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In this paper, the static bifurcation and dynamic bifurcation of rolling mill system with torsional-horizontal coupling vibration are studied. Firstly, the dynamic equation of torsional-horizontal coupled vibration of rolling mill main drive system is established. Rolling mill is driven by the gear pair, so the torsional vibration of the gear pair, the horizontal vibration and the friction factor are considered in the dynamic equation. Then the equivalent low-dimensional bifurcation equation, which can reveal the system nonlinear characteristics, is obtained using Lyapunov-Schmidt method, and the system static bifurcation characteristics are studied using singularity theory. Lastly, the bifurcation condition and stability of the system with dynamic Hopf bifurcation are studied using Hopf bifurcation theorem. Numerical simulation of the actual parameter values confirms the analytical results.

Bifurcation characteristics of torsional-horizontal coupled vibration of rolling mill system