This study establishes a vertical–horizontal coupling vibration model of hot rolling mill rolls under multi-piecewise nonlinear constraints considering the piecewise nonlinear spring force and piecewise nonlinear friction force constraints of the hydraulic cylinder in the vertical direction of the rolls, the piecewise stiffness constraints in the horizontal direction, and the influence of the nonlinear dynamic rolling force in the rolling process. Using the average method to solve the amplitude–frequency response equation of the coupled vibration system and taking the actual parameters of a 1780 mm hot rolling mill (Chengde Steel Co., Ltd., Chengde, China) as an example, we study the amplitude–frequency characteristics of the mill rolls under different parameter settings. The results show that the amplitude and resonance region can be reduced by appropriately reducing the external disturbance force and the nonlinear spring force of the hydraulic cylinder, appropriately increasing the nonlinear friction force, and eliminating the gap between the bearing seat and the mill housing, to avoid the amplitude jump phenomenon due to piecewise variation. Furthermore, using the singularity theory to study the static bifurcation characteristics of the coupled vibration system, we establish a relationship between the vibration parameters and the topological bifurcation solution of the coupled system. The transition sets and their corresponding bifurcation topological structure in three cases are given, and the steady and unsteady process parameter regions of the rolls are obtained. The dynamic behavior of the coupled vibration system can be controlled by varying the bifurcation parameter. This study provides a theoretical basis for restraining the vibration of hot rolling mill rolls and optimizing the process parameters.

中文翻译：

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多段非线性约束下热轧机轧辊的水平-水平耦合振动

本研究建立了在多段非线性约束条件下热轧机轧辊的垂直-水平耦合振动模型，其中考虑了液压缸在轧辊垂直方向上的分段非线性弹簧力和分段非线性摩擦力约束，以及在垂直方向上的分段刚度约束。水平方向以及非线性动态轧制力在轧制过程中的影响。使用平均法求解耦合振动系统的振幅-频率响应方程，并以1780 mm热轧机（承德市承德钢铁有限公司）的实际参数为例，研究振幅–不同参数设置下轧辊的频率特性。结果表明，通过适当减小液压缸的外部干扰力和非线性弹簧力，适当增大非线性摩擦力以及消除轴承座与磨机壳体之间的间隙，可以减小振幅和共振区域。避免由于分段变化而引起的幅度跳跃现象。此外，使用奇异性理论研究耦合振动系统的静态分叉特性，建立了振动参数与耦合系统拓扑分叉解之间的关系。给出了三种情况下的过渡集及其对应的分叉拓扑结构，并获得了轧辊的稳态和非稳态过程参数区域。耦合振动系统的动态行为可以通过改变分叉参数来控制。该研究为抑制热轧机轧辊的振动和优化工艺参数提供了理论依据。