Central Composite Design in Optimization of the
Factors of Automatic Flux Cored Arc Welding for Steel
ST37
Narongchai Sathavornvichit1, Putipong Bookkamana2,
Bandhita Plubin 3
1
School of Mathematics and Statistics
Faculty of Science and Technology
Rajamangala University of Technology Lanna Tak, Thailand
jammies_un@yahoo.co.th
2
Department of Statistics, Chiangmai University, Thailand
scipbkkm@chiangmai.ac.th
3
Department of Statistics, Chiangmai University, Thailand
b_plubin@yahoo.com
Abstract. The purpose of this research is to determine the optimal
factors of Flux Cored Arc Welding process for Steel ST37. The
process variables current, voltage, stick out and angle of welding
are use in the study of optimization of tensile of weldment by
response surface methodology follow a central composite design.
The result indicated that the optimum conditions are 300 ampere of
current, 30 volt of voltage, 45 millimeter of stick out and 60 degree
of angle.
Keywords: Central Composite Designs, Response Surface
Methodology, Steel Flux Cored Arc Welding.
1. Introduction
The Flux – Cored Arc Welding, (FCAW) is the process of arc
welding between electrode and specimen. The electrode will be in line to
crucible continuity or added with the covering external gas.
The Flux-Cored welding was heated from arc of electrode and
specimen, the surface of the specimen and the edge of electrode will send
through arc to the specimen which causes the marking. The melting of flux
will turn to be the gas, which flux also be the deoxidizer that causes the more
purified marking. The electrode will send out from wire reel automatically.
[1]
2. Material and Method
2.1 Material
Flux- core electrode E70T-4, brand name Lincoln and specimen: steel
ST37 with size 100x125x10 mm are used in the experiment.
1
2
2.2 Method
The specimens were taken to run the experiments by initiate the value
of the factors (current, voltage, stick out and angle) vary by the design. The
welded specimens will cut into the standardized size (ASME Section IX) and
gouge out the marking with 5 mm diameter and depth. These specimens
were test the tensile with the machine and recorded the results.
2.3 Experimental design and statistical analysis
A four-factors, three-level Central Composite design was use to
determine the optimal factors of Flux Cored Arc welding process for Steel
ST37. The central composite design (CCD) with a quadratic model was
employed. [2,3] Four independent variables namely current (x1), voltage (x2),
stick out (x3) and angle (x4) was chosen. Each independent variable had 3
levels which were – 1, 0 and +1. A total 31 different combinations (including
seven replicates of centre point each sighed the coded value 0) were chose in
random order according to a CCD configuration for four factors. The coded
values of independent variables were found from equation
X 1  275
25
X  27.5
x2  2
2.5
X  50
x3  3
5
X  60
x4  4
15
x1 
(1)
(2)
(3)
(4)
are given in Table 1.
Coded levels
-1
0
1
Current (Amp)
250
275
300
Voltage (Volt)
25
27.5
30
Stick out (mm)
45
50
55
Angle (degree)
45
60
75
Table 1. Uncoded and coded levels of the independent variables
Independent variables
The study was carried out according to the central composite design and
the experimental points used according to the design are shown in Table 2.
A second-order polynomial equation was used to express the tensile as a
function of independent variables,
y  b0  b1 x1  b2 x 2  b3 x3  b4 x 4  b11 x12  b22 x 22  b33 x32  b44 x 42
(5)
 b12 x1 x 2  b13 x1 x3  b14 x1 x 4  b23 x 2 x3  b24 x 2 x 4  b34 x3 x 4 ,
3
where y represent tensile of weldment ( unit: kgf)
The coefficients of the response surface equation were determined by
using Minitab software (Minitab Inc., Minitab release 12.1, 1998).
Exp.No.*
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
current
voltage
stick out
angle
tensile(kgf)
x1
x2
x3
x4
y
-1
+1
-1
+1
-1
+1
-1
+1
-1
+1
-1
+1
-1
+1
-1
+1
-1
+1
0
0
0
0
0
0
0
0
0
0
0
0
0
-1
-1
+1
+1
-1
-1
+1
+1
-1
-1
+1
+1
-1
-1
+1
+1
0
0
-1
+1
0
0
0
0
0
0
0
0
0
0
0
-1
-1
-1
-1
+1
+1
+1
+1
-1
-1
-1
-1
+1
+1
+1
+1
0
0
0
0
-1
+1
0
0
0
0
0
0
0
0
0
-1
-1
-1
-1
-1
-1
-1
-1
+1
+1
+1
+1
+1
+1
+1
+1
0
0
0
0
0
0
-1
+1
0
0
0
0
0
0
0
4730
4990
4240
7320
7130
4920
4110
5020
5560
4910
5330
7490
6820
4030
3690
4210
5830
6210
6230
6530
6370
5510
6390
6110
6550
6650
6750
6610
6340
6600
6780
Table 2. Shows the Central composite design with four independent
variables (code variables) and experimental tensile of weldment
The experiments in Table 2 were performed in random order.
3. Results and discussion
Effects of current, voltage, stick out and angle on tensile of weldment
were investigated by response surface methodology. The levels of
independent parameters (Table 1) were determined based on preliminary
experiments.
The experimental values for tensile of weldment under difference
treatment conditions are presented in Table 2. The regression coefficients for
the second order polynomial equations and results for the linear, quadratic
4
and interaction term are presented in Table 3. The statistical analysis
indicates that the model was adequate, possessing no significant lack of fit
and with very satisfactory of the R 2 (0.985). The closer the value of R 2 to
the unity, the better the empirical model fits the actual data.
The effect of current, voltage, sticks out and angle on tensile of weldment
Variables
Reg. coefficient
S.D.
t-value
P
Constant
6544.2
53.12
123.188
0.000
current
92.2
42.21
2.185
0.044
voltage
-76.7
42.21
-1.816
0.088
stick out
-305.6
42.21
-7.239
0.000
angle
-38.9
42.21
-0.921
0.371
current*current
-445.7
111.16
-4.009
0.001
voltage*voltage
-85.7
111.16
-0.771
0.452
stick out*stick out
-525.7
111.16
-4.729
0.000
angle*angle
-215.7
111.16
-1.940
0.070
current*voltage
753.7
44.77
16.836
0.000
current*stick out
-526.2
44.77
-11.755
0.000
current*angle
-175.0
44.77
-3.909
0.001
voltage*stick out
-628.7
44.77
-14.044
0.000
voltage*angle
30.0
44.77
0.670
0.512
stick out*angle
-277.5
44.77
-6.198
0.000
S = 179.1
R 2 = 98.5%
Table 3. Regression coefficients, p or probability for tensile of weldment
7000
y
6000
5000
250
260
270
current 280290
300
28
29
30
(a)
27
26
25
voltage
5
Contour Plot of y
30
5700
6200
6700
voltage
29
28
27
26
25
250
260
270
280
290
300
current
Hold values: stickout: 50.0 angle: 60.0
(b)
Figure 1. Shows the Response surface (a) and Contour plot (b) for tensile
of weldment as a function of voltage and current (at stick out
50 mm. and angle 60°)
From figure 1, the graph shows 2 highest values of tensile of
weldment. The first is the voltage at 30 volts with current 300A; the second
is the pressure approximately 25 volts with current 260A (when fixed the
stick out at 50 mm. and angle 600).
6500
6000
y 5500
5000
250
260
270
current 280290
300
45
50
stickout
55
(a)
6
Contour Plot of y
55
5500
6000
6500
54
53
stickout
52
51
50
49
48
47
46
45
250
260
270
280
290
300
current
Hold values: voltage: 27.5 angle: 60.0
(b)
Figure 2. Shows the Response surface (a) and Contour plot (b) for tensile
of weldment as a function of stick out and current (at voltage
27.5 volt and angle 60°)
From figure 2, the graph shows the highest value of tensile of
weldment at the stick out 47 mm. and current 285A (when fixed the voltage
at 27.5 volts and angle 600)
6600
y
6100
5600
250
260
270
current 280290
300
45
55
65
75
(a)
angle
7
Contour Plot of y
75
6050
6300
6550
angle
65
55
45
250
260
270
280
290
300
current
Hold values: voltage: 27.5 stickout: 50.0
(b)
Figure 3.Shows the Response surface (a) and Contour plot (b) for tensile
of weldment as a function of angle and current (at voltage
27.5volt and stick out 50 mm.)
From figure 3, the graph shows the highest value of tensile of
weldment at angle 57o and current 280A (when fixed the voltage at 2705
volts and stick out 50 mm.)
The most appropriate value of the factors from the models is 300
ampere of current, 30 volts of voltage, 45 millimeter of stick out, and 60
degree of angle which give the tensile of weldment equal to 7410 kgf.
4. Acknowledgement
I would like to thank Dr.Watchara Thongngok, an instructor of
Department of Industrial Engineering, Faculty of Engineering, Chiang Mai
University, for providing beneficial advice and data courtesy.
5. Copyright
School of Mathematical Science USM, reserves the right to publish
paper at this conference.
6. References
[1] Kennedy, G.A. (1980), Welding Technology, Bobbs-Merrill Education,
Indianapolis.
[2] Box, G.E.P., Hunter, W.G., Hunter, J.S. (1978), Statistics for
experimenters, John Wiley, New York.
[3] Myer, R. and Montgomery, D.C. (2002), Response surface methodology,
John Wiley, New York.