# Finite Element Simulation of HELICOIL(r) Inserts
## 7 Results
### Initial Screening Phase  
At first, we used Adding function \(1\)\(add_{1}(\mathbf{P},N^{*})\). The whole interval \((u_{0}=0,u_{2}\approx 0.9)\) [mm] was divided into \(N^{*}=9\) parts, and the points \([u_{i}^{*},p_{i}^{*}]\) were calculated based on the current best solution presented in the previous section, as listed at the top of Table 10. The screening data \((u_{i}^{*},p_{i}^{*},g^{*},f^{*},f_{i}^{*})\) are shown at the bottom of Table 10.  
It can be seen, from Table 10, that the POF \(f_{i}\) for \(i>3\) had a lower value. In Section 4.4.4, we presented certain rules. * The second rule: We add all points from the previous solution: \[\mathbf{P}=Re_{2}(\mathbf{P})\approx\{[0,0],[0.4,33],[0.9,10]\}.\]
* The third rule: We divide the points roughly into two parts, according to the value of \(f_{i}\), with limit value \(f_{5}\approx 20\),000. We add the following points: \[\mathbf{P}^{*}=Re_{3}(\mathbf{P},f_{S})=\{[0.1,8.25],[0.2,16.5],[0.3,24.75]\}.\]
* The fifth rule: We add a maximum of one point to each interval. The designated points are as follows: \[Re_{4}(\mathbf{P}^{*},\mathbf{P})=\{[0.2,16.5]\}.\] \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(i\) & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline \(u_{i}^{*}\) [mm] & 0.1 & 0.2 & 0.3 & 0.4 & 0.5 & 0.6 & 0.7 & 0.8 & 0.9 \\ \(p_{i}^{*}\) [MPa] & 8.25 & 16.5 & 24.75 & 33 & 28.4 & 23.8 & 19.2 & 14.6 & 10 \\ \hline \(i\) & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline \(g^{*}\) [N\({}^{2}\)] & 532,321 & 532,408 & 534,356 & 534,799 & 535,936 & 535,517 & 535,380 & 534,705 & 535,226 \\ \(f^{*}\) [N\({}^{2}\)] & 613,231 & 612,804 & 615,016 & 614,108 & 617,708 & 616,586 & 616,258 & 614,061 & 615,757 \\ \hline \(f_{1}^{*}\) [N\({}^{2}\)] & 197,132 & 198,858 & 199,402 & 199,404 & 199,436 & 199,414 & 199,404 & 199,393 & 199,401 \\ \(f_{2}^{*}\) [N\({}^{2}\)] & 269,807 & 268,337 & 270,229 & 270,620 & 270,630 & 270,623 & 270,620 & 270,618 & 270,620 \\ \(f_{3}^{*}\) [N\({}^{2}\)] & 87,798 & 87,243 & 87,040 & 87,788 & 87,823 & 87,805 & 87,799 & 87,786 & 87,795 \\ \(f_{4}^{*}\) [N\({}^{2}\)] & 16,781 & 16,750 & 16,739 & 16,067 & 17,061 & 16,823 & 16,774 & 16,101 & 16,622 \\ \(f_{5}^{*}\) [N\({}^{2}\)] & 9820 & 9786 & 9791 & 9861 & 10,261 & 9933 & 9781 & 9681 & 9758 \\ \(f_{6}^{*}\) [N\({}^{2}\)] & 7936 & 7906 & 7911 & 8066 & 8337 & 8044 & 7906 & 7875 & 7892 \\ \(f_{7}^{*}\) [N\({}^{2}\)] & 438 & 438 & 437 & 416 & 441 & 440 & 447 & 413 & 433 \\ \(f_{8}^{*}\) [N\({}^{2}\)] & 11,758 & 11,742 & 11,731 & 10,940 & 11,857 & 11,750 & 11,762 & 11,095 & 11,616 \\ \hline \(f_{9}^{*}\) [N\({}^{2}\)] & 11,758 & 11,742 & 11,731 & 10,940 & 11,857 & 11,750 & 11,762 & 11,095 & 11,616 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Data from the initial screening phase. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Phase** & \(N_{C}\) [-] & \(g\) [N\({}^{2}\)] & \(i\) & **1** & **2** \\ \hline  & & & \(u_{i}\) [mm] & 0.456 & 0.92 \\ Initial & - & 875,144 & \(p_{i}\) [MPa] & 31 & 0 \\ Final & 38 & 685,502 & \(p_{i}\) [MPa] & 33.1 & 9.9 \\ \hline \(N_{C}\) [-] & \(g\) [N\({}^{2}\)] & \(f\) [N\({}^{2}\)] & \(f_{1}\) [N\({}^{2}\)] & \(f_{2}\) [N\({}^{2}\)] & \\ \hline
0 & 875,144 & 467,790 & 324,089 & 143,701 & \\
48 & 685,502 & 134,869 & 115,875 & 18,994 & \\ \hline \end{tabular}
\end{table} 
Table 9: Input table for the bilinear model. Finally, we selected the points for the next identification step (40), \(N=3\):  
\[\mathbf{P}^{a+1}=\{[0,0],[0.2,16.5],[0.4,33],[0.9,10]\}.\]  
The resulting graphs for the screening phase are shown in Figure 12.  
We arrived at a similar result when using the graphs. It can be seen, from the figure, that the parameter values for \(i>3\) had a less significant effect on the result. The parameters with \(i>3\) manifested themselves as POP values at a time greater than 15 [s]. Therefore, the first three points were selected for the next identification process. We added a maximum of one point to each interval; that is, the point marked with the index \(i=2\).