A Preliminary Study on the Optimum Parameters in Sheet Metal Forming

Abstract

The sheet metal forming process is used in many industries because this process is simple and is suited to the purpose of mass production. Since the process typically has some phenomena such as springback, tearing, failure of material and others, the desired final shape is quite difficult to obtain. The problems, which are caused by these phenomena, can be improved by optimization of the sheet metal forming process. The design variables of metal forming optimization are process parameters and structural parameters. The process parameters are the blank holding force (BHF), the drawbead restraining force (DBRF), the friction factor, etc. and the structural parameters are the initial blank shape and others. Metal forming optimization is nonlinear dynamic response optimization because this process has geometric, material and boundary nonlinearities. In this paper, the two groups of parameters are separately optimized by the response surface method (RSM) and structural optimization, respectively. The two optimization process iteratively proceeds until the convergence criteria are satisfied. First, the RSM is utilized to determine the process parameters such as BHF and DBRF. Because BHF and DBRF are input in conventional structural optimization, they cannot be used as design variables. On the other hand, they can be used as design variables in RSM. Moreover, since the number of process variables is small, RSM can be exploited to determine the process variables. An optimization problem is formulated and solved. Second, structural optimization is employed to determine the initial blank shape which can be deformed to the desired final shape after metal forming. The process parameters determined in the first process are regarded as input parameters, and then an optimization problem is formulated. Since the formulated problem is nonlinear dynamic response optimization, a new approach is adopted for this process. This approach is called as the equivalent static loads method for non linear static response structural optimization (ESLSO). Equivalent static loads (ESLs) are defined as the loads for linear analysis, which generate the same response field as that of nonlinear analysis. In ESLSO, nonlinear dynamic loads are transformed to ESLs and the ESLs are used as the loading conditions in linear static response optimization. The design is updated in linear static response optimization. Nonlinear analysis is performed with the updated design and the process proceeds in a cyclic manner until the convergence criterion is satisfied. The existing ESLSO is modified to fit into the metal forming optimization problem. An advantage of ESLSO is that the nodes in the design domain can be controlled easily and exactly because linear static response optimization is utilized. However, various design variables cannot be selected because only the design variables for linear static response optimization can be used in optimization using ESLSO. Several examples are solved by the iterative use of the RSM and ESLSO and the solutions are discussed.