The GTAW process simulation is performed in COMSOL. Initially, the simulation for the ideal condition is performed using the geometrical parameters extracted from the macro results (refer Table1 1 and Fig. 1). The temperature distribution and isotherm curve are shown in Fig. 3. Figure 3-c clearly shows the weld bead profile made from the COMSOL environment. The temperature distribution caused by the moving heat source at 19.3 seconds is taken and plotted. Along with this temperature plot, the corresponding weld bead profile with temperature distribution in the specimen is showed in Fig. 3. For the rest of the combination the simulation is performed and the results are tabulated. Table 3 showing the results of the parameters selected from the Table 1 and their impact on the temperature distribution. The last column indicates the number of ranks and it is arranged based on the temperature deviations as compared with the ideal trial results. Under set 2, the parameter weld bead depth “b = 0.7” has scored the first rank followed by the weld bead width having “a = 4.7” scoring the second rank. The extreme ends of the rear and front ellipse parameters “Cf = 5 and Cr = 5” are showed constant results and holding the rank as 7.
Table 3
GTAW process simulation conditions and their results
S.no | Trial Condition | Parameter Condition | Output Temperature °C | Difference | Rank |
Variable parameter | Constant parameters |
1 | Set 1 | -1 | a 4.7 | Remaining all | 1903 | 102 | 2 |
2 | + 1 | a 6.7 | Remaining all | 1722 | -79 | 3 |
3 | Set 2 | -1 | b 0.7 | Remaining all | 1947 | 146 | 1 |
4 | + 1 | b 1.5 | Remaining all | 1738 | -63 | 6 |
5 | Set 3 | -1 | Cf 3 | Remaining all | 1729 | -72 | 4 |
6 | + 1 | Cf 5 | Remaining all | 1796 | -5 | 7 |
7 | Set 4 | -1 | Cr 3 | Remaining all | 1729 | -72 | 4 |
8 | + 1 | Cr 5 | Remaining all | 1796 | -5 | 7 |
Ideal trail temperature is1801 °C – Difference is calculated by concerning this temperature |
The amount of heat input is applied in all the trials are constant. So, it is found that the main reason for the changes in temperature is due to the modification of the bead geometries. This modifies the temperature distribution in the GTAW process, and it is revealed through the simulation study. Chujutalli et al discussed the parametric analysis on the GTAW heat source while in moving or performing the welding operation in the simulation environment. The results were studied for 2-d and 3-d model. But in our research the bead profile after the welding process the bead profile and their details are analysed. There are slight conflicts are happened due to this modification of result analysis. This made the impact on finding the influence of the parameter that controls the outputs [20]. So in-depth analysis is needed to find out the significance of all the variable involved in the Goldack model.
Next, it is necessary to identify the contribution of these parameters. For this purpose, the input and output are arranged in Taguchi L9 orthogonal array [17]. In the previous discussion, it is concluded that Cf and Cr showed the same result. So, input for the third column “Cf” is taken and the orthogonal array is formed for further investigation. The trial arrangement based on these parameters with the predefined level are shown in supporting Table 1.
Within the trials the temperature difference between is about 357 °C (refer supporting Table 1). This is a huge difference and it may have a significant role on the temperature distribution. These much temperature deviations can make wrong perdition in phase predictions, microstructure analysis and grain size analysis related studies. The effect of variation in input parameters to the temperature distribution is very much essential to concentrate. Hence it is necessary to optimize the response characteristics and also the prediction of the optimal combination of process parameters. The optimization done using the observed values and Grey Relational Analysis (GRA) had been one of the suggested techniques to predict the optimum conditions. This also to identify the influence of each input parameters on the response characteristics [21].
GRA process starts with the calculation of Signal-to-Noise ratio (S/N ratio) and it was done for the response characteristic by considering the objective function of smaller-the-better concept. Then the normalization process was carried out for the ratio and it was rated between 0 and 1. By assuming the coefficient constant value ξ = 0.5, the grey relational coefficient was calculated and considered as a grey relational grade [21]. Table 4 shows the S/N ratio and grey relational grades for each experimental run.
Table 4
Ex. No | Input | Output |
a | b | Cf | T | S/N ratio | Normalized | Pre-processing | GRC | Order |
1 | 0.7 | 4.7 | 3 | 1895 | -65.5522 | 0.866353 | 0.133647 | 0.789083 | 3 |
2 | 0.7 | 5.7 | 4 | 1947 | -65.7873 | 1 | 0 | 1 | 1 |
3 | 0.7 | 6.7 | 5 | 1847 | -65.3293 | 0.739691 | 0.260309 | 0.657628 | 4 |
4 | 1.1 | 4.7 | 4 | 1898 | -65.5659 | 0.874163 | 0.125837 | 0.79893 | 2 |
5 | 1.1 | 5.7 | 5 | 1732 | -64.771 | 0.422317 | 0.577683 | 0.463958 | 6 |
6 | 1.1 | 6.7 | 3 | 1651 | -64.3549 | 0.185861 | 0.814139 | 0.380477 | 8 |
7 | 1.5 | 4.7 | 5 | 1825 | -65.2253 | 0.680534 | 0.319466 | 0.610153 | 5 |
8 | 1.5 | 5.7 | 3 | 1675 | -64.4803 | 0.25711 | 0.74289 | 0.402288 | 7 |
9 | 1.5 | 6.7 | 4 | 1590 | -64.0279 | 0 | 1 | 0.333333 | 9 |
Weld bead width (a), Weld bead depth (b), The front half ellipsoidal (Cf), Temperature °C(T) |
Table 4 and Supporting Fig. 2 shows that a higher grey relational grade (1) is observed from the experimental trail 2. On the other hand, the better combination of input variables to end with the minimum temperature rise in the width as 0.7 mm, depth as 5.7 mm and frontal factor as 4.
Table 5
Response values obtained from the Grey relational analysis
Parameters/ Levels | L1 | L2 | L3 | Max-Min |
Width | 0.8156 | 0.5478 | 0.4486 | 0.367 |
Depth | 0.7327 | 0.6221 | 0.4571 | 0.2756 |
Frontal factor | 0.5239 | 0.7108 | 0.5772 | 0.1869 |
Error | 0.5288 | 0.6635 | 0.6196 | 0.1347 |
Average Mean: 0.604 |
Table 5 shows the response value of each level of individual input parameters and the mean value. This value is also used to identify the maximum influence among the three levels of each parameter. The significant contribution of each parameter is also shown in Table 6.
Table 6
Results of ANOVA for the input parameters
Parameters | Degrees of Freedom | Sum of Squares | Mean Squares | Contribution (%) | F value |
Width | 2 | 0.216246 | 0.10812324 | 52.03278 | 7.636917 |
Depth | 2 | 0.115413 | 0.05770636 | 27.77037 | 4.075892 |
Frontal factor | 2 | 0.055621 | 0.02781073 | 13.38352 | 1.964316 |
Error | 2 | 0.028316 | 0.0141580 | 6.813323 | ---- |
Total | 8 | 0.415597 | ---- | ---- | ---- |
ANOVA is the statistical tool used to understand the effect and influence of individual variables on the response characteristics. From Table 7, it is understood that the width contributes higher on affecting the output temperature (Q = 52.03%) followed by the bead depth (Q = 27.77%) and frontal factor (Q = 13.38%).
Table 6 and Supporting Figure. 3 represents the bar chart for the contribution of each factor on the temperature rise during the welding process. To ensure the statistical influence of parameters, F-test at 95% confidence level was conducted. The significant influence of width and depth was noticed and F-test values for these factors are greater than F0.05, 2, 8 = 3.11. This represents that the parameters chosen are having a statistical and physical influence on affecting the output variable simultaneously.