Curvature area prediction for the deep drawing-ironing process of a cylindrical cup using finite element method and regression analysis

Products with long, cylindrical or rectangular can-shaped sidewalls are manufactured using a deep drawing-ironing (DDI) process. The volume of a typical cylindrical, axisymmetric product after the DDI process can be broadly divided into bottom, curvature, and side wall portions. In sheet metal forming, the volume of a product before and after forming is easily calculated from the law of volume constancy. Cylindrical, axisymmetric products can be represented as a two-dimensional axisymmetric problem, thus converting the volume calculation to an area calculation in two dimensions. The curvature area of an axisymmetric product can be geometrically expressed using a formula obtained by subtracting the area of a circle from the area of an ellipse. However, the geometrical curvature area obtained using this formula differs from the curvature area of the real product. Therefore, in this study, a finite element analysis is performed under the same condition as the actual product to which the DDI process is applied, and the validity of the analysis is verified by comparing the data. Finally, a regression analysis is conducted on the data obtained from the finite element analysis to derive an equation to predict the curvature area. In addition, the proposed method is verified by comparing with the data pertaining to a real part.