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					International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
 INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME
                           AND TECHNOLOGY (IJMET)

ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)                                                     IJMET
Volume 4, Issue 5, September - October (2013), pp. 173-181
© IAEME: www.iaeme.com/ijmet.asp
Journal Impact Factor (2013): 5.7731 (Calculated by GISI)                ©IAEME
www.jifactor.com




     A COMPARATIVE STUDY ON MATERIAL REMOVAL RATE BY
   EXPERIMENTAL METHOD AND FINITE ELEMENT MODELLING IN
             ELECTRICAL DISCHARGE MACHINING

                                   *S. K. Sahu, **Saipad Sahu
      *Asst. Prof., Department of Mechanical Engineering, Gandhi Institute for Technological
                                   Advancement, Bhubaneswar
     **Asst. Prof., Department of Mechanical Engineering, Gandhi Institute for Technological
                                   Advancement, Bhubaneswar



ABSTRACT

        Electrical discharge machining (EDM) is one of the most important non-traditional
machining processes. The important process parameters in this technique are discharge pulse on
time, discharge pulse off time and gap current. The values of these parameters significantly affect
such machining outputs as material removal rate and electrodes wear. In this paper, an axisymmetric
thermo-physical finite element model for the simulation of single sparks machining during electrical
discharge machining (EDM) process is exhibited. The model has been solved using ANSYS 11.0
software. A transient thermal analysis assuming a Gaussian distribution heat source with
temperature-dependent material properties has been used to investigate the temperature distribution.
Further, single spark model was extended to simulate the second discharge. For multi-discharge
machining material removal was calculated by calculating the number of pulses. Validation of model
has been done by comparing the experimental results obtained under the same process parameters
with the analytical results. A good agreement was found between the experimental results and the
theoretical value.

1. INTRODUCTION

       EDM is among the earliest and the most popular non-conventional machining process with
extensively and effectively used in a wide range of industries such as die and mould-making,
aerospace, automotive, medical, micromechanics, etc. The high-density thermal energy discharge
creates during machining causes the local temperature in the work piece gets close to the
vaporization temperature of the work piece, leads to the thermal erosion.


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6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME

         EDM is a very complex process involving several disciplines of science and branches of
engineering it combines several phenomena, but excluding very tiny discharges, it can be considered
with small error that the thermal effect takes over (Hargrove et al 2007, Salah et al 2006). The
theories revolving around the formation of plasma channel between the tool and the work piece,
thermodynamics of the repetitive spark causing melting and evaporating the electrodes, micro-
structural changes, and metallurgical transformations of material, are still not clearly understood.
However, it is widely accepted that the mechanism of material erosion is due to intense local heating
of the work piece causing melting and evaporation of work piece. The thermal problem to be solved
so as to model an EDM discharge is fundamentally a heat transmission problem in which the heat
input is representing the electric spark. By solving this thermal problem yields the temperature
distribution inside the workpiece, from which the shape of the generated craters can be estimated.
For solving these numerical models finite-element method or the finite-differences method are
normally used with single spark analysis (Erden et al. (1995)). Yadav et al. (2002) investigated the
thermal stress generated in EDM of Cr die steel. The influence of different process variables on
temperature distribution and thermal stress distribution has been reported. The thermal stresses
exceed the yield strength of the work piece mostly in an extremely thin zone near the spark. Salah
and Ghanem (2006) presented temperature distribution in EDM process and from these thermal
results, MRR and roughness are inferred and compared with experimental explanation.
In this work, a finite-element modelling of the EDM process using ANSYS software is presented.
Conduction, convection, thermal properties of material with temperature, the latent heat of melting
and evaporation, the percentage of discharge energy transferred to the work piece, the thermal
property of D2 tool steel, the plasma channel radius and Gaussian distribution of heat flux based on
discharge duration has been used to develop and calculate a numerical model of the EDM process.
An attempt has been made to investigate the effect of machining parameters on temperature
distribution, which is the deciding factor of MRR.

2. THERMAL MODEL OF EDM

    a. Description of the model
       In this process, electrodes are submerged in dielectric and they are physically separated by a
gap, called inter-electrode gap. It can be modelled as the heating of the work electrode by the
incident plasma channel. Figure shows the idealised case where work piece is being heated by a heat
source with Gaussian distribution. Due to axisymmetric nature of the heat transfer in the electrode
and the work piece, a two-dimensional physical model is assumed. The various assumptions made to
simplify the random and complex nature of EDM and as it simultaneously interact with the thermal,
mechanical, chemical, electromagnetism phenomena (Pradhan (2010)).

   b.   Assumptions
   1.   The work piece domain is considered to be axisymmetric.
   2.   The composition of work piece material is quasihomogeneous.
   3.   The heat transfer to the work piece is by conduction.
   4.   Inertia and body force effects are negligible during stress development.
   5.   The work piece material is elastic-perfectly plastic and yield stress in tension is same as that
        in compression.
   6.   The initial temperature was set to room temperature in single discharge analysis.
   7.   Analysis is done considering 100% flushing efficiency.
   8.   The work piece is assumed as stress-free before EDM.
   9.   The thermal properties of work piece material are considered as a function of temperature. It
        is assumed that due to thermal expansion, density and element shape are not affected.

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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME

   10. The heat source is assumed to have Gaussian distribution of heat flux on the surface of the
       work piece.

    c. Governing Equation
        The governing heat transfer differential equation without internal heat generation written in a
cylindrical coordinates of an axis symmetric thermal model for calculating the heat flux is given by
[12 F].
        The governing heat transfer differential equation without internal heat generation written in a
cylindrical coordinates of an axis symmetric thermal model for calculating the heat flux is given by
[12].

      ∂T   1 ∂         ∂T  ∂  ∂T 
ρC p      =  r ∂r  K r ∂r  + ∂Z  K ∂Z 
      ∂t                              

Where ρ is density, Cp is specific heat, K is thermal conductivity of the work piece, T is temperature,
t is the time and r& z are coordinates of the work piece.

    d. Heat Distribution
       Plasma channel incident on the work piece surface causes the temperature to rise in the work
piece. The distribution of plasma channel can be assumed as uniform disk source [13]-[16] or
Gaussian heat distribution [17]-[21], for EDM. Gaussian distribution of heat flux is more realistic
and accurate than disc heat source. Fig. 1 shows the schematic diagram of thermal model with the
applied boundary conditions.

                                  R
                      Y



                                                               hf (T-T0)




                                                   1
                   ∂T
                      =0                                                       ∂T
                   ∂p         4                                            2      =0
                                                                               ∂p




                                                       3

                                                       ∂T                              X
                                                          =0
                                                       ∂p


                                                 Figure No: 1

   e. Boundary Conditions
       The work piece domain is considered to be axisymmetric about z axis. Therefore taking this
advantage, analysis is done only for one small half (ABCD) of the work piece. The work piece
domain considered for analysis is shown in Fig. 1.It is clearly evident from Fig. 1 that the maximum
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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME

heat input will be at point A. On the top surface, the heat transferred to the work piece is shown by
Gaussian heat flux distribution. Heat flux is applied on boundary 1 up to spark radius R, beyond R
convection takes place due to dielectric fluids. As 2 & 3 are far from the spark location no heat
transfer conditions have been assumed for them. For boundary 4, as it is axis of symmetry the heat
transfer is zero. In mathematical terms, the applied boundary conditions are given as follows:

    ∂T
K      = Q (r ) , when R< r for boundary 1
    ∂Z

    ∂T
K      = h f (T − T0 ) , when R ≥ r for boundary 1
    ∂Z

    ∂T
K      = 0 , at boundary 2, 3 & 4
    ∂n

Where hf is heat transfer coefficient of dielectric fluid, Q(r) is heat flux due to the spark and T0 is the
initial temperature.

   f. Heat Flux
A Gaussian distribution for heat flux [21] is assumed in present analysis.

           4.45 PVI    
                            r 
                                 2
                                   
Q (r ) =            exp− 4.5  
             πR 2      
                             R 

where P is the percentage heat input to the workpiece, V is the discharge voltage, I is the current and
R is the spark radius. Earlier many researchers have assumed that there is no heat loss between the
tool and the workpiece. But Yadav et al. [21] have done experiment on conventional EDM and
calculated the value of heat input to the workpiece to be 0.08. Shankar et al. [22] calculated the value
of P about 0.4-0.5 using water as dielectric.

    g. Solution of thermal model
        For the solution of the model of the EDM process commercial ANSYS 12.0 software was
used. An axisymmetric model was created treating the model as semi-infinite and the dimension
considered is 6 times the spark radius. A non-uniformly quadrilateral distributed finite element mesh
with elements mapped towards the heat-affected regions was meshed, with a total number of 2640
elements and 2734 nodes with the size of the smallest element is of the order of 1.28 × 1.28 cm. The
approximate temperature-dependent material properties of AISI D2 tool steel, which are given to
ANSYS modeler, are taken from (Pradhan, 2010). The governing equation with boundary conditions
mentioned above is solved by finite element method to predict the temperature distribution and
thermal stress with the heat flux at the spark location and the discharge duration as the total time
step. First, the whole domain is considered to obtain the temperature profile during the heating cycle.
The temperature profile just after the heating period is shown in Fig.3, which depicts four distinct
regions signifying the state of the workpiece. Figure 4 and 5 shows typical temperature contour for
AISI D2 steel under machining conditions: current 1A, and discharge duration 20 µs and 9A, and
discharge duration 100 us .



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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME

3. MATERIAL PROPERTIES FOR FEA

                 Material Property      Copper (Cathode)        En-19 (anode)
                 Density (g/mm3)        8290 x 10-6             7700 x 10-6
                 Conductivity (W/mmK)   400 x 10-3              222 x 10-12
                 Resistivity ( -mm)     1.7 x 10-11             22.2 x 10-11
                 Specific heat (J/gK)   385 x 10-3              473 x 10-3


4. EXPERIMENTAL RESULT




  Figure No: 2 (Experimental Setup)               Figure No: 3 (Work piece after machining)


Experimental Data Table:

                              Gap        Pulse on       Electrode
               Current                                                MRR/min
                            Voltage        time         Diameter
               In Amp.                                                In m3/min
                            In Volt.      In µs          In mm
                  6            6           500             14           0.0145
                  6            8           1000            16           0.022
                  6            9           2000            18           0.0845
                  7            6           1000            18           0.0245
                  7            8           2000            14           0.044
                  7            9           500             16            0.03
                  9            6           2000            16           0.022
                  9            8           500             18           0.0715
                  9            9           1000            14           0.0785



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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME



                           variation of MRR vs current at                                     variation of MRR vs current at
                                 different voltages                                                 different voltages
                     0.1                                                                0.1




                                                                       MRR in gm/min
    MRR in gm/min



                    0.08                                                               0.08
                    0.06                                                               0.06
                                                            6V                         0.04                              14.5 mm
                    0.04
                    0.02                                    7V                         0.02                              16.5 mm
                       0                                                                  0
                                                            9V                                                           18.5 mm
                                6           8         9                                            6        8       9
                                    current in ampere                                              current in ampere




5. FINITE ELEMENT SIMULATION




          Figure No: 4 (Temperature Profile)                                              Figure No: 5 (Profile After Melting
                                                                                                     of Material)


6. SAMPLE CALCULATION FOR MRR FROM SIMULATION RESULT

The morphology of crater is assumed to be spherical dome shape.
Where r is the radius of spherical dome and h is depth of dome. And the volume is calculated by
given formula of spherical dome volume.

From geometry:
h = 0.004 m
r = 0.008 m

     1
C v = πh(3r 2 + h 2 ) = 0.000000435552 m3
     6

The NOP can be calculated by dividing the total machining time to pulse duration as given in (6).


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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME

          Tmach      20 × 60
NOP =             =             =1200000
        Ton + Toff 1000 × 10 −3

Where Tmach is the machining time, Ton is pulse-on time and Toff is pulse-off time. Knowing the
Cv and NOP one can easily derive the MRR for multi-discharge by using.

        Cv × NOP 0.000000435552 × 1200000
MRR =           =                         = 0.0261 m3/min
          Tmach            20


                                    Gap           Pulse on        Electrode       MRR/min      MRR/min
           Current
                                   Voltage          time          Diameter      (Experimental)  (FEM)
              6                       6               500              14          0.0145         0.0158
              6                       8            1000                16           0.022        0.0261 *
              6                       9            2000                18          0.0845         0.0559
              7                       6            1000                18          0.0245         0.0275
              7                       8            2000                14           0.044         0.0507
              7                       9               500              16            0.03         0.0225
              9                       6            2000                16           0.022         0.0489
              9                       8               500              18          0.0715         0.0257
              9                       9            1000                14          0.0785         0.0242



                            Comparison between Experimental
                             MRR to the FEM Calculated MRR
                             0.1

                            0.08
                  MRR/min




                            0.06

                            0.04                                                    Experimental MRR
                            0.02                                                    FEM MRR

                              0
                                     1    2   3   4    5     6    7    8    9
                                    Number of Experiment at different levels of factors




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International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 5, September - October (2013) © IAEME

7. RESULTS AND DISCUSSION

         Fig. 5 shows the FEA model after material removal, it is evident from the temperature
distribution that, during the spark-on time the temperature rises in the work piece and temperature
rise is sufficient enough to melt the matrix due to its low melting temperature but the reinforcement
remains in solid form due to its very high melting temperature. After the melting of matrix material
no binding exists between the matrix and reinforcement, therefore the reinforcement evacuates the
crater without getting melted.

8. CONCLUSION

        In the present investigation, an axisymmetric thermal model is developed to predict the
material removal. The important features of this process such as individual material properties, shape
and size of heat source (Gaussian heat distribution), percentage of heat input to the work piece, pulse
on/off time are taken into account in the development of the model. FEA based model has been
developed to analyze the temperature distribution and its effect on material removal rate. To validate
the model, the predicted theoretical MRR is compared with the experimentally determined MRR
values. A very good agreement between experimental and theoretical results has been obtained. The
model developed in present study can be further used to obtain residual stress distributions, thermal
stress distribution mechanism of reinforcement particle bursting phenomenon.

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