## 2 Fatigue Strength Assessment of Real Components
### Fatigue Assessment of the Compressor Mounting Bracket
#### 2.1.5 Method Verification  
To verify the method, strain gauges were employed to control strains on the compressor bracket under random vibration test using PSD input from Table 1. Strain gauges were glued at the reference points A-F according to Figure 9. An example of the used strain gauges and measurement location is shown in Figure 12.  
Similarly to the accelerations, the strain time history was recorded and converted into power spectral density. Based on that, the stress components were calculated, and example results for point A are presented in Figure 13. The PSD results clearly show that the stress response closely follows the acceleration pattern, with two distinct peaks observed.  
Figure 11: S–N curve defined for the compressor bracket.  
Figure 12: Strain rosette in points A and B on the compressor bracket.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Method** & **Test Time** & \(\sigma_{RMS}\) & \(\sigma_{MAX}\) & \(E[\mathbf{0}]\) & \(E[P]\) & \(\gamma_{2}\) & \(T_{cal}\) & \(D\) \\  & **(Hours)** & (**MPa**) & (**MPa**) & (**Hz**) & (**Hz**) & (\(-\)) & **(Hours)** & (\(-\)) \\ \hline Dirlik & 50 & 43.44 & 217.2 & 8.65 & 9.44 & 0.92 & 2.41 \(\times\) 10\({}^{3}\) & 0.0207 \\ Tovo–Benasciutti & 50 & 43.44 & 217.2 & 8.65 & 9.44 & 0.92 & 2.49 \(\times\) 10\({}^{3}\) & 0.0201 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Vibration fatigue results for notch region.  
In each reference point, RMS stress was calculated and are finally compared with FEM results in Table 4.  
The above comparison of RMS stresses shows that the FEM model results deviate by an average of \(+/-37\%\) from laboratory test values. Despite differences in absolute stress values, the proposed equivalent effective acceleration method follows the trend observed in real measurements, indicating that the FEM model captured the general behavior and stress distribution in the system. Another important aspect is that, although the differences between the FEM results and the experimental data are noticeable, all these differences are of the same order of magnitude for stresses. This is a significant achievement, considering the high complexity of the system and the loading conditions. This makes the method suitable for finding critical regions and preliminary fatigue calculations of new compressor suspension prototypes and provides a solid basis for further development.  
Although the goal in this case was to create a simple FEM model for easy control and adjustment, the compressor suspension FEM model is still quite complex. Therefore, factors like contact definition, mass distribution and boundary conditions affect the accuracy of the results. The current model assumes that the compressor only vibrates vertically at a single frequency. In reality, it also rotates slightly and vibrates at several frequencies within the testing range. The differences between the FEM and experimental results may be due to the exclusion of transverse stiffness in the isolator definition. Another important factor could be the lack of Cross-PSD analysis at all collision points, as the current study focuses only on one isolator position. Future research should explore how the vibrations at all collision regions interact with each other. Considering this aspect in future studies could improve the results.  
\begin{table}
\begin{tabular}{l c c c} \hline \hline \multicolumn{4}{c}{**Equivalent Stress \(\sigma_{\text{RMS}}\); Input RMS 0.9 g**} \\ \hline \multirow{2}{*}{**Point ID**} & **FEM** & **Test** & **Ratio** \\  & **(MPa)** & **(MPa)** & **FEM/Test** \\ \hline A & 22.7 & 13.7 & 1.66 \\ B & 15.8 & 11.8 & 1.34 \\ C & 7 & 9.9 & 0.71 \\ D & 4.9 & 7.2 & 0.68 \\ E & 3.2 & 6.1 & 0.52 \\ F & 9.5 & 10.9 & 0.87 \\ Notch & 42.8 & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 4: Equivalent RMS stress comparison between FEM and measurements.  
Figure 13: Normal and shear stresses in measurement point A: (**a**) Stress time history; (**b**) Stress PSD.