Journal of Materials Processing Technology 147 (2004) 321–327 Sensitivity analysis of a deep drawing process for miniaturized products Amit Jaisingh a , K. Narasimhan a , P.P. Date b , S.K. Maiti b , U.P. Singh c,∗ a Department of Metallurgical Engineering and Materials Science, IIT Bombay, Bombay, India b Department of Mechanical Engineering, IIT Bombay, Bombay, India c Advanced Forming Technology Group, University of Ulster, Jordanstown, UK Received 6 March 2002; received in revised form 20 February 2003; accepted 26 November 2003 Abstract Deep drawing is a widely used sheet metal forming technique, and its successful implementation has been a subject of research since many years. It has undergone many developments, one of the important ones being the application of numerical modeling techniques, like the finite element method (FEM) to simulate the process. Although deep drawing has been a subject of research for many years, there is still not much data available on deep drawing of miniature components, which find extensive application in electronics industry. The deep drawing process is affected by many material and process parameters, like the strain-hardening exponent, plastic strain ratio, friction and lubrication, blank holder force, presence of drawbeads, punch velocity, etc. This paper aims at identifying the important parameters that affect the deep drawing process and quantitatively studying the effect of these parameters on the deep drawing operation for components of similar shape but different sizes. Thus, establishing a correlation between the size of a component and the effect of the parameters on the deep drawing of the component. The study consists of a plane strain analysis of bell shaped geometry. Taguchi’s robust design technique [Quality Engineering Using Robust Design, Prentice-Hall, New Jersey, 1989, p. 145] has been used to design the experiments using the maximum thinning strain developed in the walls as the quality characteristic. Since carrying out actual experiments is both expensive and time consuming, computer modeling has been used to simulate the experi- ments. A FEM-based program, SHEET-S, developed by Wagoner and co-workers [Int. J. Meth. Eng. 30 (8) (1990) 1471] has been used for this purpose. © 2003 Published by Elsevier B.V. Keywords: FEM analysis; Deep drawing process; Forming process sensitivity 1. Robust design technique Robust design is an engineering methodology for improv- ing productivity during research and development by aiding the determination of optimum settings of control parameters so that the process becomes insensitive to the noise factors, thus enabling the production of high quality products at a low cost [3]. This methodology consists of three major steps: 1. planning the experiment, 2. performing the experiment, 3. analyzing and verifying the results. The first step, i.e., ‘planning the experiments’ consists of identifying the main function of the process, its failure ∗ Corresponding author. Present address: School of Electrical and Me- chanical Engineering, University of Ulster, Newtownabbey, Shore Road, Co. Antrim, UK. Tel.: +44-2890-366273; fax: +44-1232-366804. E-mail address: up.singh@ulster.ac.uk (U.P. Singh). modes, noise factors (factors which are difficult or expensive to control), testing conditions, quality characteristics (char- acteristic of the quality of output), control factors (factors which can be easily controlled), and objective function to be optimized. The testing conditions should be chosen such that they capture the effect of the important noise factors. The two factors, which influence the quality characteristic, are (i) noise factors, (ii) control factors. Robust design methodology aims at maximizing the signal-to-noise (S/N) ratio which thus forms the objective function; i.e., minimization of sensitivity to noise factors. The S/N ratios are derived from quadratic loss functions [4] (cf. [3]). The most commonly used S/N ratios are (i) Nominal the ‘best’ type: in this type the objective func- tion is targeted to have a non-zero and finite value: 0924-0136/$ – see front matter © 2003 Published by Elsevier B.V. doi:10.1016/j.jmatprotec.2003.11.023