A model for prediction of profile and flatness of hot and cold rolled flat products in four-high mills

For flat rolled products, the thickness profile in the transversal direction is one of the most important product properties. For further processing, a defined crown of the product is necessary. In the rolling process, several mechanical and thermal influences interact with each other to form the strip shape at the roll gap exit. In the present analysis, a process model for rolling of strip and sheet is presented. The core feature of the process model is a two-dimensional stress distribution model based on von Karman’s differential equation. Sub models for the mechanical influences of work roll flattening as well as work and backup roll deflection and the thermal influence of work roll expansion have been developed or extended. The two-dimensional stress distribution serves as an input parameter for the roll deformation models. For work roll flattening, a three-dimensional model based on the Boussinesq problem is adopted, while the work and backup roll deflection, including contact flattening is calculated by means of finite beam elements. The thermal work roll crown is calculated with help of an axisymmetric numerical solution of the heat equation for the work roll, considering azimuthal averaging for the boundary conditions at the work roll surface. Results are presented for hot rolling of a strip in a seven-stand finishing train of a hot strip mill, showing the calculated evolution of the strip profile. A variation of the strip profile from the first to the 20th rolled strip is shown. This variation is addressed to the progressive increase of work roll temperature during the first 20 strips. It is shown that a CVC® system can lead to improvements in strip profile and therefore flatness.