## 5 Conclusions  
In this study, TPJB design parameters such as the pivot radius, pad preload, pivot offset, and L/D ratio were selected and their effects on the pad-pivot friction-induced rotordynamic instability and the associated bifurcations were studied. Numerical techniques such as Poincare sections were employed for rotor spin speed ranges (bifurcation diagram) accumulated with regard to the TPJB design parameters. The primary observations from this numerical study are summarized as follows:  
Pivot radius:  
* An increase in the pivot radius induces higher vibration amplitude;
* The Hopf bifurcation event was marginally delayed;
* The higher disc mass eccentricity condition undermined the effect of the pivot radius.  
Pad preload:* An increase in the pad preload significantly delayed the outbreaks of Hopf bifurcation points;
* The amplitude of the response remained relatively constant;
* In the larger disc unbalance condition, the preload stabilized the instability.  
Pivot offset:  
* An increase of the pivot offset delayed the outbreaks of Hopf bifurcation points;
* The amplitude of the response decreased;
* The larger disc mass unbalance undermines the effect of pivot offset.  
L/D ratio:  
* A higher L/D ratio tended to stabilize the response; however, it did not display any conspicuous effect. Nevertheless, the fully balanced condition was clearly observed;
* An increase in the disc mass eccentricity undermined the effect of the L/D ratio;
* Nonetheless, a higher L/D ratio led to an enhanced damping effect, which stabilized the quasi-periodic to the 1/2 sub-synchronous responses.  
The pad preload and pivot offset play significant roles in decreasing the rotordynamic instability induced by the pad-pivot friction effects. Accurate selection of pad design parameters is essential, especially for high-speed, high-unbalance operation environments in rotor-TPJB systems. These conclusions serve a general purpose. However, they do not essentially hold true for all turbomachineries.  
Conceptualization, S.K. and J.S.; methodology, S.K.; software, S.K.; validation, S.K., S.B. and J.S.; formal analysis, S.K.; investigation, S.K. and S.B.; resources, S.K. and J.S.; data curation, S.K. and S.B.; writing--original draft preparation, S.K.; writing--review and editing, S.K. and J.S.; visualization, S.K.; supervision, J.S.; project administration, S.K. and J.S.; funding acquisition, S.K. and J.S. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the National Research Foundation of Korea (Project no. 2017R1C1B507655014, 2020R1F1A107197611).  
The authors declare no conflict of interest.  
The majority of symbols and notations used throughout the paper are defined below for quick reference. Others are clarified with their appearance in case of need.  
\(C_{\text{b}}\): Bearing clearance  
\(C_{\text{p}}\): Pad clearance  
\(D\): Bearing diameter  
\(F_{\text{f}}\): Counter force according to surface friction state  
\(h\): Film thickness  
\(I_{p}\): Pad moment of inertia  
\(L\): Bearing length  
\(m_{j}\): Rotor mass  
\(m_{\text{p}}\): Pad preload  
\(M_{f}\): Friction moment  
\(M_{p}\): Pad tilting moment  
\(p\): Hydrodynamic pressure of lubricant film  
\(R\): Bearing radius  
\(R_{\text{pvt}}\): Pivot radius  
\(W_{\text{pad}}\): Normal force on pad  
\(W_{\text{s}}\): Static load on rotor  
\(W_{\text{d}}\): Dynamic load on rotor  
\(z\): Axial position of bearing