Abstract: A kind of hysteretic nonlinear vertical vibration dynamic model is established which considers hysteresis of strips plastic deformation. The stability of the hysteretic nonlinear system is analyzed by using stability theory of singularity, and the conditions for the emergence of various singular points are obtained. Then the analytical approximate solution of the system under periodic excitation is accounted, and the primary resonance amplitude-frequency equation of the system is obtained. Finally, according to the actual parameters of rolling mill, the influence of nonlinear stiffness and nonlinear damp of rolled piece on the primary resonance amplitude-frequency response of rolling mill is analyzed, and the bifurcation behaviors of rolling mill under different external disturbances are studied. It is found that the rolling mill exhibits many dynamic behaviors such as periodic, period-doubling motion and chaos. The results provide theoretical reference for researching and suppressing rolling mill vibration.

Key words: Bifurcation, Hysteretic nonlinear, Rolling mill, Vertical vibration