Design Optimization of Springback in a Deepdrawing Process

Abstract

The design optimization of springback in a deepdrawing process is proposed to control the e nal shape of the workpiece. The manufacturing process design problem is formulated to minimize the difference between the shape of the desired workpiece geometry and the e nal analysis result after elastic springback. The rigid die shape and the workpiece thickness are treated as design variables. A nonlinear structural problem that includes e nitedeformation elastoplasticity withfrictional contactissolved usinga mesh-freemethod in which thestructural domain is discretized by a set of particles. Continuum-based design sensitivity analysis is carried out to obtain gradient information for the optimization efe ciently. The accuracy of the sensitivity result is compared with the e nite difference result with excellent agreement. The optimum deepdrawing process signie cantly improves the quality of the e nal product. ESPITE signie cant simulation and design capability developments in modern technology, gaps still remain between the simulation-based design and the manufacturing process itself. One major reason for these gaps is the lack of efe cient and accurate numerical methods in the design process. First, accurate numerical methods have to be used to simulate manufacturing processes, and these methods must take into account large deformations, complicated constitutive relations, and a sliding contact between workpiece and die. Second, efe cient numerical methods have to be used to make the deepdrawing optimization process practical. It is the purpose of this paper to demonstrate that these two obstacles can be resolved by using accurate numerical methods and an efe cient design sensitivity analysis (DSA). The deepdrawingprocessinvolvesa large degree ofplastic deformation and rigid-body rotations, as well as a complicated contact between workpiece and die. Many simplie ed approaches have been proposedinsimulationanddesignofthemetalformingprocess.One