Nickel-based super-alloys have been widely used in the aircraft and nuclear industry due to their exceptional thermal resistance and their ability to retain mechanical properties at elevated temperatures [1, 2], strong corrosion resistance and excellent thermal fatigue properties as well as thermal stability [3, 4]. Consequently, these alloys are classified to be difficult-to-machine materials  [1-3]. The  tool  wear during machining of the Inconel 718 depends on the combined effect of several factors which is the result of complicated physical, chemical and thermo- mechanical phenomena forming through the different mechanisms  such  as  adhesion,  abrasion,  diffusion and oxidation [1, 5]. Because of low thermal conductivity, machining of the nickel-based super- alloys in general and the Inconel 718 materials in particular,  leads  to  a   significant  increase in  the cutting temperature  and  high  tresses;  the  adhesive wear through welding is thus developed rapidly and forming built-up-edge (BUE), it occurs even at a low cutting speed of 20m/min [6].Several research efforts have been conducted in order to improve the machined surface accuracy, reduce the tool  wear  and  subsequently  extend  the  tool  life; which directly affects to the cost of machining and productivity. Some of the solutions have recommended concerning with the cutting tool selection: using PVD coated (TiAlN) cutting tool [6] or multilayer coating of TiAl/TiAlN [7, 8] can be improved   the   cutting   speed   up   to   100m/min compared   to   uncoated   cutting   tool   (less   than 30m/min). By considering the different coating materials,  I.  Ucun et  al.[8]  have  reported that  the performance of cutting tools coated with AlTiN, TiAlN+AlCrN, and AlCrN are improved, while the coated with TiAlN+WC/C and DLC are more significant against BUE formation. So far, it is also believed that polycrystalline cubic boron nitride (PCBN) tooling [9-11], and ceramic cutting tools [12,13]  allows  machining  at  higher  cutting  speed  in comparison  with  the  coated  carbides  due  to  their superior hot hardness and notch wear resistant. Although  machining  of  the  Inconel  718  has  been carried out in several various studied; however, most of  main  characteristics  and  the  results  of  cutting surface quality, and performance could only be determined experimentally [14]. The experimental studies should therefore be investigated with any further improvement of the cutting tool, machine design, the workpiece materials or methodology approaches. In the case of cutting process, Response Surface Methodology (RSM); which is a set of sequential experimental design [15] has been already proved in regard to efficient analyzing the effect of cutting conditions on the response factors such of the tool wear [16], surface roughness and cutting force [17, 18]. The relationship between the cutting parameters and the respond factors has mainly analyzed of variables (ANOVA) by using a quadratic regression through transformation of square root.In  this  sense,  it  is  thus  worthy  to  use  such  the response surface methodology within the present framework.  Furthermore,  with  the  aim  of  getting more precise information about the tool wear mechanism and the surface roughness during machining process; the quadratic regression through transformation of natural logarithm will be applied for the first time according to our best knowledge in the  field.  First  of  all,  the  flank  wear  mechanism during machining of the Inconel 718 steel (hardened ∼  44HRC) using PVD coated cutting tool  will be investigated; part of the work is then analyzing effect of the cutting parameters on the flank wear and surface roughness. The  machining experiments are performed with assistance of the response surface methodology in accordance to central composite design (CCD). The experimental design was considered three level of each factor for the cutting speed in range of Vc=10-110m/min, feed rate f=0.02-0.12mm/min and depth of cut ap=0.05-0.55mm. 2. EXPERIMENTAL PROCEDURE 2.1. Experimental design The matrix of the experiment should be well planned to optimize the number of the machining test and evaluate  the  effects  of  certain  factors  on  some specific results; as well as quantify the effects of one or  more  input  variables  on  the  response  factors. Based on the CCD method, the matrix design for k factor experiment is defined through the level of independent variables and the number of the experiment as given by :

where  are experiments in factorial design are experiments in star design and is the number of central point. In current experimentation, three experimental factors and six central points have led to twenty of the total runs are considered. The level of independent parameters is then modeled as summarized in the table 1; therein, the lowest and highest values are calculated through the scaled parameter (α). It depends on the number of the factor experiment   considered   through   the   relation   of formula α = (2k  )1/ 4 ; with the three mentioned factors, one obtains α=1.682.

Table 1 level of independent variables for CCD


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