# Multi-Objective Optimisation of Welding Parameters for AZ91D/AA6082 Rotary Friction Welded Joints
## 5 Results and Discussion  
Table 9 shows the thirty-two solutions (No. 1-32) of the optimal set in the _Pareto_ sense. Table 9 shows that the best solutions were obtained for a low friction force of 35 kN and a friction welding time of 10 s. According to the results (see Table 9, No. 7-10), the tensile strength was about 80 MPa, and the average joint shortening was only 3.5 mm. For these solutions, the upsetting force was also low. Increasing the upsetting force to almost the maximum value (48 kN) caused more significant material losses of up to 8 mm. It is worth noting that in the optimisation case, a lower material loss of about 50% was achieved, comparing Table 4, No. 7, 8 with Table 9, No. 7, 8. The Pareto curve of UTS and ML using genetic algorithms is presented in Figure 7.  
The set of solutions consists of 32 points, forming a _Pareto_ curve, with limits defined by the extreme points ID1 and ID2 (see No. 1 and 2, Table 9). Point ID2 in Figure 7 is the highest point on the _Pareto_ curve with the highest UTS = 80.13 MPa and the highest metal loss ML = 8.25 in mm (see Table 9, point No. 2). For point ID2, the welding parameters are as follows: friction force is 35 kN, friction time is 6 s, and upsetting force is 48 kN. The lowest point on the _Pareto_ curve is ID1 (see Figure 7). For point ID = 1, the lowest metal loss is 0.23 mm, while the lowest UTS = 30 MPa is received (see No. 1 in Table 9). For point ID1, the following welding parameters (FF = 35 kN, FT = 9 s and UF = 40 kN) were found. \begin{table}
\begin{tabular}{c c c c c c} \hline
**No. ** & **FF (kN)** & **UF (kN)** & **FT (s)** & **TS (MPa)** & **ML (mm)** \\ \hline
1 & 35 & 40 & 9 & 30.06 & 0.23 \\
2 & 35 & 48 & 6 & 80.13 & 8.25 \\
3 & 35 & 48 & 8 & 79.76 & 7.84 \\
4 & 35 & 41 & 9 & 44.23 & 0.30  
When the _Pareto_ solutions are analysed further, more information regarding the variation in the process parameters is exposed. All the Pareto solutions are numbered and sorted in order to increase the tensile strength of the joint and decrease metal loss for all cases. Figure 8 shows the variation in UTS and ML values of the _Pareto_ solutions for the AZ91D/6061 joint (arranged in ascending order and plotted as the population size (_PopSize_). Conflicting relations between the objective functions (UTS and ML) of welding process quality have been observed. The _Pareto_ solution number of UTS vs. ML was optimised using a combination of _Ngen_ and population size. In this optimisation task, the \(N_{gen}\) and \(Pop_{size}\) values were 80. The probability crossover of 0.9 and mutation of 0.2 are kept constant in all optimisation procedures. In this problem, the UTS and ML were optimised simultaneously. However, finding a solution that simultaneously optimises UTS and ML is not possible. From Figure 8, it can be observed that the range of region (A-B) of higher UTS (68-80 MPA) with metal loss that changed in the range (0.7-7 mm) was selected for further analysis of the _Pareto_ results. The solution numbers corresponding to the region (A-B) are 25 to 60, which could be used to determine the ranges of best FF, FT, and UF welding parameters. The process parameter solutions FF (a), UF (b) and FT (c) in all 80 _Pareto_ solutions with increasing tensile strength are shown in Figure 9.  
Figure 8: The ultimate tensile strength and metal loss in the _Pareto_ solution number for AZ91D/6082 joints. Figure 7: _Pareto_ front solutions of tensile strength and metal loss for AZ91D/6082 joint. The optimisation results in Figure 9 show many variants of _Pareto_ solutions for welding parameters. Figure 9a indicates the average value of 35 kN for FF, whereas UF increases linearly from 67 to 80 MPa (Figure 9b). Figure 9b,c show the increasing UF and UT values in the A-B range. Moreover, the constant values outside the range are visible. The UF and UF values are 48 kN and 6 s, respectively. Figure 10 shows the variation in the FF, UF and FT parameters in all 80 _Pareto_ solutions with decreasing metal loss.