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Engineering Science and Technology, an International Journal

journal homepage: www.elsevier.com/locate/jestch

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Full Length Article

An intelligent approach to optimize the EDM process parameters using utility concept and QPSO algorithm

Chinmaya P. Mohantya, Siba Sankar Mahapatrab'*, Manas Ranjan Singhc

a Faculty of Science and Technology, IFHE University, Hyderabad 501504, India b National Institute of Technology, Rourkela 769008, India c Silicon Institute of Technology, Bhubaneswar 751024, India

ARTICLE INFO

Article history: Received 9 February 2016 Revised 28 June 2016 Accepted 6 July 2016 Available online xxxx

Keywords:

Electrical discharge machining Utility concept

Quantum behaved particle swarm

optimization

Radial over cut

ABSTRACT

Although significant research has gone into the field of electrical discharge machining (EDM), analysis related to the machining efficiency of the process with different electrodes has not been adequately made. Copper and brass are frequently used as electrode materials but graphite can be used as a potential electrode material due to its high melting point temperature and good electrical conductivity. In view of this, the present work attempts to compare the machinability of copper, graphite and brass electrodes while machining Inconel 718 super alloy. Taguchi's L27 orthogonal array has been employed to collect data for the study and analyze effect of machining parameters on performance measures. The important performance measures selected for this study are material removal rate, tool wear rate, surface roughness and radial overcut. Machining parameters considered for analysis are open circuit voltage, discharge current, pulse-on-time, duty factor, flushing pressure and electrode material. From the experimental analysis, it is observed that electrode material, discharge current and pulse-on-time are the important parameters for all the performance measures. Utility concept has been implemented to transform a multiple performance characteristics into an equivalent performance characteristic. Non-linear regression analysis is carried out to develop a model relating process parameters and overall utility index. Finally, the quantum behaved particle swarm optimization (QPSO) and particle swarm optimization (PSO) algorithms have been used to compare the optimal level of cutting parameters. Results demonstrate the elegance of QPSO in terms of convergence and computational effort. The optimal parametric setting obtained through both the approaches is validated by conducting confirmation experiments. © 2016 The Authors. Publishing services by Elsevier B.V. on behalf of Karabuk University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Nickel based super alloys such as Inconel 718 and Inconel 713 are the class of metallic materials with excellent characteristic of toughness and resistance to high temperature, oxidization and corrosion. The high strength-to-weight ratio and corrosion resistance properties possessed by these alloys have led to a wide and diversified range of successful applications in aerospace and other industrial applications. Their capability to sustain mechanical strength at elevated temperature causes difficulty in machining with conventional machining processes. Due to these difficulties, it is difficult to machine Inconel 718 by conventional machining

* Corresponding author. E-mail addresses: chinmaymohantymech@gmail.com (C.P. Mohanty), mahapatrass2003@gmail.com (S.S. Mahapatra), manasranjan.singh@gmail.com (M.R. Singh).

Peer review under responsibility of Karabuk University.

processes using conventional tool materials. However, machining of composites, super alloys, and ceramics can be accomplished with ease by the use of non-conventional machining process like electrical discharge machining (EDM). In today's manufacturing scenario, EDM contributes a major share in manufacturing automobile parts, intricate part shapes, complex shaped dies and moulds and other industrial usages. In EDM process, the material removal takes place owing to a series of spark discharges through enormous amount of heat generation between the electrodes. The heat generated is enough to vaporize and melt material from both the electrodes. The molten material is flushed by dielectric fluid from the crater cavity in from of dirt and debris and the replica of the tool is transferred onto the work surface. However, accuracy and versatility of the process, economical machining and accurate prediction of performance measures are the major concerns for tool engineers and researchers till now.

Extensive literature review suggests that different studies on EDM focus on improvement/modification of the process to

http://dx.doi.Org/10.1016/j.jestch.2016.07.003

2215-0986/® 2016 The Authors. Publishing services by Elsevier B.V. on behalf of Karabuk University.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

enhance certain performance measures, control circuits, analysis on the microstructure of the machined surface and effect of machining parameters. Literature also reveals that only a few controllable machining parameters viz., pulse-on-time, discharge current and open circuit voltage mostly influence the performance measures of the EDM process [1-3]. In EDM copper and brass are frequently used electrode material. However, graphite can be used as a potential electrode material due to its high melting point temperature and good electrical conductivity. The temperature resistance property makes graphite a suitable electrode material. However, studies on analysis of machining efficiency of the process with variety of electrodes are extremely scarce in literature [4-5]. Moreover, the studies are limited to application of commonly used work-tool pairs, machines and shop conditions. Even though optimization of multiple machining characterises is beneficial from practical point of view, little efforts have been made in this direction. Few studies report application of evolutionary algorithm like particle swarm optimization (PSO) to obtain the best process states of EDM process [6-8]. Due to the simple concept, easy implementation, and rapid convergence, PSO has gained much attention and been successfully applied to a wide range of applications such as job scheduling, power and voltage control, fiber-reinforced laminates problems [9-14]. Many studies report that QPSO with its global search ability can perform better than PSO [15-18]. However, past studies hardly provide any report to compare the effectiveness of both the algorithms in terms of obtaining the optimal level of machining parameters for multiple performance characteristics of EDM process.

In view of this, the present work focuses on experimental investigation on machinability of Inconel 718 super alloy in EDM process for the multiple performance characteristics viz. material removal rate (MRR), tool wear rate (TWR), surface roughness (SR), and radial overcut (RO) which are functions of process variables viz., open circuit voltage, discharge current, pulse-on-time, duty factor, flushing pressure and electrode material. The experimental architecture is planned as per Taguchi's L27 orthogonal array to extract maximum information from the study with limited number of experimental runs. Utility concept is used to convert the multiple performance measures into an equivalent single performance measure by calculating the overall utility index. Nonlinear regression analysis is conducted to develop a valid empirical model relating process parameters and overall utility index. The model is further used as an objective function in quantum behaved particle swarm optimization (QPSO) and particle swarm optimization (PSO) algorithm to obtain optimal level of cutting parameters. The optimal solutions so obtained are compared to justify goodness of the algorithm in solving such a machining problem. Finally, the optimal levels of cutting parameters obtained in both the algorithms are validated through confirmation test. This model will help in selecting ideal process states during actual machining and increasing productivity of the process for tool engineers.

2. Literature review

In the past two decades, electrical discharge machining has emerged as a subject of extensive research among the non-conventional machining process. To improve the machining efficiency of the process various technological, statistical and numerical studies have been reported. Lee and Li [4] have experimentally analyzed the effect of process variables such as electrode material, polarity, discharge current, open circuit voltage, pulse duration, pulse interval and flushing pressure on material removal rate, relative wear ratio and surface roughness of tungsten carbide work piece. Prabhu and Vinayagam [19] have proposed a grey relational analysis and fuzzy logic approach for simultaneous optimization of

several performance characteristics of the process when dielectric fluid is mixed with carbon nano-tube (CNT). Dewangan and Biswas [20] have adopted Taguchi's experimental design combined with grey relational analysis for optimization of multiple responses such as material removal rate and tool wear rate of EDM using AISI P20 tool steel as the work piece material and copper as electrode.

Meena et al. [21] have analyzed the effect of various flushing conditions on the accuracy of deep holes drilled by micro-EDM. Beri et al. [22] have concluded that improved performance characteristics can be achieved with the use of copper-tungsten (CuW) electrode produced through powder metallurgy route in comparison with conventional copper electrode. Similarly, Senthilkumar and Reddy [23] have demonstrated that copper composite with 40% boron carbide reinforcement developed through powder metallurgy route exhibits better metal removal rate (MRR) and tool removal rate (TRR) compared to conventional copper electrode. Wang and Han [24] have proposed a three-dimensional model of flow field with liquid, gas and solid phases for the movement of debris and bubbles within the machining gap in EDM. The model is validated through experimentation with conclusion that bubble expansion becomes strong with the increase of the discharge current and pulse-on-time. Shen et al. [25] have investigated effect of different machining parameters such as inter electrode distance, pulse duration, polarity and electrode shape on energy distribution using titanium alloy as work piece. The results show that energy distribution characteristics are largely influenced by the power density applied on the electrodes.

Tripathy and Tripathy [26] have used Taguchi experimental design in combination with TOPSIS and Grey Relational Analysis (GRA) to optimize the process variables such as powder concentration, peak current, pulse on time, duty cycle and gap voltage on multiple responses such as MRR, TWR, EWR and SR. Talla et al.

[27] have used aluminum powder in kerosene dielectric to improve the machining efficiency of the EDM process. The study showed an increase in MRR and improvement in surface quality of the machined surface compared to conventional EDM. Talla et al.

[28] have studied the effect process parameters powder concentration, peak current, pulse on time and duty cycle on two performance measures viz. MRR and SR. The study revealed that the powder concentration of 6 g/L gives the best result to maximize MRR and minimize surface roughness. Many studies have recently reported that controlled cryogenic treatment of electrode and work piece materials improves the machining characteristics in EDM as well as wire-EDM for various work-tool combinations [29-32].

Numerical models have been proposed to study the process behavior to reduce the cost of experimentation and machining time. In this direction, Paramashivan et al. [33] have proposed a mathematical model which quantifies the aerosol generated from the die sinking EDM process while machining steel work piece with copper electrode. Joshi and Pande [34] have suggested a numeral model for EDM for prediction of performance characteristics such as material removal rate and tool wear rate using finite element method. The proposed model is also validated through experimentation by the same researchers [35]. Mohanty et al. [36] have proposed a non-dominated sorting genetic algorithm (NSGA-II) for multi-objective optimization of EDM parameters using a thermo-structural model. Chen and Mahdivian [37] have suggested a theoretical model to estimate the material removal rate and surface quality considering process parameters like discharge current and pulse duration. The theoretical results have shown to be in good agreement with experimental data.

In recent times, artificial intelligence (AI) techniques are extensively applied for process modelling and optimization of the process [38-41]. Padhee et al. [42] have used non-dominated sorted genetic algorithm (NSGA-II) to optimize MRR and surface roughness for machining parameters such as concentration of silicon

powder in the dielectric fluid, pulse-on-time, duty cycle and peak current. Pradhan and Biswas [43] have proposed neuro-fuzzy and neural network models for prediction of material removal rate, tool wear rate and radial overcut when AISI D2 steel is machined with copper electrode. Pradhan and Das [44] have proposed an Elman network for the prediction of material removal rate for EDM process. Yang et al. [45] have employed simulated annealing in conjunction with artificial neural network for optimization of materials removal rate and surface roughness.

Critical review of past studies suggests that a good amount of work is devoted towards technological enhancement and statistical and numerical modelling to improve and analyse EDM process. However, reports to analyse the machining efficiency of the process with different electrode materials seems to be less. Furthermore, it is also observed that limited number of attempts have been made to machine a relatively low conductive material like Inconel 718 which has a diversified application in aerospace engineering. Inconel 718, an aerospace material has abundant usage in manufacturing of components for liquid fueled rockets, rings and casings, sheet metal parts for aircraft, land-based gas turbine engines, cryogenic tank fasteners and instrumentation parts. Literature review reveals that few studies have been reported to obtain the optimal parametric setting for EDM process applying PSO algorithm [6-8]. Numerous studies reported that QPSO with the global search ability can achieve better results than PSO [15-18]. However, it is also observed that no attempt has been reported in application of utility concept in combination with QPSO to obtain the best parametric setting for EDM. Therefore, there exist a vital need to compare and check the effectiveness of both the algorithms to find the optimal level of machining parameters.

3. Utility concept

According to Walia et al. [46] the overall usefulness of a process can be denoted by a unified index called as utility which is the sum of the individual utilities of various quality characteristics of the process. If Vr is the measure of effectiveness of an attribute (or quality characteristic) r and there are n attributes estimating the outcome space, then the joint utility function can be expressed as [46-47].

U(Vi, V2,.....Vn)= f (Ui (Vi), Ui (Vi ),......Un (Vn))

where Ur(Vr) is the utility of the rth attribute.

If the attributes are independent, the overall utility function is the sum of individual utilities and can be calculated as

U(Vi, V2,.....Vn)=£ Ur(Vr)

After assigning weights to the attributes, the overall utility function can be calculated as

U(Vi, V2,.....Vn)=£ WrUr(Vr)

where Wr is the weight assigned to the attribute r.

In this work, there are four attributes and equal weight i.e. 0.25 has been assigned to each attributes. The utility value for each quality characteristic is estimated by a preference scale. The acceptable and the best value of the quality characteristic are assigned two arbitrary numerical values 0 and 9 (preference number) respectively and the preference number Pr can be expressed on a logarithmic scale as

Pr = A x log-T xr

where Xr represents quality characteristic of any value and X^. represents just an acceptable value of quality the characteristic r and A has been used as a constant. Here, value of A can be calculated by equation 5 and if Xr = X*, then preference number will be 9 where X* is the optimal or best value.

The overall utility index can be calculated as

U = ¿WrPr

Subject to condition that = i

In this work, overall utility index servers as the single performance measure objective value for optimization which has been accumulated from utility values of individual performance characteristic.

4. Particle swarm optimization

Particle swarm optimization (PSO) algorithm, originally introduced by Kennedy and Eberhart [9], is a population based evolutionary computation method influenced by the behavior of organisms such as bird flocking and fish schooling. In PSO, each member is called particle and each particle moves around in the search space with a velocity which is continuously updated by the particle's individual contribution and the contribution of the particle's neighbors or the contribution of the whole swarm. The members of the whole population are maintained during the search procedure so that information can be socially shared among all individuals to direct the search towards the best position in the search space. Each particle moves towards its best previous position and towards the best particle in the whole swarm called the gbest based on the global neighborhood. Each particle moves towards its best previous position and towards the best particle in its restricted neighbourhood based on the local variant so called the pbest model. PSO is basically characterized as a simple heuristic of well-balanced mechanism with flexibility to progress and adjust to both global and local exploration capabilities. All the particles tend to converge to the best solution rapidly even in the local version in most cases as compared to genetic algorithm. Due to the simple concept, easy implementation, and rapid convergence, PSO has gained much attention and been successfully applied to a wide range of applications viz. as job scheduling, power and voltage control problems [11-12].

In PSO, the initial population is generated randomly and parameters are initialized. After evaluation of the fitness function, the PSO algorithm repeats the following steps iteratively:

• Personal best (best value of each individual so far) is updated if a better value is discovered.

• Then, the velocities of all the particles are updated based on the experiences of personal best and the global best in order to update the position of each particle with the velocities currently updated.

After finding the personal best and global best values, velocities and positions of each particle are updated using Eqs. (8) and (9) respectively.

+ ciri (p!,-1 - x-1)-

c2r2(gyi - xj1)

t i t i

vij = w

where vjj represents velocity of particle i at iteration t with respect to

jth dimension (j = 1,2.......n).pjj represents the position value of the ith

personal best with respect to the jth dimension gjj represents the global best (gbest) i.e. the best of pbest among all the particles. xjj is the position value of the ith particle with respect to jth dimension. c1 and c2 are positive acceleration parameters which provide the correct balance between exploration and exploitation and are called the cognitive parameter and the social parameter respectively. r1 and r2 are the random numbers provide a stochastic characteristic for the particles velocities in order to simulate the real behavior of the birds in a flock. The inertia weight parameter w is a control parameter which is used to control the impact of the previous velocities on the current velocity of each particle. Hence, the parameter w regulates the trade-off between global and local exploration ability of the swarm. The recommended value of the inertia weight w is to set it to a large value for the initial stages in order to enhance the global search of the search space and gradually decrease it to get more refined solutions facilitating the local search in the last stages. In general, the inertia weight is set according to the following Eq. (10) [48].

w = wmax - wiT ~ wmin X iter (10)

itermax

where wmin and wmax are initial and final weights and itermax is the maximum number of iterations and iter is the current iteration number.

4.1. Quantum behaved particle swarm optimization (QPSO)

The main drawback of the PSO algorithm is that it does not assure global convergence because it is trapped into local optima although it converges fast and loose its exploration-exploitation ability. The reason being that the velocity vectors assume very small values as iterations proceed. Clerc and Kennedy [49] have presented that PSO is capable to find a reasonable quality solution much faster than other evolutionary algorithms but it cannot improve the quality of the solution as the number of generations is increased. If pbest and gbest of a particle stay very close to each other then it becomes inactive in the swarm. In other words, when (pt-1 - xt-1) and (gy-1 - x'-1) are both small in Eq. (8) and at the same time vitj has a small value then this particle loses its exploration ability. This could happen at early stages for the gbest particle and as a consequence the PSO is trapped in local minima. QPSO is proposed and stimulated to avoid the drawbacks of original PSO. In the quantum PSO, the state of a particle is described by wave function W(x, t) instead of velocity. The difference between QPSO and classical PSO is the dynamic behavior of the particle i.e. the exact values of x and v cannot be determined simultaneously in QPSO. The probability of the particle's appearing in position x can be learnt from probability density function |W(x, t)|2. The probability density function is used to estimate the probability distribution function of the particle's position.

Employing the Monte-Carlo method, the particle position is updated according to the following equations,

j+1) = Pi,(t+1) - b * (Meesti - j * InO/u) if k P 0.5

j+1) = Pi,(t+1) + b * (MBestJt - Xit) * ln(!/u) if k < O.5 j

pl„)= e * p^ +(1 - 9)*

MBestj = nEP

(11) (12)

where Pi is the local attractor, PBestj is the best positions which the

of particle i at iteration t with respect to jth dimension has achieved so far and gBej is the best position of all particles in current gener-

ation. Mbestj is the mean best position which is defined as the mean

of all the best positions of the population in current generation, k ,u, 6 k , u ,6 are random numbers distributed uniformly on [0,1]. p in Eqs. (11) and (12) is the tuning parameter to control the convergence speed of the particle and is called as contraction expansion (CE) coefficient. Value of p is tuned from 1 to 0.4 for initially accommodating a more global search with an objective to terminate the QPSO algorithm with a better local search.

The p value is adaptively allocated as per the Eq. (15)

b = bmax - [{(bmax - bmin)/iterationmax} * iter]

where pmax is the initial contraction expansion factor value, pmin is the final contraction expansion factor value, iter is the current iteration number and iterationmax is the maximum number of iterations. The termination criterion for the algorithm is the maximum number of iterations. The pseudo code for the search procedure of the QPSO given below. Fig. 1 shows the flow chart of the QPSO algorithm.

The pseudo code of proposed QPSO

Initialize the population size, the current position and the dimensions of the particles;

While (termination condition i.e. maximum Iteration)

t=t+1;

Compute the mean best position MBest by Eq. (14);

Select a value of p by Eq. (15);

for i=1 to population size

for j=1 to dimensions of the particles

If k p 0.5

X(t+1) = Pj,(t+1) + p * (MBest; - X;t) * ln(1/u); end if end for

Evaluate the fitness value ofXi

function Update the pBest,_t and gBesU , t end for end do end

that is the objective

5. Experimental details

In this work, Taguchi method, a powerful tool for parametric analysis of the performance characteristics is used to extract maximum information with least number of experimental runs. Computer numerical control (CNC) die sinking EDM machine (ECOWIN PS 50ZNC) with servo-head (constant gap) is used for conducting the experiment. Paraffin oil of specific gravity of 0.820is used as dielectric fluid with positive polarity for electrode with side flushing to conduct the experiments. Inconel alloy 718, a nickel-chromium alloy characterized by high-strength, high corrosion-resistant, good tensile and high creep rupture strength has been used as the work material in this study. The chemical composition of the materials is given in Table 1. Table 2 shows the thermal property of the work material. The X-ray diffraction plot of the Inconel 718 sample used in the present study is shown in Fig. 2. It clearly shows that there are no peaks other than y-phase (austenite) phase which corresponds to face-centred cubic

xj = xj-1 + vj

Fig. 1. Flow chart of QPSO algorithm.

Ni-based y-phase of Inconel 718 super alloy. The sharp peak of the diffraction patterns reveals the crystalline nature of the alloy.

In EDM process, the tool has to deal with a series of spark discharges. Hence, the tool must be of a good conductive material with high melting temperature, ability to withstand against high temperature and dissipate the heat. Therefore, commercially available brass, copper, and graphite are used as the electrode material. The machining diameters of the three electrodes are in cylindrical shape of diameter 13.5 mm. The EDM process is accomplished on Inconel 718 alloy plate of 8 mm thickness and 10 x 11.5 cm2 cross sectional area. Each experiment runs for 30 min. For weighing pur-

pose, the work piece and the electrodes are detached from the machine after each observation and cleaned and dried out. A precision electronic balance (accuracy 0.01 g) is used for measuring the weights of the work and tool materials before and after machining. Surface roughness tester (Surftest SJ 210, Mitutoyo) is used for measuring the surface quality. A tool maker's microscope (Carl Zeiss) is used for measuring the crater diameter on the machined surface on the work material.

The weight loss due to machining of work material noted before and after machining is used to calculate the material removal rate (MRR) using Eq. (16).

1000 x DWw Pw x T

where DWw is difference in weight of work material during machining, pw is the density of work material and T is the machining time.

The weight loss due to machining of tool material noted before and after machining is used to calculate tool wear rate (TWR) using Eq. (17).

1000 x DWt Pt x T

where DWt is difference in weight of tool material during machining and pt is the density of tool material (pbrass=8565 kg/ m3, pcopper=8960 kg/m3 and PgrapWte=2130 kg/m3).

Mitutoyo (Surftest SJ 210) is used to complete the surface roughness (SR) measurements on the machined surface of the work material. Five readings on the traverse direction of the machined surface are taken and average of five readings of surface roughness values are noted down.

The high temperature gradient developed due to series spark of discharges causes dimensional irregularities on the machined edges of the crater cavity. The deviation between the maximum diameter of the cavity and electrode diameter is called radial overcut. Although sufficient compensations are being provided during design of the tool and machining, radial overcut is quite common in EDM process. Minimization of overcut is essential for precise and accurate EDMed machining. Radial overcut is given by relation

dw - dt

Here, dw is the maximum diameter of the crater cavity and dt is the diameter of the tool.

Fig. 3 shows the wok material Inconel 718 after machining with three electrodes. Table 3 shows process parameters and their levels. Table 4 shows the L27 orthogonal array along with obtained responses and overall utility index.

6. Result and discussion

Taguchi's L27 orthogonal array (experimental design) along with obtained performance measures and the overall utility index have been depicted in Table 4. Analysis of variance (ANOVA) is carried out on performance measures such as material removal rate, tool wear rate, surface roughness and radial over cut with a view to analyse the effect of important process parameters. Table 5 shows the ANOVA table for MRR. For MRR, tool material is found to be the

Table 1

Chemical composition of Inconel 718 sample used in the study.

Chemical C% Si% Mn% S% P% Cr% Fe% Mo% Co% Nb% Cu% V% Al% Ti% W% Ni%

Amount 0.039 0.027 0.032 0.005 0.008 17.21 20.143 3.121 0.086 4.989 0.009 0.015 0.568 0.816 0.214 52.739

Table 2

Thermal properties of Inconel 718.

Properties Density Melting Temperature Thermal Conductivity Thermal expansion Possions ratio

Value 8190 kg/m3 1609 K 15 W/m.K 13.0 im/m°C 0.27-0.3

8000 70006000 50004000 300020001000

2 theta (in degree)

Fig. 2. X-ray diffraction plot of the Inconel 718 work material.

I jÉP

Graphite Copper Brass

Fig. 3. Work material Inconel 718 after machining with three electrodes.

Table 3

Process parameters and their levels.

Process Parameters

Levels

Open circuit voltage (A) Voltage 70 80 90

Discharge current (B) Ampere 3 5 7

Pulse-on-time (C) Microsecond 100 200 300

Duty factor (D) Percentage 80 85 90

Flushing pressure (E) Bar 0.2 0.3 0.4

Tool material (F) Brass Copper Graphite

most important process parameter with a percentage contribution of 58.04% followed by discharge current, pulse-on-time, duty factor, open circuit voltage and interactions terms discharge current x tool and pulse-on-time x tool with percentage contributions of 22.7%, 12.33%, 2.63%, 2.27%, 0.90% and 0.79% respectively. Flushing pressure is found to be an insignificant parameter for MRR with a percentage contribution of 0.12%. Table 6 shows the ANOVA for TWR. The table shows that tool material is again found to be the most important process parameter with a percentage contribution of 84.04%, followed by discharge current, pulse-on-time, and interactions terms like discharge current x tool with percentage contributions of 7.71%, 6.29% and 0.51% respectively. Flushing pressure, duty factor and open circuit voltage are found to be an insignificant parameter for TWR with a percentage contribution of 0.3%, 0.14% and 0.05% respectively. Table 7 shows the ANOVA table for overall utility index and it indicates that discharge current is the most influential parameter with a percentage contribution of 51.20% followed by tool material, pulse-on-time, open circuit voltage and interaction terms such as discharge current x tool and pulse-on-time x tool with percentage contribution of 18.98%, 15.09%, 4.82%, 2.31%, and 1.66% respectively. Flushing pressure and duty factor are found to be insignificant parameters with percentage contribution of 1.08%, and 0.77% respectively. Similarly, analysis of variance for surface roughness reveals that tool material is the most influential process parameter with percentage contribution of 72.71% followed by discharge current, pulse-on-time, interaction terms like discharge current x tool with percentage contribution of 36.38%, 3.16% and 0.42% respectively. Parameters such as open circuit voltage, duty factor and flushing pressure have little effect on surface roughness with a percentage of contribution of 0.26%, 0.08% and 0.04% respectively. Analysis of variance for radial overcut reveals that tool material, discharge current, pulse-on-time and interaction term discharge current x tool are the important process parameters with percentage contribution of 83.09%, 10.36%, 2.21% and 1.03% respectively. Open circuit voltage, duty factor and flushing pressure have little effect on radial overcut with a percentage contribution of 0.45%, 0.39% and 0.16% respectively. A scanning electron microscope (SEM) micrograph analysis is also carried out to study the formation of recast layers on the machined surface after machining. From the SEM micrographs, it is observed that recast layer thickness increases with increase in spark energy while machining with graphite and copper electrode. However, brass electrode at smaller spark discharges produces thinner recast layer in comparisons with graphite and copper electrodes.

Fig. 4 shows the main effect plot for MRR. The plot shows that the MRR decreases with increase of open circuit voltage from 70 V to 90 V but the decreases is more pronounced between 70 V and 80 V. Low values of open circuit voltage can lead to higher MRR whereas higher values of open circuit voltage can cause relatively lower material removal rates. However, the effect of open circuit voltage on MRR is not significant in comparison with discharge current. The figure indicates that material removal rate increases rapidly with the increase of discharge current from 3A to 7A. Increase in discharge current directly increases the spark energy which in turn causes an increase in the crater dimension resulting in higher removal of metal from the work surface. The figure shows that material removal rate decreases with increase in pulse-on-time and the decrease is rapid when pulse-on time is set beyond 200 is. Increasing the pulse-on-time means applying

Table 4

L27 orthogonal array along with responses.

Run order A B C D E F MRR in mm3/min TWR in mm3/min SR in im RO in mm Overall utility index

1 70 3 100 80 0.2 Brass 11.5221 6.8540 8.4179 0.0282 5.8440

2 70 3 100 80 0.3 Copper 25.5444 4.5742 14.2626 0.1076 5.2514

3 70 3 100 80 0.4 Graphite 31.7515 3.5681 19.3699 0.2563 4.5499

4 70 5 200 85 0.2 Brass 12.1862 7.2991 11.1324 0.0780 4.5216

5 70 5 200 85 0.3 Copper 27.5620 4.8501 19.0233 0.2557 4.0588

6 70 5 200 85 0.4 Graphite 38.3034 3.2952 25.0787 0.4354 3.6527

7 70 7 300 90 0.2 Brass 22.5026 7.1806 18.3226 0.1818 3.5755

8 70 7 300 90 0.3 Copper 33.4826 5.2938 24.0778 0.2838 3.6078

9 70 7 300 90 0.4 Graphite 40.8613 3.0006 30.2353 0.4450 3.5734

10 80 3 200 90 0.2 Copper 23.9502 4.2463 14.0796 0.1464 5.0969

11 80 3 200 90 0.3 Graphite 32.5885 2.6482 20.3344 0.3364 4.4646

12 80 3 200 90 0.4 Brass 6.3664 7.0477 7.7977 0.0734 4.6651

13 80 5 300 80 0.2 Copper 14.8303 3.8907 20.4310 0.3056 3.6324

14 80 5 300 80 0.3 Graphite 26.2129 2.4188 25.6183 0.4877 3.0508

15 80 5 300 80 0.4 Brass 3.3944 6.9065 12.4431 0.0708 3.4151

16 80 7 100 85 0.2 Copper 37.7847 6.1202 21.0403 0.2659 3.7487

17 80 7 100 85 0.3 Graphite 47.6497 3.9141 27.4052 0.4790 3.4744

18 80 7 100 85 0.4 Brass 21.6813 8.9148 13.9793 0.1232 3.9462

19 90 3 300 85 0.2 Graphite 16.4502 2.2543 22.3897 0.3899 3.7696

20 90 3 300 85 0.3 Brass 4.4495 6.3105 9.1573 0.0315 4.9417

21 90 3 300 85 0.4 Copper 12.3846 3.4282 17.2583 0.2355 4.1719

22 90 5 100 90 0.2 Graphite 39.7088 3.7379 24.9953 0.4058 3.4782

23 90 5 100 90 0.3 Brass 15.2592 8.4282 9.5444 0.0736 4.7791

24 90 5 100 90 0.4 Copper 31.3547 5.5108 18.4393 0.2132 4.1549

25 90 7 200 80 0.2 Graphite 41.3635 3.7707 26.5567 0.4544 3.4088

26 90 7 200 80 0.3 Brass 14.4506 7.9370 15.0112 0.0929 3.8953

27 90 7 200 80 0.4 Copper 30.1753 5.4724 21.7047 0.2877 3.6264

Table 5

ANOVA for MRR.

Source DF Seq SS Adj SS Adj MS F P % Contribution

Open circuit voltage 2.0000 92.5100 92.5100 46.2600 30.5400 0.0010 2.270708

Discharge current 2.0000 927.7300 927.7300 463.8700 306.2500 0.0000 22.77163

Pulse-on-time 2.0000 498.4200 498.4200 249.2100 164.5300 0.0000 12.23399

Duty factor 2.0000 107.1900 107.1900 53.6000 35.3800 0.0000 2.631036

Flushing pressure 2.0000 5.1300 5.1300 2.5600 1.6900 0.2610 0.125919

Tool 2.0000 2364.5900 2364.5900 1182.3000 780.5700 0.0000 58.04014

Discharge current x Tool 4.0000 36.8300 36.8300 9.2100 6.0800 0.0260 0.904012

Pulse-on-time x Tool 4.0000 32.5700 32.5700 8.1400 5.3800 0.0350 0.799448

Residual error 6.0000 9.0900 9.0900 1.5100

Total 26.0000 4074.0600

Table 6

ANOVA for TWR.

Source DF Seq SS Adj SS Adj MS F P % Contribu

Open circuit voltage 2.0000 0.0523 0.0523 0.0261 0.2900 0.7570 0.053926

Discharge current 2.0000 7.4812 7.4812 3.7406 40.9700 0.0000 7.713858

Pulse-on-time 2.0000 6.1046 6.1046 3.0523 33.4300 0.0000 6.294447

Duty factor 2.0000 0.1359 0.1359 0.0679 0.7400 0.5000 0.140126

Flushing pressure 2.0000 0.2933 0.2933 0.1466 1.6100 0.2480 0.302421

Tool 2.0000 81.5084 81.5084 40.7542 446.3800 0.0000 84.04323

Discharge current x Tool 4.0000 0.4953 0.4953 0.1238 1.3600 0.3160 0.510703

Residual error 10.0000 0.9130 0.9130 0.09130

Total 26.0000 96.9839

the same heat flux for longer duration. The pressure inside the plasma channel decreases due to continuous application of the same heat flux for longer duration. Since the volume of molten metal remains unaffected, further increase in pulse-on-time results in decrease of MRR. MRR increases monotonically with increase of duty factor. Increase in duty factor causes an increase in the spark energy across the gap between the electrodes resulting in increase of temperature which ultimately leads to increase in MRR. Similar observations have been reported in experimental observation of Pradhan and Biswas [43]. Material removal is higher while machining with graphite electrode followed by copper and brass respec-

tively. Copper and graphite electrodes have higher thermal conductivity and higher melting point temperature whereas brass electrode having smaller thermal conductivity and lower melting point temperature. Subsequently, the spark energy across graphite and copper electrodes are higher which in turn removes higher material than brass electrode.

The machining cost of the EDM process is largely affected by erosion rate of tool. Fig. 5 shows the main effect plot of TWR with important process parameters. The plot shows that tool erodes rapidly with increase in discharge current. Increase in discharge current increases the spark energy and hence more heat is

Table 7

ANOVA for overall utility index.

Source DF Seq SS Adj SS Adj MS F P % contribution

Open circuit voltage 2.0000 2.3922 2.3922 1.1961 3.5900 0.0940 4.829654

Discharge current 2.0000 25.3644 25.3644 12.6822 38.0800 0.0000 51.20862

Pulse-on-time 2.0000 7.4792 7.4792 3.7396 11.2300 0.0090 15.09989

Duty factor 2.0000 0.3838 0.3838 0.1919 0.5800 0.5900 0.77486

Flushing pressure 2.0000 0.5398 0.5398 0.2699 0.8100 0.4880 1.089812

Tool 2.0000 9.4018 9.4018 4.7009 14.1200 0.0050 18.98146

Discharge current x Tool 4.0000 1.1486 1.1486 0.2871 0.8600 0.5360 2.318928

Pulse-on-time x Tool 4.0000 0.8235 0.8235 0.2059 0.6200 0.6660 1.662578

Residual error 6.0000 1.9982 1.9982 0.3330

Total 26.0000 49.5315

Fig. 4. Main effect plot of MRR.

Fig. 5. Main effect plot of TWR.

generated across the electrodes resulting in higher melting and evaporation of the electrodes. The plot also shows that tool wear rate varies inversely with pulse-on-time. As conductivity of tool materials is higher than that of work material, the discharge of heat at the time of machining from the tool material is quick in comparison to work material. Therefore, tool wear decreases at higher pulse-on-time. Attachment of carbon particles onto the sur-

face of tool is another reason of low tool wear rate at high pulseon-time. While machining Inconel 718, erosion of tool is faster with the use of brass tool followed by copper and graphite tool. Erosion of tool with graphite electrode is minimum due to its extremely high melting point temperature. As graphite and copper have reasonably high melting point temperature and good thermal conductivity than brass tool, the erosion rate of brass tool is faster in comparison to other electrodes. The figure also shows that open circuit voltage, duty factor and flushing pressure do not contribute much for the variation of TWR.

The machined surface quality and crater dimension mainly depends up the discharge energy. Higher the discharge energy, higher is the material removed which in turn produces poor surface quality. Fig. 6 shows the main effect plot of surface roughness through which analysis of the effect of various machining parameters on surface quality has been made. It shows that surface quality deteriorates with increases in discharge current. The discharge energy is directly governed by discharge current. Hence, more heat is produced between the electrodes resulting in larger size material to be removed from the work surface. This degrades the surface quality produced on the machined surface. The plot also indicates surface roughness increases with increase in pulse-on-time gradually. Increase in pulse-on-time increases the spark energy across electrodes which in turn cause larger size material to be removed from work surface degrading the surface quality. Inconel 718 work material machined with graphite electrode produces the poorest performance with regard to the surface finish. Brass electrode at smaller values of discharge energy produces an excellent surface quality while machining Inconel 718. The work material while

Fig. 6. Main effect plot of Surface roughness.

machining with copper electrode produces surface quality between those of brass and graphite. The size of material removed by graphite and copper electrodes is larger on the machined surface. It decreases the surface quality produced whereas brass electrode at the smaller value of discharge energy produces finest surface quality at the expense of more tool erosion. Hence, it can be concluded that good surface quality can only be produced at smaller value of spark energy with brass as the electrode material. The effect of open circuit voltage, duty factor and flushing pressure for variation of surface roughness is minimal. Yet, it is observed that surface roughness increases slowly with increase in open circuit voltage.

In EDM, precise and accurate machining means reduction of overcut. Fig. 7 shows the variation of radial overcut with important process parameters. It shows that radial overcut varies directly with increase in discharge current. Higher values discharge current causes increase in spark energy resulting in increase of temperature between the tool and work material and thus producing wider and larger craters on the machined surface. This, in turn, increases the radial overcut. The plot also shows that radial overcut increases gradually with increase of pulse-on-time. Increase of pulse-on-time causes prolonged occurrence of sparks on the machined surface. It results in increase of the radial overcut on the machined surface due to increase in spark energy. However, it observed that the effect of discharge current on radial overcut is higher as compared to pulse-on-time. Radial overcut is higher while machining with graphite electrode followed by copper and brass electrode respectively. As craters produced in graphite and copper electrodes are wider and larger, radial overcut on the machined surface is also larger. Thus, it can be concluded that brass electrode at the smaller value of spark energy can be used for producing precise and accurate EDMed parts at the expense of more tool erosion. The other factors such as open circuit voltage, duty factor and flushing pressure hardly contribute to radial overcut in comparison to discharge current, pulse-on-time and tool material.

In this work, utility concept has been used to convert the multiple performance measures into an equivalent single performance measure by calculating the overall utility index. The single performance measure is ranked between 0 to 9 with highest value of overall utility index of 5.84. The process model relating overall utility index with process parameters have been developed through non-linear regression analysis using SYSTAT software has been shown in Eq. (19). The coefficient of determination (R2) and

adjusted R2 values are found to be 98.9% and 99.1% respectively which confirms the validation of the model.

Overall utility index(U) = -0.010 + 0.709 x A - 0.310 x B

- 0.015 x C - 0.477 x D + 8.499 x E

- 1.637 x F + 0.002 x A2 - 0.011 x B2

+ 0.009 x D2 - 15.592 x E2 + 0.114 x F2

+ 0.073 x B x F + 0.004 x C x F

- 0.001 x B x C - 0.012 x A x D (19)

Present work aims at maximizing MRR and minimizing TWR, surface roughness and over cut which are functions of process parameters viz. open circuit voltage, discharge current, pulse-on-time, duty factor, flushing pressure and tool material. In this work, PSO and QPSO algorithm have been proposed to obtain the optimal parametric setting with an objective to maximize MRR and minimize TWR, surface roughness and radial over cut. The QPSO and PSO algorithms are coded in MATLAB 14 and run on a Pentium IV desktop. The empirical relation between process parameters and overall utility index obtained through non-linear regression analysis is used as objective function (Eq. (19)) for solving the optimization problem. Open circuit voltage, discharge current, pulseon-time, duty factor, flushing pressure are quantitative process parameters whereas tool material is a qualitative process parameter. The quantitative parameters are real values that lie within the scope of experiment set up as shown in Table 1. The qualitative parameters are coded in the algorithm as 1 as brass tool, 2 as copper tool and 3 as graphite tool. For the qualitative parameter tool material, the nearest integer part of the real numbers has been considered. The range of qualitative parameter (tool material) are considered in the manner if the values lie in the range [1-1.4], it is treated as 1 or brass tool, [1.7-2.3] as 2 or copper tool and [2.4-3] as 3 or graphite tool. Fig. 8 shows the convergence of QPSO and PSO algorithms. The figure illustrates the performance of both the algorithms. It is convincible to note that QPSO algorithm is superior to PSO as it converges rapidly towards the best solution. It can be observed that after end of 100 iterations, the value of overall utility index is obtained as 6.91 for QPSO whereas the value for PSO is 6.52. The overall utility index value obtained through QPSO algorithm is higher than the overall utility index shown in Table 3 and PSO algorithm. Once the optimal parametric settings have been identified, it is mandatory to validate the same through

Fig. 7. Main effect plot of radial over cut.

iteration

Fig. 8. Convergence curve for QPSO and PSO algorithm.

Table 8

Confirmative test result for optimal parametric setting.

Algorithm Optimal parametric setting

Voltage Discharge Pulse- Duty Flushing Tool current on-time factor pressure

MRR TWR Surface Radial Overall utility Overall utility Error %

mm3/min mm3/min roughness overcut index index from

im mm from confirmatory

algorithm test

QPSO PSO

80 V 75 V

6 A 5A

100 is 180 is

80% 85%

0.2 bar 0.2 bar

Brass 26.5600 Brass 25.0100

6.3100 6.5900

7.2100 7.7500

0.0732 0.0874

6.9100 6.5200

6.2100 5.8900

confirmative tests. Table 8 shows the confirmative test results obtained through both the approaches along with the optimal parametric setting with obtained value of overall utility index.

The calculated values of the overall utility index for the confirmatory test are found to be 6.21 and 5.89 with errors value of 10.1% and 9.6% for QPSO and PSO respectively. From the table, it can be clearly noticed that the results obtained through QPSO algorithm is more favorable to achieve improved machining efficiency.

7. Conclusions

Although Inconel 718 has wide-spread application, its machining both in conventional and non-conventional methods becomes difficult due to low thermal conductivity. In this work, an extensive experimental investigation has been carried out to analyse the effect of various electrode materials on the machinability of Inconel 718 super alloy in the EDM process. It is observed that material removal rate can be improved through the use of graphite tool but surface roughness and radial overcut are seriously affected due to high discharge energy. Brass can be used as tool electrode when better surface integrity is desired but the material removal rare is rather less. As far as tool wear is concerned, graphite tool performs superior to copper and brass tool. A hybrid approach of utility concept embedded with QPSO and PSO algorithms have been proposed and compared for obtaining best parametric setting for EDM process. From the performance comparison curve of both the algorithms, it is observed that QPSO provides better result than PSO owing to inherent capability of avoiding premature convergence. The optimal parametric setting obtained through both approaches is validated by conducting confirmative tests. The test results reveal that QPSO provides better solution in comparison to PSO resulting in improved machining efficiency. This analysis helps in identifying the important process parameters which can be effectively controlled to reduce the cost of machining, experimentation time and experimental error to increase productivity and quality of the process.

In spite of several major findings obtained through this study, analysis on recast layer formation, surface integrity and microstructure of the machined surface can be considered as some of the key limitations of the research. Numerical analysis can be carried out on this experimental investigation. In this work, QPSO has been applied without considering any constraints. In future, process related constraints can be incorporated during formulation of optimization problem.

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