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CHAPTER 3
CASE STUDY-II FORM TOLERANCE OPTIMIZATION
USING GREY RELATIONAL ANALYSIS
3.1 INTRODUCTION (CIRCULAR ELECTRODE)
This case study II reports an experimental investigation on EDM of
Inconel 718 using circular copper electrodes. The parameters namely, peak
current, pulse on time, and pulse off time were chosen to study the
experimental characteristics. An electrolytic copper which is in the form of
cylindrical rod with 4mm and 3mm diameter were used as electrodes. Inconel
718 is a High Strength Temperature Resistant (HSTR) nickel-based super
alloy. It is extensively used in aerospace applications, gas turbines, rocket
motors, spacecraft, nuclear reactor, pumps, and tools. Now a days, this is
being effectively used in tools and gas turbines applications. There is also a
newer version of this alloy (718 SPF) that is used specifically for super-plastic
forming. It possesses good creep-rupture strength at temperatures as high as
1,300° F. However, machinability of the material is considered to be poor due
to its inherent characteristics. Hence, Inconel 718, is a difficult to machine
material because of its poor thermal properties, high hardness, high work
hardening rate, and strong tendency to form build up edge. As a result, high
tool wear have been reported during conventional machining of Inconel 718.
On the other hand, an alternate way to effectively machine this material, is
non-traditional machining processes.
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EDM is achieved by applying a succession of discrete discharge
between electrode (cathode) and an electrically conducting work piece,
separated by small gap and the total set up is immersed in dielectric fluid. The
gap between tool and work piece known as spark gap, is maintained between
the tool and work piece to cause the spark to discharge. Many researchers
have carried out experimental works and used many algorithms and methods
with an aim to optimize MRR, EWR, and Surface Roughness.
However, there are only few works that have been carried out with
an objective to optimize the tolerance. Moreover, it can be said that there are
no works that have been carried out with an objective to optimize the form
tolerance. In this case study, we had introduced the use of grey relational
analysis in selecting Taguchi application for multiple performance
characteristic optimizations with the usage of weighted factor.
The Taguchi method has become a powerful tool to optimize
manufacturing processes. Original Taguchi method had been designed to
optimize a single performance characteristic. As further development,
Taguchi method has been designed with few modifications for handling
multiple performance characteristics. The Grey theory can provide a solution
of a system in which the model is unsure or the information is incomplete. It
also provides an efficient solution to the uncertainty, multi-input, and discrete
data problem.
In this case study, the orthogonal arrays with the grey relational
analysis technique are used to investigate the multiple performance
characteristics in the EDM process.
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3.2 DESIGN OF EXPERIMENTS AND OPTIMIZATION
The requirements for the application of Design-of-Experiments
(DoE) are careful planning, prudent layout of the experiment, and expert
analysis of the results. Lin and Lin, and Oxley have used the DOE approach
with the use of orthogonal array with grey relational analysis to optimize the
electrical discharge machining process with multiple performance
characteristics, and modeling machining processes with a view to their
optimization and the adaptive control of metal machining machine tools.
Similarly, many researchers have used the DOE in their works. Taguchi has
standardized methods for each of these DoE application steps. This Taguchi
approach can reduce the number of experiments required to obtain necessary
data for optimization. Therefore, DoE using Taguchi approach has become a
much more attractive tool for those who attempt the optimization of any
system.
3.2.1 Experimental Design
A total of three parameters namely current, pulse on time, and pulse
off time were chosen as the controlling factor, and each parameter was
designed to have four levels denoted by 1, 2, 3 and 4, as shown in Table 3.1.
Table 3.1 Machining parameters and their levels
Parameter Unit Level 1 Level 2 Level 3 Level 4
A Peak current Amps 6 9 12 15
B Pulse on time µs 200 400 600 800
C Pulse off time µs 10 20 30 40
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3.2.2 Running Experiment
The chemical composition of Inconel 718 used in this work was
analyzed by using Bruker SI turbo alloying Analyzer which is shown in
Figure 3.1 (A-B). The hardness of the Inconel 718 was measured by using a
hardness tester, HT-7 which is shown in Figure 3.2 (A-B). The experiments
were conducted by using a die sinking SPARKONIX – Electric Discharge
machine with a capacity of 15 Amps as maximum current rating. The die
sinking EDM setup is shown in Figure 3.3. The work piece, Inconel 718,
which is in the form of disc, is shown in Figure 3.4. The work piece was
connected to positive terminal and cylindrical copper electrode of 4mm and
3mm diameter, was connected to negative terminal of the D.C power supply.
The electrodes were prepared by using CNC lathe as shown in Figure 3.5 to
improve the surface finish of electrode, which in turn affects the surface finish
of work piece. Kerosene was used as dielectric fluid with pressure of 0.2
kg/cm², and side flushing technique was used to conduct all the experiments.
The weight of the electrode and work piece were measured before machining
and after machining for each trial run, by using digital weighing balance, with
an accuracy of 0.001 grams.
The Material Removal Rate (MRR) was calculated using the
formula given below
Timeremovedmateriale workpiecofWeight MRR (g / min) (3.1)
The Electrode Wear Rate (EWR) was calculated using the formula
given below
TimeremovedmaterialelectrodeofWeightEWR (g / min) (3.2)
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The form tolerance, cylindricity and circularity were measured by
using a Swiss made Co-ordinate Measuring Machine (CMM) TESA micro-
hite 3D, which is shown in Figure 3.7 (A-B). Then, grey based orthogonal
array was used in this multi-objective optimization and process parameters
were optimized. Experimental values with responses for 3 mm and 4 mm
circular electrode is shown in Table A 6.1 in ‘Appendix 6’ and Table A 7.1 in
‘Appendix 8’
1 A 1 B
Figure 3.1 Bruker S1 Turbo Alloying Analyzers (Chemical composition)
Table 3.2 Chemical composition of Inconel 718
Element Weight % ±2Sn 0.030 0.008Mo 3.06 0.02Nb 5.69 0.02Zn 0.050 0.008Ni 53.23 0.014Co 0.071 0.032Fe 19.78 0.07Cr 17.02 0.05Sb 0.022 0.010Ti 1.18 0.11Al 0.41 0.02
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3.3 RESULT AND DISCUSSION
3.3.1 Chemical Composition
The chemical composition of Inconel 718 used in this work is given
in Table 3.2. Inconel 718 is a precipitation-hardened nickel-chromium alloy
which contains substantial levels of iron, molybdenum, and niobium as well
as trace amounts of titanium and aluminum, with a high level of strength and
flexibility. It possesses high corrosive resistance and high temperature
resistance. It is suitable for use at cryogenic temperature and also for use at
high temperature of the order of 1300° F. The hardeness of Inconel 718
measured is shown in Table 3.3. Though, the hardness of Inconel 718 seems
to be less, it has problem in its machinability as explained earlier in
introduction section.
2 (a) 2 (a) Figure 3.2 Hardness Tester HT-7
Table 3.3 Hardness value of Inconel 718
Scale Trial 1 Trial 2 Trial 3 Average Rockwell B 81.3 79.1 79.1 80.13Vickers 145 144.8 145 144.93
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Figure 3.3 Photograph of Electrical Discharge Machine
Figure 3.4 Inconel 718 workpiece Figure 3.5 Copper Electrodes
7 (a) 7 (b) Figure 3.7 Co-ordinate Measuring Machine (CMM)
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3.3.2 Multi Response Optimization using Grey Relational Analysis
Taguchi method is designed to optimize single response
characteristic. The higher-the-better performance for one factor may affect the
performance because another factor may demand lower-the-better
characteristics as given by Narender Singh et al (2004). Hence, multi-
response optimization characteristics are complex. In this section, the use of
orthogonal array with Grey relational analysis optimization methodology for
multi-response optimization is discussed. The optimization of the process
parameter has been explained in the following steps:
(a) Normalizing the experimental results of MRR, EWR,
cylindricity and circularity of all the trials is shown in Table A
8.1 and A 9.1 in ‘Appendix 8’ and ‘Appendix 9’ respectively.
(b) Performing the Grey relational generation and calculation of
Grey relational coefficient.
(c) Calculation of the Grey relational grade by averaging the Grey
relational coefficient by multiplying by the weighted factor
Table A 8.1 and A 9.1 in ‘Appendix 8’ and ‘Appendix 9’
respectively.
(d) Performing statistical analysis of variance (ANOVA) for the
input parameters with the Grey relational grade and to find
which parameter significantly affects the process.
(e) Selecting the optimal levels of process parameters.
(f) Conduct conformation experiment and verify the optimal
process parameters setting.
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3.3.3 Normalization of the Experimental Results
A linear normalization of the experimental results for the responses
viz. MRR, EWR, cylindricity and circularity is performed in the range
between 0 and 1, which is called as the Grey relational generation. The
normalized results Xij can be expressed as
)......2,1min()......2,1,max()...........3,2,1min(
,
,
niyniyniyy
Xijijij
ijij (3.3)
(To be used for Larger the better)
)......2,1min()......2,1,max()......3,2,1max(
,
,
niyniyyniy
Xijijij
ijij (3.4)
(To be used for smaller the better)
Where yij is the i th experimental results in the j th experiment.
According to the Equation (3.3) and (3.4), larger normalized results
corresponding to the better performance and the best normalized result should
be equal to 1.
3.3.4 Computing the Grey Relational Coefficients
The Grey relational coefficients are calculated to express the
relationship between the ideal (best =1) and the actual experimental results.
The grey relational coefficient ij can be expressed as
ijjiij
ijjiijji
xxxx
xxxxij
ii
ii
00
00
maxmax
maxmaxminmin (3.5)
Where 0ix is the ideal normalized results for the i th performance
characteristics and is the distinguishing coefficient which is defined in the
range 0 1.
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* The weighted grey relational coefficient is a weighting adjustment
of the grey relational coefficient and defines as
,)(*)( iii KKn
i
i1
1 (3.6)
In this work, the weighting factor i assigned are 0.5, 0.2, 0.2, and
0.1 for metal removal rate, electrode wear rate, cylindricity, and circularity
respectively. The four responses for optimization of EDM parameters and
form tolerances for Inconel 718 discussed herein correspond to the two
foregoing definitions.
3.3.5 Computing the Grey Relational Grades
The Grey relational grade corresponding to each performance
characteristic is to be computed and the overall evaluation of the multi
response characteristic is based on the Grey relational grade, which is given
by:
m
iijj m 1
1 (3.7)
Where j is the Grey relational grade for the jth experiment and m
is the number of performance characteristics. The results of the Grey
relational grade are tabulated. The higher Grey relational grade represents that
the experimental result is closer to the ideally normalized value. In the present
chapter, experiment 10 has the best multi response characteristics among the
16 experiments conducted for both 3 mm and 4 mm diameter of the electrode.
The mean of the Grey relational grade for each level of the
machining parameter can be calculated by averaging the Grey relational grade
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for experiment number 1-4, 5-8, 9-12 and 13-16 for level 1, 2, 3 and 4
respectively. Similarly, it is calculated for the respective level of pulse-on
time and pulse-off time and is summarized in Table 3.4 and Table 3.5 for
corresponding 3 mm and 4 mm diameter electrode. The larger the value of the
Grey relational grade, the better is the multi response characteristic.
3.3.6 Determine the Optimal Factor and its Level Combination
From the response table for the Grey relational grade as shown in
Table 3.4 and Table 3.5, the optimal machining parameter setting is to
maintain current at level 3, pulse on- time at level 1 and the pulse off- time at
level 3 for maximizing MRR and minimizing EWR, cylindricity and
circularity simultaneously among the 16 experiments for both 3mm diameter
and 4mm diameter electrode.
For example, to estimate the effect of factor i, the average of grade
values (AGV) for each level j was calculated and denoted as AGVij, then the
effect, Ei, is defined as:
Ei=max(AGVij)–min(AGVij) (3.8)
If the factor i is controllable, the best level j*, is determined by
j = maxj (AGVij) (3.9)
Table 3.4 Response table for the grey relational grade for 3 mm diameter electrodes
Grade Level 1 Level 2 Level 3 Level 4 Max - Min A Current A 0.5134 0.5368 0.5687 0.5231 0.0552B Ton s 0.5445 0.4457 0.4525 0.4561 0.0988C Toff s 0.4077 0.4377 0.5972 0.0423 0.1894
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Table 3.5 Response table for the grey relational grade for 4 mm diameter electrodes
Grade Level 1 Level 2 Level 3 Level 4 Max - Min
A Current A 0.5183 0.5583 0.6621 0.4335 0.2285
B Ton s 0.5393 0.4390 0.5397 0.4356 0.1041
C Toff s 0.4707 0.4362 0.6110 0.5234 0.1748
3.3.7 Performing Analysis of Variance (ANOVA)
Furthermore, a statistical analysis of variance (ANOVA) is
performed to determine parameters which significantly affect the performance
characteristics. With the grey relational analysis and statistical analysis of
variance, optimal combination of the process parameters can be predicted.
The percentage contribution by each of the process parameter in the total sum
of the squared deviations can be used to evaluate the importance of the
Table 3.6 and Table 3.7.
The parameter symbols typically used in ANOVA are described below:
a). Source. The source includes the controlling factors A, B, C. . .
and the error factor, e, and the sum of all observations, T.
(A-Current, B-pulse on time, and C-pulse off time)
b). SS (sum of squares). SSA, SSB, SSC denote the sum of the
squares of A, B, C; SSE denotes the error sum of squares; SST
denotes the total variation. Thus, the equation can be written
as:
CFiationtotalSSTm
jj
1
2)var( (3.10)
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mfactorCorrectionCF
m
jj
1
2)()( (3.11)
m = the total number of experiments
j = grey relational grade of individual experiments
SSE=SST–SSA–SSB–SSC (3.12)
c). DoF (degree of freedom). DoF denotes the number of
independent variables. In the ANOVA table, the degree of
freedom for each factor is the number of its levels -1. The total
degree of freedom is the number of total measurement values -
1. The error of the degree of freedom is the total degree of
freedom minus the sum of the degree of freedom of each
factor.
d). P (Percentage of the contribution to the total variation).
%100'SST
iSSPi (i = A, B, C, E, T …) (3.13)
Table 3.6 Results of ANOVA for diameter 4mm diameter electrodes
Symbol Machining parameter
Degrees of freedom
Sum ofsquares
Contribution %
A Peak current A 3 0.194928 55.37937
B Pulse on Time s 3 0.083975 23.85731
C Pulse off Time s 3 0.043967 12.49115
- Error 6 0.029117 08.27216
- Total 15 0.351987 100
54
Table 3.7 Results of ANOVA for diameter 3mm diameter electrodes
SymbolMachining parameter
Degreesof
freedom
Sum of squares
Contribution %
A Peak current A 3 0.037924 29.51032B Pulse on Time s 3 0.072629 56.51562C Pulse off Time s 3 0.009666 7.521845- Error 6 0.008292 6.452224- Total 15 0.128512 100
Results of the ANOVA indicate that Peak current time is the most
significant EDM parameter in terms of affecting the form tolerance for 4mm
diameter electrode.
Results of the ANOVA indicate that Pulse on time is the most
significant EDM parameter in terms of affecting the form tolerance for 3mm
diameter electrode.
For 4mm Electrode
Peak current is the most dominant factor, with a percentage
contribution as high as 55.37937 % higher than pulse on time 23.85731 % and
pulse off time 12.49115 %. Based on the above discussion, the optimal EDM
process parameters are peak current at level 3 pulse on time at level 2 and
pulse off time at level 3.
For 3mm Electrode
Pulse on time is the most dominant factor, with a percentage
contribution as high as 56.51562 % higher than peak current 29.51032 % and
pulse off time 7.521845 %. Based on the above discussion, the optimal EDM
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process parameters are peak current at level 3, pulse on time at level 2 and
pulse off time at level 3.
3.3.8 Confirmation Tests
The estimated grey relational grade opt using the optimal level of
the design parameters can be calculated as
0
1
( )op t jj
(3.14)
where ‘ ’ the total mean of the grey relational grade, j is is the grey
relational grade at the optimal level and ‘o’ is the number of significant
design parameters that affect the multiple performance characteristics. The
confirmation experiments are conducted to verify whether the quality
performance is enhanced. Based on the Equation (3.14), the estimated Grey
relational grade using the optimal machining parameters can be found out
even for the setting not available in the Orthogonal Array.
Table 3.8 and Table 3.9 gives a comparison of the multiple process
responses for initial and optimal EDM parameters for 4 mm and 3 mm
diameter copper electrodes used for machining Inconel 718 work piece.
As noted from Table 3.8 (Inconel 718) MRR is increased from
0.834 mm3 /min to 0.995 mm3 /min, (Copper 4mm Diameter) EWR is
decreased from 0.095 g /min to 0.009 g /min, cylindricity is decreased from
0.044 mm to 0.038 mm and the circularity is decreased from 0.034 mm to
0.0103 mm respectively. It is clearly shown that the form tolerances in the
EDM process are improved by 26.40 % from the initial condition.
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Table 3.8 Results of initial and optimal electric discharge machining performance for 4mm diameter electrodes
Initial Machining parameters Optimal machining
parameters
Prediction ExperimentalLevels A3B2C3 - A3B1C3
MRR, mm3 /min 0.834 - 0.995
EWR g/min 0.095 - 0.009
Cylindricity, mm 0.044 - 0.038
Circularity, mm 0.034 - 0.0103Grey Relational Grade 0.71463* 0.859191 0.87886
*Improvement of grey relational grade = 0.16423
Table 3.9 Results of initial and optimal electric discharge machining performance for 3mm diameter electrodes
Initial Machining parameters Optimal machining
parameters
Prediction ExperimentalLevels A2B2C1 - A3B1C3
MRR, mm3 /min 0.560 - 0.643
EWR g/min 0.007 - 0.004Cylindricity, mm 0.079 - 0.055
Circularity, mm 0.021 - 0.013
Grey Relational Grade 0.63385* 0.68568 0.79499 *Improvement of grey relational grade = 0.16114
As noted from Table 3.9 (Inconel 718) MRR is increased from
0.56 g/min to 0.643 g/min, (Copper 3mm Diameter) EWR is decreased from
0.007 g /min to 0.004 g /min, cylindricity is decreased from 0.079 mm to
0.055 mm, and the circularity is decreased from 0.021 mm to 0.013 mm
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respectively. It is clearly shown that the form tolerances in the EDM process
are improved by 18.96 % from the initial condition.
3.4 SUMMARY OF RESULTS
Orthogonal array with Grey relational analysis was used to optimize
the multi response characteristics which include form tolerance of Electrical
Discharge Machining of Inconel 718. The experimental result for the optimal
combination shows that there is a considerable improvement in the process.
The application of this technique converts the multi response variable to a
single response Grey relational grade and simplifies the optimization
procedure. Particularly, the form tolerance which is important in precision
manufacturing of the Inconel 718 can be improved.
3.5 INTRODUCTION (SQUARE AND HEXAGONAL ELECTRODES)
The previous case study, deals the multi-objective optimization for
EDM process parameters for circular electrodes only. This case study deals
the square and hexagonal electrodes while machining of Inconel 718 in EDM
process. Handling of multiple performance characteristics by the Taguchi
method requires further effective researches. This is because, optimization of
the multiple performance characteristics is concerned with optimization of
vector objectives. While optimizing the Electrical Discharge Machining
(EDM) process, it is expected to have a higher material removal rate and a
lower electrode wear rate, a good form tolerances and orientation tolerances.
Moreover, an improvement of one performance characteristic may degrade
one or more of the other performance characteristics. Therefore, the multiple
performance characteristics are much more complicated than the optimization
of a single performance characteristic.
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The purpose of the present study is also to introduce the use of grey
relational analysis in Taguchi application for multiple performance
characteristics optimization with the usage of weighted factor. The orthogonal
array with the grey relational analysis is used to investigate the multiple
performance characteristics and to optimize the form tolerance and orientation
tolerance in the EDM process of machining Inconel 718.
These components have small-sized cooling holes as they are
working in a hostile environment (i.e. at high speed at elevated temperatures).
There is also a newer version of the alloy (718 SPF) that is used specifically
for super-plastic forming. It contains substantial levels of iron, molybdenum,
and niobium as well as trace amounts of titanium and aluminum, with a high
level of strength and flexibility. It will maintain good creep-rupture strength at
temperatures as high as 978 K (Chiang & Ko-Ta 2008). From literature, it is
clear that Inconel 718 is a difficult to machine material, because of its poor
thermal properties, high toughness, high work hardening rate, presence of
highly abrasive carbide particles, and strong tendency to weld to the tool to
form build up edge. As a result, high tool wear has been reported during
conventional machining of material. On the other hand, an alternative method
to effectively machine this material is non-traditional machining processes.
The EDM process, sometimes referred to as spark-erosion machining, is a
nontraditional method of removing metal by a series of rapidly recurring
discrete electrical discharges between an electrode (the cutting tool) and the
workpiece in the presence of a dielectric fluid.
From the past decades, it is also observed that no plausible works
were conducted on form tolerances in electrical discharge machined Inconel
718. Though many research works have been carried out on EDM process,
there is no analytical and experimental work carried out for form tolerance
and orientation tolerance namely flatness, perpendicularity and angularity.
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Moreover, the form tolerance and orientation tolerance are the important
responses in Non-conventional machining process.
Thus, this experimental work is attempted here to evaluate the form
tolerance and orientation tolerance in EDM of Inconel 718 by using square
and hexagonal electrodes. Taguchi technique was used to develop Design of
Experiments (DoE) to reduce the number of trails. Additionally, the ANOVA
used to found the significant parameter.
In this case study, the designed electrodes are used to machine the
features such as square and hexagonal holes and the geometric tolerance of
the above features are measured by using CMM. The responses were
optimized by using Grey Relational Analysis. Confirm optimized
combination level of machining parameters values of Inconel 718 was also
done.
3.6 DESIGN OF EXPERIMENTS AND OPTIMIZATION
In Electrical Discharge machining, removal of material from a work
piece is an electrical spark erosion process. Common methods of evaluating
machining performances in the EDM operation are based on the following
performance characteristics: material removal rate, electrode wear rate,
perpendicularity, angularity, and straightness. The above performance
characteristics are correlated with machining parameters such as peak current,
pulse-on time, pulse-off time, etc. The proper selection of machining
parameters can result in a higher value of material removal rate, lower value
of electrode wear, lower value of perpendicularity, and lower value of
angularity. A total of three parameters namely peak current, pulse on time,
and pulse off time were chosen for the controlling factor, and each parameter
was designed to have four levels denoted by 1, 2, 3 and 4, as shown in the
Table 3.10.
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Table 3.10 Machining parameters and their levels
Parameter Unit Level 1 Level 2 Level 3 Level 4A Peak current Amps 6 9 12 15
B Pulse on time µs 200 400 600 800C Pulse off time µs 10 20 30 40
3.6.1 Running Experiment
The work piece, Inconel 718, in the form of disc was connected with
positive terminal and square and hexagon profile copper electrodes were
connected with negative terminal of the D.C power supply. Kerosene was
used as dielectric fluid with pressure of 0.2 kg/cm², and side flushing
technique was used to conduct all the experiments. The weight of the
electrode and work piece before machining and after machining were
measured by using SHIMADZU BL series electronic balance with an
accuracy of 0.001 grams for accuracy of every trial run.
3.7 RESULTS AND DISCUSSIONS
The 16 experimental runs were conducted in duplicate, and the
average values of MRR, EWR and perpendicularity for square electrode,
angularity for hexagonal electrode along with the design of experiments
(DoE) are listed in Table A 10.1 in ‘Appendix 10’ and Table A 11.1 in
‘Appendix 11’.
3.7.1 Multi Response Optimization
A group of responses often characterize the performance of a
manufactured product. These responses are generally measured by a different
measurement scale. The multi-response optimization characteristics are
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complex. In this section, the use of orthogonal array with Grey relational
analysis optimization methodology for multi-response optimization is
discussed. The optimization of the process parameter has been explained in
the following steps:
(a) Normalizing the experimental results of MRR, EWR,
perpendicularity (for square electrode), angularity (for
hexagonal electrode) of all the trials as shown in Table A 12.1
in ‘Appendix 12’ and Table A 13.1. in ‘Appendix 13’
(b) Performing the Grey relational generation and calculating the
Grey relational coefficient as shown in Table A 12.1 in
‘Appendix 12’ (for square electrode) and Table A 13.1. in
‘Appendix 13’ (for hexagonal electrode).
(c) Calculating the Grey relational grade by averaging the Grey
relational coefficient with multiplication of the weighted
factor for square electrode and hexagonal electrode as shown
in Table A 12.1 and A 13.1 in ‘Appendix 12’ and ‘Appendix
13’respectively.
(d) Performing statistical analysis of variance (ANOVA) for the
input parameters with the Grey relational grade and verify
significant parameters which are affecting the process.
(e) Selecting the optimal levels of process parameters.
(f) Conducting confirmation experiment and verifying the
optimal process parameters setting.
In this case study, the weighting factor i assigned are 0.5, 0.2, 0.3
and 0.1 (50% MRR, 20% EWR, 30% for perpendicularity and angularity) for
metal removal rate, electrode wear rate, perpendicularity (square electrode),
62
and angularity (for hexagonal electrode) respectively. Weighting factor is
assigned based on the performance characteristics of this study or application
3.7.2 Optimal Factor and its Level Combination
The mean of the Grey relational grade for each level of the
machining parameters can be calculated by averaging the Grey relational
grade for current for experiment number 1-4 for level 1, for experiment
number 5-8 for level 2, experiment number 9-12 for level 3 and for
experiment number 13-16 for level 4. Similarly, it is calculated for the
respective levels for pulse on time and pulse off time and is summarized in
Table 3.11 and Table 3.12. The larger the value of the grey relational grade,
the better is the multi response characteristics.
Table 3.11 Response table for the grey relational Grade for Square profile electrode
Symbol Grade Level 1 Level 2 Level 3 Level 4 Max - MinA Current A 0.6090 0.5812 0.6341 0.5213 0.1128
B Ton µs 0.5751 0.5862 0.4627 0.5121 0.1234
C Toff µs 0.4233 0.4881 0.6605 0.4451 0.2371
Table 3.12 Response table for the grey relational Grade for Hexagonal profile electrode
Symbol Grade Level 1 Level 2 Level 3 Level 4 Max - MinA Current A 0.5587 0.5091 0.6108 0.5623 0.1016 B Ton µs 0.5522 0.5876 0.4635 0.5344 0.1240
C Toff µs 0.4668 0.3952 0.6130 0.5013 0.2178
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3.7.3 Performing analysis of variance (ANOVA)
Furthermore, a statistical analysis of variance (ANOVA) is
performed to determine parameters which significantly affect the performance
characteristics. With the grey relational analysis and statistical analysis of
variance, optimal combinations of the process parameters are predicted.
Table 3.13 Results of ANOVA for multiple performance characteristics Inconel 718 for Square profile electrode
Symbol Machining parameter Degrees
of freedom
Sum of squares MS F
A Peak current A 3 0.136487 0.058244 9.183243B Pulse on Time (Ton) µs 3 0.097491 0.046246 7.291532C Pulse off Time (Toff) µs 3 0.039697 0.006830 1.076917
Error 6 0.018730 0.006342 -Total 15 0.292406 - -
Table 3.14 Results of ANOVA for multiple performance characteristics Inconel 718 for Hexagonal profile electrode
Symbol Machining parameterDegrees
of freedom
Sum of squares MS F
A Peak current A 3 0.099999 0.049901 11.35767B Pulse on Time (Ton) µs 3 0.065553 0.032776 7.460075C Pulse off Time
(Toff) µs 3 0.030052 0.000761 0.173196
Error 6 0.019602 0.004394 -
Total 15 0.215205 - -
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Results of the ANOVA indicate that Peak current is the most
significant factor than other factors in terms of affecting the multiple
responses, form tolerance, and orientation tolerance for both square and
hexagon profile of the electrodes. This is accomplished by separating the total
variability of the grey relational grade, which is measured by the sum of
squared deviation from the total mean of the grey relational grade, into
contributions by each of the process parameters and the error.
The F-test is used to determine the significance. The change of the
process parameters has a significant effect on the performance characteristics
when the F-value is large. The result of the ANOVA (Table 3.13 and
Table 3.14) shows that peak current and pulse on time are the significant
machining parameters that affect the multiple performance characteristics.
3.7.4 Confirmation Tests
The estimated Grey relational grade opt using the optimal level of
the design parameters can be calculated as
0
1
( )opt jj
(3.15)
where ‘ ’ is the total mean of the Grey relational grade, j is the mean of the
Grey relational grade at the optimal level and ‘o’ is the number of machining
parameters that affect the multiple performance characteristics. Based on
the Equation (3.15), the estimated Grey relational grade using the optimal
machining parameters can be found out even for the setting which is not
available in the Orthogonal Array.
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Table 3.15 Results of initial and optimal electric discharge machining performance Square Electrode
Initial Machining parameters Optimal machining
parameters Prediction Experimental
Levels A3B3C1 - A3B2C3 MRR g/min 0.116 - 0.134EWR g/min 0.025 - 0.016Perpendicularity Degrees 89.98 º - 89.67 º Grey Relational Grade 0.6980* 0.69754 0.9004
*Improvement of grey relational grade = 0.2024
Table 3.16 Results of initial and optimal electric discharge machining performance Hexagonal Electrode
Initial Machining parameters Optimal machining
parameters Prediction Experimental
Levels A3B3C1 - A3B2C3 MRR g/min 0.089 - 0.132EWR g/min 0.04 - 0.01Angularity Degrees 119.86 º - 120.11 º Grey Relational Grade 0.7435* 0.73240 0.8208
*Improvement of grey relational grade = 0.0773
Table 3.15 and Table 3.16 gives a comparison of the multiple
process responses for initial and optimal EDM parameters for square and
hexagon copper electrodes used for machined Inconel 718 work piece.
As noted from Table 3.15 (Inconel 718-Square electrode) MRR is
accelerated from 0.116 g /min to 0.132 g/min, EWR is greatly reduced from
0.025 g/min to 0.016 g/min and the square angle is greatly reduced from
89.98 º to 89.67 º.
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As noted from Table 3.16 (Inconel 718-Haxagonal electrode) MRR is
accelerated from 0.089 g /min to 0.132 g/min, EWR is greatly reduced from
0.04 g/min to 0.01 g/min and the angularity increased from 119.86 º to
120.11 º.
It is clearly shown that the electrode wear rate, material removal
rate, form tolerances, and orientation tolerances are greatly improved through
the both approaches.
3.8 SUMMARY OF RESULTS
The paper presented the use of the Grey relational grade analysis
based on the orthogonal array for the optimization of the electrical discharge
machining process with the multiple performance characteristics. Grey
relational coefficients analyze the relational degree of the multiple responses
(electrode wear rate, material removal rate, form tolerances, and orientation
tolerances). As a result, these approaches can greatly improve the process
responses such as the electrode wear rate, material removal rate, form
tolerances, and orientation tolerances in the electrical discharge machining
process during machining of Inconel 718 by using hexagonal and square
profile copper electrodes.
Confirmation test results proved that the determined optimum
combination of electrical discharge machining parameters satisfy the real
requirement of electrical discharge machining process while machining of
Inconel 718.
It is clearly shown that the multiple performance characteristics in
EDM of Inconel 718 material are greatly improved. So the best parameter for
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machining Inconel 718 by using square electrodes is A3B2C3 and hexagonal
electrodes are A3B2C3. The optimal EDM parameters for multiple
performance characteristics while machining Inconel 718 by using square
electrodes are Peak current 12 Amps, Pulse on time 400 s, and Pulse off time
30 s. Using hexagonal electrodes we obtain Peak current 12 Amps, Pulse on
time 400 s, and Pulse off time 30 s. For the same optimum parameters, the
angularity in square and hexagonal hole is optimized as 89.67º, 120.11º
respectively which are in acceptable range.
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