M-424 Basics of Vibration Analysis

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g BASICS OF VIBRATION ANALYSIS

GENERAL

Through many years of experience gained in the operation of turbine-generators, it has become veryevident that all components of these units should operate at the loest possible vibration levels! "nits

that operate at high vibration levels for long periods of time are li#ely to incur increased maintenancecosts and loss of revenue due to the inherent dontime! The ever increasing costs of maintenance

outages and the importance of vibration free operation ma#e it necessary that $%&E engineers ac'uires#ills to effectively execute accurate balance programs! (efore ac'uiring these s#ills, the field engineer

must understand vibration characteristics, critical speeds, and high spot theory! $n addition, he must be

able to or# ith the tools that are necessary to accurately measure vibration levels in all components ofany particular unit! This section ill discuss these basic items!

)E*T+R ANAL&$& AN .+LAR *++R$NATE&

.roper use of vector analysis is an important tool hen evaluating vibration data! )ibration data is

analy/ed by using vectors because they accurately indicate the magnitude and direction of theunbalanced condition! A set of vectors as used in vibration analysis is defined as a set of arros that

have a given length, point in a given direction, and combine by addition using the parallelogram la!

$f a vector Ais immediately folloed, tip to tail, by a second vector (, the arro hich runs from the

beginning of Ato the end of (is the sum of A0 (! *onversely, if A+12 (, then 12 (-

A! The mathematical las of vector addition and subtraction are the same as in ordinary algebra! Let

1 and be the rectangular coordinates and 3r, 4 the polar coordinates of a given .oint, .! 3&ee 5igure

6!4 Then,

1 2 r *os = r &in

2 arc tan 71

r821808

Example9

)ectorially add the folloing set of vectors

A= : units at ; units at 6


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BASICS OF VIBRATION ANALYSIS

5igure 6

5igure 8

- 8 - :8:


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The preceding example can also be resolved by using trigonometric functions! Each vector is resolved

into its 1 and components!

1 2 A10(10*1

2 : cos ; cos 6 2 3180

84 D2 6B

2 arctan 3714 2 ;>!BC=

Therefore, 2 6B units at ;>!BC=

The ability to properly utili/e vector analysis on .olar *oordinate paper is extremely important in theimplementation of successful balance programs!

*ARA*TER$&T$*& +5 )$(RAT$+N

The subFect of vibration deals ith the oscillatory behavior of all bodies possessing mass and elasticity!

The simplest form of oscillation, #non as harmonic motion, ill be described!

armonic motion is illustrated in 5igure C by a rotating vector 3A4 hich results in a sine ave! Thepoint on the sine ave 3hich repeats itself over e'ual time intervals4 is represented by the

trigonometric functions A sin t or A cos t! The time elapsed hile the motion repeats itself is called a

period, and motion during this period is a cycle! 5re'uency of vibration is the number of completecycles in a specified time period, and the pea# value, or amplitude of the motion is A!

5igure C! armonic otion 5ormed by a Rotating )ector

- C - :8:


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This amplitude is referred to as the pea#-to-pea# displacement of the sine ave, and is expressed in mils

36 mil = ! depicts the shape of a rotor that is operating nearthe first critical speed! 5or purposes of illustration this shape is highly distorted!

A rotor in this condition is often balanced by placing eights in the planes provided near the ends of therotor! oever, it is balanced most effectively at midspan 3as determined by 5igure >4, but this is not

alays possible for many rotors! The end planes and midspan are the locations here the centrifugal

force of the balance eight counteracts the unbalanced condition as shon by the arros!

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5igure >! 5irst *ritical ode

(alance eights of e'ual effective si/e 3eight x moment arm4 are located at each end of the rotor, or

one eight at midspan, in order to counteract the situation shon in 5igure >! A correction of this type is

called a static pair or a midspan static! $f a coupling span is operating in an unbalanced condition, ittends to run in the static mode! All components of a turbine-generator unit do not reach their critical

speed at the same time! Typical first critical speeds for a G-C type turbine-generator are as follos9

Rotor &peed3R.4igh .ressure 86 - :8:


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Again, using a G-C type of turbine-generator unit, the second critical speeds are as follos9

Rotor &peed3R.4

igh .ressure ::


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determined by using this information! After a balance shot is made, repeated plots ill result in an

accurate measured effect method for any refinement that may be necessary!

$G &.+T TE+R

)ibration is caused by a stimulus created by pulsating forces due to a rotor that rotates about itsgeometric center rather than the center of mass! An ideal system shon in 5igure @ consists of a single

disc of mass 34 symmetrically located on a shaft that is supported by to bearings! The center of mass

3*4 of the disc is at a radial distance 3E4 from the geometric center 3>4 of the disc! The centerline ofthe bearings intersects the plane of the disc at 3


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ividing by J,

r 2 M37 N4838E4 7 M36- 37 N4

8 3E'uation C4

E'uation C relates the lateral deflection 3r4 as n function of the operating speed 34 and the natural

fre'uency of lateral vibration 3N4 of the shaft and disc! 5rom this e'uation e can ma#e the folloing

conclusions9

6! Ihen unit speed 34 is less than the natural fre'uency 3N4, the denominator is positive!

ence, the lateral deflection 3r4 is in the positive direction!

8! Ihen unit speed is e'ual to the natural fre'uency, the denominator is /ero! Therefore, the

magnitude of lateral deflection is infinite and a self-destruct condition exists!

C! Ihen unit speed is greater than the natural fre'uency, the denominator ill be negative!

ence, the direction of lateral deflection is negativeK compared to conclusion 6!

:! Ihen unit speed is much greater than the natural fre'uency, the lateral deflection approaches

the value of radial distance 3E4! Therefore, the disc ould be rotating about its center of

gravity 3*4!

The comparison of conclusions 6 and C is important! $f the lateral deflection is ta#en as the high spot, ecan see that it changed position relative to the geometric center by 6@


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The presence of the frictional force 354 no enables line E to lead liner by an angle as shon in

5igure ?! The forces indicated in the diagram presuppose that the points indicates that is constant at any given speed and thereby substantiates the assumption

that +, &, and G remain fixed relative to each other and rotate about + ith speed ! To observations

can be made ith the damping factor remaining constant9

6! As speed varies from a value much less than the Onatural fre'uency to a value Fust belo

natural fre'uency, Tan varies from 0< to + , and varies from


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$G &.+T *+N)ENT$+N

Revie 5igure ? and E'uation >! Refer to 5igure 66 and consider the disc to be lengthless and mounted

on a massless shaft 3similar to 5igure @ except damping exists4! This model may be used to analy/e shaftbehavior at the first critical speed!

The center of rotation is not coincident to the center of mass, and as the shaft accelerates, a smalldeflection develops in line ith the center of mass! This point is called igh &pot 6 here =


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Ihen the standard convention is used, the rotor and7or stator is mar#ed by one of the to methods

shon in 5igure 6:!

&TAT+R RE5EREN*E ET+ R+T+R RE5EREN*E ET+

5igure 6:! Rotor and &tator ar#ing *onventions

The rotor reference method has a reference point mar#ed on the rotor hich passes angles that aremar#ed on a stationary turbine component! +n the other hand, the stator reference method has the anglesmar#ed on the shaft and the hori/ontal Foint is used as the reference point! This method is preferred for

large shafts here it is difficult to strobe the shaft at all angles! Iith each method, the reference mar#

sees an increasing angle as the rotor turns, thus adhering to the convention! The rotor /ero mar# shouldbe set to correspond ith the T&$ phase meter bolt here applicable!

$t may be necessary to deviate from the stated convention hen or#ing ith older turbine-generator

units for the folloing reasons9

6! The customer may already have his e'uipment mar#ed by another convention 3this situation

often occurs4! Exercise extreme care in this case by ma#ing sure the procedure utili/ed is

ell documented on the data sheets!

8! &ometimes there isnKt any visible mar#ing system and the machine is in operation! $n this

case, try to identify an existing mar# on the shaft by using the strobe light! Ihen it is found,

use it as the


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Ihen no shaft riding probe is present, a shaft stic# 35igure 6>4 may be used to ride the shaft near the

bearing that is being measured! The shaft stic# should be made of ood and thoroughly soa#ed in oil!

*oupling covers contain drilled access holes sealed ith pipe plugs! These holes permit access to thecoupling rims in order to obtain vibration readings! These readings are usually ta#en by using a ood

doel rod thoroughly soa#ed in oil! The oil acts as a lubricant and helps to diminish the burning that

ta#es place as the ood rides the shaft!

)ibration readings on the collector rings may be ta#en directly off the brushes by using doel rods!oever, hen this is done ma#e sure the rod is ell insulated!

5igure 6> &haft Riding &tic#

&TAT$+NAR REA$NG&

Ihen access to the shaft is not readily available, bearing cap readings may be used! These readings areta#en in the hori/ontal, vertical, and axial directions! $f stationary readings are ta#en on stationary parts

other than bearing caps, the location and type of reading should be ell documented!

ATA RE*+R$NG

*are must be exercised hen recording any data that is pertinent to a vibration problem! .referably, thisdata is recorded hen the unit is loaded and operating under steady state conditions! $t should also be

consistent and repeatable! Locations and severity of critical speeds 3magnitude and phase angle4 are very

useful tools hen analy/ing data properly!

The folloing items indicate available data that is generally useful hen conducting a balance program!6! ate - All data sheets, graphical plots, etc!, should be properly dated including the time of

day!

8! *ustomer, "nit, and Turbine Number!

C! Turbine *ode, Last &tage (uc#et Length and Type of Exhaust ood here applicable!

:! E'uipment "sed - .roperly identify the vibration recording e'uipment because the

e'uipment constant is very important!

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>! ethod used hen referencing data to turbine position! Rotor Reference ethod, &tator

Reference ethod, or anotherP $f an abnormal method is used, a short explanation or

illustration is arranted!

;! .ic#up Angle - &tationary angle of vibration probe! *onfusion is minimi/ed by #eeping this

angle constant!

B! *ritical &peed - agnitude, phase angle, and turbine speed!

@! Load - JI and J)A!

?! &hot Number - Aids in chronological record #eeping!

6


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L$GT (EA

The )ibration isplacement $ndicator 3)$ or Light (eam4 is a hand-held, mechanical optical device

that measures vibration displacement! $f properly used, it gives direct and accurate vibrationmeasurements at speeds beteen 68


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these lo speeds is not sufficient to actuate the e'uipment! )ibration readings should be considered

approximate beteen ;


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$n order to find the shaft High &pot from the meter reading, the folloing e'uation is used9

HS= M- RG+ CAL-90 3E'uation ;4

Ihere HS angle against rotation from the phase reference generator bolt to the high spot

M resolved phase meter reading

RG angle against rotation from the shaft vibration pic#up to the phase reference generator -

usually /ero

CAL pic#up speed calibration angle hich is alays positive as follos9

&peed CAL

+ver C


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The sine ave produced by the vibration probe can be compared to the signal generated every

revolution! The angle displacement beteen the spi#e and the next maximum of the sine ave is the

phase angle! &ome units utili/e a igital )ector 5ilter that displays this phase angle digitally!

The field engineer ill re'uire the use of a dual trace oscilloscope for most units! Ihen using the

oscilloscope, set the time scales so that the displayed distance beteen the reference probe spi#es ill be

ten centimeters! $ntroduce the sine ave form from the vibration channels and read the phase angle 3see5igure 6B4!

5igure 6B! .hase Angle Readout on ual-Trace +scilloscope

5or the example in 5igure 6B, the maximum point of the vibration generated sine ave occurs at to

centimeters on the 6< centimeter scale, or 8


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C! isplacement-velocity selector

:! 5ilter-oscillator selector

>! 5re'uency meter

;! .oer selector

B! 5re'uency range selector

@! .ic#up selector

?! 5ilter turning dial

6

66! .oer indicator lamp

The accessories include a strobe light and a vibration pic#up!

Ihen ta#ing vibration readings on a turbine-generator unit, the $R e'uipment is used as described in

the folloing paragraphs!

&etup

6! etermine here the shaft is mar#ed for the recording of phase angles! The $R set must be

placed near this location!

8! "se shielded cables ith Amphenol connector to lin# the pic#up and strobe to the instrument!

.reparation of 5ilter-Tuner

6! &et the filter-oscillator selector to the oscillator mode! The strobe light ill no fire at a rate

set by the filter tuner dial!

8! AdFust the fre'uency range selector to the range that covers the unit operating speed

3normally >


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*aution9 $f a vibration trip circuit exists on the T&$ system, this trip should be disabled prior to

performing this step! $f a shaft riding probe doesnKt exist, a shaft stic# should be used! Alays use

the shaft stic# at the same angle from the hori/ontal Foint, and record the angle!

>! Iith the probe in place, the $R ill indicate the filtered vibration magnitude! AdFust the

amplitude range selector until the magnitude is indicated near the center of the scale!

;! The phase angle of the vibration high spot ill electronically fire the strobe! Read and record

the angle! This may be accomplished by the &tator Reference ethod of the Rotor Referenceethod!

B! After recording the values in &teps > and ;, turn the filter-oscillator selector to the filter out

position! This mode of operation permits indications of all fre'uencies of vibration! &hould

the filter out reading differ from the filter in reading, a problem other than, or in addition to, astraightforard mechanical unbalance may exist! The cause of this difference may arrant

further investigation!

5re'uency &cans for Non-operational &peeds6! The filter oscillator selector should be in the Ofilter inK or sharp mode!

8! &loly adFust the filter tuner dial and monitor the magnitude of vibration!

C! Ihen the filter tuner set point is other than operating fre'uency, the amplitude meter shouldindicate near /ero!

:! $f magnitudes increase, adFust the set point until the magnitude pea#s! This point is the

probable extraneous fre'uency!

E'uipment *onstant

An $R set has an inherent e'uipment lag or e'uipment constant! The values of this lag varies as afunction of rotor speed and portable e'uipment model number! *onsult 5igure 6@ for the e'uivalent lag

that applies to your situation!

+ther (alance E'uipment

A field engineer may find himself using vibration measuring e'uipment other than the units already

described! anufacturers of this e'uipment include Reliance Electric and .* 3.recision easurement*orp!4! The operation of these portable units is very similar to the $R in most cases hence there is no

real need for added discussion here! The e'uipment constant curves for these units are shon in 5igure

6?!

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5igure 6@! $R E'uipment *onstants

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5igure 6?! E'uipment *onstants

M-424 Basics of Vibration Analysis

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