# Probabilistic Sensitivity Analysis of Wear Property for MEMS Gas Bearing
## 3 Results and Discussion
### Sensitivity Analysis of Circumferential Wear  
Figure 14 shows the static performance point distribution of the MEMS gas bearing with wear in different circumferential regions. The analysis results show that the wear in regions 1 and 2 has very little effect on the dynamic and static characteristics of the gas bearing. Therefore, for the convenience of expression, only the performances distribution of region 3 to region 6 are shown below. Fifty working conditions were calculated for each wear case. In the same coordinate system, when the wear exists in region 4, the dispersion degree of the static performance test points is the most obvious, and the dispersion degree gradually decreases when the wear position moves away from region 4. When the wear exits in regions 1, 2, and 6, the points dispersion degree is very small, which indicates that the effect of wear on the bearing performance can be neglected in these three regions. From the perspective of bearing geometry, these three regions are away from the main loading area of the bearing and the gas film is relatively thick, therefore, the perturbation of the gas film has a very limited effect on the static characteristics of the bearing. Under the condition without considering wear, the attitude angle of the gas bearing is \(40.65^{\circ}\), which indicates that the minimum thickness area of the gas film falls at region 4. At this position, the film thickness is more sensitive to the wall wear, and the change of film thickness has a more obvious effect on the film pressure, which further affects  
Figure 14: Static performance point distribution with wear in circumferential regions. (**a**) circumferential region 3. (**b**) circumferential region 4. (**c**) circumferential region 5. (**d**) circumferential region 6. For the direct stiffness coefficients group (\(K_{xx}\), \(K_{yy}\)), when wear occurs in region 4, most of the red (circle) points are in the upper left direction of the blue (triangle) point, indicating that \(K_{xx}\) will decrease and \(K_{yy}\) will increase with a high probability. For the cross stiffness coefficients (\(K_{xy}\), \(K_{yx}\)), when wear occurs in region 4, most of the red points are in the upper right direction of the blue point, indicating that both of the \(K_{xy}\) and \(K_{yx}\) will increase with a high probability. For the direct damping coefficients group (\(D_{xx}\), \(D_{yy}\)), when wear occurs in region 4, most of the red (circle) points are in the upper left direction of the blue (triangle) point, indicating that \(D_{xx}\) will decrease and \(D_{yy}\) will increase with a high probability. For the cross stiffness coefficients (\(D_{xy}\), \(D_{yx}\)), when wear occurs in region 4, most of the red points are in the lower left of the blue point, indicating that both of \(D_{xy}\) and \(D_{yx}\) will decrease with a high probability. Figure 19 shows the standard deviation of the eight dimensionless dynamic coefficients when there is wear in different circumferential positions. The conclusion can be drawn that all the sample standard deviations of the eight dynamic coefficients reach the maximum when there is wear in region 4. The results above indicate the uncertainty of the dynamic characteristic reaches the largest, which means the influence of wear on the bearing is most obvious in this case. Figure 16: Cross stiffness coefficients distribution with wear in circumferential regions. (**a**) circumferential region 3. (**b**) circumferential region 4. (**c**) circumferential region 5. (**d**) circumferential region 6. Table 4 shows the correlation coefficients of dimensionless dynamic coefficients for circumferential wear. It can be seen that most of the correlation coefficients are greater than 0.6 as a whole, which indicates that there is a strong correlation between each coefficient. When the wear occurs in the regions away from the minimum film thickness area, the influence of the wear on the gas flow field is very small, so the wear can be equivalent to a small perturbation.