Independent parameters with their levels for CCD.
Abstract
Analysis of bead geometry is very important in product design and manufacturing. Defect-free products with reliability are the demanding parameter in the manufacturing Industry. In this study, we have analyzed and optimized bead geometry parameters such as height of reinforcement (HOR), depth of Heat Affected Zone (DOH), and width of Heat Affected Zone (WOH) by using Central Composite Design (CCD) of response surface methodology (RSM). In this study, peak current and pulse frequency are the most important process parameters for HOR and the optimum combination obtained are (160 A, 80 A, 100 Hz, and 45%) further HOR at this optimum was found to be 1.41 mm, which is close to 1.45 mm. Similarly, peak current and pulse frequency are the most important process parameter for WOH and the optimum combination obtained are (160 A, 80 A, 150 Hz, and 45%) further WOH at this optimum was found to be 1.32 mm, which is close to 1.37 mm. Again, similarly peak current and pulse frequency are the most important process parameter for DOH and the optimum combination obtained are (160 A, 80 A, 100 Hz, and 45%) further DOH at this optimum was found to be 1.26 mm which is close to 1.58 mm.
Keywords
- bead geometry
- height of reinforcement
- depth of Haz
- response surface methodology
1. Introduction
The traditional method of selecting one parameter is time taking process and therefore not considered nowadays in the manufacturing industry, hence an optimization technique concerning the design of experiment (DOE) such as CCD of response surface methodology (RSM) to establish an optimum condition for tensile strength. In this study, the surface plot is used to explain the main and interaction effect of the process parameter to identify the optimum parameter with their values. RSM is a widely used statistical technique in process optimization [1]. RSM is a set of mathematical and statistical methodologies for assessing problems in which multiple independent factors influence a dependent variable or response, to optimize the answer. RSM facilitates the examination of the interaction between experiment variables within the range under consideration, allowing for a better knowledge of the process while lowering experiment time and cost [2, 3].
2. Steps of Response Surface Methodology
Major steps of RSM are shown in Figure 1.
2.1 Input parameters and their operating range
Based on a review of the literature and previous research, the most important process parameters that have a greater influence on bead geometry and mechanical properties have been identified. The butt joint was made from AISI 316 stainless steel sheets with dimensions of 100 × 75 × 4 mm by used pulsed TIG welding [4]. This experiment's input parameters are peak current, base current, pulse frequency, and pulse on time [2]. Input parameters with their levels are given in Table 1. The experiment was carried out at an optimum in the laboratory.
Input parameter | Factor symbol | Level 1 | Level 2 | Level 3 | Level 4 | Level 5 |
---|---|---|---|---|---|---|
− | −γ | γ | ||||
Peak current ( | A | 140 | 150 | 160 | 170 | 180 |
Base current ( | B | 60 | 70 | 80 | 90 | 100 |
Pulse frequency (Hz) | C | 50 | 75 | 100 | 125 | 150 |
Pulse on time (%) | D | 35 | 40 | 45 | 50 | 55 |
2.2 Design of experiment
The experimental design for this investigation is CCD and the response is measured by RSM. Examine the combined effect of four different input parameters on bead geometry and mechanical properties to optimize the process parameter of pulse TIG welding and drive a mathematical model. Five levels, four-parameter CCD which include 24 = 16 factorial points plus 6 central points and 2 × 4-star points (24 + 2*4 + 6) [2, 5], with a total of 30 experiments were made in this investigation as shown in Table 2. The framework for the four factors ranged between five levels, −
Std | Factor symbol | Actual factor | ||||||
---|---|---|---|---|---|---|---|---|
A | B | C | D | A | B | C | D | |
1 | 150 | 70 | 75 | 40 | ||||
2 | 170 | 70 | 75 | 40 | ||||
3 | 150 | 90 | 75 | 40 | ||||
4 | 170 | 90 | 75 | 40 | ||||
5 | 150 | 70 | 125 | 40 | ||||
6 | 170 | 70 | 125 | 40 | ||||
7 | 150 | 90 | 125 | 40 | ||||
8 | 170 | 90 | 125 | 40 | ||||
9 | 150 | 70 | 75 | 50 | ||||
10 | 170 | 70 | 75 | 50 | ||||
11 | 150 | 90 | 75 | 50 | ||||
12 | 170 | 90 | 75 | 50 | ||||
13 | 150 | 70 | 125 | 50 | ||||
14 | 170 | 70 | 125 | 50 | ||||
15 | 150 | 90 | 125 | 50 | ||||
16 | 170 | 90 | 125 | 50 | ||||
17 | 140 | 80 | 100 | 45 | ||||
18 | 180 | 80 | 100 | 45 | ||||
19 | 160 | 60 | 100 | 45 | ||||
20 | 160 | 100 | 100 | 45 | ||||
21 | 160 | 80 | 50 | 45 | ||||
22 | 160 | 80 | 150 | 45 | ||||
23 | 160 | 80 | 100 | 35 | ||||
24 | 160 | 80 | 100 | 55 | ||||
25 | 160 | 80 | 100 | 45 | ||||
26 | 160 | 80 | 100 | 45 | ||||
27 | 160 | 80 | 100 | 45 | ||||
28 | 160 | 80 | 100 | 45 | ||||
29 | 160 | 80 | 100 | 45 | ||||
30 | 160 | 80 | 100 | 45 |
3. RSM statistical analysis for reinforcement height
By varying the input process parameter, CCD was used to experiment. The experiment was carried out by varying the input parameters with the experimental design CCD. The experiment was carried out using various parameter combinations, as shown in Table 3. The CCD experiment results were fitted to the polynomial regression equation created by Design Expert Software 18.0 [2, 6].
3.1 Development and evaluation of regression equation HOR
The correlation between process parameters and output response was obtained by using CCD The second-order polynomial regression equation fitted between the output response and the input process parameter. From the ANOVA result shown in Table 4, it has been found adequacy of the model is suitable to analyze the experimental value [2, 6].
Std | Factor symbol | Actual factor | Exp. value Bead width | ||||||
---|---|---|---|---|---|---|---|---|---|
A | B | C | D | A | B | C | D | ||
1 | 150 | 70 | 75 | 40 | 0.85 | ||||
2 | 170 | 70 | 75 | 40 | 0.68 | ||||
3 | 150 | 90 | 75 | 40 | 0.57 | ||||
4 | 170 | 90 | 75 | 40 | 0.93 | ||||
5 | 150 | 70 | 125 | 40 | 0.74 | ||||
6 | 170 | 70 | 125 | 40 | 0.64 | ||||
7 | 150 | 90 | 125 | 40 | 1.01 | ||||
8 | 170 | 90 | 125 | 40 | 0.76 | ||||
9 | 150 | 70 | 75 | 50 | 0.67 | ||||
10 | 170 | 70 | 75 | 50 | 1.05 | ||||
11 | 150 | 90 | 75 | 50 | 0.75 | ||||
12 | 170 | 90 | 75 | 50 | 0.63 | ||||
13 | 150 | 70 | 125 | 50 | 1.08 | ||||
14 | 170 | 70 | 125 | 50 | 0.80 | ||||
15 | 150 | 90 | 125 | 50 | 0.71 | ||||
16 | 170 | 90 | 125 | 50 | 1.14 | ||||
17 | 140 | 80 | 100 | 45 | 0.88 | ||||
18 | 180 | 80 | 100 | 45 | 0.78 | ||||
19 | 160 | 60 | 100 | 45 | 1.14 | ||||
20 | 160 | 100 | 100 | 45 | 0.81 | ||||
21 | 160 | 80 | 50 | 45 | 0.67 | ||||
22 | 160 | 80 | 150 | 45 | 1.17 | ||||
23 | 160 | 80 | 100 | 35 | 0.87 | ||||
24 | 160 | 80 | 100 | 55 | 0.71 | ||||
25 | 160 | 80 | 100 | 45 | 1.31 | ||||
26 | 160 | 80 | 100 | 45 | 0.92 | ||||
27 | 160 | 80 | 100 | 45 | 0.76 | ||||
28 | 160 | 80 | 100 | 45 | 1.07 | ||||
29 | 160 | 80 | 100 | 45 | 1.18 | ||||
30 | 160 | 80 | 100 | 45 | 1.45 |
Source | Coefficient | Sum of squares | df | Mean square | |||
---|---|---|---|---|---|---|---|
Model | 1.11 | 0.7246 | 14 | 0.7246 | 1.10 | 0.0425 | Significant |
A | 0.0024 | 0.0003 | 1 | 0.0003 | 3.003 | 0.047 | |
B | −0.0275 | 0.0181 | 1 | 0.0181 | 0.087 | 0.5331 | |
C | 0.0691 | 0.1307 | 1 | 0.1307 | 2.79 | 0.0115 | |
D | 0.0144 | 0.0044 | 1 | 0.0044 | 0.1028 | 0.7456 | |
A × B | 0.0375 | 0.0235 | 1 | 0.0235 | 0.4609 | 0.0498 | |
A × C | −0.0406 | 0.0276 | 1 | 0.0276 | 0.5849 | 0.4643 | |
A × D | 0.0356 | 0.0208 | 1 | 0.0208 | 0.4268 | 0.5107 | |
B × C | 0.0444 | 0.0328 | 1 | 0.0328 | 0.5729 | 0.4359 | |
B × D | −0.0456 | 0.0356 | 1 | 0.0356 | 0.7023 | 0.4123 | |
C × D | 0.0325 | 0.0168 | 1 | 0.0168 | 0.3508 | 0.5670 | |
A2 | −0.0824 | 0.1862 | 1 | 0.1862 | 3.98 | 0.0447 | |
B2 | −0.0461 | 0.0584 | 1 | 0.0584 | 1.25 | 0.2817 | |
C2 | −0.0599 | 0.0984 | 1 | 0.0984 | 2.10 | 0.1678 | |
D2 | −0.0918 | 0.2310 | 1 | 0.2310 | 4.93 | 0.0422 | |
Residual | 0.7025 | 15 | 0.0468 | ||||
Lack of fit | 0.3837 | 10 | 0.0384 | 0.6017 | 0.7691 | Not significant | |
Pure error | 0.3188 | 5 | 0.0638 | ||||
Cor total | 1.11 | 0.7230 | 14 | 0.0516 | 1.10 | 0.0425 | Significant |
The regression equation based on the regression coefficient of ANOVA results is shown in Eq. (1).
To obtain a statistically significant regression model
Std | Factor sign | Estimated value | Remaining error | |||
---|---|---|---|---|---|---|
A | B | C | D | |||
1 | 0.849 | 0.012 | ||||
2 | 0.789 | −0.098 | ||||
3 | 0.722 | −0.136 | ||||
4 | 0.812 | 0.134 | ||||
5 | 0.924 | −0.168 | ||||
6 | 0.702 | −0.046 | ||||
7 | 0.974 | 0.047 | ||||
8 | 0.902 | −0.126 | ||||
9 | 0.832 | −0.151 | ||||
10 | 0.915 | 0.146 | ||||
11 | 0.522 | 0.239 | ||||
12 | 0.755 | −0.109 | ||||
13 | 1.037 | 0.059 | ||||
14 | 0.957 | −0.141 | ||||
15 | 0.905 | −0.179 | ||||
16 | 0.975 | 0.181 | ||||
17 | 0.794 | 0.097 | ||||
18 | 0.804 | −0.013 | ||||
19 | 0.999 | 0.152 | ||||
20 | 0.889 | −0.068 | ||||
21 | 0.741 | −0.060 | ||||
22 | 1.036 | 0.145 | ||||
23 | 0.733 | 0.148 | ||||
24 | 0.790 | −0.064 | ||||
25 | 1.129 | 0.193 | ||||
26 | 1.129 | −0.193 | ||||
27 | 1.129 | −0.358 | ||||
28 | 1.129 | −0.043 | ||||
29 | 1.129 | 0.068 | ||||
30 | 1.129 | 0.333 |
3.2 Adequacy check of the mathematical model for height of reinforcement
ANOVA represents that the polynomial regression equation was significant to represent the relationship between input parameters and output parameters. The adequacy and significance of the established model were also elaborated by the high value of the coefficient of determination (
Figure 2 demonstrates that the regression model generated with Design Expert 18.0 has a good correlation between the experimental and predicted values since all of the points are very close to the line of perfect fit or line of unit slope. Furthermore, residuals were investigated to validate the model’s adequacy. The difference between the observed and predicted responses is referred to as the residual. This analysis was examined using the normal probability plot of residuals [2, 5]. The normal probability plot of the residuals shows that the errors are distributed normally in a straight line and are insignificant as shown in Figure 3.
3.3 Perturbation plot: height of reinforcement
The perturbation plot shows the effect of all the parameters on a single plot A perturbation plot to compare the effect of all the process parameters at the center point on bead width is presented in Figure 4. It has been noted that HOR peak current (A) is increasing and then HOR decreases [1, 6].
The plot also shows that the HOR decreases as the base current (B) increases because no melting occurs during this stage. This plot shows that HOR increases as pulse frequency (C) increases. The plot also shows that HOR increases as pulse on-time increases (D) and then decreases [2].
3.4 Response surface plot: height of reinforcement
The 3D surface plot and 2D contour effect developed by design expert 18.0 software represent the interaction effect between process parameters and HOR as shown in Figures 5–10 [3].
The coefficient of the linear interactive effect of peak current and base current is positive as given in Table 4. HOR is increased as the value of the above parameter is increased as shown in Figure 5a of the 3D surface plot and Figure 5b of the contour plot. HOR increases with concurrent increases in peak current and base current to approximately 180−100 A, respectively, beyond which the value of HOR decreases [2, 3]. As shown in Table 4, the coefficient of linear interactive effects of peak current and pulse frequency is negative. As shown in Figure 6c of 3D surface plots and Figure 6d of contour plots, HOR increases as the value of the above parameter increases. The HOR declined beyond the peak current of 180 A and pulse frequency of 125 Hz respectively [2, 6].
As shown in Table 4, the coefficient of the linear effect of peak current and pulse on time is positive. As shown in Figure 7e of the 3D surface plot and Figure 7f of the contour plot, HOR increases as the value of the above parameter increases. DOP is increasing with simultaneously increasing in peak current and pulse on time to about 180 A and 50% respectively beyond which the value of HOR declined. Table 4 shows that the coefficient of the linear effect of base current and pulse frequency is positive. As shown in Figure 8g of the 3D surface plot and Figure 8h of the contour plot, HOR increases as the value of the above parameter increases. DOP rises as peak current and pulse on time rise to around 180 A and 50%, respectively, beyond which the value of HOR tends to fall. Table 4 shows that the coefficient of linear interactive effects of base current and pulse on time is negative [2]. As shown in Figure 9i of the 3D surface plots and Figure 9j of the contour plot, BW increases as the value of the above parameter increases. Beyond the base current of 100 A, the HOR and pulse on time both decreased by 50%. The coefficient of the linear interactive effect of pulse frequency and pulse on time is positive as given in Table 4. As the value of the above parameter is increased, BW increases, as shown in Figure 10k of the 3D surface plot and Figure 10l of the contour plot [1, 2]. HOR is increasing with simultaneously increasing pulse frequency and pulse on time to about 125 Hz and 50% respectively beyond which the value of HOR declined.
4. Statistical analysis for depth of heat affected zone using RSM
By varying the input process parameter, CCD was used to experiment. The experiment was carried out by varying the input parameters with the experimental design CCD. The experiment was carried out using various parameter combinations, as shown in Table 6. The CCD experiment results were fitted to the polynomial regression equation created by Design Expert Software 18.0 [2, 5].
4.1 Development and evaluation of regression equation: depth of HAZ
The correlation between process parameters and output response was obtained by using CCD. The second-order polynomial regression equation fitted between the output response and input process parameter. From the ANOVA result shown in Table 7, it has been found adequacy of the model is suitable to analyze the experimental value.
Std | Factor symbol | Experimental value Bead width | |||
---|---|---|---|---|---|
A | B | C | D | ||
1 | 0.87 | ||||
2 | 0.60 | ||||
3 | 0.52 | ||||
4 | 0.98 | ||||
5 | 0.67 | ||||
6 | 0.59 | ||||
7 | 1.07 | ||||
8 | 0.76 | ||||
9 | 0.62 | ||||
10 | 1.25 | ||||
11 | 0.74 | ||||
12 | 0.62 | ||||
13 | 1.33 | ||||
14 | 0.83 | ||||
15 | 0.68 | ||||
16 | 1.37 | ||||
17 | 0.94 | ||||
18 | 0.80 | ||||
19 | 1.53 | ||||
20 | 0.92 | ||||
21 | 0.74 | ||||
22 | 1.68 | ||||
23 | 0.97 | ||||
24 | 0.76 | ||||
25 | 1.65 | ||||
26 | 1.05 | ||||
27 | 0.78 | ||||
28 | 1.00 | ||||
29 | 1.05 | ||||
30 | 1.16 |
Source | Coefficient | Sum of squares | df | Mean square | |||
---|---|---|---|---|---|---|---|
Model | 1.12 | 1.26 | 14 | 0.0902 | 0.8929 | 0.5814 | Significant |
A | 0.0087 | 0.0018 | 1 | 0.0018 | 4.71 | 0.045 | |
B | −0.0529 | 0.0672 | 1 | 0.0672 | 0.3801 | 0.4275 | |
C | 0.1225 | 0.3601 | 1 | 0.3601 | 3.56 | 0.0478 | |
D | 0.0400 | 0.0384 | 1 | 0.0384 | 0.6652 | 0.5468 | |
A × B | 0.0594 | 0.0564 | 1 | 0.0564 | 0.5583 | 0.4665 | |
A × C | −0.0562 | 0.0506 | 1 | 0.0506 | 0.5011 | 0.4899 | |
A × D | 0.0563 | 0.0506 | 1 | 0.0506 | 0.5011 | 0.4899 | |
B × C | 0.0594 | 0.0564 | 1 | 0.0564 | 0.5583 | 0.0466 | |
B × D | −0.0769 | 0.0946 | 1 | 0.0946 | 0.9359 | 0.3487 | |
C × D | 0.0538 | 0.0462 | 1 | 0.0462 | 0.4575 | 0.5091 | |
A2 | −0.0976 | 0.2613 | 1 | 0.2613 | 2.59 | 0.1286 | |
B2 | −0.0095 | 0.0025 | 1 | 0.0025 | 0.0244 | 0.8780 | |
C2 | −0.0120 | 0.0039 | 1 | 0.0039 | 0.0390 | 0.8462 | |
D2 | −0.0920 | 0.2321 | 1 | 0.2321 | 2.30 | 0.1504 | |
Residual | 1.52 | 15 | 0.1010 | ||||
Lack of fit | 1.19 | 10 | 0.1189 | 1.82 | 0.2639 | Not significant | |
Pure error | 0.3266 | 5 | 0.0653 | ||||
Cor total | 2.78 | 29 |
The regression equation based on the regression coefficient of ANOVA results is shown in Eq. (3).
To obtain a statistically significant regression model
Std | Factor sign | Estimated value | Remaining error | |||
---|---|---|---|---|---|---|
A | B | C | D | |||
1 | 0.89 | −0.01625 | ||||
2 | 0.79 | −0.185 | ||||
3 | 0.70 | −0.18167 | ||||
4 | 0.84 | 0.142083 | ||||
5 | 1.02 | −0.3475 | ||||
6 | 0.69 | −0.10625 | ||||
7 | 1.07 | 0.004583 | ||||
8 | 0.98 | −0.21667 | ||||
9 | 0.90 | −0.28 | ||||
10 | 1.03 | 0.22125 | ||||
11 | 0.41 | 0.332083 | ||||
12 | 0.77 | −0.14917 | ||||
13 | 1.25 | 0.08375 | ||||
14 | 1.15 | −0.315 | ||||
15 | 0.99 | −0.31167 | ||||
16 | 1.13 | 0.242083 | ||||
17 | 0.71 | 0.222917 | ||||
18 | 0.75 | 0.047917 | ||||
19 | 1.19 | 0.337083 | ||||
20 | 0.98 | −0.06625 | ||||
21 | 0.83 | −0.07708 | ||||
22 | 1.32 | 0.347917 | ||||
23 | 0.67 | 0.317917 | ||||
24 | 0.83 | −0.04708 | ||||
25 | 1.12 | 0.49 | ||||
26 | 1.12 | −0.04 | ||||
27 | 1.12 | −0.245 | ||||
28 | 1.12 | −0.125 | ||||
29 | 1.12 | −0.095 | ||||
30 | 1.12 | 0.015 |
4.2 Adequacy check of the mathematical model for depth of HAZ
ANOVA represents that the polynomial regression equation was significant to represent the relationship between input parameters and output parameters. The adequacy and significance of the established model were also elaborated by the high value of the coefficient of determination (
4.3 Perturbation plot: depth of heat affected zone
The perturbation plot shows the effect of all the parameters on a single plot. Figure 13 shows a perturbation plot that compares the effect of all process parameters at the center point on bead width. It has been observed that HOR peak current (A) increases before decreasing. The plot also shows that the HOR decreases as the base current (B) increases because no melting occurs during this stage. This plot shows that HOR increases as the pulse frequency (C) increases. The plot also shows that HOR increases as a pulse on time increases (D) and then decreases [2].
4.4 Response surface plot: depth of heat affected zone
The 3D surface plot and 2D contour effect developed by design expert 18.0 software represent the interaction effect between process parameters and BW as shown in Figures 14–19.
The coefficient of the linear interactive effect of peak current and base current is +ve as given in Table 7, DOH is increased as the value of the above parameter is increased as shown in Figure 14a of the 3D surface plot and Figure 14b of the contour plot. DOH rises in tandem with increases in peak and base current to around 180 and 100 A, respectively, after which the value of DOH falls. Table 7 shows that the coefficients of linear effects of peak current and pulse frequency are negative. As shown in Figure 15c of 3D surface plots and Figure 15d of contour plots, DOH increases as the value of an above parameter increases. The DOH decreased after reaching a peak current of 180 A and a pulse frequency of 125 Hz. The linear effect of peak current and pulse on time has a positive coefficient, as shown in Table 7, and DOH increases as the value of the above parameter increases, as shown in Figure 16e of the 3D surface plot and Figure 16f of the contour plot [1, 2]. DOH is increasing with simultaneously increasing in peak current and pulse on time to about 180 A and 50% respectively beyond which the value of DOH declines.
The coefficient of the linear interactive effect of base current and pulse frequency is positive as given in Table 7. DOH is increased as the value of the above parameter is increased as shown in Figure 17g of the 3D surface plot and Figure 17h of the contour plot. DOH rises as the base current and pulse frequency rise to around 100 A and 125 Hz, respectively, beyond which the value of DOH falls. As shown in Table 7, the coefficient of the linear effect of base current and pulse frequency is positive. As shown in Figure 18i of the 3D surface plot and Figure 18j of the contour plot, DOH increases as the value of the above parameter increases [1, 2]. DOH is increasing with simultaneously increasing base current and pulse frequency to about 100 A and 125 Hz respectively beyond which the value of DOH decline.
Table 7 shows that the coefficient of linear effects of base current and pulse on time is −ve. As shown in Figure 19k of 3D surface plots and Figure 19l of contour plots, DOH increases as the value of the above parameter increases. The DOH declined beyond the base current of 100 A and pulse on time by 50% respectively [2, 3].
Table 7 shows that the coefficient of the linear effect of pulse frequency and pulse on time is positive. As shown in Figure 19k of the 3D surface plot and Figure 19l of the contour plot, DOH increases as the value of the above parameter increases [2, 6]. DOH is increasing with simultaneously increasing pulse frequency and pulse on time to about 100 Hz and 50% respectively beyond which the value of DOH declines.
5. Statistical analysis for the width of heat affected zone using RSM
CCD was used to experiment by changing the input process parameter. The experiment was carried out by varying the input parameters using the experimental design CCD. The experiment was carried out using various parameter combinations, as shown in Table 9. The CCD experiment results were fitted to the polynomial regression equation created by Design Expert Software 18.0 [1, 2].
5.1 Development and evaluation of regression equation: width of HAZ
The correlation between process parameters and output response was obtained by using CCD. The second-order polynomial regression equation fitted between the output response and input process parameter. From the ANOVA result shown in Table 10, it has been found adequacy of the model is suitable to analyze the experimental value [2, 3].
Std | Factor symbol | Exp. value WOH | |||
---|---|---|---|---|---|
A | B | C | D | ||
1 | 0.92 | ||||
2 | 0.68 | ||||
3 | 0.57 | ||||
4 | 1.11 | ||||
5 | 0.82 | ||||
6 | 0.67 | ||||
7 | 1.23 | ||||
8 | 0.93 | ||||
9 | 0.74 | ||||
10 | 1.13 | ||||
11 | 0.87 | ||||
12 | 0.70 | ||||
13 | 1.21 | ||||
14 | 0.95 | ||||
15 | 0.79 | ||||
16 | 1.40 | ||||
17 | 1.02 | ||||
18 | 0.90 | ||||
19 | 1.36 | ||||
20 | 0.98 | ||||
21 | 0.77 | ||||
22 | 1.45 | ||||
23 | 1.08 | ||||
24 | 0.88 | ||||
25 | 1.28 | ||||
26 | 1.36 | ||||
27 | 1.09 | ||||
28 | 1.15 | ||||
29 | 1.19 | ||||
30 | 1.21 |
Source | Coefficient | Sum of squares | df | Mean square | |||
---|---|---|---|---|---|---|---|
Model | 1.26 | 1.04 | 14 | 0.0741 | 1.26 | 0.3307 | Significant |
A | 0.0079 | 0.0015 | 1 | 0.0015 | 5.025 | 0.0463 | |
B | −0.0125 | 0.0038 | 1 | 0.0038 | 0.0163 | 0.8042 | |
C | 0.1108 | 0.2948 | 1 | 0.2948 | 5.01 | 0.0408 | |
D | 0.0192 | 0.0088 | 1 | 0.0088 | 0.6498 | 0.7042 | |
A × B | 0.0581 | 0.0541 | 1 | 0.0541 | 0.9183 | 0.0353 | |
A × B | −0.0394 | 0.0248 | 1 | 0.0248 | 0.4214 | 0.5261 | |
A × D | 0.0463 | 0.0342 | 1 | 0.0342 | 0.5814 | 0.4576 | |
B × C | 0.0575 | 0.0529 | 1 | 0.0529 | 0.8986 | 0.3582 | |
B × D | −0.0631 | 0.0638 | 1 | 0.0638 | 1.08 | 0.3145 | |
C × D | 0.0344 | 0.0189 | 1 | 0.0189 | 0.3212 | 0.5793 | |
A2 | −0.0978 | 0.2624 | 1 | 0.2624 | 4.46 | 0.0419 | |
B2 | −0.0453 | 0.0563 | 1 | 0.0563 | 0.9567 | 0.3435 | |
C2 | −0.0603 | 0.0998 | 1 | 0.0998 | 1.69 | 0.2126 | |
D2 | −0.0922 | 0.2331 | 1 | 0.2331 | 3.96 | 0.0651 | |
Residual | 0.8830 | 15 | 0.0589 | ||||
Lack of fit | 0.7191 | 10 | 0.0719 | 2.19 | 0.1997 | Not significant | |
Pure error | 0.1639 | 5 | 0.0328 | ||||
Cor total | 1.92 | 29 |
The regression equation based on the regression coefficient of ANOVA results is shown in Eq. (5).
To obtain a statistically significant regression model
Std | Factor sign | Estimated value | Remaining error | |||
---|---|---|---|---|---|---|
A | B | C | D | |||
1 | 0.93 | −0.01 | ||||
2 | 0.82 | −0.14 | ||||
3 | 0.80 | −0.23 | ||||
4 | 0.92 | 0.18 | ||||
5 | 1.05 | −0.23 | ||||
6 | 0.78 | −0.11 | ||||
7 | 1.15 | 0.08 | ||||
8 | 1.11 | −0.18 | ||||
9 | 0.94 | −0.20 | ||||
10 | 1.01 | 0.12 | ||||
11 | 0.55 | 0.31 | ||||
12 | 0.86 | −0.16 | ||||
13 | 1.19 | 0.02 | ||||
14 | 1.10 | −0.15 | ||||
15 | 1.04 | −0.25 | ||||
16 | 1.18 | 0.22 | ||||
17 | 0.85 | 0.16 | ||||
18 | 0.88 | 0.02 | ||||
19 | 1.10 | 0.26 | ||||
20 | 1.05 | −0.08 | ||||
21 | 0.80 | −0.03 | ||||
22 | 1.24 | 0.21 | ||||
23 | 0.85 | 0.23 | ||||
24 | 0.93 | −0.05 | ||||
25 | 1.26 | 0.32 | ||||
26 | 1.26 | 0.10 | ||||
27 | 1.26 | −0.17 | ||||
28 | 1.26 | −0.11 | ||||
29 | 1.26 | −0.07 | ||||
30 | 1.26 | −0.05 |
5.2 Adequacy check of the mathematical model for the width of HAZ
ANOVA represents that the polynomial regression equation was significant to represent the relationship between input parameters and output parameters. The high value of the coefficient of determination (
5.3 Perturbation plot: width of heat affected zone
The perturbation plot shows the effect of all the parameters on a single plot. Figure 22 shows a perturbation plot that compares the effect of all process parameters at the center point on bead width. WOH has been observed to increase as peak current (A) increases, and then decreases. The plot also shows that the WOH decreases as the base current (B) increases because no melting occurs during this stage. This plot shows that WOH increases as the pulse frequency (C) increases. The plot also shows that WOH increases as a pulse on time increases (D) and then decreases [2, 3].
5.4 Response surface plot: width of heat affected zone
The 3D surface plot and 2D contour effect developed by design expert 18.0 software represent the interaction effect between process parameters and WOH as shown in Figures 23–28. The coefficient of the linear effect of peak current and base current is positive as given in Table 10, WOH is increased as the value of the above parameter is increased as shown in Figure 23a of the 3D surface plot and Figure 23b of the contour plot. Peak current and base current are both rising at the same time as WOH, reaching nearly 180 and 100 A, respectively, beyond which the value of WOH starts to drop. According to Table 10, the peak current and pulse frequency's coefficient of linear effects is both negative. WOH rises when the value of the aforementioned parameter rises, as demonstrated in Figure 24c and d of 3D surface plots and contour plots, respectively [2, 3]. The WOH declined beyond the peak current of 180 A and pulse frequency of 125 Hz respectively.
According to Table 10, the coefficient of the linear relationship between peak current and pulse on time is positive. WOH increases when the value of the aforementioned parameter increases, as demonstrated in Figure 25e and f of the 3D surface plot and the contour plot, respectively [2, 5]. WOH is increasing with simultaneously increasing in peak current and pulse on time to about 180 A and 50% respectively beyond which the value of WOH declines.
The coefficient of the linear effect of base current and pulse frequency is positive as given in Table 10, WOH is increased as the value of the above parameter is increased as shown in Figure 26g of the 3D surface plot and Figure 26h of the contour plot. WOH rises as base current and pulse frequency increase at the same time, peaking at roughly 100 A and 125 Hz, respectively, after which the value of WOH begins to decrease. According to Table 10, the coefficient of linear effects for base current and pulse on time is negative. When illustrated in Figure 27i of 3D surface plots and Figure 27j of contour plots, WOH increases as the value of the above parameter increases [1, 2]. The WOH declined beyond the base current 100 A and pulse on-time 50% respectively.
The coefficient linear effect of pulse frequency and pulse on time is positive as given in Table 10. WOH is increased as the value of the above parameter is increased as shown in Figure 28k of the 3D surface plot and Figure 28l of the contour plot [2, 3]. WOH is increasing with simultaneously increasing pulse frequency and pulse on time to about 125 Hz and 50% respectively beyond which the value of WOH declines.
6. Conclusion: Height of reinforcement
According to their greatest
7. Conclusion: Depth of HAZ
Peak current and pulse frequency are the most significant process parameter that effects the DOH as indicated by their highest
8. Conclusion: The width of HAZ
Peak current and pulse frequency are the most significant process parameter that effects the WOH as indicated by their highest
Prediction | Experiment | |
---|---|---|
Level | (160 A, 80 A, 100 Hz, 45%) | (160 A, 80 A, 100 Hz, 45%) |
HOR mm | 1.41 | 1.45 |
Prediction | Experiment | |
---|---|---|
Level | (160 A, 80 A, 150 Hz, 45%) | (160 A, 80 A, 150 Hz, 45%) |
DOH mm | 1.32 | 1.37 |
Prediction | Experiment | |
---|---|---|
Level | (160 A, 80 A, 100 Hz, 45%) | (160 A, 80 A, 100 Hz, 45%) |
WOH mm | 1.26 | 1.58 |
Acknowledgments
The author made sincere thanks to all the technical staff of the ACMS laboratory of IIT Kanpur who directly and indirectly help in the experimental and analysis work. I would express my deep sense of gratitude to Dr. Shahnawaz Alam Sir and Dr. P.K. Bharti Sir for their valuable suggestions during this research work. I would also like to thank Chairman Sir (Shri Pranveer Singh Ji), Director Sir (Dr. Sanjeev Kumar Bhalla), and Shri Manmohan Shukla Ji (T&P) of Pranveer Singh Institute of Technology, Kanpur for their consistent encouragement and motivation.
References
- 1.
Ezekannagha CB, Ude CN, Onukwuli OD. Optimization of the methanolysis of lard oil in the production of biodiesel with response surface methodology. Egyptian Journal of Petroleum. 2017; 26 (4):1001-1011 - 2.
Ahmad A. Microstructure analysis and multi-objective optimization of pulsed TIG welding of 316/316L Austenite Stainless Steel. Handbook of Smart Materials, Technologies, and Devices: Applications of Industry 4.0. Hussain CM, Di Sia P. Cham: Springer International Publishing; 2020. pp. 1-33 - 3.
Song C, Dong S, He P, Yan S, Zhao X. Correlation of process parameters and porosity in laser welding of 7A52 aluminum alloy using response surface methodology. Procedia Manufacturing. 2019; 37 :294-298 - 4.
Varkey MJ, Sumesh A, Ramesh Kumar K. A Computational approach in optimizing process parameters influencing the heat input and depth of penetration of tungsten inert gas welding of Austenitic Stainless Steel (AISI 316L) using Response Surface Methodology. Materials Today: Proceedings. 2020; 24 :1199-1209 - 5.
Iliyasu I, Bello JB, Oyedeji AN, Salami KA, Oyedeji EO. Response surface methodology for the optimization of the effect of fibre parameters on the physical and mechanical properties of deleb palm fibre reinforced epoxy composites. Scientific African. 2022; 16 :e01269 - 6.
Ahmad A, Alam S. Parametric optimization of TIG welding using response surface methodology. Materials Today: Proceedings. 2019; 18 :3071-3079