Research On Analitical Algorithm Of Contact Problem Using Finite Element Analysis For Bulk Forming

Metal plastic forming is a process of making billet with simple shape to become the needed workpiece through dies or tools, so dynamic contact problem arises between die and billet during metal plastic forming process, and it becomes a significant aspect to handle this problem in finite element analysis. It depends on determining the corresponding geometric position relationship between die and deformation body in numerical form to solve the contact problem, which means the relationship between the finite element grid node on the surface of deformation body and the surface of die cavity. So the expression method of die shape is an important aspect in handling contact problem, and has an influence on accuracy and efficiency of finite element analysis.Usually the expression method of die shape is divided into analytical method and numerical method, and correspondingly the analytical method is easy, precise and not complicated and has a simple algorithm on contact judgment, however, this method is only limited to die with simple and regular shape. The die with complicated shape expressed in numerical method has large amount of computation and complicated contact judgment algorithm.In this paper, the high-order algebraic analytical method was experimentally applied to the die expression in high-order curved shape, and according to the research results of high-order curve analytical equation in the past few years, we put forward a new way to express the die shape in high-order algebraic curve. We considered two-dimension deformation process as a case study, probed to express the die shape in high-order curve analytical equation, analyzed effect factors of the die shape expression in high-order curve analytical equation, and gave analytical examples.Based on the proposal, we analyzed the relationship between die shape expressed in high-order curve analytical equation and the finite element grid node on the surface of deformation body, presented a finite element analytical contact judgment algorithm on the foundation of expression of die shape in high-order curve analytical equation, programmed the corresponding finite element analysis program, and added available plastic finite element analysis program.Utilizing the finite element analysis program of contact judgment algorithm based on expression of high-order curve analytical equation, we analyzed the process of the local compression of cylinder with dies of different curved shapes, and then compared the analytical results with the business software DEFORM-2D to verify the reliability of expression of die shape in high-order curve analytical equation and relevant contact judgment algorithm.