41

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.

42

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.

43

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

44

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)

45

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

46

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

47

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)

48

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.

49

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.

50

* 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

51

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

52

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)

53

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

55

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.

56

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

57

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.

58

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.

59

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.

60

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

61

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

63

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 - -

64

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.