A Method to Optimize Process Parameters of Turning

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

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

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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