International Journal of Engineering Materials and Manufacture (2022) 7(2) 54-60
https://doi.org/10.26776/ijemm.07.02.2022.02
Mohammad Yeakub Ali
1
, Md. Abdul Mazid
2
, Abdus Sabur
3
and Mohamed Abd Rahman
4
1
Mechanical Engineering Programme Area, Universiti Teknologi Brunie, Gadong BE 1410, Brunei Darussalam
2
School of Engineering and Technology, Central Queensland University, Australia
3
Ministry of Fisheries and Livestock, Bangladesh Secretariat, Dhaka, Bangladesh
4
Department of Manufacturing and Materials Engineering, International Islamic University Malaysia,
PO Box 10, 50728 Kuala Lumpur, Malaysia
E-mail: yeakub.ali@utb.edu.bn
Reference: Ali et al. (2022). Comparative Study of Material Removal Rate of Single-Spark and Multi-Spark Micro-EDM of Copper.
International Journal of Engineering Materials and Manufacture, 7(2), 54-60.
Comparative Study of Material Removal Rate of Single-Spark and Multi-
Spark Micro-EDM of Copper
Mohammad Yeakub Ali
1
, Abdul Md Mazid
2
, Abdus Sabur
3
and Mohamed Abd Rahman
4
Received: 03 April 2022
Accepted: 13 April 2022
Published: 16 April 2022
Publisher: Deer Hill Publications
© 2022 The Author(s)
Creative Commons: CC BY 4.0
ABSTRACT
Micro-electro discharge machining (micro-EDM), a noncontact material removal process, is a well-established
technique for making mold cavity on any workpiece materials having a minimal electrical conductivity of 0.1 Scm
-1
.
The spark between tool electrode (-ve) and workpiece electrode (+ve) removes materials mostly from workpiece.
Knowing the time and amount of material removed in a single spark, MRR can be estimated. A number of analytical
study have been reported for the estimation of MRR based on the ideal situation single-spark erosion. In case of
multi-spark micro-EDM, charging and discharging do not always follow the ideal conditions of the circuit and a lot
of unwanted pulses such as arching and short circuit are produced which in turn reduce the effective number of pulses
per second. Moreover, in RC pulse micro-EDM, the discharges are not uniform and the current and voltage are not
constant with time. As a consequence, the performances estimated based on single-spark erosion formula could be
misleading in multi-spark cases. This paper presents an analytical estimation of MRR as a function of machining
parameters capacitance and voltage for single spark which is then compared with the multi-spark erosion of RC pulse
micro-EDM. The single spark erosion rate is estimated using the electro-thermal theories in which charging and
discharging duration are derived from the RC pulse time constant and the number of sparks per unit time is counted
from the single spark duration. The expression of single spark erosion volume is estimated using heat transfer
equations. It is also difficult to conduct single-spark EDM experiment and it has very little practical implications.
Experiments are conducted to investigate the multi-spark erosion rate. It is shown that, theoretically, the number of
sparks depends on the capacitance and resistance of the circuit. However, in multi-spark erosion, it is found that the
number of effective sparks depend not only the capacitance and voltages but also the conditions of micro-EDM such
as the workpiece and tool materials, flushing conditions, depth of cut. It is shown that the multi-spark MRR is almost
half of the calculated value which is found using the equation of single spark MRR in micro-EDM of copper. Therefore,
the single spark erosion formula needs to be adjusted for each of the workpiece to incorporate with the multi-spark
erosion in real conditions.
Keywords: Micro-electro discharge machining, material removal rate, time constant, multi-spark, nonconductive
ceramic
Nomenclature
C = Capacitance (F)
cp = Specific heat at constant pressure (J/KgK)
E = Total circuit energy per spark (J)
Ew = Energy absorbed by workpiece (J)
Hm = Heat of melting (J/Kg)
Hv = Heat of vaporization (J/Kg)
k = Fraction of total energy consumed for material removal
k1 = Fraction of Ew used for material removal by melting
k2 = Fraction of Ew used for material removal by vaporization
Comparative Study of Material Removal Rate of Single-Spark and Multi-Spark Micro-EDM of Copper
55
Lm = Latent heat of melting (J/Kg)
Lv = Latent heat of vaporization (J/Kg)
Ns = No of sparks per second
R = Resistance (Ω)
T = Temperature (K)
Tb = Boiling temperature (K)
tc = Capacitance charging time (s)
tdc = Capacitance discharging time (s)
Ti = Initial temperature (K)
Tm = Melting temperature (K)
V = Voltage (V)
VC = Voltage between capacitance terminals (V)
Vr = Material removed by vaporization and melting (mm
3
)
VR = Voltage drop over the resistance (V)
ρ = Density of the workpiece material (Kg/mm3)
τ = Time constant circuit (s)
1 Introduction
Micro-electro discharge machining (micro-EDM), a noncontact material removal process, is a suitable technique for
microstructuring of any material having a minimal electrical conductivity of 0.1 Scm
-1
. A series of electrical sparks or
discharges occur rapidly in a short span of time between tool electrode and workpiece during micro-EDM [1, 2]. The
electrical energy is converted into thermal energy instantaneously in micro-EDM and spark energy results in melting
and vaporization of both the workpiece and tool materials [3-6]. About 90% of the molten material is removed by
vaporization and the material beneath the surface gets less energy which is removed by melting [6]. In micro-EDM,
the material is removed precisely by low level of input energy [7]. Therefore, an RC circuit is used in micro-EDM for
pulse creation due to its capability of producing very small energy with a significantly short pulse in nanosecond
duration [7].
The main process characteristics of micro-EDM are material removal rate (MRR), average surface roughness and
tool wear ratio. During micro-EDM, workpiece material is removed by thermal energy created due to the
impingement of ion or electrons. Thus, every spark removes specific amount of material. Knowing the time and
amount of material removed in a single spark, MRR is estimated as micro-EDM process characteristics. However,
MRR is greatly influenced by the discharge duration and peak current even the same materials of both the electrode
and workpiece. Longer discharge duration and a higher peak current result in a higher MRR and TWR with poor
surface finish. On the contrary, a longer discharge duration and lower peak current reduce MRR with better surface
roughness and a lower TWR [8, 9]. The MRR also depends upon the properties of the workpiece material, the tool
material and dielectric fluid. The lower breakdown voltage causes an earlier occurrence of spark, which increases the
MRR. Since Cu has a lower breakdown voltage than CuW, a higher MRR is obtained in micro-EDM of Al2O3 with a
Cu electrode [10].
A number of analytical study have been reported for the estimation of micro-EDM characteristics [11] which are
developed based on amount of material removed in a single spark considering the ideal situations. These models
could not include some of the effects that play a vital role in real micro-EDM process and it is recommended to
consider the effect of multi-spark machining [12, 13]. In multi-spark micro-EDM, charging and discharging do not
always follow the ideal conditions of the circuit [14], and a lot of unwanted pulses such as arching and short circuit
are produced [15] which in turn reduce the effective number of pulses per second. Moreover, in RC pulse micro-
EDM, the discharges are not uniform and the current and voltage are not constant with time [11]. As a consequence,
the performances would not be same as estimated by single spark erosion and should be modified for multi-spark
machining conditions. This paper presents a simple analytical estimation of MRR as a function of machining
parameters capacitance and voltage for single spark which is then compared with the multi-spark erosion of RC pulse
micro-EDM.
2 Single Spark Micro-EDM
To make a comparison between single spark and multi-spark erosion rate, an equation of MRR hence developed
considering the ideal conditions in RC pulse micro-EDM. For single spark analysis the following assumptions are
considered.
1. The workpiece and tool materials are homogeneous in nature.
2. The thermo-physical properties of the workpiece material remain constant during the machining process [3].
3. A fraction of the total spark energy is absorbed into the workpiece by conduction and rest of the energy is
dissipated to the surroundings by convection and radiation [6].
4. The entire material is removed from the cavity after each discharge [16] and debris is not resolidified inside or
around the cavity.
5. The capacitor has no initial voltage and it is charged from a constant voltage source.
6. Ignition delay time is negligible compared to total charging and discharging time.
Ali et al. (2021). International Journal of Engineering Materials and Manufacture, 7(2), 54-60.
56
A diagram of a RC pulse micro-EDM circuit with the voltages at different parts is shown in Fig. 1. It has mainly two
parts; the charging part is connected to a high resistor in series and the discharging part has no resistor or is connected
to a very low resistor. The energy stored in the capacitor during the charging period is completely released through
the gap. The energy discharged (E) in a single spark micro-EDM is given by Eqn. (1) where C is the capacitance and
V is the voltage gap.
2
2
1
CVE = (1)
Thus, charging and discharging time depends on the amount of capacitance and resistances connected to the circuit.
To make a very quick discharge, generally the discharge circuit is kept resistance-free in the ideal condition. However,
the discharging circuit exerts small resistance from dielectric fluid and the machine system. It is obvious that the smaller
the time constant, the more rapidly the voltage gain or decrease that is, the faster the response and the quicker the
dissipation of circuit energy [17].
Figure 1. Schematic diagram of a RC pulse micro-EDM circuit showing the voltages in different parts of charging side
2.1 Estimation of Material Removal per Spark
The single spark energy of a RC micro-EDM circuit as expressed by Eqn. (1) is not utilized completely for material
removal of the workpiece. Only a fraction of the spark energy causes melting and vaporization of the material and
creates a micro-crater. The remaining energy supplied into the gap is lost to the surroundings. Assuming k fraction of
E is utilized to remove material by melting and vaporization, thus, the discharged energy used for material removal
per spark, Ew is given by:
2
2
1
k CVE
w
= (2)
The value of k depends upon the thermal properties of the workpiece material. It is observed that the material is
removed by vaporization (during the discharge) and melting (during the charging) [6]. Assuming, k1 fraction of Ew is
used to vaporize the material and k2 fraction of Ew is used to melt the material only. Thus, the volume of material
removed per spark can be found using Eqn. (3).
+=
mv
r
H
k
H
kkCV
V
21
2
2
(3)
According to Equation (3), the crater volume is the function of capacitance, voltage and volumetric heat of
vaporization and melting. Thus, material removal is controlled by both the electrical parameters and thermal
properties of the work material in RC pulse micro-EDM.
The number of sparks can be found from the RC circuit charging and discharging period estimation. It is observed
that each spark has three stages. In the first stage, the discharge circuit is kept off, the charges are stored in the capacitor
from the electric source and the capacitor voltage rises to its full capacity from zero while its current decreases to
zero. The first stage is called charging or pulse-off time. In the second stage, dielectric breakdown occurs under the
electromagnetic field, the resistance between the tool electrode and the workpiece decreases to zero. The second
stage is referred to as ignition delay time. In the third stage, when there is virtually no resistance between the tool
electrode and the workpiece, spark occurs with high current. The capacitance voltage decreases to zero. This stage is
called discharging or pulse-on time. In this study, ignition delay time is assumed negligible compared to the total
charging and discharging time. Therefore, the total time required for single spark in a RC pulse circuit is the summation
of charging and discharging time of capacitor. Total number of sparks per second (Ns), is the reciprocal of total time
required for single spark and it can be expressed by Equation (4).
)(5
1
55
11
2121
RRCCRCRtt
N
dcc
s
+
=
+
=
+
= (4))
Comparative Study of Material Removal Rate of Single-Spark and Multi-Spark Micro-EDM of Copper
57
The total number of sparks in unit time is the function of capacitance and resistances. Therefore, Ns can be increased
or decreased by changing either the capacitance or resistances or both in a RC pulse micro-EDM circuit.
2.2 MRR for Single Spark
The material removal rate (MRR) is defined as the volume of material removed per unit time. It is calculated by
multiplying the volume of material removed in a single spark by the number of sparks occurring in unit time assuming
that each of the sparks removes same amount of materials. Thus, the MRR is expressed by Eqn. (5) as below.
+=
mv
s
H
k
H
kkCV
NMRR 21
2
2
(5)
This is the expression of MRR for single spark erosion in RC pulse micro-EDM which shows that the electrical
parameters, number of sparks per unit time and thermal properties of the material directly controls the erosion rate.
3 MRR for Multi-spark micro-EDM
Effective spark generation depends on many conditions such as the electrical and physical properties of workpiece
and tool electrode, flushing conditions, spark gap, depth of the machining [16, 19, 20]. Due to the stochastic nature
of micro-EDM, it is difficult to estimate the number of effective sparks theoretically. Therefore, micro-EDM of copper
is conducted to investigate the deviation of experimental MRR from the MRR of ideal conditions. Experiments were
accomplished by a multi-purpose miniature machine tool (DT-110, Mikrotools Inc., Singapore) using the machining
conditions as given in Table 1. The DOE was done based on two parameters capacitance and voltage of four levels
as shown in Table 2.
Twelve experiments based on selected parameters (Table 2) were designed and conducted. Micro-holes were drilled
on copper workpiece with 1 mm diameter copper tool electrode using kerosene dielectric fluid. To investigate the
material removal mechanism and crater geometry, a SEM micrograph of the machined copper workpiece was
captured as shown in Fig. 2. Copper micro-craters are observed to have a clear and identical geometric pattern
because of the uniform removal of material by melting and vaporization. The micrograph also showed no cracks on
the machined surface and micro-crater is spherical in shape.
Finally, actual volume of the removed material was found by measuring the depth and diameter of the drilled
holes. Then MRR was then calculated for each of the experiments. The twelve experiments and their corresponding
MRR are listed in Table 3. The theoretical MRR (Eqn. 5) and experimental actual MRR are compared graphically as
shown in Fig. 3. It is observed from Fig. 3 that the experimental MRR is about half of the theoretical MRR. Eqn. (5)
has been formulated considering the ideal situation based on a single spark erosion volume. In multi-spark machining,
charging and discharging do not follow the estimated time constant and there are many missing sparks among the
estimated number of theoretical sparks. As such the number of effective sparks is less than the theoretical number of
sparks in micro-EDM which reduces the MRR in multi-spark machining condition. Therefore, the MRR as expressed
by Eqn. (5) is found to be valid for single spark machining only and it is not valid for multi-spark machining for real
application in making molds and or other products. However, the single-spark MRR expression can be adjusted to
use for multi-spark MRR purposes. As such based on experimental study as discussed above, Eqn. (5) can be
transformed for multi-spark MRR purposes by with a multiplying factor, η as expressed by Eqn. (6). The value of the
correction factor would be different for different materials and conditions which would be estimated empirically. In
this experimental study of copper workpiece material, the value of the multiplying factor was found to be η = 0.5.
+=
mv
sadj
H
k
H
kkCV
NMRR 21
2
2
(6)
Table 1. Micro-EDM conditions for copper material [6]
Conditions Values
Variable parameter
Capacitance, C (nF) 10, 1, 0.22, 0.1
Voltage, V (V) 100, 90, 80
Constant conditions
Specific heat, cp (J/Kg
0
C) 390
Melting temperature, Tm (
0
C) 1084
Boiling temperature, Tb (
0
C) 2562
Room temperature, T0 (
0
C) 20
Latent heat of melting, Lm (J/Kg) 207000
Latent heat of vaporization, Lv (J/Kg) 4730000
Density, ρ (Kg/m3) 8960
RC circuit resistance, R1 (Ω) 1000
Ali et al. (2021). International Journal of Engineering Materials and Manufacture, 7(2), 54-60.
58
Conditions Values
Fraction of energy consumed for material removal, k (%) 4.35
Fraction of energy consumed for material removal by melting, k1 0.11xk
Fraction of energy consumed for material removal by vaporization, k2 0.89xk
Dielectric fluid Kerosene
Cylindrical copper rod tool electrode diameter (mm) 1
Tool polarity -ve
Feed rate, f (µm/s) 0.2
Speed, n (rpm) 300
Table 2. Experimental Micro-EDM parameters for MRR of copper workpiece
Parameter Level
I II III IV
Capacitance C (nF) 0.1 0.22 1 10
Voltage V (V) 80 90 100 110
Table 3. Theoretical and experimental MRR in micro-EDM
C
(nF)
V
(V)
MRR (mm
3
/s)
(Eqn. 5)
MRRex
(mm
3
/s) MRR
MRR
ex
1 10 100 0.001586 0.000726 0.458
2 10 90 0.001285 0.000664 0.517
3 10 80 0.001015 0.000523 0.516
4 1.0 100 0.001586 0.000633 0.400
5 1.0 90 0.001285 0.000603 0.470
6 1.0 80 0.001015 0.000503 0.496
7 0.22 100 0.001586 0.000876 0.552
8 0.22 90 0.001285 0.000790 0.615
9 0.22 80 0.001015 0.000669 0.660
10 0.1 100 0.001586 0.000654 0.412
11 0.1 90 0.001285 0.000510 0.397
12 0.1 80 0.001015 0.000458 0.451
Figure 2. SEM micrograph of surface texture in micro-EDM of copper showing a spherical micro-crater.
Spherical cavity created by
single spark
10 µm
1.
Comparative Study of Material Removal Rate of Single-Spark and Multi-Spark Micro-EDM of Copper
59
Figure 3. Comparison of theoretical and experimental MRR of micro-EDM of copper
4 Conclusions
In this study, the mechanism of material removal and the MRR for single-spark and multi-spark micro-EDM are
compared. MRR due to single spark is formulated based on electro-thermal mechanism. Then during real
experimental machining number of sparks and total machining time are counted. The volume of material removal
was measured and then converted into MRR. The experiments were repeated many times and a significant difference
in MRR due to single-spark and multi-spark micro EDM was observed. The specific findings of this study are as
follows:
1. In ideal conditions, number of spark depends on capacitance and resistance. The number of effective sparks is
found to be identical with theoretically calculated values at the initial machining stage. However, the frequency
of effective discharges decreases with the progress of the machining due to inability of debris flushing.
2. In micro-EDM of copper, it is observed that the experimental MRR in multi-spark is almost half of the theoretical
MRR in single spark. This indicates that the MRR reduces by a higher percentage due to the creation of
ineffective pulses in multi-spark erosion. Therefore, a correction factor is needed to adjust in multi-spark erosion.
3. The MRR in multi-spark micro-EDM is the function of effective sparks generated in the specified duration which
depends on many factors such as the electrical and physical properties of materials, flushing conditions, spark
gap, depth of the machining. As an experimental correction factor, it includes all these conditions in estimation
of MRR.
4. In this experimental study it was found that the correction factor is to be 0.5 for coper workpiece and copper
tool electrode (i.e., = 0.5 in Equation 6)
Acknowledgements
The authors would like to thank the Ministry of Higher Education of Malaysia (MOHE) for financial support under
Research Grant FRGS 14-131-0372.
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