# Diagnosing the Machine Set Rotor Using Its Relative Vibrations
## 4 Measurements of Relative Vibration
### Measurements of the Displacement of Rotors' Relative Vibration
#### 4.2.2 Measurements of the Displacement of Relative Axial Vibration
The signal of axial vibration from each sensor is the sum of real axial vibration and the runout signal. The runout signal is created due to errors, such as non-perpendicularity of shaft face, shape and inhomogeneity of material structure of the shaft end face. It follows from Figure 17 that summing of the signals from a pair of sensors with shift by \(\pi\) eliminates the components caused by non-perpendicularity of the end face relative to the shaft rotation axis. The average value, amplitude and phase shift of the averaged signal depend on shaft deflection. A limited area with different material structure was identified on the shaft end face surface, resulting in the generation of pulse signal components in the time waveform and \"tails\" in the XY system image, depicted as A in Figures 16 and 17. It follows from Figures 16-18 that the maximum value \(\left|p-p\right|\) of the diagonal of the figure depends on shaft deflection. For a pair of sensors with a shift by \(\pi/2\), the figure model is an ellipse, and the measure of axial vibration value is the difference between the value of greater and smaller diameters. It also follows from Figure 18 that the change of distance between the head and the shaft face results in a shift of the figure, as the average/constant value \(\Delta_{\text{ev}}\) of axial vibration changes. equipped with a locating bearing or may consist of two radial bearings and a thrust bearing (Figure 19) [23,44,59,60]. The point located on the journal axis on the flywheel side is to be considered as the point determining the position of the shaft relative to the engine body. The position of the bearing journal center on the flywheel side:  
* affects the axial vibration of the crankshaft free end;
* depends on the alignment of the machine set rotor. The fragment of the engine journal, accessible from the outside, is a fragment between the body and the flywheel. The intersection of the plane parallel to the face of the engine body with shaft and bearing hole axes determines a point on the shaft axis (the journal center) and a point on the bearing hole axis (the bearing center). For the defined plane parallel to the engine body face, the shaft position measurement will consist of the measurement of the journal eccentricity \(e\) of the journal in the shell and distance \(l\) of the shaft journal center from the face of the engine body (Figure 19). The surface parallel to the engine body face associated with the crankshaft can be the frontal surface of the shaft flange, flywheel or a special ring mounted on the shaft flange. The measurement of the running engine shaft position comes down to the measurement of relative radial and axial vibration of the shaft journal and flange on the flywheel side. The following design solution referred to as the \"shaft position head\" is proposed for vibration measurements. The head 10 (Figure 20) is composed of a holder and two pairs of eddy current sensors, X1Y1 and X2Y2. The head is rigidly fixed to the upper part of the engine body cover 2 on the flywheel side. The pairs of sensors in the head are shifted relative to each other by \(\pi/2\) (Figure 20). Figure 19: The flywheel end of the crankshaft of engine with locating bearing (part A) and thrust bearing (part B): 1—flywheel, 2—engine cover with sealing, 3—engine body, 4—main journal of shaft, 5—flange of crankshaft, 6—gear wheel for camshaft drive, 7—main bearing shell, 8—thrusting half, 9—thrust pads, H—distance between the face plane of machine body and a point on the crankshaft axis in the measuring plane, \(e\)—distance between shaft axis and axis of holes in the machine body. Sensors X1 and X2 measure the distance between the engine body and the shaft frontal surface. Sensors Y1 and Y2 measure the distance between the body and the shaft cylindrical surface, the shaft flange cylindrical surface or the cylindrical surface of the ring imposed on the flange and connected with the flywheel. The head of a position sensor requires calibration on a special calibration bushing.