Jiang Li, Yang Ting, Shi Wei, Xie Jiaquan
College of Intelligent Manufacturing, Chengdu Technological University, Chengdu, 611730, China.
Engineering Research Center of Advanced Metal Composites Forming Technology and Equipment, Ministry of Education, Taiyuan University of Technology, Taiyuan, 030024, China.
Sci Rep. 2025 Jul 1;15(1):22420. doi: 10.1038/s41598-025-04491-6.
In this paper, the main content is analyzing the combined resonance characteristics of the roller system. Firstly, established a horizontal nonlinear vibration model with fractional-order by considering the nonlinear stiffness and nonlinear damping between the roller and the material. Secondly, the multi-scale method is applied to solve the non-resonance, sub-harmonic resonance and super-harmonic resonance of the roller system. The analytical solution and the amplitude-frequency characteristic equations are obtained. Then, The relationship between the influence of different parameters on the sub-harmonic vibration of the roll system is investigated, and the results show that the nonlinear damping coefficient, nonlinear stiffness coefficient, linear stiffness coefficient and excitation force amplitude all affect the sub-harmonic vibration range and co-oscillation amplitude, and the change of the stiffness coefficient induces the system oscillation. Last, a linear and nonlinear optimal feedback controller is designed to control the sub-harmonic resonance and super-harmonic resonance phenomena of the roll system. Where the sub-harmonic resonance control parameters are selected in the range g ∈ (-0.32,0), 3.7 > g > 2.67, and the super-harmonic resonance control parameters are selected in the range g > 0, 0.5 < g < 2.5. The correctness of the theoretical study is verified by field experiments.
本文的主要内容是分析滚筒系统的组合共振特性。首先,通过考虑滚筒与物料之间的非线性刚度和非线性阻尼,建立了分数阶水平非线性振动模型。其次,应用多尺度法求解滚筒系统的非共振、亚谐波共振和超谐波共振,得到了解析解和幅频特性方程。然后,研究了不同参数对滚筒系统亚谐波振动影响的关系,结果表明,非线性阻尼系数、非线性刚度系数、线性刚度系数和激振力幅值均影响亚谐波振动范围和共振动幅值,刚度系数的变化会引发系统振荡。最后,设计了线性和非线性最优反馈控制器来控制滚筒系统的亚谐波共振和超谐波共振现象。其中,亚谐波共振控制参数在g∈(-0.32,0)、3.7>g>2.67范围内选取,超谐波共振控制参数在g>0、0.5<g<2.5范围内选取。通过现场实验验证了理论研究的正确性。