui.Finite element analysis of rolls deformation on a six-high mill[J].Metallurgical Equipment,2006(4):5.)
[9]时旭,刘相华,王国栋,等.四辊冷轧机轧辊弯曲和压扁变形的有限元分[J].东北大学学报:自然科学版,2004,25(10):957.(SHI Xu,LIU Xiang-hua,WANG Guo-dong,et al.FEM analysis for roll deformation of a 4-high cold strip mill[J].Journal of Northeastern University:Natural Science,2004,25(10):957.)
[10]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.(CAO Jian-guo,MAO Na,ZHANG Jie,et al.Study on shifting mathematical model of edge drop control in tandem cold rolling mill[J].Iron and Steel,2008,43(8):57.)
[11]麻永林,宫美娜,邢淑清,等.304不锈钢带板形控制的有限元分析[J].钢铁,2015,50(2):48.(MA Yong-lin,GONG Mei-na,XING Shu-qing,et al.FEM analysis of 304 stainless steel strip flatness control[J].Iron and Steel,2015,50(2):48.)
[12]董占斌,王雪松,才春辉,等.基于ANSYS的立-平轧制过程的有限元模拟[J].中国冶金,2015,25(4):18.(DONG Zhan-bin,WANG Xue-song,CAI Chun-hui,et al.Finite element simulation of V-H rolling process based on ANSYS[J].China Metallurgy,2015,25(4):18.)
[13]周禹成,梁国平.热塑有限元的理论分析及应用[J].中国冶金,2014,24(6):36.(ZHOU Yu-cheng,LIANG Guo-ping.Theoretical analysis and application of thermoplastic finite element[J].China Metallurgy,2014,24(6):36.)
[14]梁勋国.六辊冷连轧机弯辊力设定模型[J].钢铁,2014,49(10):40.(LIANG Xun-guo.Preset model of bending force for six-high tandem cold rolling mill[J].Iron and Steel,2014,49(10):40.)
[15]于斌,王义栋,杨旭,等.面向板形控制的辊型窜辊与弯辊技术应用[J].钢铁,2014,49(11):42.(YU Bin,WANG Yi-dong,YANG Xu,et al.Application of roll contour shifting roll and bending roll for shape control[J].Iron and Steel,2014,49(11):42.)
[16]于斌,王义栋,杨旭,等.面向局部高点控制的工作辊同宽轧制公里数[J].钢铁,2013,48(4):40.(YU Bin,WANG Yi-dong,YANG Xu,et al.Research of work roll same width rolling kilometer for local high point control[J].Iron and Steel,2013,48(4):40.)
[17]刘光明,邸洪双,郝亮.四辊CVC冷轧机辊间压力影响因素分析[J].中国冶金,2010,20(2):11.(LIU Guang-ming,DI Hongshuang,HAO Liang.Analyses on contact pressure between rolls of 4-high CVC cold rolling mill[J].China Metallurgy,2010,20(2):11.)
[18]董立杰,何安瑞,宋勇,等.热带钢轧机辊系纵向刚度在线计算模型[J].北京科技大学学报,2009,31(11):1452.(DONG Lijie,HE An-rui,SONG Yong,et al.Online calculation model of roll vertical stiffness in a hot rolling-mill[J].Journal of University of Science and Technology Beijing,2009,31(11):1452.)
[19]秦剑,缪谦.基于影响函数法的多辊轧机辊系变形矩阵迭代法[J].工程力学,2013,30(5):271.(QIN Jian,MIAO Qian.The matrix iteration method for elastic deformation of multi-roll mill based on influence function method[J].Engineering Mechanics,2013,30(5):271.)
[20]刘宏民.三维轧制理论及其应用[M].北京:科学出版社,1999.(LIU Hong-min.Three Dimensional Rolling Theory and Its Application[M].Beijing:Science Press,1999.)