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Authors Accepted Manuscript

A numerical model of the EDM process considering

the effect of multiple discharges

B. Izquierdo, J.A. Snchez, S. Plaza, I. Pombo, N.

Ortega

PII: S0890-6955(08)00225-3

DOI: doi:10.1016/j.ijmachtools.2008.11.003

Reference: MTM 2352

To appear in: International Journal of

Machine Tools & Manufacture

Received date: 18 February 2008

Revised date: 17 November 2008

Accepted date: 18 November 2008

Cite this article as: B. Izquierdo, J.A. Snchez, S. Plaza, I. Pombo and N. Ortega, A numer-

ical model of the EDM process considering the effect of multiple discharges,International

Journal of Machine Tools & Manufacture(2008), doi:10.1016/j.ijmachtools.2008.11.003

This is a PDF file of an unedited manuscript that has been accepted for publication. As

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Abstract

The EDM process is, by far, the most popular amongst the non-conventional machining

processes. The technology is optimum for accurate machining of complex geometries in

hard materials, as those required in the tooling industry. However, although a large

number of EDM machines are sold every year, scientific knowledge of the process is

still limited. The complex nature of the process involves simultaneous interaction of

thermal, mechanical, chemical and electrical phenomena, which makes process

modelling very difficult. In this paper a new contribution to the simulation and

modelling of the EDM process is presented. Temperature fields within the workpiece

generated by the superposition of multiple discharges, as it happens during an actual

EDM operation, are numerically calculated using a finite difference schema. The

characteristics of the discharge for a given operation, namely energy transferred onto

the workpiece, diameter of the discharge channel and material removal efficiency, can

be estimated using inverse identification from the results of the numerical model. The

model has been validated through industrial EDM tests, showing that it can efficiently

predict material removal rate and surface roughness with errors below 6%.

1. State-of-the-Art on Thermal Modelling of the EDM

Process

More than 60 years have already gone since the Russian scientists Lazarenkos, with the

help of a young researcher called Zolotykh, used the effect of electrical discharges to


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remove material from a metallic part. Nowadays the Electrical Discharge Machining

(EDM) process is, by far, the most popular amongst the non-conventional material

removal techniques with applications in a broad variety of industries such as die and

mould-making, aerospace, automotive, medical, micromechanics, etc.

The feature that makes EDM unique with respect to those conventional processes is that

the removal mechanism is not related to mechanical contact between tool (electrode)

and part. In short, during the EDM process, a series of discrete electrical discharges

occur between electrode and workpiece in a dielectric medium During the application of

each discharge local temperature rises at several thousands degrees. As a consequence,

part material melts and vaporises generating craters on the surface of the workpiece, and

it is removed in the form of debris by dielectric flushing. This is the core of the

phenomena involved (Fig. 1), although scientists still argue on some points of this

explanation. The result is an EDMed surface whose roughness depends mainly on

electrical parameters and on materials properties, and in which the craters produced are

responsible for a non-directional surface finish.

As it has been said, EDM combines several phenomena, but except for very short

discharges, it can be considered with small error that the thermal effect takes over [1,9].

It is commonly accepted that the thermal problem to be solved in order to model an

EDM discharge is basically a heat transmission problem where the heat input is

representing the spark. Solving this thermal problem yields the temperature distribution

inside the workpiece, from which the shape of the generated craters can be estimated.

Fig. 1


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The parameters that define the characteristics of EDM discharges such as the percent of

energy that is transferred to the workpiece by conduction, the size and shape of the

discharge channel and the mechanism of material ejection depend on the electrode

material, the type of dielectric, on-time and current and voltage during the discharge,

and the possible relations between these parameters are difficult to establish due to the

difficulty related to their experimental measurement. The high dispersion of the data

published shows that still research work is needed for a better understanding of the

nature of the phenomena involved in the EDM process.

For very short discharges, there is not enough time for the material to be adequately

heated, almost no melting takes place, and the material is removed in vapour state. If the

discharge duration exceeds a few microseconds part of the workpiece material is

molten. In the first stage of the discharge the strong electric field at the cathode can lead

to mechanical stresses in the material [1,4,8], which may contribute to its removal.

Therefore, except for very short discharges material removal is due to melting and

posterior ejection. This is why EDM is usually modelled as a thermal transmission

problem, where the objective is to determine the temperature distribution inside the

workpiece material that results from the discharge.

The heat transmission equation (Eq. 1) needs to be solved taking into account the

boundary conditions of the problem.

t

T

k

q

z

T

y

T

x

T G

12

2

2

2

2

2

(Eq. 1)


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Different approaches for solving the thermal problem can be found in bibliography [2]

but nowadays most research work is devoted to numerical models based either on the

Finite Element Method (FEM) [3,4,5,6,8,12] or in the finite differences method [11].

Whatever the solving method used, a realistic definition of the characteristics of the

discharge is required. These characteristics can be summarized in three parameters: the

percent of energy transferred to the workpiece by conduction; the size and shape of the

discharge channel; and the mechanism of material ejection.

During a discharge part of the energy is dissipated into the surrounding dielectric and

other part is lost by radiation (Fig. 2). The rest of the energy is transferred towards both

electrode and workpiece by conduction. Part of that heat is evacuated from the

workpiece by convection, but when it comes to the local heating due to each spark this

part can be neglected [9,12]. The energy partition depends on many factors amongst

which the thermal diffusivity, as well as the boiling temperature of the material of both

electrode and workpiece must be cited [3]. Anyway, a large dispersion of results can be

found in the literature, corresponding to very different EDM conditions and

measurement method.

The second parameter is the size and shape of the plasma channel, in other words the

geometry of the heat source in the model. All the recent models assume that the heat

source has a disk shape. It is commonly assumed that the plasma channel growth shows

a steep increase in the diameter in the first microseconds of the discharge and a

posterior stabilization. It also shows a dependency on the materials physical properties.

Fig. 2


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The concept of Plasma Flushing Efficiency can also be found in the literature. This is

defined as the fraction of the molten material that is effectively removed from the

workpiece. Prez [8

the crater represents about 35% of the total molten volume. The work published shows

that the ejecting efficiency depends on the thermal expansion coefficient of the

electrode material, the amount of molten material, discharge channel radius, thermal

properties of material and dielectric flushing conditions.

If except for short pulses electrostatic forces are not responsible for erosion [1], there

must be another material ejection mechanism, and this is the so called superheating.

During the pulse on-time the material under the plasma channel is heated over its

boiling point at atmospheric pressure, but the plasma overpressure prevents it form

boiling. At the end of the on-time this overpressure disappears and the superheated melt

cavity explodes ejecting part of the molten material. Optical observations made by

Descoeudres [13] using a high speed framing camera show incandescent particles

jumping off the melting pool after the discharge finishes. Takezawa [16] performed a

study on single discharge machining with a low melting temperature alloy in order to

investigate the material removal mechanism involved in EDM. He found that for long

pulses the volume of craters is higher, but its relation with the observed resolidified

layer becomes much lower, which is a sign of inefficiency in the material ejection

mechanism.

The literature survey reveals that an important number of papers are focused on single

spark analysis. However, during an actual EDM operations some effects that are no


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present in a single discharge test occur such as the interaction between successive

discharges, or the presence of bubbles and debris in the gap. Related to this fact, a large

dispersion of data related to the characteristics of the discharge (the energy transferred

onto the workpiece, the diameter of the discharge channel and the efficiency of material

removal) is observed. In this paper a new contribution to the simulation and modelling

of the EDM process is presented. Temperature fields within the workpiece generated by

the superposition of multiple discharges, as it happens during an actual EDM operation,

are numerically calculated using a finite difference schema. Inverse identification is

proposed for the estimation of the characteristics of the discharge for a given operation,

namely energy transferred onto the workpiece, diameter of the discharge channel and

material removal efficiency.

2. A finite difference-based multi-spark thermal model

of the EDM process

2.1 Description of the model

In order to solve the thermal problem, a first order forward finite difference approach

has been proposed. The model has been programmed in C++ and runs on an Intel Xeon

platform. The workpiece is discretized into hexahedral elements. For each of these

elements appropriate boundary conditions are defined depending on its location and

whether the element is affected by the heat source or not at each time step. On each face


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of each element, diffusion, convection and/or contribution from the heat source may

happen. Fig. 3 shows an example of discretization of an irregular surface.

Eq. 4 shows the energy balance in the volume closed by an element, from which the

temperature at the next time step () can be solved. In this equation Q is expressed

in watts:

DACCUMULATEINOUTCONDUCTIONOUTIN QQQQQ SOURCEHEATCONVECTION _ (Eq. 4)

Given the boundary conditions for each element, the heat flux that enters and exits the

discrete volume can be calculated. As an example, the equation for the temperature of

the node represented in Fig. 3 will be obtained:

The differential equations for the heat flux through in the faces were conduction takes

place (the left and bottom faces) are given in Equations 5, 6.

zxx

TkQ

left

left

(Eq. 5)

yxz

TkQ

bottom

bottom

(Eq. 6)

That in the form of finite differences can be written as:

Fig. 3


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zxy

TTkQ

mkjimkji

left

,,1,,,, (Eq. 7)

yxz

TTkQ

mkjimkji

bottom

,1,,,,, (Eq. 8)

And for the faces that are affected by the heat source (q) the resulting equations are:

zxqQright (Eq. 9)

yxqQup (Eq. 10)

zyqQfront (Eq. 11)

zyqQback (Eq. 12)

The heat accumulation rate inside the discrete volume during a time step is given by Eq.

13:

t

TT

k

zyxCpQ

mkjimkji

DACCUMULATE

,,,1,,, (Eq. 13)

Therefore, replacing Equations 7 to 13 in the energy balance (Eq. 4) the following

expression can be obtained:

t

TT

k

zyxCpzyyz

zxqyxz

TTkzx

y

TTk

mkjimkji

mkjimkjimkjimkji

,,,1,,,

,1,,,,,,,1,,,,

)2

(

(Eq. 14)


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And isolating the term for the temperature in the next time step (Ti,j,k,m+1):

zyyzzxqyxz

TTk

zxy

TTk

zyxCp

tkTT

mkjimkji

mkjimkji

mkjimkji

2,1,,,,,

,,1,,,,

,,,1,,,

(Eq. 15)

In order to assure the convergence of this method,,,andmust have values so

they satisfy the following condition (this condition is valid for the element used as

example):

z

yx

y

zxk

zyxCpt

2

(Eq. 16)

Following the same procedure, the equation for the same element in the case that it is

outside the zone affected by heat source can be obtained. In this case, the equations for

the heat flux through the faces where convection takes place would be the following

ones:

zxTThQ mkjiright ,,, (Eq. 17)

yxTThQ mkjiup ,,, (Eq. 18)

zyTThQ mkjifront ,,, (Eq. 19)

zyTThQ mkjiback ,,, (Eq. 20)


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The main advantage of this approach is its flexibility to define different boundary

conditions virtually for every element, which allows the model to solve the thermal

problem even if the heat source is applied over an irregular surface, as it happens during

EDM.

The assumptions made for the development of this model are listed below:

- Thermal properties of the workpiece material are temperature dependent for

temperatures below 600C. For temperatures over this value they are kept

constant because no reliable data are available.

- Latent heat of fusion and vaporization are not taken into account since their

effect on simulation results can be neglected [20].

- Convection is considered through the faces of the elements in contact with the

dielectric.

- The fraction of the energy that is transferred into the workpiece is constant

during the pulse.

- The criterion for determining the amount of material that is effectively removed

is based on an equivalent temperature (Teq), in such a way that only the material

above this temperature is removed to form a new crater.

- The model does not reflect the formation of the rim around the crater.

- The intensity and the voltage are maintained constant during the pulse.

- At this stage of the research all the pulses are considered to be equal, that is, the

model considers that on-time, voltage and intensity of every discharge are the

same, neglecting the occurrence of abnormal pulses (arcing or short-circuits).

- The model does not consider base movements nor jumping of the plasma

channel, although they may have influence on the resulting surface properties.


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- The stochastic nature of discharge location is treated, but on the supposition that

the flushing conditions are good enough to neglect local effects attributed to the

presence of debris generated during the process. This aspect of the model is

studied in depth in Section2.4 Discharge Location.

Fig. 4 shows the shape of voltage and intensity signals (U, I) and how the heat flux

varies as the plasma channel expands, that is, as the plasma channel becomes wider the

heat flux distribution becomes less steep. First, using a signal acquisition system, the

voltage and intensity during the discharge are measured, in order to know the amount of

energy involved in the discharge process (see Eq. 21). After that, the Gaussian-shaped

heat flux is calculated using Eq. 3 and it is then applied over the elements affected by

the plasma channel. The elements outside will be affected by convection of the

dielectric around the workpiece.

2.2 Modelling of the heat source

Prior to numerically solving the equation of the thermal problem, the heat input

produced by a single discharge must be modelled. The heat input is defined by its shape

and the amount of heat that is applied to the workpiece. For a given on-time (tON),

voltage (U) and discharge intensity (I), assuming that both Uand Iremain constant in

this period, the total amount of energy (E) can be calculated using Eq. 21:

Fig. 4


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that the light emitting zone grows very rapidly in the first few microseconds and that

after that growth its size remains constant. In the images obtained by Descoeudres [13]

light originates from a zone broader than the electrode itself, which could indicate that

the light emitted during the discharge is strong enough to saturate the light sensor of the

camera. This makes it difficult to use optical measurements to study the size and shape

of the plasma channel during EDM.

2.3 Criterion for material removal

Once the temperature distribution inside the workpiece due to the discharge has been

calculated, the criterion for crater generation (material removal) based on those

temperatures must be adopted. The present model uses the concept of equivalent

temperature (Teq) [3]: every element on the workpiece that has reached a temperature

higher than Teq is removed. When this material disappears, a new crater is generated on

the surface, and elements that were inside the bulk material until this stage will become

now the free surface of the workpiece. The present model takes this fact into account

and changes the boundary conditions of the elements in order to reflect the convection

cooling of the material in contact with the dielectric.

The effect of establishing different values of Teq on the geometry of the generated

crater is shown in Fig. 5. The figure represents a plane section of the three dimensional

temperature distribution inside the workpiece due to a discharge. The isotherms

corresponding to equivalent temperatures of 1500, 2500 and 3200C have been

represented. Obviously, the material removed in each case varies largely, with

differences in volume that can reach up to 80%. It can be seen that the model must solve


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To measure the influence of the local gap width on discharge probability, discharge

sequences were made on several stepped workpieces, and the number of discharges that

occurred on the top and bottom surfaces were counted. Fig. 7 shows that if the step is

higher than surfaces and that as the step height

tends to zero, the probability approaches 50% for the bottom and the top steps on the

workpiece.

From this experiment a probability function was obtained, so that for points whose

distance to the electrode is short (peaks on the eroded surface) discharge probability will

be higher than for points farther from the electrode (valleys of the EDM-ed surface).

This probability function is used to determine the element of the discretized surface on

which the next discharge will take place.

The sequence of events during simulation is presented in Fig. 8.

Fig. 8

Fig. 7

Fig. 6


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3. Single-spark vs. multi-spark modelling

The studies referenced in the State-of-the-Art are focused on specific discharge

properties, materials and dielectric media. As a consequence, dispersion between results

is evident. What is more, published models are based on single-discharge experiments,

which present different discharge conditions compared to discharges that take place in

the continuous EDM process.

Schulze [19] observed that under different electrode arrangements the single-discharge

craters presented distinct characteristics, and the arrangement that most accurately

reflected the real erosion with pulse sequences was chosen for their studies. In his study

about discharge location movements induced by debris concentration, Kojima [14]

determined that the presence of debris enlarges the gap between electrode and

workpiece and Revaz [7] found that the amount of energy delivered to the workpiece

obtained by fitting thermal calculations to calorimetric experiments was different if this

fitting was done based on single discharge experiments or based on a long discharge

sequence.

Takeuchi [17] in his study on volume fraction of bubbles in the EDM gap concluded

that for cylindrical shape workpiece/electrode with 30mm diameter, this volume

fraction reaches its steady state in 100ms and that corresponds to 52-96% of the total

gap volume depending on the flushing conditions. Therefore, discharges might not be

taking place in single phase liquid medium, as in single-discharge experiments. He also

found that debris size, crater diameters and surface roughness generated by continuous


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EDM are intermediate between those observed in single-discharge experiments in single

phase liquid and in air.

At the sight of the cited previous studies, it can be stated that multiple different

situations occur during the actual EDM process, involving bubble and debris generation.

Single-discharge experiments can only partially represent the actual situation. In this

work, the concept of average discharge, which accounts for the different situations, is

introduced. Using this new concept, superposition of multiple discharges to generate the

EDM-ed surface can be effectively carried out.

In Fig. 9 the variation of the volume removed per discharge as the EDM operation

advances is represented. It can be seen that once all the surface has been affected by

sparks, a steady value of volume removed per spark is reached. This is due to the fact

that when the surface becomes irregular the boundary conditions of the thermal problem

associated to each discharge are different, and therefore the calculated temperature

distribution and the resulting crater differ from the ones obtained when the surface is

plane. Fig. 9 also shows the variance of the removed volume per discharge, and that it

strongly depends on the local geometry of the surface over which the heat source is

applied.

Fig. 9


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4. Inverse determination of discharge characteristics

and equivalent temperature

At this point the basis of the multi-spark thermal-numerical model of the EDM process

has been set. Still, at the sight of the comments collected in the previous sections, it is

evident that there are a number of input variables to the model that are not known, and

about which little knowledge is available in literature. These variables are the fraction of

heat transferred into the workpiece (Qw), the radius of the plasma channel (Rp) and the

equivalent temperature (Teq) of material removal. Of course, the soundness of the

predictions obtained by the model will be strongly affected by these variables.

As shown in the literature survey, little reliable data for these variables can be found in

literature. In this work a new approach for the determination of their values for a given

EDM regime and operation is proposed. Inverse estimation using the multi-spark

thermal model described can be effectively used. In order to do so, an error function that

accounts for the deviations between an actual EDM operation and a numerical

simulation in terms of material removal rate and surface finish must be defined. The

error function used is given by Equation 23:

2 2 2 2 2 2 2

5

s e s e s e s e s e s e s e

e e e e e e e

Sa Sa Sq Sq Sz Sz Sdq Sdq Sdr Sdr Vvc Vvc MRR MRR

Sa Sq Sz Sdq Sdr Vvc MRRError

(Eq. 23)

For a given EDM regime, characterized by a certain material renoval rate and surface

finish, computer simulations are carried out with different values of Qw,Rp and Teq, and

the value of the error is obtained for each combination. The combination of parameters


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that minimize the error function will be chosen as the optimum that characterizes the

EDM regime. In order to illustrate the methodology, the adjustment of the parameters

for an EDM regime characterized by a material removal rate of 12.92mm3/min and

Sa) will be shown. EDM conditions and workpiece material

(AISI D2 tool steel) characteristics are shown in Tables 1 and 2. EDM experiments have

been carried out on an ONA TECHNO H300 SEDM machine using square section

copper electrodes of size 30x30mm and external flushing provided by a flushing nozzle.

The dielectric fluid is a commercial EDM oil (see Table 1).

The limits between which Qw,Rp and Teq have been varied in the simulations are shown

in Table 3. For an on-time of 50

maximum values of Rp (this is, 377 and 1255, see Table 3) correspond to radii of the

More than 120 simulations have been carried out in order to precisely define the error

function. Data interpolation using appropriate MatLab function has been performed for

those points that have not been simulated.

Table 3

Table 2

Table 1


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Fig. 10 illustrates the scheme followed in this analysis, which is based on the density

of minimum error points within the range of the input variables. The maximum error

value has been found to be 5.13 and the minimum one 0.106. For this study the number

of points with error values within the 5% lowest error band been taken into account

(errors lower than 0.357). If the number of points with low error values for each

combination of Rp-Teq, of Qw-Teq, and combination of Qw-Rp are plotted, it can be

observed that each of these planes presents a zone where the highest number of points

representing a good adjustment is located. These projections are plotted in Fig. 10 and

the dark areas show the zones with higher density of low error points. It can be seen that

in the Qw-Teqplane there is a linear zone that covers a wide range of Qw and Teq where

points with low error are located, but for the other two planes considered the areas with

highest density of good points are well delimited. Namely, these zones are enclosed by

17.5% and 21% values of Qw, equivalent temperatures of 2700C and 3100C, and Rp

values ranging from 778 to 853. These two zones coincide well with the linear zone on

the Qw-Teq plane mentioned earlier, so it can be stated that there is a small volume

(represented by the small blue cube in Fig. 10) within the studied range of the input

variables which contains the majority of the optimum points.

It can be concluded that inside the volume delimited by the mentioned values of Qw, Teq

and Rp we can find the best adjustment for the studied erosion regime. After

determining the extent of the optimum area, additional simulations have been performed

forRp = 816 (which represents a plasma channel diameter of 225

Fig. 10


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), and for Qw and Teq values corresponding to points inside the mentioned

optimum values in order to determine the optimum point more precisely. TheRp value

of 816 has been chosen because it is the mean value of the values that delimit the

optimum area (namelyRp = 778 andRp = 853). The results of the calculated error values

obtained are shown in Fig. 11, and as it can be seen the minimum error is given forRp =

816 (fixed for this set of simulations), Qw = 18.8% and Teq = 2950C.

Four simulations have been performed with the optimum inputs, and the results of these

simulations, together with the experimental values of the material removal rate and

surface characteristics obtained with a contact profilometer (Taylor Hobson Talysurf

Series 2) are listed in Table 4.

Fig. 12 shows an example of a simulated surface and an experimental one and as it can

be seen both surfaces have similar appearance. These images together with the results

included in Table 4 prove that the present model is capable of generating surfaces

comparable to those obtained with an actual EDM process, and that after adjusting the

model predicted and measured results show very good agreement, with errors below

10% for all the considered parameters. In relation to the material ejection efficiency,

simulations at the optimum point and simulations in which the equivalent temperature

Table 4

Fig. 11


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has been set to 1550C (equal to the melting temperature of the material) have been

compared, and a material ejection efficiency of 29.4% has been calculated.

5. Conclusions

The present paper presents an original thermal model capable of simulating discharge

superposition and representing EDM-ed surfaces. The main conclusions obtained from

this study are:

- Single-discharge modelling has been expensively studied in literature in order to

characterize the EDM process. In this work it has been shown that superposition

of multiple discharges must be considered, since the amount of material

removed per discharge increases (as much as 50%) as the operation progresses.

This effect is related both to the stochastic nature of the process (discharge type

and location) and the development of temperature fields on irregular surfaces.

- An original numerical model for simulation of the EDM process has been

presented. The model generates EDM-ed surfaces by calculating temperature

fields inside the workpiece using a finite difference-based approach, and taking

into account the effect of successive discharges.

- Based on the proposed thermal model, inverse determination of characteristics

of the discharge has been performed. For the studied erosion regime discharge

process is characterized by a plasma channel diame Rp = 816), an

Fig. 12


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energy transference to the workpiece of 18.8% of the total discharge energy (Qw

= 18.8) and a material ejection efficiency of 29.4%, referred to the total amount

of molten material (which corresponds to Teq = 2950).

- Following the procedure presented in this article for other erosion regimes it will

be possible to find values of the characteristics of the discharge, and therefore

gather very helpful information about the interdependence between process

parameters established by the EDM user (such as tON, V0, Vgap and I) and the

parameters defining the discharge process (plasma channel size, percent of

energy transferred to the workpiece and material ejection efficiency).

- When performing simulations employing the optimum input values the error in

the prediction of surface finish is under 6% and the error in the prediction of

material removal rate is lower than 3%.

6. Nomenclature

mass density, kg/m3

k thermal conductivity, W/(m K)

Cp specific heat, J/(kg K)

thermal diffusivity, m2/s

h convection coefficient, W/(m2 K)

T ambient temperature, C

Ti,j,k,t temperature of the element with i,j,kcoordinates in instant t, C

U(t) voltage during pulse, V

I(t) intensity during pulse, A


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E pulse energy, J

Q heat flux rate on faces of the elemental volumes, W

q(r) heat flux (function of radius), W/m2

Qw percent of pulse energy transferred to workpiece, %

Teq equivalent temperature, C

Rp constant defining the size of the plasma channel

R(t) plasma channel radius function of time, m

tON pulse on-time, s

dimensions of the elemental volumes, m

time step, s

ES error of the of the simulated surface

Sa Average absolute deviation of the surface

Sq Root mean square deviation of the surface

Sz Ten point height of the surface

Sdq Root mean square slope of the surface

Sdr Developed surface area ratio, %

Vvc Core void volume 3/mm

3

MRR Material Removal Rate, mm3/min

7. Acknowledgements

The authors wish to thank the Spanish Ministry of Education (MEC) for its support of

the Research Project An original numerical model for the simulation of material

removal, electrode wear and surface integrity in the Electrical Discharge Machining


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(EDM) process, DPI2007-60143, and to the Department of Industry of the Basque

Government for its support to the project ETORTEK 08 Manufacturing 0.0.

8. Bibliography

[1] Singh A., Ghosh A., A thermo-electric model of material removal during electric

discharge machining, Int. J. of Machine Tools & Manufacture 39 (1999), pp.669-

682.

[2] Erden A., Arin F., Kgmen M., Comparison of Mathematical Models for Electric

Discharge Machining, J. of Material Processing & Manufacturing Science, 4,

pp.163-176, 1995.

[3] Shankar P., Jain V.K., Sundarajan T., Analysis of Spark Profiles during EDM

Process, Machining Science and Technology, 1 (2), pp.195-217, 1997.

[4] Yadav V., Jain V. K., Dixit P. M., Thermal Stresses due to Electrical Discharge

Machining, Int. J. of Machine Tools and Manufacture, 42, pp.877-888, 2002.

[5] Marafona J., Chousal J.A.G., A Finite Element Model of EDM Based on the Joule

Effect, Int. J. of Machine Tools and Manufacture, 46 (6), pp.592-602, 2006.

[6] Han F., Jiang J., Dingwen Y., Influence of Discharge Current on machined surfaces

by thermo-analysis in finish cut of WEDM, Int. J. of Machine Tools and

Manufacture, 47 (7-8), pp.1187-1196, 2007.

[7] Revaz B., Witz G., Flkiger R., Properties of the plasma channel in liquid

discharges inferred from cathode local temperature measurements, J. of Applied

Physics, 98, 113305, 2005.


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[8] Prez R., Carron J., Rappaz M., Wlder G., Revaz B., Flkiger R., Measurement

and Metallurgical Modelling of the Thermal Impact of EDM Discharges on Steel,

Proceedings of the 15th

International Symposium on Electromachining, ISEM XV,

pp.17-22, 2007.

[9] Jilani S. T., Pandey P.C., Analysis and modelling of EDM parameters, Precis. Eng.

4 (4) 1982, pp.215221.

[10] Murali M.S., Yeo S-H., Process Simulation and Residual Stress Estimations of

Micro-Electrodischarge Machining Using Finite Element Method, Japanese Journal

of Applied Physics, Vol. 44, No. 7A, (2005) pp.5254-5263.

[11] Ben Salah N., Ghanem F., Ben Atig K., Numerical Study of thermal aspects of

electric discharge machining process, Int. J. of Machine Tools and Manufacture 46

(2006), pp.908-911.

[12] Xia H., Kunieda M., Nishiwaki N., Removal Amount Difference between Anode

and Cathode in EDM Process, Int. J. of Electrical Machining 1, January 1996,

pp.45-52.

[13] Descoeudres A., Hollenstein Ch., Wlder G., Prez R., Time-resolved imaging

and spatially-resolved spectroscopy of electrical discharge machining plasma, J. of

Applied Physics 38 (2005), pp. 4066-4073.

[14] Kojima A., Natsu W., Kunieda M., Observation of Arc Plasma Expansion and

Delayed Growth of Discharge Crater in EDM, Proceedings of the 15th International

Symposium on Electromachining, ISEM XV (2007) pp.14.

[15] Natsu W., Shimoyamada M., Kunieda M., Study on Expansion Process of EDM

Arc Plasma, JSME International Journal, Series C, Vol. 49, No. 2 (2006) pp.600-

605.


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[16] Takezawa H., Kokubo H., Mohri N., Horio K., Yanagida D., Saito N., A Study

on Single Discharge Machining with Low Melting Temperature Alloy, Proceedings

of the 15th International Symposium on Electromachining, ISEM XV (2007) pp.69

73.

[17] Takeuchi H., Kunieda M., Effects of volume fraction of bubbles in discharge

gap on machining phenomena of EDM, Proceedings of the 15th International

Symposium on Electromachining, ISEM XV (2007) pp.6368.

[18] Kunieda M., Kiyohara M., Simulation of Die-Sinking EDM by Discharge

Location searching Algorithm, Int. J. of Electrical Machining 3, January 1998,

pp.79-85.

[19] Schulze H.P., Herms R., Juhr, H., Schaetzing W., Wollenberg G., Comparison of

measured and simulated crater morphology for EDM, J. of Materials Processing

Technology 149, pp.316-322, 2004.

[20] Patel M. R., DiBitonto D. D., Barrufet M. A., Eubank P. T., Theoretical model

of the Electrical Machining Process II. The anode erosion model, J. of Applied

Physics 66 (9), pp.4104-4111, 1989.


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Dielectric

Electrode

Workpiece

Discharge

Crater

Debris

Fig. 1: Discharge and crater generation during an EDM operation.

ure 1


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Away with debrisAway with debris

Absorbed by dielectric medium

and evacuated by radiation

Conduction to the anode

(electrode)

Conduction to the cathode

(workpiece)

Fig.2: Energy balance during the discharge.

ure 2


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Si el cubo estfuera de la fuente

de calor

Si el cubo est

dentro de la fuente

de calor

j

k

i

If the cube is

inside the plasma

channel

If the cubeis

outside the plasma

channel

HEAT INPUT

HEAT INPUT

HEAT INPUT

HEAT INPUT

CONVECTION

CONVECTION

CONVECTION

CONVECTION

CONDUCTION

CONDUCTION

CONDUCTION

Fig.3 Example of hexahedral element and its boundary conditions

Figure 3


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190 195 200 205 210 215 220 225

0

5

10

15

20

25

30

35

1000

2000

3000

4000

5000

6000

Teq = 3200Teq = 2500Teq = 1550

Temp [C]

Fig. 5 Temperature distribution, isotherms and crater shape for equivalent temperatures of 1500,

2500 and 3200 C.

Figure 5


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Fig. 6 Stepped sample used for experimental calculation of the discharge location function. Groupsof discharges can be identified.

Figure 6


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Step

height

50

60

70

80

90

100

110

0 10 20 30 40 50 60 70 80

Probabilityofdischargeonthetop

step(%)

Fig. 7 Discharge probability on the step nearest to the workpiece.

Figure 7


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Surface initialization

Discharge location

Heat flux calculation

Temperature distribution for (t+t)

Generation of new crater

Change boundary conditions

Temperature distribution after pause-time

FINAL SURFACE

Calculation of new

discharge probability distribution

Qw

End of simulation?

Teq

No

Yes

Inputs of themodel

End of on-time?

Yes

No

Plasma channel radius

for (t+t)Rp

Fig. 8 Algorithm for numerical simulation.

Figure 8


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0 500 1000 1500 2000 2500 3000 35004

5

6

7

8

9

10

11

12x 10

-5

N of discharges

Materia

lremovalperdischarge[m

m3]

Fig. 9 Variation of volume of material removed per discharge as the operation progresses.

Figure 9


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Rp

Teq

600 700 800 900 1000 1100 1200

1600

1800

2000

2200

2400

2600

2800

3000

3200

Qw

Teq

5 10 15 20 25 30 35 40

1600

1800

2000

2200

2400

2600

2800

3000

3200

Qw

Rp

5 10 15 20 25 30 35 40

600

700

800

900

1000

1100

1200

Qw [%]

Teq [C]

Rp

17.5% - 21%

778 853

2700C3100C

Projection on Rp-Teq plane Projection on Qw-Teq plane

Projection on Qw-Rp plane

Fig. 10 Scheme of the analysis of the results obtained for the error function and results of projections

of the density of low error points.

Figure 10


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Qw

Teq

17.5 18 18.5 19 19.5 20 20.5 212700

2750

2800

2850

2900

2950

3000

3050

3100

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Fig. 11 Results of the error value obtained in the final adjustment.

Figure 11


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m

0

5

10

15

20

25

30

35

40

45

50

51.2 m

1.4 mm 1.4 mm

Alpha = 45 Beta = 30m

0

5

10

15

20

25

30

35

40

45

50

50.9 m

1.4 mm 1.4 mm

Alpha = 45 Beta = 30

51.2m

1.4mm1.4mm1.4mm 1.4mm

50.9m

50

45

40

35

30

25

20

15

10

5

0

50

45

40

35

30

25

20

15

10

5

0

Fig. 12 Comparison between simulated (left) and measured (right) surfaces.

Figure 12


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Limits of the input values

Min. Max.

Qw[%] 2.5 40

Rp 377 1255

Teq[C] 1550 3200

Table 3 Limits of the input values used for simulations.

Table 3


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PREDICTED VALUESMEASURED

VALUES

MEAN

ERROR

[%]SIM 1 SIM 2 SIM 3 SIM4MEAN OF FOUR

SIMULATIONS

5.54 6 5.74 5.91 5.8 5.79 0.17

Sq 6.86 7.49 7.17 7.46 7.25 7.15 1.4

Sz 41.9 48 45.4 47.2 45.6 43 6.05Sdq [

0.352 0.365 0.364 0.36 0.36 0.354 1.7

Sdr [%] 6.03 6.48 6.45 6.29 6.31 6.18 2.1

Vvc

3/mm2]0.00877 0.00918 0.00883 0.00945 0.00906 0.0091 0.44

MRR

[mm3/min]12.57 12.53 12.57 12.66 12.58 12.92 2.63

Table 4 Comparison between predicted and measured values of material removal rate and

roughness.

Table 4

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