Abstract: The dynamic model of multi-degree-of-freedom main drive system with clearance is established. The equations are decoupled by transforming them into principal coordinates. The method of modified Lindstedt-Poincare(MLP) is employed to obtain the analytical solutions of the nonlinear system under loaded friction of rolling and out disturbance excitation. The bifurcation equation of the system is deduced by the modified Lindstedt-Poincare combined with the multiple scales. The characteristics of bifurcation of non-autonomy system are analyzed by means of singularity theory, respectively, and different topological structure of solution is obtained under different parameters and obtaining the variation area of parameters under which the rolling mill could vibrate stably. The numerical simulation bases on some steel mill. Rolling mill’s main drive system which simplifies as a four-degree-of-freedom is given. It exhibits many changes of the relationship between amplitude and frequency under the variation of parameters like nonlinear stiffness, clearance, torque disturbance and rolling force and obtaining clearance and torque disturbance are the main factors which influent the vibration. To reduce the amplitude of torsional vibration, the value of clearance and torque disturbance are regulated. The research results provide theory basis and reference for analyzing torsional vibration of rolling mill’s transmission system caused by clearance.

Key words: Bifurcation, Clearance, Drive system of rolling mill, Multi-degree-of-freedom