Abstract: A dynamic rolling force model with variable friction factor in vertical and horizontal directions were obtained using the Orowan deformation area force balance theory. Then， a verticalhorizontal coupling nonlinear vibration dynamic model of strip mill was established considering the effect of the structure vibration. The approximate solution was solved by the multiplescale method， and the amplitudefrequency equation was obtained. Based on the actual parameters of 1780 rolling mill， the characteristics of amplitudefrequency were analyzed under different nonlinear parameters. Finally， the bifurcation behaviors of the coupling system was analyzed by the singularity theory， and 6 group different transition sets and bifurcation diagrams in the 2 parameter planes of the coupling system were obtained， which provided theoretical guidance for the further suppression of mill roll system vibration.

Key words: rolling mill, variable friction, verticalhorizontal coupling vibration, bifurcation