## Nomenclature
\begin{tabular}{l l} \(f_{\rm i}\) & groove curvature coefficients of inner raceway \\ \(I\) & mass moment of inertia, kg\(\cdot\)mm\({}^{2}\) \\ \(\rho\) & density, kg/m\({}^{3}\) \\ \(m\) & ball mass, kg \\ \(N\) & number of beam elements \\ \(Z\) & number of balls \\ \(\gamma_{\rm e}\) & \(D\cos\alpha_{\rm e}/d_{\rm m}\) \\ \(\gamma_{\rm i}\) & \(D\cos\alpha_{\rm i}/d_{\rm m}\) \\ \(\gamma^{\prime}\) & \(D/d_{\rm m}\) \\ \(\gamma\) & \(D\cos\alpha_{\rm i}/d_{\rm m}\) \\ \(\alpha_{\rm 0}\) & initial contact angle, rad \\ \(\alpha_{\rm e}\) & contact angle at ball-outer raceway contact, rad \\ \(\alpha_{\rm i}\) & contact angle at ball-inner raceway contact, rad \\ \(\beta\) & ball pitch angle, rad \\ \(\omega_{\rm i}\) & angular speed of inner ring/shaft around the bearing axis, rad/s \\ \(\omega_{\rm c}\) & ball orbital speed around the bearing axis, rad/s \\ \(\omega_{\rm b}\) & ball spinning speed around its own axis, rad/s \\ \(M_{\rm be}^{\rm S}\) & friction moment at ball-outer raceway contact due to spinning, N\(\cdot\)mm \\ \(M_{\rm bi}^{\rm S}\) & friction moment at ball-inner raceway contact due to spinning, N\(\cdot\)mm \\ \(L_{\rm 2}(\cdot)\) & second kind of elliptic integral function \\ \(Q_{\rm i}\) & contact force at ball-inner raceway contact, N \\ \(Q_{\rm e}\) & contact force at ball-outer raceway contact, N \\ \(F_{\rm c}\) & ball centrifugal force, N \\ \(M_{\rm g}\) & gyroscopic moment, N\(\cdot\)mm \\ \(F_{\rm i}\) & friction force at ball-inner raceway contact, N \\ \(F_{\rm e}\) & friction force at ball-outer raceway contact, N \\ \(F_{\rm x}\) & bearing force applied on the inner ring of ball bearing along \(x\)-axis of bearing local coordinate system, N \\ \(F_{\rm y}\) & bearing force applied on the inner ring of ball bearing along \(y\)-axis of bearing local coordinate system, N \\ \(F_{\rm z}\) & bearing force applied on the inner ring of ball bearing along \(z\)-axis of bearing local coordinate system, N \\ \(M_{\rm x}\) & moment applied on the inner ring of ball bearing around \(x\)-axis of bearing local coordinate system, N\(\cdot\)mm \\ \(M_{\rm y}\) & moment applied on the inner ring of ball bearing around \(y\)-axis of bearing local coordinate system, N\(\cdot\)mm \\ \(F\) & external load vector applied on the shaft nodes, N \\ \(\mu\) & ball-raceway friction coefficient \\ \(\rm O\) & initial position of ball center \\ \(\rm O^{\prime}\) & final position of ball center \\ \(\rm O_{\rm e}\) & outer raceway groove curvature center \\ \(\rm O_{\rm i}\) & initial position of inner raceway groove curvature center \\ \(\rm O^{\prime}_{\rm i}\) & final position of inner raceway groove curvature center \\ \(X_{\rm 1}\) & axial distance between ball center \(\rm O^{\prime}\) and outer raceway groove curvature center \(\rm O_{\rm e}\), mm \\ \(X_{\rm 2}\) & radial distance between ball center \(\rm O^{\prime}\) and outer raceway groove curvature center \(\rm O_{\rm e}\), mm \\ \(\delta_{\rm x}\) & translational displacement of inner ring along \(x\)-axis of bearing local coordinate system, mm \\ \(\delta_{\rm y}\) & translational displacement of inner ring along \(y\)-axis of bearing local coordinate system, mm \\ \(\delta_{\rm z}\) & translational displacement of inner ring along \(z\)-axis of bearing local coordinate system, mm \\ \(\delta_{\rm x}\) & angular displacement of inner ring around \(x\)-axis of bearing local coordinate system, rad \\ \(\delta_{\rm y}\) & angular displacement of inner ring around \(y\)-axis of bearing local coordinate system, rad \\ \(\delta_{\rm e}\) & ball-outer raceway contact deformation, mm \\ \(\delta_{\rm i}\) & ball-inner raceway contact deformation, mm \\ \(n_{\rm i}\) & rotational speed of inner ring/shaft, rpm \\ \(R_{\rm i}\) & radius of locus of inner raceway groove curvature centers, mm \\ \end{tabular}