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

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