A New Combined Finite Element - Analytical Model for Strip Profile Control in Cold Rolling Mills

The strip profile control problem in cold rolling mills is of paramount importance to ensure product quality. The paper presents a new combined finite element - analytical model of a 20-high cold rolling mill suitable for strip profile simulation and control. The model features rolls, nonlinear contacts between rolls, backup bearings, and mill housing. Rolls are modelled with Timoshenko beam elements and consider roll crown and taper. Contacts between rolls are modelled by Winkler foundation elements with nonlinear stiffness constant derived by the Hertz contact model. The mill housing is introduced by the matrix condensation method and the backup rolling bearings are defined by nonlinear Winkler foundation elements. A full 3D finite element model of the 20-high rolling mill is built by using a commercial software and used to validate the developed finite element - analytical model. A comparison with data extracted from measurements on a real case study is also provided. Finally, the developed combined finite element - analytical model is exploited to solve a strip profile control problem. A Singular Value Decomposition (SVD) optimization of the taper and backup actuators positions is performed, aiming to achieve a desired strip profile. Actuators saturation is considered. The actuators' influence maps are also obtained.