高速冷轧机辊系非线性动力学模型及控制参数优化
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摘要
综合运用轧制过程动态轧制力模型、轧机系统分段非线性弹性力模型和分段非线性摩擦力模型,建立了考虑非线性因素耦合的高速冷轧机辊系动力学模型,采用平均法求解幅频响应方程,研究了轧机系统主要参数对轧机垂直振动的影响。分析结果表明:动态轧制力一次项刚度越小,轧机系统固有频率越大;动态轧制力三次项刚度不为零时,轧机系统出现明显跳跃现象;非线性弹性力起主导作用时,易发生跳跃现象;非线性摩擦力越大,轧机系统振动幅值越小,分段特性减弱;外扰力幅值越大,振动幅值越大,振动越剧烈;线性阻尼越大,振动幅值越小且减小幅度越缓慢。
The dynamics model of high-speed cold rolling mills considering nonlinear factors coupling was established based on the model of dynamic rolling forces of rolling processes, the model of segmented nonlinear elastic forces and nonlinear friction forces in rolling mill systems. Average method was used to solve the amplitude frequency response equation of this model and the influences of main parameters on the vertical vibration were analyzed. The results show that the primary stiffness of dynamic rolling forces is negatively proportional to the inherent frequency of the rolling system; jumping phenomenon is obvious when the cubic stiffness is not zero or when the nonlinear elastic forces plays a leading role; the nonlinear friction forces is negatively proportional to the vibration amplitude; the segmented characteristic is weakened when nonlinear friction forces is great; the extraneous forces is positively proportional to the vibration amplitude; the rate of vibration amplitude reduction is slower with the increase of linear damping.
The dynamics model of high-speed cold rolling mills considering nonlinear factors coupling was established based on the model of dynamic rolling forces of rolling processes, the model of segmented nonlinear elastic forces and nonlinear friction forces in rolling mill systems. Average method was used to solve the amplitude frequency response equation of this model and the influences of main parameters on the vertical vibration were analyzed. The results show that the primary stiffness of dynamic rolling forces is negatively proportional to the inherent frequency of the rolling system; jumping phenomenon is obvious when the cubic stiffness is not zero or when the nonlinear elastic forces plays a leading role; the nonlinear friction forces is negatively proportional to the vibration amplitude; the segmented characteristic is weakened when nonlinear friction forces is great; the extraneous forces is positively proportional to the vibration amplitude; the rate of vibration amplitude reduction is slower with the increase of linear damping.
引文
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[4] SUN Jianliang,PENG Yan,LIU Hongmin.Non-Linear Vibration and Stability of Moving Strip with Time-dependent Tension in Rolling Process[J].Journal of Iron and Steel Research,International,2010,17(6):11-15.
[5] YANG Xu,TONG Chaonan,YUE Guangfeng,et al.Coupling Dynamic Model of Chatter for Cold Rolling[J].Journal of Iron and Steel Research,International,2010,17(12):30-34.
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[9] 刘晓潺,臧勇,郜志英,等.多方向耦合振动连轧机再生颤振建模及应用[J].中南大学学报(自然科学版),2017,48(3):635-643.LIU Xiaochan,ZANG Yong,GAO Zhiying,et al.Multidirectional Regenerative Chatter Model of Tandem Rolling Mills and Its Application[J].Journal of Central South University (Natural Science),2017,48(3):635-643.
[10] 刘浩然,刘飞,侯东晓,等.多非线性弹性约束下轧机辊系振动特性[J].机械工程学报,2012,48(9):89-94.LIU Haoran,LIU Fei,HOU Dongxiao,et al.Vibration Characteristics of Mill Rolls under Multi-segment Nonlinear Elastic Constraints[J].Journal of Mechanical Engineering,2012,48(9):89-94.
[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):45-50.HOU Dongxiao,ZHU Yue,LIU Haoran,et al.Research on Nonlinear Vibration Characteristics of Cold Rolling Mill Based on Dynamic Rolling Force[J].Journal of Mechanical Engineering,2013,49(14):45-50.
[12] 刘彬,赵红旭,朱月,等.基于动态轧制力的冷轧机两自由度垂直振动特性[J].中国机械工程,2014,25(17):2344-2350.LIU Bin,ZHAO Hongxu,ZHU Yue,et al.TwoDegree of Freedom Vertical Vibration Characteristics of Cold Rolling Mill Based on Dynamic Rolling Force[J].Journal of Mechanical Engineering,2014,25(17):2344-2350.
[13] NIROOMAND M R,FOROUZAN M R,SALIMI M.Theoretical and Experimental Analysis of Chatter in Tandem Cold Rolling Mills Based on Wave Propagation Theory[J].ISIJ International,2015,55(3):637-646.
[14] XU Yang,QING Li,TONG Chaonan,et al.Vertical Vibration Model for Unsteady Lubrication in Rolls-strip Interface of Cold Rolling Mills[J].Advances in Mechanical Engineering,2012,4:734510.
[15] 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):87-112.GAO Zhiying,ZANG Yong,ZENG Lingqiang.Review of Modeling and Theoretical Studies on Chatter in the Rolling Mills[J].Journal of Mechanical Engineering,2015,51(16):87-112.
[16] 刘浩然,张莹,时培明,等.基于动态轧制力的四辊冷轧机七自由度振动特性研究[J].振动与冲击,2015,34(22):92-120.LIU Haoran,ZHANG Ying,SHI Peiming,et al.Vibration Characteristics of a Cold Rolling Mill with a Model of Seven Degrees of Freedom and Their Influence on Dynamic Rolling Force[J].Journal of Vibration and Shock,2015,34(22):92-120.
[2] BRUSA E,LEMMA L.Numerical and Experimental Analysis of the Dynamic Effects in Compact Cluster Mills for Cold Rolling [J].Journal of Materials Processing Technology,2009,209 (5):2436-2445.
[3] 王桥医,黄海军,李志华.金属塑性加工工作界面非稳态润滑轧机振动控制[J].中南大学学报(自然科学版),2010,41(4):1418-1423.WANG Qiaoyi,HUANG Haijun,LI Zhihua.Control of Mill Vibration for Unsteady Lubrication Based on Metal-forming Process[J].Journal of Central South University (Natural Science),2010,41(4):1418-1423.
[4] SUN Jianliang,PENG Yan,LIU Hongmin.Non-Linear Vibration and Stability of Moving Strip with Time-dependent Tension in Rolling Process[J].Journal of Iron and Steel Research,International,2010,17(6):11-15.
[5] YANG Xu,TONG Chaonan,YUE Guangfeng,et al.Coupling Dynamic Model of Chatter for Cold Rolling[J].Journal of Iron and Steel Research,International,2010,17(12):30-34.
[6] SUN J L,PENG Y,LIU H M,et al.Vibration of Moving Strip with Distributed Stress in Rolling Process[J].Journal of Iron and Steel Research,2010,17(4):24-30.
[7] ALI H,MOHAMMAD R F.Optimization of Cold Rolling Process Parameters in Order to Increasing Rolling Speed Limited by Chatter Vibrations[J].Journal of Advanced Research,2013,4(1):27-34.
[8] 闫晓强,王辉,周杰,等.现代连轧机耦合振动抑制重要进展[J].中国冶金,2014,24(4):1-4.YAN Xiaoqiang,WANG Hui,ZHOU Jie,et al.Important Progress of Coupling Vibration Inhibition on Modern Tandem Mill[J].China Metallurgy,2014,24(4):1-4.
[9] 刘晓潺,臧勇,郜志英,等.多方向耦合振动连轧机再生颤振建模及应用[J].中南大学学报(自然科学版),2017,48(3):635-643.LIU Xiaochan,ZANG Yong,GAO Zhiying,et al.Multidirectional Regenerative Chatter Model of Tandem Rolling Mills and Its Application[J].Journal of Central South University (Natural Science),2017,48(3):635-643.
[10] 刘浩然,刘飞,侯东晓,等.多非线性弹性约束下轧机辊系振动特性[J].机械工程学报,2012,48(9):89-94.LIU Haoran,LIU Fei,HOU Dongxiao,et al.Vibration Characteristics of Mill Rolls under Multi-segment Nonlinear Elastic Constraints[J].Journal of Mechanical Engineering,2012,48(9):89-94.
[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):45-50.HOU Dongxiao,ZHU Yue,LIU Haoran,et al.Research on Nonlinear Vibration Characteristics of Cold Rolling Mill Based on Dynamic Rolling Force[J].Journal of Mechanical Engineering,2013,49(14):45-50.
[12] 刘彬,赵红旭,朱月,等.基于动态轧制力的冷轧机两自由度垂直振动特性[J].中国机械工程,2014,25(17):2344-2350.LIU Bin,ZHAO Hongxu,ZHU Yue,et al.TwoDegree of Freedom Vertical Vibration Characteristics of Cold Rolling Mill Based on Dynamic Rolling Force[J].Journal of Mechanical Engineering,2014,25(17):2344-2350.
[13] NIROOMAND M R,FOROUZAN M R,SALIMI M.Theoretical and Experimental Analysis of Chatter in Tandem Cold Rolling Mills Based on Wave Propagation Theory[J].ISIJ International,2015,55(3):637-646.
[14] XU Yang,QING Li,TONG Chaonan,et al.Vertical Vibration Model for Unsteady Lubrication in Rolls-strip Interface of Cold Rolling Mills[J].Advances in Mechanical Engineering,2012,4:734510.
[15] 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):87-112.GAO Zhiying,ZANG Yong,ZENG Lingqiang.Review of Modeling and Theoretical Studies on Chatter in the Rolling Mills[J].Journal of Mechanical Engineering,2015,51(16):87-112.
[16] 刘浩然,张莹,时培明,等.基于动态轧制力的四辊冷轧机七自由度振动特性研究[J].振动与冲击,2015,34(22):92-120.LIU Haoran,ZHANG Ying,SHI Peiming,et al.Vibration Characteristics of a Cold Rolling Mill with a Model of Seven Degrees of Freedom and Their Influence on Dynamic Rolling Force[J].Journal of Vibration and Shock,2015,34(22):92-120.
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