Abstract: The parametrically excited dynamic equation under nonlinear dynamic rolling force is constructed， which considers the dynamic rolling force and the nonlinear parametrically excited stiffness caused by chatter mark of roll surface. Then the 1/2 subharmonic resonance amplitude-frequency equation of the system is calculated by the method of multiple scales， and the subharmonic resonance characteristics with the change of damping and parametrically excited stiffness are obtained， then the bifurcation characteristics of the system in the situation of non-autonomy is obtained by the use of singularity theory. Finally， by taking the actual parameters of the rolling mill， the amplitude-frequency characteristics， bifurcation and chaos characteristics in different parameters are analyzed， it is found that many different movement patterns such as periodic motion and chaos arises with the change of nonlinear parametrically excited stiffness， which provides a theoretical reference for the further suppression of the rolling mill vibration.

Key words: cold rolling mill, dynamic rolling force, parametrically excited vibration, resonance, bifurcation