# Design of a Spin Test System for Burst Phenomen Considering Nonlinear Rotordynamic Effects
## 3 Results  
In this section of this study, the results from finite element analysis, Simulink, and impact tests are presented. The finite element analysis results are provided for both general axisymmetric (in other words, the 2D model) and 3D approaches. Detailed comparisons of these results are shown in Table 3 for the 10 kg test specimen. Additionally, the results from the finite element modal analysis, conducted using the general axisymmetric approach with varying numbers of node planes, are presented in Table 4. The modal analysis identified natural frequencies at 234 Hz and 528 Hz for the 10 kg test specimen. These frequency values were obtained from both the general axisymmetric and 3D modal analyses. Additionally, for the 10 kg test specimen, the maximum discrepancy between the finite element analysis results and the Simulink results was found to be 4.2% at the first natural frequency of 232 Hz. The difference was calculated to be 0.73% in the 532 Hz region, where the second natural frequency occurs. The general axisymmetric and 3D analysis results are illustrated in Figure 11.  
The defined material properties were used as input data for the analysis model. Contact loads arising from interference fit, bolt pretensions, and angular velocity were applied as boundary conditions for the 3D structural simulations. The Von Mises stress distribution for the shaft is shown in Figure 13 for a 10 kg test specimen. Based on the stress distribution, the maximum equivalent stress was calculated to be 374.39 MPa. This value is below the yield limit, indicating that no plastic deformation is expected to occur in the shaft. The stress distribution calculated from the structural analysis, using 31,920 rpm (equivalent to 532 Hz) as input data for a 10 kg test specimen, is shown in Figure 13. However, the alternating stresses resulting from the critical speed that would occur if the shaft operated at 532 Hz were calculated using harmonic analysis. When applying a damping coefficient of 0.5%, as determined from local impact tests, the maximum alternating stress is found to be 64.87 MPa. In contrast, applying a damping ratio of 2.8%, obtained from the hammer test conducted on the assembly, results in a maximum alternating stress of 11.54 MPa. Both the maximum equivalent stress from the structural analysis and the maximum alternating stress from the harmonic analysis affect the same section of the shaft. Therefore, a high cycle fatigue evaluation was performed for this region, and the material yield limit was not exceeded even when the lowest damping ratio was applied. Alternating stress evaluation was conducted based on the damping ratios for the region where the maximum equivalent stress (Von Mises Stress) was calculated. The stress distribution and the alternating stress graph obtained from the 3D harmonic analysis are presented in Figure 14 for a 10 kg test specimen. The alternating stress graphs, generated using damping ratios of 0.5% and 2.8% in the harmonic analysis, are shown in Figure 15. In  
Figure 13: Stress distribution of 3D analysis model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**General Axisymmetric** & **Element** & **Node** & **1 st Natural** & **2 nd Natural** & **3 rd Natural** & **Solution** \\
**Mesh Element Size [mm]** & **Number** & **Number** & **Frequency** & **Frequency** & **Frequency** & **Time** \\ \hline
0.5 & 31,011 & 374,760 & 239.32 Hz & 446.41 Hz & 641.62 Hz & 1 h 30 m \\
1 & 7688 & 93,714 & 240.08 Hz & 447 Hz & 643.27 Hz & 15 m 6 s \\
2 & 2016 & 24,948 & 241.08 Hz & 448.48 Hz & 646.79 Hz & 2 m 12 s \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Natural frequencies according to mesh element size for general axisymmetric analysis [4 kg test specimen]. these calculations, the force applied to the rotor, which underwent a G6.3 balancing process according to the standard [34], was determined to be 404 N.  
Based on the layout created according to the Matlab Simulink model, finite element and testing studies were also carried out for a test specimen with a mass of 4 kg.