Probabilistic design of aluminum sheet drawing for reduced risk of wrinkling and fracture

Often, sheet drawing processes are designed to provide the geometry of the final part, and then the process parameters such as blank dimensions, blank holder forces (BHFs), press strokes and interface friction are designed and controlled to provide the greatest drawability (largest depth of draw without violating the wrinkling and thinning constraints). The exclusion of inherent process variations in this design can often lead to process designs that are unreliable and uncontrollable. In this paper, a general multi-criteria design approach is presented to quantify the uncertainties and to incorporate them into the response surface method (RSM) based model so as to conduct probabilistic optimization. A surrogate RSM model of the process mechanics is generated using FEM-based high-fidelity models and design of experiments (DOEs), and a simple linear weighted approach is used to formulate the objective function or the quality index (QI). To demonstrate this approach, deep drawing of an aluminum Hishida part is analyzed. With the predetermined blank shape, tooling design and fixed drawing depth, a probabilistic design (PD) is successfully carried out to find the optimal combination of BHF and friction coefficient under variation of material properties. The results show that with the probabilistic approach, the QI improved by 42% over the traditional deterministic design (DD). It also shows that by further reducing the variation of friction coefficient to 2%, the QI will improve further to 98.97%.