Shape optimization of the workpiece in the forging process using equivalent static loads

Abstract

The forging process, which is the shaping of a workpiece using compressive loads, is a representative plastic manufacturing process and typically consists of a multi-step process with a preforming process. The workpiece shape is an important factor because it influences the quality of the final product. After the forging process, defects such as an unfilled area, flash and crack can occur, and the effective strains may not be evenly distributed. Shape optimization of the workpiece is nonlinear dynamic response optimization because nonlinearities are involved in the analysis of the forging process. Many researches are performed to predetermine the workpiece shape using conventional methods. It is well known that the conventional methods are quite costly due to repeated nonlinear analysis for the calculation of function and sensitivity information. In this paper, the equivalent static loads method for non linear static response structural optimization (ESLSO) is employed to determine the workpiece shape which leads to the desired final shape and even distribution of the effective strain. Equivalent static loads (ESLs) are defined as the static loads for linear analysis, which generate the same response field as that of nonlinear analysis. In ESLSO, the dynamic loads for nonlinear analysis are transformed to ESLs. The ESLs, which have the characteristics of nonlinearities and dynamic loads, are utilized as the loading conditions in linear static response optimization. The design is updated from the results of linear static response optimization using ESLs. Nonlinear analysis is carried out with the updated design, and the process proceeds in a cyclic manner until the convergence criteria of the design variables are satisfied. Two kinds of ESLs are proposed and they are the ESLs for the displacements and the ESLs for the effective strains. Examples of the forging process are formulated and solved.