Short Communication Numerical study of thermal aspects of electric discharge machining process Nizar Ben Salah * , Farhat Ghanem, Kaı ¨s Ben Atig Laboratoire de Me ´canique, Mate ´riaux et Proce ´de ´s, ESSTT, 5 Avenue Taha Hussein, Montfleury 1008, Tunisia Received 10 November 2004; accepted 14 April 2005 Available online 23 September 2005 Abstract This paper presents numerical results concerning the temperature distribution due to electric discharge machining process. From these thermal results, the material removal rate and the total roughness are deduced and compared with experimental observations. It is shown that taking into account the temperature variation of conductivity is of crucial importance and gives the better correlations with experimental data. q 2005 Elsevier Ltd. All rights reserved. Keywords: Electric discharge machining; Numerical methods; Experimental observations; Roughness; Erosion rate 1. Introduction Electric discharge machining (EDM), is now a well known process particularly used in precise machining for complex shaped work pieces, as an alternative to more traditional approaches [1], and for details concerning the physical phenomena inherent to this process, one can consult Ghanem et al. [3,4]. Although real electric discharge machining requires numerous successive moving pulses, the interest must first be put on the prediction of the results of a single pulse; and the aim of the present work is to present a numerical model enabling the computation of the temperature distribution resulting from such single pulse. This model takes into account the real physical boundary conditions and the temperature dependence of physical proprieties of the work piece. The rest of the paper is organized into four sections. The next section presents the mathematical modelling of the physical phenomena involved during a typical electric discharge machining process. The third section is dedicated to the numerical method used to solve the governing equations. Main numerical results are presented in the fourth section showing that taking into account the temperature dependence of the thermal conductivity changes drastically the computed temperature distributions. Results are then validated, through the comparison with experimental observations in terms of the total roughness of the machined piecework and the material removal rate. Leading conclusions are drawn and presented in the last section. 2. Model details 2.1. Heat input In the literature, mainly two heat input models are used, the point source model and the Gaussian heat input. For an overview of these two models, one can consult Patel et al. [5–7], and in the present work, the Gaussian heat input model has been used to approximate the heat from the plasma. This model has two factors, the fraction of heat applied to the work piece and the radius of the area heated by the plasma [2,4,8], and can then be recast as QðrÞ Z UIF c T d S 0 e f K 4:5ðr=RÞ 2 g (1) where R is the radius of the plasma channel in mm, U the electric potential, I the current density, T d the time of International Journal of Machine Tools & Manufacture 46 (2006) 908–911 www.elsevier.com/locate/ijmactool 0890-6955/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2005.04.022 * Corresponding author. Tel.: C216 71 39 60 66x433; fax: C216 71 39 11 66. E-mail addresses: nizar.bensalah@esstt.rnu.tn (N.B. Salah), farhat. ghanem@isetn.rnu.tn (F. Ghanem), kais.ben.atig@voila.fr (K.B. Atig).