# 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 displacement of axial vibration of a machine rotor can be measured using heads with eddy current sensors attached to the machine body. The head can include (Figure 14):  
* one sensor located on the shaft axis; sensor axis is aligned with the rotor shaft axis;
* two sensors with the axes set parallel to the rotor shaft axis, and the same distance of both sensor axes to the shaft axis. The sensors can be mounted circumferentially:  
* shifted by \(\pi/2\),
* shifted by \(\pi\). We should find or place an electric conductor element on the vibrating rotor, with a plane perpendicular to the rotor axis. The surface of this plane cannot be subject to wear. These elements can be as follows:  
* face of the rotor shaft free end;
* face of the flange made together with the rotor shaft;
* end face of the flywheel or the face of a special disc mounted on the shaft, etc. With two sensors, we can analyze the time waveforms \(x(t)\) and \(y(t)\) from both sensors or images of the value changes in the XY system. The sensors in the head must be set so that they show the same value of axial vibration of the component with the front plane perpendicular to the sensor axis. When a shaft generates only axial harmonic vibration:  
* both time waveforms should be identical, have the same average values and should not have a phase shift (\(\varphi=0\));
* in the XY system, the image should be a straight section corresponding to the Lissajous curve for \(\varphi=0\) (Table 2). The face of the shaft or flange may be positioned non-perpendicularly to the sensors axes and/or have shape errors, and the material under its surface can be inhomogeneous. The measured signals will then contain additional components with a phase angle other than the measured axial vibration. For the most common error, a non-perpendicular shaft face, the phase shift will be \(\pi\) or \(\pi/2\), depending on the sensor configuration in the head, and the image in the XY system will be a straight section for \(\varphi=\pi\) and a circle for \(\varphi=\pi/2\) (Table 2). When the head has a pair of sensors with a shift by \(\pi\), the components resulting from the shaft face non-perpendicularity errors or shaft bending can be eliminated mathematically by summing both signals and dividing by 2. For the machine set with a piston machine, specific planes perpendicular to the machine set rotor axis are the plane of the thrust or locating bearing flange and the face of the free end of the shaft. The value of the displacement of axial vibration of the free end face of the machine set rotor shaft is, inter alia, affected by:  
* vibration dependent on the rotor alignment (values of cranks deflection);
* vibration as the result of rotor displacement in the axial bearing clearance. Figure 14: The configuration of sensors of the rotor relative axial vibration: 1—eddy current sensor; 2—rotor shaft; 3—head; 4—machine body. Axial vibration of the crankshaft free end face was tested, with the shaft mounted on a large lathe. The crankshaft flange on the flywheel side was connected with the flange of the lathe spindle. The lathe spindle axial motion was blocked. The main journals of the crankshaft were supported on rollers. The position of the rollers could be altered vertically and horizontally, which enabled forcing crank deflections, leading to forced axial displacements of the shaft free end. The head with sensors was mounted to the tailstock, so the distance between the shaft end and the head could be changed. The tests made use of the head with a pair of sensors with shift by \(\pi\) and a pair of sensors with shift by \(\pi/2\) for various shaft deflections. Some of the test results are shown in Figures 15-18. It was found that minor changes in crank deflection resulted in measurable changes in axial vibration of the shaft free end. These changes are visible in the time waveforms of sensor signals and in images in the XY system (Figures 17 and 18).