# Probabilistic Sensitivity Analysis of Wear Property for MEMS Gas Bearing
## 1 Introduction  
The smoothness of a bearing's inner wall directly affects its static and dynamic characteristics, which results in a deviation of the actual working point from the designed operating state. It is of great importance to study the sensitivity of gas bearing performance to the smoothness of the wall to ensure its safe and stable operation. The manufacturing deviation and wear of a bearing in the manufacturing process will lead to a change in the surface morphology of the bearing's inner wall. For micro gas bearing, because the designed size of the bearing is very small, the slight change of the surface structure leads to an obvious change of the gas film morphology. Further, this change may have an obvious influence on the characteristics of the bearing [1]. As a typical micro gas bearing, MEMS (Micro-Electro-Mechanical System) gas bearing is one of the core components of the micro power electromechanical system (power MEMS). Due to its small size, high precision, and fast speed, it is widely used in various precision applications. The study by [PERSON] et al. [2; 3] comprehensively analyzed the static and dynamic performance of MEMS gas bearing, however did not consider the influence of the rarefaction effect. Previous studies on bearings' rarefaction effect mainly focused on slider bearings [4; 5; 6] and axial thrust bearings [7; 8; 9]. Direct simulation of Monte Carlo (DSMC) based on molecular dynamics was the mainstream method for studying slider bearings of a small size. This method was proposed by [PERSON] [10] and has been verified and extended by many scholars. Some meaningful models for dealing with the rarefaction effect were proposed and applied in the solution of lubricated problems. [PERSON] and [PERSON] [11; 12] unified the continuous flow model with the molecular flow model by using the correlation formula and suggested that the lubrication equation is applicable to arbitrary _Kn_ number. The approximate value of the Poiseuille flow rate at a high _Kn_ number was given. Then, the comparison between the solutionresults of this method and the results of the DSMC method was carried out, and the accuracy of the FK ([PERSON] and [PERSON]) model was verified. This method greatly simplified the calculation cost of the gas bearing performance with the rarefied flow model, which made the large-scale repeated calculation of the micro bearing easier and, furthermore, laid the foundation for the statistical analysis of MEMS gas bearings. [PERSON] et al. (2013) used the FK model to introduce the rarefaction effect and studied the transient characteristics of the bearing in the start-stop state, and then calculated the transient performance of the gas bearing considering the rarefaction effect. [PERSON] et al. (2014) compared the bearing load capacity between the continuous flow model and the rarefied model, and the conclusion indicated that the bearing capacity considering the rarefaction effect was only 90% of that without considering the rarefaction effect. [PERSON] (2015) used the first-order slip-flow model with non-symmetric accommodation coefficients to simulate the rarefaction effect and coupled the surface roughness model with the dynamic analysis of the bearing. His research showed that the decrease of the _Kn_ number enhanced the rarefaction effect. All the above previous studies have shown that the rarefaction effect has a great influence on bearing performance when the radius clearance is small. Wear and roughness of the gas bearing's inner wall directly affect the evenness of the film distribution, which furthermore influences the performance of the bearing, and investigation of wear and roughness properties holds great importance in understanding the change law of static and dynamic characteristics of gas bearings. [PERSON] (2016) conducted numerical studies on wedge bearings with transverse sinusoidal roughness and explored the effect of bearing surface roughness on fluid film.