Deduction of a quadratic velocity field and its application to rolling force of extra-thick plate

A quadratic velocity field that meets the kinematically admissible condition is constructed. To check the reliability of the proposed velocity field, the software ANSYS/LS-DYNA is used, and the change law of metal flow in the deformation zone is analyzed. Based on this velocity field, a three-dimensional rolling force model of extra-thick plate is established. During the analysis, the problem of integral difficulty due to the nonlinear Mises yield criterion is settled, and the internal power of deformation is deduced based on the method of inner product and accumulative summation of vector component. Meanwhile, the friction power and the shear power are also calculated by the method of co-line vector inner product and the variable upper bound integration method, respectively. The rolling force is acquired by the energy method and validated with the site measured value. The calculated deviations of the rolling forces between the model and the measured data are within 5.14%. Furthermore, the influences of the temperature difference of the workpiece, relative reduction, thickness-radius ratio, and friction factor on the rolling force model are analyzed. It is showing that the change law of the metal flow by simulation is consistent with the proposed velocity field, and the rolling force model accounting for the temperature difference of the workpiece is much closer to the actual situation.