# CFD Research for Air Bearing with Gradient-Depth Recesses
## 4 Analysis and Discussion  
For intuitive comparison, the UDF method was used to calculate the bearing capacity W with unified and gradient recesses. The experimental principle and equipment are consistent with the method described in ref. [3]. The comparison results are shown in Figure 9.  
It can be seen that the bearing capacity \(W\) curves of the two types of bearing working faces calculated using the AFVM by UDF are consistent with the experimental results. Comparing the bearing capacity curves under different values of air film clearance \(h\), it can be concluded that when \(h\) is small (1 \(\mu\)m \(\leq h\leq\) 4 \(\mu\)m) and large (\(h\geq 14\)\(\mu\)m), the bearing capacity \(W\) of the air flotation working face changes steadily with the air film  
Figure 8: The performance increasing of \(M_{r}\) (**a**) and \(K_{\theta}\) (**b**) by gradient-depth recesses.  
Figure 9: Results of \(W\) of guideway working surface with air film clearance.  
clearance \(h\). When \(h\) is medium (4 \(\upmu\)m \(\leq h\leq\) 14 \(\upmu\)m), it is the working zone with the air film thickness. Within this range, the bearing capacity \(W\) of the air flotation working face changes significantly with the air film clearance \(h\). The \(h\) corresponding to the maximum slope of the \(W\) curve is the \(\bigtriangleup\) of the air film thickness at the maximum stiffness of the air flotation working face.  
By comparing the two types of bearings without air tubes, it can be seen that the \(\bigtriangleup\) of the gradient recesses bearing obtained by the UDF method is around 9 \(\upmu\)m, while the \(\bigtriangleup\) of the original unified recesses one is around 11 \(\upmu\)m. Therefore, the working point \(\bigtriangleup\) of the air film thickness of the gradient recesses bearing is lower, reducing by at least 2 \(\upmu\)m. At the same time, the air bearing capacity of the gradient recesses bearing is greater, the working band is wider, and the variation in bearing capacity within the working band is greater. This indicates that the idea of using UDF methods to adjust the working point \(\bigtriangleup\) of the air film thickness through the design of microstructure parameters, thereby changing the bearing capacity and stiffness performance of the bearing, is effective and feasible. The experimental results have verified the correctness of the CFD analytical hybrid design method based on AFVM.  
The above experimental results indicate that the bearing capacity and stiffness of the gradient recess bearings' working surface obtained by using the UDF design method based on AFVM are higher than those of the original guide air flotation working surface. The reason for this gain effect is that the design method proposed in this article considers the influence of microstructure parameters on the performance of the guide rail and adjusts the working point of the gas film thickness. The essence of this parameter adjustment is to establish a connection between microstructure parameters and throttling coefficients, and to correct the throttling coefficients in the analytical model. Through this experiment, it has been confirmed that the throttling coefficient varies with the gas film clearance, especially for small bearings without an air tube.