Optimizing electric discharge machining parameters for tungsten-carbide utilizing thermo-mathematical modelling

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International Journal of Thermal Sciences 59 (2012) 161e175

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International Journal of Thermal Sciences

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Optimizing electric discharge machining parameters for tungsten-carbideutilizing thermo-mathematical modelling

Harminder Singh a,*, D.K. Shukla b

aGuru Nanak Dev University, Regional Campus, Jalandhar, Punjab 144007, IndiabDr. B.R. Ambedkar National Institute of Technology (NIT), Jalandhar, Punjab, India

a r t i c l e i n f o

Article history:Received 18 November 2011Received in revised form28 March 2012Accepted 28 March 2012Available online 10 May 2012

Keywords:EDMEnergy distributionTungsten carbideThermal model

* Corresponding author. Tel.: þ91 9914405782.E-mail address: [email protected] (H. Sing

1290-0729/$ e see front matter � 2012 Elsevier Masdoi:10.1016/j.ijthermalsci.2012.03.017

a b s t r a c t

The energy distribution in the Electrical Discharge Machining (EDM) process influences the materialremoval rate, and other machining characteristics like crater geometry, relative wear ratio and surfaceroughness. During this process the electrical energy is converted into heat energy and this energy isdistributed among the electrode, workpiece and the dielectric fluid. The fraction of the energy which istransferred to the workpiece, is the useful energy and this energy should be maximum, for optimumutilization of energy. This fraction of energy is one of the important parameters used in the existingthermo-physical models of EDM process. Due to apparent incongruities and conflicting data earlyresearchers conjectured the same value of fraction of energy transferred to electrodes for all machiningparameters in their models for numerically calculating the volume and geometry of the crater formed.This assumption is one of the reasons of error in the models from the experimental data. So this study isplanned to experimentally study the variation of this fraction of input discharge energy with the help ofthermo-mathematical models during EDM of Tungsten-Carbide by varying the machining parameterscurrent and pulse duration. The data calculated in this study can be further used in the existing thermo-physical models, expecting to bring the models preciously more close to the real conditions. This datawill also be helpful for numerically calculating the optimum parameters using optimum value of thefraction of energy transferred to the electrodes especially workpiece. The results obtained showed thatthe energy effectively transferred to the workpiece varies with the discharge current and pulse durationfrom 6.5% to 17.7%, which proves that the fixed value assumed in the models is not in line with real EDMprocess.

� 2012 Elsevier Masson SAS. All rights reserved.

1. Introduction

Since the discovery of EDM process by the Soviet scientistsLazarenko B.R. and Lazarenko N.I., nearly five decades ago, theresearches and improvements of the process are still going on toidentify the basic physical process involved during the process.The usual method of making some simplifying assumptions andformulating thermal models that yield results does not work inmany cases where the problem is complex and random. ElectricalDischarge machining is such a process that is not only compli-cated and random but also physically little understood. Asystematic study of the phenomenon of the electrical dischargein a liquid dielectric has proven to be very difficult due to its

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complexity and also the difficulty in its scientific observation.Therefore a comprehensive quantitative theory concerning themechanism of material removal by spark erosion is yet to beformulated, though the basic physical laws have been laid formany years. Currently there is no complete and definite modelexplaining in all details the different processes that take placeduring a discharge in EDM process. From the last few yearsextensive research in this area has been taking place [1e8].

The erosion by an electric discharge involves phenomena suchas heat conduction, energy distribution, melting, evaporation,ionization, formation and collapse of gas bubbles in the dischargechannel. The complicated phenomenon, coupled with surfaceirregularities of electrodes, interaction between two successivedischarges, and the presence of debris particles, make the processrandom in time as well as space and therefore, deterministicallyderived thermal models yield results that do not match favourablywith the experimental evidence. Several investigators [6,9e27]showed that the distribution of the energy supplied to the gap in

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H. Singh, D.K. Shukla / International Journal of Thermal Sciences 59 (2012) 161e175162

the EDM process influences the removal rate, crater geometry,surface roughness and accuracy greatly. From the perspective ofmachining energy, each pulse during the discharge process is anoutput of energy.

Eubank et al. [15] reported that the energy distribution factor forcathode and anode increases with increase in the applied dischargeenergy, due to the fact that the higher energy plasma produceslarge temperatures, which further dissipate more heat to theelectrodes. The applied discharge energy increases with increaseddischarge current and pulse duration, results in more energyentering into the workpiece and consequently increases MRR asreported by Salonities et al. [3].

The thermo-physical finite element model for EDM developedby Pradhan [1] predicts that the percentage of discharge energytransferred to the workpiece is one of the important parameter forprecision development of the model. The thermo-physical modelsproposed by Joshi and Pande [2], Salonities et al. [3], Yeo [11],DiBitonto et al.[16], Jilani and Pandey [17,18], Beck [19,20], Dijck andDutré [22], Snoeys and Van Dijck [23] shows the dependence ofMRR and Crater geometry and roughness on the fraction of energytransferred to the workpiece. Tebni et al. [10] also proposed a EDMprocess model based upon thermal, metallurgical, mechanical andin situ test conditions.

The comparative analysis, of five EDM models done by Yeo etal. [4] found that models from Snoeys and Van Dijck [23], Dijckand Dutré [22], Beck [19,20], Jilani and Pandey [17,18] overestimatethe temperature distribution of the workpiece, resulting in largercrater geometry and erosion rate, as compared to DiBitonto’smodel [16] which predict the dimensional geometry and erosionwith good accuracy. This is found to be due to the assumption ofdifferent fractions of input energy transferred to workpiece;DiBitonto’s model [16] assumed Fc ¼ 0.18 (18%), while the othermodels assumed Fc ¼ 0.5 (50%). But these assumptions are not inline with the real EDM process. Also the prediction accuracy of thethermo-physical model of Joshi and Pande [2] improved byvarying the values of fraction of discharge energy transferred tothe workpiece with current and pulse duration. It was noted that itis essential to apply higher energy distribution factor for higherenergy zones. The study recommended energy distribution factors0.183 for lower energy zone (up to 100 mJ), while 0.183e0.2 formedium energy zone (100e650 mJ). Yeo et al. [4] recommendsthat the thermo-physical models especially based upon the diskheat source model can be improved further if appropriateapproximations are taken for the energy fraction determinedeither empirically or theoretically. But as reported by Salonities etal. [3] the fraction of the generated heat entering the electrode andthe actual effective removal energy depends on the thermalproperties like melting point, density, specific heat, thermalconductivity and yield strength of the electrode, distance betweenthe electrodes, flushing pressure, conductivity of the dielectric,discharge current and discharge on time. So it is very difficult topredict theoretically the generally accepted fraction of energy forthermo-physical models.

So this study is planned to experimentally study the variationof this fraction of input discharge energy with the help ofthermo-mathematical models suggested by Konig [21] duringEDM of Tungsten-Carbide by varying the machining parameterscurrent and pulse duration. The data calculated in this study canbe further used in the existing thermo-physical models, expect-ing to bring the models preciously more close to the realconditions. This data will also be helpful for numerically calcu-lating the optimum parameters using optimum value of thefraction of energy transferred to the electrodes especiallyworkpiece.

There are very few studies on this subject so far.

2. Past work

Several studies on distribution of available energy, in generaland specifically for EDM process is reported [7,28e37], though thetheoretical/experimental study during EDM process is generally onEDM of steel workpiece and not much on Tungsten-Carbidematerial. The EDM of Tungsten-Carbide and effect and applicationof this machining process is reported by many authors [38e49].Rappaz [28] explains that in order to reduce the average roughnessof EDM machined surface to values well below 100 nm, it isnecessary to establish the precise energy distribution aftera discharge. It was found that the 14.9% of energy effectivelytransferred to the workpiece (steel cylinder of DIN 1.2343 compo-sition) during EDM process for I ¼ 4 A and ti ¼ 25 ms. Liao [12,30]gives a new concept of specific discharge energy (SDE) a quantitydefining as the real energy required to remove a unit volume ofmaterial and the materials having close value of SDE demonstratevery similar machining characteristics.

Daryl and Philip [6,31] estimated that 8% and 18% of the totaldischarge energy is distributed into the cathode and anoderespectively. The study explained qualitatively on the grounds ofelectron emission theory that energy distributed to the anode andcathode changes with the pulse duration. It is shown that energysupplied to the cathode under EDM conditions comes from photonrather than positive ion bombardment. This point heat sourcemodel accepts power rather than temperature as the boundarycondition at the plasma/cathode interface. A constant fraction ofthe total power supplied to the gap is transferred to the cathode.Compton’s original energy balance for gas discharges is amendedfor EDM conditions. Konig [21] found the energy distributionduring EDM of steel using graphite as tool electrode. The optimalregion is found by varying pulse duration and discharge current.The energy distribution is calculated using heat conduction model.

3. Thermal modelling of the discharge process in EDM

EDM is a thermal erosion process where heat transfer takesplace. The problems of heat transfer with a change of phase are alsoencountered in other fields, such as solidification of castings anddesign of shields for re-entry vehicles on the basis of aerodynamicablation. Therefore a number of simplified thermo-mathematicalmodels of the EDM process based on the equations of heatconduction into solids are available. However, a generally acceptedtheory does not yet exist because development of an accuratemodel of the process is extremely tedious due to complicatednature of metal removal mechanism accompanying the electricdischarge in the dielectric medium and the process involvesnumerous phenomena like energy distribution, heat conduction,phase changes etc [35]. Pradhan [1] predicts the parameters whichneeds consideration during the EDM modelling to reach nearer toreal process conditions are the percentage of discharge energytransferred to the workpiece, spark radius equation based ondischarge current and discharge duration, the latent heat, theplasma channel radius and Gaussian distribution of heat flux. Anexact modelling of the heat transfer problem has to incorporatesimultaneously all the above mentioned phenomena. Therefore inevery model simplifying assumptions have been made, which givereasonably accurate results. The discharge phenomenon in electricdischarge machining can be modelled as the heating of the work-piece material by the incident plasma channel which is assumed tobe a surface heat source in which a large amount of heat is evolved.Heat which is propagated in the metal as a consequence of thermalconductivity is transmitted through the surface which forms thecontact between the discharge channel and the electrode and thuspasses into the metal and finally causes the fusion of the metal

H. Singh, D.K. Shukla / International Journal of Thermal Sciences 59 (2012) 161e175 163

[9e12]. Since the distance between the electrodes is very small incomparison to the electrode dimensions, the scattering of heat inthe dielectric layer between the electrodes can be neglected.

The mathematical models for the analysis of EDM process arebased on the theory of heat conduction into the solids and use thefollowing differential equation with suitable boundary conditions:

1a2

vTvt

¼ V2T (1)

where a ¼ffiffiffiffiffiffiffiffiffiffik=cg

pThe models, which have been employed for the study of the

EDM process can be classified according to the idealized geomet-rical shapes of the heat source (discharge channel). These may be:Point heat source, Plane heat source and circular heat source havinga finite radius.

Zingerman [26,27] give a mathematical relation to find thetemperature distribution in a homogeneous body of infinitedimensions which is heated by a surface heat source for which theamount of heat evolved per unit time is known and specified bya time function.

3.1. Plane heat source

If the heat source is assumed to have an infinitely large radius,the heat flow problem can be reduced to an uni-dimensionalproblem. Zingerman [27] gives the solution of Eq. (1) for planeheat source as:

TðtÞ ¼ ðcgÞ1=28ðpKÞ3=2

Zs

dSZt

0

Qtðt� sÞ�3=2exp�� r2

4a2ðt� sÞ�ds (2)

3.2. Circular heat source

If the radius of the heat source assumed to have a finite valuethen heat source is considered as circular heat source. Zingerman[27] and Zolotykh [36] used this model and find a very close rela-tion between experimental and theoretical results.

Zingerman gives the solution of equation (1) for circular heatsource as:

TðtÞ ¼ ðcgÞ1=28ðpkÞ3=2

Zb

0

xdxZt

0

Qtðt� sÞ�3=2exp�� h2 þ x2


3.3. Point heat source

The source radius and plasma channel diameter assumed to bevery small for small discharge durations and for these problemsheat source is assumed as instantaneous point heat source. Zin-german [27] gives the solution of equation (1) for point heatsource as:

Tðr; tÞ ¼ cg

8ðpkÞ3=2Zt

0

Qtðt � sÞ�3=2exp�� r2


Hocheng (1997) [14] gives the solution for induced temperaturefor instantaneous point heat source as:

T � To ¼ P

8ðpatÞ3=2eð�r2=4atÞ where P is energy intensity (5)

Using these equations it is possible to find the effect of themagnitude of the area of the heat source upon depth of depression(crater). The knowledge of the heat source area is necessary inorder to verify the theoretical derivations and the neglect of thisareawould lead to great errors. The directmeasurement of this areais impossible, but can be determined according to the Drabkinaformula [26]. It is only possible to measure the diameter of thedepression (crater) reliably, which is used many EDM models.Based upon two-dimensional transient heat conduction problem,Dijck [22] numerically calculate the craters obtained in EDMprocess and suggests that theoretical model should include thepossibility of accounting for the plasma channel widening in orderto obtain acceptable agreement with experimental data or topredict the optimal operating conditions. This widening of plasmachannel further effect the energy transferred to the electrodes andhence effects the crater formed during the process. The resultsobtained indicate that the diameter of the column is a function ofthe energy generated in the column.

Researchers have generally assumed point heat source modelwith hemispherical crater cavity as used by DeBitonto model [16]or uniformly distributed heat flux model with paraboloid cratercavity used by Salonitis [3] or disk heat source model by Snoeys[23] and Beck [19,20] with bowl shape crater, Jilani [17,18] withcrescent like shaped cavity, and Dijck [22] with hemisphericalshape and Praveen [9] uniformly distributed heat flux model.Theese results are not in good agreement with the real condition.Joshi and Pande [2] successfully incorporated Gaussian distributionof heat flux with shallow bowl shaped cavity and this modelconsider EDM spark radius as a function of discharge current anddischarge duration. Gaussian distribution of heat flux model givesthe best approximation of EDM plasma shape, along with thevarying fraction of energy distributed with current and pulseduration.

The heat flux equation used by Joshi and Pande [2] is:

qðtÞ ¼ 3:4878� 105FcVI0:14

t0:88onexp

�� 4:5

�tton

�0:88�(6)

where Fc is the fraction of total power going to the cathode; V is thedischarge voltage; I is the discharge current; t is the time (ms) andton is time (ms) at the end of electric discharge.

It is also established in all the models that the prediction ofdepth of a depression(crater) in EDM close to real process isbased on the accurate prediction of the amount of heat which istransmitted to the metal from the discharge channel for shortand long gaps, for positive and negative polarity, for pulseswith a duration of from several microseconds to several milli-seconds, and for materials with large and small values of heatconductivity.

4. Calculations of energy distribution during EDM process

The heat distribution in the material can be calculated with theaid of the physical properties and on the assumption that all theelectric energy will be transferred into heat on the materialsurface. Since the main mode of heat transfer in EDM process is byconduction only, a mathematical modelling can be done by heattransfer techniques. The theoretical and experimental work inEDM has demonstrated that crater size and dimensions are func-tion of energy supplied at the discharge. Konig [21] gives rela-tionship between volume of a crater and energy and is discussedbelow:

The input energy Win ¼ Sum of the pulse energies We of all thepulses


Win ¼Xn

We (7)
x¼1
The input energy per unit time is as follows:

Win

:¼ VItifph where fp ¼ 1=ðti þ toÞ; ti �on time; to�off time

(8)

The input energy Win can be split among all modes of energy inthe primary energy distribution as shown in Fig.1 and appear in thethree parts of the closed system: electrode, workpiece and dielec-tric fluid with varying intensity and duration. The energy releasedin workpiece and electrode can be divided into conducted energy,stored energy and energy used in the erosion (of the workpiece)and the unwanted wear (of the electrode). Only stored and directlyconducted energy are distinguished in the dielectric fluid. Theremainder of the dischargewhich cannot be assigned to a particularelement of the closed system appears as different form of energylike radiation, light, sound etc. The components of the primaryenergy distribution are defined by the following:E1 - energy forerosion/removal of workpiece, E2 - energy conducted through theworkpiece, E3 - energy stored in the workpiece, E4 - energy forerosion/removal of electrode, E5 - energy conducted through theelectrode, E6 - energy stored in the electrode, E7 - energy conductedthrough the dielectric fluid, E8 - energy stored in dielectric fluid, E9 -residual energies like radiation, light, sound or ionization.

Using above designations following energy balance can beobtained:

Xnx¼1

We:

¼ Win

:¼

X9y¼1

Ey:

(9)

This primary energy distribution changes to the secondarydistribution due to conversion and transfer processes between thedifferent modes of energy and various components of the system asshown in Fig. 2. For example, the energies E1 and E4, causing erosionand wear respectively are partly liberated by cooling subsequent toerosion. The major portion of this energy is dissipated in the elec-trodes by conduction of heat and in the dielectric fluid by convec-tion and radiation. The secondary energy distribution can be

Fig. 1. Primary energy distri

divided into two groups corresponding to the form of energy: Allstored and conducted heats are collected in the first group. Theseare relatively easily measurable, e.g. by temperature sensors. Thesecond group includes all other forms of energy that are not storedand given off in the form of heat, which are designated as residualenergies and are difficult to measure. The components of thesecondary energy distribution are defined by the following:Q1 e

Heat stored in eroded (from workpiece) particles, Q2 e Heat con-ducted through the workpiece, Q3 e Heat stored in the workpiece,Q4 e Heat stored in worn (from electrode) particles, Q5 e Heatconducted through the electrode, Q6 eHeat stored in the electrode,Q7 e Heat conducted through the dielectric fluid, Q8 e Heat storedin the dielectric fluid, Q9 e Residual energies like radiation, light &sound energies The sum for all components of both distributionsper unit of time is equal to the input energy:

Win

:

¼X9y¼1

Ey:

¼X9z¼1

Qz:

(10)

Theoretically, the primary distribution is changed completelyinto the secondary distribution. The transformation can bedescribed by the following linear relations:

Ey:

¼X9z¼1

KyzEy:

y ¼ 1; 2; 3; :::::; 9 (11)

For example, a portion K11E1:of energy E

:

1 goes to Q:

1, KyzEy:goes

toQ:

z, K19E1:goes to Q

:

9.The following relation must be valid for the coefficient to satisfy

Eq. (11):

X9z¼1

Kyz ¼ 1 y ¼ 1; 2; 3; :::::::; 9 (12)

Following linear relations can be written for the secondarydistribution:

Qz

:

¼X9y¼1

KyzEy:

z ¼ 1; 2; 3; ::::; 9 (13)

bution in EDM process.

Fig. 2. Secondary energy distribution in EDM process.


For example, the energy Q:

1 is obtained from the sum ofportions K11E1

:

of energyE:

1, K21E2:

of energy E:

2..., K91E9:

ofenergy E

:

9.If primary and secondary distribution are expressed in matrix

form, they may be related with the help of matrix (K):

ðKÞðE:Þ ¼ ðQ

:

Þ (14)

Thus from the secondary distribution primary distribution canbe calculated by transposing Eq. (14)

ðE:Þ ¼

K�1ðQ: Þ (15)

for ðK�1Þ ¼ ðRÞ the following relation is obtained:

ðE:Þ ¼ ðRÞðQ

:

Þ (16)

or

Ey:

¼X9z¼1

RyzQz:

y ¼ 1; 2; 3; ::::; 9 (17)

0BBBBBBBBBBBB@

Q1Q2Q3Q4Q5Q6Q7Q8Q9

1CCCCCCCCCCCCA

¼

0BBBBBBBBBBBB@

K11 K21 K31 K41 K51 K61 K71 K81 K91K12 K22 K32 K42 K52 K62 K72 K82 K92K13 K23 K33 K43 K53 K63 K73 K83 K93K14 K24 K34 K44 K54 K64 K74 K84 K94K15 K25 K35 K45 K55 K65 K75 K85 K95K16 K26 K36 K46 K56 K66 K76 K86 K96K17 K27 K37 K47 K57 K67 K77 K87 K97K18 K28 K38 K48 K58 K68 K78 K88 K98K19 K29 K39 K49 K59 K69 K79 K89 K99

1CCCCCCCCCCCCA

0BBBBBBBBBBBB@

E1E2E3E4E5E6E7E8E9

1CCCCCCCCCCCCA

K11 ¼ Q1=E1; K44 ¼ Q4=E4K12 ¼ ½ð1� Q1=E1ÞQ2�=XK15 ¼ ½ð1� Q1=E1ÞQ5�=XK17 ¼ ½ð1� Q1=E1ÞQ7�=XK42 ¼ ½ð1� Q4=E4ÞQ2�=XK45 ¼ ½ð1� Q4=E4ÞQ5�=XK47 ¼ ½ð1� Q4=E4ÞQ7�=Xwhere X ¼ Q2þ Q5þ Q7;

K22 ¼ K55 ¼ K77 ¼ K99 ¼ 1

At the beginning of EDM process, both primary and secondarydistribution is in transient state. A steady state energy distribution,appear after a certain period, depending on the operating condi-tions, where the heat stored in the electrodes approaches zero andcan be neglected in drawing up the energy balance for steady states

as shown in Fig. 3. The portions of the energy stored in the work-piece, electrode and the dielectric fluid become significant if theenergy distribution is evaluated from the start of the experiment.

4.1. Calculation of the secondary energy distribution

It is not possible to calculate primary energy distributionexperimentally, so first secondary energy distribution is foundusing simple heat transfer equations and then using Konig [21]model secondary energy is converted into primary energy whichis then calculated as percentage fraction of input energy. Anumerical evaluation of the temperature as a function of time andof a single space coordinate enables calculation of the abovementioned components of the secondary energy distribution. Heatstored in workpiece and electrode is given below:

Q3;6 ¼ prcr2lf1=2½ðq1 � q2Þ$ð11 �13=12Þþ q1 þ q2� � qog (18)

Heat stored in the dielectric fluid Q8 is calculated by similarlinearization of the temperature profile in the dielectric fluid. Nowafter calculation of the stored energy from the start of machining to

the momentary time of measurement tx, the energy stored per unitof time is approximately obtained from:

Q:

3;6;8 ¼ �Q3;6;8ðtxÞ � Q3;6;8ðtx�1Þ

� ðtx � tx�1Þ (19)

Fig. 3. Variation of energy with respect to time [21].


Q3:

andQ6:

become negligible after a certain time tx. Thus thetransition region from transition to steady state can be determinedfrom the heat stored in the electrodes.

Heat conducted by the workpiece and electrode in the axialdirection is given below:

Q:

2;5 ¼ pd2W;EkW;Eðq1 � q2Þ=4l2 (20)

Heat stored in eroded and worn particles is given below:

Q:

1;4 ¼ VW;Ercðqd1 � qoÞ (21)

Heat conduction in the dielectric fluid is given below:

Q:

7 ¼ 2pkdhdðqd1 � qd2Þ=ln ðrd2=rd1Þ (22)

The residual energy Q9:

is given below:

Q:

9 ¼ Inputenergy� sumof all other energycomponents (23)

Fig. 4. Schematic diagram of experimental set-up of EDM with

Energy required to melt and evaporate the eroded particles iscalculated as:

E:

1;4 ¼ VW;E$r$ncsolidðqM � qOÞ þ Sþ KV

hcliquidðqV � qMÞ þ R

io

(24)

The components of primary energy distribution are taken aspercentage fraction of input energy:

My ¼ Ey:

Win

: y ¼ 1; 2; 3; ::::; 9 (25)

The components of the fraction of primary energy distributionare defined by the following:

� M1 - fraction of energy for erosion/removal of workpiece� M2 - fraction of energy conducted through the workpiece� M3 - fraction of energy stored in the workpiece� M4 - fraction of energy for erosion/removal of electrode� M5 - fraction of energy conducted through the electrode� M6 - fraction of energy stored in the electrode� M7 - fraction of energy conducted by the dielectric fluid� M8 - fraction of energy stored in dielectric fluid� M9 - fraction of residual energy losses

Some of the assumption to be made during calculation of elec-trical discharge machining:

� The electrodes and the dielectric fluid are considered ascontinuum in calculating the stored and conducted heats.

� It is assumed that the radial conduction in the electrodes andthe axial conduction in the dielectric fluid are neglected withrespect to the axial and radial components respectively.

� The relative frequency h ¼ 1, used in Eq. (8) to calculate inputenergy,

Insulating dielectric container, workpiece and electrode.

Table 1Fixed parameters.

Voltage 60 VPulse Interval (Off time, to) 20 msPolarity Straight or Positive polarity:

Workpiece - Anode (positive)Electrode - Cathode(negative)

Fig. 5. Specimen of workpiece and electrode with insulation and thermocouples.


� It is assumed that all the erosion during process is due tomelting and the energy due to evaporation is negligible.

5. Experimental seteup

During this study, a series of experiments on EDM of Tungsten-Carbide(P20-grade) were conducted by using die sinking electricaldischarge machine (Electronica made Model EMS 60A), usingCoppereTungsten as tool electrode. Commercially availableKerosene oil was used as dielectric fluid during all the experimentsin a specially designed and fabricated insulated tank. The sche-matic diagram of the EDM set-up is shown in Fig. 4. To minimize

Fig. 6. Schematic drawing of workpiece and electrode with insulation (1,2, 3, 4 are thepositions of thermocouples).

the heat loss, insulation of glass wool was provided on the walls ofthe tank and the lateral surface of electrode and workpiece werecovered with Teflon insulation such that they were exposed to theEDM process on their upper surface as shown in Fig. 5. Thetemperature at different locations of electrode, workpiece anddielectric fluid was measured by J-type Iron/Constantan thermo-couples, with a range of �40 �C to 750 �C. The Thermocoupleswere attached to temperature indicators which directly measurethe temperature with a resolution of 0.1 �C. The Thermocoupleswere inserted in the space provided in the Teflon insulation atpoints 1,2 around workpiece and 3,4 around electrode at distanceof l1, l2, l3 as shown in Fig. 6. q1and q2 are the temperature ofworkpiece at upper and lower end and q3and q4are temperature ofelectrode at lower and upper end as shown in Fig. 5. Also Ther-mocouples were fixed in the specially made fixture to measure thetemperature of dielectric fluid at different locations, qd1 qd2are thetemperature measured in dielectric fluid as shown in schematicdiagram in Fig. 4.

5.1. Process parameters

The range of parameters have been selected with the help ofpast work on Tungsten-Carbide workpiece, where the experimentscan be conducted without facing the hindrance of arcing etc. Theprocess parameters are of two types i.e. Fixed parameters, whichare kept fixed or constant during all the experiments and Variableparameters, which varies with every experiment, so as to find theoptimum parameters where there is a better utilization of energyas shown in Tables 1 and 2 respectively.

6. Experimental procedure

Experiments on Tungsten-Carbide as workpiece material werecarried out using different machining parameter settings, withCoppereTungsten as tool electrode. Temperatures of the individualmeasuring points were measured with the help of Thermocouplesbefore each experiment as well as after different machiningduration of the process. The time of machining has been noted onthe monitor of the electrical discharge machine, and theobservations are given in Tables 3 and 4. The material removalrate MRR, in mm3/min. has been calculated at the time wheresteady state temperature is obtained using the results of Tables 3and 4. The MRR at different current density and at different pulseduration after achieving the steady state condition is given inTable 3. Material removal rate was calculated by measuring thediameter and depth of the cavity in workpiece machined duringEDM machining. During machining the variation in peak currentwas controlled manually by percentage setting knob. Also at the

Table 2Variable parameters.

Discharge current (A) 4 10 16 24Pulse Duration (ms) 25 50 100 200

Table 3Experimental readings for workpiece to calculate energy distribution.

Voltage (V) e 60 V, off time(to) e 20 ms, initial temperature qo ¼ 28 �C

Current (I), a Pulse Duration(ms) MRR (mm3/min.) q1oC q2

oC qd1o C qd2

o C l1w (mm) L2w (mm) L3w (mm)

4 25 0.46 52.4 35.5 35.6 32.9 11.52 36 2.244 50 0.65 63.7 37.4 36.8 34.1 11.18 36 2.244 100 0.81 76 40.1 38.3 36.2 10.75 36 2.244 200 0.63 81.4 43.3 41 38.9 10.42 36 2.2410 25 0.603 56.6 40.3 35.3 32.5 10.06 36 2.2410 50 1.02 63.4 40.9 37.1 34.3 9.56 36 2.2410 100 1.62 77.3 50.8 39.4 37 8.7 36 2.2410 200 1.772 82.2 54 39.4 36.9 7.76 36 2.2416 25 0.94 58.2 40.5 39.4 38.7 7.26 36 2.2416 50 1.32 66.3 41.8 39.5 38.7 6.56 36 2.2416 100 1.7 78 48.8 40.4 39.6 5.66 36 2.2416 200 1.51 86.7 54.2 40.4 39.6 4.86 36 2.2424 25 3.09 76.3 63.2 45.3 44.6 9.83 36 2.2424 50 4.19 75.4 60.1 45.1 44.3 7.48 36 2.2424 100 4.95 88.2 70.1 45.2 44.2 4.91 36 2.2424 200 4.3 112.3 93.4 46.2 45.7 2.66 36 2.24


same time volume of material eroded from electrode (mm3/min.)has been calculated. At steady state the temperature of electrodeand workpiece is almost constant with machining duration andstored energy is negligible, due to transition of primary energy tosecondary energy. The results obtained at steady state were used tocalculate secondary distribution of input energy by using heattransfer equations, given in section 4.1 and the results are given inTable 5.The primary energy distribution has been calculated fromsecondary distribution by the using the equations given in section4,with the help of Matlab Software, the results are given in Table 6.The fraction (in percentage of input energy from M1 to M9) ofprimary energy distribution was calculated from secondary distri-bution, given in Table 7. The above procedure to calculate energydistribution was repeated by varying pulse duration (on time) andinput discharge current with discharge voltage and pulse interval(off time) were held constant at 60 V and 20 ms respectively. Alsostraight or positive polarity was used i.e. workpiece as anode(positive) and tool electrode as cathode (negative) for allexperiments.

6.1. ANOVA analysis of variance

To find the suitability of the experiments conducted, two wayANOVA analysis have been performed with the help of MINITABsoftware, on selected significance factors, using data given in

Table 4Experimental readings for electrode to calculate energy distribution.

Voltage (V) e 60 V, off time(to) – 20ms, initial temperature qo ¼ 28 �C

Current (I), A Pulse Duration(ms) q3oC q4

oC

4 25 44.3 36.44 50 50.1 39.34 100 53 40.24 200 61.9 43.610 25 45.3 37.310 50 52.3 39.110 100 63.3 42.410 200 68.9 44.216 25 47.4 3516 50 60.5 39.316 100 70.4 42.416 200 75.9 44.624 25 72.3 61.124 50 84.4 62.324 100 90.3 6224 200 109.6 72.3

Table 7. The results are given in Table 8. The degree of freedom isthree as expected and the P value varies is near to zero from0 to0.021, indicating that experiments performed are within standardacceptable limits of 5%.

7. Results and discussion

The machining parameters studied are the pulse duration andcurrent, whilst the machining response factors evaluated arematerial removal rate (mm3/min), and specific material removalrate, percentage fraction of distribution of primary energy distri-bution. Specific material removal rate is calculated as materialremoval rate (MRR) divided by input discharge current. Theexperimentation has two stages, i.e. unsteady state and steadystate. During steady state the temperature of electrode and work-piece is almost constant with machining duration and storedenergy is negligible as shown in Fig. 3. The results have been pre-sented in graphical forms for the purpose of comparison anddiscussion.

7.1. Effect of pulse duration

7.1.1. Material removal rateThe variation in MRR and specific MRR for different pulse

duration and at different current density, when machined, at a gap

qd1o C qd2

oC l1E(mm) L2E(mm) L3E(mm)

35.6 32.9 7.89 26.6 4.936.8 34.1 7.64 26.6 4.938.3 36.2 7.28 26.6 4.941 38.9 6.9 26.6 4.935.3 32.5 6.79 26.6 3.937.1 34.3 6.53 26.6 3.939.4 37 6.16 26.6 3.939.4 36.9 5.77 26.6 3.939.4 38.7 5.4 26.6 4.939.5 38.7 4.65 26.6 4.940.4 39.6 3.76 26.6 4.940.4 39.6 2.86 26.6 4.945.3 44.6 5.27 26.6 1.945.1 44.3 4.27 26.6 1.945.2 44.2 3.05 26.6 1.946.2 45.7 1.45 26.6 1.9

Table 5Secondary energy distribution.

Voltage (V) e 60 V Workpiece Electrode Dielectric Residualenergy(Watts)

Off time(to) �20 ms

Pulseduration(ms)

Energy storedin erodedparticles fromworkpiece (Watts)

Energy conductedthroughworkpiece (Watts)

Energy storedin workpiece(Watts)

Energy stored inworn particlesfrom electrode(Watts)

Energy conductedthrough electrode(Watts)

Energy storedin electrode(Watts)

Energy conductedthrough dielectricfluid (Watts)

Energy storedin dielectricfluid (Watts)

Current (I), A Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9

4 25 0.25 � 10�3 1.12 1.11 � 10�3 0.957 � 10�3 3.38 1.22 � 10�3 0.52 1.764 126.544 50 0.40 � 10�3 1.74 2.11 � 10�3 0.252 � 10�3 4.62 2.26 � 10�3 0.52 4.415 160.134 100 0.60 � 10�3 2.37 2.36 � 10�3 0.425 � 10�3 5.48 2.46 � 10�3 0.4 5.298 186.444 200 0.58 � 10�3 2.51 2.38 � 10�3 0.569 � 10�3 7.83 2.59 � 10�3 0.4 5.787 201.6310 25 0.31 � 10�3 1.03 2.04 � 10�3 0.932 � 10�4 3.42 4.01 � 10�3 0.54 3.01 325.3210 50 0.65 � 10�3 1.49 4.15 � 10�3 2.71 � 10�4 5.65 8.12 � 10�3 0.54 7.42 413.510 100 1.30 � 10�3 1.75 6.89 � 10�3 4.78 � 10�4 8.95 14.76 � 10�3 0.46 9.13 479.6810 200 1.42 � 10�3 1.86 8.74 � 10�3 5.13 � 10�4 10.57 18.92 � 10�3 0.48 11.42 519.4116 25 0.76 � 10�3 1.168 6.55 � 10�3 0.483 � 10�3 5.31 5.99 � 10�3 0.134 3.53 523.1716 50 1.07 � 10�3 1.617 9.01 � 10�3 9.86 � 10�3 9.07 17.56 � 10�3 0.153 10.587 664.2416 100 1.50 � 10�3 1.93 11.29 � 10�3 1.27 � 10�3 11.98 21.48 � 10�3 0.153 12.984 775.3216 200 1.32 � 10�3 2.145 13.35 � 10�3 1.28 � 10�3 13.396 23.72 � 10�3 0.153 14.976 844.6324 25 3.0 � 10�3 0.87 13.41 � 10�3 0.89 � 10�3 4.82 3.97 � 10�3 0.134 11.77 788.8724 50 3.9 � 10�3 1.01 15.32 � 10�3 1.5 � 10�3 9.48 11.28 � 10�3 0.153 14.72 1003.224 100 4.6 � 10�3 1.2 19.33 � 10�3 1.8 � 10�3 12.17 14.75 � 10�3 0.1916 17.66 1168.7424 200 4.3 � 10�3 1.25 22.27 � 10�3 2.6 � 10�3 16.02 18.59 � 10�3 0.096 20.61 1271.1

Table 6Primary energy distribution.

Voltage (V) – 60 V Workpiece Electrode Dielectric Residualenergy(Watts)

Off time(to) e20 ms

PulseDuration(ms)

Energy for erosionof Workpiece(Watts)

Energy conductedthrough Workpiece(Watts)

Energy Storedin Workpiece(Watts)

Energy for erosionof Electrode (Watts)

Energy conductedthrough Electrode(Watts)

Energy Storedin Electrode(Watts)

Energy conductedthrough dielectricfluid (Watts)

Energy Storedin dielectricfluid (Watts)

Current (I), A E1 E2 E3 E4 E5 E6 E7 E8 E9

4 25 0.137 1.08 11.067 0.056 3.245 12.16 0.483 17.64 87.464 50 0.197 1.665 21.12 0.127 4.393 22.63 0.485 44.15 76.664 100 0.243 2.26 23.6 0.183 5.18 24.6 0.383 52.98 90.574 200 0.19 2.43 23.782 0.195 5.69 25.97 0.385 57.87 101.6710 25 0.181 1.031 20.399 0.0567 3.258 40.1 0.51 30.1 237.6910 50 0.306 1.39 41.499 0.1323 5.356 81.214 0.487 74.2 223.9810 100 0.486 1.655 68.85 0.1863 8.387 147.6 0.43 91.3 181.0910 200 0.532 1.779 87.436 0.195 9.941 189.217 0.457 114.22 141.6916 25 0.283 1.074 65.493 0.188 4.93 59.99 0.119 35.3 365.9516 50 0.398 1.46 90.033 0.381 8.45 175.54 0.138 105.87 299.8716 100 0.512 1.872 112.88 0.454 11.28 214.8 0.147 129.84 328.2216 200 0.454 2.078 133.53 0.462 12.55 237.12 0.145 149.76 336.6124 25 0.927 0.681 134.1 0.3 3.664 39.64 0.102 52.88 591.7624 50 1.257 0.878 153.2 0.513 7.41 112.84 0.111 147.17 605.2324 100 1.485 1.011 193.32 0.621 10.322 147.48 0.163 176.6 668.9324 200 1.29 1.116 222.68 0.81 16.084 185.95 0.086 206.04 676.81

H.Singh,D

.K.Shukla

/International

Journalof

Thermal

Sciences59

(2012)161

e175

169

Table

7Pe

rcen

tage

fraction

ofprimaryen

ergy

distribution

.

Voltage

(V)–60

VW

orkp

iece

Electrod

eDielectric

Offtime

(to)

e20

ms

Pulse

duration

(ms)

Energy

for

erosionof

workp

iece

(%)

Energy

conducted

through

workp

iece

(%)

Energy

stored

inworkp

iece

(%)

Energy

for

erosionof

electrod

e(%)

Energy

conducted

through

electrod

e(%)

Energy

stored

inelectrod

e(%)

Energy

conducted

through

dielectric

fluid

(%)

Energy

stored

indielectric

fluid

(%)

Residual

energy

(%)

Curren

t(I),A

M1

M2

M3

M4

M5

M6

M7

M8

M9

425

0.10

30.81

8.3

0.04

22.43

9.12

0.36

213

.23

65.603

450

0.11

50.97

12.32

0.07

42.56

13.2

0.28

125

.76

44.72

410

00.12

11.13

11.8

0.09

22.58

12.3

0.19

426

.49

45.293

420

00.08

71.11

10.9

0.08

92.61

11.9

0.17

726

.53

46.597

1025

0.05

50.31

6.12

0.01

70.98

12.03

0.15

9.03

71.308

1050

0.07

130.32

49.68

30.03

11.25

18.95

0.11

517

.313

52.263

1010

00.09

70.33

113

.77

0.03

81.68

29.52

0.08

618

.26

36.218

1020

00.09

750.32

616

.03

0.03

71.82

34.69

0.08

320

.94

25.977

1625

0.05

30.20

112

.28

0.03

60.92

11.25

0.02

16.62

68.62

1650

0.05

80.21

313

.13

0.05

61.23

25.6

0.01

915

.44

43.732

1610

00.06

40.23

414

.11

0.05

71.41

26.85

0.01

816

.23

41.027

1620

00.05

20.23

815

.30.05

31.44

27.17

0.01

717

.16

38.57

2425

0.11

60.08

513

.75

0.03

60.46

4.96

0.01

56.61

73.97

2450

0.12

20.08

5414

.89

0.05

0.72

10.97

0.01

314

.31

58.84

2410

00.12

50.08

616

.11

0.05

20.86

12.29

0.01

214

.72

55.75

2420

00.09

90.08

5517

.01

0.05

81.1

14.204

0.00

715

.74

51.7

Table 8Two-way ANOVA.

Source DF SS MS F P

Two-way ANOVA: M3 versus pulse duration, currentPulse Duration 3 0.633 16.8778 5.43 0.021Current 3 54.479 18.1596 5.85 0.017Error 9 27.955 0.1061Total 15 133.068Two-way ANOVA: M8 versus Pulse Duration, CurrentPulse Duration 3 286.709 95.5697 40.11 0.000Current 3 274.196 91.3986 38.36 0.000Error 9 21.442 2.3825Total 15 582.347

0

1

2

3

4

5

6

0 50 100 150 200 250

Mat

eria

l Rem

oval

Rat

e (m

m3/

min

.)

Pulse Duration (µs)

Material Removal Rate Vs Pulse Duration

4A

10A

16A

24A

Fig. 7. Effect of pulse duration on material removal rate.


voltage of 60 V, pulse interval of 20 ms is shown in Figs. 7 and 8. Ithas been seen observed that when the pulse duration wasextremely short, the amount of electrical discharge conducted intothe machining gap was very small. Therefore, the MRR was smallas can be seen in Fig. 7. Since the cemented carbide has highmelting point and for machining such a high melting pointsubstance the energy level should be high. This can be obtained byincreasing pulse duration till optimum condition is achieved. Ithas been seen that the highest value of MRR for tungsten-carbideis obtained for pulse duration of 100 ms and after that a downwardtrend is observed. The results are in agreement with the resultsobtained by other authors for machining of hard materials. Leeet al. [38e40] have also reported the similar nature in their workon EDM of tungsten-carbide over a wide range of current density.It is expected that the MRR should increase with increasing pulseduration because higher pulse duration may give rise to higher

0

0.05

0.1

0.15

0.2

0.25

0 50 100 150 200 250

Spec

ific

MR

R (

mm

3/m

in.A

)

Pulse Duration (µs)

Specific MRR Vs Pulse Duration

4A

10A

16A

24A

Fig. 8. Effect of pulse duration on specific material removal rate.

R² = 0.9986

R² = 0.9986

R² = 0.9977

R² = 0.9999

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 50 100 150 200 250

Fra

ctio

n of

pri

mar

y en

ergy

%

Pulse Duration(µs)

M1 Vs Pulse Duration

4 A

10 A

16 A

24 A

Fig. 9. Comparison between pulse duration and fraction of primary energy for erosionof workpiece for different current.

0

2

4

6

8

10

12

14

16

18

0 50 100 150 200 250

Fra

ctio

n of

pri

mar

y en

ergy

%

Pulse Duration(µs)


4 A

10 A

16 A

24 A

Fig. 11. Comparison between pulse duration and fraction of primary energy stored inworkpiece for different current.


electrode discharge energy which get accumulated at the surfaceand will rapidly melt and evaporate the substance. This unexpectedtrend is due to expansion of the plasma channel at high pulseduration. When the plasma channel becomes large, its energydensity decreases and the heat energy absorbed by the workpieceper unit area is reduced. This causes the reduction in MRR.

7.1.2. Percentage fraction of primary energy distributionThe effect of pulse duration on percentage fraction of primary

energy distribution for 4 A, 10 A, 16 A and 24 A current, is depictedin Figs. 9e12. The useful energy transferred for the erosion ofworkpiece (M1), calculated using heat transfer equations given inprevious section, at different currents and varying pulse durations,is shown in Fig. 9. The eroding energy increases steadily withincrease of pulse duration. This behaviour may be because for shortpulses, metal does not get enough time to get adequately heatedand almost no melting takes place and also the electrostatic forcesare the major cause of metal removal for short pulses and for longpulses melting becomes the dominant phenomenon. Also for shortpulses the dominant factors for energy losses are by ionization,excitation and evaporation. The result shows that with a pulseduration longer than 100 ms, this energy decreases or almostconstant. A further increase of pulse duration does not givea significant erosion increase, since the additional energy suppliedis lost in maintaining the channel, further heating of moltenmaterial, evaporation of dielectric fluid and conduction by systemelements. The large pulse durationwill expand the plasma channel,that leads to decrease in energy density and the heat energyabsorbed by theworkpiece per unit area is reduced. This also causesthe reduction in MRR as shown in Fig. 7. Also the erosion energy

0

0.02

0.04

0.06

0.08

0.1

0.12

0 50 100 150 200 250

Fra

ctio

n of

pri

mar

y en

ergy

%

Pulse Duration(µs)


4 A

10 A

16 A

24 A

Fig. 10. Comparison between pulse duration and fraction of primary energy for erosionof electrode for different current.

follows the same trend as of specific material removal rate asshown in Fig. 8. The effect of pulse duration on energy stored inworkpiece and electrode is shown in Figs. 11 and 12 respectively.For all pulse durations the energy stored in theworkpiece is highestand stored in electrode is lowest for 24 A current, which isfavourable trend.

This data is helpful for the proper utilization of energy observedin this study. Also for all experimental settings the fresh dielectric isused to avoid any errors in the readings.

7.2. Effect of current

7.2.1. Material removal rateThe variation in MRR at different current density, when

machined for different pulse duration, at a gap voltage of 60 V,pulse interval of 20 ms is shown in Fig. 13. It is observed that there isno significance increase in MRR up to 16 A current. The MRR isconsiderably increased at 24 A current as compared to MRR at 4, 10and 16 A for all pulse levels. Steep rise from 2 to 3 times, in MRR isobserved from 16 to 24 A indicate that melting and evaporation ofmaterial is on higher side in this range of current. It is mainly due tothe fact that in the beginning the energy is consumed in conductionof workpiece, electrode and dielectric. The saturation point isreached at the level of 16 A current and after this level when thecurrent is increased to next level of 24 A the energy supplied to thesystem is consumed for removal of material from the workpiece.This leads to steep rise in MRR. Singh et al. [49] have reported

Fig. 12. Comparison between pulse duration and fraction of primary energy stored inelectrode for different current.

0

1

2

3

4

5

6

0 5 10 15 20 25 30Mat

eria

l Rem

oval

Rat

e (m

m3/

min

.)

Current (Ampere)

Material Removal Rate Vs Current

25µs

50µs

100µs

200µs

Fig. 13. Effect of current on material removal rate.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 5 10 15 20 25 30

Fra

ctio

n of

pri

mar

y en

ergy

%

Current (Ampere)

M1 Vs Current

25 (µs)

50 (µs)

100 (µs)

200 (µs)

Fig. 14. Comparison between current and fraction of primary energy for erosion ofworkpiece for different pulse duration.

0

2

4

6

8

10

12

14

16

18

0 5 10 15 20 25 30

Fra

ctio

n of

pri

mar

y en

ergy

%

Current (Ampere)

M3 Vs Current

25 (µs)

50 (µs)

100 (µs)

200 (µs)

Fig. 16. Comparison between current and fraction of primary energy stored in work-piece for different pulse duration.


a steep rise in MRR beyond 9 A discharge current for EN-31 alloy.Lee et al. [38] have also reported a similar trend in machining ofWC. They have also observed that MRR increases rapidly beyond 16A current up to 32 A. After that increase is not so rapid. Resultsobtained in this work are also in similar lines as reported by Leeet al. [38e40].

7.2.2. Percentage fraction of primary energy distributionThe effect of current on percentage fraction of primary energy

distribution is depicted.in Figs. 14e17, for different pulse duration,

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 5 10 15 20 25 30

Fra

ctio

n of

pri

mar

y en

ergy

%

Current (Ampere)

M4 Vs Current

25 (µs)

50 (µs)

100 (µs)

200 (µs)

Fig. 15. Comparison between current and fraction of primary energy for erosion ofelectrode for different pulse duration.

at a gap voltage of 60 V. The effect of current on the energytransferred for erosion of workpiece is shown in Fig. 14. The energyfor erosion decreases up to lowest 0.05%with increase of current till16A and then increases and is maximum for 24 A for all pulsedurations. The variation is 0.05%e0.12%, i.e. total variation is 0.07%at all pulse duration levels. Though this variation is very little bututilization factor for 200 ms is less because of expansion of plasmachannel. For 24A this useful energy is maximum for 100 ms andminimum for 200 ms. Also the amount of material removal isproportional to the energy used for erosion and energy inputdepends upon current and pulse duration and hence the energyused for erosion follows the curve similar to specific materialremoval rate for all currents as shown in Fig. 8. The energy forunwanted wear of tool electrode decreases till 10A and thenincreases and for 24 A current it is maximum for 200 ms as shown inFig. 15. The percentage utilisation energy for tool electrode variesfrom 0.04 to 0.09% at 4 A and 0.04e0.06% at 24 A with variation inpulse duration. The effect of current on stored energy in workpieceand tool electrode is shown in Figs. 16 and 17 respectively. Thestored energy increases to a maximumwith increase of current forboth workpiece and electrode, except for decrease in stored energyin workpiece between current of 4 A and 10 A and for 25 ms and50 ms pulse duration and for more than 10 A current an increasingtrend is observed for all pulse durations. For electrode there isa variation of only 5% at 25 ms pulse duration as the current isincreased from 4 to 24 A current. At 16 A current all the pulseduration showed maximum. At 200 ms pulse duration more than30% stored energy is observed.

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30

Fra

ctio

n of

pri

mar

y en

ergy

%

Current (Ampere)

M6 Vs Current

25 (µs)

50 (µs)

100 (µs)

200 (µs)

Fig. 17. Comparison between current and fraction of primary energy stored in elec-trode for different pulse duration.

0

5

10

15

20

25

30

0 50 100 150 200 250

Fra

ctio

n of

pri

mar

y en

ergy

%

Pulse Duration(µs)

Energy Distributed to Workpiece, Electrode and Dielectric Fluid Vs Pulse Duration 4A

Workpiece

Electrode

Dielectric Fluid

Fig. 18. Comparison between pulse duration and fraction of primary energy distri-buted between workpiece, electrode and dielectric fluid for current of 4 A.

0

5

10

15

20

25

30

35

40

0 50 100 150 200 250

Fra

ctio

n of

pri

mar

y en

ergy

%

Pulse Duration(µs)


Workpiece

Electrode

Dielectric Fluid


02468

101214161820

0 50 100 150 200 250

Fra

ctio

n of

pri

mar

y en

ergy

%

Pulse Duration(µs)


Workpiece

Electrode

Dielectric Fluid



7.3. Energy distribution in workpiece, electrode and dielectric fluid

The comparison between energy distributed between work-piece, electrode and dielectric fluid for current of 4 A, 10 A, 16 A and24 A at varying pulse duration is given in Figs.18e21 respectively. Itis shown that useful energy i.e. energy which is transferred toworkpiece (sum of eroding energy, stored energy and conductedenergy) varies with current and pulse duration between 6.5% and17.7% as calculated from Table 7. It reaches to maxima and maxima

0

5

10

15

20

25

30

35

0 50 100 150 200 250

Fra

ctio

n of

pri

mar

y en

ergy

%

Pulse Duration(µs)


Workpiece

Electrode

Dielectric Fluid


is attained at low pulse duration for low current than for highercurrent. It is observed that for 4 A current as shown in Fig. 18.,theenergy transferred to dielectric fluid is maximum as compared toworkpiece and electrode, and energy increases from 25 to 50 mspulse duration in workpiece and electrode, after that it remainsnearly constant. These results are not in agreement with normalrequirement for machining as the energy utilisation for the work-piece should be more. It is observed that for and 16 A current, asshown in Figs. 19 and 20 repectively the maximum energy isconsumed by the electrode. These results are in the reverse order ofnormal requirement, i.e. to optimise the process the energy uti-lisation by workpiece should be more as compared to electrode.Theese results are for straight polarity, so reverse polarity can beconsidered to improve the results. For 24 A current, as shown inFig. 21, useful energy towards workpiece is highest and unwantedenergy towards electrode is lowest for all pulse durations except at200 ms due to arcing. In order to have maximum utility of energy,the useful energy towards workpiece material should be more,which is obtained for 24 A current for all pulse durations this is wellin agreement with the observations of the authors’ experiments onMRR shown in Fig. 13.

8. Conclusions

From the results obtained on energy distribution, it is observedthat the energy effectively transferred to the workpiece duringEDM process, varies with discharge current density and pulseduration, and is of a small percentage of total energy. The rest of theenergy leads to unwanted wear of electrode, in the dielectric fluidand also lost in the radiations. The results obtained in the study forenergy transferred to electrodes will help to develop theoreticalmodeling and to improve the precision of existing EDM models formaterial removal rate and crater geometry, as all existing thermo-physical models are considering the fraction of energy transferredto electrodes as an important parameter. This study will also helpfor training and testing of the neural based EDM process models.The optimum parameters obtained by Lee [38e40] for Tungsten-carbide workpiece experimentally, are due to the effective utiliza-tion of energy distributed as reported in this study.

The main conclusion of this work is as follows:

1. The energy effectively transferred to the workpiece duringEDM process is small percentage of total energy, it varies withcurrent and pulse duration from 6.5% to 17.7%, as against the50% energy used in many EDM models.

2. The prediction of Joshi [2] model is confirmed that fraction ofenergy transferred to workpiece varies with discharge current


and pulse duration and this study will help to increase theprecision of theoretical models.

3. This study will help in prediction of optimum parameters usingexisting thermo-physical models by using the values of currentand pulse duration where maximum fraction of energy istransferred to workpiece.

4. The effective energy distributed to workpiece increases withthe increase in pulse duration at high current and the optimumutilization of energy is at 24 A current. The effective utilizationof energy is less for low current (4 A) than for higher current,but if pulse duration is considered it is find that the optimumpulse duration at which utilization of energy is maximum alsodecreases with the decrease of current.

5. For fine machining (low current) optimum utilization of energyis at low pulse duration as compared to the rough machining(high current), it is at high values of pulse duration.

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Nomenclature

C: specific heatD: diameterEy: component of primary energy distributionfp: pulse frequencyh: depth of dielectric fluidI: average discharge currentK: Heat conductivityKv: fraction of eroded material which is evaporated


Kyz: coefficientsL: lengthMy: percentage fraction primary energy distributionQz: component of secondary energy distributionR: latent heat of evaporationR: radiusRyz: coefficientsS: latent heat of meltingT: timet0: off timeti: pulse durationV: average discharge voltageVW,E: erosion and wear volumetric rate (respectively)We: pulse energy

Win: energy input

Greek symbolsh: Relative frequencyq: Temperaturer: Density

Subscriptsd: dielectric fluidE: electrodeM: meltingo: initialv: evaporationw: workpiece

Documents

Optimizing electric discharge machining parameters for tungsten-carbide utilizing thermo-mathematical modelling