The work piece used for experimentation was an AISI D2 steel with dimensions of 165.1 mm in length and 50.8 mm in diameter. The hardness of the steel before heat treatment measured 30 HRC; the steel was tempered at 1025˚C for 30 min and quenched oil, after tempering and quenching hardness was 65 HRC. A CNC lathe model TITANIUM™, with control FANUC^TM and maximum spindle speed 1620 rpm, was utilized. The machining was performed upon dry environment in order to evaluate the behavior of machined surface roughness and flank wear on the cutting tool. The cutting experiments were conducted using coated WC inserts ISO WNMG 432-MSPH6225, 80˚ negative rake angle, whit break chip and nose radius of 0.8 mm, PVD-TiAlN coated. The inserts were rigidly mounted on a tool holder designated by ISOMWLNL16-4D. Figure 1 shows the chemical composition of the coating obtained through X-ray energy dispersion spectrometry (EDS).

The arithmetic average surface roughness (Ra) of the workpiece was measured by employing a Mitutoyo^TM SJ301 surface roughness tester as shown in Figure 2(a), where the cutoff length and assessment length was fixed as 0.8 mm and 4 mm respectively. The instrument was calibrated using a standard calibration block prior to the measurements. The measurement was taken at three locations (120˚) around the circumference of the workpieces and two point on the long of the machined surface (counterpoint and end chuck), Figure 2(b). The average values of Ra were reported for the response (Table 2).

In the present study, the tool wear area was considered as the criterion and would affect the results of cutting process. The measurement in width of flank wear land of the cutting tool was used to evaluate the tool wear. The maximum value of flank wear (VB_max) was adopted as the machinability evaluation when machining AISI D2 steel. In comparable research work, the maximum flank wear was measured at the tool corner (VB_max) and the value 0.3 mm was adopted as criteria [2]. Here, the flank wear was measured using scanning electron microscope (SEM) micrographs as shown in Figure 3.

The Taguchi method is an experimental design technique, which is useful in reducing the number of experiments dramatically by using orthogonal arrays and also to minimize effects of the factors out of control. The most reliable of Taguchi method is the use of the parameter-design technique, which is an engineering method for product or process design that focuses on determining the parameter (factor) settings producing the best levels of a quality characteristic (performance measure) with minimum variation [1]. The Taguchi design experiments L₉, 3³ was used to establish the cutting parameters that optimize (minimize) the maximum wear of cutting tool flank (VB_max) and the surface roughness (Ra). The cutting parameters and the conditions for machining AISI D2 steel are listed in Table 1. Three levels for each variable of cutting was established (low, medium, high), according of reported in [6] , [8] , [9] and dates recommended for tool manufacturing. Three variables of cutting up-on three levels led to a trial of 9 sets, Table 1.

The performance characteristic of the signal-to-noise ratio (S/N) used in this study is given by Equation (1), low the better, when the characteristic is continuous [10] :

S / N = − 10 log 1 n ( ∑ y 2 ) (1)

With the above S/N ratio transformation; the highest the S/N ratio, the better the result, when considering output tool wear and surface roughness. Table 2 shows the level values S/N according to the Taguchi design for VB_max and Ra, respectively.

T_Ra (surface roughness total mean value) = 0.8718 µm; T_VBmax (flank wear total mean value) = 1.074 mm.

By performing a statistical analysis of the variance (ANOVA), the impact of each factor on the outputs is obtained and the process parameters statistically significant are identified. With the S/N and ANOVA analyses, the optimal combination of the process parameters can be predicted, these parameters optimize (minimize) the values of VB_max and Ra. The 3D response surface graphs are obtained by means of the response surface method (RMS) and the variation of the different parameters used in the experiment. The regression analysis was formulated, obtaining linear and quadratic regression models to predict the values of VB_max and Ra. The data analysis described was done through the Minitab 17™ software.

Surface roughness (Ra) and maximum flank wear (VB_max) were measured via the experimental design for each combination of the controlling factors by using Taguchi´s technique, the optimization of the measured controlling factors were provided via (S/N) ratios. The lowest values of surface roughness and tool wear are quite relevant for quality improvement. Table 2, shows the values for observations of S/N ratios for VB_max and Ra. At the end of turning tests, the average values of the surface roughness and flank wear were calculated to be Ra = 0.8718 μm y VB_max = 1.074 mm respectively. The analysis about the effect of every controlling factor (Vc, ap, f) on the surface roughness and flank wear was performed with S/N ratios as listed in Table 3. The optimal level values for the controlling factors Ra and VB_max are plotted in Figure 4 and Figure 5. The best level for each controlling factor was established according to the highest S/N ratio among the levels. Based on the above mentioned; the levels and S/N ratios for the factors giving the best Ra value were specified as factor Vc (Level 2, S/N = 7.2473), factor ap(Level 1, S/N = 9.4022) and factor f (Level 1, S/N = 6.2499). In other words, an optimum Ra value was obtained with a cutting speed (Vc) in level 2 (200 m/min), at depth cut (ap) in level 1 (0.2 mm) and at a feed rate (f) in level 1 (0.20 mm/rev), see Figure 4. Similarly, the levels and S/N ratios for the factors giving the best VB_max were specified as factor Vc (Level 1, S/N = 0.8645), factor

Values in bold shows the most influential factor.

ap (Level 2, S/N = 2.4045) and factor f (Level 3, S/N = 3.4353). From the point of machining conditions, the optimum VB_max value was obtained with a cutting speed (Vc) in level 1 (150 m/min), at depth cut (ap) in level 2 (0.4 mm) and at a feedrate (f) in level 3 (0.30 mm/rev), see Figure 5.

Figure 6 shows that when increasing the depth of cut and feed rate, respectively; the surface roughness increases. The cutting speed has not significant direct effect on the surface roughness but interacts with the depth cut and feed rate parameters. The surface roughness is a function of feed rate; an increasing feed rate caused a significant increase in the Ra values. In [11] it was found that the best surface roughness was obtained when using high cutting speeds and low feed rates.

Figure 7 shows that the flank wears increases as a function of both: the cutting speed and depth of cut, in this case the flank wear increases slightly. The variation

in the increase of the feed rate and cutting speed had an important effect of interaction on the increase of flank wear; this may be a result of the rapid deformation of the sharp tool edge due to the thickness of the PVD coating. In [12] rapid deterioration of the cutting edge and catastrophic failure due to accelerated crater wear was normally observed when using PVD-coated insert after the removal of the thin layer of coating. In both cases, when increasing the cutting speed and the cutting depth, it was observed that increases the roughness of the machined surface and the wear of the cutting tool, therefore when increasing the cutting speed and the advance rate; increase the values of Ra and VB_max. It is verified that there is a relation between the wear of the cutting tool and the roughness of the machined surface obtained in the experiment.

The wear and failure for fracture in the flank of tool from the inserts used in the experiments for different cutting parameters are shown in Figure 8. High cutting speeds and feed rates were observed to be effective in the increase of flank wear during the experiment. Increasing the cutting speed of PVD coated tools has always been an important parameter in the increase of flank wear; for instance, by increasing the cutting speed promotes thermal and mechanical loading thus raising the temperatures in the cutting area, hence, speeding up the deformation of the cutting tools [13].

ANOVA was used to determine individual interactions of all the controlling factors during the test, as well as to analyze the effects of the cutting speed (Vc), depth cut (ap) and feed rate (f), over Ra and VB_max. ANOVA results for surface roughness and flank wear are provided in Table 4. The analysis was carried out

Values in bold shows the most influential factor.

at 5% significance level and a 95% confidence level. The significance statistic of control factors in ANOVA is determined by comparing the F values of each controlling factor. The factors with value higher of F have a significant effect on the response. The contribution rate of each parameter indicates the influence on Ra and VB_max [14]. Table 4 indicates for Ra the contribution of each factor was: depth cut (factor ap 35.50%), feed rate (factor f 33.47%) and cutting speed (factor Vc 28.22%). The most important factor affecting the surface roughness was the depth cut with contribution ratio of 35.50%. For VB_max the percent contributions were found to be (f 40.16%), (Vc 23.31%) and (ap 22.04%), respectively. This showed that the most effective factor on flank wear was feed rate (40.16%). The percent of error was considerably low at 2.81% and 14.49% for Ra and VB_max respectively.

In this study, the dependent variables are surface roughness (Ra) and flank wear (VB_max), whereas the independent variables are cutting speed (Vc), depth cut (ap) and feed rate (f). For obtaining predictive equations of the surface roughness and tool wear; regression analysis was used. These predictive equations were made for both linear and quadratic regression models. The predictive equations which were obtained by the linear regression model of surface roughness and flank wear are given below.

R a = − 1.68 + 0.00277 V c + 1.253 a p + 6.09 f (2)

R 2 = 59.74 % y R 2 a d j = 35.58 %

V B max = 1.69 + 0.00222 V c + 0.28 a p − 4.61 f (3)

R 2 = 21.28 % y R 2 a d j = 0.0 %

Predictive equations upon quadratic regression of surface roughness and flank wear are given below:

R a = 12.63 − 0.1679 V c + 7.78 a p + 4.5 f + 0.000466 V c 2 − 8.16 a p 2 + 3.3 f 2 (4)

R 2 = 97.18 % y R 2 a d j = 88.74 %

V B max = − 30.70 + 0.2141 V c − 11.25 a p + 120.9 f − 0.000447 V c 2     + 13.21 a p 2 − 177.5 f 2 − 0.1933 V c * f (5)

R 2 = 99.15 % y R 2 a d j = 93.21 %

A comparison of the experimental results and the predicted values obtained upon quadratic regression model are shown in Figure 9. There is an acceptable relationship among predicted values and experimental results. The effectivity of the model has been verified with R² called coefficient of determination, it is used to judge the adequacy of the developed regression models [15]. The second order model explains about 97.18% and 99.15% of the variability of responses in predicting new observations compared to first order model.

When employing Taguchi optimization technique; a confirmation experiment is required for validating of the optimized condition [13]. By estimating optimum surface roughness and flank wear: Equations (6) and (7) were used respectively:

R a o p t = ( V c 2 − T R a ) + ( a p 1 − T R a ) + ( f 1 − T R a ) + T R a (6)

V B o p t = ( V c 1 − T V B max ) + ( a p 2 − T V B max ) + ( f 3 − T V B max ) + T V B max (7)

Here, (Vc₂, ap₁, f₁) and (Vc₁, ap₂, f₃) represent the optimum level average values of surface roughness (Ra_opt) and flank wear (VB_opt) respectively as listed in Table 5. T_Ra and T V B max state the average of all of the Ra and VB_max values obtained from the experimental study (Table 1).

Substituting the values mentioned of the Table 1 and Table 5 into the Equations (6) and (7) respectively, as a result of the calculations, it was estimated that Ra_opt = 0.054 μm and VB_opt = 0.238 mm.

Whether the system had realized the optimization accurately enough needed to be evaluated. For this purpose, the following equations were used in the specification of the confidence interval (Cl) for estimated surface roughness and flank wear [13] :

C I R a , V B max = F α , 1 , f e V e [ 1 n e f f + 1 R ] (8)

n e f f = N 1 + T d o f (9)

Here, F α , 1 , f e is the F ratio at a 95% confidence, α is the significance level, f_e is the degrees-of-freedom of error, V_e is error variance, η_eff is the effective number of replications, R is the number of replications for confirmation experiments, Equation (8). N is the total number of experiments, and T_dof is the total main factor degrees of freedom, Equation (9). F_0.05,1,2= 18.51 (from F test table), V_eRa = 0.02340 and V e V B max = 0.1289 (Table 4), R = 1 (Equation (8)), N = 9, T_dof = 6 and η_eff = 1.29 (Equation (9)).

By using the Equations (8) and (9) the confidence intervals were calculated as CI_Ra = ±0.876 and C I V B max = ±2.06 The estimated average optimal surface roughness and flank wear with the confidence interval at 95% confidence is:

[ R a o p t − C I R a ] < R a exp < [ R a o p t − C I R a ] , i.e.;

[ 0.054 − 0.876 ] < 0.14 < [ 0.054 + 0.876 ] = − 0.822 < 0.14 < 0.93

[ V B max , o p t − C I V B max ] < V B max , exp < [ V B max , o p t − C I V B max ] , i.e.;

[ 0.238 − 2.06 ] < 0.909 < [ 0.238 + 2.06 ] = − 1.8 < 0.909 < 2.298

Values in bold shows the Ra and VB_max values obtained from the experimental study.

The Ra_exp and VB_max,exp values, obtained from the experimental study stayed within the confidence interval limits. Thus, the system optimization for surface roughness and flank wear was achieved using the Taguchi method at a significance level of 0.05.

Confirmation tests of the controlling factors were made for the Taguchi method and regression equations at optimum and random levels. In Table 6, the comparison of experimental results and the predicted values (obtained by Taguchi method and regression equations 4 to 7) are listed. The predicted values and the experimental values are very close to each other in quadratic regression models for Ra and VB_max. For reliable statistical analyses, error values must be less than 20% [16]. Although the error percentages calculated in the flank wear are higher than the ones in surface roughness, they are within acceptable limits. Therefore, the results obtained from the confirmation tests reflect successful optimization.