## 7 Conclusions  
This paper proposes a novel concept of the bump-type GFB with the ability to control bearing preloads and piezoelectric preloads in real time for stabilizing rotordynamic instability. The bearing has three PZT actuators located in the circumferential direction and connected to the bearing housing at \(60^{\circ}\), \(180^{\circ}\), and \(300^{\circ}\). Hydrodynamic wedge effects can be obtained by adjusting the driving voltages of the PZT actuators. An equivalent spring model of the PZT actuators and foil structures is introduced to predict the piezoelectric preloads of C-GFBs. The model is based on a constitutive equation of PZT stacks and stiffness mechanism of the PZT actuator and the bump foil. Structural characterization aids in identifying the unknown parameters of the mechanical and piezoelectric properties of PZT actuators, \(k_{p}\), \(D_{33,1}\), and \(D_{33,2}\). The first-order curve fitting is used to estimate the nonlinear PZT stack displacement; \(\delta_{3}=-0.0028V_{3}^{2}+0.9122V_{3}\) with \(R^{2}=0.9926\). The static performance analyses are carried out for the C-GFB with driving voltages of 0, 50, 100, and 150 V, and the results are compared with the shimmed GFBs. The analysis result indicates that the high driving voltage generates large peaks in the gas-film pressure, showing a favorable indication in terms of the stabilization of the performance. However, the reduction in the piezoelectric preloads, especially at the loaded region \(\theta=180^{\circ}\), is caused by the peak gas-film pressure at the preload locations, which is a significant discrepancy between the C-GFB and traditional shimmed GFBs during operation, in terms of the generation of preload. It turns out that the PZT stack stiffness should be carefully designed to maximize the piezoelectric preload effects of C-GFBs. The nonlinear orbit simulation with real-time preload control is performed during the speed-up process from 3 to 90 krpm. Note that real-time control is the exceptional capability of the C-GFB that distinguishes it from conventional GFBs. The real-time control at 32.6 krpm stabilizes the growing oil whip immediately. In particular, a high voltage damps the oil whip relatively rapidly and alters the journal equilibrium position close to the bearing center. Consequently, the piezoelectric-preload control alters static and dynamic characteristics of gas film by changing the voltage in real time, implying that the control can be used to shift the oil whip by certain degrees to prevent additional resonance of the other components of the system that may be affected by rotor vibration as well as delaying the onset speed of the oil whip. We expect that C-GFBs are highly effective lubrication elements suitable for several applications, in that they can adjust bearing configurations in real time according to varied system requirements and conditions by controlling the driving voltage of PZT actuators. Figure 15: Filtered subsynchronous amplitudes of journal vertical motions (oil whip) during the speed-up process. **Author Contributions:** Conceptualization, K.S. ; methodology, J.P.; model development, J.P.; experimental parameter identification, J.P. and D.K. ; formal analysis, J.P.; model prediction, J.P.; writing--original draft preparation, J.P. and D.K. ; writing--review, K.S. ; visualization, J.P.; supervision, K.S. ; project administration, K.S. ; funding acquisition, K.S. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. 2018201010633B). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Not applicable. **Conflicts of Interest:** The authors declare no conflict of interest. **Abbreviations**