## 3 Verification of Mode Properties of a Dual-Rotor  
### Dual-Rotor Rotordynamic Test Rig  
Prior to the rotordynamic test, the natural frequency and mode shape properties of the dual-rotor rotodynamic test rig were considered. In the case of a single-rotor system supported by gas bearings, the first two eigenmodes occur in the rigid-body modes, the cylinder and the conical mode, so that the system is rarely dangerous due to excessive vibration. However, in the case of a dual-rotor system, since the first two eigenmodes occur as a bending mode of the coupling, excessive vibration may break the coupling and cause the rotor to disengage. Therefore, in the dual-rotor system, it is essential to understand the natural mode characteristics of the system in advance before rotordynamic tests.  
Figure 5 shows a dual-rotor rotodynamic test rig. The test rig consists of a high-speed motor and a test rotor powered by the electric motor. The motor is a 13-kW permanent-magnet type that can run up to 100 krpm [9]. The motor rotor and the test rotor are connected by a beam-type coupling for power transfer.  
Figure 4: Measured static load versus displacement during consecutive static loading–unloading process for GFB and GFPB.  
Figure 3: Static load–deflection test setup: (**a**) photograph of test environment, and (**b**) schematic view of the test.  
The motor rotor is supported by two journal GFBs, with a diameter of 40 mm, length of 237.5 mm, and mass of 2.0 kg. The detailed motor rotor dimensions and inertial information are described in [9]. The test rotor is supported by two journal GFBs or GFPBs, which can be replaced by bearings depending on the test conditions. The test rotor is made of high-temperature material, Inconel 718, in the form of a hollow shaft. Its diameter and length are 40 and 245 mm, respectively, and its mass is 1.338 kg. Information on the rotors and couplings is presented in Table 2. Meanwhile, the rotordynamic performance of the dual rotor system with controlled imbalances was evaluated in Appendix A in detail.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Part** & **Parameters** & **Values** \\ \hline \multirow{4}{*}{Test rotor} & Diameter & 40.00 mm \\  & Length & 245 mm \\  & Mass & 1.338 kg \\  & Material & Inconel718 \\  & Moment of inertia (polar, transverse) & 0.35 g-m\({}^{2}\), 6.39 g-m\({}^{2}\) \\ \hline \multirow{4}{*}{Motor rotor} & Diameter & 40.00 mm \\  & Length & 237.5 mm \\  & Mass & 2.0 kg \\ \hline \multirow{4}{*}{Coupling} & Beam diameter & 3.00 mm \\  & Beam length & 70.00 mm \\  & Mass & 38.7 \(\times\) 10\({}^{3}\) kg \\  & Moment of inertia (polar, transverse) & 4.45 \(\times\) 10\({}^{-3}\) g-m\({}^{2}\), 6.82 \(\times\) 10\({}^{-2}\) g-m\({}^{2}\) \\  & Material & Titanium alloy \\  & Lateral stiffness & 1.47 \(\times\) 10\({}^{-4}\) N/m \\ \hline Test bearings & Geometric clearance & 150 \(\mu\)m (adjusted with shim) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Design parameters of the dual-rotor rotordynamic test rig.  
Figure 5: Dual-rotor rotordynamic test rig: (**a**) schematic view of the test rig and sensor locations, and (**b**) photographs of the test rig, rotors, and a coupling.  
Figure 6 shows the natural frequency test environment for a dual rotor. The dual rotor was made in a free-free condition with a string. An accelerometer was attached to the drive end (DE) side of the test rotor to measure the vibration response of the rotor. The impact force applied on the rotor was measured using an impact hammer. The frequency response function was calculated at all rotor positions by repeated measurements, as the points were shifted.