Strip/Foil Rolling Mill Stochastic Excitation Model and Its Stability

Based on the stochastic rolling force data from aluminum hot strip tandem mill, the ARMA time series model and the stochastic excitation power spectral density (PSD) model are established, and the stochastic rolling forces excitation model is established by utilizing Levenberg-Marquardt combined with generalized global planning algorithm. 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 was researched by solving the Fokker-Planck-Kolmogorov (FPK) equation. The results show that the stochastic excitation model obtained has significance for analyzing and researching stochastic dynamics characteristics to the system, and also 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.