Sliding bifurcation research of a horizontal–torsional coupled main drive system of rolling mill

Sliding bifurcation of a horizontal–torsional coupled main drive system of rolling mill along with the change of mixed friction coefficient under the conditions of autonomy and non-autonomy is studied in this paper. Considering the friction between the roller and the strip, the torsional vibration of gear pair and the horizontal vibration of the roller, the dynamical equation of a horizontal–torsional coupled main drive system of rolling mill is deduced. The stability of the equilibrium point in the autonomous system is analyzed by using the Hopf bifurcation theorem. The Filippov convex method is used to extend the system. The theoretical conditions of the stick–slip motion are given, which are used to numerically predict the sliding bifurcation. The stability of periodic solutions in the non-autonomous system is analyzed by using the Floquet theory. The influences of mixed friction coefficient on the dynamic behaviors of the system under the conditions of autonomy and non-autonomy are compared. Numerical simulations are also given, which confirm the analytical results.