## 3 Linear Mathematical Model of the Bearing Stationary State
### Discussion of the Results of Static Characteristics Calculating
#### 3.5.1 Characteristics of Bearings with Slot Feeders of SECT  
The graphs in Figure 2 show the curves of the dependence of the compliance \(K\) on the adjustment coefficient \(\chi\) of the SECT with slotted feeders, where each curve corresponds to different values of \(K_{e}=iK_{e0}\) for \(i=0,1,2,3\) and \(4\). Here, the value of the elastic coefficient \(K_{e0}=2.54\), at which the bearing has zero compliance at the design point, and is calculated by Formula (34).  
Figure 3: Dependences of the compliance \(K\) of the slotted feeder bearing on the weight coefficient \(\varsigma\) SECT for different values of the elasticity coefficient \(K_{e}\).  
Figure 2: Dependences of the compliance \(K\) of the slotted feeder bearing on the coefficient \(\chi\) of the system of external combined throttling (SECT) for different values of the elasticity coefficient \(K_{e}\).  
As can be seen from the figure, the curves are graphs of unimodal functions with a single extremum minimum. The curve for \(i=0\) corresponds to the compliance of a conventional bearing with SECT and the rigid suspension (6), for which \(K_{e}=0\). Such a bearing always has a positive compliance. For this mode, \(\chi=0.4\) is optimal. With the increasing \(K_{e}\), the compliance of the bearing decreases. Therefore, already at i = 1 (at \(K_{e}=K_{e0}\)), the bearing at the minimum point of the function \(K(\chi)\) reaches zero compliance (infinite stiffness). In this case, the value of the optimal \(\chi\) shifts towards its increase (\(\chi\approx 0.55\)). With a further increase in \(K_{e}\), the bearing compliance becomes negative. Therefore, at \(K_{e}=4K_{e0}\) (\(i=4\)), the optimal value of the negative compliance is approximately four times higher in absolute value than the positive compliance of a conventional bearing (\(K_{e}=0\)). For this mode, \(\chi=0.68\) is optimal.  
The influence of the weight parameter \(\varsigma\) of the resistance of the slotted SECT is shown in Figure 3. The value of the parameter is determined by the same formula: \(K_{e}=iK_{e0}\). With a rigid suspension, \(\varsigma\) does not affect the compliance of the bearing. This is due to the fact that the flow principle for both feeders is the same; therefore, the total resistance of the feeders is equivalent to the presence of any of them with the same resistance.  
With the increasing \(K_{e}\), the curves become monotonically increased. In this case, the total eccentricity \(\varepsilon_{s}\) receives an addition to the eccentricity \(\varepsilon\) component \(\varepsilon_{p}\), which is formed under the action of the aerostatic reaction force \(W_{p}\) in the inter-throttle chambers upon deformation of the elastic suspension (6), contributing to the change in the nature of the curves. Moreover, the larger the \(K_{e}\), the steeper the \(K(\varsigma)\) curve.  
Noteworthy is the presence of a common point \(\varsigma=\varsigma_{c}\) on the curves, where the compliance \(K\) does not depend on \(K_{e}\). For those shown in Figure 3, \(\varsigma_{c}\approx 0.275\). From Formula (33), it follows that this regime takes place at \(W=W_{p}\), when the aerostatic reactions on the surfaces of the sleeve (3) are equal to each other, and, therefore, the deformation of the elastic suspension is absent for any \(K_{e}\). Taking this into account, Expressions (26) and (27) make it possible to derive an equation for calculating \(\varsigma_{c}\) for the design point mode:  
\[A_{wk}U_{k}=A_{wp}U_{p}. \tag{35}\]  
It follows from the graphs that a decrease in compliance is possible only if \(0\leq\varsigma<\varsigma_{c}\). Moreover, the smaller the \(\varsigma\), the lower the bearing compliance. At the same time, as the study of the dynamics of other types of aerostatic bearings using SECT shows, a decrease in compliance is almost always accompanied by a deterioration in their dynamics up to a loss of stability [12,27]. Therefore, in order to ensure acceptable dynamics, it is recommended to calculate and design low-compliance bearings for the \(\varsigma\in[0.1,0.2]\).