Prediction and analysis of rolling force and width spread in rough rolling
WANG Zhen-hua1,2, LIU Yuan-ming1,2, WANG Tao1,2, SUN Jie3, ZHANG Dian-hua3
1. College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China; 2. Engineering Research Center of Advanced Metal Composites Forming Technology and Equipment, Ministry of Education, Taiyuan University of Technology,Taiyuan 030024, Shanxi, China; 3. State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110819, Liaoning, China
Abstract:The mathematical model of plate-strip rolling is the basis of automatic control,and the high-precision mathematical model is an important guarantee to improve product quality and market competitiveness. Rolling force and width spread are the key parameters in the hot continuous rolling process control. Their model accuracy not only affects the setting of rough rolling procedures,but also affects the profile of the final strip product. The rectangular slab rolling process of hot continuous rolling was taken as the research object and the three dimensional kinematically admissible weighted velocity field of rough rolling was established for the rolling deformation zone. Considering the width spread effect,based on the first variation principle of rigid-plastic material,the variable upper limit integration method was used to integrate plastic deformation,shear and friction power to get the total power functional of the deformation zone. The theoretical analytical solutions of the rolling force and width distribution were obtained by minimizing the total power functional using the Matlab optimization toolbox. Finally,the slab width spread model and weighted coefficient model of velocity field were obtained by using the data regression of the calculation results of the theoretical analytical model. The rolling force and spread predicted by the model proposed were compared with the on-line measured data and the predicted values of the model established by some relevant scholars. The results verified the accuracy of the model established. The spread model and the expression of velocity field weight coefficient are obtained from the research can be conveniently,flexibly and quickly applied to the rough rolling site,which lays a solid foundation for the production of higher quality hot strip products.
王振华, 刘元铭, 王涛, 孙杰, 张殿华. 粗轧过程中轧制力和宽展的预测与分析[J]. 钢铁, 2022, 57(9): 95-102.
WANG Zhen-hua, LIU Yuan-ming, WANG Tao, SUN Jie, ZHANG Dian-hua. Prediction and analysis of rolling force and width spread in rough rolling[J]. Iron and Steel, 2022, 57(9): 95-102.
[1] Lee J D. A large-strain elastic-plastic finite element analysis of rolling process[J]. Computer Methods in Applied Mechanics and Engineering,1998,161(3/4):315. [2] Duan X,Sheppard T. Three dimensional thermal mechanical coupled simulation during hot rolling of aluminium alloy 3003[J]. lnternational Journal of Mechanical Sciences,2002,44(10):2155. [3] Kim Y K,Kwak W J,Shin T J,et al. A new model for the prediction of roll force and tension profiles in flat rolling[J]. ISIJ International,2010,50(11):1644. [4] ZHANG J L,CUI Z S. Continuous FEM simulation of multi-pass plate hot rolling suitable for plate shape analysis[J]. Journal of Central South University of Technology Volume,2011,18(1):16. [5] MEI R B,LI C S,LIU X H. A NR-BFGS method for fast rigid-plastic FEM in strip rolling[J]. Finite Elements in Analysis and Design,2012,61:44. [6] 柳翠茹,张立文,张驰,等. 摩擦因数对宽厚板轧制宽展影响的数值模拟[J]. 塑性工程学报,2016,23(6):106. (LIU Cui-ru,ZHANG Li-wen,ZHANG Chi,et al. Numerical simulation for the effect of friction coefficient on width spread of wide and heavy plate rolling[J]. Journal of Plasticity Engineering,2016,23(6):106.) [7] 赵峻,周玉,胡绪照,等. 异步轧制宽展行为的数值模拟研究[J]. 热加工工艺,2020,49(13):115. (ZHAO Jun,ZHOU Yu,HU Xu-zhao,et al. Numerical simulation study on width spreading behavior of asynchronous rolling[J]. Hot Working Technology,2020,49(13):115.) [8] 李启尧,胡玉坤. 粗轧过程中摩擦因数对强迫宽展的影响[J]. 现代制造技术与装备,2020,56(10):139. (LI Qi-yao,HU Yu-kun. Effect of friction coefficient on forced spreading in rough rolling[J]. Modern Manufacturing Technology and Equipment, 2020,56(10):139.) [9] Sims R B. The calculation of roll force and torque in hot rolling mills[J]. Proceedings of the Institution of Mechanical Engineers, 1954,168(1):191. [10] Oh S I,Kobayashi S. An approximate method for a three-dimensional analysis of rolling[J]. International Journal of Mechanical Sciences,1975,17(4):293. [11] Sezek S,Aksakal B,Can Y. Analysis of cold and hot plate rolling using dual stream functions[J]. Materials and Design,2008,29(3):584. [12] LIU Y M,MA G S,ZHANG D H,et al. Upper bound analysis of rolling force and dog-bone shape via sine function model in vertical rolling[J]. Journal of Materials Processing Technology,2015,223:91. [13] LIU Y M,MA G S,ZHAO D W,et al. Analysis of hot strip rolling using exponent velocity field and MY criterion[J]. International Journal of Mechanical Sciences,2015,98:126. [14] LIU Y M,ZHANG D H,ZHAO D W,et al. Analysis of vertical rolling using double parabolic model and stream function velocity field[J]. The International Journal of Advanced Manufacturing Technology,2016,82(5):1153. [15] LIU Y M,WANG Z H,WANG T,et al. Prediction and mechanism analysis of the force and shape parameters using cubic function model in vertical rolling[J]. Journal of Materials Processing Technology,2022:117500. [16] ZHANG S H,DENG L,TIAN W H,et al. Deduction of a quadratic velocity field and its application to rolling force of extra-thick plate[J]. Computers and Mathematics with Applications,2022,109:58. [17] YANG B,XU H,AN Q. Analysis of 3D plastic deformation in vertical rolling based on global weighted velocity field[J]. 2022. DOI:https://doi.org/10.21203/rs.3.rs-1234080/v1. [18] ZHANG S H,DENG L,LI P. Analysis of rolling force for extra-thick plate with CA criterion[J]. Mathematical Problems in Engineering,2020. https://doi.org/10.1155/2020/2326868. [19] YANG Y,PENG Y. Theoretical model and experimental study of dynamic hot rolling[J]. Metals,2021,11(9):1346. [20] 卫垚宇,甄涛,黄金博,等. 热轧宽厚板异步轧制力能参数建模与分析[J]. 重型机械,2021(1):52. (WEI Yao-yu,ZHEN Tao,HUANG Jin-bo,et al. Modeling and analysis of the asymmetric rolling mechanical parameters for the hot rolled heavy steel plate[J]. Heavy Machinery,2021(1):52.) [21] 赵强,杜凤山,燕猛. 基于上限法的大型筒节轧制力能参数建模分析[J]. 塑性工程学报,2022,29(3):66. (ZHAO Qiang,DU Feng-shan,YAN Meng. Modeling analysis of force-energy parameters in large-scale cylinder rolling based on upper limit method[J]. Journal of Plasticity Engineering,2022,29(3):66.) [22] Hill R. A general method of analysis for metal-working processes[J]. Journal of the Mechanics and Physics of Solids,1963,11(5):305. [23] Ginzburg V B,Ballas R. Flat Rolling Fundamentals[M]. New York:Marcel Dekker,2000. [24] Chitkara N,Johnson W. Some experimental results concerning spread in the rolling of lead[J]. Journal of Fluids Engineering,1966,88:489. [25] Shibahara T,Misaka Y,Kono T,et al. Edger set-up model at roughing train in a hot strip mill[J]. Tetsu To Hagane,1981,67(15):2509. [26] 熊尚武,朱祥霖,刘相华,等. 热带粗轧机组调宽工艺中数学模型的建立[J]. 上海金属,1997(1):39. (XIONG Shang-wu, ZHU Xiang-lin,LIU Xiang-hua,et al. Mathematical model of width reduction process of roughing trains of hot strip mills[J]. Shanghai Metals,1997(1):39.) [27] 熊尚武,姜正义,刘相华,等. 粗轧机组板坯调宽预测模型的实验验证与应用[J]. 钢铁,1999,34(8):43. (XIONG Shang-wu,JIANG Zheng-yi,LIU Xiang-hua,et al. Experiment and application of slab width reduction prediction model on roughing stands of hot strip mill[J]. Iron and Steel,1999,34(8):41.) [28] 曹建宁,白冰,刘斌,等. 中厚板角轧宽展技术的研发与应用[J]. 轧钢,2021,38(4):10. (CAO Jian-ning,BAI Bing,LIU Bin,et al. Research and application of angle rolling spreading technology for plate[J]. Steel Rolling,2021,38(4):10.) [29] Dogruoglu A N. On constructing kinematically admissible velocity fields in cold sheet rolling[J]. Journal of Materials Processing Technology,2001,110(3):287. [30] Chandra S,Dixit U S. A rigid-plastic finite element analysis of temper rolling process[J]. Journal of Materials Processing Technology,2004,152(1):9. [31] ZHANG S H,ZHAO D W,GAO C R. The calculation of roll torque and roll separating force for broadside rolling by stream function method[J]. International Journal of Mechanical Sciences,2012,57(1):74. [32] 孙一康. 冷热轧板带轧机的模型与控制[M]. 北京:冶金工业出版社,2010. (SUN Yi-kang. Model and Control of Cold and Hot Rolling Mill for Sheets and Strips[M]. Beijing:Metallurgical Industry Press,2010.)