An analytical model of plate rolling force with a simple available velocity field and equal perimeter yield criterion

To analyze plate rolling force, a simple available velocity field is first proposed in this article. Based on the velocity field, the internal deformation energy rate and the friction energy rate are analyzed by the equal perimeter yield criterion and the method of the collinear vector inner product, respectively. Finally, the rolling force accounting for the elastic flattening of the roller and the temperature rise of the rolled piece are ultimately obtained through the minimization of the total energy rate. The theoretical rolling forces are compared with actual measured data, and a good consistency is found since the maximum error between them is less than 4.7%. In addition, the discussion of different rolling conditions, such as friction factor, thickness reduction, and shape factor, upon rolling force, location of neutral angle, and stress state coefficient is also carried out.