## 4 Results and Discussion  
The effects of gaseous rarefaction on the static and dynamic characteristics such as pressure distribution, load-carrying capacity as well as dynamic stiffness and damping coefficients with respect to different bearing parameters and perturbation frequencies are compared and analyzed by using the numerical scheme above. To validate the method developed in this paper, the results are compared with [PERSON] et al. [34] based on the first order slip boundary condition. Figure 2 shows the dimensionless steady-state pressure profile along the bearing midplane with different Knudsen numbers, respectively. The geometry parameters of micro gas journal bearing are \(R=2.0\) mm, \(B=0.4\) mm, \(p_{a}=1.033\times 10^{5}\) N/m, \(\Lambda=2.4\) and \(\varepsilon=0.8\). It can be seen that the present numerical results are in good agreement with those of [PERSON] et al. and errors are less than 3%. In the following discussions, the continuum flow model means that the effects of gas rarefaction effects is not considered. Figure 3 demonstrates the effect of Knudsen number on the pressure profiles in the circumferential direction at the bearing mid-plane for different rarefaction models with \(\varepsilon=0.6\), \(\Lambda=4\) and \(B/D=0.3\). The normalized pressure distribution has similar changing tendency along the sliding direction. The gas film pressure decreases significantly as the Knudsen number increases, namely, the pronounced degree of the rarefied gas. It is found that the maximum gas film pressure of FK model is lowest, and the result of Boltzmann model is largest for the \(K_{n}=0.0325\) case. Nevertheless, when \(K_{n}=0.325\), by comparison with Boltzmann model, the first-order slip model overpredicts the dimensionless pressure profile while the second-order slip model underestimates it in the transition regime. The FK model is closer to the Boltzmann model than other rarefaction models. Figures 4 and 5 compare the dimensionless load capacities \(C_{L}\) and attitude angles \(\theta\) of Boltzmann model with eccentricity ratio \(\varepsilon\) for different values of Knudsen number. The \(C_{L}\) is seen to increase with \(\varepsilon\) while the reverse trend is observed for the attitude angle. In comparison with the continuum flow case, the influence of gas rarefaction decrease the load carrying capacity. Therefore, the larger Knudsen number will result in the lower load capacity of microbearing. Figure 2: Comparisons of dimensionless gas film pressure distributions with [PERSON] et al. for different Knudsen numbers. Figure 4: The load capacity of Boltzmann model versus eccentricity ratio for different Knudsen numbers (\(\Lambda=3\), \(B/D=0.5\)). Figure 3: The circumferential fluid film pressure distributions at the mid-plane of microbearings for different Knudsen numbers (\(\varepsilon=0.6\), \(\Lambda=4\), \(B/D=0.3\)). Figure 6 indicates the relationship between the bearing number and non-dimensional load carrying capacity at different Knudsen numbers for \(\varepsilon=0.6\) and \(B/D=1.4\). It is noted that the load capacities obtained from all models increase when the bearing number \(\Lambda\) increases, whereas the magnitude of \(C_{L}\) decreases dramatically with the increase of Knudsen number. The results with and without considering rarefied gas lubrication are approximately the same when \(K_{n}\) is equal to 0.0054. This is because the characteristic length scale of gas flow is less than 0.01 which the continuum hypothesis remains valid. As \(K_{n}\) increases to 0.0325 in the slip regime, the dimensionless load capacities of different modified models lie below that of the continuum model with nonslip boundary condition. The reason is that the gas flow is less restricted with the increasing slip velocity. Furthermore, the prediction of load carrying capacity for FK model is the smallest and for Boltzmann model is the largest. The curves of first-order and second-order slip model are situated between them.