Robust design of spatially distributed friction for reduced wrinkling and thinning failure in sheet drawing

This paper investigates optimal design of spatially varying frictional constraints in reducing the risk of failure due to wrinkling and thinning. First, this problem is formulated deterministically as a multi-objective optimization with spatially distributed frictional constraints, and pre-determined BHF. An FEM-based genetic algorithm approach (NSGA-II) is used to determine the deterministic Pareto front for multiple design alternatives, and a tradeoff strategy is used to identify an optimal design. Further, using a first order mean-value approach, a probabilistic formulation is proposed. The deterministic and probabilistic designs are compared to the conventional spatially uniform friction case. The results show that in the drawing of a Hishida oil pan part, an overall improvement of 33% in strain distribution can be obtained and a further 12% improvement can be obtained with probabilistic design. A covariance based approach is used to explore a reliable design that is robust to process uncertainties.