Optimal blank shape design by the iterative sensitivity method

Abstract

In order to realize net shape manufacturing of drawn parts, determination of the optimal blank shape plays a key role in the process development stage. The sensitivity method has many successful applications of the optimal blank design. In the method, the undeformed blank shape is modified iteratively by moving boundary nodes in the initial moving direction until the deformed shape satisfies a target shape. To determine the magnitude of the movement of the nodes, both the shape error measured at the deformed shape and the shape sensitivity defined by the effect of initial shape change on the final shape are utilized. To obtain shape sensitivity for each boundary node numerically, a couple of deformation processes has been analysed at each design stage with an original blank and offset blank. Drawings of the trapezoidal cup, cross-shaped cup and oil pan have been chosen as examples to verify the sensitivity method. Both the cross-shaped cup and oil pan are examples of complicated material flow during forming while the trapezoidal cup is of a simple flow. For every case the optimal blank shape has been obtained after only a few modifications without any predetermined deformation path. With the predicted optimal blank, a corresponding experiment has been carried out. The deformed shapes of the experiment almost exactly coincide with the desired target shape in every case. Through the investigation, the sensitivity method is found to be excellent in the blank design of arbitrary shaped drawing products.