Stochastic Stability of Hot Strip Rolling Mill Rolls

A two dimensional stochastic nonlinear dynamical model of rolls is presented considering the stochastic factor of the rolling force. The Hamilton function is also described as one dimension diffusion process by using stochastic average method, the singular boundary theory was taken for analyzing the global stochastic stability of the system, and the system's stochastic stability is researched by solving the Fokker-Planck-Kolmogorov (FPK) equation. The results show that the generalized energy H in the range of 0.02 to 0.4, the system's response has the minimum transition probability density, and the system state is not easy to change, therefore the system generalized energy H should be to limit in this range in the design and operation of the rolling mill.