Nonlinear vibration of corrugated rolling mill based on dynamic rolling force
HE Dong-ping1,2,3, XU Hui-dong1,2,3, WANG Tao1,2,3, LIU Jiang-lin1,2,3, LIU Yuan-ming1,2,3, ZHANG Jin-zhu1,2,3
1. College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China; 2. Institute of Advanced Forming and Intelligent Equipment, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China; 3. Engineering Research Center of Advanced Metal CompositesForming Technology and Equipment, Ministry of Education, Taiyuan 030024, Shanxi, China
Abstract：The composite sheet corrugated roll rolling technology is revolutionary. In order to study the influence of dynamic rolling force on the vibration characteristics and bifurcation behavior of the corrugated roll mill, the dynamic rolling force,the nonlinear stiffness within the corrugated interface and the nonlinear damping of the corrugated rolling mill are considered,and the mathematical model of the nonlinear vibration of the corrugated rolling mill is established based on the dynamic rolling force. The amplitude-frequency characteristic equations of nonlinear vibration of the roller system excited by dynamic rolling force are carried out by using the multiple-scale method. The influences of dynamic rolling force amplitude,nonlinear stiffness coefficient,and nonlinear damping coefficient on vibration are analyzed. The influence of dynamic rolling force changes on system stability is analyzed by the largest Lyapunov exponent,bifurcation chaos diagram,Poincaré section map,and phase trajectory. The dynamic bifurcation feedback controller is designed to control the bifurcation behavior induced by the dynamic change of rolling force and the correctness and feasibility of the controller are verified by numerical simulation.
和东平, 徐慧东, 王涛, 刘江林, 刘元铭, 张金柱. 基于动态轧制力的波纹辊轧机非线性振动[J]. 钢铁, 2021, 56(6): 75-81.
HE Dong-ping, XU Hui-dong, WANG Tao, LIU Jiang-lin, LIU Yuan-ming, ZHANG Jin-zhu. Nonlinear vibration of corrugated rolling mill based on dynamic rolling force[J]. Iron and Steel, 2021, 56(6): 75-81.
[1] 陈爱华,闫晨,孟志立. 铜基复合材料制备及研究新进展[J]. 中国冶金,2019,29(2):7.(CHEN Ai-hua,YAN Chen,MENG Zhi-li. Preparation and research progress of copper matrix composites[J]. China Metallurgy,2019,29(2):7.) [2] WANG T,LI S,REN Z K,et al. Microstructure characterization and mechanical property of Mg/Al laminated composite prepared by the novel approach:Corrugated+flat rolling(CFR)[J]. Metals,2019,9(6),690. [3] Johnson R E,Qi Q. Chatter dynamics in sheet rolling[J]. International Journal of Mechanical Sciences,1994,36(7):617. [4] Switoniowski A. Interdependence between rolling mill vibrations and the plastic deformation process[J]. Journal of Materials Processing Technology,1996,61(4):354. [5] Yarita I,Furukawa K,Seino Y. Analysis of chattering in cold rolling for ultrathin gauge steel strip[J]. Transactions ISIJ,1978,18(1):1. [6] Bar A,Switoniowski A. Interdependence between the rolling speed and non-linear vibrations of the mill system[J]. Journal of Materials Processing Technology,2004,155(10):2116. [7] Kapil S,Eberhard P,Dwivedy S K. Nonlinear dynamic analysis of a parametrically excited cold rolling mill[J]. Journal of Manufacturing Science and Engineering,2014,136(4):4. [8] 李鸿光,闻邦椿. 具有间隙和振动边界的自激振动系统的非线性振动[J]. 振动工程学报,2000,13(1):122.(LI Hong-guang,WEN Bang-chun. Nonlinear vibrations of self-excited vibration systems with clearances and oscillating boundaries[J]. Journal of Vibration Engineering,2000,13(1):122.) [9] 孟令启,徐如松,王建勋,等. 中厚板轧机非线性参激的振动[J]. 重庆大学学报,2008,31(4):393.(MENG Ling-qi,XU Ru-song,WANG Jian-xun,et al. Parametrically excited nonlinear vibration of medium and heavy plate milling[J]. Journal of Chongqing University,2008,31(4):393.) [10] 黄华栋,臧勇. 非线性摩阻引起的轧机主传动系统自激振动分析[J]. 煤炭技术,2012,31(10):222.(HUANG Hua-dong,ZANG Yong. Analysis nonlinear friction caused of self-excited vibration of main drive system on rolling mill[J]. Coal Technology,2012,31(10):222.) [11] 侯东晓,朱月,刘浩然,等. 基于动态轧制力的冷轧机非线性振动特性研究[J]. 机械工程学报,2013,49(14):45.(HOU Dong-xiao,ZHU Yue,LIU Hao-ran,et al. Research on nonlinear vibration characteristics of cold rolling mill based on dynamic rolling force[J]. Journal of Mechanical Engineering,2013,49(14):45.) [12] 侯东晓,刘彬,时培明,等. 分段非线性轧机辊系系统的分岔行为研究[J]. 振动与冲击,2010,29(12):132.(HOU Dong-xiao,LIU Bin,SHI Pei-ming,et al. Bifurcation of piecewise nonlinear roll system of rolling mill[J]. Journal of Vibration and Shock,2010,29(12):132.) [13] 王博华. 轧机主传动非线性扭振系统分岔和混沌行为研究[D]. 秦皇岛:燕山大学,2012.(WANG Bo-hua. Study on Bifurcation and Chaotic Behaviors of Rolling Mill′s Main Drive Nonlinear Torsional Vibration System[D]. Qinhuangdao:Yanshan University,2012.) [14] 刘飞. 轧机非线性垂振系统动力学特性及稳定性控制策略研究[D]. 秦皇岛:燕山大学,2015.(LIU Fei. Study on Dynamics and Stability Control Strategy of the Nonlinear Vertical Vibration System of Rolling Mill[D]. Qinhuangdao:Yanshan University,2015.) [15] 潘贵翔. 液压缸非线性约束力下轧机辊系振动特性及抑制研究[D]. 秦皇岛:燕山大学,2018.(PAN Gui-xiang. Study on Vibration Characteristics and Control of Rolling Mill Roll System under Nonlinear Binding Force of Hydraulic Cylinder[D]. Qinhuangdao:Yanshan University,2018.) [16] 彭荣荣,巩长芬,王国威,等. 动态轧制力下冷连轧机超亚谐共振特性分析[J]. 机械设计与制造,2018,8(6):49.(PENG Rong-rong,GONG Chang-fen,WANG Guo-wei,et al. Analysis of super-harmonic and sub-harmonic resonance characteristics of tandem cold mill under dynamic rolling force[J]. Machinery Design and Manufacture,2018,8(6):49.) [17] 张瑞成,马寅州. 基于动态轧制力的轧机垂扭耦合系统非线性振动机理研究[J]. 机械设计与制造,2016,7(3):146.(ZHANG Rui-cheng,MA Yin-zhou. Study on the non-linear vibration of the vertical-torsion coupling system for rolling mill based on dynamic rolling force[J]. Machinery Design and Manufacture,2016,7(3):146.) [18] 张永顺,姜万录,李振宝,等. 轧机液压压下系统非线性振动诱因分析[J]. 钢铁,2020,55(4):111.(ZHANG Yong-shun,JIANG Wan-lu,LI Zhen-bao,et al. Inducement analysis of nonlinear vibration in rolling mill hydraulic screw down system[J]. Iron and steel,2020,55(4):111.) [19] 凌启辉,张维,赵前程,等. 轧机垂直系统动力学参数辨识[J]. 钢铁,2019,54(11):129.(LING Qi-hui,ZHANG Wei,ZHAO Qian-cheng,et al. Dynamic parameter identification of rolling mill vertical system[J]. Iron and steel,2019,54(11):129.) [20] 郜志英,臧勇,曾令强. 轧机颤振建模及理论研究进展[J]. 机械工程学报,2015,51(16):87.(GAO Zhi-ying,ZANG Yong,ZENG Ling-qiang. Review of modelling and theoretical studies on chatter in the rolling mills[J]. Journal of Mechanical Engineering,2015,51(16):87.) [21] 和东平,王涛,解加全,等. 波纹辊轧机辊系主共振分岔控制研究[J]. 机械工程学报,2020,56(7):109.(HE Dong-ping,WANG Tao,XIE Jia-quan,et al. Research on principal resonance bifurcation control of roller system in corrugated rolling mills[J]. Journal of Mechanical Engineering,2020,56(7):109.) [22] 刘延柱,陈立群. 非线性振动[M]. 北京:高等教育出版社,2001.(LIU Yan-zhu,CHEN Li-qun. Nonlinear Vibrations[M]. Beijing:Higher Education Press,2001.)
2021, Vol. 56 
