考虑轧机主传动系统扭振的带钢非线性振动研究
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摘要
带钢振动在连轧过程中不可避免,其弹塑性体与主传动系统间的耦合作用直接影响轧机轧制的整体动态性能。基于带钢与主传动系统的运动机理,将主传动系统简化为2自由度的离散模型,带钢简化为具有轴向运动速度的Euler梁,建立带钢橫、纵向振动与主传动系统扭振相耦合的力学模型。然后根据哈密顿原理建立该耦合模型的非线性振动微分方程,采用修正迭代法和Kantorovich时间平均法联合对所建立方程进行求解。最后利用Matlab软件进行数值模拟,讨论出主传动系统扭振基频对带钢振动特性的影响。研究结果能够丰富轧机振动研究方面的理论成果,对于理论成果转化为工程应用具有重要的实用价值。
Strip steel vibrations is inevitable in the rolling process of tandem mill, and the coupled model between elastoplastic body of strip steel and main drive system directly affects the overall dynamic performance of rolling mill. According to the movement mechanism of strip steel and main drive system, the main drive system was simplified to a two-degree-of-freedom discrete model and the strip steel was simplified to an axially moving Euler beam, the coupled vibration mechanical model of transverse and longitudinal vibrations of strip steel and torsional vibration of main drive system was established. Then, the nonlinear vibration differential equations of the coupled model were derived with Hamilton's principle. The modified iteration method and the Kantorovich averaging method were used to solve the differential equations. Finally, by using the Matlab simulation, the influence of torsional vibration fundamental frequency of main drive system on strip steel vibration characteristics was discussed. The results can enrich the theoretical achievements on vibration of rolling mill, and it is valuable for transforming theoretical results into engineering applications.
Strip steel vibrations is inevitable in the rolling process of tandem mill, and the coupled model between elastoplastic body of strip steel and main drive system directly affects the overall dynamic performance of rolling mill. According to the movement mechanism of strip steel and main drive system, the main drive system was simplified to a two-degree-of-freedom discrete model and the strip steel was simplified to an axially moving Euler beam, the coupled vibration mechanical model of transverse and longitudinal vibrations of strip steel and torsional vibration of main drive system was established. Then, the nonlinear vibration differential equations of the coupled model were derived with Hamilton's principle. The modified iteration method and the Kantorovich averaging method were used to solve the differential equations. Finally, by using the Matlab simulation, the influence of torsional vibration fundamental frequency of main drive system on strip steel vibration characteristics was discussed. The results can enrich the theoretical achievements on vibration of rolling mill, and it is valuable for transforming theoretical results into engineering applications.
引文
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[12] Sun Jianliang, Peng Yan, Liu Hongmin. Dynamic characteristics of cold rolling mill and strip based on flatness and thickness control in rolling process[J]. Journal of Central South University, 2014, 21(2): 567-576.
[13] 杨旭, 李擎, 童朝南, 等. 基于辊缝动态摩擦方程的铝板冷轧机垂振机理分析[J]. 北京科技大学学报, 2014, 36(1): 104-109.YANG Xu, LI Qing, TONG ChaoNan, et al. Vertical vibration mechanism analysis of aluminum cold rolling mills based on the dynamic friction equation in roll gap[J]. Journal of University of Science and Technology Beijing, 2014, 36(1): 104-109 (In Chinese).
[14] 王洋, 许飞, 李勇, 等. 带钢-辊子-柔性支承混杂系统动力学建模与耦合振动研究[J]. 振动工程学报, 2013, 26(4): 599-607.WANG Yang, XU Fei, LI Yong, et al. Dynamic modeling and coupling vibration analysis of hybrid systems consisting of strip rolls and flexible supports[J]. Journal of Vibration Engineering, 2013, 26(4): 599-607 (In Chinese).
[15] 许飞, 李勇, 李路雷. 带钢及其支承系统的参数振动分析[J]. 机械研究与应用, 2013, 26(3): 27-30.XU Fei, LI Yong, LI LuLei. Parametric Vibration Analysis for Sheet Metal and its Supporting System[J]. Mechanical Research and Application, 2013, 26(3): 27-30 (In Chinese).
[16] 高崇一, 杜国君, 李建雄, 等. 惯性边界下带钢的非线性振动分析[J]. 振动与冲击, 2016, 35(1): 5-10.GAO ChongYi, DU GuoJun, LI JianXiong, et al.Nonlinear vibration of strip steel under inertial boundary conditions[J]. Journal of Vibration and Shock, 2016, 35(1): 5-10 (In Chinese).
[17] 高崇一, 杜国君, 李建雄, 等. 考虑带钢的轧机主传动系统扭振数值研究[J]. 燕山大学学报, 2016, 40(1): 58-65.GAO ChongYi, DU GuoJun, LI JianXiong, et al.Numerical analysis on torsional vibration of main driving system of rolling mill with strip steel[J]. Journal of Yanshan University, 2016, 40(1): 58-65 (In Chinese).
[18] 王波, 陈立群. 微分求积法处理轴向变速黏弹性梁混杂边界条件[J]. 振动与冲击, 2012, 31(5): 87-91.WANG Bo, CHEN LiQun. Treating hybrid boundary condition of an Aaxially accelerating viscoelastic beam via a differential quadrature scheme[J]. Journal of Vibration and Shock, 2012, 31(5): 87-91 (In Chinese).
[19] Chen Liqun, Yang Xiaodong. Steady-state response of axially moving viscoelastic beams with pulsating speed: comparison of two nonlinear models[J]. International Journal of Solids and Structures, 2005, 42(1): 37-50.
[2] Fan Xiaobin, Zang Yong, Wang Feng, et al. Hot strip mill nonlinear torsional vibration with multi-stand coupling[J]. Journal of Vibroengineering, 2015, 17(4): 1623-1633.
[3] Moller R H, Hoggart J S. Periodic surface finish and torque effects during cold strip rolling[J]. Journal of the Australian Institute of Metals, 1967, 12(2): 155-164.
[4] 钟掘, 杨勇学, 古可, 等. 1600高速铝带轧机扭振研究[J]. 冶金设备, 1986 (3): 1-19.ZHONG Jue, YANG YongXue, GU Ke, et al. Torsional vibration research of high-speed aluminium strip of 1600 rolling mill[J]. Metallurgical Equipment, 1986 (3): 1-19 (In Chinese).
[5] 申延智, 刘宏民, 熊杰, 等. 厚板轧机含间隙主传动系统混沌动力学分析[J]. 工程力学, 2010, 27(7): 232-236.SHEN YanZhi, LIU HongMin, XIONG Jie, et al. Analysis of chaotic behavior of the main drive system of a heavey plate mill[J]. Engineering Mechanics, 2010, 27(7): 232-236 (In Chinese).
[6] 时培明, 夏克伟, 刘彬, 等. 多自由度轧机传动系统非线性非主共振扭振特性[J]. 振动与冲击, 2015, 34(12): 35-41.SHI PeiMing, XIA KeWei, LIU Bin, et al. Non-main resonance characteristics of nonlinear torsional vibrationof rolling mill’s multi-degree-of-freedom main drive system[J]. Journal of Vibration and Shock, 2015, 34(12): 35-41. (In Chinese)
[7] Zhang Yifang, Yan Xiaoqiang, Lin Qihui. Characteristic of torsional vibration of mill main drive excited by electromechanical coupling[J]. Chinese Journal of Mechanical Engineering, 2016, 29(1): 180-187.
[8] Swiatoniowski A, Bar A. Parametrical excitement vibration in tandem mills-mathematical model and its analysis[J]. Journal of Materials Processing Technology, 2003, 134(2): 214-224.
[9] Bar A, Swiatoniowski A. Interdependence between the rolling speed and non-linear vibrations of the mill system[J]. Journal of Materials Processing Technology, 2004, 155(1): 2116-2121.
[10] Kim C H, Perkins N C, Lee C W. Parametric resonance of plates in a sheet metal coating process[J]. Journal of Sound and Vibration, 2003, 268(4): 679-697.
[11] 孙建亮, 张明, 彭艳. 六辊轧机扭振动态建模及与板带钢质量关系研究[J]. 工程力学, 2014, 31(4): 239-244.SUN JianLiang, ZHANG Ming, PENG Yan. Torsional vibration of 6 rolling mill based on continuum dynamics and its relationship with strip quality[J]. Engineering Mechanics, 2014, 31(4): 239-244 (In Chinese).
[12] Sun Jianliang, Peng Yan, Liu Hongmin. Dynamic characteristics of cold rolling mill and strip based on flatness and thickness control in rolling process[J]. Journal of Central South University, 2014, 21(2): 567-576.
[13] 杨旭, 李擎, 童朝南, 等. 基于辊缝动态摩擦方程的铝板冷轧机垂振机理分析[J]. 北京科技大学学报, 2014, 36(1): 104-109.YANG Xu, LI Qing, TONG ChaoNan, et al. Vertical vibration mechanism analysis of aluminum cold rolling mills based on the dynamic friction equation in roll gap[J]. Journal of University of Science and Technology Beijing, 2014, 36(1): 104-109 (In Chinese).
[14] 王洋, 许飞, 李勇, 等. 带钢-辊子-柔性支承混杂系统动力学建模与耦合振动研究[J]. 振动工程学报, 2013, 26(4): 599-607.WANG Yang, XU Fei, LI Yong, et al. Dynamic modeling and coupling vibration analysis of hybrid systems consisting of strip rolls and flexible supports[J]. Journal of Vibration Engineering, 2013, 26(4): 599-607 (In Chinese).
[15] 许飞, 李勇, 李路雷. 带钢及其支承系统的参数振动分析[J]. 机械研究与应用, 2013, 26(3): 27-30.XU Fei, LI Yong, LI LuLei. Parametric Vibration Analysis for Sheet Metal and its Supporting System[J]. Mechanical Research and Application, 2013, 26(3): 27-30 (In Chinese).
[16] 高崇一, 杜国君, 李建雄, 等. 惯性边界下带钢的非线性振动分析[J]. 振动与冲击, 2016, 35(1): 5-10.GAO ChongYi, DU GuoJun, LI JianXiong, et al.Nonlinear vibration of strip steel under inertial boundary conditions[J]. Journal of Vibration and Shock, 2016, 35(1): 5-10 (In Chinese).
[17] 高崇一, 杜国君, 李建雄, 等. 考虑带钢的轧机主传动系统扭振数值研究[J]. 燕山大学学报, 2016, 40(1): 58-65.GAO ChongYi, DU GuoJun, LI JianXiong, et al.Numerical analysis on torsional vibration of main driving system of rolling mill with strip steel[J]. Journal of Yanshan University, 2016, 40(1): 58-65 (In Chinese).
[18] 王波, 陈立群. 微分求积法处理轴向变速黏弹性梁混杂边界条件[J]. 振动与冲击, 2012, 31(5): 87-91.WANG Bo, CHEN LiQun. Treating hybrid boundary condition of an Aaxially accelerating viscoelastic beam via a differential quadrature scheme[J]. Journal of Vibration and Shock, 2012, 31(5): 87-91 (In Chinese).
[19] Chen Liqun, Yang Xiaodong. Steady-state response of axially moving viscoelastic beams with pulsating speed: comparison of two nonlinear models[J]. International Journal of Solids and Structures, 2005, 42(1): 37-50.