## 5 Discussion  
The proposed theory is also valid for the stiffness of the static pressure spindle and slide in other directions, which can also be verified. However, the influence of FSI on the radial stiffness of static pressure spindles is generally small. This is because the small radial solid deformation hardly changes the shape and dimensions of the journal bearing, and the radial structural stiffness is large. Moreover, for the angular stiffness of static pressure spindles and slides, the supporting forces change the shapes and dimensions of the supporting bearings and thus change the angular stiffness of the bearings. However, the external moment is basically counteracted by the reaction moment due to the deformation of the supporting bearings. In other words, the angular structural stiffness is much greater than the angular stiffness of the supporting bearings. The angular stiffness of the static spindle or slide is nearly equal to that of their supporting bearings. For the above reasons, the proposed theory for the stiffness in these directions will not be introduced in this paper.  
Based on the proposed theory, there are two ways to enhance the stiffness of the static pressure spindle and slide. One is to increase the stiffness of the supporting bearings, and the other is to increase the structural stiffness. For a system with only a supporting bearing, suppose the structural stiffness is \(\lambda\) times the stiffness of the bearing. According to the proposed theory, the system stiffness, \(k\), is shown in Equation (27) where \(k_{\rm{f}}\) is the stiffness of the bearing.  
\[k=\frac{\lambda}{1+\lambda}k_{\rm{f}} \tag{27}\]  
The ratio of \(k\) to \(k_{\rm{f}}\) is \(\lambda/(1+\lambda)\), which increases with the increase of \(\lambda\), as shown in Figure 11. It can be seen that when \(\lambda\) is less than 2, the ratio grows fast with the increase of \(\lambda\). But when \(\lambda\) is greater than 4, the growth of the ratio slows considerably. Increasing the structural stiffness will inevitably increase the dimensions and mass of the solid, which will decrease the natural frequencies and degrade the drive properties of the spindle and slide. Therefore, \(\lambda\) should be in a reasonable range. This paper suggests that \(\lambda\) should be around 3. When \(\lambda\) is 3, the system stiffness is 75% of the stiffness of the bearing. When \(\lambda\) is greater than 4, the increase of \(\lambda\) will not enhance the system stiffness effectively. In this case, increasing \(k_{\rm{f}}\) will be a more proper way to enhance \(k\).  
When the structure of a static pressure spindle or slide is confirmed, the next step is to choose suitable structural dimensions \(s\) and a designed film thickness \(h_{0}\), which are critical at the design stage. To make the stiffness value of the static pressure spindle or slide \(k_{\rm{c}}\) reach the designed value \(k\), lots of \(k_{\rm{c}}\) under different structural dimensions and designed film thicknesses have been calculated to find the suitable parameters based on the conventional method, as shown in Figure 12a. It can be seen that the conventional method is a little bit blind and inefficient. For this problem, a method based on the proposed theory is proposed to choose suitable structural dimensions and designed film thickness, as shown in Figure 12b. First, the bearing and structural stiffness values, \(k_{\rm{f}}\) and \(k_{\rm{s}}\), can be obtainedon the basis of \(k\) and \(\lambda\), and thus the actual film thickness after the solid deforms \(h\) and structural dimensions \(s\) can be determined, respectively. Then, based on the FSI method, the designed film thickness \(h_{0}\) can also be obtained. Hence, \(s\) and \(h_{0}\) can be determined on the basis of \(k\) and \(\lambda\). It can be seen that the method based on the proposed theory is more efficient than the conventional method.