## 3 Results
### Rotor Dynamic Analysis  
The results of the calculations of the bearing characteristics using XLHydroDynTM are reported for three pad configurations with \(R_{h}=65\) mm. K0 is the reference configuration with no equivalent rotational stiffness; KA is the configuration with \(R_{b}=58\) mm; KB is the configuration with \(R_{b}=64\) mm. In Figure 7, the non-dimensional eccentricity, defined as the journal eccentricity over the bearing radial clearance, is reported.  
Figure 5: Comparison of finite element analysis and analytical formula: (**a**) pivot back radius, \(R_{b}=58\) mm; housing radius \(R_{h}=65\) mm; a uniform pressure of \(1.1\) MPa is applied, which corresponds to a pad normal load \(F_{\xi}=5742\) N; for a \(45\) mm long pad; (**b**) pivot back radius \(R_{b}=64\) mm; housing radius \(R_{h}=65\) mm; a uniform pressure of \(1.0\) MPa is applied, which corresponds to a pad normal load \(F_{\xi}=5760\) N for a \(45\) mm long pad.  
Figure 6: Equivalent von Mises stress for pivot back radius \(R_{b}=64\) mm and housing radius \(R_{h}=65\) mm: (**a**) no moment applied at time step = 10; (**b**) maximum moment applied at time step = 30.  
Figure 7 shows the journal static eccentricity for increasing applied load, with similar incremental eccentricity variations for all the examined configurations. However, while little difference between configurations K0 and KA is observed, a significant difference in the attitude angle can be seen between configurations KA and KB.  
The results of the calculations of the bearing dynamic coefficients are shown in Figures 8-11.  
Figure 7: Bearing static eccentricity as a function of load for the reference configuration K0 (no rotational stiffness), KA (\(R_{b}=58\) mm), and KB (\(R_{b}=64\) mm). The rotating speed is set to 10,000 rpm.  
Figure 8: Bearing direct dynamic coefficients as a function of rotating speed. The specific load is set to 1 MPa.  
Figure 9: Bearing cross-coupled dynamic coefficients as a function of rotating speed. The specific load is set to 1 MPa.  
Figure 8 shows the direct dynamic coefficients as a function of rotating speed for a given load. Their trend with speed is similar for all configurations. They increase with \(K_{rot}\) with a maximum increase at lower speeds of KB with respect to K0 of about 30% for direct stiffness and 10-20% for direct damping.  
Figure 11: Bearing cross-coupled dynamic coefficients as a function of specific load. The rotating speed is set to 10,000 rpm.  
Figure 10: Bearing direct dynamic coefficients as a function of specific load. The rotating speed is set to 10,000 rpm.  
Figure 9 shows the cross-coupled dynamic coefficients as a function of rotating speed for a given load. A much higher sensitivity to the choice of pivot back radius compared to the direct coefficients can be observed, as well as order of magnitude increases and changes of sign, with respect to the reference case.  
Figure 10 shows the direct coefficients as a function of specific load for a given rotating speed. Their trend with load is similar for all configurations. They increase with \(K_{rot}\) with a maximum increase of KB with respect to K0 of less than 30% for direct stiffness at higher loads, and of about 10-15% for direct damping at intermediate loads.  
Figure 11 shows the cross-coupled dynamic coefficients as a function of specific load for a given rotating speed. Their trend with load is similar for all configurations. A much higher sensitivity to the choice of pivot back radius compared to the direct coefficients can be observed as well as order of magnitude increases and changes of sign with respect to the reference case.  
The destabilizing energy [20; 22] acting on the rotor is proportional to \(K_{xy}-K_{yx}\). In the explored range, there was a notable increase in the destabilizing energy with larger rotational stiffness. In configuration K0, the destabilizing energy was negative; in configuration KA, the destabilizing energy was positive; from configuration KA to KB, the increase was approximately fivefold.