Optimum blank design by the predictor-corrector scheme of SLM and FSQP in the deep drawing process of square cup with flange

This paper presents a more accurate predictor-corrector scheme that combines the stream line method (SLM) and feasible sequential quadratic programming (FSQP) using the explicit dynamic finite element method (FEM) to design the optimum blank in the deep drawing process of square cup with flange. It is clear that faster convergence and better results of calculating optimum blank shape are guaranteed when FSQP uses a better initial guess. But it is not easy to guess the initial blank shape due to the variation of blank thickness, material anisotropy, and friction on the flange area at the beginning in the deep drawing process. SLM can obtain a preliminary prediction of the optimum blank shape with a little computational effort, so with SLM it is feasible to predict the initial guess of optimum blank with the assumption of fixed height of square cup with flange. FSQP can continue to adopt the predictor obtained by SLM to correct the optimum blank efficiently and accurately. Then the optimum blank is used in the final simulation and experiment. From comparison of the target shape between the simulated and experimental results, a good correspondence is confirmed. Other comparisons of the punch load, punch stroke, and wall thickness of the target square cup also show good agreement.