Energy analysis of tailor rolled blank rolling process based on a new velocity field and the unified yield criterion

The upward rolling process is an important forming method of producing cold tailor rolled blank (TRB). In order to describe the flow rule of the deformation workpiece of the TRB accurately, a new three-dimensional (3D) velocity field is firstly obtained based on the weighting of two special velocity fields under extreme conditions. Upon this 3D velocity field, an analytical solution of the force-energy parameters of the above rolling process is strictly derived using the energy method in combination with the unified yield (UY) criterion. After the energy analysis, four kinds of deformation power consumed by upward rolling are solved respectively, and the analytical solutions of rolling torque, rolling force, and stress state coefficient are obtained according to the upper bound theory. Furthermore, the predicted rolling forces are compared with the measured data of upward rolling of CR340 steel. It indicates that the theoretical model using the Tresca yield criterion has the highest prediction accuracy, with an average error of 11.57%, which has demonstrated the importance of the selection of a yield criterion. Meanwhile, it is verified that the theoretical rolling model without considering spread will induce slightly higher results than those considering spread, with an average deviation of 9.80 kN. Finally, the variation of various rolling parameters over time is analyzed, and a reasonable selection range of the ratio of entrance speed to roller speed is obtained, which is around (0.51, 0.67). For the present research, it is seen that the parameter relationship in the present model is clear and the accuracy is reliable, which can be used for the design and optimization of the process parameters of the upward rolling process.