Abstract
Abstract
A new method of optimal blank shape design for the drawings of arbitrary shapes has been proposed. Similar to the sensitivity method, as detailed in past work of the present author, the basic nature of this method is iterative modification of an undeformed blank shape by moving the nodal positions at the boundary of the blank, until the final shape satisfies a target shape. The main difference from the sensitivity method is that the radius vector, determined by three adjacent boundary nodes during the deformation, is utilized in this method. The direction of the radius vector is utilized as a main parameter for the blank shape modification. Even though the sensitivity method has been proven to be excellent through both comparison and experiment, there still remain problems such as two runs of finite element analyses for each design stage, and hence huge computational effort. For the rigid-body rotation dominant problems, the method often fails to find the optimal shape. The present method requires only a single deformation analysis for each design step and there is no problem due to the rigid-body rotation during forming. Drawings of L-shaped cup, oil pan and wheel housing have been chosen as the examples to verify the present method through comparison with the result predicted by the sensitivity method. In every case the optimal blank shapes have been obtained after a few iterations without a predetermined deformation path and it has been verified that the deformed shape with the predicted optimal blank almost coincides with the target shape. Through this investigation, the present method is found to be as good as or better than the sensitivity method in the optimal blank design.