DOI : 10.17577/IJERTV8IS010013
- Open Access
- Total Downloads : 5
- Authors : Dr. Pallavi H. Agarwal, Mr. Ketulkumar R. Patel
- Paper ID : IJERTV8IS010013
- Volume & Issue : Volume 08, Issue 01 (January – 2019)
- Published (First Online): 09-01-2019
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
Optimizing Plasma Arc Cutting Parameters for Structural Steel using Grey Relational Analysis
Dr. Pallavi H. Agarwal
Professor, Department of Mechanical Engineering, Babaria Institute of Technology, Varnama, Vadodara, India -391240
Mr. Ketulkumar R. Patel
Assistant Professor, Department of Mechanical Engineering, Babaria Institute of Technology, Varnama, Vadodara, India -391240
Abstract
This paper represents the experimental investigation on the plasma arc cutting of structural steel (IS 2062 E250 BR). The response parameters considered are material removal rate (MRR), top and bottom kerf widths and bevel angle: while machining variables are current, standoff distance (SOD), pressure and speed. Experiments are performed using response surface methodology (RSM). Further grey relational analysis is used to optimize the parameters. For material removal rate, higher the better output performance characteristic is considered whereas lower the better characteristic is considered for top kerf width, bottom kerf width and bevel angle. Optimization can be used for selecting the values of process variables to get the desired values of response parameters.
Keywords Plasma Arc Cutting, Structural Steel, Process Parameters, MRR, DOE, RSM, Optimization, Grey Relational Analysis (GRA).
-
INTRODUCTION
Structural steel: IS 2062 E250 BR is suitable for welded, bolted and reveted structures and for general engineering purpose. Plasma cutting was developed at the end of the 1950s for cutting high-alloy steels and aluminium. It was designed to be used on all metals which, due to their chemical composition, could not be subjected to oxy-fuel cutting owing to its extremely high cutting speeds especially with thin materials and narrow heat-affected zone. The technique is also used today for cutting non-alloy steels and low-alloy steels. Plasma arc cutting is used for cutting normal structural steel upto about 40 mm in thickness and results in very little distortion, particularly in case of thin work pieces. The high cutting speeds are especially important in the preliminary fabricating process. In comparision with oxyfuel cutting, cutting speeds of 5 to 6 times greater can be achieved by plasma arc cutting [1].
Many researchers have done work on plasma arc cutting of different materials like EN 31 steel, AISI 31 stainless steel, St 37 mild steel, hardox-400, S235 mild steel, EN 10025 low alloy steel and AISI 304 stainless steel [2-11]. But the optimization of parameters using GRA is yet to be done. This paper attempts to perform GRA of plasma arc cutting process for the cutting of structural steel to get the optimum combination of process parameters for desired results.
-
MATERIAL SELECTION
Experiments are conducted on Structural Steel: IS 2062 E250 BR material (density 7.9 g/cm3) which is suitable for welded, bolted and riveted structures and for general
engineering purposes. The work piece size is 100 mm x 50 mm x 5 mm.
Table 1: Chemical composition of IS 2062 E250 BR
Element
C
Mn
S
P
Si
% Contribution
0.22
1.50
0.045
0.045
0.40
Table 2: Mechanical Properties of IS 2062 E250 BR
Tensile Strength (MPa)
Yield Stress (MPa)
%
Elongation
410
< 20 mm
20-40 mm
>40 mm
23
250
240
230
-
DESIGN OF EXPERIMENT: RESPONSE SURFACE METHODOLOGY
Response surface methodology (RSM) Box-Behnken design is selected. The Box-Behnken Design is quadratic and does not contain embedded factorial or fractional factorial design. As a result, Box-Behnken Design has a limited capability of orthogonal blocking, compared to Central Composite Design. The main difference of Box- Behnken Design from Central Composite Design is that Box-Behnken is a three level quadratic design, in which the explored space of factors is represented by [-1,0,+ 1]. The true physical lower and upper limits are corresponding to [-1, 0, +1]. In this design, however, the sample combinations are treated such that they are located at midpoints of edges formed by any two factors [17].
Figure 1: Box Behnken Design [17]
-
EXPERIMENTATION
The experiments are conducted using a Quality CUT 40 Air Plasma Cutting Machine. In this cutting machine manual plasma arc cutting torch as well as trolley mounted automatic plasma arc cutting torch are provided. For
experimentation, trolley based plasma arc cutting torch is used for maintaining stand-off distance and cutting speed during actual cutting.
The levels of factors selected for the final experiment runs by response surface methodology are as shown in Table 3 and 4 and final experiments are conducted and the results are shown in table 5.
Table 3: Levels of Current, SOD and Pressure
Level
Current
SOD
Pressure
A
mm
Bar
-1
30
1.5
4
0
35
2
4.5
1
40
2.5
5
Speed (m/min)
Level
Current 30A
Current 35A
Current 40A
-1
0.24
0.15
0.38
0
0.3
0.3
0.43
1
0.38
0.43
0.5
Speed (m/min)
Level
Current 30A
Current 35A
Current 40A
-1
0.24
0.15
0.38
0
0.3
0.3
0.43
1
0.38
0.43
0.5
Table 4: Levels of Speed for different currents
The three terms that are typical symbols and features for Grey System are:
-
The Grey number in Grey system is a number with incomplete information.
-
The Grey element represents an element with incomplete information.
-
The Grey relation is the relation with incomplete information.
B. Grey relational analysis
The generation of Grey relation for experimental runs is shown in Figure 2. The process is elaborated here.
Let the number of the experimental runs be m, and the number of the response parameters be n. Then a m x n value matrix (called eigen value matrix) is set up.
x1 (1), x1 (2),…..x1 (n)
x2 (1), x2 (2),….x2 (n)
X = ….
….
(1),
Runs
Input Parameters
Response Parameters
Current
SOD
/td>
Pressure
Speed
MRR
TKW
BKW
BA
mm3/min
mm
mm
Degree
1
-1
-1
0
0
1783.90
2.24
1.66
9.13
2
1
-1
0
0
1852.22
2.06
1.65
5.37
3
-1
1
0
0
1257.01
2.32
1.76
6.56
4
1
1
0
0
1854.39
2.20
1.94
4.21
5
0
0
-1
-1
897.10
2.27
2.21
9.22
6
0
0
1
-1
778.91
2.30
2.24
7.75
7
0
0
-1
1
1982.60
2.10
1.42
7.93
8
0
0
1
1
2685.80
2.03
1.47
8.77
9
-1
0
-1
0
1804.81
2.20
1.48
10.92
10
1
0
-1
0
1944.89
2.06
1.82
4.21
11
-1
0
1
0
1241.80
2.17
1.42
11.25
12
1
0
1
0
2364.58
2.03
1.69
5.65
13
0
-1
0
-1
862.87
2.25
2.06
7.57
14
0
1
0
-1
1011.73
2.40
2.36
7.24
15
0
-1
0
1
2553.43
2.06
1.33
7.60
16
0
1
0
1
1973.82
2.07
1.66
4.24
17
-1
0
0
-1
1278.17
2.30
1.92
9.48
18
1
0
0
-1
1833.25
2.34
2.17
4.94
19
-1
0
0
1
2553.60
2.22
1.15
8.48
20
1
0
0
1
3188.66
2.03
1.37
3.66
21
0
-1
-1
0
1419.64
2.06
1.49
6.58
22
0
1
-1
0
1447.53
2.31
2.05
5.83
23
0
-1
1
0
1367.31
2.20
1.78
8.98
24
0
1
1
0
1471.40
2.12
1.65
6.33
25
0
0
0
0
2101.64
2.10
1.62
7.16
26
0
0
0
0
1789.94
2.05
1.59
8.46
27
0
0
0
0
1700.17
2.06
1.57
6.76
Runs
Input Parameters
Response Parameters
Current
SOD
Pressure
Speed
MRR
TKW
BKW
BA
mm3/min
mm
mm
Degree
1
-1
-1
0
0
1783.90
2.24
1.66
9.13
2
1
-1
0
0
1852.22
2.06
1.65
5.37
3
-1
1
0
0
1257.01
2.32
1.76
6.56
4
1
1
0
0
1854.39
2.20
1.94
4.21
5
0
0
-1
-1
897.10
2.27
2.21
9.22
6
0
0
1
-1
778.91
2.30
2.24
7.75
7
0
0
-1
1
1982.60
2.10
1.42
7.93
8
0
0
1
1
2685.80
2.03
1.47
8.77
9
-1
0
-1
0
1804.81
2.20
1.48
10.92
10
1
0
-1
0
1944.89
2.06
1.82
4.21
11
-1
0
1
0
1241.80
2.17
1.42
11.25
12
1
0
1
0
2364.58
2.03
1.69
5.65
13
0
-1
0
-1
862.87
2.25
2.06
7.57
14
0
1
0
-1
1011.73
2.40
2.36
7.24
15
0
-1
0
1
2553.43
2.06
1.33
7.60
16
0
1
0
1
1973.82
2.07
1.66
4.24
17
-1
0
0
-1
1278.17
2.30
1.92
9.48
18
1
0
0
-1
1833.25
2.34
2.17
4.94
19
-1
0
0
1
2553.60
2.22
1.15
8.48
20
1
0
0
1
3188.66
2.03
1.37
3.66
21
0
-1
-1
0
1419.64
2.06
1.49
6.58
22
0
1
-1
0
1447.53
2.31
2.05
5.83
23
0
-1
1
0
1367.31
2.20
1.78
8.98
24
0
1
1
0
1471.40
2.12
1.65
6.33
25
0
0
0
0
2101.64
2.10
1.62
7.16
26
0
0
0
0
1789.94
2.05
1.59
8.46
27
0
0
0
0
1700.17
2.06
1.57
6.76
Table 5: Experimental runs
xm
(1), xm
(2),….xm
(n)
Where,
xi (k)
is the value of the number i experiment
run and the number k response factors.
Usually, three kinds of influence factors are included, they are:
-
Benefit type factor (the bigger the better),
-
Defect type (the smaller the better)
-
Setting up eigenvalue matrix, input original data
-
Standardized data transformation, formulas:
-
the bigger the better (2),
-
the smaller the better (3), or
-
nominal-the best (4)
-
-
Calculation of Grey relational degree:
-
getting absolute difference of compared series and referential series using formula (5)
-
find out minimum and maximum
-
choose the constant p (set to 0.5)
-
calculation of relational coeficient and relational degree
4. Set up the ranking of software projects based on influence factors
-
Setting up eigenvalue matrix, input original data
-
Standardized data transformation, formulas:
-
the bigger the better (2),
-
the smaller the better (3), or
-
nominal-the best (4)
-
-
Calculation of Grey relational degree:
-
getting absolute difference of compared series and referential series using formula (5)
-
find out minimum and maximum
-
choose the constant p (set to 0.5)
-
calculation of relational coeficient and relational degree
4. Set up the ranking of software projects based on influence factors
-
-
Medium type, or nominal-the-best (the nearer to a certain standard value the better).
-
-
GREY RELATIONAL ANAYSIS
A. Grey theory steps
The information that is either incomplete or undetermined is called Grey. The Grey system provides multidisciplinary approaches for analysis and abstract modeling of systems for which the information is limited, incomplete and characterized by random uncertainty [14].
Figure 2: The generation of Grey relation degree
It is difficult to compare between the different kinds of factors because they exert a different influence. Therefore, the standardized transformation of these factors must be done. Three formulas can be used for this purpose.
xi (k)
xi (k) min xi (k) max x (k) min x (k)
(2)
C. Grey Relational Optimization for Plasma Arc Cutting process
i i Based on the theory and procedure of grey analysis
discussed above the grey relational analysis for plasma arc
The first standardized formula is suitable for the benefit type factor.
cutting of Structural Steel (IS 2062 E250 Br) is carried out. The result of data Grey Relational generating is shown in table 6.
xi (k)
max xi (k) xi (k) max x (k) min x (k)
(3)
The determination of grey relational co-efficient is carried out for each quality parameters considering value of
i i distinguishing coefficient as 0.5. The Grey Relational grade
is calculated and rank is given as shown in table 7.
The second standardized formula is suitable for defect type factor.
Plasma arc cutting is used as a primary cutting process to obtain rough dimension size for components. The component edges should not be very highly taper giving
i
i
x (k )
xi (k ) x0 (k )
larger requirement of post processing. The MRR should be
max xi (k ) x0
(k )
(4)
relatively high for primary cutting process. At the same time the kerf width should be as small as possible to reduce metal loss. To apply grey analysis similar weight is given to MRR,
The third standardized formula is suitable for the medium
type factor.
The grey relation degree can be calculated by steps as follows:
Ex. No.
MRR
TKW
BKW
BA
Ideal
1.0000
1.0000
1.0000
1.0000
1
0.4171
0.4324
0.5785
0.2793
2
0.4454
0.9189
0.5868
0.7747
3
0.1984
0.2162
0.4959
0.6179
4
0.4463
0.5405
0.3471
0.9275
5
0.0490
0.3514
0.1240
0.2675
6
0.0000
0.2703
0.0992
0.4611
7
0.4995
0.8108
0.7769
0.4374
8
0.7913
1.0000
0.7355
0.3267
9
0.4257
0.5405
0.7273
0.0435
10
0.4839
0.9189
0.4463
0.9275
11
0.1921
0.6216
0.7769
0.0000
12
0.6580
1.0000
0.5537
0.7378
13
0.0348
0.4054
0.2479
0.4848
14
0.0966
0.0000
0.0000
0.5283
15
0.7364
09189
0.8512
0.4809
16
0.4959
0.8919
0.5785
0.9236
17
0.2072
0.2703
0.3636
0.2332
18
0.4375
0.1622
0.1570
0.8314
19
0.7365
0.4865
1.0000
0.3650
20
1.0000
1.0000
0.8182
1.0000
21
0.2659
0.9189
0.7190
0.6153
22
0.2775
0.2432
0.2562
0.7141
23
0.2442
0.5405
0.4793
0.2991
24
0.2874
0.7568
0.5868
0.6482
25
0.5489
0.8108
0.6116
0.5389
26
0.4196
0.9459
0.6364
0.3676
27
0.3823
0.9189
0.6529
0.5916
Ex. No.
MRR
TKW
BKW
BA
Ideal
1.0000
1.0000
1.0000
1.0000
1
0.4171
0.4324
0.5785
0.2793
2
0.4454
0.9189
0.5868
0.7747
3
0.1984
0.2162
0.4959
0.6179
4
0.4463
0.5405
0.3471
0.9275
5
0.0490
0.3514
0.1240
0.2675
6
0.0000
0.2703
0.0992
0.4611
7
0.4995
0.8108
0.7769
0.4374
8
0.7913
1.0000
0.7355
0.3267
9
0.4257
0.5405
0.7273
0.0435
10
0.4839
0.9189
0.4463
0.9275
11
0.1921
0.6216
0.7769
0.0000
12
0.6580
1.0000
0.5537
0.7378
13
0.0348
0.4054
0.2479
0.4848
14
0.0966
0.0000
0.0000
0.5283
15
0.7364
0.9189
0.8512
0.4809
16
0.4959
0.8919
0.5785
0.9236
17
0.2072
0.2703
0.3636
0.2332
18
0.4375
0.1622
0.1570
0.8314
19
0.7365
0.4865
1.0000
0.3650
20
1.0000
1.0000
0.8182
1.0000
21
0.2659
0.9189
0.7190
0.6153
22
0.2775
0.2432
0.2562
0.7141
23
0.2442
0.5405
0.4793
0.2991
24
0.2874
0.7568
0.5868
0.6482
25
0.5489
0.8108
0.6116
0.5389
26
0.4196
0.9459
0.6364
0.3676
27
0.3823
0.9189
0.6529
0.5916
-
The absolute difference of the compared series and the referential series should be obtained by using the following formula:
reduction of kerf width and obtaining straight parallel cut edges. This work is mainly concerned with studying the effect of process parameters on MRR of Structural Steel using Plasma Arc Cutting. MRR is given more weight of 70%. Top kerf width, bottom kerf width and bevel angle is given the weight of 10% each. These weights are used to calculate grey relational grade and its order in optimization process as shown in Table 8.
x (k) x (k) x (k)
(5)
Table 6: Grey Relational Generating
i 0 i
and the maximum and the minimum difference should be found.
-
The distinguishing coefficient p is between 0 and 1. Generally, the distinguishing coefficient p is set to 0.5.
-
Calculation of the relational coefficient and relational degree by (6) as follows.
In Grey relational analysis, Grey relational coefficient
can be expressed as follows:
min p max
i
i
i (k) x (k) p max
and then the relational degree follows as:
ri w(k) (k)
(6)
(7)
In equation (7), is the Grey relational coefficient, w (k) is the proportion of the number k influence factor to the total influence indicators. The sum of w (k) is 100%. The result obtained when using (6) can be applied to measure the
effectiveness of the experimental run.
Ex. No.
MRR
TKW
BKW
BA
Grade
Rank
Weight
0.7000
0.1000
0.1000
0.1000
1
0.4617
0.4684
0.5426
0.4096
0.4652
18
2
0.4741
0.8605
0.5475
0.6894
0.5416
9
3
0.3841
0.3895
0.4979
0.5668
0.4143
22
4
0.4745
0.5211
0.4337
0.8734
0.5150
12
5
0.3446
0.4353
0.3634
0.4057
0.3617
26
6
0.3333
0.4066
0.3569
0.4813
0.3578
27
7
0.4998
0.7255
0.6914
0.4706
0.5386
10
8
0.7055
1.0000
0.6541
0.4262
0.7019
2
9
0.4654
0.5211
0.6471
0.3433
0.4769
16
10
0.4921
0.8605
0.4745
0.8734
0.5653
7
11
0.3823
0.5692
0.6914
0.3333
0.4270
20
12
0.5938
1.0000
0.5284
0.6560
0.6341
5
13
0.3413
0.4568
0.3993
0.4925
0.3737
24
14
0.3563
0.3333
0.3333
0.5146
0.3675
25
15
0.6548
0.8605
0.7707
0.4906
0.6705
3
16
0.4979
0.8222
0.5426
0.8674
0.5718
6
17
0.3868
0.4066
0.4400
0.3947
0.3949
23
18
0.4706
0.3737
0.3723
0.7478
0.4788
15
19
0.6548
0.4933
1.0000
0.4405
0.6518
4
20
1.0000
1.0000
0.7333
1.0000
0.9733
1
21
0.4052
0.8605
0.6402
0.5652
0.4902
14
22
0.4090
0.3978
0.4020
0.6362
0.4299
19
23
0.3981
0.5211
0.4899
0.4163
0.4214
21
24
0.4123
0.6727
0.5475
0.5870
0.4694
17
25
0.5257
0.7255
0.5628
0.5202
0.5488
8
26
0.4628
0.9024
0.5789
0.4415
0.5162
11
27
0.4473
0.8605
0.5902
0.5504
0.5133
13
Ex. No.
MRR
TKW
BKW
BA
Grade
Rank
Weight
0.7000
0.1000
0.1000
0.1000
1
0.4617
0.4684
0.5426
0.4096
0.4652
18
2
0.4741
0.8605
0.5475
0.6894
0.5416
9
3
0.3841
0.3895
0.4979
0.5668
0.4143
22
4
0.4745
0.5211
0.4337
0.8734
0.5150
12
5
0.3446
0.4353
0.3634
0.4057
0.3617
26
6
0.3333
0.4066
0.3569
0.4813
0.3578
27
7
0.4998
0.7255
0.6914
0.4706
0.5386
10
8
0.7055
1.0000
0.6541
0.4262
0.7019
2
9
0.4654
0.5211
0.6471
0.3433
0.4769
16
10
0.4921
0.8605
0.4745
0.8734
0.5653
7
11
0.3823
0.5692
0.6914
0.3333
0.4270
20
12
0.5938
1.0000
0.5284
0.6560
0.6341
5
13
0.3413
0.4568
0.3993
0.4925
0.3737
24
14
0.3563
0.3333
0.3333
0.5146
0.3675
25
15
0.6548
0.8605
0.7707
0.4906
0.6705
3
16
0.4979
0.8222
0.5426
0.8674
0.5718
6
17
0.3868
0.4066
0.4400
0.3947
0.3949
23
18
0.4706
0.3737
0.3723
0.7478
0.4788
15
19
0.6548
0.4933
1.0000
0.4405
0.6518
4
20
1.0000
1.0000
0.7333
1.0000
0.9733
1
21
0.4052
0.8605
0.6402
0.5652
0.4902
14
22
0.4090
0.3978
0.4020
0.6362
0.4299
19
23
0.3981
0.5211
0.4899
0.4163
0.4214
21
24
0.4123
0.6727
0.5475
0.5870
0.4694
17
25
0.5257
0.7255
0.5628
0.5202
0.5488
8
26
0.4628
0.9024
0.5789
0.4415
0.5162
11
27
0.4473
0.8605
0.5902
0.5504
0.5133
13
Table 7: Gray relational coefficients of the individual quality characteristics, Grey Relational Grade and its Order
-
-
CONCLUSION
The effect of selected input parameters on the output responses like MRR, top kerf width, bottom kerf width and bevel angle are studied by experimentation performed using Response Surface Methodology.
Grey relational analysis helps to grade the experimental levels for each of the individual variables and to find the most suitable levels for weighted combination of response variables. Here, for the selected weighted combination of responses, higher levels of speed and current; and medium levels of stand-off distance and pressure are observed to be the optimum levels.
After calculating grey relational grade and its order in optimization process the effect of each level of each parameter is calculated and the results are listed in Table 8 and shown in Figure 3.
Table 8: Response table for grey relational grade
|
Factor |
Grey Relational Grade |
Max-Min |
||
|
Level 1 |
Level 2 |
Level 3 |
||
|
Current |
0.4717 |
0.4888 |
0.6180 |
0.1463 |
|
SOD |
0.4938 |
0.5427 |
0.4613 |
0.0814 |
|
Pressure |
0.4771 |
0.5331 |
0.5019 |
0.0560 |
|
Speed |
0.3891 |
0.4952 |
0.6846 |
0.2955 |
Figure 3: Effect of plasma arc cutting process parameters on multi- performance characteristics
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