The finite element method (FEM) has been widely used since the late 1980s. Recently, with the development of computer output, the analytical technique has been developed from two-dimensional to three-dimensional advanced deformation analysis. This improves the dimensional accuracy and quality of the product. The following representative analytical techniques are introduced.

1. Analytical technique of extension rolling of seamless steel pipe.The mandrel mill is rolled by a mandrel and a perforated roll. Therefore, unlike the plate rolling, there is a free deformation zone in which the roll and the mandrel are not in contact in the circumferential direction of the roll. Since the free deformation zone is rolled on the next frame, it is important to predict the deformation including the free deformation zone in order to properly understand the comprehensive characteristics of the mandrel mill.

This kind of complex deformation prediction requires high precision if the algorithm is implemented by the conventional cache, so high-precision analysis is required. Considering the shear deformation in the rolling direction, an approximate three-dimensional analysis is performed using the normal expansion plane deformation analysis. As a result, it was found that the calculated value and the experimental value were consistent. Recently, with the development of computer technology, the development of the full three-dimensional finite element method analysis technology has been accelerated, and it can also be used for the analysis of the influence of the tension between the stands and the analysis of the speed difference between the rolls and the tube blank.

2. Analytical technique for sizing rolling When sizing is used, since there is no tool on the inner surface, the inner surface shape of the rolled material is not uniform when the thick-walled tube is rolled. When a three-roll mill is used, the inner surface of the rolled material has a hexagonal shape. Through the analysis of the three-dimensional finite element method, the mechanism of the inner edge phenomenon and the countermeasures should be clarified.

A substantially uniform wall thickness can be obtained when a hole shape close to a perfect circle with an ellipticity of 0.998 is obtained, but a sharp inner hexagonal angle appears when a hole shape close to a perfect circle with an ellipticity of 0.960 is used. This analysis can predict the change in wall thickness during rolling with a reducer, and clarify the influence of the hole shape characteristics of the roll and the tension between the frames on the inner hexagonal angle.