Nonlinear coupled vibration and control of roll system for twenty-high rolling mill

Precision ultra-thin strips with high precision, corrosion resistance, excellent surface finish and other properties are widely used in micro-manufacturing, microelectronics, and other high-tech fields. The vibration characteristics of twenty-high rolling mills significantly affect the surface quality of extremely thin strips. In this study, a coupled nonlinear dynamic model of a twenty-high rolling mill with linear damping and nonlinear stiffness between the roll and strip was established. The amplitude-frequency equations of the main, super-harmonic and sub-harmonic resonances, and internal resonances were obtained using the multi-scale method. The influence of different parameters on the amplitude-frequency curves was analyzed. According to Lyapunov's first approximation stability criterion, the stability of the roll system was analyzed using a moving phase plane phase trajectory diagram. A tuned mass damper was designed to control the nonlinear vibration characteristics of the twenty-high rolling mill, and a coupling dynamics model between the tuned mass damper and the roll system was established. The influences of the mass, stiffness, and damping ratios on the dynamic magnification coefficient of the roll were analyzed. To minimize the peak value of the dynamic amplification coefficient, an adaptive genetic algorithm was used to optimize the parameters of the tuned mass damper, and the optimal mass, stiffness, and damping ratios were determined. Finally, the feasibility and effectiveness of the tuned-mass damper were verified using time-domain, phase, and Poincare section diagrams, which provide an important reference values and theoretical basis for the design and analysis of the roll system for the twenty-high rolling mill.