A Method to Optimize Process Parameters of Turning

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A Method to Optimize Process Parameters of Turning

Pawan Kumar

Mechanical Engineering

Einstein Academy of Technology & Management Bhubaneswar, India

Prashanta Kumar Pradhan

Mechanical Engineering

Veer Surendra Sai University of Technology Burla, India

Abstract-It is well known that the relation between different input process parameters and surface roughness in all machining operations. The same things happen in turning operation also. In turning operation, the input parameters speed, feed, depth of cut etc. affect the surface finish. Many engineer and researchers have tried to do optimize of this. But still, there is a gap in determining of the exact contribution of speed, feed and depth of cut (S, F&D) to get optimum surface finish.

Keyword:-ANOVA, Taguchi, surface finish, S/N ratio, orthogonal array, Grey.

  1. INTRODUCTION

    A common process to manufacture parts to a precise dimension has the removal of excess material by

    machining operation with the help of cutting tool. Turning process is the one of the methods to remove material from cylindrical and non-cylindrical parts. Taguchi method is a dominant tool for the design of high quality systems. It offers simple, effective and methodical tactic to optimize design for performance, quality and cost. Taguchi method is efficient method for designing process that operates consistently and optimally over a variety of conditions. Taguchi approach to design the of experiments easy to adopt and apply for users with limited knowledge of statics, hence grew wide popularity in the engineering and scientific community.

  2. PHYSICAL DESCRIPTION OF THE PROBLEM

    Equipments used in the Machining Process: High Speed Precision Lathe NH22

    Cutting Tool Used: Tungsten Carbide Tip Tool

    Work Piece Used: Mild steel bars of diameter 32mm and length 200 mm.

    Roughness Measurement: Surface Profile Roughness measurement has been done using a portable stylus-type profilometer,

    Process variables and their limits for L27

    Taguchi method is efficient method for designing process that operates consistently and optimally over a variety of conditions. Taguchi approach to design of experiments easy to adopt and apply for users with limited knowledge of statics, hence gained wide popularity in the engineering and scientific community. The desired cutting parameters determined by handbook. Cutting parameter are reflected on surface roughness.

    Levels

    Speed (RPM)

    Feed (mm/rev)

    Depth of Cut (mm)

    1

    740

    0.09

    0.15

    2

    580

    0.07

    0.10

    3

    450

    0.05

    0.05

    TABLE 1.

    1. EXPERIMENTATION

Design of experiment techniques, i.e. Taguchis technique has been used to accomplish the objective. L27 orthogonal array used for conducting the experiments. ANOVA and factorial design technique is employed to analyse the PC and influence of Process Parameters.

  1. RESULTS AND DISCUSSION

    The results and discussion of the present work mainly consists of the following;

    1. Percentages contribution of input variables on surface finish using Grey Relational Analysis technique.

    2. Percentages contribution of input variables on Ra, MMR&PC using Grey Relational Analysis technique.

    3. Percentages contribution of input variables on Ra, MMR&PC using Weighted Signal to Noise Ratio (WSNR) technique.

    4. Percentages contribution of input variables on Ra, MMR&PC using Multi-Response Signal-to-Noise Ratio (MRSN) technique.

3.1. Percentages contribution of input variables on multi response using Taguchi using Gray relational analysis (GRA)

The data obtained from the experiments (L27) have been used to get the PC of the input variables.

Experimental Results For 27

17

0.362

56

0.91530

0.860

369

0.439

58

0.855

134

0.781

7

0.692

139

18

0.446

97

0.60586

0.718

48

0.474

82

0.559

196

0.639

779

0.557

932

19

0.542

11

0.76707

0.358

845

0.521

98

0.682

193

0.438

152

0.547

442

20

0.490

13

0.27615

0.745

995

0.495

12

0.408

545

0.663

126

0.522

262

21

1.000

00

0.62115

0.408

17

1.000

00

0.568

928

0.457

947

0.675

625

22

0.193

79

0.77983

0.983

072

0.382

79

0.694

28

0.967

252

0.681

44

23

0.437

08

0.92275

0.821

088

0.470

40

0.866

183

0.736

472

0.691

018

24

0.803

14

0.10682

0.677

427

0.717

51

0.358

892

0.607

849

0.561

416

25

0.224

55

0.84091

0.522

656

0.392

02

0.758

625

0.511

591

0.554

078

26

0.772

57

0.00000

0.639

089

0.687

35

0.333

333

0.580

78

0.533

822

27

0.700

97

0.11026

1

0.625

76

0.359

779

1

0.661

847

4

Sl

. N

o.

Ra(µ m)

MRR(

3/

)

PC(K W)

Ra

MRR

PC

1

0.706

44

1.00000

0.198

281

0.630

08

1

0.384

107

0.671

394

2

0.306

62

0.69516

0

0.418

98

0.621

243

0.333

333

0.457

851

3

0.715

01

0.51074

0.108

704

0.636

95

0.505

429

0.359

377

0.500

586

0.617

30

0.72395

0.095

206

0.566

45

0.644

286

0.355

924

0.522

219

5

0.290

25

0.94381

0.255

436

0.413

31

0.898

968

0.401

747

0.571

342

6

0.319

61

0.81745

0.361

378

0.423

59

0.732

55

0.439

127

0.531

755

7

0.219

73

0.87470

0.215

109

0.390

54

0.799

616

0.389

138

0.526

432

8

0.408

13

0.75819

0.369

379

0.457

93

0.674

026

0.442

235

0.524

73

9

0.446

97

0.81745

0.685

388

0.474

82

0.732

55

0.613

789

0.607

054

10

0.738

55

0.99975

0.413

324

0.656

64

0.999

501

0.460

119

0.705

42

11

0.138

17

0.76707

0.719

954

0.367

15

0.682

193

0.640

988

0.563

445

12

0.695

68

0.79291

0.557

281

0.621

64

0.707

124

0.530

381

0.619

715

13

0.290

43

0.92153

0.348

929

0.413

37

0.864

352

0.434

378

0.570

7

14

0.388

96

0.86648

0.482

876

0.450

03

0.789

247

0.491

582

0.576

952

15

0.490

41

0.76575

0.253

217

0.495

25

0.680

971

0.401

032

0.525

751

16

0.000

00

0.91777

0.666

428

0.333

33

0.858

77

0.599

828

0.597

311

Sl

. N

o.

Ra(µ m)

MRR(

3/

)

PC(K W)

Ra

MRR

PC

1

0.706

44

1.00000

0.198

281

0.630

08

1

0.384

107

0.671

394

2

0.306

62

0.69516

0

0.418

98

0.621

243

0.333

333

0.457

851

3

0.715

01

0.51074

0.108

704

0.636

95

0.505

429

0.359

377

0.500

586

4

0.617

30

0.72395

0.095

206

0.566

45

0.644

286

0.355

924

0.522

219

5

0.290

25

0.94381

0.255

436

0.413

31

0.898

968

0.401

747

0.571

342

6

0.319

61

0.81745

0.361

378

0.423

59

0.732

55

0.439

127

0.531

755

7

0.219

73

0.87470

0.215

109

0.390

54

0.799

616

0.389

138

0.526

432

8

0.408

13

0.75819

0.369

379

0.457

93

0.674

026

0.442

235

0.524

73

9

0.446

97

0.81745

0.685

388

0.474

82

0.732

55

0.613

789

0.607

054

10

0.738

55

0.99975

0.413

324

0.656

64

0.999

501

0.460

119

0.705

42

11

0.138

17

0.76707

0.719

954

0.367

15

0.682

193

0.640

988

0.563

445

12

0.695

68

0.79291

0.557

281

0.621

64

0.707

124

0.530

381

0.619

715

13

0.290

43

0.92153

0.348

929

0.413

37

0.864

352

0.434

378

0.570

7

14

0.388

96

0.86648

0.482

876

0.450

03

0.789

247

0.491

582

0.576

952

15

0.490

41

0.76575

0.253

217

0.495

25

0.680

971

0.401

032

0.525

751

16

0.000

00

0.91777

0.666

428

0.333

33

0.858

77

0.599

828

0.597

311

TABLE 2.

Figure 1: variation of Gray relational grade

Level of parameters

Speed (S)

Feed (F)

Depth of cut (D)

1

0.545929

0.58486

0.597382

2

0.601041

0.581399

0.570396

3

0.603217

0.583927

0.582409

Delta(Max- Min)

0.057288

0.003461

0.026986

Rank

1

3

2

TABLE 3.( ANOVA Results for Gray relational analysis)

Figure 2: variation of level average of parameters

0.003184

Facto rs(Fa

)

Sum of Square (SS)

Degree of Freedom (DOF)

Mean Square(MS

)

PC

S

0.00636

77

2

5.234443

F

0.02544

08

2

0.01272

20.91311

D

0.00062

62

2

0.000313

0.514755

S*F

0.02553

74

4

0.006384

20.99252

S*D

0.00673

77

4

0.001684

5.538594

F*D

0.01969

06

4

0.004923

16.18627

S*F* D

0.03724

94

8

0.004656

30.62014

Error

———

0

———–

————

Total

0.12164

98

26

———-

100

Facto rs(Fa

)

Sum of Square (SS)

Degree of Freedom (DOF)

Mean Square(MS

)

PC

S

0.00636

77

2

0.003184

5.234443

F

0.02544

08

2

0.01272

20.91311

D

0.00062

62

2

0.000313

0.514755

S*F

0.02553

74

4

0.006384

20.99252

S*D

0.00673

77

4

0.001684

5.538594

F*D

0.01969

06

4

0.004923

16.18627

S*F* D

0.03724

94

8

0.004656

30.62014

Error

———

0

———–

————

Total

0.12164

98

26

———-

100

S

. N

.

S/N ratio ()

Scaled S/N ratio ()

WS N

Ra

MR R

PC

Ra

MR R

PC

1

– 8.730

25

– 2.61

537

– 19.3

056

0.70

644

0.99

3339

0.19

828

0.63

2688

2

– 13.26

67

– 8.29

756

– 21.3

227

0.30

661

0.69

5336

0

0.33

3983

3

– 8.633

06

– 11.8

149

– 20.2

168

0.71

501

0.51

0868

0.10

8709

0.44

4863

4

– 9.741

64

– 7.74

856

– 20.3

542

0.61

730

0.72

4128

0.09

5203

0.47

8878

5

– 13.45

23

– 3.55

533

– 18.7

242

0.29

025

0.94

4043

0.25

5431

0.49

6576

6

– 13.11

93

– 5.96

519

– 17.6

464

0.31

960

0.81

7657

0.36

1378

0.49

9547

7

– 14.25

25

– 4.87

336

– 19.1

344

0.21

973

0.87

4918

0.21

5109

0.43

6585

8

– 12.11

49

– 7.09

549

– 17.5

65

0.40

813

0.75

8378

0.36

938

0.51

1963

9

– 11.67

42

– 5.96

519

– 14.3

502

0.44

697

0.81

7657

0.68

5393

0.65

0007

1

0

– 8.366

03

– 2.48

836

– 17.1

18

0.73

855

1

0.41

332

0.71

7289

1

1

– 15.17

78

– 6.92

610

– 13.9

986

0.13

817

0.76

7262

0.71

9955

0.54

1797

1

2

– 8.852

42

– 6.43

328

– 15.6

535

0.69

568

0.79

3108

0.55

7279

0.68

2021

1

3

– 13.45

03

– 3.98

016

– 17.7

73

0.29

043

0.92

1762

0.34

8933

0.52

0376

1

4

– 12.33

25

– 5.03

004

– 16.4

104

0.38

895

0.86

6701

0.48

2876

0.57

951

1

5

– 11.18

14

– 6.95

121

– 18.7

467

0.49

041

0.76

5945

0.25

3219

0.50

319

1

6

– 16.74

55

– 4.05

188

– 14.5

431

0.00

000

0.91

8001

0.66

6431

0.52

8144

1

7

– 12.63

19

– 4.09

909

– 12.5

702

0.36

256

0.91

5525

0.86

0366

0.71

2818

1

8

– 11.67

42

– 10.0

008

– 14.0

136

0.44

697

0.60

6009

0.71

848

0.59

0487

1

9

– 10.59

48

– 6.92

610

– 17.6

722

0.54

211

0.76

7262

0.35

8842

0.55

6071

2

0

– 11.18

45

– 16.2

892

– 13.7

337

0.49

013

0.27

6213

0.74

5994

0.50

4113

2

1

– 5.399

59

– 9.70

904

– 17.1

704

1.00

000

0.62

131

0.40

8169

0.67

6493

2

2

– 14.54

– 6.68

– 11.3

0.19

379

0.78

0025

0.98

3073

0.65

2295

S

. N

.

S/N ratio ()

Scaled S/N ratio ()

WS N

Ra

MR R

PC

Ra

MR R

PC

1

– 8.730

25

– 2.61

537

– 19.3

056

0.70

644

0.99

3339

0.19

828

0.63

2688

2

– 13.26

67

– 8.29

756

– 21.3

227

0.30

661

0.69

5336

0

0.33

3983

3

– 8.633

06

– 11.8

149

– 20.2

168

0.71

501

0.51

0868

0.10

8709

0.44

4863

4

– 9.741

64

– 7.74

856

– 20.3

542

0.61

730

0.72

4128

0.09

5203

0.47

8878

5

– 13.45

23

– 3.55

533

– 18.7

242

0.29

025

0.94

4043

0.25

5431

0.49

6576

6

– 13.11

93

– 5.96

519

– 17.6

464

0.31

960

0.81

7657

0.36

1378

0.49

9547

7

– 14.25

25

– 4.87

336

– 19.1

344

0.21

973

0.87

4918

0.21

5109

0.43

6585

8

– 12.11

49

– 7.09

549

– 17.5

65

0.40

813

0.75

8378

0.36

938

0.51

1963

9

– 11.67

42

– 5.96

519

– 14.3

502

0.44

697

0.81

7657

0.68

5393

0.65

0007

1

0

– 8.366

03

– 2.48

836

– 17.1

18

0.73

855

1

0.41

332

0.71

7289

1

1

– 15.17

78

– 6.92

610

– 13.9

986

0.13

817

0.76

7262

0.71

9955

0.54

1797

1

2

– 8.852

42

– 6.43

328

– 15.6

535

0.69

568

0.79

3108

0.55

7279

0.68

2021

1

3

– 13.45

03

– 3.98

016

– 17.7

73

0.29

043

0.92

1762

0.34

8933

0.52

0376

1

4

– 12.33

25

– 5.03

004

– 16.4

104

0.38

895

0.86

6701

0.48

2876

0.57

951

1

5

– 11.18

14

– 6.95

121

– 18.7

467

0.49

041

0.76

5945

0.25

3219

0.50

319

1

6

– 16.74

55

– 4.05

188

– 14.5

431

0.00

000

0.91

8001

0.66

6431

0.52

8144

1

7

– 12.63

19

– 4.09

909

– 12.5

702

0.36

256

0.91

5525

0.86

0366

0.71

2818

1

8

– 11.67

42

– 10.0

008

– 14.0

136

0.44

697

0.60

6009

0.71

848

0.59

0487

1

9

– 10.59

48

– 6.92

610

– 17.6

722

0.54

211

0.76

7262

0.35

8842

0.55

6071

2

0

– 11.18

45

– 16.2

892

– 13.7

337

0.49

013

0.27

6213

0.74

5994

0.50

4113

2

1

– 5.399

59

– 9.70

904

– 17.1

704

1.00

000

0.62

131

0.40

8169

0.67

6493

2

2

– 14.54

– 6.68

– 11.3

0.19

379

0.78

0025

0.98

3073

0.65

2295

Table 3.4: weighted S/N ratio for L27

TABLE 4.

40

30

20

10

0

40

30

20

10

0

Figure 3: PC of factors

It is observed from above (L27-GRA) analysis that S3-F1- D1 is the optimal combination for getting best output results and corresponding Gray relational grade is 0.547442. The best output results mean the combination of all output parameters, these are surface finish, MRR and power consumption with equal weightage. The PC of speed is 5.23 %, of feed is 20.91 % and of depth of cut is 0.52 %. Similarly, the PC of speed and feed is 20.99%, of speed and depth of cut is 5.53%, of feed and depth of cut is 16.18%, and the combination of S, F&Dof cut is 30.62%. It indicates that, for the above ranges of input levels, the feed is most (single) effective parameters and as a combination, S-F-D is most effective.

Percentages contribution of input variables on surface finish using weighted signal-to-noise ratio technique.

Using the data obtained from the table (Table 5.7), the weighted signal-to-noise ratio (WSN) of input variables have been calculated.

WSN

40

30

20

10

0

WSN

40

30

20

10

0

Figure3.4: Variation of WSN

Table 3.5: Level Average for WSN

Level

Speed (S)

Feed(F)

Depth of Cut

1

0.498343

0.56548

0.561307

2

0.597292

0.554062

0.54204

3

0.583212

0.559306

0.57550

Delta (Max- Min)

0.098949

0.011418

0.03346

Rank

1

3

2

Fa

SS

DOF

MS

PC

S

0.004096

2

0.0020478

1.672439

F

0.017957

2

0.0089788

7.332784

D

0.01138

2

0.0056848

4.646902

S*F

0.080264

4

0.0200659

32.77565

S*D

0.028104

4

0.0070261

11.47643

F*D

0.050021

4

0.0125052

20.42596

S*F*D

0.053067

8

0.0066334

21.66987

Error

———–

0

————

————

Total

0.2448879

26

———–

100

Fa

SS

DOF

MS

PC

S

0.004096

2

0.0020478

1.672439

F

0.017957

2

0.0089788

7.332784

D

0.01138

2

0.0056848

4.646902

S*F

0.080264

4

0.0200659

32.77565

S*D

0.028104

4

0.0070261

11.47643

F*D

0.050021

4

0.0125052

20.42596

S*F*D

0.053067

8

0.0066334

21.66987

Error

———–

0

————

————

Total

0.2448879

26

———–

100

Figure 3.5: Variation of level average of parameter Table 3.6: ANOVA for WSN:

Figure 3.6: PC of input parameters

68

275

219

2

3

– 11.78

65

– 3.95

684

– 12.9

698

0.43

707

0.92

2985

0.82

1085

0.72

7048

2

4

– 7.633

13

– 19.5

185

– 14.4

312

0.80

314

0.10

6852

0.67

743

0.52

9141

2

5

– 14.19

78

– 5.51

776

– 16.0

057

0.22

455

0.84

1123

0.52

2658

0.52

9443

2

6

– 7.979

97

– 21.5

559

– 14.8

213

0.77

257

0

0.63

9084

0.47

0552

2

7

– 8.792

34

– 19.4

530

– 11.1

497

0.70

097

0.11

0287

1

0.60

3753

68

275

219

2

3

– 11.78

65

– 3.95

684

– 12.9

698

0.43

707

0.92

2985

0.82

1085

0.72

7048

2

4

– 7.633

13

– 19.5

185

– 14.4

312

0.80

314

0.10

6852

0.67

743

0.52

9141

2

5

– 14.19

78

– 5.51

776

– 16.0

057

0.22

455

0.84

1123

0.52

2658

0.52

9443

2

6

– 7.979

97

– 21.5

559

– 14.8

213

0.77

257

0

0.63

9084

0.47

0552

2

7

– 8.792

34

– 19.4

530

– 11.1

497

0.70

097

0.11

0287

1

0.60

3753

It is observed from above (L27-WSN) analysis that S2- F1-D3 is the optimal combination for getting best output results and corresponding weighted signal-to-noise ratio is 0.619715. The best output results mean the combination of all output parameters, these are surface finish, MRR and power consumption with equal weightage. The PC of speed is 1.67 %, of feed is 7.33 %, and of depth of cut is 4.64 %. Similarly, the PC of speed and feed is 32.77%, of speed and depth of cut is 11.48%, of feed and depth of cut is 20.43%, and the combination of S, F&Dis 21.67%. It indicates that, for the above ranges of input levels, the feed is most (single) effective parameters and as a combination S-F is most effective.

Percentages contribution of input variables on surface finish using Multi-response signal-to-noise ratio technique.

Using the data obtained from the table (Table5.7), the multi-response signal-to-noise ratio (MRSN) of input variables have been calculated.

Sl

. N

o

Quality loss()

Normalised loss ()

Tota l quali ty loss(

)

M RS N

Ra

MR R

PC

Ra

MR R

PC

1

7.4

64

9

1.82

61

85.2

233

0.45

456

0.10

419

1.67

265

0.74

380

1.2

85

42

2

21.

21

61

6.75

70

135.

603

1.29

192

0.38

551

2.66

144

1.44

629

1.6

02

5

3

7.2

99

72

15.1

87

105.

119

0.44

450

0.86

6513

2.06

315

1.12

472

0.5

10

4

4

9.4

22

44

5.95

46

108.

496

0.57

376

0.33

9738

2.12

943

1.01

431

0.0

61

7

5

22.

14

26

2.26

74

74.5

444

1.34

834

0.12

936

1.46

306

0.98

025

0.0

86

6

6

20.

50

8

3.94

92

58.1

621

1.24

881

0.22

532

1.14

153

0.87

189

0.5

95

38

7

26.

62

3.07

14

81.9

293

1.62

113

0.17

5237

1.60

800

1.13

479

0.5

Sl

. N

o

Quality loss()

Normalised loss ()

Tota l quali ty loss(

)

M RS N

Ra

MR R

PC

Ra

MR R

PC

1

7.4

64

9

1.82

61

85.2

233

0.45

456

0.10

419

1.67

265

0.74

380

1.2

85

42

2

21.

21

61

6.75

70

135.

603

1.29

192

0.38

551

2.66

144

1.44

629

1.6

02

5

3

7.2

99

72

15.1

87

105.

119

0.44

450

0.86

6513

2.06

315

1.12

472

0.5

10

4

4

9.4

22

44

5.95

46

108.

496

0.57

376

0.33

9738

2.12

943

1.01

431

0.0

61

7

5

22.

14

26

2.26

74

74.5

444

1.34

834

0.12

936

1.46

306

0.98

025

0.0

86

6

6

20.

50

8

3.94

92

58.1

621

1.24

881

0.22

532

1.14

153

0.87

189

0.5

95

38

7

26.

62

3.07

14

81.9

293

1.62

113

0.17

5237

1.60

800

1.13

479

0.5

Table 3.7: Multi-response signal-to-noise ratio

25

49

1

8

16.

27

39

5.12

32

57.0

822

0.99

097

0.29

2305

1.12

033

0.80

120

0.9

62

55

9

14.

70

33

3.94

92

27.2

285

0.89

534

0.22

532

0.53

440

0.55

169

2.5

83

04

1

0

6.8

64

1.77

35

51.4

985

0.41

799

0.10

118

1.01

074

0.50

997

2.9

24

49

1

1

32.

94

41

4.92

73

25.1

108

2.00

608

0.28

1124

0.49

284

0.92

668

0.3

30

68

1

2

7.6

77

88

4.39

87

36.7

576

0.46

753

0.25

096

0.72

143

0.47

997

3.1

87

79

1

3

22.

13

23

2.50

04

59.8

831

1.34

771

0.14

2661

1.17

530

0.88

856

0.5

13

12

1

4

17.

10

98

3.18

42

43.7

562

1.04

187

0.18

1674

0.85

879

0.69

411

1.5

85

69

1

5

13.

12

61

4.95

58

74.9

329

0.79

929

0.28

2754

1.47

068

0.85

091

0.7

01

15

1

6

47.

26

56

2.54

20

28.4

651

2.87

816

0.14

5036

0.55

867

1.19

396

0.7

69

9

1

7

18.

33

12

2.56

98

18.0

724

1.11

625

0.14

6621

0.35

470

0.53

919

2.6

82

56

1

8

14.

70

33

10.0

01

25.1

976

0.89

534

0.57

0643

0.49

454

0.65

351

1.8

47

47

1

9

11.

46

77

4.92

73

58.5

082

0.69

830

0.28

1124

1.14

832

0.70

925

1.4

91

99

2

0

13.

13

55

42.5

51

23.6

248

0.79

986

2.42

775

0.46

367

1.23

043

0.9

00

5

2

1

3.4

67

04

9.35

2

52.1

240

0.21

112

0.53

3572

1.02

302

0.58

923

2.2

97

08

2

2

28.

48

89

4.65

88

13.5

578

1.73

478

0.26

5805

0.26

609

0.75

556

1.2

17

29

2

3

15.

08

85

2.48

70

19.8

142

0.91

879

0.14

1897

0.38

888

0.48

319

3.1

58

79

2

4

5.7

98

46

89.5

05

27.7

410

0.35

308

5.10

6675

0.54

446

2.00

141

3.0

13

3

2

5

26.

28

92

3.56

26

39.8

631

1.60

084

0.20

3266

0.78

238

0.86

216

0.6

44

10

2

6

6.2

80

53

143.

08

30.3

476

0.38

244

8.16

3486

0.59

562

3.04

718

4.8

38

9

2

7

7.5

72

40

88.1

65

13.0

308

0.46

111

5.03

0243

0.25

1.91

570

2.8

23

2

25

49

1

8

16.

27

39

5.12

32

57.0

822

0.99

097

0.29

2305

1.12

033

0.80

120

0.9

62

55

9

14.

70

33

3.94

92

27.2

285

0.89

534

0.22

532

0.53

440

0.55

169

2.5

83

04

1

0

6.8

64

1.77

35

51.4

985

0.41

799

0.10

118

1.01

074

0.50

997

2.9

24

49

1

1

32.

94

41

4.92

73

25.1

108

2.00

608

0.28

1124

0.49

284

0.92

668

0.3

30

68

1

2

7.6

77

88

4.39

87

36.7

576

0.46

753

0.25

096

0.72

143

0.47

997

3.1

87

79

1

3

22.

13

23

2.50

04

59.8

831

1.34

771

0.14

2661

1.17

530

0.88

856

0.5

13

12

1

4

17.

10

98

3.18

42

43.7

562

1.04

187

0.18

1674

0.85

879

0.69

411

1.5

85

69

1

5

13.

12

61

4.95

58

74.9

329

0.79

929

0.28

2754

1.47

068

0.85

091

0.7

01

15

1

6

47.

26

56

2.54

20

28.4

651

2.87

816

0.14

5036

0.55

867

1.19

396

0.7

69

9

1

7

18.

33

12

2.56

98

18.0

724

1.11

625

0.14

6621

0.35

470

0.53

919

2.6

82

56

1

8

14.

70

33

10.0

01

25.1

976

0.89

534

0.57

0643

0.49

454

0.65

351

1.8

47

47

1

9

11.

46

77

4.92

73

58.5

082

0.69

830

0.28

1124

1.14

832

0.70

925

1.4

91

99

2

0

13.

13

55

42.5

51

23.6

248

0.79

986

2.42

775

0.46

367

1.23

043

0.9

00

5

2

1

3.4

67

04

9.35

2

52.1

240

0.21

112

0.53

3572

1.02

302

0.58

923

2.2

97

08

2

2

28.

48

89

4.65

88

13.5

578

1.73

478

0.26

5805

0.26

609

0.75

556

1.2

17

29

2

3

15.

08

85

2.48

70

19.8

142

0.91

879

0.14

1897

0.38

888

0.48

319

3.1

58

79

2

4

5.7

98

46

89.5

05

27.7

410

0.35

308

5.10

6675

0.54

446

2.00

141

3.0

13

3

2

5

26.

28

92

3.56

26

39.8

631

1.60

084

0.20

3266

0.78

238

0.86

216

0.6

44

10

2

6

6.2

80

53

143.

08

30.3

476

0.38

244

8.16

3486

0.59

562

3.04

718

4.8

38

9

2

7

7.5

72

40

88.1

65

13.0

308

0.46

111

5.03

0243

0.25

575

1.91

570

2.8

23

2

Figure 3.7: variation of MRSN

Table 3.8: Level average of MRSN

Level

Speed (S)

Feed (F)

Depth of Cut (D)

1

0.309898

0.944874

0.743962

2

1.444788

0.53144

0.16275

3

-0.30744

-0.02906

0.540537

Delta (max- min)

1.752228

0.973934

0.581212

Rank

1

2

3

Level average for MRSN

2

1

0

-1 S1 S2 S3 F1 F2 F3 D1 D2 D3

Figure 3.8: variation of MRSN of input parameters Table 3.9: ANOVA for multi-response S/N ratio:

Fa

SS

DOF

MS

PC

S

3.4258

2

1.7129

3.41181

F

15.4770

2

7.7385

15.4138

D

7.2379

2

3.61895

7.20834

S*F

16.2841

4

4.07102

16.2176

S*D

3.8167

4

0.954175

3.8011

F*D

12.9914

4

3.24785

12.9383

S*F*D

41.1786

8

5.147325

41.0018

Error

———–

——–

————

———–

Total

100.4115

26

————

100

MRSN

50

40

30

20

10

0

S F D S*F S*D F*D S*F*D

Figure 3.9: contribution of parameters

It is observed from above (L27-MRSN) analysis that S2-F1- D1 is the optimal combination for getting best output results and corresponding multi-response signal-to-noise ratio is 0.924494. The PC of speed is 3.41 %, of feed is

    1. %, and of depth of cut is 7.20 %. Similarly, the PC of speed and feed is 16.21%, of speed and depth of cut is 3.80%, of feed and depth of cut is 12.93% and the combination of speed, feed, and depth of cut is 41.00%. It indicates that, for the above ranges of input levels, the feed is most (single) effective parameters and as a combination S-F-D is most effective.

      Table 3.10: compression of different optimise results

      Optimization method

      Performance characteristics

      Optimized setting

      SN ratio

      GRA(m)

      GRG(m)

      S3F1D1

      0.547442

      WSN(m)

      WSN ratio

      S2F1D3

      0.619715

      MRSN(m)

      MRSN ratio

      S2F1D1

      0.924494

      From the above table, it is observed that for single response, combination S1-F1-D1 is the best for getting best surface finish. Also it is observed that combinations of input parameters for multi response optimization are different when the different techniques used. Since the SN ratio is highest in MRSN technique, so S2-F1-D1 combination can be chosen for getting best multi response output.

      IV. CONCLUSIONS

      In present work, turning operation has been optimised and PC of parameters calculated with different optimisation techniques. On the basis of results, the following conclusions can be drawn.

      1. In the multi response optimization, feed is effective (single) parameter, which is evaluated by all the three techniques (GRA, WSN, and MRSN).

      2. For multi response, optimal parametric settings for GRA, WSN, and MRSN, are S3-F1-D1, S2-F1-D3, and S2-F2-D1 respectively. Hence, there has been considerable difference among the optimal settings yielded by the methods investigated.

      3. On the basis of computations performed, MRSN method yielded highest magnitude of S/N response

(0.924494dB) and therefore, its outcomes S2-F2-D1 can be recommended for getting best output results.

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