The prediction of metal flow, forging load and distributions of strain ans stress in the forging processes is very important. It provides necessary information and guidelines for the effective design and manufacture of the forging dies. It is desirable to develop a computer simulation code in order to predict such information more realistically. In the present work, a three-dimensional finite element formulation is presented on the basis of rigid-plastic material model by considering the work-hardening effect. The discretization is made with 8-node hexahedral isoparametric elements and 6-node triangular prismatic elements. A finite element code has been developed, where the three-dimensional cold forging processes with arbitrarily curved die geometries can be analyzed.
A systematic method to generate an initial velocity field is proposed by assuming a linear viscous material. The effectiveness of the proposed initial guess generation scheme is shown for the analysis of some forging processes with complicated die geometry. In order to impose velocity boundary conditions on arbitrarily curved die surfaces, an effective method is suggested by using the skew boundary condition. The description of the die surface is made easily by employing the parametric form.
The treatment of the frictional boundary condition on curved three-dimensional surfaces is formulated for 4-node rectangular patches and 3-node triangular ones which are generated from the 8-node hexahedral solid elements and 6-node triangular prismatic elements, respctively. In order to treat the contact problem, an iterative method is used by checking the contact condition during the iterations of the finite element procedures. The position and the velocity of sliding nodes and the penetrating nodes are adjusted so that they satisfy the contact condition during the iterations.
Furthermore, a three-dimensional remeshing technique is proposed by introducing a modular concept. The computational region is divided into several modules which are designed so that they can be used as a library of geometric parts. Criteria for remeshing as well as a scheme for mapping of state variables are proposed for the three-dimensional remeshing.
In order to show the validity and effectiveness of the proposed schemes, several forging processes are simulated and the computations are compared with the experiments. Industrially useful forging processes such as upset forging of various shaped blocks with flat dies, forging of various shaped blocks with flat dies, forging of square blocks with hemispherical punches, steady-steady extrusion of billet with shaped sections and forging of a bevel gear have been simulated. The predicted results are shown to be in good agreement with the experiments. The computational results show that the proposed shemes can be applied to other more complicated die geometry together with the proposed remeshing technique.
단조공정에서 금속유동, 단조하중 그리고 변형도와 응력은 단조금형의 설계및 제작에 대한 정보를 제공해 주므로, 이들에 대한 예측은 매우 중요하다. 따라서 이러한 정보들을 좀더 실제적으로 잘 예측할 수 있는 컴퓨터 시뮬레이션 프로그램을 개발할 필요가 있다. 본 논문에서는 가공경화효과를 고려한 강소성 유한요소 수식화를 도입하여 해석프로그램을 개발하였다.
선형점성재료를 가정하여 초기 속도장을 생성하는 체계적인 방법을 제안하였다. 임의형상의 금형에서 속도 경계조건을 부여하기 위하여 경사경계조건 (skew boundary condition)을 이용한 효율적인 방법을 제안하였다. 3차원 곡면에서 마찰경계조건을 처리하는 방법을 수식화 하였다. 접촉 문제를 해결하기 위하여 시행착오법을 이용하여 유한요소 과정의 반복수행중에 접촉영역을 찾도록 하였다.
모듀울 개념을 도입하여 3차원 격자재구성 기법을 제안하였다. 이때 계산영역을 몇개의 모듀울로 분할하고, 각 모듀울은 기하학적 형상의 라이브러리(library)로 사용된다. 상태변수의 변환(mapping of state variables)과 격자재구성을 위한 판정기준 (criteria for remeshing)을 3차원 격자재구성에 대해 제안하였다.
제안된 각 방법들의 타당성과 효율성을 검증하기 위하여, 몇가지 예제에 적용하고, 그 계산결과를 실험과 비교하였다. 계산에 의해 예측된 결과는 실험과 잘 일치하고 있음을 확인할 수 있었으며, 따라서 본논문에서 제안된 방법들이 좀더 복잡한 3차원 형상의 금형에 의한 단조 공정에도 적용될 수 있음을 알 수 있다.
