# Probabilistic Sensitivity Analysis of Wear Property for MEMS Gas Bearing
## 3 Results and Discussion
### Sensitivity Analysis of Axial Wear
It can be found from the figures that as the wear position moves toward the center, the distributions of dimensionless stiffness coefficients and dimensionless damping coefficients are more concentrated, indicating that the sensitivity of eight dynamic coefficients to wear is reduced. Figure 9: Direct stiffness coefficients 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. Figure 9 shows the direct stiffness coefficients distribution with wear in different axial regions. When the wear region closes to both ends of the bearing, most of the red (cicle) points are in the upper left of the blue point, which indicates that the \(K_{xx}\) will decrease and \(K_{yy}\) will increase with a high probability. When the wear regions move to the center, more and more red points move to the lower right of the blue point, which indicates that the probability PRB (\(K_{xx}>K_{xx0}\)) and PRB (\(K_{yy}<K_{yy0}\)) will increase. Figure 10: Cross stiffness coefficients 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. Figure 10 shows the cross stiffness coefficients distribution characteristics of K\({}_{xy}\) and K\({}_{yx}\). When the wear region is near both ends of the bearing, in the high probability, both of the cross stiffness coefficients \(K_{xy}\) and \(K_{yx}\) will increase. As the wear position moves toward the center of the bearing, the probability \(PRB\) (\(K_{xy}>K_{xy0}\)) and \(PRB\) (\(K_{yx}>K_{yx0}\)) increases. Figure 11 shows the direct damping coefficients distribution characteristics of \(D_{xx}\) and \(D_{yy}\). When the wear region is near both ends of the bearing, there are more test points on the upper left side of the reference point, indicating that \(D_{xx}\) will decrease and \(D_{yy}\) will increase with a high probability. As the wear position shifts toward the center, there are more test points on the lower right side of the reference point, which indicates that the probability \(PRB\) (\(D_{xx}>D_{xx0}\)) and \(PRB\) (\(D_{yy}<D_{yy0}\)) will increase. Figure 11: Direct damping coefficients 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. Figure 12 shows the cross damping coefficients distribution characteristics of \(D_{xy}\) and \(D_{yx}\). When the wear region is near both ends of the bearing, there are more test points on the lower left side of the reference point, indicating that both \(D_{xy}\) and \(D_{yy}\) will decrease with a high probability. As the wear position shifts toward the center, the occurrence frequency of the test points at the upper right side of the reference point increases, which indicates that the probability \(PRB\) (\(D_{xx}>D_{xx0}\)) and \(PRB\) (\(D_{yy}>D_{yy0}\)) will increase. Figure 12: Cross damping coefficients 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. The wear in this investigation can be equivalent to a small perturbation when the value of parameter \(\sigma\) is small. In this situation, each parameter of the bearing varies approximately linearly with perturbation, therefore the absolute value of the correlation coefficient here is close to 1.