Blank Optimization in Elliptical-Shape Sheet Metal Forming Using Response Surface Model Coupled with Reduced Basis Technique and Finite Element Analysis

Abstract

The present study aims to determine the optimum blank shape design for the deep drawing of Elliptical-shape cups with a uniform trimming allowance at the flange i.e. cups without ears. This earing defect is caused by planar anisotropy in the sheet and the friction between the blank and punch/die. In this research, a new method for optimum blank shape design using finite element analysis has been proposed. Present study describes the approach of applying Response Surface Methodology (RSM) with Reduced Basis Technique (RBT) to assist engineers in the blank optimization in sheet metal forming. The primary objective of the method is to reduce the enormous number of design variables required to define the blank shape. RBT is a weighted combination of several basis shapes. The aim of the method is to find the best combination using the weights for each blank shape as the design variables. A multi-level design process is developed to find suitable basis shapes or trial shapes at each level that can be used in the reduced basis technique. Each level is treated as a separated optimization problem until the required objective – minimum earing function – is achieved. The experimental design of RSM method is used to build the approximation model and to perform optimization. MATLAB software has been used for building RSM model. Explicit non-linear finite element (FE) Code Abaqus/CAE is used to simulate the deep drawing process. FE models are constructed incorporating the exact physical conditions of the process such as tooling design like die profile radius, punch corner radius, etc., material used, coefficient of friction, punch speed and blank holder force. The material used for the analysis is Stainless steel St12. A quantitative earing function is defined to measure the amount of earing and to compare the deformed shape and target shape set for each stage of the analysis. The cycle is repeated until the converged results are achieved. This iterative design process leads to optimal blank shape. So through the investigation the proposed method of optimal blank design is found to be very effective in the deep drawing process and can be further applied to other stamping applications.