Shaft Displacement Measurement Using A PROTOR System

Shaft displacement is an important vibration measurement for rotating machines. Shaft displacement is usually monitored by non-contact shaft displacement probes such as eddy-current probes. These probes produce a voltage proportional to the distance of the shaft surface relative to the tip of the probe. For maximum benefit, ideally two shaft displacement probes will be fitted to measure the displacement in both the horizontal and vertical directions. Actually the probes do not have to be exactly horizontal and vertical as Prosig’s PROTOR system is able to resolve into the horizontal and vertical directions.

Eddy-Current Probes

The diagram in Figure 1 shows a typical arrangement.

Positioning probes
Figure 1 : Positioning probes

NOTE: For a normal setup with a gap between the probe tip and the shaft surface then the output will be negative voltage. If the shaft is touching the probe (zero gap) then the output will be zero. The output will get more negative as the shaft moves away from the probe.

This shows that the vibration signal from shaft displacement probes contains both AC and DC components. The DC component is a measure of the overall distance of the shaft from the probe, this is called the gap. The AC component is measure of the movement of the rotating shaft about its central position. In general the DC component is large (typically -15V) with a much smaller AC component.

The PROTOR data acquisition hardware includes dedicated signal conditioning which allows both the AC and DC components to be measured with high accuracy using only a single input channel.

Shaft Vibration

The AC component is usually analyzed with respect to a ‘once per revolution’ tachometer signal to provide measurements which are an indication of the movement of the shaft on a rotational or ‘per cycle’ basis. This provides information which is used to detect phenomena such as unbalance, misalignment, rotor bends, cracks and so on.

Bending of rotor shaft
Figure 2 : Bending of rotor shaft

For example, assume a rotor, supported by two bearings, has a bend or bow as shown in Figure 2 (greatly exaggerated for display purposes). Measuring the shaft displacement at the bearing would show a sinusoidal-type waveform as the shaft moves towards and then away from the probe tip for each revolution of the shaft. This is called eccentricity.

Note that bends or bows of this nature can sometimes be found in rotors which are left stationary; some rotors bend under their own weight due to gravity and sometimes different thermal gradients whilst cooling down will cause a bend. To avoid this rotors are usually rotated at low speeds, called barring. Attempting to run a rotor at full speed whilst it has a bend may and often will cause destructive damage to the shaft or bearing.

When a shaft is running at full speed then similar displacement time histories may be encountered due to out-of balance conditions.

The PROTOR system measures the AC signal for displacement probes and performs frequency analysis on the signal with reference to the tachometer signal to identify the Overall displacement on a cyclic basis together with its constituent components such as the 1st, 2nd, 3rd, 4th and higher harmonics (both amplitude and phase), sub-harmonic (amplitude and frequency) and intra-harmonic components. These measured components are collected and stored on a regular basis and made available for real-time mimic diagrams, trend displays, vector diagrams, alert processing and also for historical analysis.

Transducer Orientation

To be of most benefit a pair of perpendicular shaft displacement probes are often used to allow measurement of the movement in both the vertical and horizontal directions.

NOTE: It is often not physically possible to mount probes in the actual vertical and horizontal planes. The PROTOR system configuration allows the actual transducer mounting position to be defined. It can then mathematically combine the contributions of a pair of probes to estimate the actual displacement in the true vertical and horizontal planes. Transducer orientation angles may be set directly or common mounting positions selected from a pull-down menu.

Button 1Orientation Transformation turned off.Button 4Apply Orientation Transformation assuming transducers mounted 45 degs from top of bearing with Y to left and X to right.
Button 2Apply Orientation Transformation from user specified angles given in the Configuration file.Button 5Apply Orientation Transformation assuming transducers mounted 45 degs from bottom of bearing with Y to left and X to right.
Button 3Assume transducers mounted in Horizontal (X) and Vertical (Y) directions

Orbit Plots

Two perpendicular shaft displacement signals may be either directly measured or determined through the orientation software. When two such signals are available then PROTOR is able to display the data in the form of a shaft ‘Orbit’. An Orbit display is essentially the same as connecting the pair of shaft displacement signals into two channels on an oscilloscope, AC coupling both and selecting an X-Y display. The resultant display is effectively a dynamic display of the movement of the centre of the shaft. When displaying on an oscilloscope the display contains contributions from all frequencies. Within PROTOR it is possible to display the ‘filtered’ orbits, that is the individual contributions from each of the measured orders. Alternatively you can select which orders to include in the orbit display.

Time history from probe
Figure 3: Time history from probe
Time history from second probe
Figure 4: Time history from second probe

The two time histories in Figure 3 & 4 are typical examples of using a pair of perpendicular displacement probes to measure shaft movement. These displays show time history traces of two perpendicular shaft displacement probes for a bearing on a turbine generator. These result in the ‘unfiltered’ orbit plot shown in Figure 5.

We now control the orders to include in the filtered orbit plot (Figure 6). The display shown includes orders x1, x2, x3 and x4. The actual displacement probes were mounted 45 degrees from the vertical plane and at the top of the bearing as indicated by the two small arrows on the right of the plot.
If we now apply the orientation correction we get the display shown in Figure 7. If we further select the 1st order-only filtered orbit then Figure 8 is obtained. The highlight on the trace shows us the position of the phase marker. This display is most useful as it shows us the relative motion in both the vertical and horizontal planes.

Oil Whirl and Whip

Another important phenomenon found in fluid lubricated journal bearings is Oil-Whirl. In normal operation an oil film flows around the bearing to lubricate and cool the bearing. This oil film usually rotates at a speed of just below 50% of the shaft rotational speed.

As rotational speed increases the shaft rises up the side of the bearing. The amount of rise depends on the speed, rotor weight and oil pressure. As the shaft rises the oil tends to form a ‘wedge’ on which the shaft sits. If, for some reason, the shaft receives a disturbance causing the shaft to move from this equilibrium position then the oil pressure gradient changes. This may result in a whirl or precession where the wedge ‘pushes’ the shaft around the bearing as seen in Figure 14. Oil whirl can be unstable when whirl frequencies coincide with one of the natural frequencies of the rotor.

Unfiltered orbit plotFiltered orbit plotAfter orientation correction
Figure 5: Unfiltered orbit plotFigure 6: Filtered orbit plotFigure 7: After orientation correction
First order onlyFFT of bearing showing Oil WhirlShaft gap display
Figure 8: First order onlyFigure 9: FFT of bearing showing Oil WhirlFigure 10: Shaft gap display
After orientation correctionWith 'zero gap' specifiedWith limits displayed
Figure 11: After orientation correctionFigure 12: With ‘zero gap’ specifiedFigure 13: With limits displayed

Note that if the machine speed approaches twice the critical speed then the whirl component can become ‘locked’ to the first critical speed and does not change even when the speed increases. This is known as Oil Whip.

The FFT of a bearing suffering from Oil Whirl will show a high component just below the 0.5x order. In Figure 9 the running speed is 50Hz and the sub-harmonic frequency is around 22Hz.

Shaft Gaps

As mentioned above the signal from a shaft displacement probe also has a DC component which is proportional to the average gap between the probe tip and the shaft surface. The PROTOR system also measures and logs these components and makes them available for trending and display.

A dedicated Shaft Gap display (Figure 10) allows the DC component of two perpendicular shaft displacement probes to be displayed against each other. This produces a display of the movement of the shaft centreline within a bearing. The data displayed may be for a complete runup or rundown or for a selected period of interest.

Oil whirl
Figure 14 : Oil whirl

As with the Orbit display, transducer orientation may be applied to the display (Figure 11) for cases where the probes are not fitted in the true vertical and horizontal planes.

In order to obtain a true feeling for the amount of movement within the bearing PROTOR allows the user to specify a ‘zero’ gap position (Figure 12) . This is usually when the shaft is rotating at very low speeds or is at rest. This ensures that the shaft is at the bottom of the bearing.

When set all subsequent values are taken relative to the shaft ‘bottom’ values.

Finally, if the clearance information is known for the bearing then these limits may be superimposed onto the display (Figure 13). Data points may be displayed as symbols or lines or both. The user may use the cursor to interrogate the data and view parameters such as speed, load or oil pressure at each sample.
PROTOR also features a play-back visualisation function so that users may view an event as if it were happening live.

Shaft gap information is captured and stored by PROTOR for all machine states which includes when the shaft is at rest, through barring, run-up and run-down events to full speed operation. Additional features also include the measurement of the total ‘lift’ of the shaft through a run-up event. These bearings lifts may then be trended over long periods of time to check that operation is satisfactory.


One important aspect to be aware of when using this type of probe is a known as Runout. This phenomenon is the combination of the inherent vibration measurement of a rotating object together with any error caused by the measurement system. Runout may consist of the following components:

Mechanical Runout – An error in measuring the position of the shaft centreline with a displacement probe that is caused by out-of-roundness and surface imperfections.

Electrical Runout – An error signal that occurs in eddy current displacement measurements when shaft surface conductivity varies.

That is, any measurement made by a probe of this type is subject to error which is due both the surface and shape of the object being measured and also due to its electro-magnetic properties.

Runout Compensation

It is important to understand the amount of runout present for a particular setup as runout affects all measurements and may in some circumstances mask or corrupt actual shaft vibration measurements possibly causing incorrect diagnosis. Providing the amount of runout is measured then it is possible to compensate or subtract these base levels to reveal the actual vibration measurement. The PROTOR system has had the ability to subtract runout data from vibration measurements for several years.

Runout Example

For a perfectly round shaft then the gap between probe tip and shaft surface will be constant and provided the shaft is the rotated about its axis centre then will remain constant with speed. However, if the shaft is not perfectly round then the gap measurement will change as the shaft rotates. Similarly a perfectly round shaft which has non-uniform electro-magnetic properties will also result in an output which changes even though the physical gap remains constant.

For illustration, the following diagram shows an extremely non-circular shaft. This represents the signal seen by a proximity type probe at the position marked as 0°.

Runout Example

In this example it can be seen that the out of roundness occurs at both the 90° and 270° positions. This produces a time history signal which has a frequency of twice the rotational speed (2nd order runout). In this case, if runout were not considered then it would appear as if we had a large 2nd order vibration when in fact there is none. An even more misleading situation would be if the runout were in anti-phase to the true vibration. In such a case it may appear as if there is little or no vibration when in fact there is a significant amount.

Runout is not a function of speed. At low-speed where there is not expected to be any dynamic vibration then PROTOR will capture the vibration vectors from eddy-current probes and save them as the runout data. These may then be used at any speed to remove the effect of runout by means of a vector subtraction to produce the runout free vibration data. When displaying displacements there is an option to apply ‘Runout Subtraction’ to show visually the effects of any runout. It is sometimes desirable to remove runout data prior to performing alarm checks.

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Don Davies

Applications Group Manager at Prosig
Don Davies graduated from the Institute of Sound and Vibration Research (ISVR) at Southampton University in 1979. Don specialises in the capture and analysis of vibration data from rotating machines such as power station turbine generators. He created and developed the PROTOR system and is Applications Group Manager at Prosig. Don is a member of the British Computer Society.

This Post Has 13 Comments

  1. joel

    i have one doubt .in vibration probe nagative voltage is using why?we can use positive voltage?pl give me advantage,dis advantage

  2. Don Davies

    Hi Joel – I think it depends on the probe manufacturer as to whether they can accept a positive or negative driver voltage. The majority of the eddy current probes we see require -24V but I see that there are some around which will accept +24V.

    Basically the operation is the same in that the voltage applied to the driver creates an RF signal which is transmitted to the probe tip by a tuned extension cable. There is a coil in the probe tip which generates an electromagnetic field. Any conductive material in this field will have eddy currents setup in its surface which absorb the energy and cause the output of the probe to decrease proportional to distance between the probe tip and the target. If the target is very close to the probe tip then the absorbtion is high and the output of the probe is greatly reduced (zero when touching). If the target is very far away then the absorbtion is less and the probe output is close to its drive voltage.

  3. Ben

    I’ll like to determine the shaft orbit of mixer shaft with accelerometers. The shaft is rotating at 130 rpm. Can I integrate the accelerometer signals to determine the shaft orbit.

  4. Don Davies

    Hi Ben,

    I presume your accelerometers are mounted externally and will therefore measure the ‘seismic’ or overall vibration of the complete bearing assembly. This is not necessarily the same as the movement of the shaft internally. Most of the energy measured externally will be related to movement of the shaft but will be influenced by various effects such as the bearing stiffness in the direction in which the transducers are mounted. To measure the actual movement or orbit of the shaft in the bearing you will need to use non-contact shaft displacement probes.

  5. Ndama PY


    I need a conversion table or formula for vibration units, say microns, mm/sec or whatever. My mail address will do.


    1. Alan W

      Go to and download their Vib Calculator, its very good.

  6. Kishore

    As per my knowledge, shaft runout is observed as slow roll vibration during diagnostics. I wanted to know how sensitive is the runout to the overall vibration.

    Say the runout is 15 microns and shaft vibration as measured by proximity probes is 30 microns. Does it mean that 15 microns is contributed by runout and other 15 can be attributed to other causes?
    Or is it like runout has magnified it’s effect on overall vibration?
    PS : the unbalance is very less and the possibility of unbalance causing vibration is very remote.

  7. 510Ken

    Negative voltages a proximity probe gaps comply with API Specification. API specifies the movement toward a measuring device will produce a positive indication from the device. A dial indicator produces a positive going indication when the space between the gauge and the measurement gets smaller. Take a probe gapped at -10 Vdc; when the shaft moves closer to the probe, the shaft absorbs more eddie currents. When the physical gap between the probe and shaft is moved closer by +0.005″. The gap voltage changes from -10 Vdc (more negative) to -9 Vdc (less negative). This result is a positive going indication from the measuring device (prox probe). API specification is satisfed.

    1. Ramesh

      Does water entry in the oil lubricated bearing will increase the displacement of rotor shaft in micron

  8. Mihai

    How can I verfy the calibration betwen a tachometer and a vibrometer

  9. Fauzan

    Hi,kindly help me,

    currently we are facing high vibration (trip) in the NDE side of 11 stage of pump,
    i notice something strange in the orbit, timebase, the orbit showing reverse direction of shaft movement compared with the operation condition during first running.

    The waveform showing the high vibration value in the 1x and followed by 2x, 3x, 4x vibration increase. there are also increasing vibration in value less than 1x rpm. however somehow, there is too low spectrum in 1x rpm, which is only 30% of it normal value during operation.

  10. Mohamed Khalifa

    if the shaft vibration system is reading in micro meter peak to peak a X value of 100 and a Y value of 30, what does this mean?


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