锻压技术

轧辊偏心影响下耦合振动系统主共振时滞反馈控制

英文标题：Feedback control on main resonance time-lag of coupled vibration system under influence of roller eccentricity

作者：张瑞成赵文斌梁卫征

分类号：TH113.1

出版年,卷(期):页码：2025,50(2):185-194

摘要：

考虑轧辊偏心和轧制界面非线性摩擦力的影响，建立了轧机垂直-水平耦合非线性振动的动力学模型。首先，采用多尺度法求解了在轧辊偏心力影响下的主共振幅频特性方程，分析了线性和非线性阻尼、非线性刚度以及轧辊偏心力的变化对耦合系统的影响；然后，利用奇异性理论探讨了主共振情况下系统的分岔特性，得到了系统的迁移集和不同开折参数下的拓扑结构；最后，设计了线性和非线性复合作用的时滞反馈控制器对主共振进行控制，并通过数值仿真验证了控制器设计的可行性。研究结果表明，所设计的控制器能够有效控制轧辊偏心对耦合系统主共振的影响。

Considering the effects of roller eccentricity and nonlinear friction forces at the rolling interface, the dynamics model of vertical-horizontal coupled nonlinear vibration for the rolling mill was established. Firstly, the amplitude-frequency characteristic equations of the main resonance under the influence of roller eccentricity force were solved by the multi-scale method, and the influences of linear and nonlinear damping, nonlinear stiffness and roller eccentricity force changes on the system were analyzed. Furthermore, the bifurcation characteristics of the system under the main resonance were explored by using the singularity theory, and the transition set of the system and the topology structure under different open-folding parameters were obtained. Finally, a time-lag feedback controller with the combination of linear and nonlinear effects was designed to control the main resonance, and the feasibility of the controller design was verified by numerical simulation. The research results show that the designed controller can effectively control the influence of roller eccentricity on the main resonance of the coupled system.

基金项目：

河北省自然科学基金资助项目(F2018209201);唐山市人才资助项目(B202302009);唐山市科技局科技计划项目(22130213G)

作者简介：张瑞成（1975-），男，博士，教授,E-mail：1063974891@qq.com;通信作者：梁卫征（1982-），女，硕士，副教授,E-mail：wzliang1982@126.com

参考文献：

[1]田学伯. 我国窄带钢生产现状及发展趋势[J]. 机械设计, 2018, 35 (S1): 276-278.

Tian X B. Production status and development trend of narrow strip steel in China [J]. Journal of Machine Design, 2018, 35 (S1): 276-278.

[2]康永林.“十三五”中国轧钢技术进步及展望[J].钢铁,2021,56(10):1-15.

Kang Y L. China steel rolling technology progress in the 13th five-year plan and prospection [J]. Iron and Steel,2021,56(10):1-15.

[3]曹建国,江军,邱澜,等.新一代高技术宽带钢冷轧机全机组一体化板形控制[J].中南大学学报(自然科学版),2019,50(7):1584-1591.

Cao J G, Jiang J, Qiu L, et al. High precision integrated profile and flatness control for new-generation high-tech wide strip cold rolling mills [J]. Journal of Central South University (Science and Technology),2019,50(7):1584-1591.

[4]曹建国,宋纯宁,孙磊,等.新一代高技术宽带钢轧机电工钢高精度板形控制研究进展[J].塑性工程学报,2024,31(4):131-142.

Cao J G, Song C N, Sun L, et al. Research progress on high precision profile contour and flatness control of electrical steel for new generation of high-tech wide strip rolling mills [J]. Journal of Plasticity Engineering,2024,31(4):131-142.

[5]杨志刚, 郭德福, 徐浩淼. 2250 mm热连轧高强薄规格轧制稳定性分析及控制[J]. 轧钢, 2020, 37 (4): 81-85.

Yang Z G, Guo D F, Xu H M. Analysis of rolling stability of high strength and thin gauge strip in 2250 mm hot rolling mill [J]. Steel Rolling, 2020, 37 (4): 81-85.

[6]黄金磊, 臧勇, 郜志英. 工艺参数对热轧机振动固有特性影响分析[J]. 钢铁, 2021, 56 (2): 93-98，109.

Hang J L, Zang Y, Gao Z Y. Influence of process parameters on vibration natural characteristics of hot rolling mill [J]. Iron and Steel, 2021, 56 (2): 93-98，109.

[7]张义方, 何成, 崔立,等. 轧件激励诱发CSP轧机振动问题研究[J]. 振动与冲击, 2023, 42 (20): 222-229.

Zhang Y F, He C, Cui L, et al. Research on vibration of a CSP rolling mill induced by workpiece excitation [J]. Journal of Vibration and Shock, 2023, 42 (20): 222-229.

[8]齐杰斌. 多源激励的冷连轧机耦合振动研究[D].北京：北京科技大学,2023.

Qi J B. Study on Coupled Vibration of Cold Rolling Mill with Multi-source Excitation [D]. Beijing:University of Science and Technology Beijing,2023.

[9]和东平,王涛,刘元铭,等. 板带轧机振动理论研究进展[J]. 机械工程学报，2024，60（7）：93-113.

He D P, Wang T, Liu Y M, et al. Review of theoretical studies on vibration in strip rolling mill[J]. Journal of Mechanical Engineering，2024，60（7）：93-113.

[10]Qian C, Xu J J, Hua C C, et al. Modeling and vertical torsional coupling vibration control of the rolling mill with full state constraints [J]. International Journal of Robust and Nonlinear Control, 2022, 32 (9): 5501-5519.

[11]Liu S, Shi Y T, Zhang Y P, et al. Bifurcation characteristics of torsional-horizontal coupled vibration of rolling mill system [J]. Journal of Vibroengineering, 2017, 19 (3): 2188-2201.

[12]Zeng L Q, Zang Y, Gao Z Y. Hopf bifurcation control for rolling mill multiple-mode-coupling vibration under nonlinear friction [J]. Journal of Vibration and Acoustics, 2017, 139 (6):061015.

[13]Hou D X, Xu L, Shi P M. Vertical-horizontal coupling nonlinear vibration characteristics of rolling mill under mixed lubrication[J]. Journal of Iron and Steel Research International, 2021, 28 (5): 1-12.

[14]黄金磊,臧勇,郜志英. 热轧过程中摩擦系数非对称性对轧机振动及稳定性的影响[J]. 工程科学学报,2019,41(11):1465-1472.

Huang J L, Zang Y, Gao Z Y. Influence of friction coefficient asymmetry on vibration and stability of rolling mills during hot rolling [J]. Chinese Journal of Engineering,2019,41(11):1465-1472.

[15]钱长照,唐驾时. 一类非自治时滞反馈系统的分岔控制[J]. 物理学报,2006(2):617-621.

Qian C Z, Tang J S. Bifurcation control for a non-autonomous system with two time delays [J]. Acta Physica Sinica,2006(2):617-621.

[16]赵艳影,徐鉴.利用时滞反馈控制自参数振动系统的振动[J].力学学报,2011,43(5):894-904.

Zhao Y Y, Xu J. Using the delayed feedback to control the vibration of the auto-parametric dynamical system [J]. Chinese Journal of Theoretical and Applied Mechanics,2011,43(5):894-904.

[17]孙韵韵,肖会芳,徐金梧.考虑轧制界面粗糙形貌的轧机辊系非线性振动特性研究[J].振动与冲击,2017,36(8):113-120.

Sun Y Y, Xiao H F, Xu J W. Nonlinear vibration characteristics of a rolling mill system considering the roughness of rolling interface [J]. Journal of Vibration and Shock,2017,36(8):113-120.

[18]Peng R R, Zhang X Z, Shi P M. Coupled vibration behavior of hot rolling mill rolls under multinonlinear effects[J]. Shock and Vibration,2020(6): 1-14.

[19]侯东晓,彭荣荣,刘浩然.变摩擦力下板带轧机辊系垂直-水平耦合振动特性[J].东北大学学报(自然科学版),2013,34(11):1615-1619.

Hou D X, Peng R R, Liu H R. Vertical-horizontal coupling vibration characteristics of strip mill rolls under the variable friction [J]. Journal of Northeastern University (Natural Science),2013,34(11):1615-1619.

[20]唐驾时，符文彬，钱长照，等.非线性系统的分岔控制[M].北京：科学出版社,2016.

Tang J S, Fu W B, Qian C Z, et al. Bifurcation Control of Nonlinear Systems [M]. Beijing: Science Press,2016.

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