关键词: 参数激励, 颤振, 共振, 混沌, 轧机

Abstract: Vibration analysis of nonlinear parametrically and self-excited 4-h cold rolling system of two degrees of freedom is carried out. The model contains two van der Pol oscillators coupled by a linear spring with a periodically changing stiffness. By means of a multiple-scales method, the existence and stability of periodic solutions in a first-order approximation close to the main parametric resonance are investigated, and the fre-quency-response equations are provided. Bifurcations of the system and regions of chaotic solutions are found. It follows from the maximal Lyapunov exponent and Poincaré map that vibrations of the rolling system appear more complex with larger excitation amplitude.

Key words: Chaos, Chatter, Parametric excitation, Resonance vibration, Rolling mill