## 1 Introduction
[24] adopted the finite volume method and atomic force microscope data to study the random surface roughness effect on the flow characteristics in gas microbearing. The calculations showed that the larger roughness exponent causes the bigger variation of the gas slip velocity at the bottom wall. [PERSON] et al. [25] derived an extended slip velocity boundary condition, treating the slip coefficients as functions of wall accommodation coefficient and Knudsen number through the regularized 13 moment equations. The work showed that the solution of improved Reynolds equation has more accurate prediction of pressure distribution in the near transition flow regime. The effects of rarefaction and manufacturing defects on the linear and nonlinear bearing performances of micro flexure pivot tilting pad gas bearings were studied by [PERSON] et al. [26], they emphasized the importance of pad preload on the dynamic characteristics of power MEMS. [PERSON] et al. [27] used the Greenwood-Williamson model and modified Reynolds equation to calculate the bearing force and asperity contact force, their studies concerned gas spiral groove thrust microbearing with different groove depth and standard deviation of asperity height. Research into the lubrication performance of textured journal bearings was stimulated by [PERSON] et al. [28] who concluded that the concave spherical texture decreases the load capacity while the convex texture increases it. [PERSON] and [PERSON] [29] analyzed the stability characteristics of gas bearing-soft rotor system by two way coupled fluid structure interaction and derived the stiffness coefficients with the influence coefficients and harmonic excitation methods. They remarked that the stabilities of herringbone groove gas bearing and the plain gas bearing enhance as the bearing capacity increases. [PERSON] et al. [30] numerically and experimentally studied the characteristics of hybrid bearings including friction between silicon nitride and bearing steel by molecular dynamics methods. They showed that the effect of graphene on the lubrication of friction pair becomes greater when the pressure and shear velocity increases. However, probably due to the irregular oscillation and the drawback of poor convergence easily appeared in the finite difference methods for the dynamic analysis, a relatively small number of papers have focused on the dynamic behaviors of microbearings in the open literature. In addition, understanding the flow dynamics of rarefied gas flow is essential for the design of micro gas bearing and the improvement of its characteristics is important to guarantee the stability of micro-rotating machinery. Therefore,a proper method with less complexity is necessary. Systematic investigations on the stiffness and damping coefficients of gas journal microbearings should be undertaken. In this paper, the partial derivative method and iteration technique are applied to solve the modified Reynolds equations with different Poiseuille flow correctors, and the static and dynamic characteristics of micro gas journal bearings such as gas pressure distributions, dimensionless load capacity, friction coefficient and dynamic stiffness and damping coefficients are obtained for various Knudsen numbers. This work maybe provides new perspectives in understanding the dynamic properties of aerodynamic journal microbearings, which lays a foundation for the further stability of microbearing-rotor systems.