Statistical Study on Correlation between Design Variables and Shape Errors in Flexible Stretch Forming Process

Abstract

In order to reduce the elastic recovery of a sheet material and eliminate a great number of solid dies used in the forming process of various shapes, a flexible stretch forming process (FSFP) is considered in this study. Especially, the relationship among design variables, such as the punch size, objective radius of curvature, and elastic pad thickness is quantitatively evaluated to find out their respective influences on the shape errors of a formed sheet plate using the statistical method based on the FE simulation result planned by the three-way factorial design. The shape errors are divided into two types based on the material behavior according to the widthwise- and tensile- directions. The correlations of the shape errors and the design variables are estimated through the Pearson correlation analyses. The punch size has a strong positive linear correlation with the widthwise- and tensile- shape errors, and the correlation between the objective curvature radius and tensile-direction shape error is weak and negative. Although the effect of the elastic pad thickness is less than those of the other variables, it prevents effectively surface defects. Subsequently, the mathematical model is assumed to clarify their relationship. Two regression equations are estimated in terms of the design variables regarding the widthwise- and tensile- shape errors. The shape errors could be inferred by the assumed model in the particular combination of the design variables; then, the acceptable punch size and elastic pad thickness can be determined according to the objective curvature radius.