Mathematical model for vertical rolling deformation based on energy method

An approach to analyzing three-dimensional vertical rolling is presented on the basis of energy method. The double parabola function model is applied to describe dog bone shape in the deformed region between the vertical rolls. The DSF (dual stream function) method is utilized to obtain three-dimensional velocity and strain rate fields. The values of dog bone shape dimensions and roll force are obtained when the total power functional achieves minimum, which is received according to double parabola model, velocity field, and the first variational principle. The validity of the proposed approach is discussed by contradistinguishing the present predictions with other models’ results and measured data in a hot strip plant in miscellaneous rolling conditions. Moreover, the impacts of different rolling conditions on the dog bone shape and stress state coefficient are researched, respectively.