Indian J.Sci.Res.1(2) : 416-423, 2014 ISSN:2250-0138(Online) ISSN : 0976-2876 (Print) 1 Corresponding author BLANK SHAPE OPTIMIZATION IN DEEP DRAWING PROCESS TO MINIMIZE EARRING DEFECT ALI JABBARI 1a a Asistant Professor, Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak 38156-8-8849, Iran ABSTRACT A blank shape optimization method is presented in this research for reduction of earring defect due to sheet anisotropy behaviour in deep drawing process by using the reduced basis technique coupled by finite element and design of experiments methods. The primary objective of the proposed method is to reduce the enormous number of design variables required to define the initial blank shape. This method is demonstrated on the blank shape optimization of deep drawing of a round cup. KEYWORDS: Deep drawing process, earring defect, reduced basis technique, Design of Experiments (DOE) method, sheet anisotropy behavior. Recently deep drawing process has been widely used to form round cups from a round (circular) blank shape because of high deformation rate compared to other production methods, including casting and machining. Various conditions of the forming process should be controlled for the desired shape. These conditions are the velocity of the punch, the friction factor, the blank holding force, the initial shape of the blank and others. However, the earring defect caused by anisotropy behavior of sheet metal seriously affects the process performance. Since the earring defect is produced by the sheet metal anisotropy, it is greatly affected by the initial blank shape. Earring height minimization can be performed using blank shape optimization to obtain better stress distribution and also to reduce the number of production stages (Pradeep kumar et al., 2013; Sharvari et al., 2005). An integrated algorithm is presented in this research and it is conducted to blank shape optimization in a sheet metal deep drawing process of a round cup. An innovative, comprehensive way of using an efficient design variables linking method, termed as reduced basis technique (Jabbari et al., 2009; Jabbari et al., 2010). is demonstrated for blank shape optimization. In the reduced basis technique, many initial blank shapes, called basis shapes, are combined linearly by assigning weight factors. Different resultant shapes can be generated by changing their weight factors. Therefore, the number of design variables required to define the blank shape is reduced to the number of basis shapes. So, the weights assigned for each basis shapes are the design variables and the optimization goal is to find the best possible combination of these weights to minimize earring height. The algorithm presented in this paper focuses on the Taguchi design of experiments method which is the combination of mathematical and statistical techniques used in the empirical study of relationships and optimization, in which several independent variables influence a dependent variable or response. EARRING PHENOMENON Plannar Anisotropy is due to cold roll forming of sheet metal. In an anisotropic sheet metal, mechanical properties vary in different directions. In the deep drawing of anisotropic sheet, material flow is high in some directions and is low in other direction, i.e., sheet metal is drawn in a direction more than other direction and cup height is high in direction that the sheet is drawn further. For anisotropic sheet metals, the ratio of true plastic strain is defined as follow  ε  ε  This strain ratio is a criterion of sheet metal strength to thickness reduction. Equation (2), show another criteria called planar anisotropy which predict earrings directions. If Δ is positive, earring are created in zero and 90 degrees respect to the direction of rolling. If Δ is negative, earring is created in 45 degree respect to direction of rolling. In an ideal sheet metal with zero planar anisotropy, earring defect is not appeared. Δ        Normal anisotropy is expressed by equation (3). Higher the normal anisotropy, sheet metal drawing will be better.          (3)