Abstract: Considering the role of nonlinear elastic constraint of the hydraulic pressure cylinder and compensating cylinder in the four-high rolling mill process, a multi-segmented nonlinear vibration dynamic equation of rolling mill rolls is established. Averaging method is used to get frequency response equation of the system, singularity theory is applied to analysis it and then 6 group transition sets and bifurcation diagrams are obtained, which show the various bifurcation forms of this system. The actual parameters of rolling mill is used to analyze the impact law that every nonlinear parameter on vibration characteristics of this system, after the numerical simulation the characteristics that the amplitude-frequency characteristic curves both show turning to the high frequency in each segment are found. Choosing proper system parameter can restrain this behave effectively, which provides a theoretical basis to suppress vibration of rolling mill rolls.

Key words: Bifurcation, Elastic constraints, Multi-segment nonlinear, Rolling mill