## 4 Results and Discussion
With the continuous increase of \(K_{n}\), the dimensionless load capacity shows a linearly increasing trend when the bearing number becomes larger. In the meantime, the result of FK model is coincident with that of Boltzmann model, while the first-order slip model overestimates and the second-order slip model underpredicts in comparison with the Boltzmann model. Figure 5: The attitude angle of Boltzmann model versus eccentricity ratio for different Knudsen numbers (\(\Lambda=3\), \(B/D=0.5\)). Figure 6: _Cont._  
The influence of aspect ratio and Knudsen number on load capacity and friction coefficient of [PERSON] model are shown in Figures 7 and 8 for \(\varepsilon=0.6\) and \(\Lambda=5\). As the value of aspect ratio increases, it is noted that both the load capacity and friction coefficient increase. The \(C_{L}\) firstly increases and then subsequently asymptote to a constant value for a small Knudsen number regime. When the Knudsen number is further increased, the load capacity and friction coefficient are nearly proportional to the aspect ratio, and it causes a slight change in dimensionless load capacity at nanometer scale. This is because the lower clearance may weaken the shear stress of the rarefied gas flow and the extent of the flow in the sliding direction is quickly decreased. Figure 6: Relationship between the dimensionless load capacity and the bearing number for different gas rarefaction models (\(\varepsilon=0.6\), \(B/D=1.4\)). (**a**) \(K_{n}=0.0054\); (**b**) \(K_{n}=0.0325\); (**c**) \(K_{n}=0.65\); (**d**) \(K_{n}=2.1667\). Figure 7: Non-dimensional load carrying capacity of Boltzmann model vs. aspect ratio for different Knudsen numbers (\(\Lambda=5\), \(\varepsilon=0.6\)). Figures 9 and 10 present the variations of the dynamic stiffness and damping coefficients of different correction models with perturbation frequency for \(\varepsilon=0.5\), \(B/D=0.8\) and \(\Lambda=3\) when \(K_{n}=0.65\). It is seen that the perturbation frequency has great influence on the dynamic coefficients. As the perturbation frequency increases, the dynamic stiffness and damping coefficients \(K_{xx}\), \(K_{xy}\), \(K_{yy}\) and \(D_{yx}\) increase. The increasing extent of \(K_{yy}\) is bigger than \(K_{xx}\) because of the gas film mainly supports the weight of high-speed rotor along the vertical direction, while \(K_{yx}\), \(D_{xx}\), \(D_{xy}\) and \(D_{yy}\) decrease quickly. With gas rarefaction effects taken into account, the direct stiffness coefficients \(K_{xx}\) and \(K_{yy}\) are linearly proportional to the perturbation frequency, but the direct terms of the damping coefficients \(D_{xx}\) and \(D_{yy}\) decrease slightly with the rise of frequency. Meanwhile, the cross coupled stiffness coefficients \(K_{xy}\) and \(K_{yx}\) gradually approach to the constant values with increasing \(\Omega\), yet the \(D_{xy}\) and \(D_{yx}\) are hardly affected by perturbation frequency. The dynamic stiffness coefficients for rarefaction models are less than those of continuum flow. When \(\Omega>2.0\), the direct damping coefficients with the effects of gas rarefaction are higher than those of continuum flow. The reason might be that the energy transport by gas molecule collision is less, to some extent, which gives a larger value of fluid film stiffness and a larger gas film damping coefficient. The first-order slip model overestimates the stiffness coefficients of micro gas journal bearing compared with the simulation results of Boltzmann model, while the second-order velocity slip model underestimates it. Because the FK model is obtained based on the linearized Boltzmann equation, its results are in good agreement with those of the Boltzmann model. Figure 8: Friction coefficient of Boltzmann model vs. aspect ratio for different Knudsen numbers (\(\Lambda=5\), \(\varepsilon=0.6\)). Figure 10: _Cont_. Figure 9: Effect of perturbation frequency \(\Omega\) on dynamic stiffness coefficients of gas microbearings.