# Effect of the Lubrication Parameters on the Ceramic Ball Bearing Vibration in Starved Conditions
## 5 Conclusions
### Nomenclature \begin{tabular}{l l} \(a\) & The long half axis of the ellipse \\ \(b\) & The short half axis of the ellipse \\ \(D\) & The normal ball diameter \\ \(d\) & The pitch diameter of the bearing \\ e & The constant of nature \\ \(E\) & Equivalent elastic modulus \\ \(E_{1}\), \(E_{2}\) & Elastic moduli of the two contact materials \\ \(F_{x,r}\), \(F_{y,r}\), \(F_{z}\) & Components externally applied forces of X, Y, and Z directions \\ \(F_{\rm R\phi j}\), \(F_{\rm R\eta ej}\), \(F_{\rm R\eta ej}\), \(F_{\rm R\xi j}\), \(F_{\rm R\xi ej}\) & Hydrodynamic frictional forces at the inlet zone \\ \(F_{\rm\eta j}\), \(F_{\rm\tau j}\) & Inertial force component of the ball \\ \(F_{\rm Dj}\) & Aerodynamic resistance acting on the ball by the gas-oil mixture; \\ \(f_{x,r}\), \(f_{y}\) & The natural frequency of bearing vibration in axial and radial directions \\ \(G\) & Material parameter \\ \(G_{\rm\eta j}\), \(G_{\rm zj}\) & Components of the ball's inertia moment of \(y_{\rm bj}\) and \(z_{\rm bj}\) directions \\ \(h_{b}\) & The oil film thickness at the lubrication inlet \\ \(H_{\rm c}\) & A dimensionless central oil film thickness \\ \(h_{\rm c}\) & The central oil film thickness \\ \(h_{\rm min}\) & The minimum oil film thickness \\ \(h_{\rm c1}\) & The actual central oil film thickness \\ \(I_{\rm bj}\) & Moments of inertia of the \(j\)th ball \\ \(I_{\rm ix}\), \(I_{\rm iy}\), \(I_{\rm iz}\) & The principal moments of inertia of the inner ring in the inertial coordinate system \\ \(J_{x,r}\), \(J_{y,r}\) & Components of the ball's moment of inertia of \(x_{\rm bj}\), \(y_{\rm bj}\), and \(z_{\rm bj}\) directions \\ \(j\) & The \(j\)th ball \\ \(K_{\rm oil}\) & The oil film stiffness between the ball and the raceway \\ \(K_{\rm c}\) & The contact stiffness \\ \(K\) & The contact coefficient between the ball and the raceway \\ \(K_{\rm r\eta j}\) & The radial component of the comprehensive stiffness between the \(j\)th ball and the inner ring \\ \(K_{\rm oil}\) & The axial component of the comprehensive stiffness between the \(j\)th ball and the inner ring \\ \(K_{\rm aij}\) & inner ring \\ \(K_{\rm a\eta j}\) & The axial component of the comprehensive stiffness between the \(j\)th ball and the outer ring \\ \(K_{\rm a\eta j}\) & Outer ring \\ \(K_{\rm r\eta j}\) & The radial component of the comprehensive stiffness between the \(j\)th ball and the inner ring \\ \((K_{\rm oil})_{\rm j}\) & Outer ring \\ \((K_{\rm oil})_{\rm j}\) & The oil film stiffness of the \(j\)th ball and the inner ring \\ \((K_{\rm oil})_{\rm ej}\) & The oil film stiffness of the \(j\)th ball and the outer ring \\ \((K_{\rm c})_{\rm ij}\) & The contact stiffness between the \(j\)th ball and the inner ring \\ \((K_{\rm c})_{\rm ej}\) & The contact stiffness between the \(j\)th ball and the outer ring \\ \(K_{\rm a}\) & Axial stiffness \\ \(K_{\rm r}\) & Radial stiffness \\ \(k\) & Ellipticity \\ \(L\) & The dimensionless distance between the inlet and the Hertz contact center \\ \(L^{\star}\) & The boundary between fully flooded and starved \\ \(M_{y}\), \(M_{z}\) & Externally applied torques \\ \(m_{\rm i}\) & Mass of the inner ring \\ \(m_{\rm b}\) & Mass of the ball \\ \(M\) & Mass of the bearing system \\ \([\)O; X, Y, \(Z]\) & The inertial coordinate system of the bearing \\ \([\)O; X\({}_{i}\), \(Y_{i}\), \(Z_{i}]\) & The inner ring coordinate system of the bearing \\ \([\)O\({}_{\rm bj}\); X\({}_{\rm bj}\), \(Y_{\rm bj}\), \(Z_{\rm bj}]\) & The coordinate system of the \(j\)th ball \\ \(P_{\rm R\eta j}\), \(P_{\rm R\xi j}\) & Rolling frictional forces acting on the ball's surface \\ \(P_{\rm S\eta j}\), \(P_{\rm S\xi j}\) & Sliding frictional forces acting on the ball's surface \\ \end{tabular}