## 3 Proposed Method
### Weibull FEA Stress Data Analysis  
The proposed Weibull analysis is performed by using the \(\sigma_{1}\) and \(\sigma_{2}\) principal stress values that are acting on the flat spring device; thus, in this study they are determined by performing a FEA simulation. The analysis is performed by presenting the FEA stress data procedure [30] first, in Section 4.1, and then the corresponding cycles to failure (Ni) analysis in Section 4.2. The procedure will begin by following the steps to the static stress outlined in Section 2. Therefore, from Equation (4) the estimated inertia moment is \(I=0.256\) mm\({}^{4}\). Then, by using the minimum and maximum generated deflection \(Y_{2}=3\) mm and \(Y_{1}=8\) mm values and the elasticity module of E = 207 GPa in Equation (3), the deflection forces are \(F_{1}~{}=~{}4.63\) N and \(F_{2}~{}=~{}1.74\) N Those forces are introduced in the FEA simulation to determine the corresponding principal stress values used to determine the Weibull parameters. Once this is done, the principal stresses values obtained are, \(\sigma_{1}\) = 491.75 MPa and \(\sigma_{2}\) = 184.8 MPa.  
The FEA analysis of the flat spring is shown in Figure 4. The used material is a steel AISI 4340 OQT 1300, with a Young's modulus of 207 GPa and a Poisson's ratio of 0.29.  
The application was performed using the ANSYS software. The FEA model of the flat spring device with the dimensional features and the loading condition given in Section 4 was dispersed by using an adaptive sizing mesh of 148 mm, that uses the first-order element, with a total of 1343 nodes and 160 elements. The corresponding stress results are shown in Table 1.  
Based on Figure 4, and to reflect the real service loads obtained by Equation (3), the stress calculations are performed based on the maximum and the minimum applied forces of 4.63 N and 1.74 N, respectively. Since to determine the principal stress values, based on which we determine the random behavior of \(N\), we need to know both how the stresses are distributed and how much the element is deflected, then Figure 5 shows the stress distribution; and Figure 6 shows the corresponding deflection.  
As can be seen in Figure 5, the stress concentration occurs in the red area (point A); that is why the analysis was performed there.  
In Figure 6 it can be observed that the maximum deflection occurs in the blue area where the force is being applied. Then, the red area shown in Figure 5 and the blue area shown in Figure 6 are both analyzed. Finally, the estimated \(\sigma_{1}\) and \(\sigma_{2}\) stress values of the FEA simulation given in Table 1 is compared to the static stress analysis. Both results are given in Table 2, where it can be seen that no significant difference exists.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Maximum Principal Stress (MPa)** & **Minimum Principal Stress (MPa)** & **Deformation (mm)** & **Deformation (mm)** \\
**Force \(F_{1}\) = 4.63 N** & **Force \(F_{2}\) = 1.74 N** & **Force \(F_{2}\) = 1.74 N** \\ \hline
491.75 & 184.8 & 8.02 & 2.99 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Stresses and deformation results from the finite element analysis (FEA).  
Figure 4: The finite element model of the flat spring.