Computer aided Genetic Algorithm based Optimization of Electrical Discharge Drilling in Titanium alloy (Grade-5) Sheet

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ScienceDirect Materials Today: Proceedings 18 (2019) 4869–4881

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ICMPC-2019

Computer aided Genetic Algorithm based Optimization of Electrical Discharge Drilling in Titanium alloy (Grade-5) Sheet *Arun Kumar Pandey 1

Mechanical Engineering Department, Bundelkhand Institute of Engineering & Technology, Kanpur Road, Jhansi (UP) India

Abstract Precise and micro holes in the different advanced materials such as Ti and their alloys is a very challenging task due to unfavourable characteristics of these materials by conventional machining. These problems may be minimised upto some extent by using new class of machining processes such as advanced machining processes. In the category of advanced machining processes, the electrical discharge drilling is the efficient and cost effective machining process for the machining of these materials. But some quality characteristics such as hole circularity, hole taper and hole dilation are the main problem associated during the machining of these materials by using electrical discharge machining. These may be minimized by selecting the optimum process parameter levels. In this study, the experiments have been conducted by using L27 orthogonal array. The discharge current, pulse on time, pulse off time and dielectric pressure have been selected as input process parameters and hole circularity, hole taper and hole dilation as output parameters. The multi regression models for hole circularity, hole dilation and hole taper have been developed by using the experimental data. The statistical analysis for the developed models shows that the models are reliable and adequate and may be used for predicting these quality characteristics satisfactorily. These quality characteristics have been optimized by using computer aided genetic algorithm based optimization method. For the optimization, the multi regression models for circularity, dilation and taper have been considered as objective function. The multi-objective optimization result obtained by computer aided genetic algorithm based optimization method, show improvements in all of the quality characteristics. © 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the 9th International Conference of Materials Processing and Characterization, ICMPC-2019 Keywords: Electrical Discharge Drilling; Hole Circularity; Hole dilation, Hole Taper; Multi-objective Optimization; Computer Aided Genetic Algorithm.

*Corresponding Author Tel: +91-9575272128 E-Mail Id: [email protected] 2214-7853 © 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the 9th International Conference of Materials Processing and Characterization, ICMPC-2019

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1.

Introduction

The Electrical Discharge Drilling (EDD) is a controlled metal-removal process in which the material is removed by the erosion i.e. particle by particle process [1]. In this process electric sparks are generated between two electrodes which are separated by a very small distance and a dielectric fluid is flooded between these electrodes. When the applied voltage reaches at a particular voltage, the spark is generated between the electrodes. The materal is melted with the help of intense heat of spark and the melted material is removed with the help of dielectric fluid in the form of debris particles [2-3]. The schematic diagram of electrical discharge drilling is shown in Fig. 1. .

Fig. 1 Schematic diagram of Electrical Discharge Drilling

Titanium and its alloys are most commonly used for different technologically advanced industries such as aeronautics, marine, chemical and medical transplant due to their better mechanical properties. The Ti-6Al-4V is an alloy (grade 5) of Ti, has very wide applications is such industries for making different components such as airframes, fastener components, vessels, cases, hubs, forgings, bone plates, rods, expendable ribs cages, finger and toe replacements, spinal fusion cages and dental implants, pistons and piston rings [4]. This material is also most commonly used for the bio transplantation due to better compactability from bio tissues. But these applications requires very complex and precise cuts which may not be obtained by conventional machining methods due to better mechanical properties, low thermal conductivity and diffusivity, low elastic modulus and high chemical affinity to different gases and material. So, this material may be processed by using electrical discharge drilling. Most of the researchers have carried out experimental investigation for the different category of materials such as metals, ceramics, composites and super-alloys. Kilickap et.al have developed the regression models for the surface roughness in electrical discharge drilling of Aluminium alloy sheet [5]. They concluded that a considerable amount of saving in time and cost may be obtained by using this model. Kliuev et.al have proposed the optimum method for drilling the holes in inconel turbine blades by using electrical discharge drilling machine. They have concluded that the material removal rate has increased to77 mm3/min, relative tool wear has reduced to 20 % and the average recast layer thickness has reduced to 8 µm at optimum parameters level [6]. Ding et.al have also presented rough machining of turbine blades by the hybrid application of CNC electrical discharge drilling machine and computer aided manufacturing system [7]. Singh et.al have applied grey relational analysis for the multi-objective

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optimization of electrical discharge drilling of Al6063/10% SiC metal matrix composite [8]. They have found that the output quality characteristics have been enhanced upto certain limit. Wang et.al have experimentally investigated the micro hole drilling in poly crystalline diamond by using electrical discharge drilling. The Experimental results show that negative polarity is suitable for micro-EDD of poly crystalline diamond due to sticking adhesion over electrode [9]. Lee and Liu have proposed the strain gauge method to measure residual stresses in electrical discharge drilling. The experimental results show that the induced stress emerged in electrical discharge hole drilling measurement when the discharge coefficient is more than 0.99 [10]. These stresses can be reduced substantially and becomes insensitive to the parameters of the pulse current and pulse-on duration [10]. Eyercioglu et. al have done experimental work on the investigation of the effects of electro-discharge drilling parameters on the surface integrity in small-hole (dia. 2 mm) drilling of cold work steel. The experimental results indicate that by increasing the stability during the process, dimensional accuracy increases and a better finish may be obtained [11]. Govindan and Joshi have carried out the experimental characterization of material removal rate in dry electrical discharge drilling. They have shown that at low discharge energies, single-discharge in dry EDM give larger MRR and crater radius as compared to that of the conventional liquid dielectric EDM [12]. The artificial intelligence based neural network and genetic algorithm has been applied by Somashekhar et.al for the modelling and optimization of the materials removal rate during the micro electrical discharge drilling [13]. The developed model by neural network has been found reliable and adequate. Lal et.al have done multi-objective optimization of wire electrical discharge machining process parameters for Al7075/Al2O3/SiC hybrid composite by using Taguchi-based grey relational analysis. The found the order of significance of pulse on time, pulse current, pulse off time and the wire drum speed as 50.02%, 39.50%, 4.58% and 2.75%, respectively [14]. The literature survey shows that only some researchers have done experimental work on the electrical discharge drilling of Titanium alloy sheet. Most of the researches are based on the one parameter at time study. Very few papers have been found on the well planned robust parameter design methodology. Most of the researchers have applied design of experiments based methods for the modelling and optimization. Only few papers have been found on modelling and optimization based on artificial intelligence based methods. As per author knowledge, no paper has been found for the electrical discharge drilling of Titanium alloy sheet for modelling and optimization based on the computer aided genetic algorithm based optimization method. In this research, the experimental investigation of electrical discharge drilling of Titanium alloy sheet has been carried out. A well planned experimental matrix (orthogonal array) has been used for the experimentation. For the experimentation, four input process parameters pulse on time, pulse off time, dielectric pressure and discharge current have been used. The output quality characteristics hole circularity, hole taper and hole dilation have been analysed. The second order regression models for all three quality characteristics have been developed. The developed models have been also validated statistically as well as experimentally. These models have been further used as objective functions for the multi-objective optimization by using computer aided genetic algorithm based optimization method. 2.

Experimentation

2.1 Experiments Parameters: This experimental work was carried out on Electrical Discharge Drilling (EDD), 3X-spark DRO (EDM-Drill) with a DC stepper motor. The workpiece material for EDD is a 1 mm thick sheet of Titanium alloy (grade-5) sheet and its chemical compositions is shown in Table 1. Single hole brass tubular electrode of diameter of 1mm and length 400 mm has been used for experimentation. The chemical composition of the brass electrode is given in Table 2.

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A.K. Pandey/ Materials Today: Proceedings 18 (2019) 4869–4881 Table 1 Chemical composition of Titanium alloy (Grade-5) Al%

Fe%

6.47

Mn%

0.08

V%

0.05

3.53

Ti% 89.87

Table 2 Chemical composition of brass electrode Chemical Composition Percentage Copper 56.7 Aluminum

0.03

Tin

0.02

Phosphorous

0.02

Lead

3.00

Iron

0.10

Zinc

39.85

Nickel

0.08

Based on the literature survey and expert knowledge, four important input process parameters as discharge current (I), pulse on time (µs), pulse off time (µs) and dielectric pressure (kg/cm2) have been selected for experimentation. The discharge current basically controls the intensity of the electrical spark generated between the workpiece and electrode. The pulse on time and pulse off time controls the melting and removal of materials during electrical discharge drilling. Whereas pressurised dielectric is used to generate the spark as well as to remove the debris particles from the inter electrode gap. An exhaustive pilot experiments have been performed to determine their feasible range in which a desired through hole may be achieved. Based on the pilot experiments, the range and levels of different process parameters are listed in Table 3. Table 3 Input Process Parameters and their levels

Symbol

Parameter

Levels

Unit 1

X1 X2 X3 X4

2

3

Pulse on time

(µs)

8

9

10

Pulse off time

(µs)

2

4

6

Dielectric Pressure

(𝑘𝑔⁄𝑐𝑚 )

60

70

80

Discharge Current

(Amp)

14

15

16

2.2 Quality Characteristics: The different quality characteristics considered for the analysis of a hole are hole circularity, hole dilation and hole taper. The experiments have been conducted based on the well planned orthogonal array L27 [15]. One mm diameter of the hole has been done on the workpiece for experimental runs. For each experimental run, the hole diameter is measured at four different places at equal intervals along the circumference of the drilled hole as shown in Fig.2. The average of all these four diameters has been taken to obtain the mean or average diameter. Similar procedure may be applied at the bottom. The top and bottom diameter of hole has been

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Table 4 Values of Different Quality Characteristics

Dielectric Pressure

Discharge Current

Hole Circularity Hole Taper (radian)

Hole Dilation (mm)

0.71

2.15

0.32

15

0.62

3.46

0.29

80

16

0.63

2.76

0.12

4

60

15

0.60

0.12

0.1

8

4

70

16

0.61

2.72

0.24

6

8

4

80

14

0.60

0.14

0.24

7

8

6

60

16

0.72

1.00

0.27

8

8

6

70

14

0.59

0.79

0.23

9

8

6

80

15

0.66

2.22

0.05

10

9

2

60

15

0.66

1.19

0.08

11

9

2

70

16

0.69

1.43

0.27

12

9

2

80

14

0.66

3.15

0.28

13

9

4

60

16

0.56

2.58

0.20

14

9

4

70

14

0.90

1.72

0.03

15

9

4

80

15

0.66

4.12

0.30

16

9

6

60

14

0.69

3.01

0.12

17

9

6

70

15

0.66

1.56

0.38

18

9

6

80

16

0.65

0.57

0.38

19

10

2

60

16

0.63

4.57

0.41

20

10

2

70

14

0.61

0.43

0.23

21

10

2

80

15

0.60

0.43

0.19

22

10

4

60

14

0.93

0.14

0.47

23

10

4

70

15

0.69

3.72

0.19

24

10

4

80

16

0.64

1.14

0.41

25

10

6

60

15

0.62

2.00

0.29

26

10

6

70

16

0.90

0.86

0.48

27

10

6

80

14

0.64

1.93

0.14

Pulse on time (µs)

Pulse off time (µs)

(kg/cm2)

(Amp.)

1

8

2

60

14

2

8

2

70

3

8

2

4

8

5

Ex. No.

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Fig. 2 Hole diameter measurement of the drilled hole

After measuring the hole diameters at top and bottom, the hole circularity, hole dilation and hole taper has been computed by using Equations (1), (2) and (3), respectively. HC =

d d

max

HD = D mean − d electrode

(2)

 −  −1  HT =  tan  d ent d exit   2t    

(3)

Where

D

(1)

min

d

min

and

d

max

are the minimum and maximum diameter of the hole respectively,

is the mean diameter of the hole,

mean

d

electrode

is the electrode diameter,

mean diameter of hole at exit and entry side respectively.

D

mean

d

ent

and

d

exit

are the

has been obtained by using the

following equation;

D

mean

Where

=

d +d +d +d 1

2

3

4

(4)

4

d ,d ,d 1

2

3

and

d

4

are the measured hole diameters at four different places along the

periphery of the hole. The values different quality characteristics obtained by using Eq. (1-4) are given in Table 4. 3.

Modelling

3.1 Multiple Regression Analysis: Usually, multiple regression analysis method is used to obtain the relation between machining process parameters and performances. In this study, multiple regression analysis has been used to establish a mathematical model between the experimentally obtained hole taper, hole circularity and hole dilation values and electrical discharge process parameters. For developing the second order regression models of hole circularity, hole dilation and hole taper, Minitab 14 software has been used. The final developed models for hole circularity, hole dilation and hole taper are shown by Equation (5-7), respectively;

A.K. Pandey/ Materials Today: Proceedings 18 (2019) 4869–4881

HC = 6.36+1.11*X1 0.332*X2 -0.0289* X3-1.19*X4 0.000239*X3*X3+0.0311*X4*X4-0.00167*X1*X2-0.00267*X1*X3-0.0227*X1*X4 X2*X3+0.0167*X2*X4+0.00533* X3*X4

4875

0.0306*X1*X1-0.00139*X2*X2+0.00153* (5)

HD = 25.7 - 1.26*X1 - 0.595*X2 + 0.0281*X3 - 2.70*X4 + 0.0172*X1*X1 + 0.00720*X2*X2 0.000123*X3*X3+0.0660*X4*X4+0.00488*X1*X2-0.00153*X1*X3+0.0720*X1*X+ 0.000683* X2*X3 + 0.0298*X2*X4 (6) - 0.000011*X3*X4

HT = -178+3.34*X1-0.96*X2+0.969*X3+18.0*X4-0.246*X1*X1-0.172*X2*X2+0.00392 0.470*X4*X4+0.327*X1*X2-0.0458*X1*X3+0.170*X1*X4+0.00344*X2*X3-0.0686* X2*X4-0.0737*X3*X4 (7)

*X3*X3-

Where, X1, X2, X3 and X4 are the pulse on time, pulse off time, Dielectric pressure and discharge current, respectively. 3.2 Model validation: In order to find the adequacy of the developed models, the validation of the developed models is required. The models may be validated either statistically or experimentally. 3.2.1 Statistical validation of developed models: To validate the developed models, the S-values and coefficients of determination (R2) and adjusted- R2 values have been calculated for each models by using the Minitab 14 software. These values for all developed models such as hole circularity, hole dilation and hole taper are mentioned in Table 5. Table 5 Regression Parameters of Developed Models Response HC HT HD

S value 0.0387285 0.407881 0.0293188

Regression parameters R2 Adjusted-R2 0.935 0.852 0.955

0.86 0.78 0.92

From the Table 5, it is clear that the R2 values for hole circularity, hole dilation and hole taper are as 0.935, 0.955 and 0.852, respectively i.e. the values of regression coefficient (R) for hole circularity, hole dilation and hole taper is 0.967, 0.977 and 0.923, respectively. The regression coefficient values for all quality characteristics are greater than 0.9 i.e. in the acceptable ranges and close to 1. Also, the values of R2 and Adj. R2 to close to each other i.e. the scattering of the data are very less. Hence, the developed models for the hole circularity, hole dilation and hole taper are reliable and adequate [16]. These models may be used for the prediction of these quality characteristics satisfactorily. 3.2.2 ANOVA Analysis: Analysis of variance (ANOVA) has been performed to check the adequacy of the developed models by using Minitab 14 software. The ANOVA results for different models are shown in Table 6. The p-values for the source of regression in all three models are lower than 0.05. Moreover, the calculated F-ratios for source of regressions are 4.98, 5.41 and 18.16 for hole taper, hole circularity and hole dilation, respectively. These values are more than the critical F-ratio at the 99% confidence level [16]. Therefore, the developed empirical relationships or regression models for all the quality characteristics are significant and adequate for the prediction of these quality characteristics [16].

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A.K. Pandey/ Materials Today: Proceedings 18 (2019) 4869–4881 Table 6 ANOVA Results for the Developed Models Response

Source

Degree of freedom

Sum of square

Mean sum of square

F value

P value

HT

Regression

14

24.1600

1.7257

4.98

0.004

Residual error

12

4.1562

0.34

Total

26

28.3162

Regression Residual error

14 12

0.104465 0.016542

0.007462 0.001379

5.41

0.003

Total

26

0.121007

Regression Residual error

14 12

0.218548 0.010315

0.015611 0.000860

18.16

0.000

Total

26

0.228863

HC

HD

Table 7 Comparison Results of Experimental Vs Predicted data for different Characteristics Ex. No.

1 2 3 4 5 6 7 8 9 10

Experimental Quality Characteristics

Predicted Quality Characteristics

HC

HD

HT

HC

HD

HT

0.76

0.18

1.25

0.71

0.16

1.19

6.57

11.11

4.80

0.89

0.27

1.38

0.82

0.25

1.43

7.86

7.40

3.62

0.76

0.28

3.26

0.73

0.26

3.15

3.94

7.14

3.37

0.72

0.2

2.75

0.75

0.18

2.58

-4.16

10.00

6.18

0.9

0.13

1.82

0.87

0.14

1.72

3.33

-7.69

5.49

0.83

0.3

4.12

0.79

0.28

3.89

4.87

6.66

5.58

0.79

0.12

3.01

0.76

0.11

2.98

3.79

8.33

0.99

0.66

0.38

2.33

0.68

0.35

2.25

-3.03

7.89

3.43

0.75

0.38

1.57

0.72

0.36

1.47

4.00

5.26

6.36

0.69

0.41

3.27 0.66 Average Prediction Error

0.39

3.34

4.34

4.87

2.14

7.63

4.19

Total Average Prediction Error

% Error HC

4.59

HD

HT

5.47

3.2.3 Experimental validation: The developed models for hole circularity, hole dilation and hole taper have also validated experimentally. For the validation, the experiments have been conducted at different input process parameters settings. Finally, the values of hole circularity, hole dilation and hole taper are calculated by different equations. The experimental values are compared with the predicted values at different input process parameters settings. The comparison results are given in Table 7 and these results are also shown graphically in Fig. 3. The average percentage prediction error (APPE) and total percentage prediction error (TPPE) are calculated by using equation 8 and 9, respectively. These errors are shown in Table 7. From the Table 7, it is clear that the average percentage error for hole circularity, hole dilation and hole taper is 4.59, 7.63 and 4.19, respectively. The total average prediction percentage error is 5.47. These errors are in acceptable ranges and the developed models of hole circularity, hole dilation and hole taper are reliable and adequate. From the Fig. 3, it may also be seen that the experimental data and predicted data for different quality characteristics follow the same trend i.e. the developed models are reliable and adequate.

A.K. Pandey/ Materials Today: Proceedings 18 (2019) 4869–4881

APPE =

( Experimentalvalue − Pr edictedvalue ) *100

Experimentalvalue ( sumofAPPE ) TPPE = NumberofqualityCharacteristics

4877

(8) (9)

Fig. 3 Experimental Vs Predicted Quality Characteristics 4.

Optimization

The multi-objective optimization has been carried out by using computer aided Genetic Algorithm based optimization method. Genetic Algorithm (GA) is an artificial intelligence based popular stochastic search method based on the natural law of survival of the fittest. The GAs as a soft-computing tool have been widely employed for searching the optimum performance conditions for complex and nonlinear systems with the number of variables. It is preferred over some conventional statistical methods because it provides global searching, robustness, and a computationally efficient approach [17]. The objective functions to be optimized have been defined separately in the M-files of MATLAB2008a software. The Equations (5-7) have been used as an objective function for the multi-objective optimization of hole circularity, hole dilation and hole taper, respectively. For maximizing the hole circularity, 1=Cent has been considered as objective functions as genetic algorithm is used directly to minimize the function [18]. The selection criteria of different individuals used for the optimization are shown in Fig. 4. In the next step, the critical parameters of selection, crossover, and mutation such as population size, population type, and crossover and mutation

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probability have been chosen based on better GA performance results. In this analysis, population size= 200, population type=double vector, crossover probability=0.8, mutation probability=0.07, Max. Generations = 800, initial population=20*4 double and initial scores=200*3 double vector have been selected. The distance of different individuals’ child used for the optimization is shown in Fig. 5.

Fig. 4 Selection Function

Fig. 6 Pareto Front for hole taper and 1/hole circularity

Fig.5 Distance of individuals

Fig. 7 Score histogram

After selecting these parameters, the optimization solver has been run and after 800 generations, the optimization has been terminated. Two-point crossover function for crossover and uniform function for mutation has been adopted for the study. This combination of GA parameters are selected after trying different combinations for better results out of different initial scores and formed different children based on crossover and mutation. Finally, 80 sets of optimum solutions have been obtained based on the best fitness values, which are shown in Fig. 6. Such types of solutions are known as Pareto optimal solutions and the graph showing these solutions are known as Pareto front that showing the different possible sets of optimal solutions based on the values of objective 1 and objective 2. The Objective 1 represents hole taper while objective 2 represents 1/circularity at entrance. All solutions shown in Pareto front are optimal solutions. The single optimal solution may be selected based on the values of objective 1 and objective 2. From the Fig. 6, we can see that if we are decreasing the value of objective 1, then the value of objective 2 will increases. Our optimal solution will be that solution for which, the values of objective 1 and objective 2 are in the permissible ranges. The Pareto front is showing only two objectives but in this problem, there are three objectives used for the optimization. The different optimal solutions obtained for all three objective functions/ quality characteristics corresponding to the different values of control factors have been shown in Table 8. The maximum and the minimum values for all three quality characteristics obtained after optimization are shown in Fig. 7.

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Table 8 Suggested optimal solutions for HT, Cent and HD X1

X2

X3

X4

Taper (Function 1)

1

9.98

2.06

60.24

14.04

2

8.02

5.93

60.2

3

8.02

4.18

60.24

4

8.02

4.62

5

8.02

6 7

1/Cent (Function 2)

Cent

HD (Funct ion 3)

% improve Taper

% improve Cent

% improve HD

% improve Avg.

0.28

1.15

0.86

0.26

86.97

21.12

18.75

42.28

14.00

0.01

1.67

0.59

0.15

99.53

16.90

53.12

45.25

15.24

2.56

1.78

0.56

0.12

-19.06

-21.12

62.5

7.44

60.24

14.77

2.02

1.73

0.57

0.12

6.04

-19.71

62.5

16.27

4.62

64.23

15.24

2.18

1.69

0.59

0.13

-1.39

-16.90

59.37

13.69

9.98

2.06

67.37

14.04

0.16

1.23

0.80

0.25

92.55

12.67

21.87

42.36

8.02

5.93

67.37

14.00

0.64

1.62

0.61

0.18

72.09

-14.08

43.75

33.92

8

9.98

2.56

67.37

14.04

0.55

1.25

0.79

0.22

74.41

11.26

31.25

38.97

S. No.

9

8.02

4.18

60.70

14.77

2.31

1.70

0.58

0.12

-7.44

-18.30

62.5

12.25

10

9.45

4.62

60.24

14.00

1.41

1.29

0.77

0.15

34.41

8.45

53.12

31.99

11

8.02

3.58

64.23

15.24

2.78

1.68

0.59

0.13

-29.30

-16.90

59.37

4.39

12

9.98

3.58

60.24

14.04

1.16

1.22

0.81

0.19

46.04

14.08

40.62

33.58

13

9.98

4.62

64.23

14.04

1.22

1.29

0.77

0.16

43.25

8.45

50

33.9

14

8.02

5.93

60.24

14.77

0.76

1.82

0.54

0.12

64.65

-23.94

62.5

34.40

15

8.02

4.18

60.70

15.24

2.54

1.76

0.56

0.12

-18.13

-21.12

62.5

7.75

16

9.98

5.93

60.24

14.04

0.95

1.35

0.73

0.15

55.81

2.81

53.12

37.24

17

8.02

3.58

60.24

15.24

2.86

1.76

0.56

0.12

-33.02

-21.12

62.5

2.78

18

8.00

5.93

64.23

14.03

0.32

1.64

0.60

0.17

85.11

-15.49

46.87

38.83

19

9.98

2.06

60.24

14.04

0.28

1.15

0.86

0.26

86.97

21.12

18.75

42.28

20

9.45

4.18

60.24

14.00

1.47

1.27

0.78

0.16

31.62

9.85

50

30.49

21

9.45

5.93

60.21

14.00

0.83

1.38

0.72

0.13

61.39

1.40

59.37

40.72

5.

Results and discussion The set of solutions obtained after the optimization are optimal solution. All the solutions shown in Pareto front or Table 8 are the optimal solution for different cases. The optimal solution will depend upon the requirement of the production engineer. For example, If the permissible limit of the Cent is 0.86 i.e. maximum improvement in circularity is obtained at the process parameters corresponding to the S. No. 1 in Table 8 where as maximum percentage improvement in hole taper and hole dilation are obtained corresponding to the S. No. 2 and 17 of Table 8, respectively. If we are considering the individual quality characteristics, then the process parameters corresponding to the S. No. 1, 2 and 17 of Table 8 will be the optimum parameter settings for getting the maximum improvements in hole circularity, hole taper and hole dilation, respectively. The maximum percentage improvements in hole circularity, hole taper and hole dilation (considering individual) are obtained as 21.12%, 99.53% and 62.50%, respectively (as shown in Table 8). But our aim in this research is to optimize all three quality characteristics simultaneously. Keeping this fact in mind, from Table 8, it is clear that S. No. 2 is showing minimum value of taper and hole dilation, and maximum value of hole circularity. By considering equal importance of three quality characteristics, the maximum percentage average improvement is obtained corresponding to the S. No.2 of Table 8. The optimum level of control factors for simultaneous optimization of all three quality characteristics are: 8.02 µs of pulse on time, 5.93 µs of pulse off time, 60 kgf/cm2 of distilled water pressure and 14 A of discharge current. The optimum values of hole taper, hole circularity and hole dilation are 0.01, 0.59 and 0.15, respectively. Which show an improvement of 99.53 %, 16.90% and 53.12 % in hole taper, hole circularity and hole dilation, respectively i.e. an overall average percentage improvement of 45% ( as given in Table 9).

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A.K. Pandey/ Materials Today: Proceedings 18 (2019) 4869–4881

Table 9 Percentage improvements in HT, Cent and HD Importance of quality characteristics S. No

S. No. From Table 6

HT

Responses Cent HD

HT

Cent

Improvements (%) HD Total

1

Individual (Cent)

1

0.28

0.86

0.26

86.97

21.12

18.75

42.28

2

Individual (HT)

2

0.01

0.59

0.15

99.53

21.12

18.75

45.25

3

Individual (HD)

17

2.86

0.56

0.12

-33.02

-21.12

62.50

2.78

4

All three (Cent, HT and HD)

2

0.01

0.59

0.15

99.53

21.12

18.75

45.25

6.

Conclusions

In this study, the experimental investigation of electric discharge drilling of Titanium alloy sheet has been carried out. The main conclusions drawn by this study are as; 1. The second order regression models for hole taper, hole circularity and hole dilation have been developed successfully. The regression analysis shows that the R2 values for hole circularity, hole dilation and hole taper are as 0.935, 0.955 and 0.852, respectively i.e. the values of regression coefficient (R) for hole circularity, hole dilation and hole taper is 0.967, 0.977 and 0.923, respectively. 2. The ANOVA results show that the developed models for all three quality characteristics are adequate and reliable. These models may be used for the prediction of hole taper, hole circularity and hole dilation. 3. The experimental validation of the developed models also shows that the models may be used for the prediction of hole taper, hole circularity and hole dilation satisfactorily. The total average prediction error has been found only 5.4%. 4. The multi-objective optimization of hole taper, hole circularity and hole dilation have been carried out successfully by using Computer aided Genetic Algorithm based Optimization (CGAO) methodology. 5. The optimization results show that an improvement in hole circularity, hole taper and hole dilation (considering individual) are obtained as 21.12%, 99.53% and 62.50%, respectively. 6. Whereas by considering an equal importance of all three quality characteristics, an improvements of 99.53 %, 16.90% and 53.12 % in hole taper, hole circularity and hole dilation, respectively i.e. an overall average percentage improvement of 45% is obtained. 7. The optimum level of control factors for simultaneous optimization of all three quality characteristics are: 8.02 µs of pulse on time, 5.93 µs of pulse off time, 60 kgf/cm2 of distilled water pressure and 14 A of discharge current. References 1. 2. 3. 4. 5.

A. K. Pandey, A. K Dubey, Multiple quality optimization in laser cutting of difficult-to-laser-cut material using grey–fuzzy methodology, International journal of advanced manufacturing technology 65(2013) 421–431. V. K.Jain. Advanced machining processes. fourth ed. New Delhi: Allied Publishers Private Limited; 2005. R. Khanna, A. Kumar, M. P. Garg, A. Singh, N. Sharma, Multiple performance characteristics optimization for Al 7075 on electric discharge drilling by Taguchi grey relational theory, Journal of Industrial Engineering International, 11(2015) 459–472. A. K. Pandey and A. K. Dubey, Simultaneous optimization of multiple quality characteristics in laser cutting of titanium alloy sheet, Optics and Laser Technology, Vol. 44, 2012, pp.1858-1865. E. Kilickap, M. Huseyinoglu and A. Yardimeden, Optimization of drilling parameters on surface roughness in drilling of AISI 1045 using response surface methodology and genetic algorithm, International Journal of Advanced Manufacturing Technology 52 (2011)79 – 88.

A.K. Pandey/ Materials Today: Proceedings 18 (2019) 4869–4881 6. 7. 8. 9. 10. 11. 12. 13. 14.

15. 16. 17.

4881

M. Kliuev, M. Boccadoro, R. Perez, W. Dal Bó, J. Stirnimann, F. Kuster and K. Wegener, EDM Drilling and Shaping of Cooling Holes in Inconel 718 Turbine Blades, Procedia CIRP, 42 ( 2016 ) 322 – 327. S Ding, R Yuan, Z Li, and K Wang, CNC electrical discharge rough machining of turbine blades, Proceedings of The Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 220 (2006) 1027-1033. Sarbjit Singh, Inderdeep Singh and Akshay Dvivedi, Multi objective optimization in drilling of Al6063/10% SiC metal matrix composite based on grey relational analysis, Proceedings of The Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 227(12) 1767–1776. D. Wang, W.S. Zhao, L. Gu, and X.M. Kang, A study on micro-hole machining of polycrystalline diamond by micro-electrical discharge machining, Journal of Materials Processing Technology, 211 (2011) 3–11. H.T. Lee and C. Liu, Optimizing the EDM hole-drilling strain gage method for the measurement of residual stress, Journal of Materials Processing Technology, 209 (2009) 5626-5635. Omer Eyercioglu, Mehmet V Cakir and Kursad Gov, Influence of machining parameters on the surface integrity in small-hole electrical discharge machining, Proceedings of The Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 228(2014) 51– 61. P. Govindan and Suhas S. Joshi , Experimental characterization of material removal in dry electrical discharge drilling, International Journal of Machine Tools and Manufacture, 50 (2010) 431–443. Somashekhar, K. and Ramachandran, N. and Mathew, J., Optimization of material removal rate in micro-EDD using artificial neural network and genetic algorithms, Material Manufacturing Processes, 25 (2010) 467–475. Shyam Lal, Sudhir Kumar, Z A Khan and AN Siddiquee, Multi-response optimization of wire electrical discharge machining process parameters for Al7075/Al2O3/SiC hybrid composite using Taguchi-based grey relational analysis, Proceedings of The Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 229(2015) 229–237. M. S. Phadke, Quality engineering using robust design, Prentice Hall Englewood Cliffs,New Jersey(USA)(1989). Montgomery DC. Design and Analysis of Experiments, John Wiley & Sons; New York (USA) (2004). A. K. Pandey and A. K Dubey, Modeling and optimization of kerf taper and surface roughness in laser cutting of titanium alloy sheet, Journal of Mechanical Science and Technology, 27 (2013) 1-10.

18. K. Dev, Optimization for engineering design (Algorithms and examples), PHILearning NewDelhi, India, (2009).