Research On Multi-Step Inverse Method For Sheet Metal Forming Based On Optimization

Sheet metal forming simulation technology has been widely used in the development of automotive panels. The One-step Inverse Approach based on the elastic-plastic finite element model and the deformation theory, just according to the part shape and simple process parameters, can be very fast indicate the initial blank shape and give part’s formability indicates. In this paper, One-step inverse forming method, combined with the Grid mapping algorithm is applied to unfold the flanging rapidly.When the part undergoes relatively deep drawing or complex forming processes associated with loading and unloading, the One-step inverse method’s accuracy is not sufficient to provide accurate predictors. Through the introduction of the intermediate configurations to consider the actual forming process, in order to improve the formability indicates, the thickness distribution, the strain and stress distribution of part, the Multi-step inverse FEM method. This article is mainly to solve two basic questions of Multi-step inverse method:(1) Construction of intermediate configurations and its sliding constraint surface. A pseudo-minimum area method is proposed from the perspective of optimization to construct sliding constraint surface model. The method assumes that the sliding constraint surface is the smallest area-square surface of all possible surfaces that undergo the constraints of punch and die in the space. A construction of three dimensional surfaces is transformed into a quadratic programming model based on the discrete grid information. Solving efficiency of pseudo-minimum area method compared with the minimum area method can be a substantial increase. With the grid mapping method, the part configuration is mapped onto sliding constraint surface of intermediate configurations to get the intermediate configurations. In this paper, the symmetric part of square box and asymmetric part box support were simulated and analyzed.(2) Constitutive integration of Multi-step inverse FEM method. Between intermediate configurations of Multi-step inverse FEM method deformation theory is still used. But the initial configuration is attached with initial stress and the strain, at the end of iterations it is needed to update the new stress and strain in the final configuration with SIMO’s return algorithm. The algorithm consists of an assumed strain increment for the whole flexible elastic prediction step and correction step contains a plastic correction, to avoid the drift of the yielding surface.