Linear Integral Analysis of Bar Rough Rolling by Strain Rate Vector

A new linear integral method for bar hot rolling on roughing train was obtained. First, for plastic deformation energy rate, equivalent strain rate about Kobayashi's three-dimensional velocity field was expressed by two-dimensional strain rate vector; then, the two-dimensional strain rate vector was inverted into inner product and was integrated term by term. During those processes, boundary equation and mean value theorem were introduced; for friction and shear energy dissipation rate, definite integral was applied to the solution process. Sequentially, the total upper bound power was minimized, and the analytical expressions of rolling torque, separating force, and stress state factor were obtained. The calculated results by these expressions were compared with those of experimental values. The results show that the new linear integral method is available for bar rough rolling analysis and the calculated results by this method are a little higher than those of experimental ones. However, the maximum error between them is less than 10%.