## 4 Rotordynamic Test
### Test Result  
Figure 9 shows vertical rotor vibration signals measured when two bearings of the test rotor were supported by the GFB and the GFPB. Subsequently, all measured vibration signals were analyzed only in the vertical direction--the gravity direction. Both bearings showed the first harmonic synchronous components of the rotational speed, while the second harmonic components are negligible, which is known to mainly result from rotor rubbing. This means that the test GFBs and GFPBs have their bearing clearances maintained well during operations. Moreover, it can be inferred that the dual-rotor systems composed of a motor rotor-coupling-test rotor supported on four gas bearings are well aligned. represented by a vector, from which a runout vector is removed, resulting in the extraction of the pure rotor vibration vector. Mathematically, this can be expressed as:  
\[Z_{c}=Z-Z_{o} \tag{3}\]  
where, \(Z_{c}=\delta_{c}e^{-j\phi_{c}}\), \(Z=\delta e^{-j\phi}\), and \(Z_{o}=\delta_{o}e^{-j\phi_{b}}\). Here, \(Z_{c}\) is the vibration with runout removed, \(Z\) is the vibration signal measured at each rotational speed, and \(Z_{o}\) is the runout of the rotor. The runout of the rotor is equivalent to the vibration signal of the measured displacement sensor, rotating the rotor at a low speed with no dynamic rotor vibration effect [23]. The amplitude of the synchronous component is of a similar magnitude to those of the GFB and GFPB, especially at approximately 8.5 k\(\mathrm{r}\mathrm{p}\mathrm{m}\) (\(\sim\)142 Hz), resulting in an amplitude of as much as 30 \(\mathrm{\SIUnitSymbolMicro m}\) because of the critical speed. This is 20% of the bearing clearance of 150 \(\mathrm{\SIUnitSymbolMicro m}\), which is not considered to be a significant level of vibration affecting the system. It can also be inferred that the two bearings do not differ in terms of stiffness near the critical speed (\(\sim\)8.5 k\(\mathrm{r}\mathrm{p}\mathrm{m}\)). This is because the critical speed is determined by the bearing stiffness owing to the characteristics of the rotor-gas bearing system, where the rigid mode of the rotor mainly occurs [21]. However, the phenomenon of  
Figure 10: Filtered synchronous vertical motions measured at DE and NDE sides for GFB and GFPB. Figure 9: Waterfall plots of measured vertical motions during the speed-up and coast-down process. with increasing rotational speed seems to be the effect of vibration as the rotational speed approaches the third-order mode. Figure 11 shows the subsynchronous amplitude and whirl frequency ratio (WFR) of the GFB and GFPB. The WFR is the ratio of the subsynchronous frequency to the rotational speed, which can be considered as a stability indicator. For example, a WFR of 0.2 means that the sub-synchronous motion occurs with the frequency of 20% of the rotational speed; stable operation without subsynchronous instability is possible up to five times the natural frequency of the system. Note that subsynchronous instability is known to be related to the oil-whip phenomenon occurs at a natural frequency of rotor-bearing system [6; 24]. Therefore, a smaller WFR means a higher operating speed without subsynchronous instability given a system natural frequency. The onset subsynchronous speed (OSS) of the GFPB is approximately 53 krpm, which is approximately 9 krpm higher than that of the GFB. Moreover, the amplitude of the GFPB at the same speed is formed lower and is more effectively suppressed in the event of instability. In particular, the instability of the GFPB in the NDE maintains a continuously low amplitude up to 80 krpm. This phenomenon is attributed to the significant improvement in the damping properties of GFPB because of the inserted polymer layer, which effectively attenuates the instability. Meanwhile, the WFR has a GFPB range of 0.07 to 0.12 (average of 0.1) and a GFB of 0.14 to 0.19 (average of 0.17).