Most vibration data plots, including: Timebase, Orbit, Polar, and Bode, present dynamic vibration data.  For seismic transducers, this dynamic data is inertially referenced to ground.  For the case of the shaft relative proximity probe, the dynamic vibration occurs about a –dc gap voltage, with the –dc gap voltage being proportional to the average distance from the probe tip to the target (shaft).  These data plots display dynamic vibration data, but do not show changes in the average shaft radial position, an important response characteristic of the rotor system.

If the dimensions of a nearby bearing or seal are known, then a clearance circle can be added to the Average Shaft Centerline Data Plot.  This circle (or ellipse) then represents the available diametral clearance in either the bearing or seal.

The Average Shaft Centerline data plot is designed to show changes in the average radial position of the shaft; thus, the plot is effectively low-pass filtered and does not display dynamic (vibration) data. However, when the information contained within the average shaft centerline plot is combined with other information such as known bearing and seal clearances, shaft orbit data, process information, etc. a detailed picture of shaft motion relative to bearing and seal clearances and / or radial loading is obtained.

The Average Shaft Centerline plot is most often used to display changes in shaft position versus speed, but it is also used to display changes in shaft position versus time, so the changes can be correlated to changing operating conditions, i.e. load.

Note:  The dynamic (vibration) signal from a proximity transducer is commonly referred to as the “ac” component of the signal from the proximity probe. In reality, it is not an ac signal since the polarity of the voltage does not fluctuate between + and – values. The dynamic signal from a proximity transducer is a varying, –dc signal.

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There are two pieces of information always available from the output of a proximity probe transducer. First is the “ac” or more correctly stated, the instantaneously varying –dc voltage which is proportional to the dynamic motion of the shaft centerline, i.e. vibration. Vibration data plots, i.e. orbit, bode, polar, spectrum, timebase, etc. are constructed from this information.  (Refer to the Note below.)

Changes in radial shaft position can occur with or without changes in the observed vibration response. Consequently, changes in shaft radial position are important to document in order to properly understand the total response of the rotor system.

The instantaneously varying –dc voltage (vibration) occurs about the –dc gap value.  The vibration data is depicted by the shaft Orbit, while the change in shaft radial position is depicted by the Average Shaft Centerline Data. The combination of the Orbit and the Average Shaft Centerline Data Plot in one data plot format is called the DC Orbit Data Plot.

Industry standard transducers (5mm and 8mm diameter transducers with a scale factor of 200 mv/mil), are linear over a range from approximately -4 to -20 volts dc with a corresponding physical gap of 10 mils to 90 mils from the probe tip to the target (shaft). If the gap voltages from two orthogonal transducers are low-pass filtered (to only pass the dc component), the results represent the average radial position of the shaft in the plane of the transducers.

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A Dutch oil-drilling specialist needed the two large-scale bearings for a very particular application: two Floating Production Storage and Offloading (FPSO) units. They are both converted oil tankers that have been retrofitted with special drilling apparatuses. These tankers can easily navigate at sea to offshore oil fields in deep waters. Furthermore, they do not require any costly installation work, in stark contrast to offshore platforms for oil drilling. In addition, the FPSOs can process and store the oil right on board. The customer is equipping the “Olympia” and “Antarctica” tankers for drilling activities 150 kilometers off the southwest coast of Africa. “For the customer, it was sufficient proof of what we are capable of,” explains Anja Quadflieg, Sales Offshore Technology, Tunneling, Cranes at thyssenkrupp.

This average position information from two, orthogonal, coplanar transducers is combined to produce a point on a XY (Cartesian) plot. The point represents the shaft at a particular location inside the bearing clearance. When a set of this data is collected versus time or speed, the plot becomes an Average Shaft Centerline plot. The plot has equal scaling in both horizontal and vertical directions and is square in shape. Shaft rotation and plot orientation references are indicated at the top of the plot. For a horizontally oriented machine, “Up” is normally used as the orientation reference to free space. The direction of shaft rotation is referenced to the established view of the machine train, typically from “driver” to “driven”. The data may be plotted vs. rotative speed, time, eccentricity ratio, or sample number.

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Sperm whales are almost 18 meters long. So are articulated buses and tractor trailers. The width of a four-lane highway with an exit lane is also 18 meters. And that’s the diameter of the world’s biggest slewing bearing. There has never before been a slewing bearing this large. Now thyssenkrupp has manufactured two of them, which were delivered to the customer at the end of 2015.

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If the measurement plane is close to the bearing or seal, and the clearance circle is accurately depicted, then the Average Shaft Centerline Data plot is representative of the actual shaft average radial position and provides a good indicator of approaching or exceeding the limit of the available clearance. If the measurement plane is some distance away from the bearing or seal, shaft deflection and mode shape can affect the apparent shaft radial position and must be taken into consideration.

[2] Machinery Malfunction Diagnostics and Correction; Eisenmann Sr., Robert C.; Eisenmann Jr., Robert C.; pp 410-415, 418, 578, 752; Chapters 9, 11, 14; 1998; ISBN 0-13-240946-1

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The second piece of information from the proximity probe is the average –dc value referred to as the probe gap voltage. The –dc gap voltage is directly proportional to the average distance from the probe tip to the target (shaft). The average position information is contained in the -dc gap voltage of the transducers over the linear range for which they operate. The Average Shaft Centerline plot depicts changes in the average radial position of the shaft centerline in two dimensions and is constructed from the -dc gap voltage part of the proximity probe transducer signals.

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Employees in Lippstadt, Germany, manufactured enormous segmental slewing bearings for two drillships. The feat pushed them to their limits, but only in terms of space.

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The vibration data is obtained from the “ac” portion of the proximity probe signal, while the Average Shaft Centerline Data is obtained from the –dc gap voltage portion of the proximity probe signal.

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Assembly was carried out in Lippstadt. Due to the dimensions, this wasn’t so easy. “Our R&D employees had just moved into a new facility, and their previous hall was just big enough to accommodate this contract.” There was only a one-meter leeway in some areas of the building. It drew many onlookers, too. “We proudly showed our other customers what we are capable of handling,” says Quadflieg. She adds, “We could manage bigger. We can manufacture bearings with diameters measuring 25 meters, too.”

An initial request was sent by email in the summer of 2013. “The largest slewing bearings that we had manufactured previously were 14 meters,” says Anja Quadflieg, who works in Sales at thyssenkrupp rothe erde and managed the project. “For the customer, it was sufficient proof of what we are capable of.” The bearings were ready at the end of 2015 and shipped to Abu Dhabi where they were reassembled under the close supervision of four thyssenkrupp employees. Once the pipeline turret-mooring system was installed, everything was transported to the Singapore shipyard where oil tankers are being converted into FPSOs.

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When a rotor system with hydrodynamic bearings changes speed or load, the stiffness and damping characteristics of the bearings are also modified.  As a result, changes in the average radial position of the shaft will also be observed. Primary and secondary machinery malfunctions such as misalignment, fluid-induced instability, and rubs, to name a few, can produce significant changes in the rotor’s radial position within the bearings and / or seals. These changes in radial shaft position can be directly observed via the average shaft centerline data plot. Correlation of shaft average centerline data with other vibration and process data provides a much more complete understanding of the total response of the rotor system. Hence, it is important to recognize that changes in shaft radial position are just as important an indicator of machinery health as changes in the dynamic motion (vibration) of the rotor and must not be overlooked during the analysis.

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The contract was demanding for both our technology and logistics. The bearing diameters are generally based on the planned load, yet they should never be any larger than necessary. For this reason, cranes and wind turbines usually have weldless forged rings with diameters measuring up to eight meters. You couldn’t transport them otherwise. In this specific case, the diameter of the lines that the rings needed to fit around were specified. The slewing bearing for the FPSO ship had to be far larger, which meant it needed to consist of segments. Nevertheless, each segment measures six meters.

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[3]  Thomas, G. Richard;  NO VIBRATION – NO PROBLEM: OR IS THERE?; The 24th Canadian Machinery Vibration Association Machinery Vibration Seminar and Annual General Meeting; 25 – 27 October 2006; Montreal, Quebec, Canada

The position of the shaft within the clearance circle is often expressed as the eccentricity ratio. The eccentricity ratio is a dimensionless quantity representing the average radial position of the shaft within the bearing (or seal). The eccentricity ratio is obtained by measuring the distance between the centerline position of the shaft and the center of the bearing (or seal), divided by the radial clearance. Consequently, the eccentricity ratio can vary from a value of 0 (shaft centered in the bearing) to 1 (shaft touching the bearing or seal wall). Eccentricity ratio has a direct effect on stiffness, damping, and stability.

Each slewing bearing from Rothe Erde connects one FPSO ship to the oil field. There is a turret-mooring system installed in the ship’s interior, which connects the lines on the ship to the 59 well centers on the seafloor. The FPSO also dynamically positions itself to compensate for currents and rough seas without entangling the pipes.

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[1] Fundamentals of Rotating Machinery Diagnostics; Bently, Donald E.; Hatch Charles T.; Chapters 6 and 7; 2001; ISBN 0-9714081-0-6