第36卷第5期 北京科技大学学报 Vol.36 No.5 2014年5月 Journal of University of Science and Technology Beijing May 2014 热带钢轧机轧辊热变形的快速有限元模型 孔繁甫”，何安瑞四，邵健”，葛鲜玉) 1)北京科技大学高效轧制国家工程研究中心，北京1000832)中国第二重型机械集团公司设计研究院，德阳618013 ☒通信作者，E-mail:harui@ustb.cedu.cn 摘要分析了解析法与简化方法的缺点，采用有限元法建立轧辊热变形计算模型.针对轧制过程中轧辊热变形计算数据特 点，将计算任务分为负责静态数据准备的预计算和负责动态数据准备与热变形求解的更新计算，换辊时进行预计算，计算任 意时刻的热变形时只需进行更新计算，计算量远小于标准有限元程序.根据特殊处理的计算流程，编写了基于轴对称有限元 法的轧辊热变形程序，其计算结果与ANSYS结果一致，精度均高于简化方法约30%.自编轧辊热膨胀有限元程序计算精度 高，耗时少，满足在线热膨胀预报要求. 关键词带钢轧机：热轧：板形控制：轧辊：热变形：有限单元法 分类号TG333.17 Finite element model for rapidly evaluating the thermal expansion of rolls in hot strip mills KONG Fanfu",HE An-rui,SHAO Jian,GE Xian-yu? 1)National Engineering Research Center for Advanced Rolling,University of Science Technology Beijing,Beijing 100083,China 2)Design Research Institute,China National Erzhong Group Co.,Deyang 618013,China Corresponding author,E-mail:harui@ustb.edu.cn ABSTRACT The disadvantages of the analytical solution and the simplified method were analyzed and a thermal expansion model was established by the finite element method.Based on the data characteristics of the rolls'geometry in a rolling unit,the calculation task was divided into pre-ealculation responsible for static data preparation and renewal calculation responsible for renewing dynamic data and thermal expansion.The pre-calculation was called only after roll change and the renewal calculation was called when the thermal expansion data was needed to be updated.This special tailored flow contributes to a much smaller computation complexity in compari- son with standard finite element analysis.Furthermore,the corresponding program was compiled according to the tailored flow and its results are in agreement with those by ANSYS,with the accuracy of about 30%higher than the simplified method.Due to high accura- cy and short calculation time,this home-made finite element analysis program is promising to be implemented in online applications for evaluating the thermal expansion of rolls. KEY WORDS strip mills:hot rolling:shape control:rolls;thermal expansion:finite element method 在热轧带钢生产过程中，工作辊的热变形与辊 础部分之一，其计算精度对产品板形质量有直接 缝凸度在同一数量级，对带钢凸度及平坦度的影响 关系. 非常显著.同时，轧辊的热变形是影响辊间接触压 在轧辊热辊形的研究中，文献09]都将轧辊 力分布的主要因素之一，对工作辊挠曲有重要影响. 温度场与热变形放在一起研究，且研究重点皆为温 因此，轧辊热辊形的计算模型是热轧板形模型的基 度场部分，轧辊热变形计算均采用简化方法.陈宝 收稿日期：201302-18 基金项目：新世纪优秀人才支持计划资助项目(NCET-100223):中央高校基本科研业务费专项资金资助项目(FRF-TP-11O03A) DOI:10.13374/j.issn1001-053x.2014.05.016:http:/journals.ustb.edu.cn第 36 卷 第 5 期 2014 年 5 月 北京科技大学学报 Journal of University of Science and Technology Beijing Vol． 36 No． 5 May 2014 热带钢轧机轧辊热变形的快速有限元模型 孔繁甫1) ，何安瑞1) ，邵 健1) ，葛鲜玉2) 1) 北京科技大学高效轧制国家工程研究中心，北京 100083 2) 中国第二重型机械集团公司设计研究院，德阳 618013  通信作者，E-mail: harui@ ustb． edu． cn 摘 要 分析了解析法与简化方法的缺点，采用有限元法建立轧辊热变形计算模型． 针对轧制过程中轧辊热变形计算数据特 点，将计算任务分为负责静态数据准备的预计算和负责动态数据准备与热变形求解的更新计算，换辊时进行预计算，计算任 意时刻的热变形时只需进行更新计算，计算量远小于标准有限元程序． 根据特殊处理的计算流程，编写了基于轴对称有限元 法的轧辊热变形程序，其计算结果与 ANSYS 结果一致，精度均高于简化方法约 30% ． 自编轧辊热膨胀有限元程序计算精度 高，耗时少，满足在线热膨胀预报要求． 关键词 带钢轧机; 热轧; 板形控制; 轧辊; 热变形; 有限单元法 分类号 TG 333. 17 Finite element model for rapidly evaluating the thermal expansion of rolls in hot strip mills KONG Fan-fu1) ，HE An-rui1)  ，SHAO Jian1) ，GE Xian-yu2) 1) National Engineering Ｒesearch Center for Advanced Ｒolling，University of Science ＆ Technology Beijing，Beijing 100083，China 2) Design ＆ Ｒesearch Institute，China National Erzhong Group Co． ，Deyang 618013，China  Corresponding author，E-mail: harui@ ustb． edu． cn ABSTＲACT The disadvantages of the analytical solution and the simplified method were analyzed and a thermal expansion model was established by the finite element method． Based on the data characteristics of the rolls’geometry in a rolling unit，the calculation task was divided into pre-calculation responsible for static data preparation and renewal calculation responsible for renewing dynamic data and thermal expansion． The pre-calculation was called only after roll change and the renewal calculation was called when the thermal expansion data was needed to be updated． This special tailored flow contributes to a much smaller computation complexity in compari￾son with standard finite element analysis． Furthermore，the corresponding program was compiled according to the tailored flow and its results are in agreement with those by ANSYS，with the accuracy of about 30% higher than the simplified method． Due to high accura￾cy and short calculation time，this home-made finite element analysis program is promising to be implemented in online applications for evaluating the thermal expansion of rolls． KEY WOＲDS strip mills; hot rolling; shape control; rolls; thermal expansion; finite element method 收稿日期: 2013--02--18 基金项目: 新世纪优秀人才支持计划资助项目( NCET--10--0223) ; 中央高校基本科研业务费专项资金资助项目( FＲF--TP--11--003A) DOI: 10． 13374 /j． issn1001--053x． 2014． 05． 016; http: / /journals． ustb． edu． cn 在热轧带钢生产过程中，工作辊的热变形与辊 缝凸度在同一数量级，对带钢凸度及平坦度的影响 非常显著． 同时，轧辊的热变形是影响辊间接触压 力分布的主要因素之一，对工作辊挠曲有重要影响． 因此，轧辊热辊形的计算模型是热轧板形模型的基 础部分之一，其计算精度对产品板形质量有直接 关系． 在轧辊热辊形的研究中，文献［1--9］都将轧辊 温度场与热变形放在一起研究，且研究重点皆为温 度场部分，轧辊热变形计算均采用简化方法． 陈宝