## 5 Mathematical Model of the Unsteady State of the Bearing
### Bearing Dynamic Characteristics and Their Discussion  
The calculation of the limit (103) showed that, for the TF (101), the difference in the degrees of its polynomials was \(p=2\). The criteria for the dynamic quality \(\eta\) and \(\xi\), were determined with an accuracy of \(\varepsilon_{\eta}=0.001\) and \(\varepsilon_{\xi}=0.1\), respectively. In addition to the parameters affecting both the static and dynamic characteristics, three more quantities were added to the number of input parameters: the shaft mass _Mas_, the squeezing number \(\sigma\) and the volume \(V_{p}\) of the inter-throttle chambers, which affect only the dynamic characteristics. In the calculations, the dimensionless mass _Mas_ = 1 was assumed to be constant, which made it possible to establish a certain scale of the current time \(t_{0}\). After carrying out numerous calculations, it was found that the iterative process of determining the dynamic criteria usually converged with the specified accuracy at the degree of CP \(n\) = 4-7. An analysis of the calculated data showed that \(\eta\) and \(\xi\), do not depend on the elasticity coefficient \(K_{e}\). That is, the speed and oscillation of a bearing with a rigid or one with an elastic suspension (6) are the same. Therefore, the calculations of the dynamic criteria were carried out for \(K_{e}\) = 0. Thus, in contrast to the aerostatic bearings with flow compensators, where the dynamics of the structure also deteriorate as the compliance decreases, the dynamic characteristics of the free oscillations of an active bearing with a displacement compensator will be the same as those of a construction with SECT and a rigid suspension (6). It has also been established that the dynamic characteristics of slotted and throttling SECT are in full qualitative agreement, only slightly differing in quantitative terms. Therefore, below is an analysis and discussion of the dynamic characteristics of the most promising among the investigated designs of a bearing with a throttle SECT. The graphs show the dynamic characteristics in the space of changes in the three parameters \(\varsigma\), \(\sigma\) and \(V_{p}\), of which the study of the influence on the bearing dynamics is of greatest interest. The graphs are plotted for \(L\) = 1.5, \(\lambda_{1}\) = 0.8, \(\lambda_{3}\) = 0.95, \(\chi\) = 0.5, \(R_{1}\) = 1.1 and \(P_{s}\) = 4. First of all, we studied the influence of the weight coefficient \(\varsigma\) of the SECT on the bearing dynamics, because, as shown in the study of the static characteristics, its value should be small. To ensure negative compliance, the bearing must satisfy the condition \(\varsigma<\varsigma_{c}\), where, as follows from Figure 3, for this combination of parameters, \(\varsigma_{c}\approx 0.554\). Figure 11 shows the dependence of the speed criterion \(\eta\) on \(\varsigma\), and Figure 12--criterion of the fluctuations \(\xi\). As can be seen from the graph in Figure 11, the bearing has the best speed (maximum value of the criterion \(\eta\)) at different \(V_{p}\) in the range \(0.1<\varsigma<0.3\), i.e., in the region \(\varsigma<\varsigma_{c}\), where a decrease in compliance to zero and negative values can be ensured. It is noteworthy that the speed of the bearing combined with external throttling is many times higher than in the bearing with single throttling by annular diaphragms (\(\varsigma=1\)). In this case, a single  
Figure 11: Dependences of the degree of stability \(\eta\) of the bearing with the throttle SECT on the coefficient \(\varsigma\) and volume \(V_{p}\), \(\sigma=4\). throttle bearing with simple diaphragms (\(\xi=0\)) turned out to be expectedly unstable (\(\eta<0\)), because such a bearing can be stable only for those values of the volume \(V_{p}\) that are comparable or less than the volume of the carrier air gap (\(V_{p}<1\)) [32], which cannot be ensured in the design under study for design reasons.