Experimental study of distribution of energy during EDM process for utilization in thermal models

International Journal of Heat and Mass Transfer 55 (2012) 5053–5064

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International Journal of Heat and Mass Transfer

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Experimental study of distribution of energy during EDM process for utilizationin thermal models

Harminder Singh ⇑Guru Nanak Dev University, Regional Campus, Jalandhar, Punjab 144 007, India

a r t i c l e i n f o a b s t r a c t

Article history:Received 3 September 2010Received in revised form 25 April 2012Accepted 27 April 2012Available online 1 June 2012

Keywords:Energy distributionSinking electro discharge machiningEDMMathematical model

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Electrical discharge machining (EDM) has steadily gained importance over the years because of its abilityto cut and shape a wide variety of materials and complicated shapes with high accuracy. The effective-ness of the EDM process is evaluated in terms of the material removal rate, relative wear ratio and thesurface roughness of the work piece. The input discharge energy during this process is distributed to var-ious components of the process, which further influences the material removal rate and other machiningcharacteristics like surface roughness. Since during this process the electrical energy is converted intoheat energy, hence the theoretical modeling of this process is based upon the heat transfer equationsand in all existing thermal models the fraction of the energy transferred to the workpiece, is one ofthe important parameters. The accurate prediction of the fraction of energy effectively transferred tothe workpiece will help to reduce the errors of the thermal models. In this study experiments have beenperformed to study the percentage fraction of energy transferred to the workpiece utilizing heat transferequations, at different EDM parameters. This study also relates the optimum parameters with the opti-mum utilization of input discharge energy and hence will help to improve the technological performanceof this process.

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1. Introduction

Electric discharge machining (EDM) is a most popular materialremoval technique based upon the concept of material removalfrom a metallic part by electric discharges. The emergence of elec-trical discharge (EDM) from an innovation to a highly practical andprofitable process is clearly reflected in its numerous applicationsand the challenges being faced by the modern manufacturingindustries from the development of new materials that are hardand difficult-to-machine such as carbides, composites, ceramics,super alloys, stainless steels, heat resistant steel, etc. These materi-als are widely used in die and mould making industries, aerospace,aeronautics, and nuclear industries, owing to their high strength toweight ratio, hardness and heat resisting qualities [1–3]. This non-contact machining technique has been continuously evolving froma mere tool and die making process to a micro/nano scale manufac-turing applications [4,5]. It is about exploiting the very real poten-tial of an expanding market for familiar sized parts with tiny addedfeatures of unprecedented accuracy and is attracting a significantamount of research interests [6]. Since the discovery of EDM pro-cess nearly six decades ago by Russian scientists Lazarenkos, with

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the help of a young researcher Zolotykh, the researches andimprovements of the process are still going on to enhance thecapability of this process by identifying the basic physical pro-cesses involved during the process and hence a comprehensivequantitative theory concerning the mechanism of material removalby spark erosion is yet to be formulated [1–10]. From the last fewyears extensive research has been taking place in the area of ther-mal modeling for accurate prediction of machining characteristicslike MRR, surface roughness, but still there is no complete and def-inite model explaining in all details the different processes thattake place during a discharge in EDM process [1,2,11–17].

It is generally accepted that modeling of EDM discharge is basi-cally a thermal erosion process where heat transfer takes place.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 based on the equations of heat conduction into solids areavailable. The shape of the generated craters, crater depth andhence material removal rate and surface roughness can be esti-mated from these thermal models.

The erosion by an electric discharge involves phenomena such asheat conduction, energy distribution, melting, evaporation, ioniza-tion, formation and collapse of gas bubbles in the discharge channel.The complicated phenomenon, coupled with surface irregularities

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5054 H. Singh / International Journal of Heat and Mass Transfer 55 (2012) 5053–5064

of electrodes, interaction between two successive discharges, andthe presence of debris particles, make the process random in timeas well as space and therefore, deterministically derived thermalmodels yield results that do not match favourably with the experi-mental evidence. If we see from the perspective of machining en-ergy, each pulse during the discharge process is an output ofenergy and the input discharge current together with dischargeduration and relatively constant voltage for given workpiece andtool electrode materials is representative of the energy per pulse ex-pended in the spark gap region. The total energy depends on thenumber of sparks each second and the amount of energy in eachspark. The electrical energy supplied during this process is con-verted into heat energy and this energy is distributed between thevarious components of the system (workpiece, tool electrode anddielectric fluid) and is shared by large number of physical processesoccurring during the main stages (ignition, main discharge, melting,evaporation, and expulsion) of EDM process [1,2,11–17]. Salonitieset al. [13] reported that the fraction of the generated heat enteringthe electrode and the actual effective removal energy depends onthe thermal properties like melting point, density, specific heat,thermal conductivity and yield strength of the electrode, distancebetween the electrodes, flushing pressure, conductivity of thedielectric, discharge current and discharge on time.

Several investigators [1,2,11–30] show that the energy distribu-tion in the EDM processes influences the material removal rate(erosion of workpiece per unit time), relative wear ratio and thesurface roughness of the EDM machined surface and the effectiveor useful energy is the part of energy which is distributed towardsworkpiece to be machined.

In general, the material removal rate and machining characteris-tics during the EDM process depend on the distribution of the en-ergy supplied to the gap by the electrical current, shape and sizeof the discharge channel and also on the properties of the dielectricfluid and electrode material, such as melting point, density, specificheat, thermal conductivity, yield strength, etc. Hence, differentmaterials even when they are machined under the same machiningconditions would result in different machining characteristics, re-sults in less accurate thermal models. Though the percent fractionof energy that transferred to the workpiece, which is one of theimportant parameters of thermal modeling, also depends uponthe type of electrode materials, but it is extremely difficult to con-clude and pinpoint a concise and definite physical quantity that canfully reflect the material properties, and use it to predict machiningcharacteristics. Various thermal models proposed for EDM hadshown that the complexities and the stochastic nature of multipledischarges render difficulties in analyzing the process theoretically.

2. Modeling of the heat source of EDM process

The thermal analysis of the EDM process considered the con-duction as the primary mode of heat transfer between the ions ofplasma and the molecules of the electrode [12]. A number of sim-plified thermo-mathematical models of the EDM process based onthe equations of heat conduction into solids are available. How-ever, a generally accepted theory does not yet exist because ofthe complicated nature of metal removal mechanism accompany-ing the electric discharge in the dielectric medium.

Almost all existing models used the Fourier heat conductionequation as the governing equation with suitable boundary condi-tions [16]:

o2Tor2 þ

1r

oTorþ o2T

oZ2 ¼1a

oTot

ð1Þ

where T is the temperature (K), r is the radial axis (m), z is the ver-tical axis (m), t is time (s), and a is thermal diffusivity of the mate-rial (m2/s) which can be written as:

a ¼ Kt

qCp

where Kt is the thermal conductivity of the material (J/mK s), q isthe material density (kg/m3) and Cp is the specific heat (J/kg K).

If the melting heat is also considered then the thermal diffusiv-ity is given as:

a0 ¼ Kt

qðCp þm=TmÞ

where m is the latent heat of melting (kJ/kg) and Tm is the meltingtemperature (K) [16].

The important parameters which contribute to the accurateprediction by EDM models include the amount of heat input, radiusof plasma spark and the thermo-physical properties of the material[12]. The theoretical prediction of heat input is based upon the ide-alized geometrical shapes of the heat source (discharge channel).Earlier models are based upon the shape of the heat source pro-posed by Zingerman [22–25] viz., point heat source, plane heatsource and circular heat source having a finite radius.

2.1. Plane heat source

If the heat source is assumed to have an infinitely large radius,the heat flow problem can be reduced to a uni-dimensional prob-lem. Zingerman [25] gives the solution of Eq. (1) for plane heatsource as:

TðtÞ ¼ ðccÞ1=2

8ðpkÞ3=2

Zs

dSZ t

0Qtðt � sÞ�3=2exp � r2

4a2ðt � sÞ

� �ds ð2Þ

2.2. 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[25] and Zolotykh [26] used this model and find a very close rela-tion between experimental and theoretical results.

Zingerman [25] gives the solution of Eq. (1) for circular heatsource as:

TðtÞ ¼ ðccÞ1=2

8ðpkÞ3=2

Z b

0xdx

Z t

0Qtðt � sÞ�3=2exp

"� h2 þ x2

4a2ðt � sÞ

#ds ð3Þ

2.3. 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 Zinger-man [25] gives the solution of Eq. (1) for point heat source as:

Tðr; tÞ ¼ cc8ðpkÞ3=2

Z t

0Qtðt � sÞ�3=2exp � r2

4a2ðt � sÞ

� �ds ð4Þ

Hocheng [20] gives the solution for induced temperature for instan-taneous point heat source as:

T � To ¼ P

8ðpatÞ3=2 eð�r2=4atÞ where P is energy intensity ð5Þ

In these equations coefficient of volume specific heat ‘c’ is used,which will differ at the temperature of diffusion from the samecoefficient at normal temperature like difference of only 2% is forcopper and by 1% for aluminium.

The solution of these mathematical relations is based upon theknown amount of heat evolved per unit time [24,25]. Earlier EDMmodels like proposed by DiBitonto [31] have assumed point sourceand researchers Jilani [32,33], Beck [34,35], Dijck [36], Snoeys [37],

H. Singh / International Journal of Heat and Mass Transfer 55 (2012) 5053–5064 5055

assumed uniformly distributed heat flux. The heat flux generatedin the plasma channel and transmitted to the electrode for thepoint and disk heat source is defined as [16]:

q ¼FcVIpr2

c; disk heat source

FcVI2pr2 ; point heat source

(ð6Þ

where q is the heat flux (W/m2), V is the discharge voltage (V), I isthe discharge current (A), Fc is the fraction of energy transferredto the cathode, rc is the radius of the heat source at the cathode sur-face (m), and r is the radial distance from the origin (m).

These results are not in good agreement with the real condition,as neither is there a point heat source (like laser beam) nor is thereany uniform (constant) application of heat on the work piece andhence makes the reported models simple but less accurate in pre-dictions [12]. Recently, using spectroscopy techniques it is ob-served that the temperature distribution inside the plasmachannel during EDM process is not uniform [1,2,38].

The predictions of the models proposed recently by Izquierdo etal. [2] and Joshi et al. [12]are more accurate using Gaussian distri-bution of heat flux.

For Gaussian distribution, the heat flux q (W/mm2) at radial dis-tance ‘r’ from the axis of the spark (lm), as used by Joshi et al. [12]and Ali [1] for EDM model, is given by:

qðrÞ ¼ qoexp �4:5r

Rpc

� �2( )

ð7Þ

where the maximum heat flux qo can be calculated as:

q0 ¼4:57FcVI

pR2pc

where Fc is fraction of total EDM spark power going to the electrode(W); V is discharge voltage (V); I is discharge current (Amp) and Rpc

is plasma channel radius at the work surface (lm).Izquierdo et al. [2] gives the following Gaussian heat flux distri-

bution for thermal models of EDM:

qðrÞ ¼ QwUItON

2pRplasmaðtÞe�4:5ðr2=R2

plasmaÞ ð8Þ

where Qw is fraction of energy transferred to the workpiece.The heat input is defined by the amount of heat that is applied

to the workpiece and also by the shape of heat flux distribution andas shown in Fig. 1 the heat distribution becomes less steep as theplasma channel becomes wider. The �4.5 exponent used in theGaussian heat flux distribution equations (7) and (8) show how flatthe Gaussian heat flux is. For exponents lower than this value (�6for example) the heat flux distribution becomes steep, while forexponents with a value near zero it is very flat. The �4.5 value ofexponent used in these equations (7) and (8) for EDM thermalmodels is in good agreement with measurements obtained usingspectroscopy [2].

Using these equations it is possible to find the effect of the mag-nitude of the area of the heat source upon depth of crater. Theknowledge of the heat source area is necessary in order to verifythe theoretical derivations. The direct measurement of this areais impossible as the exact measurement of the plasma channel ra-dius Rplasma(Rpc) used in the Gaussian heat flux distribution equa-tions (7) and (8) is extremely difficult due to very high pulsefrequencies [1] or very short pulse duration of the few microsec-onds [12]. Different approaches have been proposed by theresearchers for calculating the plasma channel radius as:

(1) The time dependent plasma channel radius equation:

RplasmaðtÞ ¼ Rptn ð9Þ

where Rp is the constant defining the size of the plasma channel.

Different researchers used the different value of exponent ‘n’.Izquierdo [2] used the value of n = 0.2, Shuvra et al. [39], Philip etal. [40] proposed the value of n = 0.75(3/4).

(2) However, researchers [1] also proposed the time dependentequation of plasma channel radius as:

RspðtÞ ¼ KImtnon ð10Þ

where Rsp is plasma channel radius (lm), I is discharge current(Amp), ton = pulse on-time, exponents m, n and K are empiricalconstant.

Salonitis et al. [13], used the equivalent heat input radius ‘rs’ foruniform heat source intensity distribution

rsp ¼ 2040� ðIÞ0:43 � ðtonÞ0:44 ð11Þ

Joshi et al. [12] used the following approach for calculating plasmachannel radius:

Rpc ¼ ð2:04e� 3ÞI0:43t0:44on ðlmÞ ð12Þ

Using this value of Rpc in Eq. (7), the heat flux equation derived andused in thermal model for EDM by Joshi et al. [12] is,

qðtÞ ¼ 3:4878� 105FcVI0:14

t0:88on

exp �4:5t

ton

� �0:88( )

ð13Þ

Salonities et al. [13] numerically predicts the depth of the depres-sion crater as:

s ¼ qwts

qðLV þ cpðTs � ToÞÞð14Þ

where qw is the heat flux distribution.Using this theoretical prediction of depth of crater, the volume

removed per spark is determined, which is further used for estima-tion of material removal rate MRR and surface roughness. But forthis prediction geometrical shape of the crater needs to be assumed.DeBitonto [31] and Dijck [36] model assumed hemispherical cratercavity, Salonitis [13] used circular paraboloid geometry, Snoeys[37] and Beck [34,35] used bowl shape crater, Jilani [32,33] predictscrescent like shaped cavity. But these results are not in good agree-ment with the real condition. However, Joshi et al. [12] successfullyincorporated Gaussian distribution of heat flux with shallow bowlshaped cavity.

The depth of the crater depends solely; upon the dimensions ofthe discharge channel, upon the energy evolved in the dischargechannel, and upon the thermal properties of the metal. It is estab-lished (Eq. (14)) that the depth of a crater in EDM is determined bythat amount of heat ‘qw’ (Eqs. (6), (7), (8), (13)) which is transmit-ted to the metal from the discharge channel, for short and longgaps, for positive and negative polarity, for pulses with a durationof from several microseconds to several milliseconds, and formaterials with large and small values of heat conductivity.

It is shown that in all equations as discussed above, heat fluxdistribution qw depends upon the exact calculation of fraction oftotal EDM spark power going to the electrode Fc. This energy dis-tribution factor (Fc) is an important factor in the equations of qw

as it governs the amount of energy going to the electrodes. Rap-paz [41] explains that in order to reduce the average roughness ofEDM machined surface to values well below 100 nm, it is neces-sary to establish the precise energy distribution after a discharge.Yeo et al. [4] recommends that the thermo-physical models espe-cially based upon the disk heat source model can be improvedfurther if appropriate approximations are taken for the energyfraction, determined either empirically or theoretically. Variousvalues of Fc proposed in the literature. Rappaz [41] found thatthe 14.9% of energy effectively transferred to the workpiece (steelcylinder of DIN 1.2343 composition) during EDM process forI = 4 A and ti=25 ls. Izquierdo et al. [2] estimated Fc = 18.8% for

Fig. 1. Heat flux distribution as plasma channel expands [2,12].


given machining parameters, using inverse simulation techniqueof thermal models. Daryl and Philip [7,40] estimated that 8%and 18% of the total discharge energy is distributed into the cath-ode and anode respectively. The study explained qualitatively onthe grounds of electron emission theory that energy distributedto the anode and cathode changes with the pulse duration. Liao[18,42] gives a new concept of specific discharge energy (SDE) aquantity defining as the real energy required to remove a unitvolume of material and the materials having close value of SDEdemonstrate very similar machining characteristics. DiBitonto’smodel [31] assumed Fc = 0.18 (18%), while the Snoeys [37], Dijck[36], Beck [34,35], Jilani [32,33] models assumed Fc = 0.5 (50%).This assumption is one of the reasons of errors in the modelsfrom the experimental data. These assumptions are not in linewith the real EDM process and the prediction accuracy of thesemodels is less, as these models are assuming fixed value of Fc

for all machining parameters. The prediction accuracy of the ther-mo-physical model of Joshi et al. [12] improved by varying thevalues of fraction of discharge energy transferred to the work-piece with current and pulse duration. It was noted that it isessential to apply higher energy distribution factor for higher en-ergy zones. The study recommended energy distribution factors0.183 for lower energy zone (up to 100 mJ), while 0.183–0.2 formedium energy zone (100–650 mJ).

It is very difficult to predict theoretically the generally acceptedfraction of energy for thermo-physical models and due to apparentincongruities and conflicting data early researchers conjecturedthe same value of fraction of energy transferred to electrodes forall machining parameters in their models for numerically calculat-ing the volume and geometry of the crater formed. Hence, it is nec-essary to establish experimentally the precise distribution of inputdischarge energy during EDM process for different electrode mate-rial combinations and different machining parameters, for furtheruse in the theoretical thermal models.

So this study is planned to experimentally study the variation ofthis fraction of input discharge energy with the help of thermo-mathematical models suggested by Konig [21] during EDM ofTungsten-Carbide by varying the machining parameters currentand pulse duration. The data calculated in this study can be furtherused in the existing thermo-physical models, expecting to bringthe models preciously more close to the real conditions.

3. Energy distribution calculations

Konig [21] mathematical modeling is used, to calculate theenergy distribution in the material with the aid of the physicalproperties of the material, assuming heat transfer in EDM processis by conduction only and all the electric energy will be transferredinto heat on the material surface.

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

W in ¼Xn

x¼1

We ð15Þ

The input energy per unit time is as follows:

_W in ¼ VItifpg ð16Þ

where fp ¼ 1=ðti þ toÞ, ti – on time, to – off time.The input energy Win can be split among all modes of energy in

the primary energy distribution and appear in the three parts ofthe closed system: workpiece, tool electrode and dielectric fluidwith varying intensity and duration. The energy released in work-piece and tool electrode can be divided into conducted energy,stored energy and energy used in the erosion (of the workpiece)and the unwanted wear (of the tool electrode) (Fig. 2). Only storedand directly conducted energy are distinguished in the dielectricfluid. The remainder of the discharge which cannot be assignedto a particular element of the closed system appears as differentform of energy like radiation, light, sound etc. The components ofthe primary energy distribution are defined by the following: E1

– energy for erosion/removal of workpiece, E2 – energy conductedthrough the workpiece, E3 – energy stored in the workpiece, E4 –energy for erosion/removal of tool electrode, E5 – energy con-ducted through the tool electrode, E6 – energy stored in the toolelectrode, E7 – energy conducted through the dielectric fluid, E8 –energy stored in dielectric fluid, E9 – residual energies like radia-tion, light, sound or ionization.

Using above designations following energy balance can beobtained:

Xn

x¼1

_We ¼ _W in ¼X9

y¼1

_Ey ð17Þ

Fig. 2. Energy distribution during EDM process.


This primary energy distribution changes to the secondary distribu-tion due to conversion and transfer processes between the differentmodes of energy and various components of the system. For exam-ple, the energies E1 and E4, causing erosion and wear respectivelyare partly liberated by cooling subsequent to erosion. The majorportion of this energy is dissipated in the electrodes by conductionof heat and in the dielectric fluid by convection and radiation. Thesecondary energy distribution can be divided into two groups, cor-responding to the form of energy: All stored and conducted heatsare collected in the first group. These are relatively easily measur-able, e.g., by temperature sensors. The second group includes allother forms of energy that are not stored and given off in the formof heat, which are designated as residual energies and are difficultto measure. The components of the secondary energy distributionare defined by the following: Q1 – Heat stored in eroded (fromworkpiece) particles, Q2 – Heat conducted through the workpiece,Q3 – Heat stored in the workpiece, Q4 – Heat stored in worn (fromtool electrode) particles, Q5 – Heat conducted through the tool elec-trode, Q6 – Heat stored in the tool electrode, Q7 – Heat conductedthrough the dielectric fluid, Q8 – Heat stored in the dielectric fluid,Q9 – Residual energies like radiation, light & sound energies Thesum for all components of both distributions per unit of time isequal to the input energy:

_W in ¼X9

y¼1

_Ey ¼X9

z¼1

_Q z ð18Þ

Theoretically, the primary distribution is changed completelyinto the secondary distribution. The transformation can be de-scribed by the following linear relations:

_Ey ¼X9

z¼1

Kyz_Ey; y ¼ 1;2;3; . . . ;9 ð19Þ

For example, a portion K11_E1 of energy _E1 goes to _Q1, Kyz

_Ey goes to_Qz, K19

_E1 goes to _Q9 .The following relation must be valid for the coefficient to satisfy

Eq. (19):

X9

z¼1

Kyz ¼ 1; y ¼ 1;2;3; . . . ;9 ð20Þ

Following linear relations can be written for the secondarydistribution:

_Qz ¼X9

y¼1

Kyz_Ey; z ¼ 1;2;3; . . . ;9 ð21Þ

For example, the energy _Q1 is obtained from the sum of portionsK11

_E1 of energy _E1, K21_E2 of energy _E2; . . . ;K91

_E9 of energy _E9.If primary and secondary distribution are expressed in matrix

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

ðKÞð _EÞ ¼ ð _QÞ ð22ÞThus from the secondary distribution primary distribution can becalculated by transposing equation (22)

ð _EÞ ¼ ðK�1Þð _QÞ ð23Þ

for (K�1) = (R) the following relation is obtained:

ð _EÞ ¼ ðRÞð _QÞ ð24Þ

or

_Ey ¼X9

z¼1

Ryz_Q z; y ¼ 1;2;3; . . . ;9 ð25Þ

3.1. Secondary energy distribution

It is not possible to calculate primary energy distribution exper-imentally, so first secondary energy distribution is found usingsimple heat transfer equations and then using Konig [21] modelsecondary energy is converted into primary energy which is thencalculated as percentage fraction of input energy. A numericalevaluation of the temperature as a function of time and of a singlespace coordinate enables calculation of the above mentioned com-ponents of the secondary energy distribution. Heat stored in theworkpiece and tool electrode is given below:

Q3;6 ¼ pqcr2lf1=2½ðh1 � h2Þ:ðl1 � l3=l2Þ þ h1 þ h2� � hog ð26Þ


Heat stored in the dielectric fluid Q8 is calculated by similar linear-ization of the temperature profile in the dielectric fluid.

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 conditions.Now on achieving steady state the heat stored in the electrodesapproaches zero and can be neglected in drawing up the energy bal-ance for steady state. The portions of the energy stored in the work-piece, tool electrode and the dielectric fluid become significant if theenergy distribution is evaluated from the start of the experiment.

Now after calculation of the stored energy equation (26) fromthe start of machining to the momentary time of measurementtx, the energy stored per unit of time is approximately obtainedfrom:

_Q 3;6;8 ¼ ½Q 3;6;8ðtxÞ � Q 3;6;8ðtx�1Þ�=ðtx � tx�1Þ ð27Þ_Q3 and _Q6 become negligible after a certain time tx. Thus the tran-

sition region from transition to steady state can be determined fromthe heat stored in the electrodes.

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

_Q 2;5 ¼ pd2W;EkW;Eðh1 � h2Þ=4l2 ð28Þ

Heat stored in eroded and worn particles is given below:

_Q 1;4 ¼ VW ;Eqcðhd1 � hoÞ ð29Þ

Heat conduction in the dielectric fluid is given below:

_Q 7 ¼ 2pkdhdðhd1 � hd2Þ= lnðrd2=rd1Þ ð30Þ

The residual energy _Q9 is given below:

_Q 9 ¼ Input energy� sum of all other energy components ð31Þ

Energy required to melt and evaporate the eroded particles is calcu-lated as:

_E1;4 ¼ VW ;EqfcsolidðhM � hoÞ þ Sþ Kv½cliquidðhV � hMÞ þ R�g ð32Þ

The components of primary energy distribution are taken as per-centage fraction of input energy:

Fig. 3. Schematic diagram o

My ¼_Ey

_W in

; y ¼ 1;2;3; . . . ;9 ð33Þ

The components of the fraction of primary energy distributionare defined by the following: M1 – fraction of energy for erosion/re-moval of workpiece, M2 – fraction of energy conducted through theworkpiece, M3 – fraction of energy stored in the workpiece, M4 –fraction of energy for erosion/removal of electrode, M5 – fractionof energy conducted through the electrode, M6 – fraction of energystored in the electrode, M7 – fraction of energy conducted by thedielectric 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 as contin-uum in calculating the stored and conducted heats.� It is assumed that the radial conduction in the electrodes and

the axial conduction in the dielectric fluid are neglected withrespect to the axial and radial components respectively.� The relative frequency g = 1, used in Eq. (16) to calculate input

energy.

4. Experimental set-up

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), using Cop-per–Tungsten as tool electrode. Commercially available Keroseneoil was used as dielectric fluid during all the experiments in a spe-cially designed and fabricated insulated tank. The schematic dia-gram of the EDM set-up is shown in Fig. 3. To minimize the heatloss, insulation of glass wool was provided on the walls of the tankand the lateral surface of tool electrode and workpiece were cov-ered with Teflon insulation such that they were exposed to theEDM process on their upper surface as shown in Fig. 4. The temper-ature at different locations of workpiece, tool electrode, and dielec-tric fluid was measured by J-type Iron/Constantan thermocouples,

f experimental set-up.

Fig. 4. Sample of workpiece/electrode used in the experiment.

Table 1Machining parameters.

Voltage: 60 V, pulse interval (to): 10 lsPolarity: straight or positive polarity

Discharge current (A) 2 8 16 24Pulse duration (ls) 20 50 100 200

Table 2Experimental readings for workpiece to calculate energy distribution.

Voltage (V) – 60 V, off time (to) – 10 ls, initial temperature h� = 18 �C

Current(I), A

Pulseduration(ls)

h1

(�C)h2

(�C)hd1

(�C)hd2

(�C)l1w

(mm)L2w

(mm)L3w

(mm)

2 20 36 27 25 23 11 36 2.242 50 50 37 27 25 10.5 36 2.242 100 53 39 29 28 10.1 36 2.242 200 55 40 31 30 9.8 36 2.248 20 36.5 27 25.3 23 11.2 36 2.248 50 52.1 36.8 27 24.2 10.2 36 2.248 100 55.3 38.9 28.8 27.2 8.8 36 2.248 200 58.8 41.1 29 27.2 7.3 36 2.2416 20 52 42 28.3 27.9 8.0 36 2.2416 50 62 47 28 27.5 6.4 36 2.2416 100 56 39 27 26.5 4.7 36 2.2416 200 61 43 27.2 26.6 2.9 36 2.2424 20 66.3 53.2 35.3 34.6 9.8 36 2.2424 50 65.4 50.1 35.1 34.3 7.53 36 2.2424 100 78.2 60.1 35.2 34.2 4.45 36 2.2424 200 100.3 83.4 36.2 35.7 2.26 36 2.24

Table 3Experimental readings for electrode to calculate energy distribution.

Voltage (V) – 60 V, off time (to) – 10 ls, initial temperature h� = 18 �C

Current(I), A

Pulseduration(ls)

h3

(�C)h4

(�C)hd1

(�C)hd2

(�C)l1E

(mm)L2E

(mm)L3E

(mm)

2 20 37 32 25 23 7.8 26.7 4.92 50 55 49 27 25 7.5 26.7 4.92 100 59 53 29 28 7.1 26.7 4.92 200 62 54 31 30 6.7 26.7 4.98 20 37.7 32.3 25.3 23 2.7 26.7 3.98 50 60.9 53.6 27 24.2 2.1 26.7 3.98 100 70.7 55.3 28.8 27.2 1.7 26.7 3.98 200 72.6 50.2 29 27.2 0.9 26.7 3.916 20 57 51 28.3 27.9 6.0 26.7 4.916 50 75 66 28 27.5 5.5 26.7 4.916 100 93 60 27 26.5 3.7 26.7 4.916 200 84 49 27.2 26.6 1.9 26.7 4.924 20 62.3 51.1 35.3 34.6 6.7 26.7 4.924 50 74.4 52.3 35.1 34.3 5.7 26.7 4.924 100 80.3 52 35.2 34.2 4.48 26.7 4.924 200 99.6 62.3 36.2 35.7 2.88 26.7 4.9


with a range of �40 �C to 750 �C. The Thermocouples wereattached to temperature indicators which directly measure thetemperature 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. 4. h1 and h2 are the temperature of work-piece at upper and lower end and h3 and h4 are temperature of elec-trode at lower and upper end as shown in Fig. 4. AlsoThermocouples were fixed in the specially made fixture to measurethe temperature of dielectric fluid at different locations, hd1 hd2 arethe temperature measured in dielectric fluid as shown in sche-matic diagram in Fig. 3.

4.1. Machining parameters

The range of parameters have been selected (by trial and errortechnique) where the experiments can be conducted without fac-ing the hindrance of arcing etc. The process parameters are oftwo types, i.e., fixed parameters, which are kept fixed or constantduring all the experiments (voltage, pulse interval, polarity) andVariable parameters, which varies with every experiment (current,pulse duration), so as to find the optimum parameters where thereis a better utilization of energy, as shown in Table 1.

5. Methodology

Electric discharge machining of Tungsten–Carbide material asworkpiece were carried out on die-sinking electric discharge ma-chine with Copper–Tungsten as tool electrode and by varyingmachining parameters settings. The temperatures of the individualmeasuring points as shown in Fig. 4 were measured with the helpof the thermocouples before each experiment as well as after dif-ferent machining duration of the process. The time of machining

Fig. 5. Effect of pulse duration on percentage fraction of primary energy transferred to workpiece for different current.

Fig. 6. Effect of current on percentage fraction of primary energy transferred to workpiece for different pulse durations.

Fig. 7. Percentage fraction of primary energy transferred to workpiece for differentcurrent and pulse durations.


has been noted on the monitor of the electrical discharge machine.The observations are given in Tables 2 and 3. The material removalrate MRR, in mm3/min. has been calculated at the time wheresteady state temperature is obtained using the results of Tables 2and 3. During machining the variation in peak current was con-trolled manually by percentage setting knob. Also at the same timevolume of material eroded from tool electrode (mm3/min) hasbeen calculated. At steady state the temperature of electrode andworkpiece is almost constant with machining duration and storedenergy is negligible. The results obtained at steady state were usedto calculate secondary distribution of input energy by using heattransfer equations given in Section 3. The primary energy distribu-tion has been calculated from secondary distribution by the usingthe equations given in Section 3. A computer programme isdesigned on Matlab software for the heat transfer equations. Thefraction (in percentage of input energy M1 to M9 as discussed inSection 3) of primary energy distribution was calculated from sec-ondary distribution. The above procedure to calculate energy dis-

Fig. 8. Comparison between pulse duration and percentage fraction of primary energy transferred to workpiece, tool and dielectric fluid for 2 A current.



tribution was repeated by varying pulse duration (on time) and in-put discharge current with discharge voltage and pulse interval (offtime) were held constant at 60 V and 10 ls respectively. Alsostraight or positive polarity was used, i.e., workpiece as anode (po-sitive) and tool electrode as cathode (negative) for all experiments.The percentage of energy transferred to workpiece (Fcw), tool elec-trode, and dielectric fluid is calculated and given in graphical formin Figs. 5–11.

5.1. 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. The results are given inTable 4. The degree of freedom is three as expected and the P value

varies is near to zero from0 to 0.009, indicating that experimentsperformed are within standard acceptable limits of 5%.

6. Results and discussion

The graphical representation of the experimental results ob-tained using heat transfer equations for distribution of input en-ergy during electric discharge machining are shown in Figs. 5–11,for various current and pulse duration parameters.

The percentage fraction of energy transferred to the workpiece(Fcw) for different pulse duration and current intensities at a gapvoltage of 60 V and pulse interval of 10 ls is shown in Figs. 5–7.It is clearly shown that Fcw varies with variation of either pulseduration or current. These results prove that fixed value of Fcw

for all currents and pulse duration used by many thermal models




is one of the reasons of errors in the prediction accuracy of themodels. Hence to increase the accuracy of the theoretical thermalmodels used for the prediction of machining characteristics likeMRR and surface roughness, value of Fcw needs to be varied withvariation of machining parameters. This study experimentallyshows that Fcw varies from 6.1% to 26.82%, from low to high currentand for different pulse durations as shown in Fig. 7.

Fig. 5 shows that Fcw varies with pulse duration following par-abolic equations for almost all current durations except for verylow current 2 A. For all currents Fcw increases to maxima and asshown in Fig. 5 maxima is attained for low pulse duration for 2 Acurrent and for higher currents it is attained at higher pulse dura-tion. For short pulse durations exceptions in the trend is observedin Fig. 5, this behaviour may be because for short pulses, metaldoes not get enough time to get adequately heated and almostno melting takes place and also the electrostatic forces are the ma-jor cause of metal removal for short pulses as compared to longpulse durations where melting becomes the dominant phenome-non. Also for short pulses the dominant factors for energy lossesare by ionization and excitation. It is observed in Fig. 5 that Fcw

is maximum for 24 A current for all pulse durations and for thiscurrent, maxima is attained at 100 ls pulse duration as shown inFig. 6. These results are in agreement with the results obtainedfor MRR by other authors for machining hard materials [43–45].Lee et al. [43] reported increase of MRR with increasing pulse dura-tion and this is possible due to same trend shown by Fcw as re-ported in this study as shown in Fig. 5.

The effective utilization of the energy is the energy transferred tothe workpiece, which is further used for erosion of the workpiece.For optimum utilization of input discharge energy the energy trans-ferred to the workpiece (Fcw) should be more as compared to tooland dielectric fluid. The comparison of the energy transferred toworkpiece, tool and dielectric fluid is given in Figs. 8–11. It is ob-served that for 8 A and 16 A current as shown in Figs. 9 and 10respectively, the maximum energy is consumed by the tool elec-trode. These results are in the reverse order of normal requirement,i.e., to optimize the EDM process, the energy utilization by the work-piece should be more as compared to the tool electrode. Though,these results are for straight polarity, hence reverse polarity can beconsidered to improve the results. It is observed in Fig. 11 for 24 A

Table 4Two-way ANOVA.

Two-way ANOVA: energy to workpiece (Fcw) versus pulse duration, current

Source DF SS MS F P

Pulse Duration 3 259.285 86.4283 7.19 0.009Current 3 259.094 86.3646 7.18 0.009Error 9 108.220 12.0244

Total 15 626.598


current, the useful energy transferred to the workpiece (Fcw) ishighest as compared to unwanted energy towards the tool electrodefor all pulse durations and for straight polarity used in these exper-iments. For 24 A current as shown in Figs. 5 and 11, the energytransferred to the workpiece (Fcw) shows downward trend for pulseduration more than 100 ls because at higher pulse duration there isexpansion of plasma channel and additional energy supplied is lostin maintaining the plasma channel, and hence energy transferred tothe workpiece is reduced. Also problem of arcing is observed at200 ls pulse duration. Hence reduction of Fcw and MRR is observedfor pulse duration more than 100 ls for 24 A current. So the maxi-mum energy transfer to the workpiece (Fcw) is observed at 24 A cur-rent and 100 ls pulse duration and hence these are the optimumparameters for optimum utilization of input energy.

7. Conclusions

The present study experimentally calculated the distribution ofinput discharge energy during electric discharge machining, usingheat transfer equations. The results obtained especially of fractionof energy transferred to the workpiece (Fcw) for different machin-ing parameters are in good concurrence with the results obtainedby other authors for the effect of Fcw, i.e., MRR, for same combina-tion of electrodes. In the light of the present study following con-clusions have been drawn:

1. The input energy is a function of pulse duration and current andMRR depends upon the fraction of energy transferred to theworkpiece (Fcw).

2. The fraction of energy transferred to the workpiece (Fcw) is afunction of the pulse duration, current, polarity of electrodesand combination of workpiece and tool electrodes. It varieswith current and pulse duration from 6.1% to 26.82%, as com-pared to the fixed value used by many thermal models for pre-dicting MRR and surface roughness, results in less accuratemodels.

3. In general Fcw increases with the increase of current and themaximum value is attained with the increase of pulse duration.For low current maxima is attained at low pulse duration ascompared to high pulse duration for high current. Thus forlow current effective utilization of energy is at low pulse dura-tion as compared to high current where optimum value isattained at high pulse duration.

4. The results of fraction of energy transferred to the workpiece(Fcw), obtained in this study for various machining parameterscan be further used in the existing thermal models designedby other authors for electric discharge machining. It is expectedthat this study will improve the prediction accuracy of thesemodels.

8. Future scope

Since not much research has been done in the area of EnergyDistribution, therefore there is a scope of further research to findthe fraction of energy transferred to the workpiece (Fcw), and

experiments should be carried out by taking different combina-tions of materials of workpiece and tool electrode and at differentmachining parameters, to find the effect of material properties andmachining parameters on energy transferred to the workpiece.

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Documents

Experimental study of distribution of energy during EDM process for utilization in thermal models