Deformation mechanics and efficient force prediction in single point incremental forming

Incremental sheet forming (ISF) is a promising forming process which is able to deform a flat sheet into a complex 3D shape by using a generic moving tool. The flexibility, increased formability and the reduced forming force make the ISF process ideal for rapid prototype and small batch production. However, the effective production design and optimization in ISF require the efficient prediction of forming force, especially the tangential force which is the actual force component that does plastic work during the forming process. In this paper, in order to investigate the deformation mechanism in the ISF process, a comprehensive finite element (FE) model for the cone-forming process with fine solid elements is established which allows the quantitative study of the deformation behavior of stretching, bending and shearing during the process. Based on such analysis, an efficient model for tangential force prediction is deduced analytically in which all these three deformation modes are considered. In particular, the contribution from each deformation mode is related to the variation of forming parameters. Additionally, the proposed efficient model is comprehensively validated with both truncated cone and pyramid shapes by varying four forming parameters (i.e. step down, wall angle, tool radius and sheet thickness). In both cases, the predicted forces show good agreements with the experimental results. Furthermore, the proposed model is generalized to deal with more complex shapes (e.g. ellipsoidal cup). It is found that the trend of tangential force could be properly represented by the change of the curvature of the formed part. Considering the proposed model can be solved within only several minutes, it will guide the forming process and shorten the lead time.