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CHAPTER 6

OPTIMIZATION OF MULTIPLE PERFORMANCE

CHARACTERISTICS WITH GREY RELATIONAL ANALYSIS FOR

SS 304

6.1 INTRODCUTION

The optimization of parameters considering multiple performance

characteristics of the EDM process for SS 304 using the GRA is presented.

Performance characteristics including MRR, TWR, and OC are chosen to

evaluate the machining effects. Those process parameters that are closely

correlated with the selected performance characteristics in this study are the

pulse-on time, current, and voltage. Experiments based on the appropriate L9 OA

are conducted first. The normalized experimental results of the performance

characteristics are then introduced to calculate the coefficient and grades

according to GRA. Optimized process parameters simultaneously leading to

higher MRR and lower TWR and OC will then be verified through a

confirmation experiment. The details of the procedures are explained in the

following sections.

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6.2 DETERMINATION OF OPTIMAL MACHINING PARAMETERS

The experimentally obtained values of MRR, TWR and OC are also

presented in Table 6.1. In this section, the use of the OA with the GRA for

determining the optimal machining parameters is reported step by step. The

optimal machining parameters with consideration of the multiple performance

characteristics are obtained and verified.

Table 6.1- Experimental layout using an L9 OA and performance results

Expt.No.

Levels of parametersMRR

(mg/min)TWR

(mg/min)OC

(µm)Pulse-

on time(µs)

Dischargecurrent

(A)

Gapvoltage

(V)

1 1 1 1 10.3082 15.4648 122.54

2 1 2 2 12.6774 15.7829 123.16

3 1 3 3 15.0381 15.9469 118.00

4 2 1 3 13.6681 18.4328 126.46

5 2 2 1 14.7675 18.5222 119.39

6 2 3 2 17.0137 18.8164 131.77

7 3 1 2 14.6448 18.1688 132.16

8 3 2 3 17.2220 19.3948 145.35

9 3 3 1 18.2732 19.5148 150.31

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6.2.1 Data Pre-Processing

In GRA, data pre-processing is required since the range and unit in

one data sequence may differ from the others. Data pre-processing is also

necessary when the sequence scatter range is too large, or when the directions of

the target in the sequence are different. Data pre-processing is a process of

transferring the original sequence to a comparable sequence. For this purpose, the

experimental results are normalized in the range between zero and one.

Depending on the characteristics of data sequence, there are various

methodologies of data pre-processing available for the GRA. The procedure is

given below.

Identify the performance characteristics and process parameters

to be evaluated.

Determine the number of levels for the process parameters.

Select the appropriate OA and assign the process parameters to

the OA.

Conduct the experiments based on the arrangement of the OA.

Normalize the experimental results of MRR, TWR and OC.

Perform the grey relational generating and calculate the grey

relational coefficient.

Calculate the grey relational grade by averaging the grey

relational coefficients.

Analyze the experimental results using the grey relational grade

and ANOVA.

Select the optimal levels of process parameters.

Verify the optimal process parameters through the confirmation

tests.

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965.73692.2)(* kxi

2974.0)(* kxi

MRR is the dominant response in EDM which decides the

machinability of the material under consideration. For the "larger-the-better"

characteristic like MRR, the original sequence can be normalized as follows:

)k(xmin)k(xmax)k(xmin)k(x)k(x

ii

ii*i (6.1)

where, )k(x*i and )k(x i are the sequence after the data preprocessing and

comparability sequence respectively, k=1 for MRR; i=1, 2, 3…, 9 for experiment

numbers 1 to 9.

The TWR and OC are also important measures of EDM performance.

The selection of optimum process parameters for EDM of SS 304 at the

developmental stage and their effects on TWR and OC have yet to be clarified.

To obtain optimal cutting performance, the “smaller-the-better” quality

characteristic has been used for minimizing both the TWR and OC. When the

“smaller-the-better” is a characteristic of the original sequence, then the original

sequence should be normalized as follows:

)k(xmin)k(xmax)k(x)k(xmax)k(x

ii

ii*i (6.2)

where, )k(x*i and )(kxi are the sequence after the data preprocessing and

comparability sequence respectively, k=2 and 3 for TWR and OC; i=1, 2, 3…, 9

for experiment numbers 1 to 9. The )k(x*i for MRR is calculated for Expt. no. 2

using equation 5.1 as shown below.

Similarly the remaining calculations are also made and all the sequences after

data preprocessing using Equations 6.1 and 6.2 are presented in Table 6.2

3082.102732.183082.106774.12)(* kxi

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Table 6.2 - The sequences of each performance characteristic after data

processing

Expt. no. MRR TWR OC

Referencesequence 1.0000 1.0000 1.0000

1 0.0000 1.0000 0.8595

2 0.2974 0.9215 0.8403

3 0.5938 0.8810 1.0000

4 0.4218 0.2671 0.7382

5 0.5599 0.2451 0.9570

6 0.8419 0.1724 0.5738

7 0.5445 0.3324 0.5617

8 0.8680 0.0296 0.1535

9 1.0000 0.0000 0.0000

Now, )k(i0 is the deviation sequence of the reference sequence

)k(x*0 and the comparability sequence )k(x*

i , i.e.

)k(x)k(x)k( *i

*0i0 (6.3)

The deviation sequence i0 can be calculated using Eq. 6.3 as follows;

)1(x)1(x)1( *i

*0i0 = 000.1 =1.00

)2(x)2(x)2( *i

*0i0 = 00.100.1 =0.00

)3(x)3(x)3( *i

*0i0 = 8595.000.1 =0.1405

So, i0 = (1.00, 0.00, 0.1405)

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Similar calculation is performed for i=1 to 9 and the results of all

for i=1 to 9 are presented in Table 6.3.Investigating the data presented in Table

6.3, (k) and (k) are obtained and are as follow:

max = )1(01 = )2(09 = )3(09 =1.00

min = )1(09 = )2(01 = )3(03 =0.00

Table 6.3 - The deviation sequences

Deviationsequences

)1(0i )2(0i )3(0i

Exp. no. 1 1.0000 0.0000 0.1405

Exp. no. 2 0.7026 0.0785 0.1597

Exp. no. 3 0.4062 0.1190 0.0000

Exp. no. 4 0.5782 0.7329 0.2618

Exp. no. 5 0.4401 0.7549 0.0430

Exp. no. 6 0.1581 0.8276 0.4262

Exp. no. 7 0.4555 0.6676 0.4383

Exp. no. 8 0.1320 0.9704 0.8465

Exp. no. 9 0.0000 1.0000 1.0000

6.2.2 Computing the Grey Relational Coefficient and the Grey Relational

Grade

After data pre-processing is carried out, a grey relational coefficient

can be calculated with the pre-processed sequence. It expresses the relationship

between the ideal and actual normalized experimental results. The grey relational

coefficient is defined as follows:

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maxoi

maxmini )k(

)k( (6.4)

Where )k(oi is the deviation sequence of the reference sequence

)k(x*0 and the comparability sequence is )k(x*

i , distinguishing or identification

coefficient. If all the parameters are given equal preference, is taken as 0.5.

The grey relational coefficient for each experiment of the L9 OA can be

calculated using Equation 6.4 and the same is presented in Table 6.4.

The grey relational coefficient ( i) and Grey relational grade ( i) for

the MRR of the expt. No.2 using equation 6.4 is given below.

)1*5.0(1)1*5.0(0)(ki

5.15.0)(ki

3333.0)(ki

i=31 i (1) + i (2) + i (3))

i= 31 (0.333+1.000+0.7806)

i= 0.7047

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Table 6.4 - The calculated grey relational grade and its order in the

optimization process

Expt.No.

Grey relational coefficient Grey relational grade

i=31 ( i (1)+ i (2)+ i (3))

Rank

MRR

i (1)TWR

i (2)OC

i (3)

1 0.3333 1.0000 0.7806 0.7047 2

2 0.4158 0.8643 0.7579 0.6793 3

3 0.5518 0.8077 1.0000 0.7865 1

4 0.4637 0.4056 0.6563 0.5085 7

5 0.5318 0.3984 0.9208 0.6170 4

6 0.7597 0.3766 0.5398 0.5587 5

7 0.5233 0.4282 0.5329 0.4948 9

8 0.7912 0.3400 0.3713 0.5008 8

9 1.0000 0.3333 0.3333 0.5556 6

After obtaining the grey relational coefficient, the grey relational

grade is computed by averaging the grey relational coefficient corresponding to

each performance characteristic. The overall evaluation of the multiple

performance characteristics is based on the grey relational grade, that is:n

1kii )k(

n1 (6.5)

Where i the grey relational grade for the ith experiment and n is is the

number of performance characteristics. Table 6.4 shows the grey relational grade

for each experiment using L9 OA. The higher grey relational grade represents

that the corresponding experimental result is closer to the ideally normalized

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value. Experiment 3 has the best multiple performance characteristics among

nine experiments because it has the highest grey relational grade. It can be seen

that in the present study, the optimization of the complicated multiple

performance characteristics of EDM of SS 304 has been converted into

optimization of a grey relational grade.

Since the experimental design is orthogonal, it is then possible to

separate out the effect of each machining parameter on the grey relational grade

at different levels. For example, the mean of the grey relational grade for the

pulse-on time at levels 1, 2 and 3 can be calculated by averaging the grey

relational grade for the experiments 1 to 3, 4 to 6 and 7 to 9 respectively as

shown in Table 6.5

Table 6.5 - Response table for the grey relational grade

Symbol Machiningparameters

Grey relational grade Maineffect(max-min) Rank

Level 1 Level 2 Level 3

A Pulse ontime 0.7235* 0.5614 0.5171 0.2064 1

B Dischargecurrent 0.5693 0.5991 0.6336* 0.0643 2

C Gap voltage 0.6257* 0.5776 0.5986 0.0481 3

Total mean value of the grey relational grade =0.6007 * Levels for optimum grey relational grade

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The mean of the grey relational grade for each level of the other

machining parameters, namely, discharge current and gap voltage can be

computed in the same manner. The mean of the grey relational grade for each

level of the machining parameters is summarized and shown in Table 6.5. In

addition, the total mean of the grey relational grade for the nine experiments is

also calculated and presented in Table 6.5.

Figure 6.1 shows the grey relational grade obtained for different

process parameters. The mean of grey relational grade for each parameter is

shown by horizontal line. Basically, the larger the grey relation grade is, the

closer will be the product quality to the ideal value. Thus, larger grey relational

grade is desired for optimum performance. Therefore, the optimal parameters

setting for better MRR and lesser TWR and OC are (A1B3C1) as presented in

Table 6.5. Optimal level of the process parameters is the level with the highest

grey relational grade.

Figure 6.1 Effect of EDM parameters on the multi-performance

characteristics

0.0000

0.1000

0.2000

0.3000

0.4000

0.5000

0.6000

0.7000

0.8000

100 150 200 2 3 4 20 30 40

Pulse on time( s) Discharge current (A) Gap voltage(V)

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Furthermore, ANOVA has been performed on grey relational grade to

obtain contribution of each process parameter affecting the two process

characteristics jointly and is discussed in the forthcoming section.

6.2.3 Analysis of Variance

The purpose of ANOVA is to investigate which machining parameters

significantly affect the performance characteristic. This is accomplished by

separating the total variability of the grey relational grades, which is measured by

the sum of the squared deviations from the total mean of the grey relational

grade, into contributions by each machining parameter and the error. First, the

total sum of the squared deviations SST from the total mean of the grey relational

grade can be calculated as:

2m

p

1jjT )(SS (6.6)

where p is the number of experiments in the OA and j is the mean of the grey

relational grade for the jth experiment.

The total sum of the squared deviations SST is decomposed into two

sources: the sum of the squared deviations SSd due to each machining parameter

and the sum of the squared error SSe. The percentage contribution by each of the

machining parameter in the total sum of the squared deviations SST can be used

to evaluate the importance of the machining parameter change on the

performance characteristic. SSe is the sum of squared error without or with

pooled factor, which is the sum of squares corresponding to the insignificant

factors. Mean square of a factor (MSj) or error (MSe) is found by dividing its sum

of squares with its degrees of freedom. Percentage contribution ( ) of each of the

design parameters is given by following equation.

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T

jj SS

SS(6.7)

In addition, the Fisher’s F test16 can also be used to determine which

machining parameters have a significant effect on the performance characteristic.

Usually, the change of the machining parameter has a significant effect on the

performance characteristic when F is large.

ANOVA for grey relational grade is presented in Table 6.6.

Percentage contributions for each term affecting grey relational grade are shown

in Figure 6.3. The figure clearly shows that pulse-on time is the dominant

parameter that affects grey relational grade and hence contributes in improving

MRR and reducing TWR and OC. This shows that when the pulse-on time is

increased with a fixed frequency, the discharge energy becomes high that

consequently increases the MRR. The increase in discharge energy also attributes

to the removal of extra material at the entry side of the hole, which in turn

increases the OC.

(a) (b)

Figure 6.2 Entry and exit SEM micrographs of machined micro holes at (a)

100µs/4A/20 V and (b) 200µs/4A/20 V respectively.

133

It is evident from the SEM pictures shown in the figure 6.2 reveals

that when pulse-on time is increased the OC also gets increased. Based on the

above discussion, the optimal process parameters are pulse-on time at level 1,

discharge current at level 3, and gap voltage at level 1

Table 6.6 - ANOVA of grey relational grade

ParameterDegree of

freedom

Sum of

squares

Mean

squaresF

ratio

Percentage

contribution

( )

Pulse-ontime (A) 2 0.0709 0.0354 15.04 83.09

Dischargecurrent(B) 2 0.0062 0.0031 1.32 7.28

Gapvoltage(C) 2 0.0035 0.0018 0.74 4.10

Error 2 0.0047 0.0024 - 5.53

Total 8 0.0853 0.0426 - 100.00

It can be seen from Figures 6.1 and 6.3 that pulse-on time is the most

significant factor that affects the grey relational grade. Metal removal is directly

proportional to the amount of energy applied during the on-time. The energy

applied during the on-time controls the peak amperage and the length of the on-

time. Pulse duration and pulse off-time are together called pulse interval. If the

pulse duration is longer, then more workpiece material will be melted away.

Then, it will have a broader and deeper hole than using shorter pulse duration.

Even though the hole has rough surface finish, the extended pulse duration will

allow more heat sink into the workpiece and in the mean time it will spread

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which means the recast layer will be larger and the heat affected zone will be

deeper. The SEM picture in figure 6.2 also reveals that recast layer and OC is

more if the pulse-on time is increased.

Figure 6.3 Percentage contributions of factors on the grey relational grade

6.3 CONFIRMATION TEST

Confirmation test has been carried out to verify the improvement of

performance characteristics in micro-hole drilling of SS 304using EDM. The

optimum parameters are selected for the confirmation test as presented in Table

6.6. The estimated grey relational grade using the optimal level of the

machining parameters can be calculated using following equation.

)(ˆ mi

q

1im (6.8)

where m is the total mean of the grey relational grade i is the mean of the grey

relational grade at the optimal level, and q is the number of the machining

parameters that significantly affect multiple-performance characteristics.

83%

7%

4% 6%

Pulse on time Discharge current

Gap voltage others

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Table 6.7 - Improvements in grey relational grade with optimized EDM

machining parameters

Condition

description

Optimal machining parameters

Machining parameters

in third trial of OA

Grey theory prediction

design

Level A1B3C3 A1B3C1

MRR (mg/min) 15.0381 17.2614

TWR (mg/min) 15.9469 13.6240

OC ( m) 118.0000 110.8000

grey relationalgrade 0.7047 0.7814

Improvement in grey relational grade = 0.0767

The obtained process parameters, which give higher grey relational

grade, are presented in Table 6.7. The predicted MRR, TWR, OC and grey

relational grade for the optimal machining parameters are obtained using

Equation 6.8 and also presented in Table 6.7. Table 6.7 which shows the

comparison of the experimental results using the initial (OA, A1B1C1) and

optimal (grey theory prediction design, A1B3C1) machining parameters. Based on

Table 6.7, MRR is accelerated from 15.0381 to 17.2614 mg/min, the TWR is

decreased from 15.9469 to 14.6241 mg/min and the OC is also decreased from

118 to 115.8 m. The corresponding improvements in MRR, TWR and OC are

12.88%, 14.57% and 6.1% respectively. It is clearly shown that the multiple

performance characteristics in the EDM process are greatly improved through

this study.

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6.4 CONCLUDING REMARKS

The GRA based on the Taguchi method’s response table has been

proposed as a way of studying the optimization of EDM process parameters for

SS 304. The optimal machining parameters have been determined by the grey

relational grade for multiperformance characteristics that is MRR, TWR and OC.

Nine experimental runs based on OA’s have been performed. The following

conclusions can be drawn from this study.

The work has successfully evaluated the feasibility of micro-hole drilling

in EDM of SS 304.

From the response table of the average grey relational grade, it is found

that the largest value of grey relational grade for pulse-on time, discharge

current and gap voltage are 100 s, 4A and 20V, respectively. These are

the recommended levels of controllable process factors when better MRR,

lesser TWR and OC are simultaneously obtained.

The ANOVA of grey relational grade for multi-performance

characteristics reveals that the pulse-on time is the most significant

parameter. Based on the SEM picture, it is evident that when pulse-on

time is increased the MRR and OC also get increased.

Based on the confirmation test, the improvements in MRR, TWR and OC

is 12.88%, 14.57%, and 6.1% respectively.

It is shown that the performance characteristics of the EDM process

such as MRR, TWR and OC are improved together by using the method

proposed by this study. The effectiveness of this approach has been successfully

established by validation experiment.