## 12 An Example of Validation for the Static Performance of a PGB  
[PERSON] et al. [23] detailed an investigation of the static and dynamic performance of an (in-house constructed) cylindrical PGB. As in the current paper, the authors of [23] built a computational finite difference (FD) model for prediction of performance of simple PGBs and to make pertinent distinctions for operation as purely aerostatic (\(\Omega=0\)), aerodynamic (\(p_{S}=p_{a}\)), and hybrid (\(\Omega>0,p_{S}>p_{a}\)). Authors in [6] also detailed a handful of experimental results for the measurement of applied load vs. journal eccentricity for a PGB with two distinct clearances, small (\(16\)\(\mu\)m) and large (\(31\)\(\mu\)m). Table 3 details the geometry, porous layer physical properties, and the operating conditions of the test PGB in [23]. Note that the reference has many clerical errors including dubious captions in several of the figure captions. In addition, the direct force coefficients presented in [23] follow trends not in accordance with the theory, the direct stiffness not agreeing with one derived from the static load (\(\omega\to 0\)). The work also gives a cursory review of the cross-coupled force coefficients.  
Figure 9 presents comparisons of the current analytical solution and FE model predictions vis-a-vis those in [23], experimental and numerical. As Figure 9a shows, the analytical solution and FE prediction of journal eccentricity (\(e\)) agrees well with the FD prediction [23] for \(p_{S}=4.7\) bar, \(c=31\)\(\mu\)m and three static loads, \(5\) N to \(15\) N. For the top load of \(15\) N, the specific load \(W/(LD)=0.1\) bar; hence \(W/(LD)/(p_{S}-p_{a})=0.029\), i.e., a very small load. The model predictions are slightly larger than the experimental results (ref. [23] does not report uncertainty or variability for the measured parameters nor variability for the force coefficients).  
Figure 8: FE model of PGB load (\(W\)) vs. journal eccentricity ratio (\(e/c\)) at \(0\) rpm and \(25\) krpm shaft speed. Air supply pressure \(p_{S}=2\), \(4\), \(6\), and \(8\) bar; (**a**) Load at \(0\) rpm; (**b**) Load at \(25\) krpm. PGB clearance \(c=0.010\) mm. (Light colored) straight lines represent approximate load capacity derived from the exact solution at \(e=0\).  
Figure 9: Predictions from current models (analytical and FE) compared to experimental results and predictions reported in [23]. (**a**) Journal eccentricity (_e_) vs. static load (_W_); (**b**) eccentricity (_e_) vs. shaft speed (\(\Omega\)); (**c**) eccentricity (_e_) vs. supply pressure (\(p_{S}\)).  
As per the journal eccentricity (\(e\)) vs. shaft speed and a fixed load (\(W\) = 15 N) (see Figure 9b), the current analytical and FE model predictions agree well with the experimental result at the top speed of 24 krmm. For pure aerostatic operation (\(\Omega\) = 0), the current model predictions are \(\sim\)32% smaller than the experimental result. Figure 9c displays eccentricity (\(e\)) vs. supply pressure (\(p_{S}\)) for operation at 24 krmm (\(\Lambda_{\Omega}\) = 0.097 at \(p_{S}\) = 4.7 bar). For \(p_{S}\) = 5.5 and 6.3 bar, the current predictions match the experimental values, the difference \(<\)2%. For \(p_{S}\) = 4.7 bar, the models produce a slightly larger (\(e\)) than the measured one.  
Comparisons of predictions of the experimental force coefficients are omitted. As frequency grows, the test coefficients follow differing paths and have lower physical magnitudes than the model predictions, current and those in [23]. [PERSON] [28] attributes the difference to the absence of a surface restrictive layer in the constructed PGB. [PERSON] et al. [18] explain difference in the performance of PGBs with and without the said restrictive layer. Interestingly enough, the current predictive model as well as that in [23] do not apply to PGBs with restrictive layers.