# Probabilistic Sensitivity Analysis of Wear Property for MEMS Gas Bearing
## 3 Results and Discussion  
### Sensitivity Analysis of Axial Wear  
Figure 8 shows the static performance point distribution of the MEMS gas bearing with wear in different axial regions. The horizontal ordinate represents the attitude angle and the vertical ordinate represents the dimensionless load capacity. In each case, the static performances of 50 working conditions were calculated to explore the static performance range of the bearing. The red circle points are the static performance points with rough walls and the blue triangle point is the static performance point with smooth walls. A comprehensive comparison of Figure 8 shows that when the wear is near both ends of the bearing, most of the red points are in the upper left of the blue point. This distribution implies that the probability of attitude angle decrease and load capacity increase is higher. As the axial wear regions move towards the center of the bearing, there are more and more red points that gradually move to the lower right direction of the blue point, which means that the probability of attitude angle increase and load capacity decrease gradually becomes greater. In general, besides Figure 8e, there are still more points in the upper left direction of the static performance point. This result shows that when the wear region gradually shifts to the central area, the position of the journal tends to fall back, which indicates that the bearing stability will increase with a high probability in the first four cases, and this probability will become smaller and smaller. In the fifth case, when the wear region is located in the center of the bearing, there are more red points at the lower right direction of the blue point and the position of the journal tends to rise, which indicates that the bearing stability will decrease with a high probability. The results above can be explained as follows: the wear protrusion can be equivalent to the support point. When the support point is near both ends of the bearing, the support stability will be enhanced, which is shown in Figure 8 as there are more red (circle) points at the upper left side of the blue point. When the wear region goes to the center, the stability of the protrusion support is weakened, which means that there are more red points at the lower right side of the blue point. However, due to the uncertainty and randomness of wear, the enhancement or weakening was only analyzed from the perspective of probability, not absolutely, indicating that all the analyses in this paper are based on probability and absolute laws do not exist. On the other hand, comparing the figures in Figure 8, as the wear region moves toward the center, the distribution of the red points tends to be denser, which indicates that the influence of wear on the static performance of the bearing gradually decreases as the wear region goes to the center. The wear near both ends of the bearing has the most obvious effect on the static performance of the bearing. In addition, when assuming that the boundary of the discrete points is an approximate ellipse, it can be seen that the slope of the long axis is always negative when the wear position changes, which indicates that when the bearing capacity increases, the attitude angle decreases. The dynamic characteristic coefficients of the MEMS gas bearing are closely related to the perturbation frequency ratio (\(\Omega\)) of the journal [26]. The dynamic coefficients of the gas bearing when  
Figure 8: Static performance point distribution with wear in axial regions. (**a**) axial region 1. (**b**) axial region 2. (**c**) axial region 3. (**d**) axial region 4. (**e**) axial region 5. \(\Omega=1\) are taken as a demonstration here. Figures 9-12 show the sensitivity of the bearing's eight dynamic characteristic coefficients to different axial wear regions.