Dynamic modeling and analysis on rigid-flexible coupling between vertical chatter and transverse bending vibration in process of cold rolling

Considering the dynamic variation of roll gap and the transverse distribution of dynamic rolling force along the work roll width direction, the movement and deformation of rolls system, influenced by the coupling of vertical chatter and transverse bending vibration, may cause instability and also bring product defect of thickness difference. Therefore, a rigid-flexible coupling vibration model of the rolls system was presented. The influence of dynamic characteristics on the rolling process stability and strip thickness distribution was investigated. Firstly, assuming the symmetry of upper and lower structures of six-high rolling mill, a transverse bending vibration model of three-beam system under simply supported boundary conditions was established, and a semi-analytical solution method was proposed to deal with this model. Then, considering both variation and change rate of the roll gap, a roll vertical chatter model with structure and process coupled was constructed, and the critical rolling speed for self-excited instability was determined by Routh stability criterion. Furthermore, a rigid-flexible coupling vibration model of the rolls system was built by connecting the vertical chatter model and transverse bending vibration model through the distribution of dynamic rolling force, and the dynamic characteristics of rolls system were analyzed. Finally, the strip exit thickness distributions under the stable and unstable rolling process were compared, and the product shape and thickness distribution characteristics were quantitatively evaluated by the crown and maximum longitudinal thickness difference.