Design and optimization under uncertainty in sheet metal forming processes constrained with failure analysis

In manufacturing environments, uncertainties associated with metal forming processes have presented significant challenges in quality management. To address these challenges, this research aims to establish a framework for robust design of complex engineering systems (e.g., sheet metal forming processes). As demonstrated in this work, uncertainties from process parameters and material properties can make an optimal design determined by a deterministic approach infeasible or too risky. In design under uncertainty, one of bottlenecks is the computational method for estimating system variations. Since most of engineering problems are characterized by mean and variance, a weighted three-point-based method is proposed. This method yields a set of optimal sampling locations and their associated weights for a given type of distributions. Using this method, the average accuracy of prediction was approximately 98% for various functions. It was demonstrated that the computational effort is a fraction of what needed in traditional methods that achieve the same level of accuracy. The method was then integrated with the design and optimization approach for designing sheet metal forming processes. To accomplish this objective, a nonlinear explicit finite element method was used as an important tool for analyzing stress and strain in stamping processes. This research proposes a new effective analytical method for calculating springback of a straight flanging process, and further utilizes the stress-based tearing criterion and energy-based wrinkling criterion to quantify margins of tearing and wrinkling.; Through the integration of these features, the current research establishes a framework for design under uncertainty in sheet metal forming. The robust design model takes into account producibility requirements through failure analysis and uncertainties from forming conditions and material properties. The approach was demonstrated through a demonstration example of a wheelhouse stamping process used in automobile industry. In addition, model validation approaches taking uncertainty into account are demonstrated in a simulation of a sample flanging process. Overall, this research presents the methodology and feasibility of implementing the framework for design and optimization under uncertainty, which can certainly be generalized for other industrial cases.