# Design of a Spin Test System for Burst Phenomen Considering Nonlinear Rotordynamic Effects
## 2 Materials and Methods
The system used for measuring radial and axial stiffness of bearings is detailed in Figure 2.4 The system includes a 3-axis accelerometer and a thermocouple. The bearings' stiffness, characterized by nonlinear properties, is determined based on elastic displacement  
Figure 2.5 Axial and radial stiffness of bearing. values obtained from different radial and axial loading conditions. The accuracy of these measurements is crucial, requiring minimal error for the successful completion of the application. Therefore, laser displacement sensors have been utilized for the measurements. Finite element analyses of the spin test rig shaft were conducted using both general axisymmetric and 3D approaches. General axisymmetric mesh elements were employed in the general axisymmetric rotordynamics calculations. The mesh element selected was Solid 272, with the number of nodal planes set at 12. The primary advantage of using general axisymmetric rotordynamics analyses is the significantly faster computation compared to three-dimensional analysis. In the section of Results, the detailed information on the mesh number, natural frequencies, and solution times relative to the number of nodal planes will be given. In the general axisymmetric rotordynamics calculations, bolt head elements were modeled using point mass elements, allowing for the effective mass to be incorporated into the system within the general axisymmetric analysis framework. Differences between the 3D and general axisymmetric analysis mass matrices can lead to variations in the calculated natural frequencies. The use of point mass elements helps to mitigate discrepancies between the mass matrix and moment of inertia in both general axisymmetric and 3D analyses. Two-dimensional and three-dimensional finite element rotordynamics analysis models are illustrated in Figure 2.6  
3D analyses were utilized for both stress distribution and alternating stress calculations in the rotating components of the shaft assembly. The primary goal of employing 3D analysis was to accurately capture stress distribution in non-axisymmetric regions with a high degree of convergence. The 3D analysis model, which facilitated these stress  
Figure 2.7 Finite element model of system (**a**) 3D FEM model (**b**) 2D FEM model. Figure 2.8 Bearing Stiffness Test Rig. calculations, is depicted in Figure 9, with the mesh properties of the finite element model detailed in Figure 2.9 In contrast, 2D analyses would exhibit significant error rates in non-axisymmetric areas, thus necessitating the use of 3D models for precise stress calculations. Modal analyses, however, were conducted more efficiently using general axisymmetric models in 2D, which allowed for rapid computation of stiffness and mass matrices. This approach enabled the swift execution of parametric modal analyses, with results compared against other simulations and experimental data. As part of this study, an impact test was employed for the validation of the DM and finite element models. An accelerometer (Bruel & Kjaer Type 4514) is affixed to the rotor disc, and impacts are imparted using a modal hammer (Bruel & Kjaer Type 8206-003) at distinct locations on the rotor disc to effectively average out experimental noise. Subsequently, these signals are transmitted to a laptop via an ADC (Bruel & Kjaer PC Card Front End 3560-L) for the computation of frequency response functions (FRFs). The relevant test setup is shown in Figure 3.0 \begin{table}
\begin{tabular}{l l} \hline \hline
**Element Type** & **Solid 186** \\ \hline Element Number & 420,022 \\ Node Number & 1,300,804 \\ Averaged Aspect Ratio & 1.7672 \\ Averaged Element Quality & 0.85226 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mesh properties of 3D stress model. Figure 10: Experimental test set-up. Figure 9: 3D Finite element model for stress calculations with solid 186 mesh element.