Analysis of stress distribution in caliber rolling by the energy method using finite-element division

The authors previously proposed an energy method using finite-element division and applied it to the analysis of the flow of material. In this work, the authors develop this method further to obtain the stress distribution in caliber rolling. Recently, Tomita obtained the stress distribution using the grid method so that the equilibrium condition may be satisfied approximately, whereas Mori evaluated the accuracy of the result obtained by the rigid-plastic finite-element method, by considering the equivalent nodal force which is assumed to be in equilibrium. Hence, the authors combined these methods and applied them to determine the stress distribution. The following results were obtained. First, in the flat rolling of bars, the roll force agrees well with the theoretical equation proposed by Saito. Second, in square-diamond rolling and round-oval rolling, the roll force depends on the ratio of the indirectly reduced area in the cross-section to the area of the cross-section. Finally, in square-oval rolling, the roll force agrees with the theoretical equation proposed by Saito when the projected material-roll contact length is replaced by the mean projected material-roll contact length in the width direction.