# 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
\[B_{k}=\left(\overline{p}\cdot h^{2}\text{min}\right)/\left(\eta\cdot U\cdot L\right) \tag{11}\]  
For a given axial bearing, the number \(B_{k}\) should have a value lying in a specific range interval. In the standards, the number \(B_{k}\) is presented as the function of \(h_{\text{min}}/c_{\text{wed}}\). For the axial bearing, it can be noted that the distance \(H\) between the flange center plane or another plane determined on the shaft and the shell base plane depends on the minimum height of the gap \(h_{\text{min}}\) (Figure 4):  
\[h_{\text{min}}=H-H_{0} \tag{12}\]  
where \(H_{0}\)--value \(H\) for the non-working bearing after the shaft flange is pressed to the shell. If measurements of the distance \(H\) were feasible for axial bearings, changes in the distance value could be considered a measure of the bearing's wear margin symptom, whereas \(B_{k}\) could be considered a measure of the bearing's wear margin:  
* for a bearing with 100% wear margin, the value of \(B_{k}\) complies with the specification and \(B_{k}=B_{k1}\), whereas the measured values of the \(H\) symptom are \(H=H_{1}\), \(H_{0}=H_{01}\), respectively;
* if \(H=H_{2}\), \(H_{0}=H_{02}\), then for \((H_{2}-H_{02})/C_{\text{wed}}\) from the standard \(B_{k}=B_{k2}\
eq B_{k1}\). The change in the value of \(B_{k}\) can be attributable to a change in the value of one or more quantities of which \(B_{k}\) is composed (12);
* if \(H_{0}=H_{2}<H_{01}\), one of the causes is wear resulting in a change in the length of the gap \(L=\Sigma L_{\text{wed}}\). If the change in the gap length is the only cause for the change in the value of \(B_{k}\), then \(L_{2}=\overline{p}_{1}\cdot(H_{2}-H_{02})^{2}/(\eta_{1}\cdot U_{1}\cdot B_{k2})\). To characterize the load capacity of radial bearings, the dimensionless Sommerfeld number is commonly used. \[S_{O}=\left(\overline{p}\cdot\psi^{2}\right)/\left(\eta\cdot\omega\right) \tag{13}\]  
where  
\(\omega\)--angular speed of the shaft journal,  
\(\psi\)--relative clearance, \(\psi=C/D\),  
\(C\)--clearance in the bearing, \(C=D-d\),  
\(D\)--shell diameter,  
\(d\)--journal diameter. Here are the example values of the clearance in main bearings (flywheel bearings) of the ship's main engine: normal clearance (mm) 0.270-0.374; wear limit (mm) 0.525 [43]. Figure 4: Model of the axial bearings with permanent wedges for work in both directions of force \(T\) and speed \(U\): 1—shaft flange, 2—shells attached to the machine body, \(T\)—axial force exerting load on the bearing, \(U\)—linear speed of a point on the rotating shaft flange, \(h_{\text{min}}\)—minimum height of the separating gap (minimum thickness of the oil film), \(L_{\text{wed}}\)—length of the permanent wedge, \(C_{\text{wed}}\)—height of the permanent wedge. The Sommerfeld number is a similarity criterion of hydrodynamic slide bearings, in which the oil wedge principle is used. When bearings are similar, i.e., have the same relative length \(b/d\) and the same shell contact angle and the same Sommerfeld number, their working conditions are similar. They show the same position of the journal in the shell and the same friction coefficient [44]. One measure of the journal position relative to the shell is eccentricity \(e\). There is a relationship between the eccentricity \(e\), clearance in bearing \(C\) and minimum height \(h_{\min}\) of the gap. The dependences of relative eccentricity \(\varepsilon=e/(C/2)\) and relative oil film thickness \(h^{\star}_{\min}=h_{\min}/(C/2)=(1-\varepsilon)\) on the Sommerfeld number \(So\) for various \(b/d\) are presented in diagrams [45]. The inverse of Sommerfeld number \(1/So\) can be the substitute measure of the radial bearing wear margin [46]. The tribological wear of the bearing results in increased clearance and/or decrease in the liquid viscosity. The \(1/So\) decreases along with the increase in the clearance and load, and the decrease in viscosity. Figure 5 presents the position of the journal center in the clearance circle (circle of radius \(C/2\)) as the function of the rotary or angular speed.