Dynamical Bifurcation Study on Electromechanical Coupling Vibration in Rolling Mill’s Drive System

Abstract

In order to solve the problem of low frequency vibration in rolling mill drive system driven by AC motor, the nonlinear dynamics equations of rolling mill drive system with coupling action of electromagnetic energy and mechanical energy are established on the basis of Lagrange-Maxwell theory, and the vibration characteristic of this kind of multidimensional nonlinear autonomous system is studied by using the theory of dynamical bifurcation. Considering the high dimensional bifurcation caused by the nonhyperbolic fixed points when the resistances in stator and rotor change, the nonlinear differential equations’ approximate analytical solutions are solved with the aid of multiple time scales and harmonic balance, and the third-order normal form is obtained directly without application of center manifold theory. According to the normal form, the double Hopf bifurcations, 2D tori and 3D tori bifurcations are studied, and the stability of periodic and quasi-periodic solutions is analyzed by using Hurwitz criterion, and the boundary conditions of stable regions are given for each solution. The numerical simulation verifies the correctness of the conclusions, thereby providing a theoretical basis for smooth running of the rolling mill drive system.