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Volume-6, Issue-1, January-February-2016

International Journal of Engineering and Management Research

Page Number: 285-293

Multi-Objective Optimization of WEDM Process Applying Statistical Methodology

Goutam Kumar Bose1, Pritam Pain2

1,2

Mechanical Engineering Department, Haldia Institute of Technology, Haldia, West Bengal, INDIA

ABSTRACT

The present study aims at determining parametric influence and optimum process parameters of wire electrical discharge machining (WEDM) during machining mild steel by copper wire using Taguchi's technique. Experiments are designed as per Taguchi's L27 orthogonal array. The level of importance of the machining parameters on the responses is determined by using analysis of variance. Mathematical model for all three important performance measures such as high material removal rate, lower surface roughness and low overcut are developed and the responses are used for studying the inter-relationship between performance measures and process parameters viz. pulse on time, pulse off time, wire tension, and wire feed rate. An experimental plan for Box-Behenken Design has been conducted according to response surface methodology and subsequently to seek the optimal parameters. The optimal settings of operating conditions are predicted using desirability function. This paper presents a formulation and solution of a multi-objective optimization problem for the selection of the best control settings on a WEDM. Keywords— ANOVA, Material removal rate, Overcut, RSM, Surface Roughness, WEDM.

I. INTRODUCTION

Wire electrical discharge machining (WEDM) performs a significant role in the manufacturing industries to machine complex profiles. WEDM is a thermo-electrical process in which material is removed from the work piece by a series of discrete sparks between the conductive work piece and the wire electrode tool which is separated by a thin film of dielectric fluid continuously fed to the machining region to flush away the eroded particles [1]. The movement of wire is controlled numerically to achieve the required two or three-dimensional shape of the work piece. Irrespective of the hardness of the material,

WEDM contribute a prime share in making of complex-shaped dies, moulds and critical parts used in automobile, aerospace, nuclear and plastic industries. The process is best suited for parts having complex work piece configuration, the need of high repeatability, close tolerances and hard-to-work materials. The stochastic nature of the WEDM process allows the operator rarely to obtain the optimal performance. Improper selection of control parameters may result severe problems like short work surface damage, circuiting of wire and wire breakage causing interruption of production schedule and decreasing productivity. Mild steel is the most common steel which is economical and is used in nuts and bolts, chains, hinges, pipes, knives, in the construction of space-frames for any vehicle etc.

A brief review of the works of the past researchers on WEDM process is presented here. Chockalingam et. al [2] studied optimization of the machining responses like material removal rate (MRR), spark gap (SG), surface roughness (Ra) and dimensional deviation (DD) of the wire electrical discharge machining process. The variable machining parameter chosen are Pulse on-time (Ton), Pulse off-time (Toff), voltage (V), fluid injection pressure mode (Inj), wire tension (WB) and wire velocity (WS). The process model shows the dependency of machining performance on process control parameters. Kumar and Ravikumar [3] studied the optimization maximum metal removal rate and minimum surface roughness of Al-SIC (20%) in Wire Electrical Discharge Machining (Wire-EDM) process using Taguchi’s L27 Orthogonal Array, the different input parameters viz. time on, time off, wire speed and wire feed are varied during experimentation. Basil et.al [4] studied the optimization of spark gap by varying of voltage, dielectric pressure, pulse on-time and pulse off-time of Ti6AL4V alloy. It is found that pulse on time and pulse off time are more significant on the spark gap. The minimum spark gap obtained is 0.0404mm. The developed model



agrees with the conformation results by less than 6%. Malik et.al [5] studied the optimal machining parameter combination for wire electrical discharge machining (WEDM) on Tungsten Carbide ceramic using zinc coated brass wire. The process parameters considered are pulse-on time, pulse-off time, peak current and wire tension for optimization of cutting speed and surface roughness by using Taguchi methodology. Baig and Venkaiah [6] studied optimization of the responses like material removal rate and surface roughness with varying parameters like pulse on time, pulse off time, discharge current, servo voltage, tension of wire, flushing pressure, using wire EDM process on nickel based alloy, Hastelloy C276, applying both Taguchi methodology and Grey Relational Analysis (GRA). Sharma et.al [7] studied the effects of various process parameters of Wire EDM such as servo voltage (Sv), pulse on (Ton), pulse off (Toff) and wire feed (Wf) for analysing the material removal rate (MRR) while working on Al/Al2O3

The objective of the present work is to analyse the distinctive features of the WEDM process while machining mild steel as reflected through Taguchi design based experimental studies with various process parametric

/SiC composite, by applying Central Composite Design of Response Surface Methodology. Rao and Venkaiah [8] reviews the effects of various WEDM process parameters such as pulse on time, pulse off time, servo voltage, dielectric flow rate, peak current, wire speed, wire tension on different process responses like material removal rate (MRR), wire wear ratio (WWR), surface roughness (Ra), kerf (width of cut) and surface integrity factors. They have reviewed various optimization methods applied by the researchers and finally outlines their commendations and future trends in WEDM research. Nandakumar and Viswanadhan [9] studied the optimization of cutting speed (CS), material removal rate (MRR) and surface roughness (SR) by using brass wire and cryogenic treated brass wire for titanium alloy (Grade 2) on CNC WEDM based on Taguchi Method. Abinesh et.al [10] studied optimization of material removal rate (MRR), surface roughness (SR) and electrode wear rate with the various input process parameters like pulse-on time (Ton), pulse off time (Toff), pulse peak current (IP) for machining Titanium alloys by wire-cut electrical discharge machining (WEDM) process by using L-16 orthogonal array and Taguchi methodology. Pant et.al [11] studied the effect of gap voltage, pulse-on time, wire feed rate on surface roughness in wire electrical discharge machining (WEDM) process for die steel D3 using ANOVA initially and then Response Surface Methodology is used to achieve optimum levels. It had been established that pulse on-time is the most important factor affecting the surface roughness. Patil and Waghmare [12] studied the optimization of material removal rate on wire electric discharge machining process on AISI D2 steel. The machine control parameters such as pulse on time, wire tension and peak current are varied different level for machining using Response Surface Methodology. They also investigated the significant effect of the parameters on MRR by analysis of variance (ANOVA). Kumar et.al [13] studied the optimization of cutting speed and surface

roughness using wire-cut EDM process on EN31 steel material. The input parameter considered are Peak current, pulse-on time, pulse off time and wire tension. Initially in order to identify the effect of the significant parameters on the responses Taguchi’s methodology is applied and then for multi-objective optimization principle component analysis (PCA) is used. Kumar and Singh [14] highlights that investigation is oriented on newer aspects of wire EDM in the field of analysis and optimization. The mathematical models have been established to predict MRR and surface finish while machining AISI D2 tool steel at different machining situations. A neural network model and simulated annealing algorithm have been formulated in order to calculate and improve the surface roughness and cutting velocity of the WEDM process in machining of SUS 304 stainless steel materials. Kumar et.al [15] outlines the Taguchi’s parameters design approach to optimize machining parameters of dimensional precision in wire cut electric discharge machining (WEDM) on EN 24 Steel. The main objective is to find out the significant factors and combination of factors influencing the machining process to achieve the best material removal rate. Singh et.al [16] studied the optimization of Wire-EDM machining process for maximum MMR and minimum Ra. The control parameters considered are pulse on time, pulse off time, flushing rate and tension. Experiments are planned and the mathematical models associating the desired responses and the control parameters are established applying Response Surface Methodology and finally, GA is applied to obtain the optimal parametric values for the optimal responses. Kondayya et.al [17] presents two efficient and popular approaches, viz. desirability function approach and Grey relational analysis based Taguchi method to optimize the process parameters of WEDM. Experiments are conducted using Central Composite design by considering pulse-on time, pulse – off time, wire feed and wire tension as input parameters and metal removal rate, surface roughness, kerf width and wire wear ratio as the performance measures. Jangra et.al [18] presents optimization of performance characteristics in wire electrical discharge machining using Taguchi along with Grey relational analysis. Responses viz. cutting speed, surface roughness and dimensional lag are investigated during rough cutting operation. Process parameters such as peak current, pulse on, pulse off, wire speed, wire tension are investigated using L18 Orthogonal array. Rao and Sarcar [19] evaluates the optimum parameters viz. discharge current, voltage at rated wire speed and tension for Wire-cut electric discharge machine on cutting speed, MRR, surface roughness and spark gap using brass wire. Mathematical relations are obtained for cutting speed, spark gap and MRR.



combinations such as pulse on time (Ton), pulse off time (Toff), wire tension (W/Ten) and wire feed (W/Feed) on material removal rate (MRR), surface roughness (Ra) and overcut (OC). The significant process parameters are recognized using Analysis of Variance (ANOVA). These experimental facts are additionally investigated with Response Surface Methodology (RSM). The present work is intended at fulfilment of conflicting objectives simultaneously during machining having higher material removal rate (MRR) lower surface roughness (Ra) and lower overcut (OC) by utilizing a single set of optimum or near optimum process variables following response surface methodology (RSM). Response surfaces and contour plots are considered to examine the importance of the variables and their levels so as to optimize the responses. Finally, multi-response optimization is executed using overlaid contour plots and desirability functions.

II. PLANNING FOR EXPERIMENTATION

The experiments are performed using wire

electric discharge machine of Ecocut, Electronica Machine Tool, India. The De-mineralized water (specific gravity 1at 23̊ C, pH 7 and viscosity of 0.001 N·s·m −2 @ 20˚C) is used as dielectric fluid. With external lateral flushing using a Cu wire tool (0.25 mm diameter) having a pressure 0.8 kgf/cm2 is used. Experiments are performed with positive polarity of electrode. Here mild steel (MS) work piece material having dimension of 80x80x16 mm is selected for the experimentation. The chemical composition of MS is C (0.16-0.18) %, Mn (0.70-0.90) %, Si (0.40) %, S (0.04) %. The pulsed discharge current is applied in various steps in positive mode. The WEDM setup comprises of pump and circulation system, dielectric reservoir, power generator and control unit, working tank, X-Y table accommodating the working table, wire holding nozzle, work piece, flashing system as shown in Figure 1.

Figure 1: Machining Setup

The servo control unit is connected to the system

to maintain the pre-determined gap. It senses the gap voltage and compares it with the current value and the change in voltage is then used to control the movement of servo motor to adjust the gap. In this experiment 10x10

mm width of work material is made to cut. During the process, the wire diameter (0.25mm) is kept constant. The MRR for WEDM operation is calculated using Eq. (1), which is shown below: MRR = S0 x B x T (mm3

Where, S/min) (1)

0= machining speed (mm/min), B = (2Wg + d) (mm) Wg

Input Variables

= wire gap (mm) d = diameter of electrode wire (mm) T = thickness of the job (mm)

Surface roughness of the cavity surface is expressed as Ra in μmm, which is measured using Talysurf profilometer, Taylor’s Hobson Surtronic 3+ make. Overcut (OC) is expressed as the difference between length of the cavity produced to the wire and diameter of the wire measured by the digital Venire scale and Tool maker’s microscope (Mutotoyo make).

When performing the experiment, varying the levels of the factors simultaneously rather than one at a time is more effective in terms of time and money and also allows for the study of interactions between the parameters. Based on previous research works and primary investigation, four parameters are chosen as input. Initially L9 orthogonal array is employed for the experimentation to study the effect of significant process parameter following ANOVA. The input parameters are further varied with three levels in twenty-seven experimental run to study the Response Surface Methodology. There are some other factors which may influence the measured performance like Duty cycle, Flushing pressure, Lift time, wire material etc., however, did not change during experimentation. Table 1 exhibits the different levels of Input variables during machining process.

TABLE I

INPUT VARIABLES WITH THEIR LEVELS

Units Levels

Level 1

Level 2

Level 3

Pulse on Time (Ton) µ sec 15 20 25 Pulse off Time (Toff) µ sec 20 25 30 Wire Feed (W/feed) mm/min 6 9 12

Wire Tension (W/Ten) N 8 10 12

III. RESULTS ANALYSIS USING ANOVA

In this investigation, the Analysis of variance

(ANOVA) has been performed to determine the machining parameter, which has significant effect on the machining characteristics and also to find out the relative contribution of the machining parameters in controlling the responses of the WEDM process [20]. To accomplish ANOVA, the



total sum of squared deviations SST from the total mean S/N ratio (ηm

2

1( )

N

T i mi

SS η η=

= −∑) can be calculated as:

(2)

Where, N is the total number of experiments, η i is the S/N ratio at each parametric combination and ηm

d

T

SSPSS

=

is the Grand mean of S/N ratio. The percentage contribution P can be calculated as:

(3)

Where, SSd

21 10 11 110log n

in MRRη=

= − ∑

is the sum of the squared deviations. The experimental outcomes are explored to study the role of different process variables on various responses by using S/N ratio and ANOVA [21]. The result analysis is carried out by statistical software MINITAB, version 15.

S/N ratio determines the contribution of different process variables on various responses. The goal is to find out an optimum combination of control parameter settings that achieve robustness against (insensitivity to) noise factors. S/N ratio analysis pertinent to MRR (mm³/min) is conducted on the basis of larger is the better and the corresponding S/N ratio is expressed as follows:

(4)

S/N ratio analysis for Ra is modelled on the basis of smaller is the better and corresponding equation is

21 10 1

110log n

iRanη

= = − ∑ (5)

S/N ratio analysis for OC is modelled on the basis of smaller is the better and corresponding equation is

21 10 1

110log n

iOCnη

= = − ∑ (6)

The S/N plots for MRR, Ra and Overcut are shown in figure 2.

Figure 2: S/N ratio plots for MRR, Ra and Overcut

It is observed from the S/N ratio graph that the

MRR attains its peak with the control parameter combination of Ton (25 µSec), Toff (25 µsec), W/Feed (6 m/min), W/Ten (12N). For lower surface roughness, Ra in µmm is obtained at Ton (15 µSec), Toff (30 µsec), W/Feed (9 m/min), W/Ten (8 N). Similarly, lower Overcut is obtained at Ton (25 µSec), Toff (30 µsec), W/Feed (12m/min), W/Ten (12 N).

ANOVA results as exhibited from F-values and percentage contribution of the process variables states that the F values of Gap current assume value 22.337 with a yield of 82.28% in case of MRR. This implies that the variable has significant effects on MRR. Whereas in case of Ra, Pulse on Time (POT) alone is the major contributor having F value of healthy 5.34 and having % contribution of 47.24, which is widely followed by Gap Current having F value of approximately 4. Finally, in case of Overcut the Spark Gap (SG) alone is the major contributor having F value of healthy 4.0 with % contribution of 65.60. Other factors here remain insignificant.

IV. RESULTS ANALYSIS USING RESPONSE SURFACE METHODOLOGY

(RSM)

The Response Surface Methodology (RSM) is a set of mathematical and statistical techniques convenient for the modelling and analysis of problems where a response of interest is affected by several variables and the objective is to optimize this response [22]. It is the method for determining the relationship between various process parameters for several machining conditions and investigating the effects of these process parameters on the



coupled responses. The independent variables can be regulated through a designed experiment, while the response variable is an observed output of the experiment. Figure 3 illustrates the estimated relationship between a response variable and the two independent variables x1 and x2. In this graph, each value of x1 and x2 generates a y-value. This three-dimensional plot indicates the response surface from three different sides and it is known as response surface plot.

Figure 3: Response surface plot

A second order model is used to establish input-output relationship efficiently that takes the generic form:

The response surface (output) can be related with the number of controllable variables 1 2, .... kx x x as

1 2( , .... )ky f x x x ε= + (7) A second order model is used to establish input-output relationship efficiently that takes the generic form

20

1 1 1

k k k

i i ii i ij i ji i i

y x x x xβ β β β ε= = =

= + + + +∑ ∑ ∑ (8)

The predicted response for the model is

20

1 1 1

ˆ ˆ ˆ ˆˆk k k

i i ii i ij i ji i i

y x x x xβ β β β= = =

= + + +∑ ∑ ∑ (9)

In the present work, Box-Behenken Design is applied which is based on 2k (k = 4) factorials with incomplete designs and is found to be very efficient. The process variables combinations and the corresponding responses are presented in Table 2.

TABLE 2.

PARAMETRIC SETTINGS AND RESPONSES FOR

EXPERIMENTAL RUN

Expt. No.

Control Parameters Responses

Ton (µ

sec)

Toff (µ

sec)

W/Feed

(mm/min

)

W/Ten (N)

MRR (mm³/min)

Over Cut (mm

)

Ra (µm)

1 20 25 6 8 18 0.37 2.791 2 15 30 9 10 8.85 0.37 2.065 3 15 25 9 12 10.38 0.37 2.052 4 25 25 12 10 19.3 0.27 2.714 5 25 25 9 12 21.66 0.33 2.975 6 20 30 12 10 11.1 0.25 2.883 7 20 20 9 12 15.97 0.37 2.697

8 20 25 12 8 14 0.31 2.946 9 20 25 9 10 15.18 0.35 3.045

10 20 25 9 10 15.18 0.35 3.045 11 15 25 9 8 10.48 0.39 2.12 12 25 25 6 10 21.57 0.33 3.316 13 20 30 9 12 18.38 0.29 2.903 14 20 25 6 12 16.55 0.32 2.749 15 15 25 12 10 10.33 0.35 2.833 16 25 20 9 10 21.4 0.38 3.551 17 20 30 9 8 14.04 0.38 2.874 18 20 30 6 10 13.24 0.36 2.468 19 20 25 12 12 14.71 0.34 2.713 20 25 30 9 10 19.71 0.4 3.02 21 20 25 9 10 15.18 0.35 3.045 22 20 20 9 8 16.31 0.4 2.834 23 20 20 6 10 15.45 0.35 2.456 24 25 25 9 8 20.71 0.33 3.112 25 15 20 9 10 12.15 0.39 3.188 26 20 20 12 10 14.9 0.35 2.596 27 15 25 6 10 10.85 0.38 2.294

A. Analysis of test results for Material Removal Rate

(MRR) The regression equation for MRR is MRR = - 0.15 + 0.918 Ton - 0.077 Toff - 0.314 W/Feed + 0.171 W/Ten (10) The details of the regression analysis result are presented in Table 3. R-square as well as R-square (adjusted) assumes a value of 92.3% and 83.2% respectively, that implies the model is balanced to explain 83.2% variability with process variable Ton, Toff, W/Feed and W/Ten. From the T values of the process variables, it can be concluded that Ton is the most significant process variables followed by Toff, W/Feed and W/Ten.

TABLE 3 ESTIMATED REGRESSION COEFFICIENTS FOR MRR

Term Coef SE Coef T P Constant 15.18 0.846 17.942 0

Ton 4.5908 0.423 10.853 0 Toff -0.3867 0.423 -0.914 0.379

W/Feed -0.9433 0.423 -2.23 0.046 W/Ten 0.3425 0.423 0.81 0.434

Ton*Ton -0.1029 0.6345 -0.162 0.874 Toff*Toff -0.8392 0.6345 -1.322 0.211

W/Feed* W/Feed -0.2492 0.6345 -0.393 0.701 W/Ten*W/Ten 1.1496 0.6345 1.812 0.095

Ton*Toff 1.9575 0.7327 2.672 0.02 Ton*W/Feed -0.4375 0.7327 -0.597 0.562 Ton* W/Ten 0.2625 0.7327 0.358 0.726 Toff*W/Feed -0.3975 0.7327 -0.543 0.597 Toff*W/Ten 1.17 0.7327 1.597 0.136

w/feed*W/Ten 0.54 0.7327 0.737 0.475 S= 1.465 R-Sq = 92.3% R-Sq(adj)= 83.2%

B. Analysis of test results for Surface Roughness (Ra)

The estimated regression surface equation for Ra is:



Ra = 1.73 + 0.0625 Ton - 0.0351 Toff + 0.0381 W/Feed + 0.0399 W/Ten (11) The particulars of the regression analysis outcome are presented in Table 4. R-square as well as R-square (adjusted) furnishes a value of 97.5% and 94.5% respectively that implies the model is balanced to explain 97% variability with process variable Ton, Toff, W/Feed and W/Ten. From the T values of the process variables, it can be concluded that Ton is the most significant process variables followed by Toff, W/Feed and W/Ten.

TABLE 4 ESTIMATED REGRESSION COEFFICIENTS FOR RA

Term Coef SE Coef T P Constant 2.841 0.03596 79.008 0

Ton 0.3127 0.01798 17.39 0 Toff -0.1757 0.01798 -9.771 0

W/Feed 0.1144 0.01798 6.364 0 W/Ten 0.0797 0.01798 4.436 0.001

Ton*Ton -0.0036 0.02697 -0.133 0.896 Toff*Toff -0.0026 0.02697 -0.096 0.925

W/Feed* W/Feed 0.0143 0.02697 0.53 0.606 W/Ten*W/Ten 0.001 0.02697 0.039 0.97

Ton*Toff 0.0155 0.03114 0.498 0.628 Ton*W/Feed 0.012 0.03114 0.385 0.707 Ton* W/Ten 0 0.03114 0 1 Toff*W/Feed 0.0638 0.03114 2.047 0.063 Toff*W/Ten -0.0242 0.0314 -0.779 0.451

w/feed*W/Ten 0.03 0.03114 0.963 0.354 S = 0.06228 R-Sq = 97.5% R-Sq(adj)= 94.5%

C. Analysis of test results for Overcut (OC)

The estimated regression surface equation for Overcut (OC) is: OC = 0.617 - 0.00417 Ton - 0.00233 Toff - 0.00583 W/Feed - 0.00750 W/Ten (12) The particulars of the regression analysis are presented in Table 5. R-square provides a value of 95.6% that implies the model is balanced to explain 90.5% variability with process variable Ton, Toff, W/Feed and W/Ten. From the T values of the process variables, it can be concluded that Toff is the most significant process variables followed by W/Feed, W/Ten, Ton.

TABLE 5

ESTIMATED REGRESSION COEFFICIENTS FOR OC Term Coef SE Coef T P

Constant 0.35 0.004276 81.846 0 Ton -0.02083 0.002138 -9.744 0 Toff -0.01167 0.002138 -5.456 0

W/Feed -0.0175 0.002138 -8.185 0 W/Ten -0.015 0.002138 -7.015 0

Ton*Ton 0.00375 0.003207 1.169 0.265

Toff*Toff -0.0025 0.003207 -0.779 0.451 W/Feed* W/Feed -0.00625 0.003207 -1.949 0.075

W/Ten*W/Ten 0 0.003207 0 1 Ton*Toff 0.0025 0.003703 0.675 0.512

Ton*W/Feed 0 0.003703 0 1 Ton* W/Ten 0 0.003703 0 1 Toff*W/Feed -0.0075 0.003703 -2.025 0.066 Toff*W/Ten -0.01 0.003703 -2.7 0.019

w/feed*W/Ten 0.005 0.003703 1.35 0.202 S= 0.007407 R-Sq = 95.6% R-Sq(adj)= 90.5%

V. MULTI RESPONSE OPTIMIZATION USING DISAREBILITY

CONSTANT

The desirability function approach is a dual optimization technique for multiple equations [23]. The basic approach is to first convert every response into an individual desirability function that alters over the range (0 to 1). The prediction of the model is represented through these equations. Let there be N equations or function to simultaneously optimize, denoted fn (X) (n = 1 . . . N). For each of the R functions, an individual “desirability” function is constructed that is high when fn (X) is at the desirable level (such as a maximum, minimum, or target)

and low when fn(X) is at an undesirable value. There are three forms of these functions, corresponding to the type of optimization goal. For maximization of responses, fn(X), the function shown in equation (16) can be used.

max

0

( )( )

1

nn

f x pd eQ P

− = −

if

( )( )

n

n

n

f x Pp f x Q

f Q

<≤ ≤

> (16)

Where, P, Q, and ‘e’ are chosen by the investigator. When the response is to be minimized, the proposed the function is shown in equation (17) below.

max

0

( )(P )

1

nn

f x Qd eQ

− = −

if

( )( )

n

n

n

f x Qp f x Q

f P

>≤ ≤

< (17)

Equation (18) illustrates for target is best situations,



1

max2

( )(P )

( )(P )

0

n

nn

f x Q sQ

f x Qd sQ

− − − = −

if 0

0

( )( )

n

n

p f x tt f x Q

Otherwise

≤ ≤≤ ≤ (18)

These functions are on the same scale and are

discontinuous at the points P, Q, and t0. The values of e, s1 or s2 can be chosen so that the desirability criterion is easier or more difficult to satisfy. Response Optimizer facilitates to help identify the factor settings that optimize a single response or a set of responses. For multiple responses, the requirements for all the responses in the set must be satisfied. Here the goal, lower, target, upper, and weight represent the desirability function for each individual response. The importance (Import) parameters decide how the desirability functions are united into a single composite desirability. The response optimization is shown in Table 6 below. From the S/N ratio Plot of Taguchi Design the highest MRR is observed at combination of Ton (25), Toff (25), W/Feed (6), W/Ten (12), lowest Ra at combination of Ton (15), Toff (30), W/Feed (6), W/Ten (8) and minimum OC at combination of Ton (25), Toff (30), W/Feed (12), W/Ten (12). Hence an optimized combination of Ton (15), Toff (20), W/Feed (6), W/Ten (8) can be taken as starting point.

TABLE 6

DESIRABILITY FUNCTION RESULTS

Figure 4 signifies the optimization plot of the responses (MRR, OC and Ra) with the process variables. It illustrates how the factors affect the predicted responses and forbid to transform the factor settings interactively. The figure demonstrates the goal for the response, the predicted response, y, at the present factor settings and the different desirability score. The composite desirability, D, is demonstrated in the upper left corner of the graph. The label above the composite desirability refers to the current setting. When the optimization plot is formed, the label is Optimal. The vertical red lines on the graph represent the current factor settings. The horizontal blue lines signify the current response values. From the earlier limit of MRR, Ra and OC while assigning unbiased weight to the responses, the desirability of MRR becomes 0.90104 having predicted response of 14.6674 mm³/min. Whereas in case of Ra is dRa = 0.90623 with the predicted response of 2.5718 micron at the same time OC is dOC =0.97495 with predicted response of 0.3705mm. Finally, the dual desirability is observed to be 0.92680 having Ton= 20.3, Toff=30.0, W/Feed=7.83, W/Ten=8 is the near optimal combination.

Figure 4: Plot showing responses (MRR, OC and Ra)

against process variables

VI. DISCUSSION AND CONCLUSION The experimental study signifies that while machining MS using WEDM process the responses are dependent on Ton, Toff, W/Feed, W/Ten. The S/N ratio analysis in conjunction with ANOVA is a simple method to establish conjecture of a number of input parameters that controls multiple responses of the process. The experimental based result illustrates that increasing the pulse-on time, wire feed and wire tension values directs to an increase in the amount of Material Removal Rate. But the most influential factor is Gap current which assume F- value of 22.337 with a yield of 82.28% in case of MRR.

Parameters Goal Lo

wer Targe

t Uppe

r Weigh

t Impo

rt

MRR Maximum

10 15.18 19.38 1 1

OC Minimum 0.35 0.37 0.39 1 1

Ra Minimum

2.449 2.544 2.841 1 1

Predicted Responses

MRR = 14.6674, desirability = 0.90104 (90.104%)

OC = 0.3705, desirability = 0.97495 (97.495%)

Ra = 2.5718, desirability = 0.90623 (90.623%)

Composite Desirability = 0.92680

(92.68%)

Global Solution

Ton = 20.2955 Toff = 30.0000 W/Feed=7.8313 W/Ten =8.0000



Whereas in case of Ra, the most influential factors is Pulse on Time (POT) having F-value of healthy 5.34 and having % contribution of 47.24, which is widely followed by Gap Current having F value of approximately 4. Finally in case of OC, Spark Gap (SG) alone is the major contributor having F-value of healthy 4.0 with % contribution of 65.60. The present work is carried out with a view to optimize MRR (maximize), Ra (minimize) Over Cut (minimize) simultaneously by utilizing a near optimal set of process variables. This optimization is performed by RSM that is promised to tender near optimal solution with modest effort. The regression models are found to be worthy to express input-output relationship with a very high degree of predictability. The conclusions drawn from the regression analysis are emphasized with the desirability functions. The near optimal combinations of process variables are high Ton, Toff and low W/Ten, W/Feed to satisfy all the responses (MRR, Ra and OC) simultaneously. The overlaid contour plot is an excellent visual aid to recognize the feasible region in regard to a set of input variables. The individual desirability for each predicted responses are finalized. The individual desirability values are then blended into the composite desirability. The nearer the predicted responses are to the target requirements, the closer the desirability will be to 1. The composite desirability combines the individual desirability into an overall value and returns the relative significance of the responses. The higher the desirability the closer it will be to 1. Here MRR has an intermediate desirability score of 0.90104 because the predicted response for MRR of 14.667 is approximately two-thirds of the way between the target of 15.18 and the lower bound of 10. The goal for MRR was to maximize; therefore, higher values are more desirable. Similarly, Ra has a desirability score of 0.90623 because the predicted response of 2.5718 is nearer to the target of 2.544. Whereas in case of Overcut desirability score is found to be 0.97495 since the predicted response of 0.3705 is close to the target value of 0.37. The composite desirability of 0.92680 places greater emphasis on MRR (importance = 2) than on Ra and Overcut (importance = 1).

The RSM being a robust tool, its capability can be broadened to other areas of machining such as tool life, power and cutting force modelling. The experimental investigation for estimating the optimal parametric combination and the consequent effect of the parameters over the responses can accomplish as a proficient and valuable guideline for machining and manufacturing various metallic products. The imminent work in this emerging area can be considered with other parameters and different responses such as cutting force, tool life etc. to portray the process in full perspective. The estimation of the reduction of the cost using multi-response optimized Wire EDM process can be further studied. The average cost of energy consumption v/s cost of wire electrode

material (and cost for electrode manufacturing) for the typical product manufactured by Wire EDM process furnish an opportunity for future work.

REFERENCES

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[8] Rao, M. S. and Venkaiah, N., “Review on Wire-Cut EDM Process”, International Journal of Advanced Trends in Computer Science and Engineering, vol. 2, No. 6, pp. 12-17, 2013.

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[9] Nandakumar, C. and Viswanadhan, A. R., “Study of Brass Wire & Cryogenic Treated Brass Wire on Titanium Alloy using CNC WEDM”, International Journal of Research in Engineering and Technology, Vol. 3, No. 11, pp. 16-19, 2014. [10] Abinesh, P., Varatharajan, K. and Kumar, G. S., “Optimization of Process Parameters Influencing MRR, Surface Roughness and Electrode Wear During Machining of Titanium Alloys by WEDM”, International Journal of Engineering Research and General Science, vol. 2, No. 4, pp. 719-729, 2014. [11] Pant, P., Pandey, N. P., Rajesha, S. and Jain, G., “Experimental Study of Surface Roughness in WEDM Process and ANN Modelling”, International Journal of



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[13] Kumar, R., Bhatia, A., Chattopadhyaya, S., Kumar, S. and Singh, G., “Multi-objective Optimization of Wire Electric Discharge Machining of EN31 Tool Steel using Orthogonal array with Principal Component Analysis”, International Journal of Current Engineering and Technology, vol. 4, No. 2, pp. 1027-1033, 2014.

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[14] Kumar, R. and Singh, S., “Current Research Trends in Wire Electrical Discharge Machining: An Overview”, International Journal on Emerging Technology, vol. 3, No. 1, pp. 33-40, 2012. [15] Kumar, V., Kumar, V. and Jangra, K. K., “An experimental investigation and statistical modelling for trim cutting operation in WEDM of Nimonic-90”, International Journal of Industrial Engineering Computations, vol. 6, No. 3, pp. 351-364, 2015. [16] Singh, R. K., Singh, D. K. and Kumar, V., “Parametric Optimization of Wire–EDM by Using Fuzzy Logic”, International Journal of Biological Science and Technology Research, vol. 1, No. 8, pp. 37 – 41, 2013. [17] Kondayya, D., Prasad, D.V.S.S.S.V. and Krishna, A. G., “Multi-response optimization of Wire EDM using Desirability Function Approach and Grey Relational Analysis”, In International Conference on Computational Methods in Manufacturing, pp. 385-392, 2011. [18] Jangra, K., Jain, A. and Grover, S., “Optimization of multiple machining characteristics of wire electrical discharge machining of punching die using Grey relational analysis”, Journal of Scientific and Industrial Research, vol. 69, pp. 606 – 612, 2010. [19] Rao, C. V. S. P. and Sarcar, M. M. M., “Evaluation of optimum parameters for machining brass with wire cut EDM”, Journal of Scientific and Industrial Research, vol. 68, pp. 32 – 35, 2009. [20] Montgomery, D.C., “Design and Analysis of Experiments”, 5th ed., John Wiley, New York, 2000. [21] Bose G. K. and Mahapatra K. K., “Multi criteria decision making of machining parameters for Die Sinking EDM Process”, International Journal of Industrial Engineering Computations, vol. 6, No. 2, pp. 241-252, 2015. [22] Phadke, M. S., “Quality Engineering using Robust Design”, Prentice Hall, New Jersey,1989. [23] Harington, J., The Desirability Function, Industrial Quality Control, pp. 494-498, 1965.

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