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Improving Turbine Vibration Monitoring Systems with Imbalance and Bowed Rotor Detection

by Kim A. Lovejoy, PresidentLovejoy Controls Corporation© 2008 Lovejoy Controls Corporation, All rights reserved. For reproduction authorizationrequest contact info@lovejoycontrols.com.

Introduction

No matter how sophisticated a turbine supervisory system may be, the ability to detectsimple imbalance or rotor bows is missing if the system is based upon the now-conventionalsimplex or dual (x-y) proximity probes mounted on the edge of or inside journal bearings.

Further, if tighter steam seal clearances are proposed for higher turbine efficiency, thesegains will be soon hammered away if rotor imbalance and bow is present and not detected. This isnot a criticism of the proximity probes themselves or their electronic function... they can work justfine. The problem is where they are located and what they fail to report.

How can this be? Don't the proximity probes detect the shaft vibrations? Why aren't theyeffective for bowed rotors? The answers will come as a surprise to even most experiencedvibration analysis engineers and requires an understanding of what exactly moves in relationshipto what doesn't move when a large turbine generator set exhibits unbalance or a rotor bow. Butbefore we plow into the details, the history of proximity probe implementation will shed somelight on how we got here, and why we need to "tweak" vibration data acquisition systems to makethem more effective.

In the Beginning There Were Bearing Pedestal Cover and Shaft Rider VelocityTransducers...

Turbine manufacturers began commonly supplying vibration monitoring supervisorysystems in the 1960's. The vibration sensors used were almost always velocity transducers witharound 10 Hertz minimum detection frequencies. These transducers were usually located alongthe turbine-generator set in one of two (or both) locations:

(1) Fixed to the bearing pedestal cover.

(2) Set atop a "Shaft Rider" mechanism which spring-loaded the transducer to a lowfriction rod tip which came into contact with the rotating shaft at guide holesdrilled in bearing oil seals or through bearing bracket covers.

The radial position of these mounts was usually vertical, but not always. Sometimes when

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Figure 1, Turbine OEM Monitoring Points at Inboard Oil Seals

a bearing pedestal design provided more freedom for horizontal motion, a horizontal transduceror shaft rider mount position was used..

Each of these original monitoring locations had advantages and disadvantages. In the pluscolumn, phenomena like imbalance and bowed or bent rotor displacements which were zero at thejournal bearing points and increased as axial distance increased from the bearing were wellrepresented and amplified to monitoring systems.

On the minus side, the vexing plague of both Steam Whirl and Oil Whip phenomena whichaffected hundreds of turbines in the 1960's and 1970's went almost entirely undetected by theconventional velocity transducers on covers or shaft riders. Also, shaft riders were particularlysensitive to errors in readings from dinged or dented rotors from lifting slings and temporarysupports used during maintenance outage disassembly. Shaft riders also had the working tipsroutinely wear out and were a general maintenance nuisance.

Don Bently and the Proximity Probe ...

Inventor of the eddy current feedback displacement probe system, and founder of theoriginal Bently Nevada Corporation, Donald Bently, ingeniously devised a sensor system usingtwo

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Figure 2, Monitoring Location Migration for Proximity Probes

of his probes mounted an offset 90-degrees from each other to monitor instantaneous relativeshaft motion with respect to the bearing when plotting against one another in x-y coordinatesmethod. Using Bently's method, the erratic and violent path of the shaft in the bearing under bothSteam Whirl and Oil Whip phenomena could be detected, diagnosed, and plotted for engineersand operators to see. These mysterious ailments which shook turbines to their foundations were

finally reliably analyzed and soon solved respectively by the introduction of unit lift valvesequences and tilting pad bearings.

A side benefit of the proximity probes quickly became apparent to users. Since the probesdid not touch the shafts, they did not require any routine maintenance. In fact, Bently's probeswere so robust, they could be buried deep inside the bearing pedestals, mounted on the bearingend face where the exiting shafts were not dented nor dinged to distort the data. Yet anotheradvantage of the proximity probes' were their ability to produce useable displacement outputsright down to jacking gear speeds, without the velocity probe's annoying 10 Hertz lower cut off.

As often happens with technological breakthroughs, the use of proximity probes soondominated sensors in turbine vibration monitoring to the point that little else was soon used.

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Now a Look at What Moves with Respect to What...

No area of rotor dynamics is more misunderstood than the nature of shaft deflections oflarge turbine-generator set rotors. The misunderstandings result from three common errors:

Error 1: There is significant measurable relative motion between the shaft and thebearing journal lower half during operation.

Error 2: All signals produced by proximity probes are the result of relative motionto the target surface.

Error 3: Adding a velocity sensor fixed in line with a proximity probe andsubtracting the mount signal from the probe produces an "absolute"vibration signal.

Unless a massive failure occurs, or the aforementioned Oil Whip or Steam Whirl arepresent, the rotors remain atop a very thin oil wedge within 0.003-inch of the lower half of thejournal bearing. Many, but notably Dudley Fuller (Theory and Practice of Lubrication forEngineers, 1984, John Wiley & Sons), have well defined the characteristics of the oil wedge andprovided accurate formula for wedge pressure and compressibility.

Let's take a large tandem compound turbine generator set low pressure rotor which wasunder abnormally high vibration as an example and solve for the bearing forces and deflections. This example will also apply with appropriate adjustments, to all major journal supported rotors.

Nuclear 1800 RPM LP, 15 mils Static at Each IB Oil SealRotor Weight = 115 Ton Running Speed = 1800 RPM

The best vibration analysis returns to force analysis to judge the true magnitude of phenomena. The balance correction installed in this turbine's end planes which effectively eliminated thedeflection was approximately 1.9 pounds working at a balance plane radius of about thirty inches. This provides that the deflection force can be accurately calculated as the corrective weightcentripetal force:

F = mV^2/r

where : F = Force (lbf) m = mass (slugs)V = velocity (ft./sec.) r = radius (feet)

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Using the balance move numbers yields:

V = 30 cycles/second x radius in feet x 2 x ð = 30 x (30/12) x 2 x ð= 471 ft/second

m = 1.9 lbs scale / 32.1 lbs scale/slug= .059 slug

r = 30 inches / 12 in/ft= 2.5 feet

Solving for force:

F = mV^2/r= (.059 slug) x (471 ft/second)^2 / (2.5 feet)

= 5235 lbf.

To summarize the above calculation, the corrective balance weight of 1.9 lbs at 30-inchbalance end plane radius produced a corrective force of 5235 lbf (each end) to remove the staticrotor deflection of 15 mils at the inboard oil seals. This is a very large deflection, much largerthan would be tolerated for continuous operation.

In the second calculation we will determine the loading force at each rotor end supportjournal bearing. Assuming proper alignment, each bearing will support half the rotor weight:

Bearing Load = 230,000 lbs / 2 = 115,000 lbf.

We can now draw a vector force diagram representing each journal bearing. We have adownward acting force of 115,000 lbs and a rotating radial force of 5235 lbs. At it's minimum,the downward holding force at each bearing is 109,765 lbs. In other words, this very high andunacceptable level static vibration represents a force of only 4 1/2 percent that necessary to "lift"

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Figure 3, Vector Force Diagram at Bearing

the rotor off the lower bearing half.

In the final calculation we'll examine if significant motion might occur in the oil wedge. From Fuller, the stiffness of the wedge, K, is first determined by:

K = w/s Using a liberal s = 0.003 inch, K = 115,000 lbsf / 0.003 in= 3.8 x 10 lbsf/in7

The oil wedge compression due to the imbalance force is then:

ds = 5235 lbs / 3.8 x 10 lbsf/in = 1.36 x 10 inch or 0.136 Mil7 -4

What has been determined? An unacceptably massive imbalance on a large tandemcompound turbine rotor shows only 0.136 mil in differential rotor to bearing lower half motionper revolution. Proximity probes mounted at the bearings and reading the rotor surface canmeasure no greater than 0.136 mils of peak-to-peak vibration, and totally miss detecting themassive unbalance. Since rotor bows also exhibit similar static deflections during start up, theprobes will likewise fail to detect large bows which destroy steam seal fits, indicating instead thatall is well.

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Figure 4, Electrical Runout Patterns

Error #1 "There is significant measurable relative motion between the shaft and thebearing journal lower half during operation" has been exposed since a huge rotor vibration orbow phenomena produces an almost immeasurable vibration change, we must abandon the use ofproximity probes at bearings to obtain significant unbalance data.

OK, you may say, it appears that the probes won't pick much up but what about theroutine levels of 2 or 3 mils we read on the probes now? Doesn't this indicate we still see somevibration between the rotor and lower bearing half? The answer is no. What is typically displayedas vibration amplitude is actually Electrical Runout.

Electrical runout is a property of eddy current proximity probe systems caused by theprobe's sensitivity to metallurgical differences in the surface of the target rotor. The signalconditioner output under electrical runout looks very similar to and is almost always mistaken forvibration,. Two tests can be performed to distinguish electrical runout from true vibrationcomponents and are highly recommended to anyone operating a large turbine set under bearingedge proximity probe supervisory systems.

The first and most accurate test must be performed during an outage at a time when thepedestal covers are removed and access is available to the probes and shaft. This can usually bearranged when alignment readings are being taken. Install a recording oscilloscope channel oneach proximitor (probe conditioner) output, and install a mechanical dial indicator to ride thesame position as scanned by the proximity probes. Under jacking gear or mechanical rotation, rollthe rotor one full turn while recording the oscilloscope channels and observing the Total IndicatorRunout (TIR). Convert the oscilloscope peak to peak reading to mils according to the gain of theproximitor, usually 200 mV/mil. Any amplitude of the proximitor output which is not

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Figure 5, Absolute Probe System Functions

collaborated by the TIR is a false electrical runout reading which at speed is likely 99% of therecorded amplitude misinterpreted as vibration.

The second test is more of an approximation, but nonetheless useful. In this method thedigital recording scope is attached to the proximitor outputs under turbine operation. Theresulting captured waveforms are then examined. Running speed frequency vibration due toimbalance, if present, will be represented by a very smooth sine wave signal, free of steps anddiscontinuities while electrical runout will produce a more jagged pattern.

Error # 2, "All signals produced by proximity probes are the result of relative motion tothe target surface" is confirmed by misinterpretation of electrical runout.

Faced with the embarrassment of vibration monitors that don't detect vibration, severalinstrument manufacturers have offered what they term as "Absolute Probe Systems" to "solve"the problem. Their theory goes like this, if the proximity probe AND its mounting hardware areBOTH in motion, a velocity probe in line with the proximity probe will recover the "lost relativemotion" when the velocity signal is subtracted from the proximity probe signal. This sounds niceon the face of it, but after further review does not hold true for several key reasons.

The theory behind these "Absolute" probe systems seems to make sense on an electroniclevel... Take the raw eddy-current proximity probe signal and perform a real-time subtraction ofit's seismic motion as measured by a velocity or accelerometer transducer on the mountingbracket, applying a 90-degree or 180-degree correction respectively to transducer type. This isthe sort of feature that is very valuable in selling instrumentation. The idea that a signal can beobtained which has all extraneous probe mount motions automatically removed, providing an"Absolute" signal of impeccable accuracy will appeal to almost anyone buying vibrationmonitoring equipment. Too bad it doesn't work!

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For starters, as previously presented, if the probe system is located at the bearing the eddycurrent probe portion of the mix has no data of value so we have a "garbage in" scenario.

Even if we started with a correct proximity probe signal which represents vibration andnot electrical runout, three vibration properties, PHASE, RESONANCE, and BANDWIDTH,render absolute probes inaccurate on large turbines.

PHASE

Referring to Figure 5, the turbine rotor motion does not directly translate into an equalphase probe mount motion due to the viscous coupling of the bearing oil film and the bearingclearance. In other words, there is always a time delay between the high spot of the rotorvibration and the high spot of the probe mount. This delay can be measured if we plot bothsignals on an oscilloscope, and is a property of speed and the specific journal bearing's clearance,bracket, and support structure. It is not something which can be "assumed" for all rotatingmachinery. Subtracting waveforms which are out of phase yields massive inaccuracy.

RESONANCE

Note again on Figure 5 that the probes' mounting system is on a differentmass/spring/damper system than the rotor's. It is then perfectly conceivable (in fact, predictable)that the energy transfer between the rotor and the probe mount will not be uniform over the speedrange of the turbine. For example, as the rotor passes through its first critical speed (naturalresonant frequency) it will yield higher running speed frequency deflections. The probe mountsystem resonant frequency will be at a somewhat different speed due to the independent coupling. Consistent subtraction of the latter from the former ignoring the difference again yields massiveinaccuracy.

BANDWIDTH

Real-world sensors are not perfect. This fact often poses a dilemma for junior engineersor amateurs specifying turbine instrumentation. Eddy-current proximity probes operate rightdown to zero frequency since their output represents the instantaneous gap between the probe tipand the rotor. Velocity and acceleration transducers, however, have limitations on minimumdetection frequencies. For example, many velocity transducers have drop-off frequencies at 10Hz. For an 1800 RPM turbine this represents 1/3 of the speed range in which no correction ispossible even if the phase and resonance problems were addressed.

The "Absolute" probe system may be applicable in some vibration monitoring situationswhere the phase, resonance, and bandwidth differences are all clearly defined and accounted for in

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adaptive corrections and the proximity probes are not mounted at bearings.. Unfortunately this isnot the case for steam turbines. To suggest that a common product offering can successfullyaccomplish these corrections on a variety of machines is sales talk and not reality.

Thus Error 3, "Adding a velocity sensor fixed in line with a proximity probe andsubtracting the mount signal from the probe produces an "absolute" vibration signal" isconfirmed by the poor technology and application engineering of the "absolute" probe systems.

So how are these machines to be properly monitored for unbalance and bows?

In every case of vibration supervisory system failure to detect significant unbalance orrotor bow which damaged steam and combustion turbine seals, the true severity of the situationwas confirmed by older hand held meters used on bearing covers, often at the demand ofoperators whom did not believe that the entire turbine floor was shaking due to a mysteriousreasons but correctly suspected that shaft unbalance was the culprit, regardless of how low thesupervisory proximity probe data was reading.

We can take the hand held instrument confirmations to the next step and provide anengineered installed sensor system solutions to eliminate undetected, damaging vibration.

The solution, Tuned Vibration Monitors (TVM), is based upon the mechanical structureof the bearing pedestals and using the laws of simple harmonic motion to our advantage. Thisdesign is based on the following facts:

FACT #1 The rotor is the only significant source of vibration energy. It providesthe forcing function for all other vibration on the support structure andfoundation.

FACT #2 The pedestal support structure flexes to absorb the vibration energysourced by the rotor, the rotor does not "bounce" in the bearing.

FACT #3 Components attached to the pedestal support structure will vibrate in aforced and in some cases a resonant manner.

FACT #4 Important measurement bandwidth of rotor sourced vibration is from1/2 to 2 times the immediate running speed frequency with a majority

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Figure 5, TVM Internal Components

of phenomena manifesting itself at 1 x running speed frequency.

The Tuned Vibration Monitor (TVM)

The Sensor Canister Package

Using the four facts above, the TVM design starts with an integrating accelerometersensor which has a bandwidth from several Hertz to far beyond what's needed, but more on thatlater. The routine problems with using accelerometers are the adverse properties of signaldistortion from vibration components not in line (off axis) with the sensor and the sensitivity athigh frequencies to capture and amplify extraneous resonances. On the positive side, theintegrating accelerometer by functioning down to several Hertz provides start up rotor bowprotection at very low turbine speed before damage results.

To address the two integrating accelerometer drawbacks of off axis distortion and highbandwidth noise the accelerometers are installed in a specially designed canister as shown inFigure 6. The accelerometer is attached to a diaphragm which permits freedom of motion only onthe central axis thereby eliminating off axis distortion. The four tensioners on the diaphragm tabscenter the diaphragm and load it to prevent lateral motion. The accelerometer is further supportedbetween two wave springs sized in spring constant to provide a spring-mass system low passfilter. The characteristics of the spring-mass low pass filter are changed to meet the monitoringfrequency bandwidth of up to 4 times running speed frequency.

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The resulting assembled canister has a threaded mounting bolt which is installed in atapped hole on the turbine bearing pedestal cover in a location carefully determined by a vibrationsurvey. The survey determines the most appropriate surface and angle to detect the forcedexcitation of the rotor system while avoiding resonant structures which could exaggerate levels. Some system pedestals benefit from two TVM canisters to capture more than one forcedexcitation degree of freedom.

The electrical signals from the canisters are purely sinusoidal harmonic motionrepresentations of the rotor vibration energy. A correlation calibration is performed whichprovides a transfer functions to yield equivalent inboard oil seal mils displacement, the basis formost turbine manufacturer's operational limits, to the individual TVM canister velocity outputsover the operating speed range of the turbine.

Signal Conditioning

The integrating accelerometer (velocity) outputs are cabled a short distance to a smalljunction box which contains an isolating transmitter which amplifies the signal to a 4-20 mA signalfor travel to a receiving voltage converter located at or near the Turbine Supervisory Instrument(TSI) Panel. From here the signal is applied to a vibration channel input of the TSI. Flexibility inthe voltage converter permit matching signal input ranges for any TSI input.

Stand Alone TVM Signal Processing

If the existing TSI system does not have spare channels for expanding to TVM inputs, adedicated monitor with both real time alarms and data archive functions can be supplied.

Cost Benefit Analysis

COSTS

A good ballpark hardware cost estimate for adding TVMs to an existing TSI is $3K perbearing, which includes the individual pedestal evaluations and TVM specifications. If theexisting TSI cannot be expanded to include the TVM signals, add another lump sum of $25K fora monitor/analyzer. If data archive storage and retrieval are to be included (vs. periodic Ethernetor ModBus link to Plant Data Computer) this will add another $20K.

Summarizing hardware costs:

$3K x (Number of Bearings) if using existing TSI Inputs + $25K if Stand Alone Monitor/Analyzer with Data Link is Needed + $20K if Data Archive Storage & Retrieval is Needed

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Figure 6, Rotor Bow

Installation costs must cover the probe and local junction box mounting in a manner inwhich they are easily and safely detached turbine outage maintenance periods. A single cablemust also be run between the local junction boxes and the TSI or Stand Alone Monitor/Analyzeror a wireless system may be used if permitted in the plant. These costs vary from site to sitedepending on run distances and available instrument cable trays. All signals are shielded lowlevel.

BENEFITS

On the benefit side, the TVM upgrade will add detection and alarm notification tooperators for the turbine damage and plant safety threats associated with Bowed Rotors andUnbalanced Rotors. The commonly observed scenarios of each of these phenomena will bediscussed in detail.

BOWED ROTORS

A large LP turbine rotor may be temporarily bent, or bowed, if subject to differentialheating. The most common cause for differential heating is a stopped shaft. Following a coastdown the turbine case slowly cools from operating steady state temperature and as long as therotor keeps spinning (or under turning/jacking gear rotation) the rotor cools evenly. If the rotor isstopped, however, the lower side facing the condenser will be cooled faster than the upper sideresulting in greater thermal contraction of the steel on the lower side in comparison to the upper. The contraction causes the rotor to deflect upward (not "sag down" as is often misrepresented) ina single bow (static) pattern which moves the rotor center of mass to an offset position withrespect to the center of rotation. This phenomena shown in Figure 6.

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A second cause of rotor bows is found in fossil plant steam turbines which usedesuperheaters to feed gland steam sealing systems. Temperature excursions caused by poordesuperheater controls. The excessive temperature steam expands the rotor segments in the glandcases causing rotor distortions. Unlike shutdown induced bows, gland steam induced bows canoccur during normal full loaded operation.

Common operating practices of correcting for a bowed rotor due to a planned shaftstoppage is to rotate the shaft 180-degrees and maintain that position for half the originalstoppage time. This tends to lessen the bow, but is a gross generalization and in most cases doesnot fully eliminate the bow.

A bowed rotor presents both machinery damage and plant safety risks. As a bowed rotoris accelerated above about 600 RPM, the center of mass offset to the center of rotation willincrease the bow due to centripetal force. Continuing acceleration to between 1000 RPM and1250 RPM on most large rotors brings the rotor into the First Critical Speed, or the first moderesonant frequency of the shaft. As the First Critical Speed is approached, the resistive dampingto center deflection is greatly reduced and the rotor bends much further.

Damage occurs when the rotor bow at any axial location exceeds the clearance betweenstationary and rotating radial components. The closest radial fits are the interstage steam sealslocated near the center of balanced flow turbines in the area of maximum bow deflection. Thefirst level of damage is the impacting of these seals which are "pounded back" by the high spotside of the bowed rotor. The resulting impact damage opens the interstage seal clearances andrepresents a permanent loss of turbine efficiency until the seal clearances are restored. For atypical steam turbine, the loss of interstage seal fit represents a major thermal efficiency drop onthe order of 0.25% to 0.5% and rivaled only by blade loss or extreme nozzle block wear inconsequence.

A more severe threat, and the next step of bowed rotor damage in start up, happens if thebow deflection reaches the point at any axial location to contact a blade tip or shroud with thestationary element. When this occurs the chance of shroud and/or blade loss is much higher, andcatastrophic failures threatening plant personnel in the turbine floor area have resulted.

UNBALANCED ROTORS

An unbalanced rotor is one in which the operating speed center of mass does not coincidewith the center of rotation. All rotors exhibit some imbalance, and a small amount has a negligibleeffect on the machinery condition and plant safety. Large imbalance is another case.

The logical question is what constitutes an acceptable imbalance condition and how is anunacceptable level determined? Unfortunately the answer is neither simple nor straight forward. Most turbine manufacturers gauge imbalance severity by the shaft mils vibration taken at the

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Figure 7, Potential Deflections and Multiples of Inboard Oil Seal Levels

inboard side pedestal cover oil seals. A traditional Westinghouse standard, and similar for otherturbines, is given in the chart below.

Running Speed, RPM Maximum OperatingMils at Pedestal InboardOil Seals

1800 RPM 7.0 mils

3600 RPM 3.0 mils

Note that the severity limits in the chart do not address start up speeds nor do theyaccount for vibration deflection patterns. These tend to be important to determine whether thevibration will damage seals. To illustrate this, Figure 7 depicts the possible deflection patterns atrated speed for a large low pressure turbine rotor typical found in a tandem compound units.

The rotor shown, like almost all steam turbines, operates between its first and secondrotor critical speeds and therefore is capable of dynamic (red double bow) or static (blue singlebow) deflection and any combination thereof. In the cases shown in Figure 7 these deflections arerepresented as multiples of the vibration levels measured at the pedestal inboard oil seals. It isevident from Figure 7 that a key in determining whether rotating and stationary parts will comeinto contact is the shape of the deflection. Clearly it is important to analyze each turbine rotor fordamaging vibration levels and not assume a single scalar limit applies to all.

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PREVENTION OF DAMAGE

The addition of TVMs at each bearing and engineered alarm setpoints based upon rotorcontact points upgrades a TSI system to alert operators of pending damage before it occurs. Inthe acceleration of steam turbine units during startup it is imperative that a bowed or highvibration rotor not be increased to the first critical. The TVM system addition provides adequatewarning prior to seal impacting.

Operators encountering TVM alarms are instructed to cease the acceleration and decreasethe unit speed to the previous hold point, typically 600 RPM. If the cause of the TVM alarm is abowed rotor, a short period of slow roll under steam will relieve the bow and permit resumedstart up. If the cause of the TVM alarm is imbalance, a corrective balance move should beimplemented.

One can argue that there are times when the operation of the turbine-generator set is moreimportant than the survival of the steam seals, and that a small amount of damage induced byaccelerating a rough machine through the first critical is outweighed by the load dispatcher'semergency. Even given these compromise conditions, is it not better to know the damage is beinginflicted rather than to operate blindly?