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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)


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


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

Mohammed Abdulridha Abbas, Mohd Amri Bin Lajis and Ghassan Shaker Abdul Ridha


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.

A New Methodology For Predicting Quantity of Agglomeration Between Electrodes In

PMEDM Environment


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.



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.


PMEDM Environment


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.



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.


PMEDM Environment


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].



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:


PMEDM Environment


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)



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)


PMEDM Environment


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:



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 +


PMEDM Environment


∑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.



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


PMEDM Environment


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.



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


PMEDM Environment


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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