Vertical nonlinear vibration analysis of cold rolling mill considering structural gap and dynamic rolling force

To reveal the impact of vertical nonlinear vibration on the stabilization of the precision cold rolling system, the vertical nonlinear vibration model with consideration of structural gap and dynamic rolling force has been established. Utilizing the Magnus series method with high accuracy and long-term numerical stabilization, we calculate the vibration response of the cold rolling system and conduct numerical simulations to determine the bifurcation characteristics, maximum Lyapunov exponent, and two-parameter dynamical behavior. The results reveal the parameter regions of bifurcation and chaos that cause the vibration instability of the cold rolling system. It has also been found that the system has the nonlinear phenomenon of transition from period-3 motion to chaotic motion. More importantly, two-parameter matching regions for the cold rolling system performing periodic and chaotic motions are determined. Two-parameter matching solutions for improving and deteriorating the stabilization of the cold rolling system are clarified, and the preferred matching regions for the parameters coupling with the structural gap and dynamic rolling force are revealed. The results reveal the impact of system parameters upon the vertical nonlinear vibration of the cold rolling mill, which can serve as an academic reference for reducing the vibration and enhancing the stabilization of the cold rolling system.