## 13 Conclusions
### Nomenclature  
\begin{tabular}{l l} \(c\) & Bearing radial clearance (m) \\ \(c_{x}\) & (12 \(\kappa\)\(t_{p}\))\({}^{1/3}\). Equivalent clearance for layer of porous material (m) \\ \(C_{\mathit{eff}}\) & \(C_{\mathit{eff}}=(C_{XX}-K_{XY}/\omega)\). Effective damping coefficient (N-s/m) \\ \(C_{XX}\), \(C_{YY}\) & Direct damping coefficients (N-s/m) \\ \(C_{XY}\), \(C_{YX}\) & Cross-coupled damping coefficients (N-s/m) \\ \(D\) & 2\(R\). Rotor diameter (m) \\ \(e\) & Journal eccentricity (m) \\ \((e_{X},e_{Y})\) & Components of journal eccentricity (m), \(e=\sqrt{e_{X}^{2}+e_{Y}{}^{2}}\) \\ \((F_{X},F_{Y})\) & Bearing reaction force components along \(X\) and \(Y\) directions (N) \\ \(H_{e}\) & Equivalent complex stiffness at threshold speed of instability (N/m) \\ \(H_{XX}\), \(H_{YY}\) & Direct complex stiffness coefficients (N/m) \\ \(H_{XY}\), \(H_{YX}\) & Cross coupled complex stiffness coefficients (N/m) \\ \(h\) & Film thickness (m) \\ \(K_{S}\) & PGB aerostatic (zero frequency) stiffness coefficient (N/m) \\ \(K_{\mathit{eff}}\) & \(K_{\mathit{eff}}=K_{XX}+C_{XY}\cdot\omega\). Effective stiffness coefficient (N/m) \\ \(K_{\Omega}\) & \(\sqrt{K_{XX}^{2}+K_{XY}^{2}}\). PGB hybrid (zero frequency) stiffness coefficient (N/m) \\ \(K_{XX}\), \(K_{YY}\) & Direct stiffness coefficients (MN/m) \\ \(K_{XX}\), \(K_{YX}\) & Cross-coupled stiffness coefficients (MN/m) \\ \(L\) & Bearing axial length (m) \\ \(M_{r}\) & Mass of point rotor (kg) \\ \(M_{cr}\) & \(M_{cr}=K_{\mathit{eff}}/\omega^{2}\). Rotor critical mass (kg) \\ \(\dot{M}\) & Mass flow rate through a porous gas bearing (kg/s) \\ \(\dot{M}_{\max}\) & Maximum mass flow rate for a porous gas bearing as \(c\rightarrow\infty\) (kg/s) \\ \(p\) & Absolute pressure (bar) \\ \(p_{S}\), \(p_{a}\) & Supply and ambient absolute pressures (bar) \\ \(R_{g}\) & Gas constant (J/(kg K)) \\ \(T\) & Supply/ambient temperature (K) \\ \(T_{o}\) & Drag torque (Nm). Power loss = (\(T_{o}\)\(\Omega\)) \\ \(t_{p}\) & Porous layer radial thickness (m) \\ \(W\) & Applied load (N) \\ \(W^{*}\) & (\((p_{S}-p_{a})\)\(L\)). Nominal load for aerostatic operation \\ \(x=R\theta\), \(z\) & Coordinate system on bearing surface \\ \(X\), \(Y\) & Cartesian coordinate system \\ \(\beta\) & Attitude angle (deg) \\ \(\Lambda_{x}=\gamma^{2}\) & \(\frac{3}{\kappa}\frac{x}{r_{o}^{2}}\left(\frac{D}{c}\right)^{2}\). PGB feed flow parameter \\ \(\Lambda_{\Omega}\) & \(6\frac{\pi\Gamma}{p_{S}}\left(\frac{R}{c}\right)^{2}\). PGB speed number, \(\overline{\Lambda}_{\Omega}=\Lambda_{\Omega}\left(\frac{p_{S}}{P_{0}}\right)\) \\ \(\Lambda_{\omega}\) & \(12\frac{\mu}{p_{S}}\left(\frac{R}{c}\right)^{2}\). PGB frequency number. \(\overline{\Lambda}_{\omega}=\Lambda_{\omega}\left(\frac{p_{S}}{P_{0}}\right)\) \\ \(\kappa\) & Permeability coefficient for the porous material (m\({}^{2}\)) \\ \(\mu\) & Gas absolute viscosity (Pa-s) \\ \(\rho\) & \(p/(R_{g}T)\). Gas density (kg/m\({}^{3}\)) \\ \(\theta\) & Circumferential coordinate (-) \\ \(\omega\) & Whirl frequency (rad/s) \\ \(\omega\) & =\(\omega_{n}=\
icefrac{{1}}{{2}}\)\(\Omega_{T}\). Whirl frequency = natural frequency at threshold speed of instability (rad/s) \\ \(\Omega\) & Rotor speed (rad/s) \\ \(\Omega_{T}\) & Threshold speed of rotor stability (rad/s) \\
**Abbreviations** & \\ FE & Finite element \\ FD & Finite difference \\ LPM & Liter per minute \\ MOS & Mean operating speed \\ PGB & Porous gas bearing \\ SSV & Subsynchronous whirl vibration \\ \end{tabular}