# Finite Element Simulation of HELICOIL(r) Inserts
## 8 Discussion
### Results  
The curve described in Section 5 was used for identification. The displacement was adjusted with respect to the boundary conditions used for the simulations; see Section 6.3. Figure 14 shows the output curve (Force-Time) obtained from the experiment and the output curves obtained for different numbers of parameters. The curves are distinguished by colour, and the number indicates the number of parameters. The initial estimate (\(N=2\), ini) for the bilinear curve is also shown.  
With two parameters (\(N=2\)), the curve had a different shape, compared to the experimental curve found experimentally. In contrast, the curves with three (\(N=3\)), five (\(N=5\)), eight (\(N=8\)), and nine (\(N=9\)) parameters came visually close to the curve obtained experimentally. The required value of the classical target function \(g\leq 2000\) [N\({}^{2}\)] was met with the curve having nine parameters.  
Only the parameter values were tuned, and their positions were used from previous calculation cycles. It is likely that, by changing their position, a better result could have been achieved. This option was considered; however, for this application, we consider it more reasonable to focus on the design of a general model of the threaded insert in future work. We wish to use and develop the basic algorithm (described in Section 4) in the areas of material parameter identification (identification phase) or symbolic regression.  
Figure 14: Change in the output curve during the identification process.  
Figure 14 indicates that the identification process described in Section 4 leads to the finding of a suitable solution; however, it cannot be deduced from this whether the use of a cohesive contact approach produces more reliable results for the simulation of the HELICOIL\({}^{\circledR}\) insert than, for example, the use of a Glued contact.  
A comparison of the input curves (shear stress-displacement) for different numbers of parameters is shown in Figure 15. The colours and descriptions of the curves are the same as in the previous figure. For two (\(N=2\)) and three (\(N=3\)) parameters, it would likely be possible to find a better result by changing the position of the points, as in the previous paragraph. The right-hand sides of the curves were very similar with three (\(N=3\)), five (\(N=5\)), eight (\(N=8\)), and nine (\(N=9\)) parameters. The curves with eight (\(N=8\)) and nine (\(N=9\)) parameters were almost identical.  
The simultaneous adjustment of both values (position and shear stress values) was also considered; however, from the point of view of solving the given problem, it seems more advantageous to design a mathematical model for the description of the curve. As there are several similar types of connections, the procedure described in this article can be a relatively quick and easy alternative to practical use, without having to look for a mathematical model for a particular type of connection. For example, in order to simplify the identification process, it is possible to use symbolic regression to find suitable approximation functions. This could reduce the number of parameters and simplify their identification. When using an algorithm to identify more complex curve shapes, it would also be useful to consider point removal.