Development of the Sequential Voids Creation Approach in Axisymmetric Forming Dies

Abstract

Abstract The study deals with the problem of topological optimization of forming dies with a limitation on fatigue strength. As a model of a stamp, a typical geometric configuration of stamps for the manufacture of parts of the " cup " type is considered. The algorithm for finding the optimal topology is proposed to be built separately in the internal areas under the stamp flanges and under the bottom of the "cup" of forming. Mathematical regularities are presented, according to which elements that fall into the area of predicted removal have a very small elastic modulus, which is widely used in topological optimization methods, then the stress state level is analyzed according to the fatigue strength curve. In the area of the flanges, there is a "build-up" of the mass according to the quadratic law with a variation in the depth of removal of the material. In the area of the bottom of the " cup " of forming, a step-by-step addition of rod elements is proposed until the level of the stress state meets the specified restrictions. Thus, this study is a modification of the topological optimization method. The novelty of the research lies in the construction of a new geometric scheme for determining the area of stored and deleted elements. The results of the study can be further developed in the development of methods for effective redistribution of material, as well as significantly reduce the material costs for the production of metal forming dies.