# Diagnosing the Machine Set Rotor Using Its Relative Vibrations
## 3 Qualities and Symptoms of the Wear Margin of the Machine Set Rotor
### Qualities and Symptoms of the Wear Margin of Machine Rotor Slide Bearings  
The machine set rotor can be fixed spatially in radial and axial slide bearings and may, within bearing clearances, move radially and axially. The moment of friction in a slide bearing depends on the friction coefficient. The friction coefficient, a subject of many analyses, is presented in various forms, e.g., as the Stribeck curve [31]. The tribology modeled the slide bearing as two solid bodies with a converging gap filled with fluid. If between the interacting solid bodies (structural elements) a narrow and converging gap exists, filled with fluid, then a pressure is created in the fluid [32]. The pressure in the gap results from the effect of oil wedge and/or extrusion of fluid from the gap. The effect of the oil wedge occurs when the gap walls are convergent (in the geometric sense, i.e., the space between the walls becomes narrower in the direction of the motion), and along the gap, there is a relative speed of the walls \(U=w_{2}-w_{1}\), Figure 3[32,33]. The friction coefficient \(\mu\) in the convergent gap depends on the \"minimum height\" of the separating liquid \(h_{\text{min}}\) and the roughness of the interacting surfaces [34; 35]. \[\mu=f\left(h_{\text{min}},R_{\text{zz}}\right) \tag{8}\]  
\[R_{\text{zz}}=({R_{\text{a}1}}^{2}+{R_{\text{a}2}}^{2})^{0.5} \tag{9}\]  
\(h_{\text{min}}\)--minimum height of the separating gap (minimum thickness of the oil film), \(R_{\text{zz}}\)--substitute measure of the surface roughness of the interacting walls, \(R_{\text{a}1}\), \(R_{\text{a}2}\)--mean arithmetic deviations of the profile from the mean line of walls 1 and 2 forming the tribological node. The minimum thickness of the separating liquid is proportional to Hersey number \(H_{e}\)[36]  
\[H_{e}=\eta\cdot U/\overline{p} \tag{10}\]  
\(\overline{p}\)--unit load, \(\overline{p}=P/(L\cdot B)\), \(B\)--gap width, \(\eta\)--dynamic viscosity of the fluid, \(U\)--slip speed: \(U=w_{2}-w_{1}\). There is a bracket of desired values \(h_{\text{min}1}<h_{\text{min}}<h_{\text{min}2}\) for a given bearing:  
\(h_{\text{min}1}\)--the limit relevant to the bearing failure, \(h_{\text{min}2}\)--the limit relevant to the loss of energy efficiency. Table 1 presents the classification of machine set rotor slide bearings. The methodology of slide bearing design is described in a number of publications, and comprehensive descriptions are found in Refs. [37; 38; 39; 40; 41]. For bearings with the convergent lubricating film, the qualities characterizing the load capacity of the bearing have a form of a dimensionless similarity number. The similarity number of slide bearings can be considered as a measure of the bearing wear margin, while the minimum height of the separating gap \(h_{\text{min}}\) can be considered as the symptom measure of the wear margin. Dependencies between the similarity numbers and the oil \begin{table}
\begin{tabular}{l l l} \hline Direction of action of the & & \\ transferred forces: & radial & axial \\ Purpose: & supporting & thrust/locating \\ Method of obtaining the converging & eccentricity of the journal and the & - shape (wedge) giving (thrust/locating), \\ gap (wedge): & shell axes & - self-aligning bearing segments (Michell bearings) \\ Design details: & split bearing, & one-way, two-way, \\  & sleeve bearing & single-acting, double-acting \\ \hline \end{tabular}
\end{table} 
Table 1: Classification of the machine set rotor slide bearings. Figure 3: Tribological model of slide bearing. The converging gap and the distribution of fluid speed in the gap: 1, 2—elements forming a node moving at speed \(w_{1}\) and \(w_{2}\): \(w_{2}>w_{1}\); 3—separating fluid; \(L\)—length of the gap; \(h_{\text{min}}\)—minimum height of the gap; \(P\)—normal force exerting a load on the node. film thickness are described by means of differential equations or diagrams included in the corresponding standards. For axial bearings (Figure 4), the bearing load capacity is commonly expressed using the number \(B_{k}\)[37, 42].