Abstract: We established a dynamic model of a four-roll cold strip rolling mill under Gaussian white noise excitation. We simplified the system into an Ito stochastic differential equation by using the stochastic averaging method for quasi-non-integrable Hamiltonian systems. Through the maximum Lyapunov exponent of the system’s invariant measure and stochastic bifurcation theory, we analyzed the local stability and stochastic Hopf bifurcation of the system. and verified the effectiveness of the theory of stochastic averaging method by using Monte Carlo simulations. The numerical simulation results show that as the deformation resistance of the rolled material increases, the system bifurcates and loses stability.

Key words: rolling mill, stochastic averaging method, stochastic stability, stochastic Hopf bifurcation