Modelling and experimental investigation of process parameters in WEDM of WC-5 . 3 % Co using response surface methodology

Abstract. Tungsten carbide-cobalt (WC-Co) composite is a difficult-to-machine material owing to its excellent strength and hardness at elevated temperature. Wire electrical discharge machining (WEDM) is a best alternative for machining of WC-Co composite into intricate and complex shapes. Efficient machining of WC-Co composite on WEDM is a challenging task since it involves large numbers of parameters. Therefore, in present work, experimental investigation has been carried out to determine the influence of important WEDM parameters on machining performance of WC-Co composite. Response surface methodology, which is a collection of mathematical and experimental techniques, was utilised to obtain the experimental data. Using face-centered central composite design, experiments were conducted to investigate and correlate the four input parameters: pulse-on time, pulse-off time, servo voltage and wire feed for three output performance characteristics – cutting speed (CS), surface roughness (SR) and radial overcut (RoC). Using analysis of variance on experimental data, quadratic vs. two-factor interaction (2FI) models have been suggested for CS and RoC while two-factor interaction (2FI) has been proposed for SR. Using these mathematical models, optimal parameters can be determined easily for desired performance characteristics, and hence a trade-off can be made among different performance characteristics.


Introduction
Demand for tungsten carbide-cobalt (WC-Co) composite has been growing rapidly due to its excellent mechanical properties like high wear and corrosion resistance, which makes it most suitable for cutting tools, dies and other special wearresisting applications.Machining of WC-Co composite is very difficult with conventional machining processes like turning, milling and grinding (Liu and Li, 2001;Liu et al., 2003;Engqvist et al., 1999;Jia and Fischer, 1997) because of its high hardness and high melting temperature.Due to the low material removal rate and difficulty in machining of complex and intricate profiles in WC-Co composite, cost associated with conventional machining processes is very high.
Wire electrical discharge machining (WEDM) is a specialised form of electrical discharge machining (EDM) process which is potentially used to generate intricate and com-plex geometries in hard conductive materials without making any mechanical contact (Jangra et al., 2010).In WEDM, material is eroded due to the melting/evaporation of work surface which is mainly due to the localised high temperature generation in plasma channel between the work material and downward moving wire electrode (as shown in Fig. 1).In order to achieve high productivity within specified tolerance on WEDM, selection of optimal process parameters plays a key role which depends on large numbers of variables such as composition and grain size of work material, machining parameters, wire electrode material, wire diameter, cutting conditions and work geometry etc. (Jangra et al., 2011).
Several attempts have been made to determine optimal machining conditions for WC-Co composite on EDM and WEDM. Lee and Li (2001)   C and cobalt composition also shows noticeable influence on machining performance of th WEDM (Kim and Kruth, 2001;Lauwers et al., 2006).Varying the cobalt concentration , alter the thermal conductivity of the material which affects the machining performance.
ised Taguchi method, back propagation neural network and genetic algorithm to optimize rs in machining of pure tungsten.Pulse-on time was most significant parameters which speed and surface roughness both.Jangra et al. (2012) optimized the multi machining DM of WC-5.3% Co composite using an integrated approach of Taguchi, GRA and nput parameters namely taper angle, discharge current, pulse-on time, pulse-off time, wire flow rate were investigated for four output machining characteristics namely MRR, SR, .can easily machine complex profiles in WC-Co composite but damaged work surface ayer, large micro-cracks etc, is a major concern in WEDM (Caydas, 2009, Jangra, K., tain fine surface finish and low surface defects, low discharge parameters with high pulse interval and flushing on the machining characteristics, such as material removal rate (MRR), surface finish and relative tool wear in EDM of tungsten carbide.Lee and Li (2003) elucidated the effect of discharge energy on integrity of EDMed surface of tungsten carbide.It was found that the surface roughness is a function of two main parameters: peak current and pulse duration.At high peak current and/or long pulse duration, rough surface and abundance of micro-cracks were observed.Mahdavinejad and Mahdavinejad (2005) studied the instability in EDM of WC-Co composites.This machining instability was mainly due to open circuit, short circuit and arcing pulses.Increase in pulse duration results in more melting and recasting of material, which causes arcing and rougher surface.
The grain size of WC and cobalt composition also shows noticeable influence on machining performance of WC-Co composite with WEDM (Kim and Kruth, 2001;Lauwers et al., 2006).Varying the cobalt concentration and grain size of WC alters the thermal conductivity of the material, which affects the machining performance.Chen et al. (2010) utilised Taguchi method, back propagation neural network and genetic algorithm to optimize the WEDM parameters in machining of pure tungsten.Pulse-on time was the most significant parameter that influences both the cutting speed and surface roughness.Jangra et al. (2012) optimized the multimachining characteristics in WEDM of WC-5.3 % Co composite using an integrated approach of Taguchi, GRA and entropy method.Six input parameters -taper angle, discharge current, pulse-on time, pulse-off time, wire tension and dielectric flow rate -were investigated for four output machining characteristics: MRR, SR, RoC and angular error.
Although WEDM can easily machine complex profiles in WC-Co composite but damaged work surface consisting of recast layer, large micro-cracks are a major concern in WEDM (C ¸aydas ¸et al., 2009;Jangra, 2012).In order to obtain fine surface finish and low surface defects, low discharge parameters with high dielectric flushing rate are required.but they lower the cutting rate in WEDM.This implies that high cutting rate with low surface roughness and minimum surface defects is difficult to obtain in a single setting of process parameters.In order to achieve an efficient machining of WC-Co composite into desired shape, inter-relationship (mathematical modelling) between input WEDM parameters and output performance characteristics should be available to the manufacturers, so that a trade-off can be made among various performance characteristics.
Two kinds of approaches, theoretical and empirical, have been commonly used in modelling of WEDM process (Patil and Brahmankar, 2010).Owing to the simplified and unavoidable assumptions, the theoretical models yield large errors between predicted and experimental results.On the other hand empirical models are limited to specific experimental conditions.Response surface methodology (RSM) is the most used statistical technique for determining the relationship between various input parameters and output responses (Myers and Montgomery, 1995;Hewidy et al., 2005;Kansal et al., 2005).RSM is a collection of mathematical and experimental techniques that requires sufficient number of experimental data to analyse the problem and to develop mathematical models for several variables and output performance characteristics.
Because the WEDM involves multi-performance characteristics, the objective of the present study is to investigate the influence of process parameters and to develop the mathematical models for three performance characteristics namely cutting speed (CS), surface roughness (SR) and radial overcut (RoC) in WEDM of WC-5.3 % Co composite.Response surface methodology with face-centered central composite design has been utilised to conduct the experimentation which helps to investigate and to correlate the input parameters with output performance characteristics.Using these mathematical models, optimal combination of WEDM parameters can be selected for desired performance characteristics for WC-Co composite.

Work material and machining parameters
Tungsten carbide composite with low cobalt concentration (5.3 %) has been taken as a work material in the form of a rectangular block of thickness of 13 mm.The density and hardness of WC-5.3 % Co composite were measured as 14.95 g cm −3 and 77 HRC, respectively.
Experiments were performed on 5-axis sprint cut (epulse-40) WEDM, most widely used in Indian industries, manufactured by Electronica Machine Tools Ltd., India.In present machine tool, range of the important parameters is as In present investigation, four important WEDM parameters, namely pulse-on time (T on ), pulse-off time (T off ), servo voltage (SV) and wire feed (WF) have been considered with three levels each (Table 1).Discharge current is kept at optimum value of 90 amp which is taken on the basis of earlier investigations (Jangra et al., 2011(Jangra et al., , 2012)).Similarly, other parameters were kept constant at their optimal values.As the workpiece thickness is low (13 mm), wire tension was kept fixed at 10 N. Zinc-coated brass wire of diameter 0.25 mm was used as an electrode because of its good capability to sustain high discharge energy.High flow rate results in quick and complete flushing of melted debris out of the spark gap.Therefore, dielectric flow rate is kept at maximum value of 12 l min −1 .Vertical cutting was performed at zero wire offset.

Performance characteristics
CS was measured as surface area removed per minute (mm 2 min −1 ).It was obtained by multiplying the workpiece thickness (13 mm) with linear cutting speed (mm min −1 ) displaying on machine tool monitor screen.Surface roughness is a good indicator of the surface quality which can be easily measured by a tool manufacturer.In present work, SR value (in µm) was measured in terms of mean absolute deviation (Ra) using the digital surface tester Mitutoyo 201P.RoC (in µm) is the gap between machined work surface and wire periphery (as shown in Fig. 2)."D" represents the wire diameter.RoC helps to predict accurate wire offset for precise dimensional tolerance.Neglecting the wire lag compensation for straight cutting, wire offset is given by the sum of wire radius and RoC (Sarkar et al., 2008).RoC was measured using optimal microscope.

Experimental design using RSM
For developing an adequate relationship between input WEDM parameters and output performance characteristics, response surface methodology (RSM) (Myers and Montgomery, 1995) has been employed.By using the design of experiments and applying regression analysis, the modelling of the desired response (Y) to several independent input vari- ables (x i ) can be gained.In the RSM, the quantitative form of relationship between desired response and independent input variables could be represented as (1) The function Φ is called response surface or response function.The residual e r measures the experimental errors (Cochran and Cox, 1962).
In applying the RSM, the dependent variable is viewed as a surface to which a mathematical model is fitted.For the development of regression equations related to various performance characteristics of WEDM process, the second-order response surface has been assumed as This assumed surface Y contains linear, squared and cross product terms of variables X i .The model parameters can be estimated most effectively if proper experimental designs are used to collect the data.In present case, a standard secondorder experimental design called face-centered central composite design (CCD) has been adopted for analysing and modelling four input parameters.This design consists of factorial portion with all parameters at three levels, eight star points and six central points.The star points are at the face of the cube portion on the design which corresponds to α-value of 1, the distance from design centre.The centre points, as implied by the name, are points with all levels set to coded level 0, the midpoint of each parameter range.Table 2 shows the experimental conditions.

Results and discussion
The 30 experiments were conducted and CS, SR and RoC were obtained for each experimental run (as listed in Table 2).

Mathematical model for CS, SR and RoC
Using the experimental data, regression equations have been developed for correlating the output performance characteristics and input WEDM parameters.Analysis of variance (ANOVA) has been applied on the experimental data to select the adequate model.Design expert (DX8), a statistical tool, has been utilised to analyse the experimental data.Quadratic vs. two-factor interaction (2FI) models have been suggested for CS and RoC, while two-factor interaction (2FI) has been proposed for SR.Table 3 shows the fit summary for proposed models.
In Table 3, a p-value for the model terms that are less than 0.05 (i.e.α = 0.05, or 95 % confidence level) indicates that the obtained models are considered to be statistically significant (Kanagarajan et al., 2008).It shows that the terms in the model have significant effect on responses.From Table 3, coefficient of determination (R 2 ) and R 2 (adj.) for all three responses are closer to unity, which is desirable for the re-sponse model to fit the actual data.The lack of fit is a measure of the failure of the model to predict the data in the upper and lower limits of the parameters.The "lack of fit" for all three characteristics is insignificant because of high probability value (F-value), which is desirable for selecting the models.Figures 3 to 5 show that the residuals are normally distributed about a straight line and there is no problem with the observed results.Consequently, the proposed models for three responses can be considered as significant for fitting and predicting the experimental results within the specified experimental domain.
Table 4 shows the "F-value" and "p-value" for each term in performance characteristics CS, SR and RoC, respectively.The terms having p-value less than 0.05 are considered to be significant while insignificant terms can be eliminated from the final predicted models.In case of CS, the model terms A, B, C, D, AB, AD, BD, CD and A 2 are significant.Similarly, A, B, C, D and CD for SR, and A, B, C, D, AB, AD and A 2 for RoC are significant model terms.ne and there is no problem with the observed results.Consequently, the proposed models for an be considered as significant for fitting and predicting the experimental results within the ental domain.line and there is no problem with the observed results.Consequently, the proposed models for can be considered as significant for fitting and predicting the experimental results within the ental domain.Using backward elimination method, non-significant terms were eliminated.Final regression equations for performance characteristics have been obtained as follows.

Cutting speed (CS)
Regression equation is in terms of coded parameters: Regression equation is in terms of actual parameters:

Surface roughness (SR)
Regression equation is in terms of coded parameters: Regression equation is in terms of actual parameters:

Radial overcut (RoC)
Regression equation is in terms of coded parameters: Regression equation is in terms of actual parameters: These predicted models were verified by conducting confirmation tests within the selected range of the WEDM parameters.

Effect of WEDM parameters on performance characteristics
Response surface graphs (Figs. 6 to 8) have been plotted to analyse the influence of WEDM parameters on performance characteristics, namely CS, SR and RoC.Surface plots have been plotted for combined effect of two factors while keeping other two factors at their mid-values.

Effect of WEDM parameters on cutting speed
Figure 6a to c show that cutting speed increases with increasing T on and WF, while it decreases with increasing T off and  The rise in cutting speed can be highly noticed at high value of wire feed.High discharge energy results in more melting and evaporation of the work material causing liberation of large number of carbide debrises which coagulates in the spark gap and hence affects the machining process by producing arcs.Increasing wire feed rate leads to the easy and rapid escape of the eroded material out of the spark gap  and hence increases the cutting speed.This can be observed from the combined effect of WF with SV and T on as shown in Fig. 6b-c.
Increasing pulse-off time (T off ) value decreases the discharge frequency and increases the overall machining time.Also long pulse-off time at high dielectric flow rate produces the cooling effect on work material and hence decreases the CS.The interaction among WEDM parameters (T on and T off ; SV and WF) can be observed from curvature of the contour plots on response surface graphs.The low F-value (< 0.05) for these interactions effect shows a significant influence on performance characteristics as shown in Table 4.

Effect of WEDM parameters on surface roughness
Surface roughness increases with increasing pulse-on time (T on ) and decreasing servo voltage (SV) as shown in Fig. 7ab.In WEDM, SR is mainly described by the shape and size of the surface craters which mainly depends on the discharge energy and re-deposition of melted material on work surface.Increasing pulse-on time and decreasing servo voltage increases the discharge energy across the electrodes which results in deeper erosion crater on the work surface and hence increases the surface roughness (Lee and Li, 2003).
Due to the large difference between melting temperatures for WC and Co, discharge energy tends to melt, evaporate and remove cobalt even before the melting of WC.As a result WC grains may release without melting or in semi-solid state which coagulate in the spark gap (Saha et al., 2008).At high discharge energy, the probability of re-deposition of melted material of work surface is high.Increasing T off -value increases the time between two consecutive sparks which results in complete flushing of the carbide debris out of the spark gap, and hence low re-deposition of eroded material results in low surface roughness as shown by the combined effect of T on and T off in Fig. 7a.
Surface roughness shows mild tendency to decrease with increasing wire feed rate (WF) as shown in Fig. 7c.Increasing wire feed results in easy escape of carbide debris out of the spark gap which results in low re-deposition of melted residuals and hence low surface roughness.Curved contour on response graphs between WF and SV shows some interaction between these parameters.To get good surface finish, it is desirable to keep the electrical discharging energy at smaller level, by setting low T on and high T off -value.

Effect of WEDM parameters on radial overcut
RoC is the thickness of material removed perpendicular to the cutting direction as shown in Fig. 2. RoC helps to achieve accurate wire offset for rough cutting operation for obtaining precise dimensional tolerance.RoC depends on the amount of material melted and flushing it out of the spark gap.Increasing pulse-on time (T on ) results in high discharge energy which causes more melting and erosion of work surface which increases the RoC.At high value of pulse-off time (T off ), eroded carbide debris is easily flushed away from the spark gap.Therefore, RoC increases with increase in T on and T off as shown by surface plots in Fig. 8a, c and d.At low value of T off , tendency of recasting of residue material on the work surface is high, which decreases the RoC.
Increasing wire feed rate helps to clear off the spark gap quickly which results in low re-deposition of eroded material and hence increases the RoC as shown in Fig. 8b.Decreasing servo voltage (SV) results in more ionization of the spark gap which results in more melting of work material and hence increases the RoC.Curved contours on response graph show the interaction between WEDM parameters.Using response surface graphs, values of WEDM parameters can be selected for the desired value of performance characteristics.

Conclusions
In present work, experimental investigation has been reported on machining performance of WC-5.3 % Co composite on WEDM.Response surface methodology (RSM), a statistical technique, has been utilised to investigate the  influence of four important WEDM parameters -pulse-on time (T on ), pulse-off time (T off ), servo voltage (SV) and wire feed (WF) -on three performance characteristics: cutting speed (CS), surface roughness (SR) and radial overcut (RoC).Face centered central composite design was employed to conduct the experiments and to develop a correlation between the WEDM parameters and each performance characteristics.Analysis of variance (ANOVA) on experimental data shows that quadratic vs. two-factor interaction (2FI) model as the best fit for CS and RoC, while two-factor interaction (2FI) has been proposed for SR.
Response surface graphs were used to describe the influence of WEDM parameters on each performance characteristic.T on , T off , SV and WF produce significant influence on each performance characteristic.In case of cutting speed, interaction between T on and T off ; T on and WF; T off and WF; SV and WF produces significant effect, while, in SR, interaction effect of SV and WF has been found significant.In case of RoC, interaction among T on and T off ; T on and WF produces significant effect.Using mathematical models, optimal parameters can be determined easily for desired performance characteristics.Hence a trade-off can be made among various performance characteristics.
Edited by: B. Azarhoushang Reviewed by: two anonymous referees investigated the influence of EDM parameters such as the electrode materials, electrode polarity, open circuit voltage, peak current, pulse duration, Published by Copernicus Publications.
Figure 1 Representation of WEDM process

Figure 6a .
Figure 6a.Combined effect of T on and T off on CS.

Figure 6b .
Figure 6b.Combined effect of SV and WF on CS.

Figure 6c .
Figure 6c.Combined effects of T on and WF on CS.

Figure 7a .
Figure 7a.Combined effects of T on and T off on SR.

Figure 7b .
Figure 7b.Combined effects of T on and SV on SR.

Figure 7c .
Figure 7c.Combined effects of SV and WF on SR.

Figure 8a .
Figure 8a.Combined effects of T on and T off on RoC.

Figure 8b .
Figure 8b.Combined effects of SV and WF on RoC.

Figure 8c .
Figure 8c.Combined effects of T on and WF on RoC.

Figure 8d .
Figure 8d.Combined effects of WF and T off on RoC.

Table 2 .
Test conditions in face-centered central composite design.

Table 3 .
The ANOVA table for fitted models.

Table 4 .
F-value and p-value for each model term for CS, SR and RoC.