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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 2, February 2019, pp. 1461–1479, Article ID: IJMET_10_02_152
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=2
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication Scopus Indexed
A NEW METHODOLOGY FOR PREDICTING
QUANTITY OF AGGLOMERATION BETWEEN
ELECTRODES IN PMEDM ENVIRONMENT
Mohammed Abdulridha Abbas
Faculty of Mechanical and Manufacturing Engineering
University Tun Hussein Onn Malaysia, Parit Raja, Johor Bahru, Malaysia;
Sustainable Manufacturing and Recycling Technology, Advanced Manufacturing and
Materials Center (SMART-AMMC)
University Tun Hussein Onn Malaysia, Parit Raja, Johor Bahru, Malaysia;
Aeronautical Techniques Engineering Department
Al-Furat Al-Awsat Technical University (ATU), Engineering Technical College (ETCN),
Main Hilla-Baghdad Road, Iraq
Mohd Amri Bin Lajis
Faculty of Mechanical and Manufacturing Engineering
University Tun Hussein Onn Malaysia, Parit Raja, Johor Bahru, Malaysia;
Sustainable Manufacturing and Recycling Technology, Advanced Manufacturing and
Materials Center (SMART-AMMC)
University Tun Hussein Onn Malaysia, Parit Raja, Johor Bahru, Malaysia
Ghassan Shaker Abdul Ridha
Department of Mechanical Technical/Production, Kut Technical Institute, Middle Technical
University, Baghdad, Iraq
ABSTRACT
The powder mixed-EDM (PMEDM) is a prominent field in precise manufacturing
where the material removal operation depends on the electrical erosion mechanism
between electrodes in this environment. Prior studies strived to improve the
performance of this field, but the obstacles represented by controlling the parameters
of this environment created difficulties for the researchers. One of the most important
results of this situation is the agglomeration problem between the electrode tool and the
workpiece that leads to the collapse of the spark. Thus, the performance of PMEDM
environment declines. This study covers the primary reasons for the occurrence of the
agglomeration phenomenon in PMEDM. In addition, this study proposes a new
methodology to compute the quantity of agglomeration through introducing new
hypotheses and procedures. Following from here, the proposed methodology is able to
determine the dimensions of the recast layer zone and the density of this zone. Energy
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Dispersive Spectroscopy (EDS) or Optical Emission Spectrometry (OES) plays an
important role in specifying the weight percentage of workpiece elements before and
after machining in PMEDM. This study adopted a previous study which observed D2
steel before and after machining in PMEDM by using OES. Furthermore, it applies
virtual dimensions of the melting area and the recast layer zone for proving this
proposed methodology. Therefore, the total agglomeration for D2 steel is 0.003942529
mg while the active agglomeration of tungsten, carbon, molybdenum, and manganese
is 0.001971264 mg. Moreover, the square of the correlation factor (R-sq) and R-sq
(adj.) resulting from multiple linear regression analysis for the total agglomeration of
D2 steel are 99.36% and 98.97%, respectively. Finally, this methodology presents a
new mechanism to specify the performance of PMEDM through adopting the
agglomeration ratio as a new criterion. Thus, the agglomeration ratio according to the
proposed methodology came up to (50%) which implies that the agglomeration did not
exceed the critical stage.
Keywords: PMEDM, EDM, Recast layer thickness, Agglomeration, Ring method.
Cite this Article: Mohammed Abdulridha Abbas, Mohd Amri Bin Lajis and Ghassan
Shaker Abdul Ridha, A New Methodology for Predicting Quantity of Agglomeration
Between Electrodes In PMEDM Environment, International Journal of Mechanical
Engineering and Technology (IJMET) 10(2), 2019, pp. 1461–1479.
http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=2
1. INTRODUCTION
The addition of the fine powder particles to the dielectric fluid in Electrical Discharge
Machining (EDM) led to the occurrence of a qualitative leap to the performance [1]-[3]. This
emerging environment has become more active by building a separate basin collected with
EDM machine known as Powder Mixed-EDM (PMEDM) [4],[5]. Figure 1 indicates the
components of the PMEDM environment.
Figure 1 Components of PMEDM environment.
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The main reason causing the usage of the powder particles with the EDM machine is
attributing to the dielectric fluid. The dielectric fluid tries to resist the passage of electrical spark
to the workpiece. Consequently, the breakdown of the resistance of dielectric fluid depends on
the breakdown of the electric field as shown in Equation. (1) and needs a sufficient polarized
force according to Equation. (2) to overcome this resistance as given below [6]:
𝐸𝐵𝐷 = 1 (𝜀𝐷𝐹 − 𝜀𝑏) [2𝜋𝑆𝑡(2𝜀𝐷𝐹+𝜀𝑏)
𝑟𝑏{𝜋
4√
𝑉𝑏
2𝑟𝑏𝐸− 1}]
0.5
⁄ (1)
𝐹𝑝 = 0.5 𝑟𝑏3 (𝜀𝑏−𝜀𝐷𝐹)
2𝜀𝐷𝐹+𝜀𝑏𝑔𝑟𝑎𝑑 𝐸2 (2)
Where:
𝐸𝐵𝐷 : Breakdown of the electric field formed between the electrode tool and
the workpiece.
𝐸 : The electric field between the electrode tool and workpiece in EDM.
𝜀𝑏 : The permittivity of the gas bubble produced from the reaction between
the electric spark and dielectric fluid.
𝜀𝐷𝐹 : The permittivity of the dielectric fluid in EDM machine.
𝑟𝑏 : Bubble radius.
𝑉𝑏 : Minimum drop voltage in the bubble.
𝑆𝑡 : The Surface tension of the dielectric fluid.
𝐹𝑝 : The Polarized force produced from the electric field.
The polarizing force in EDM required additional electrical power to conquer the impedance
of the dielectric fluid. In PMEDM environment, this force and other forces are more active with
erosion dynamic as denoted in Figure 2 and Equations. (3)-(5) given below [7]:
𝐹𝑙 = 𝜋 8⁄ 𝑢𝑑𝑝3𝜌𝜔 (3)
𝐹𝑑 = 6𝜋𝜇𝐷𝐹𝑟𝑝𝑣𝑝 (4)
𝐹𝑐 = 𝑞𝐸 (5)
Where:
𝐹𝑙 : Particle lift force at minimal Reynolds number.
𝐹𝑑 : Drag force depending on Stokes theorem.
𝐹𝑐 : Columbic force.
𝑢 : Uniformly dielectric fluid velocity.
𝑑𝑝 : Particle diameter.
𝜌 : Dielectric fluid density.
𝜔 : Particle angular velocity.
𝜇𝐷𝐹 : Dielectric fluid viscosity.
𝑟𝑝 : Particle radius.
𝑣𝑝 : Particle velocity.
𝑞 : Particle charge.
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The zig-zag bridge between the electrode tool and the workpiece is formed relying on the
added powder particles onto the dielectric fluid. This bridge contributes effectively in breaking
down the impedance of dielectric fluid in EDM as shown in Figure 3 [8]. Thus, Equation. (1)
is enhanced to be more suitable with the new case according to Equation. (6) [7].
𝐸𝐵𝐷2 = 𝐸𝑖
2 −2𝑘𝐵𝑇
𝜀𝐷𝐹(2𝜀𝐷𝐹+𝜀𝑝
𝜀𝑝−𝜀𝐷𝐹) [
1
𝑟𝑝3 (𝑙𝑛
𝐶𝑓
𝐶𝑖)] (6)
Where:
𝐶𝑖 : The initial powder concentration.
𝐶𝑓 : The final powder concentration.
𝐸𝑖 : Initial voltage at 𝐶𝑖.
𝐸𝐵𝐷 : Breakdown voltage at 𝐶𝑓.
𝜀𝑝 : The permittivity of the particle suspended in dielectric fluid.
𝑘𝐵 : Boltzmann constant based on Stokes-Einstein predictions [9],[10].
𝑇 : Temperature of dielectric fluid [9],[10].
Figure 2 Effect forces on the particle in PMEDM environment.
Figure 3 Zig-Zag bridge resulted from mixed particle powder with dielectric liquid in EDM Machine.
A New Methodology For Predicting Quantity of Agglomeration Between Electrodes In
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Equation. (6) is formulated on the basis of neglecting the mass of particles suspended in the
dielectric fluid [7]. Unfortunately, this scientific perspective does not match the experimental
truth which proved that the agglomeration case is affected by the size and density of the powder
particles [11]. Furthermore, other suspended particles are also responsible for the status of
agglomeration between the electrodes in EDM which is generated from the decomposition of
dielectric fluid and the residues of the debris [12].
The surplus of the removal rate of any workpiece is conducive in decreasing the quality of
machining in PMEDM. As an example, CK45 alloy is machined through blending fixed amount
of Al2O3 powder at 2.9 gm/cm3 with kerosene in EDM machine and used the maximum peak
current (IP = 11 Amps) with a minimum pulse duration and discharge voltage that is (Ton = 50
µs) and (Vd = 50 Volt), respectively. Hence, these parameters contribute to mounting the
Material Removal Rate and the Average of Surface Roughness of this alloy to (MRR = 14.4
g/h) and (Ra = 5.1 µm), respectively [13]. This situation is observed through machining of
titanium alloy utilizing 2 g/L of the Carbon NanoTubes (CNTs) powder with the peaking of
both current and duration that equals to 48 Amps and 400 µs successively which leads to
growing up the level of MRR to be 1.65 mm3/min and Ra to be 0.24 µm [14].
The irrational amount of powder in EDM has side effects upon the machinability in this
environment. The evidence of this case is, in the β-Titanium alloy, the high level of
microhardness and average of surface roughness are 784.71 HV and 1.31 µm, respectively.
These responses have taken place during applying a maximal value of Ton = 100 µs and
uttermost of tungsten powder concentration (PC = 6 g/L) with IP = 5 Amps [15]. Although
reducing both the parameters related to the pulse in PMEDM, that is electric current and time,
during electrical eroding of D2 steel, the increasing of the silicon powder to be higher than 5
g/L leads up to the reduction of MRR to be 12.280 mm3/min [16].
The unreasonable growing of the peak current, pulse duration, and powder concentration in
PMEDM through these experimental results reflect the undesirable performance of the MRR
and Ra. This performance resulted from the massive electrothermal energy located in the spark
gap generated from increasing the values of these parameters. This energy is responsible for
obtaining the removal operation in the workpiece and the phenomenon of eroding in the
electrode tool. Consequently, the plasma channel is not equally distributed and only
concentrates in a limited area and produces deep craters. In addition, the debris formed by this
energy cannot be fully ejected away from the melting region. Eventually, this debris
agglomerates with the remaining of the additive powder particles and carbon particles which
results from the decomposing of the dielectric fluid. The collapse of the spark is an inevitable
result based on the agglomeration situation in order to form a short circuit with un-useful
performance in PMEDM [14],[17]–[20]. Therefore, the agglomeration phenomenon in the
PMEDM environment occurs by adding the powder in the EDM environment as an external
factor to enhance it and all interpretations presented by the previous studies in the PMEDM
meant this trend. Meanwhile, the other direction is concerned by the internal agglomeration
occurring from the debris and carbon particles that result from the workpiece, electrode tool,
and dielectric fluid. According to that, this direction does not align with the previous direction
in terms of the behaviors of parameters since it represents the environment of pure EDM.
It turned out that the primary role of the massive increase in the electrothermal energy is to
incidence the agglomeration of powder between the electrodes in PMEDM. One of the most
significant contributors to perform this is the positive polar in this environment which is done
by adding the aluminum powder to distilled water in EDM for machining W300 steel. The
positive pole produces a higher value of MRR = 33.33 mg/min and Ra = 3.94 µm as compared
to the negative pole [21]. Figure 4 refers to the summary of the reasons that led to the powder
agglomerating problem in the PMEDM environment.
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Figure 4 Schematic summary clarifies the reasons of the powder agglomeration case in PMEDM.
Table 1 Active elements of some sample after machining in PMEDM system that observed by EDX,
EDS, and OES.
N Workpiece
Type
Powder
Type
Electrode
Tool Type
Testing
Device
Active
Element
Reference
No.
1 Ti-15 Mn CuW EDX C, Mn, Cu, W [24]
2 ɣ-TiAl
Intermetallic Cr Cu EDS C, O, Cu, Cr [25]
3 Inconel 800 Co Graphite EDS C, O, Al [26]
4 Ti-6Al-4V Graphite Cu EDS C, O, Cu [27]
5 D2 Steel W Cu OES C,W, Mn, Mo [20]
Deposited powder particles, accumulated debris, and decomposed particles from dielectric
fluid represent the main idea of the external and internal agglomerated in the PMEDM
environment. Thus, the Energy Dispersive Spectroscopy (EDS or EDX) and Optical Emission
Spectrometry (OES) devices are necessary to specify the percentage of these migrated particles
to a workpiece [22],[23]. Table 1 illustrates the active elements for some samples used in
PMEDM tested by these devices. Through this brief literature available, the number of studies
achieved that applied EDS before and after machining is very limited in the PMEDM
environment. In addition, the researchers did not highlight the problem of agglomerating in this
environment. Consequently, the need to present a new methodology to predict the
agglomeration quantity is a substantial objective which will be revealed in this paper.
A New Methodology For Predicting Quantity of Agglomeration Between Electrodes In
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2. PREDICTION RECAST LAYER VOLUME
Numerous experimental studies were performed in both EDM and PMEDM fields that focused
on the machining region. This region is produced from treating plasma channel with workpiece
immersed in the pure or mixed dielectric fluid. The thickness of this region is known as Recast
Layer Thickness (TRL). This layer is located under the melting region and will be quenched
with the dielectric fluid during the pulse interval at every single spark [28]. Figure 5 clarifies
the location of TRL after machining in PMEDM.
Figure 5 Recast layer zone between melting region and Heat Affected Zone (HAZ).
The numerical prediction followed by the researchers in electrical erosion in EDM or
PMEDM is based on Finite Element Analysis (FEA). The intensity of the plasma channel in
the spark region controls the crater volume to measure the efficiency of this channel. TRL in
Equation. (7) depends on this efficiency with crater depth as clarified in Equation. (8) [29].
𝑇𝑅𝐿 = 𝑑𝑐(1 − 𝜂𝑝𝑐) (7)
𝜂𝑝𝑐 = 𝑉𝐸 𝑉𝑁⁄ × 100 (8)
Where:
𝑑𝑐 : Crater depth produced from single spark in EDM.
𝜂𝑝𝑐 : Efficiency of plasma channel.
𝑉𝐸 : Volume of crater resulted from experimental side.
𝑉𝑁 : Volume of crater resulted from numerical side based on FEA.
Equation. (9) is another procedure for estimating this thickness which also relies on FEA,
but with a different description. Area of this layer (ARL) depends on the height (TRL) and width
(we) of the number of elements (n) [30].
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Figure 6 Steps of hypotheses utilized to predict the recast layer in this study: (a) Top view (1) and
front view (2) of a sectional workpiece with the electrode tool in PMEDM; (b) SEM to observe the
melting region and recast layer for modeling it 3D CAD; (c) The ring method to predict rotational
volume.
𝑇𝑅𝐿 = ∑ 𝐴𝑅𝐿 𝑛 𝑤𝑒⁄𝑛𝑖=1 (9)
Figure 6 covers the new vision in predicting (TRL) in this study. The proposed vision in this
paper depends on the following hypotheses:
A New Methodology For Predicting Quantity of Agglomeration Between Electrodes In
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1. Adopting a sectional workpiece described in Figure 6(a.1) and (a.2) as top and side view
respectively with the experimental side of PMEDM. The motive of performing this
mechanism with the workpiece is to precisely identify the thickness of the recast layer
directly without needing to cut it after machining in the PMEDM and also to prevent the
thermal effect generated by the Wire EDM machine or any other machines upon the
machining region [18],[31].
2. Approving Scanning Electron Microscope (SEM) to observe the recast layer zone. This
observation will be converted to 3D CAD to specify the volume of the recast layer and the
thickness of it [32],[33]. Figure 6(b) reflects this idea that will be applied to measure this
region.
3. Assuming a uniform layer of the melting region and the recast layer in PMEDM. This
assumption assists to prophesy the sizes of these regions mathematically through the Ring
Method to specify the rotational volume [29],[34],[35]. Figure 6(c) refers to the melting
region and the recast layer as ring layers.
Existence of the melting region in the mathematical model is vital to determine the recast
layer volume. Therefore, the boundary conditions (BCs) will be implemented with the rotational
volume by using the Ring Method as mentioned in Equation. (10). Figure 7 illustrates the
integration slices of the fusion region and recast layer zone in the machined workpiece.
𝐵𝐶𝑠 = {0 = 𝑟 ≤ 𝑅0 = 𝑑 ≤ ℎ
(10)
Figure 7 Integration slice and radiuses of active areas in workpiece machined in PMEDM.
In Figure 7, the slices (𝑑ℎ, 𝑑𝑐) and radiuses (𝑅, 𝑅𝑐) according to the boundary conditions
in Equation. (10) will be applied in Equation. (11) [36],[37].
𝑉𝑅𝐿 = ∫ 𝐴ℎ 𝑑𝑦 −𝑦ℎ0 ∫ 𝐴𝑐 𝑑𝑦
𝑦𝑐0
= 𝜋/2∫ 𝑅2 𝑑ℎℎ
0− 𝜋/2∫ 𝑅𝑐
2 𝑑𝑐𝑐
0 (11)
Then, the recast layer volume (𝑉𝑅𝐿) is given by:
𝑉𝑅𝐿 = 𝜋/2(𝑅2 ℎ − 𝑅𝑐
2𝑐 ) (12)
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Where:
Ah : Base area of hole (mm2)
Ac : Base area of melting region (mm2)
Rc : Final machining radius (mm).
R : Total radius consists of machining radius (𝑅𝑐) and recast layer
thickness (𝑇𝑅𝐿) in (mm).
c : Final machining depth (mm).
h : Total depth consists of machining depth (𝑐) and recast layer thickness
(𝑇𝑅𝐿) in (mm).
3. COMPUTATION AGGLOMERATION QUANTITY
After the removing operation has taken place from the workpiece during machining with the
PMEDM system, the machined surface, which is considered as the upper surface of the recast
layer region will be exposed to the particle agglomeration as demonstrated in Figure 8.
Figure 8 Agglomeration area on the treated surface within the recast layer region.
The particle agglomeration reflects the influential amount concentrated in the machined
region represented by the increase in weight percentages of elements in the workpiece after
machining in PMEDM. Therefore, these particles may contribute in reducing the performance
in PMEDM. Thus, the agglomeration quantity can be calculated using the following proposed
procedures:
1. Utilize EDS or OES for inspecting the treated surface of the workpiece before and after
machining. The objective of this testing is to record the weight percentages of the workpiece
elements.
2. Assuming the density of the recast layer is the same density of workpiece in order to control
the computational model fluently. Therefore, the total weight percentage of this layer
depending on the density of this layer and the volume of it is calculated by using Equation.
(12) that leads to the appearing of the following equation:
𝑚𝑅𝐿 = 𝜌𝑅𝐿 𝑉𝑅𝐿 (13)
3. Distributing the mass of this layer (𝑚𝑅𝐿) on the recorded weight percentages of the
elements. Equation. (14) indicates the mass of every element in the workpiece either before
or after machining.
𝑚𝑒 = 𝑚𝑅𝐿 %𝑤𝑡𝑒 (14)
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4. Compute the total agglomeration (𝑚𝑇𝐴𝐺) which results from the sum of the absolute
difference of the mass at each element before machining (𝑚𝑒𝑏𝑚) and after machining
(𝑚𝑒𝑎𝑚) as expressed in Equation. (15). This amount covers the increasing and decreasing
values of mass for each element.
𝑚𝑇𝐴𝐺 = ∑ |𝑚𝑒𝑎𝑚 −𝑚𝑒𝑏𝑚| 𝑛𝑖𝑛=1 (15)
5. The active elements that will agglomerate after machining reflects the increase of the mass
value at each element. Thus, the active agglomeration depends on these increments and
interprets as in Equation. (16).
𝑚𝐴𝐺 = ∑ (𝑚𝑒𝑎𝑚 −𝑚𝑒𝑏𝑚) 𝑛𝑖𝑛=1 (16)
6. The agglomeration ratio in the PMEDM system depends on the active agglomeration per
total agglomeration. Equation. (17) provides a new interpretation of the performance of
this phenomenon depending on the agglomeration condition.
𝜂𝐴𝐺 = 𝑚𝐴𝐺 𝑚𝑇𝐴𝐺⁄ × 100% (17)
Where:
𝑚𝑅𝐿 : Mass of recast layer region (mg).
𝜌𝑅𝐿 : Recast layer density (mg/mm3).
𝑚𝑒 : Element mass (mg).
%𝑤𝑡𝑒 : Element weight percentage.
3.1. Agglomeration Environment
The new hypotheses and procedures to predict recast layer volume and agglomeration of
particles presented in this paper represents a new methodology. This methodology requires an
environment for the application to determine the quantity of agglomeration. This study adopts
Kumar and Batra [20] observations by using OES performed on D2 steel before and after
machining as can be seen in Table 2 Unfortunately, the study mentioned in Table 2 did not
mentioned the dimensions of the workpiece, electrode tool diameter, hole depth, hole radius,
and recast layer thickness [20]. Thus, to compute the agglomeration quantity according to the
methodology proposed in this paper, we assume the dimensions for the machining zone in the
workpiece is as described in Table 3:
4. INVESTIGATION MODELING
The investigation with this new methodology is carried out based on multiple linear regression
method [38]. Modeling the agglomeration equation with this method represents a validation
step with this methodology. The quantity (𝑚𝑇𝐴𝐺) is the primary response which is related to
(%𝑤𝑡𝑒𝑏) and (%𝑤𝑡𝑒𝑎) to form the desired equation. The model of total agglomeration with
multiple linear regression is:
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Table 2 OES observations performed by Kumar and Batra [20].
N Element
%𝒘𝒕𝒆
Before
Machining in
PMEDM
%𝒘𝒕𝒆𝒃
After
Machining in
PMEDM
%𝒘𝒕𝒆𝒂
1 C 1.57 1.91
2 Si 0.19 0.17
3 Mn 0.07 0.09
4 Cr 12.38 11.57
5 W - 2.43
6 V 0.96 0.93
7 Mo 0.76 0.78
8 Ni 0.09 0.09
9 Iron 83.98 82.03
Table 3 Virtual dimensions that will be utilizing in this study.
N Item Unit Dimensions
1 Workpiece volume mm3 7.5 × 7.5 × 10
2 Diameter of electrode tool mm 10
3 Final machining depth (𝑐) mm 0.02
4 Final machining radius (𝑅𝑐) mm 0.05
5 Final recast layer thickness (𝑇𝑅𝐿) mm 0.01
𝑚𝑇𝐴𝐺 = 𝐶0 + 𝐶1 %𝑤𝑡𝑒𝑏 + 𝐶2 %𝑤𝑡𝑒𝑎 + 𝐶3 %𝑤𝑡𝑒𝑏 %𝑤𝑡𝑒𝑎 + 𝑒 (18)
Then, the square of error (SE) in this quantity is:
𝑆𝐸 = ∑ (𝑚𝑇𝐴𝐺 − 𝐶0 − 𝐶1 %𝑤𝑡𝑒𝑏 − 𝐶2 %𝑤𝑡𝑒𝑎 − 𝐶3 %𝑤𝑡𝑒𝑏 %𝑤𝑡𝑒𝑎)2𝑛
𝑖=1 (19)
Here, minimum (SE) leads to:
𝜕𝑆𝐸
𝜕𝐶𝑛=
{
𝜕𝑆𝐸 𝜕𝐶0⁄
𝜕𝑆𝐸 𝜕𝐶1⁄
𝜕𝑆𝐸 𝜕𝐶2⁄
𝜕𝑆𝐸 𝜕𝐶3⁄
= 0 (20)
Then, Equation. (19) develops to be:
∑𝑚𝑇𝐴𝐺 = ∑𝐶0 + ∑𝐶1 %𝑤𝑡𝑒𝑏 + ∑𝐶2 %𝑤𝑡𝑒𝑎 + ∑𝐶3 %𝑤𝑡𝑒𝑏 %𝑤𝑡𝑒𝑎 (21)
∑𝑚𝑇𝐴𝐺%𝑤𝑡𝑒𝑏 =∑𝐶0 %𝑤𝑡𝑒𝑏 +
∑𝐶1 %𝑤𝑡𝑒𝑏2 +∑𝐶2 %𝑤𝑡𝑒𝑏 %𝑤𝑡𝑒𝑎 + ∑𝐶3 %𝑤𝑡𝑒𝑏
2 %𝑤𝑡𝑒𝑎 (22)
∑𝑚𝑇𝐴𝐺 %𝑤𝑡𝑒𝑎 =∑𝐶0 %𝑤𝑡𝑒𝑎 +
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∑𝐶1 %𝑤𝑡𝑒𝑎 %𝑤𝑡𝑒𝑏 +∑𝐶2 %𝑤𝑡𝑒𝑎2 + ∑𝐶3 %𝑤𝑡𝑒𝑏 %𝑤𝑡𝑒𝑎
2 (23)
∑𝑚𝑇𝐴𝐺%𝑤𝑡𝑒𝑏 %𝑤𝑡𝑒𝑎 =∑𝐶0%𝑤𝑡𝑒𝑏%𝑤𝑡𝑒𝑎 +
∑𝐶1%𝑤𝑡𝑒𝑏2 %𝑤𝑡𝑒𝑎 + ∑𝐶2%𝑤𝑡𝑒𝑏 %𝑤𝑡𝑒𝑎
2 +∑𝐶3%𝑤𝑡𝑒𝑏2%𝑤𝑡𝑒𝑎
2 (24)
To compute the coefficients (C0, C1, C2, C3) mentioned in Equation. (18) and the derivative
in Equations. (21)-(24), the matrix arranges the last equation to be:
=
ebeaTAG
eaTAG
ebTAG
TAG
3
2
1
0
2ea
2eb
2eaebea
2ebeaeb
2eaeb
2eaeaebea
ea2
ebeaeb2
ebeb
eaebeaeb
%wt %wt m
%wt m
%wt m
m
C
C
C
C
%wt %wt%wt %wt%wt %wt%wt %wt
%wt %wt%wt%wt %wt%wt
%wt %wt%wt %wt%wt%wt
%wt %wt%wt%wtn
(25)
Ultimately, Equation. (25) will determine these coefficients using Gaussian elimination.
The investigated model can be implemented by using Minitab software to describe the multiple
linear validations with the agglomeration quantity according to the new methodology proposed
in the present study. The flowchart elucidated in Figure 9 shows the new methodology
proposed in this paper to prognosticate the agglomeration quantity between the workpiece and
electrode tool in PMEDM.
Figure 9 New methodology to predict the agglomeration quantity.
Mohammed Abdulridha Abbas, Mohd Amri Bin Lajis and Ghassan Shaker Abdul Ridha
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5. RESULTS AND DISCUSSION
The hypotheses presented here in order to predict (𝑉𝑅𝐿) leads to assigning this volume by using
Equation. (12) The mass density of D2 steel adopted in this study is (𝜌𝑤𝑝 = 7.7 mg/mm3) with
the virtual values of dimensions in Table 3 produces (𝑉𝑅𝐿 =9.11062E-05 mm3). Also, the mass
of this region according to Equation. (13) is (𝑚𝑅𝐿 =0.000701518 mg). These outcomes have
been prepared to estimate the mass of elements using Equation. (14). Therefore, these masses
are displayed in Table 4 depending on the weight percentage mentioned in Table 2
Table 4 Mass values before and after machining in PMEDM for each element with both total and
active agglomeration according to the new methodology.
N Element
𝒎𝒆 (mg)
𝒎𝒆𝒂𝒎
−𝒎𝒆𝒃𝒎
|𝒎𝒆𝒂𝒎
−𝒎𝒆𝒃𝒎| Before
Machining in
PMEDM
After
Machining
in PMEDM
1 C 0.001101383 0.001339890 0.00023851 0.000238515
2 Si 0.000133288 0.000119258 -0.00001403 0.000014030
3 Mn 0.000049106 0.000063136 0.00001403 0.000014030
4 Cr 0.008684788 0.008116559 -0.00056822 0.000568229
5 W 0 0.001704688 0.00170468 0.001704687
6 V 0.000673457 0.000652411 -0.00002104 0.000021045
7 Mo 0.000533153 0.000547184 0.00001403 0.000014030
8 Ni 0.000063136 0.000063136 0 0
9 Iron 0.058913451 0.057545492 -0.00136795 0.001367959
𝑚𝑇𝐴𝐺 (mg) 0.003942529
𝑚𝐴𝐺 (mg) 0.00197126
The total absolute of the estimated difference in Table 4 refers to the total agglomeration
quantity (𝑚𝑇𝐴𝐺) relying on Equation. (15). The significant point within these results is the
weight percentage of elements without iron before and after machining are 16.02% and 17.97%,
respectively. The interpretation of this case is that the incremental value of the migrated
elements based on the weight percentage is 1.95%, while this value according to the mass is
0.001367959 mg. Figure 10 with the results mentioned in Table 2
Table 4 refers to the active agglomeration (𝑚𝐴𝐺) value produced by the increasing mass of
each element. This outcome represents the realistic amount of agglomeration since it focuses
on the only incremental amount of each element mass. From this point, the significant elements
that agglomerated are carbon (C = 0.000238515 mg) and tungsten (W = 0.001704687mg) with
slight effect of manganese and molybdenum. These results built on the proposed hypotheses in
the present study to predict TRL and the procedures to compute the agglomeration has proved
the experimental results of Kumar and Batra [20]. In addition, these outcomes proved that the
external agglomeration by tungsten powder occurs resulted from adding this powder in a pure
EDM environment with a slight effect of accumulated particles produced from the debris of
electrodes and decomposed dielectric fluid [12],[17],[19],[39],[40]. Table 5 clarifies the
analysis of variance (ANOVA) for the weight ratio of chemical composition before machining
(%𝑤𝑡𝑒𝑏) and after machining (%𝑤𝑡𝑒𝑎) with total agglomeration as the response (𝑚𝑇𝐴𝐺).
Through ANOVA outcomes in Table 5, the amount of (%𝑤𝑡𝑒𝑎) has a considerable
contribution in the regression modeling and demonstrated the increasing value of this
percentage and the active effect of it in (𝑚𝑇𝐴𝐺). This analysis is based on the investigation
A New Methodology For Predicting Quantity of Agglomeration Between Electrodes In
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modeling which adopts the multiple linear regression. Thus, the regression equation for the total
agglomeration with the coefficients using Equation. (18) and Equation. (25) will be:
𝑚𝑇𝐴𝐺 = −0.000044 + 0.00071 %𝑤𝑡𝑒𝑎 − 0.000606 %𝑤𝑡𝑒𝑏 − 0.000001 %𝑤𝑡𝑒𝑏 %𝑤𝑡𝑒𝑎 (26)
Figure 10 Active agglomeration of elements after machining of D2 steel in PMEDM.
Table 5 Analysis of variance (ANOVA) for the total agglomeration based on the multiple linear
regression.
Source DF Seq SS
×105 Contribution
Adj
SS
×105
Adj
MS
×105
F-Value P-Value
Regression 3 0. 3 99.36% 0.3 0.1 257.90 0.000
%𝑤𝑡𝑒𝑎 1 0. 1 32.06% 0.2 0.2 543.66 0.000
%𝑤𝑡𝑒𝑏 1 0. 2 55.42% 0.2 0.2 480.38 0.000
%𝑤𝑡𝑒𝑎 × %𝑤𝑡𝑒𝑏 1 0.0 11.89% 0.0 0.0 92.55 0.000
Error 5 0. 0 0.64% 0.0 0.0
Total 8 0. 3 100.00%
Where:
DF : Degree of freedom.
Seq SS : Sequential sum squares related to parameter variation in model.
Adj SS : Adjusted sum squares related to parameter variation in model.
Adj MS : Adjusted mean squares related to parameter variation in model.
F-Value : Criterion ratio with the highest value to determine the significant values in
ANOVA.
P-Value : Criterion ratio with the stable values (0 ≤ 𝑃 ≤ %5) to determine the
significant value in ANOVA.
Equation. (26) produces approximate values to the values that specified by the new
methodology proposed in this article. Consequently, R2 according to this equation is excellent.
The square of correlation coefficient (R2) is an influential factor for correlating between the real
and predicted cases.
Mohammed Abdulridha Abbas, Mohd Amri Bin Lajis and Ghassan Shaker Abdul Ridha
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Table 6 Fitted the total agglomeration based on multiple linear regression model.
No. of
Agglomeration Case Element
Agglomeration according to
new methodology (mg)
Agglomeration according
to investigation modeling
1 Ni 0 -0.000035050
2 V 0.000021045 0.000033722
3 Mn 0.000014030 -0.000022932
4 Si 0.000014030 -0.000038834
5 Mo 0.000014030 0.000048610
6 C 0.000238515 0.000358389
7 Cr 0.000568229 0.000548845
8 Iron 0.001367959 0.001368305
9 W 0.001704687 0.001681473
Figure 11 Fitted total agglomeration depending on investigation model.
Figure 12 Normal probability residuals plot of the total agglomeration.
Thus, the values of R-sq and R-sq (adj.) are 99.36% and 98.97%, respectively as a reflection
to the outcomes of analyzing the multiple linear regression for agglomeration phenomenon.
Table 6 with Regression fitting in Figure 11 and the Normal probability of residuals in Figure
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12 observes the effect of these predicted outcomes. This experimental situation studied by
Kumar and Batra [20] for machining D2 steel in PMEDM can be enhanced with the current
methodology by utilizing the agglomeration ratio (𝜂𝐴𝐺). Equation. (17) presented an ratio up
to (50%) of the agglomeration condition and this ratio is considered a criterion of PMEDM
performance. The main reason for this consideration is that the increase in agglomeration leads
to a reduction in PMEDM performance [17],[19]. Furthermore, the mechanism of the
agglomeration ratio was not displayed in the past studies to recognize PMEDM performance.
Thus, there was an urgent need for the relation described in Equation. (17) to determine the
agglomeration level and to reduce the side effects of this phenomenon.
5. CONCLUSION AND IMPLICATIONS
The agglomeration case is considered as a significant phenomenon in PMEDM environment.
This study presented a new methodology to predict recast layer thickness (TRL) that effectively
contributes in computing the agglomeration that happened between the workpiece and electrode
tool. This article adopted both OES inspection on D2 steel before and after machining achieved
by Kumar and Batra [20] and the proposed virtual dimensions of the machining zone. Based on
this methodology, the results obtained in this study leads to the following conclusions:
1. The total agglomeration between the electrode tool and workpiece is (𝑚𝑇𝐴𝐺 = 0.003942529 mg),
while the active agglomeration according to the decomposed element (C), fine particles powder
(W), and slight debris (Mn, Mo) is (𝑚𝐴𝐺 = 0.001971264 mg). Consequently, the active
agglomeration (𝑚𝐴𝐺) correlated with only the increasing elements in the machining region.
2. The final result from subtracting both weight percentage for D2 steel before and after machining in
the PMEDM without the iron contributes in determining the incremental value of the migrated
elements to this steel. This value according to weight ratio is 1.95%, while this value based on the
new methodology is (0.001367959 mg) of the total agglomeration.
3. The investigation between the multiple linear regression model and the total agglomeration (𝑚𝑇𝐴𝐺)
depending on the proposed methodology in this paper reached 99.36% and the adjusting value of
98.97%. These values result from the square of the correlation factor (R2) based on ANOVA.
4. The agglomeration rate (𝜂𝐴𝐺) between the electrode tool and the workpiece according to this
proposed methodology reached 50%. This is considered as a criterion which indicates that the
particles agglomerated in the machining zone did not exceed the critical case of agglomeration.
Thus, this new criterion considers a significant factor to measure the PMEDM performance.
Depending on these conclusions, the new methodology offers a mechanism to predict the
agglomeration through employing the agglomeration ratio as a novel criterion of this
phenomenon. Therefore, this study can be adopted in the experimental field to develop
PMEDM performance.
ACKNOWLEDGEMENTS
The authors would like to convey a special thanks to the Iraqi Ministry of Higher Education
and the Malaysian Ministry of Higher Education represented by Universiti Tun Hussein Onn
Malaysia (UTHM) for unlimited support to produce this article in conjunction with the teams
of Precision Machining Research Centre (PREMACH)and Advanced Manufacturing and
Materials Centre (AMMC).
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