# 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 the Machine Set Rotor with a Crankshaft  
The fixing of a crankshaft is understood as the impossibility of axial and radial displacement of the first journal center (flywheel side). Because it is impossible to fix the main journal on the flywheel end, the axial and radial positions of that journal center should be measured, and the changes should be taken into account in diagnostic inference. The signal of journal displacement at the flywheel end is contained in the signal of the axial and radial vibrations of that journal.  
The axial displacement of the crankshaft free end \(\Delta l_{f,e}\) can be measured while the machine is running. The effect of radial forces acting on the crankin journal is the so-called dynamic deflection of the crank. Like static deflection \(\Delta l\), dynamic deflection \(\Delta l_{d}\) is related to axial displacement of the main journals of the cranks and axial vibrations of the shaft ends. The signal of axial vibration of both crankshaft ends is the sum of signals generated by static and dynamic deflection of all the cranks.  
If there is only axial displacement \(\Delta H(\alpha)\) at the flywheel end, then the axial displacement of the crankshaft free end \(\Delta l_{f,e}(\alpha)\)  
\[\Delta l_{f,e}(\alpha)=\left(\sum_{1}^{n}\Delta l(\alpha)\right)+\left(\sum_{ 1}^{n}\Delta l_{d}(\alpha)\right)-\Delta H(\alpha) \tag{14}\]  
where  
\(n\)--number of cranks,  
\(\Delta H(\alpha)\)--crankshaft displacement at the flywheel end,  
\(\alpha\)--crankshaft rotation angle.  
A change in the eccentricity in the flywheel bearing from \(e_{1}\) to \(e_{2}\) causes a change in the value of crank deflection \(\Delta a\), especially on the first crank, and thus, a change in the value of \((\sum_{1}^{n}\Delta l(\alpha))\).  
If measurements of the average and instantaneous values and the phase shift of axial vibrations of the free end of the crankshaft \(\Delta l_{f,e}(\alpha)\), the average and instantaneous values of axial vibrations of the thrust bearing flange \(\Delta H(\alpha)\) and the average and instantaneous values of radial vibrations of the bearing journal at the flywheel end were possible, the quantities could be considered measures of the machine set rotor symptoms:  
* if the load is identical and constant on all cranks, the average value, amplitude and phase shift of the axial vibrations of the free end of the crankshaft \(\Delta l_{f,e}(\alpha)\) depend on the alignment of the machine set rotor;
* the values of \(e(\alpha)\) and \(\Delta H(\alpha)\) make it possible to identify the cause of the alignment change. An increase in the eccentricity \(e\) in the flywheel bearing indicates non-coaxiality of the set's shafts or wear of the bearing. Changes in the values of \(\Delta H\) indicate the effect of axial forces from another machine. Where \(e\) and \(\Delta H\) remain constant, a change in the value of vibrations of the shaft free end \(\Delta l_{f,e}(\alpha)\) indicates deformations of the support or wear of the bearings supporting the crankshaft.