Chapter 4 Bearings

7/30/2019 Chapter 4 Bearings

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149

C H A P T E R 4

Bearings and Supports 4

Bearings provide the primary interfacebetween the moving and the stationary parts of a machine. Although the seals

and process fluids (or magnetic fields) coexist, the bearings provide the majority

of the stiffness and damping for the moving assembly. I t is understandable thatdyna mic forces developed on the moving pa rts a re tra nsmitt ed to the sta tionar y

parts across these main support bearings. The forces may be static radial loads

due to rotor weight, or they may be dynamic forces due to mechanisms such as

ma ss unba lance. In either case, the ra dial bearings must carry the a pplied loa ds,

or the ma chine will fail .

Many machines a re also equipped with thrust bearings to restrain t he axial

loads imposed by differential fluid pressures across stages of compression or

expansion. Motors, generators, some gear boxes, and some double flow compres-

sors do not contain t hrust bearings. On other t ra ins, a single thrust bearing ma y

accommodate several machines connected via a series of hard couplings. In all

cases, if the th rust bearing(s) fail , the ma chinery t ra in w ill cease to function.

It is reasonable to conclude that bearings are one of the most vulnerable

machinery elements. In many cases, bearings are the scapegoat for other mal-functions. I t has been repeatedly demonstrated that bearings are often rede-

signed to handle higher and higher loads, when the problem actually originates

within some other part of the machine. In these situations it is desirable to

return to basic engineering principles, and examine the behavior of the entire

mecha nical syst em, including the intera ction w ith t he ma in bearings. The influ-

ence of loads, physical dimensions, bearing clearances, lubricant properties, and

various geometric configurations will be reviewed in this chapter. The primary

emphasis of this discussion will be on fluid film radial bearings. However, gen-

eral comments for t hrust bearings a nd roller element bearings w ill be included.

As noted in the preface to this text, excessive bearing clearances represent

a major category of common machinery malfunctions. Hence, various methods

for accurate measurement of bearing clearances will be presented. In addition,

the measurement of bearing housing support characteristics will also beaddressed within this chapter.


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150 Chapter-4

FLUID FILM RADIAL JOURNAL BEARINGS

In t he development of a na lytical ma chinery models, there is alw a ys a temp-

tation to begin the project with a detailed rotor analysis. However, the machin-ery diagnostician soon discovers that bearing characteristics must be defined

a nd included w ithin t he rotor model. In some ca ses, such as the optimizat ion of a

mecha nical system, ma ny different bea ring ty pes may be considered with differ-

ent rotor models. Hence, it is often an iterative procedure to determine the

proper combina tion of bea rings a nd r otor confi gura tion.

One of the easiest, and informative starting points is the determination of

the sta tic sha ft loading upon t he pla na r a rea of the bearing. This calcula tion con-

sists of dividing the sta tic journal loa d by the plane ar ea of the bea ring as sh own

in the following equation (4-1):

(4-1)

where: Bearing Unit Load = Static Bearing Loading (Pounds/Inch2)Journal Weight = Static Load on Bearing (Pounds)

Length = Bearing Length (Inches)Diameter = Bearing Diameter (Inches)

If th e weight of a rotor is evenly distributed between tw o bearings, then the

J ourna l Weight is equ a l to 50%of the rotor w eight. The product of bear ing length

times diameter yields the planar area of the bearing. That is, a top view of the

bottom half of a bearing will have a projected area that is determined by the

bearing dimensions. For example, consider a 14,400 pound rotor supported by

tw o bea rings t ha t a re each 6.0 inches long a nd 8.0 inches in dia meter. The sta tic

bear ing unit load m a y be comput ed from (4-1) a s follow s:

A loa ding of 150 P si is a ccepta ble for m ost indust ria l ma chines. Generally,

the range of allowable bearing loads for fluid film bearings varies between 100

a nd 300 P si. For light ly loaded bea rings (i.e., 300 Ps i), the bear ing ma y fa ilprematurely due to the excessive radial loads. Also, the bearing size with respect

to the sha ft w ould not ma ke sense. If th e original exa mple had a loa ding of 600

Psi, and the rotor weight plus bearing diameter remained constant then the

bearing length would have to be 1.5 inches. This is likewise unreasonable for a

Bea r i n g U n i t L oad B U LJ o u r n a l Weigh t

L en gt h D i am et er -------------------------------------------------------= =

BU L J o u r n a l Weigh tL en gt h D i am et er ------------------------------------------------------- 14 400, 2( ) Pounds

6.0 Inches 8.0 Inches----------------------------------------------------

==

BU L7 200 Pounds,48.0 Inches

2-------------------------------- 150 Pounds/Inches

2= =


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Fluid Film Radial Journal Bearings 151

seven ton rotor w ith a n 8.0 inch diam eter shaft .

In a ddition to these sta tic loa ds, forces due to unbala nce, misalignment, flu-

ids, gears, etc., must be considered in the bearing design. These cyclic forces do

not lend themselves to the simple analysis that was just performed. In order toevaluate these parameters, plus the oil film characteristics, the bearing analysis

must be signifi cant ly expa nded. Ma ny excellent pa pers on dyna mic bea ring char-

acteristics have been published by investigators such as

Edgar Gunter

1

, J im

McHugh

2

, Pa ul Allaire an d Ron Flack

3

, and Da na Sa lamone

4

.

In most cases, determinat ion of ma chine support coefficients is generally a

tw o step effort. The fi rst part consists of the computa tion of oil film chara cteris-

tics, and the second task requires the measurement of the bearing structural

support. The overall or effective rotor support is based upon a combination of

these individual, yet interrelated parameters.

Bearing oil film coefficients can be determined with two different types of

computer programs. The first type is a bearing look u p

program that outputs

principal stiffness K

xx

, K

yy

and damping C

xx

, C

xx

coeffi cient s, plus t he cross-cou-pling coeffi cient s of K

xy

, K

yx

, C

xy

, and C

yx

. These programs also display Sommer-

feld numbers with associated speeds, loads, and journal eccentricities. The

bearing parameters can be calculated for specific conditions, or over a defined

speed domain. P rograms of this t ype run quite ra pidly, and a re useful for exam-

ining multiple cases prior to the final definition of parameters, and the detailed

bearing ca lculat ions.

This second type of bearing coefficient program computes the equilibrium

position, plus th e stiffness an d da mping coefficients for a defined bea ring geome-

try. Programs exist for cylindrical bearings, multi-lobe bearings, pressure dam

bearings, and tilting pa d bearings. These programs a re often sophisticat ed fi nite

element s olutions tha t a llow var iable oil viscosity w ithin t he bearing, accept oil

turbulence, plus the application of vertical and horizontal external forces, and

va ria tions in preloa d (where appropria te).

Typical program output data includes the principal stiffness K

xx

, K

yy

a nd

damping C

xx

, C

xx

coeffi cient s, plus th e cross-coupling coefficient s K

xy

, K

yx

, C

xy

,

a nd C

yx

as required. These results are usually displayed graphically, as illus-

trated in Fig. 4-1. This plot describes dimensional stiffness and damping coeffi-

cients as a function of rotating speed. The presented data was calculated for a

fi ve (5) shoe tilting pa d bear ing. This bea ring ha s a length /dia meter (

L / D

) ratio

of 0.4, a 60 arc length, load on pad (LOP), a 50%offset, and a 0.25 preload. The

1 Edga r J . Gun ter, Dynam ic Sta bility of Rotor Bear ing Sy stems, NASA Report SP -113, 1966.

2 J ames D. McHugh, Principles of Turbomachinery B earings, Proceedi ngs of the Eighth Tur-bomachin ery Symposiu m

, G as Turbine La borat ories, Texas A&M U niversit y, College St at ion, Texas

(November 1979), pp. 135-145.

3 Pa ul E. Allaire, and Ronald D. Flack, Design of Journa l Bea rings for Rotat ing Machinery,

Proceedi ngs of the Tenth Tur bomachin ery Sym posium

, Turboma chinery La borat ories, Texas A&MUniversity, College Station, Texas (December 1981), pp. 25-45.

4 Da na J. S ala mone, J ournal B earing D esign Types and Their Applicat ions t o Turbomachin-ery, Proceedi ngs of the Thir teenth T ur bomachin ery Sym posium

, Turbomachinery Laboratories,Texa s A&M U niv ersit y, College St a tion , Texas (November 1984), pp 179-188.


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152 Chapter-4

a pplied bearing st a tic loa d wa s 1,750 pounds, and dia metrical clea ra nce wa s 9.0

Mils (0.009 inches). Since this is a tilting pad bearing, the cross-coupling coeffi-

cients are zero, and only the principal (xx and yy) coefficients are shown. It

should a lso be mentioned tha t d ue to the extended amplitude ra nge, this t ype ofinforma tion is normally plott ed wit h a log-log scale. B a sed on t he relative ma gni-

tudes of the coefficients, the stiffness para meters a ppea r on the top half , a nd th e

da mping curves a re towa rds t he bott om portion of the plot.

In many instances, the bearing coefficients are presented in a non-dimen-

sional format. The customary form used for non-dimensional stiffness coeffi-

cients may be expressed by:

(4-2)

where:

K

NonDim

= Non-dimensional Stiffness

K

Dim

= Stiffness (Pounds/Inch)

C

b

= Bearing Radial Clearance (Inches)

W

= Static Bearing Load (Pounds)

Fig. 41 Dimensional OilFilm Bearing Stiffness AndDamping Coefficients Ver-sus Rotor Speed

KN o n D i m KD i m

CbW-------

=


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Simila rly, the non-dimensiona l bearing da mping coefficients a re calculated by:

(4-3)

where:

C

NonDim

= Non-dimensional Damping

C

Dim

= Damping (Pounds-Seconds / Inch)

= Shaft Rotative Speed (Radians / Second)

Non-dimensional coefficients are often used to define a particular bearing

design, and they permit direct compar ison between bear ings. Non-dimensiona l

coefficients a lso allow reasona bly easy conversions betw een t est cases for varia -

tions in bearing clearances, loads, or speed. Hence, the designer may evaluate

changes in par a meters wit hout repeat ing the full arr ay of bea ring calcula tions.

Another non-dimensional parameter that is computed for fluid film bear-

ings is the Eccentricity ratio. In bearing terminology, eccentricity is defined as

the dist a nce betw een t he bearing center, and the sha ft centerline position. Divid-ing this distance by the bearing clearance yields the dimensionless quantity of

eccentricity ratio. This physical location represents the calculated equilibrium

position of the journa l. I t ma y be presented a s a vector, or a s a horizonta l an d a

vert ical eccentr icity (or offset), from t he bear ing center.

These terms ar e ea sier to underst a nd if an exa mple of a fl uid fi lm bearing is

examined. For instance, consider a shaft journal rotating within a cylindrical

bearing a s illustra ted in Fig. 4-2. In t his example, the bearing cleara nce circle is

shown, and the bearing geometric center is identified. The shaft is defined as

rotating in a counterclockwise direction, and the shaft orbit is indicated in the

lower right quadrant of the bearing. The center of the shaft orbital motion is

commonly referred to as the shaft centerline position. The physical distance

between t his sha ft centerline position an d t he geometric center of the bearing is

defined a s t he sha ft eccentr icity. As previously noted, eccentr icity ma y be st a teda s a vector qua ntit y, or a s X-Y Ca rtesia n coordina tes.

The eccentricity ratio consists of the eccentricity magnitude divided by the

bearing clearance. Most analysts use radial bearing clearance to compute the

eccentricity ratio. As a precautionary point, eccentricity should not be confused

Fig. 42 Journal EccentricityPosition Within A Plain Circu-lar Fluid Film Bearing

CN o n D i m CD i m

C bW-----------------

=

ShaftOrbit

BearingCenter

CCW Rotation

ShaftCenterlinePosition

Bearing RadialClearance

EccentricityVector

ShaftCenterlineShift Vector


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154 Chapter-4

wit h t he shift in sha ft centerline position from some initia l rest position (e.g. , at

the bottom of the bearing). Although these two vectors are directly related via

the bearing clearance, the eccentricity vector is a calculated parameter based

upon the bearing center. Whereas, the centerline position vector is measuredwit h sha ft sensing orthogona l proximity probes, and it is genera lly referenced t o

the bottom of the bearing (for a horizontal machine). Ideally, these two vectors

should termina te a t t he same point w ithin th e cleara nce circle.

Since the eccentricity ratio is associated with the minimum oil film thick-

ness, it is importa nt informa tion for t he bea ring designer, as w ell a s th e machin-

ery diagnostician. I t should be recognized that each particular bearing type or

configuration displays a unique shaft centerline position of the journal within

the bear ing. This runn ing position is a function of physica l para meters such a s

bearing geometry, operating speed, shaft weight, and lubricant characteristics.

The actual running position may be influenced by the application of shaft pre-

loads originating from normal sources such as gear contact forces, or abnormal

forces such as coupling misalignment.

In ma ny ma chinery a na lysis problems, it is difficult to separa te normal ver-

sus a bnormal forces a cting on the sha ft. The dyna mic motion of th e shaft (vibra-

tion) is altered, and the running position of the journal within the bearing is

influenced. Hence, one must evaluate the dynamic as well as the static informa-

tion. This type of evaluation is often predicated upon a comparison between nor-

ma l behavior an d t he current motion an d/or position cha ra cteristics of the sha ft

position wit hin t he journa l bearing. More specifica lly, the dia gnostician must be

aware of normal shaft position characteristics in order to identify an abnormal

position. For instance, Fig. 4-3 describes the normal shaft centerline running

position for three different types of common industrial journal bearings.

The plain journa l bear ing show n on th e left sid e of Fig. 4-3 is a t ypical bea r-

ing installed in many types of horizontal machines. On smaller machines, this

type of bearing ma y consist of upper a nd lower thin bea ring liners restra ined bya heavy bearing housing. On larger machines, the babbitt bearing surface may

be integral w ith t he bearing housing. In either ca se, this t ype of bearing gener-

ates an oil wedge in the lower right bearing quadrant (with CCW rotation). The

shaft is supported at the minimum oil film, and journal weight is supported by

the hydrodynamic forces within the bearing. In most cases, the shaft centerline

vector pivots up from 20 t o 40 a bove th e bott om horizonta l plane of th e bea ring.

Fig. 43 Shaft Centerline Position With Three Different Types Of Fluid Film Bearings

ShaftOrbit

CCW Rotation


ShaftCenterlineShift Vector

Elliptical Bearing

ShaftOrbit

CCW Rotation


ShaftCenterline

Shift Vector

Tilt Pad Bearing - Load on Pad

Shaft

Orbit

CCW Rotation

Shaft

CenterlinePosition

ShaftCenterline

Shift Vector

Plain Journal Bearing


7/50


The tilt pad bear ing displa yed in t he middle of Fig. 4-3 consists of a series of

fl oating pa ds tha t surr ound the journa l. A common configura tion for a horizonta l

machine consists of three pads in the bottom half of the bearing, and two pads

located in the top bearing half . The three bottom pads are usually configuredw ith one pad d irectly below t he sha ft (6 oclock position). This phy sical pa d loca -

tion is commonly r eferred to as a L oad on Pad

(LOP ) a rra ngement. If the bearing

pads were repositioned or rotated on the shaft circumference to allow the two

bott om pads t o stra ddle the tr ue vertical centerline, this w ould be considered as

a L oad Betw een Pad

(LBP) configuration.

For a LOP arrangement, the shaft supporting oil wedge is established and

maintained on the bottom pad. Due to the location of this oil wedge, the shaft

rises essentia lly stra ight up into the norma l running position. In most ca ses, the

shaft centerline vector pivots up from 80 to 100 above the bottom horizontal

plane of the bear ing. The norma l sha ft r unning position is slightly offset from the

tr ue vertical centerline. U sua lly this offset is in t he direction of rota tion a s noted

in t he cent er dia gra m of Fig. 4-3.

Sha ft centerline position for a lemon bore or elliptical bea ring a re shown in

the diagram located on the right side of Fig. 4-3. Within this type of fixed lobe

bearing the horizontal clearances are much larger than the vertical clearances.

Typically, a ratio of 1.5:1 or 2:1 is maintained between horizontal and vertical

cleara nces. This physica l configura tion allow s the rota ting sha ft to sli de over

in to

low er right bear ing qua dra nt for a counterclockw ise rota ting sha ft (as shown), or

the low er left bearing qua dra nt for a clockwise sha ft rota tion.

Fig. 44 Non-DimensionalStiffness And DampingCoefficients Versus JournalEccentricity Ratio


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156 Chapter-4

Although there are many types and configurations of journal bearings, the

calcula tion of expected journa l location w ithin a bearing ma y be compar ed wit h

the runn ing position as determined by D C m easurements w ith proximity probes.

Again, it should be mentioned that the probes measure shaft position from aninitial point such a s t he bott om of the bea ring. Thus, the vector a lgebra for t he

probe calculation is based upon the rest point of the shaft in the bearing,

wh ereas th e ana lytical calculations ar e referenced to the bea ring center. Signifi -

cant deviations between computed a nd mea sured sha ft centerline positions may

be useful in t he identifi cation of a ma chinery problem. Conversely, if the ra dial

position ca lculat ions a nd mea surements a gree, the validity of the computa tions

are reinforced, and the diagnostician should consider looking into other aspects

of a bnormal behavior of the ma chinery.

Refer ba ck to the fi ve shoe tilt pa d bearing da ta from Fig. 4-1, a nd t he non-

dimensiona l stiffness and da mping para meters defi ned by equa tions (4-2) a nd (4-

3). Clearly, the dimensional coefficients may be converted into non-dimensional

values. I t is common to plot these dimensionless parameters against the non-

dimensiona l eccentr icity ra tio as shown F ig. 4-4. Since this is a tilt pad bearing,

the shaft will rise vertically from the bottom pad, and the angle associated with

th e eccentricity vector will be in the vicinity of 90 . For t his common bea ring, it is

noted that vertical stiffness increases as the minimum oil film decreases (i.e. ,

lar ger eccentr icity ra tio). Hence, the computed results a re consistent wit h int ui-

tive logic and the expected beha vior for t his t ype of mechanical sy stem.

Bearing analytical programs also compute the dimensionless Sommerfeld

number based upon the inlet viscosity, speed, length, diameter, load, and clear-

a nce. This par a meter is w idely used a s a chara cteristic number for journal bear-

ing performance. Typical values for the Sommerfeld number vary from 0.01 to

10.0. The common forma t for the S ommerfeld number calcula tion is present ed in

th e following expression:

(4-4)

where

N

So

= Sommerfeld Number (Dimensionless)

= Absolute or Dynamic Oil Viscosity (Pounds-Seconds / Inch

2

)

= Shaft Rotational Speed (Radians / Second)

L

= Bearing Length (Inches)

D

= Shaft Diameter (Inches)

R

= Shaft Radius (Inches)

W

= Load on Bearing (Pounds)

C

b

= Bearing Radial Clearance (Inches)

I t should be mentioned that other forms of the Sommerfeld number are

used. Although the general intent of the expression remains intact, individual

designers m ay use different values for t his dimensionless number. For inst an ce,the rotational speed may be stated Revolutions per Second instead of Radians

per Second. In all cases, it is ma nda tory to identify the para meters a nd engineer-

ing units when attempting to compare the Sommerfeld numbers generated by

NSo L D

W-----------------------------------

R

Cb-------

2

=


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tw o or m ore bea ring designers.

A typical plot of Sommerfeld number versus the non-dimensional stiffness

and damping is presented In Fig. 4-5. This plot is based upon the same five shoe

tilting pad bearing depicted in Figs. 4-1 and 4-4. Generally, the bearing designer

w ill consider the cha ra cteristics displayed by t he Sommerfeld plots, an d t he pre-

viously discussed eccentricity ratio plots, plus the dimensional plots of bearingcoefficients versus speed. Bearing designers also examine plots of Sommerfeld

numbers versus other non-dimensiona l qua ntit ies such a s w hirl or speed ra tios.

Clearly, individual design techniques and computer programs yield a large

a ssortment of plot forma ts.

Another common calculation is the Reynolds number at the minimum oil

fi lm. This non-dimensiona l number is t he ra tio of inert ia to viscous forces, and it

ma y be computed by:

(4-5)

where: NRe = Reynolds Number (Dimensionless)

= Oil Density (Pounds / Inch3

)H = Minimum Oil Film Height (Inches) = Shaft Rotational Speed (Radians / Second)R = Shaft Radius (Inches)

G = Acceleration of Gravity (386.1 Inches / Second2) = Absolute or Dynamic Oil Viscosity (Pounds-Seconds / Inch2)

Fig. 45 Non-DimensionalStiffness And DampingCoefficients Versus Som-merfeld Number

NRe H R

G------------------------------------

=


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158 Chapter-4

The Reynolds number allows characterization of the oil flow at the mini-

mum oil film. This is useful in determination of the fluid flow regime. In most

insta nces, lam inar fl ow thr ough the minimum oil film is encountered. Ca vita tion

often occurs above the journal, but within the load carrying bottom half of thebearing, laminar flow is the normal and desired situation. In most cases, if the

minimum oil film Reynolds number is less th a n 1,000, then lam inar fl ow should

be expected. Convers ely, if this va lue exceeds 1,000, then t urbulent fl ow w ould be

a concern. The computational software should be able to handle both types of

flow regimes, and provide meaningful bearing coefficients, plus proper equilib-

rium position a nd force balan ce.

As noted on the Sommerfeld number, various forms of these equations are

in use, and dimensional analysis should always be performed to verify the con-

sistency of units. In fact, some analytical computer programs do not yield true

non-dimensional values for parameters such as the Reynolds or Sommerfeld

numbers. Often a residua l unit remains t ha t a lters the ma gnitude of the number.

Again, to avoid confusion, the machinery diagnostician should make sure that

dimensionless numbers are truly non-dimensional, or at least consistent

between compar a tive cases.

A non-dimensiona l qua ntit y t ha t most bea ring designers a gree upon is the

Preload factor for lobed or segmented bearings (e.g., tilt pad). These types of

bear ings display a pad curvature tha t is greater t han the shaf t curvat ure . This

physical configuration forces the oil to converge close to the middle of each pad

due to t he reduced clea ra nce. In essence, preload produces or forces a n oil wedge

in the bear ing pad. For t hese types of bearings, the preloa d ma y be determined

by the ra tio bea ring cleara nce Cb, and t he pad clear ance Cpa s follows:

(4-6)

Eit her ra dial or dia metrical clea ra nces ma y be used for (4-6), but both va ri-

a bles must be the sa me. Tha t is, Cba nd Cpmust be both r a dial, or both diamet ri-

cal clearances. Another way to express the shaft preload is to convert equation

(4-6) int o equiva lent dia meters. B y subst itut ion in th e previous expression, it ca n

be easily shown tha t t he Preload ma y a lso be calcula ted wit h the following:

(4-7)

where: Dp = Diameter of Pad Curvature (Inches)Db = Diameter of Bearing Clearance (Inches)Ds = Diameter of Shaft (Inches)

For a positive preload, the shaft diameter Dsis the smallest number, and

the pad dia meter Dpis the largest num ber. If the pad a nd bearing clea ra nces ar e

equal, th en the preloa d is zero. The bearing is circula r, with the pa d a nd bear ing

Pre loadCp Cb

Cp--------------------- 1

CbCp-------

= =

Pre loadDp Db

Dp Ds----------------------

=


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sha ring t he sa me center of curvat ure. At the other extreme, if preload is equa l to

1.0, then the bearing clea ra nce is zero, and t he shaft is in direct conta ct wit h th e

bearing pa d. In pra ctice, bearing preloa ds a re typically found t o be in the ra nge

of 0.1 to 0.5. As preload increa ses, the bear ing st iffness increas es, a nd t he da mp-ing often decreases. This relationship between the principal coefficients and the

bearing pad preload may be used to optimize the stiffness and damping charac-

teristics of the bear ing. Conversely, if the bear ing pad is da ma ged during insta l-

lation, or the babbitt is scraped by a well intentioned millwright, the preload

ma y be seriously a ltered, a nd th e bea ring chara cteristics tota lly corrupted.

The normal preload is a positive number, indicating that the bearing pad

radius of curvature is greater than the bearing radius. I f th is si tuation was

reversed, and the bear ing pad displayed a ra dius that wa s smaller than the bear-

ing, a negative preload would result. Physically, this means that the shaft is

riding on the pa d edges (i.e. , bea ring pa d is edge loa ded), and premat ure fa ilure

of the bearing is a certainty. On a questionable installation, bluing on the shaft

may be used to determine the actual contact area between the journal and the

bearing pads.

Additional visibility of bearing characteristics may be obtained from the

calcula ted pressure a nd t empera ture profi les for ea ch design. For example, con-

sider Fig. 4-6 of radial pressure distribution within an elliptical bearing. This

type of radia l bearing is a lso referred to as a tw o lobe, or lemon bore bearing w ith

25 Psi oil supply pressure.

The polar coordinate plot displays the circumferential pressure distribution

w ithin th e bear ing at normal load a nd speed. Note tha t t he maximum developed

pressure occurs a t the bott om of th e bearing. This point is slightly upstrea m ofthe minimum oil film, and is consistent w ith expected bea ring behavior and t he-

ory. Further examination of this diagram reveals another positive pressure

buildup at an angle of 25. This pressure buildup is due to the development of

another converging oil wedge between the journal and the top half of the bear-

Fig. 46 Oil Pressure Dis-tribution Around An Ellipti-cal Journal Bearing

-200 0 200 400 600 8000 200 400 600 800

0

30

60

90

120

150

180

210

240

270

300

330

Pressure (Psi)CCWR

otation


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160 Chapter-4

ing. This secondary oil wedge is due to the fixed lobe bearing geometry. In some

cases, the influence of forces originating in the top half of the bearing may be

responsible for driving an instability, or providing a positive stabilizing force

(e.g., pressure dam).The difference between the physical location of the maximum oil film pres-

sure, and the minimum oil film thickness points out an interesting fact in the

world of rotors and bearings. Specifically, a non-rotating shaft with a vertical

loa d w ill deflect downw a rd in th e direction of the applied loa d. Now a ssume tha t

the sha ft is turning a t a consta nt speed, and th at a n oil wedge ha s developed. In

this condition, the a pplica tion of a downw a rd force on the sha ft w ill be greeted by

a vertical shift in the direction of the a pplied vertical load, plus a h orizonta l shift

of t he sha ft w ithin t he bearing. The horizonta l shift will occur in t he direction of

rota tion. Tha t is, a sha ft rota ting in a counterclockwise direction w ill move to the

right, and a shaft turning clockwise will slide to the left. This cross-coupling

mecha nism a cross th e oil film is r esponsible for man y bear ing behaviora l cha ra c-

terist ics including th e self-excited inst a bilities discussed in cha pter 9 of this t ext.

I t should also be mentioned that most fluid film bearings are constructed

with a steel base or backing, and a babbit t coat ing tha t provides the actual bear-

ing surface. The babbitt may be either tin or lead based, and various composi-

tions ar e in common use. Since babbitt is softer t ha n t he steel journal, it is t he

first sacrificial element in a bearing assembly. Ideally, during a bearing failure,

the ba bbitt w ill susta in the ma jority of the distress, a nd the st eel journal w ill not

be damaged. Thus, the bearings may be replaced, and the rotor may be reused

without any repairs to the journals. Of course, during a major failure, the steel

journals may contact the steel backing on the bearings, and substantial damage

ma y be inflicted on both t he journals a s well as t he bea rings.

The babbitt thickness on journal bearings may range from micro-babbitt

thickness of 0.005 to 0.015 Inches (5 to 15 Mils) as a minimum, to 0.050 or 0.060

Inches (50 or 60 Mils) a s a ma ximum. The th ick babbit t w ill be a bet ter choice forconditions of dirty lube oil, or anticipated wear on the bearings. Unfortunately,

thick babbitt layers are susceptible to damage from impact loads, various bear-

ing instabilities, and shaft misalignment. In many instances, a malfunction can

break off a chunk of thick babbitt, and carry it around the entire bearing, with

disast rous consequences. Ba bbitt is a lso a poor conductor of hea t, a nd a hot bear-

ing will generally result in a premature fatigue failure. On the other hand, the

thin micro-babbitt bearings will transmit heat to the backing material more

readily, and this type of bearing is more resistant to impact loads, and other

dyna mic forces. However, the oil system must be ma inta ined in a very clea n con-

dition. Any dirt or foreign objects in the oil may seriously damage a micro-bab-

bitt coating. The oil film dynamics of thin versus thick babbitt bearings are

essentially the same. The size and the geometry of the bearing is often more

important than the babbitt thickness. However, the diagnostician should notignore this importa nt bear ing pa ra meter.


13/50


Case History 6: Shaft Position In Gas Turbine Elliptical Bearings

In most cases, it is technically difficult (if not impossible) to directly check

the validity or accuracy of the computed bearing coefficients. However, each cal-culation must conclude with a force balance, plus a position balance of the jour-

na l with in the bearing clea ra nce. It is reasonable to believe tha t if the calcula ted

eccentr icity position is correct, then the other computed pa ra meters a re a lso rep-

resentative of the bearing characteristics. Since journal position within an oil

fi lm bear ing can be measured directly w ith proximity probes, it is logical t o per-

form a check of the a na lytical predictions versus a ctual ma chine da ta .

For t his case history, consider a group of four single sha ft ga s t urbines tha t

operate between 5,000 and 5,350 RPM. These units are rated at 40,000 HP, and

they are used to drive high pressure centrifugal compressors through a single

helica l gear box. The sha ft sensing proximity probes are m ounted at 45 from

th e true vert ical centerline a s show n in Fig. 4-7. At t he tur bine inlet end #1 bea r-

ing, the probes are mounted a bove the sha ft. Conversely, at the exha ust end #2

bearing, the probes ar e locat ed below the sha ft.

The eight inch dia meter journa ls a re support ed in elliptica l bear ings. These

bearings have an average vertical diametrical clearance of 16 Mils (0.016

inches), and a normal horizontal diametrical clearance of 32 Mils (0.032 inches).

These physica l dimensions a re consistent wit h a nominal 2:1 cleara nce rat io pre-

viously mentioned in this chapter.

The sha ft centerline position for t hese ma chine journa ls wa s determined by

measuring the proximity probe DC gap voltages at a stop condition, and at full

speed. The difference between these DC voltages is divided by the transducer

scale factor to determine the position change in the direction of each transducer.

This X-Y change in radial position may be plotted on a graph that displays the

bearing cleara nce, plus the calculat ed journa l position in t he X a nd Y directions.

Fig. 4-8 depicts the radial journal positions for the turbine inlet bearings.

Sha ft centerline loca tions for t he A unit w ere obta ined on different da tes, a nd a t

slight ly different speeds var ying betw een 5,100 and 5,340 RPM. Three ad ditiona l

machines identified as the B, C, and Dunits are also included in this survey.

Speeds for these last three units varied between 5,010 and 5,350 RPM. It isnoted that excellent agreement has been achieved between the calculated posi-

tion at 5,340 RPM, an d the six sets of field dat a .

The sa me position informa tion for t he exhaust end #2 bea ring is conta ined

in Fig. 4-9. Notice that the scatter of data is much greater at this bearing, and

Fig. 47 Angular Arrange-ment Of Radial ProximityProbes On A Single ShaftGas Turbine

45 45

4545

Y-Axis X-Axis

X-Axis Y-Axis

Inlet Bearing Exhaust Bearing

CCW

CCW


14/50

162 Chapter-4

the deviations from the calculated position are substantial. Initially, it might be

concluded t ha t t he theory does not support the a ctua l ma chinery beha vior. How-ever, a partial explanation for these aberrations resides within the characteris-

tics of the proximity probe measurements. Specifically, the early vintage of both

the proximity probes, an d t he compan ion dr ivers ar e sensitive to opera ting t em-

perature. The temperature limit specification for this specific probe and cable

wa s 350F ; and the oscilla tor-demodulat or opera ting limit w a s specified a s 150F

for a sta nda rd unit, or 212F for a n extended temperat ure ra nge version.

As shown in Fig. 4-7, the exhaust end probes are mounted outboard of the

#2 bearing, and below the horizontal centerline. These probes are subjected to a

high temperature environment tha t can easi ly heat the tra nsducers to tempera -

tures in excess of 200F. The oscillator-demodulators are mounted in an explo-

sion proof housing. Although a heat shield is installed between the turbine

exhaust and this box, the electrical components often operate at temperatures

a bove 130 F. Thus, the exha ust end probes, cables, and drivers a re a ll exposed toelevat ed tempera tur es tha t a ffect the calibra tion curve slope.

For many years, the instrumentation vendors have recognized that operat-

Fig. 48 Shaft Centerline Position On Four Gas Turbines At Inlet End #1 Bearing

Fig. 49 Shaft Centerline Position On Four Gas Turbines At Exhaust End #2 BearingBased On Direct Probe Gap Measurements Without Temperature Correction

T

V

W

1

-8

-4

0

4

8

-16 -12 -8 -4 0 4 8 12 16

VerticalClearance(M

ils)

Horizontal Clearance (Mils)

T

A-5,330 RPM

V

A-5,100 RPM

W

A-5,340 RPM

B-5,350 RPM

C-5,010 RPM

D-5,350 RPM

1

Calculated

Inlet End #1 Bearing

CCW Rotation

T

V

W

1

-8

-4

0

4

8

-16 -12 -8 -4 0 4 8 12 16

V

erticalClearance(Mils)


T

A-5,330 RPM

V

A-5,100 RPM

W

A-5,340 RPM

B-5,350 RPM

C-5,010 RPM

D-5,350 RPM

1

Calculated

Exhaust End #2 Bearing

CCW Rotation


15/50


ing temperature will influence probe calibration. For instance, Fig. 4-10 depicts

the variation in calibration curves at temperatures of 75, 200, and 350F. This

data was published by the manufacturer of the proximity probes installed on

these particular gas turbines. The plotted data is for a 0.300 inch diameter

probe. La rger excursions ar e normally exhibited by sm a ller dia meter probe tips.

From this fa mily of curves, it is clea r t ha t t he ca librat ion curve will bend down-

wa rd a s t empera ture increases. At 200F, the ca librat ion curve is nominally 0.5

volts below the normal curve for gaps in the vicinity of -9.0 to -10.0 volts DC.

Hence, for a given distance between the probe and shaft, the output DC voltage

from the P roximitor is reduced by a bout 0.5 volts. Since the mea surement sys-

tem operat es with a negat ive bias, the gap volta ges are likew ise negat ive.

The correction for t his t empera ture behavior requires a dding t he incremen-

ta l volta ge to the Pr oximitor output volta ge. Thus, the measured output DC

voltage should be corrected by -0.5 volts DC to yield a temperature compensated

va lue. Specifica lly, Ta ble 4-1 summa rizes t he cold (a t stop) ga p volta ges, plus t he

hot (running) ga p volta ges for t he B ma chine. The differentia l ga p volta ges a remerely the cold minus the hot gap voltages at the turbine exhaust bearing.

Dividing the Y-Axis (vertical) probe differential gap voltage by the normal trans-

ducer s ensit ivit y of 0.2 Volts/Mil (200 mv/Mil) yields a displa cement cha nge of

2.15 Mils towa rds t he probe. Simila rly, th e X-Axis (horizonta l) tr a nsdu cer exhib-

its a -1.24 volt change, which is equivalent to a 6.20 Mil position shift away from

the probe. This is equivalent to an overall shaft vector shift of 6.56 Mils at 26

Fig. 410 Influence OfOperating Temperature OnProximity Probe SystemOutput Voltage

Table 41 Direct Proximity Probe Gap Voltages At Turbine Exhaust End #2 Bearing

Probe andAngular Location Cold GapVoltage Hot GapVoltage DifferentialGap Voltage DifferentialPosition

Y-Axis @ 315 -9.66 volt s D C -9.23 volt s DC + 0.43 volt s D C + 2.15 Mils

X-Axis @ 225 -9.23 volt s D C -10.47 volt s D C -1.24 volt s D C -6.20 Mils


16/50

164 Chapter-4

from th e cold t o the hot position.

However, if the measured hot probe gap voltages are corrected by -0.5 volts

DC to compensate for the transducer temperature sensitivity, the results are

shown in Ta ble 4-2. The init ia l cold ga p volta ges (zero speed) rema in t he sa me a s

before. The displacement shift is a gain determined by dividing t he differentia l

ga p volta ges by 0.2 Volts/Mil t o determin e t he dist a nce shift . For th e Y-Axis

probe, this yields a displacement change of 0.35 Mils away from the probe. TheX-Axis tr a nsdu cer now displa ys a -1.74 volt cha nge, which is equa l to a n 8.70 Mil

position shift a wa y from t he tr a nsducer. The tota l shift of the journa l centerline

position is therefore equivalent to a vector shift of 8.71 Mils at 47 (cold to hot

position). Thus, the temperat ure correction reveals t ha t the sha ft is r eally riding

higher in the bearing th a n the uncorrected data revealed.

Cert a inly the a ccura cy of this correction ma y be improved by detailed tem-

perature sensitivity calibration of each transducer on each machinery train.

However, that type of information is often not available, or the expense of pro-

ducing and maintaining this database might be cost prohibitive. Hence, the use

of a reasona ble volta ge correction is considered to be a dequa te a nd a ccepta ble for

this si tua tion.

Correcting each of the hot ga p volta ges from t he initial sha ft centerline dia-

gram produces the journal positions presented in Fig. 4-11. Again, the exhaustend probes are mounted on the bottom of the shaft, and the corrected DC volt-

ages reveal a shaf t r ise. I t is evident tha t a greement between the calculated a nd

Table 42 Corrected Proximity Probe Gap Voltages At Turbine Exhaust End #2 Bearing

Probe andAngular Location

Cold GapVoltage

Hot GapVoltage

DifferentialGap Voltage

DifferentialPosition

Y-Axis @ 315 -9.66 volt s D C -9.73 volt s D C -0.07 volt s D C -0.35 Mils

X-Axis @ 225 -9.23 volt s D C -10.97 volt s D C -1.74 volt s D C -8.70 Mils

Fig. 411 Shaft Centerline Position On Four Gas Turbines At Exhaust End #2 BearingBased On Temperature Corrections To The Proximity Probe Gap Voltages

T

V

W

1

-8

-4

0

4

8

-16 -12 -8 -4 0 4 8 12 16V

erticalClearance(Mils)


T

A-5,330 RPM

V

A-5,100 RPM

W

A-5,340 RPM

B-5,350 RPM

C-5,010 RPM

D-5,350 RPM

1

Calculated

Exhaust End #2 Bearing

with Hot Probe Gap Correction

CCW Rotation


17/50

Fluid Film Radial Bearing Clearance Measurements 165

measur ed journa l position ha s been significan tly improved by t his simple probe

ga p temperat ure correction. The rema ining deviations in mea sured ra dial posi-

tion between both ends of the turbine ma y now be at tribut ed to the presence of

external loads, moments, or other infl uences acting upon the sha ft.Sin ce th e inlet end #1 bear ing is a djacent t o th e accessory coupling, very lit-

tle torque is t ra nsmitt ed during norma l operat ion. Thus, the presence of externa l

forces, and misalignment loads are minimal at the front end bearing. As previ-

ously observed, the mea sured positions agr ee very well w ith t he theoretica l cal-

cula tions tha t consider only the load due t o the applied journa l weight.

However, at the gas turbine exhaust end bearing, the full power output

from the turbine is transmitted across the load coupling. Dependent upon cou-

pling t ype, a lignment position and a ssociat ed external forces, the a ctua l journa l

location would probably deviate from the predicted eccentricity that was com-

puted with only the journal weight. In fact, the reverse statement might also be

a ppropriat e. Tha t is, since the exha ust end sha ft centerline position agr ees w ith

the computed location, the influence of external forces may be considered to be

minim a l (i.e., indicat ive of a w ell-a ligned Load coupling).

Overall , the eccentr icity ca lculat ions a t both ends of the tur bine appea r t o

be realistic and representative of average machine behavior. This correlation

between t he mea sured journa l positions, an d t he computed equilibrium locat ion

is considered to be supportive of the accuracy of the an a lytical fl uid fi lm bearing

calculations. Similar measurements and comparisons with calculated results

may be performed at other speeds or different oil supply conditions. In most

cases there should be a respectable correlation between the measured and the

calcula ted sha ft centerline position. This technique may a lso be used as a diag-

nostic tool. For example, if the mea sured sha ft opera ting position is subst a ntia lly

different from the calculated position, the diagnostician should give strong con-

siderat ion t o the presence of interna l or externa l sha ft preloa ds.

FLUID FILM RADIAL BEARING CLEARANCE MEASUREMENTS

Assuming a proper bea ring design, consta nt mecha nical confi gura tion, a nd

the availability of a suitable lubricant at the required flow, temperature, and

pressure most of the variables shown in the bearing equations migrate

towa rds consta nt va lues. The one para meter th at generally does not rema in con-

stant is the bearing clearance. Although fluid film bearings are often touted as

l i fe t imebearings, the reality is that these babbitt bearings are subject to physi-

cal damage whenever the oil film collapses. This could be caused by heavy shock

loads on the bearings, loss of lubricant, or the detrimental long-term effects from

excessive unba lance or misa lignment. Many other physica l mecha nisms w ill also

produce attrition in bearing babbitt thickness. In all cases, it is necessary tomonitor journa l position at each ra dial bea ring w ith X-Y proximity probes, and

to compare a nd trend this da ta within a ccurat e bear ing cleara nce diagra ms.

The total diametrical clearance between the stationary bearing and the

rotat ing sha f t ma y a ppear t o be an easi ly mea surable value. Unfortunately, i t is


18/50

166 Chapter-4

often quite difficult to accurately determine the true assembly clearance of a

journal bear ing. For a simple bearing confi gura tion such a s a plain circular bore,

the clear a nce is the difference between the sha ft dia meter a nd th e inner dia me-

ter bore of the bear ing. Dependent on the length of the journa l, the shaft diam e-ter is normally measured at two or more axial locations (minimum fore and aft

positions). Each axial location is typically measured at three to five different

diameters. Besides providing the necessary average shaft diameter, this data

checks for any gross diameter va riat ions, or t a per a cross th e length of the jour-

nal. I f the bearing is assembled (without the shaft), the inner diameter of the

bearing should be measured in a manner similar to the shaft. The average dia-

metrical clea ra nce for a plain circula r bore bearing is t herefore:

(4-8)

where: Cd-plain = Average Diametrical Bearing Clearance (Mils)

Db = Average Bearing Inner Diameter (Inches)

Ds = Average Shaft Outer Diameter (Inches)

If the shaft is resting solidly in the bottom half of the bearing, Plastigage

may be placed on top of the shaft, and the upper bearing half installed, bolted

down, unbolted, and then removed. Comparison of the deformed width of the

Plas t igage aga ins t the Width Chartsupplied on each pa cka ge of P last igage w ill

identify the diametrical clearance. Care should be taken to insure that the cor-

rect thickness of P last igage be used for t he bearing cleara nce mea surement. The

common colors a nd mea surement ra nges ar e as follows:

G reen Pla stiga ge . . . .. . . .. . . .. . . ..1 to 3 Mils

Red Plastigage .....................2 to 6 Mils

B lue Pla stiga ge . . . . . .. . . .. . . .. . . .. 4 to 9 Mils

If these ranges are not appropriate, or if Plastigage is not available, then

lead w ire (or soft solder) may be used. For t his measur ement, the lead w ire ma y

be pla ced on top of th e sha ft, the t op half of the bearing insta lled, bolted down,

unbolted, and then removed. The thickness of the lead wire may then be mea-

sured with a 0 to 1 inch micrometer. The resultant thickness will correspond to

the diam etrical bea ring cleara nce.

For long journal bea rings, a st rip of P last igage or lead w ire should be placed

at either end of the bearing (i.e., fore and aft). Ideally, the clearances should be

the sa me at both ends of the bearing. If var iat ions do appear, the journa l should

be checked for a possible taper, and the bearing should be checked for wear or

any evidence of a conical bore. In addressing this type of incongruity, it might be

desirable to run a strip of Plastigage or lead wire axially along the top of the

shaft. This would help to identify if the dissimilar bearing clearances vary uni-formly a long the length of th e journa l, or if some type of step chan ge in clear a nce

ha s occurred somewhere w ithin t he bea ring.

For a fi xed tw o lobe bea ring such as a n elliptical or lemon bore bearing, the

Cdp l a i n 1 000 Db Ds( ),=


19/50


previous techniques ma y be used to mea sure th e vertical bearing cleara nce. Hor-

izonta l cleara nces a re somewha t more difficult to determine. One approa ch is to

measure across the assembled width of the bearing to determine the horizontal

bearing dia meter. Since these types of bearings a re often provided w ith a xial oilsupply grooves at the splitline, it is important to measure the distance from

aboveone groove t o belowthe opposite groove as shown in Fig. 4-12. Two mea-

surements are obtained at each end of the bearing, and they are averaged to

determine the horizontal bearing inner diameter. Subtracting the shaft diame-

ter, a nd m ultiplying by 1,000 will yield t he a verage horizonta l clea ra nce in Mils.

This should be compa red wit h th e vert ical clea ra nce to verify t ha t a proper ra tio

exists. Typically, a large steam turbine will have a horizontal to vertical clear-

a nce rat io of 1.5:1, and a n industr ial ga s tur bine will generally be in the vicinity

of 2:1. Another w ay to measur e horizonta l cleara nce on a n elliptical bearing is to

use feeler gages between the shaft and the bottom half of the bearing (top half

removed). Measurements must be made on both sides of the journal, and their

sum is a good approximat ion of the horizonta l diam etrical bearing cleara nce.

As bearing complexity increases, the techniques used to measure bearingclearances become more sophisticated. For stationary multi-lobe bearings,

devices such as custom t a per ga uges, var ious mult ipoint measur ement devices,

or profi le measurement m a chines ma y be used to determine bea ring dimensions.

Once again, when the minimum inner bearing dimensions are determined, sub-

traction of the shaft diameter yields the effective diametrical clearance. In

essence, an expression similar to equation (4-8) may be used to determine the

running cleara nce of fi xed pad bear ings. For pressure da m bear ings, ca re should

be taken to insure that the primary clearance measurement is based upon the

da m lip, and not th e pressure dam depth.

A further complica tion is introduced when t ilt pad ra dial bea rings a re con-

sidered inst ead of fixed geometry bearings. In t hese assemblies, the clea ra nce is

influenced by pivoting of the bearing shoes. For instance, Fig. 4-13 depicts a five

shoe bearing w ith a n interna l shaft journa l. This is the same ty pe of bearing th a t

was used for computation of the Fig. 4-1 data. For illustration purposes, the jour-

na l in Fig. 4-13 is dra stically undersized to a llow a n improved gra phica l visual-

ization of the pad motion. If the five bearing pads are uniformly positioned

Fig. 412 Horizontal Diam-

eter Of Elliptical BearingWith Axial Oil Grooves

Dh1

Dh2

Oil Inlet Groove


20/50

168 Chapter-4

around the journal (i.e., no tilt), and the journal center is coincident with the

bearing center the dista nce from the journa l surfa ce to th e center of ea ch pad

is equal to the radial bearing clearance Cb. I f the journal is lif ted vertically

upward (left side of Fig. 4-13), the shaft will stop at the center of the upper pad.

The tota l vert ica l tra vel from the bearing center w ill be equa l to the radia l bea r-

ing clearance Cb. I f the shaft is now allowed to sink into the bottom half of the

bear ing, the condition shown on the r ight side of Fig. 4-13 w ill occur. In t his dia -

gram, the shaft will sink below the physical bearing clearance circle due to the

rota tion of the t wo bott om pa ds. The am ount of the vert ica l shift w ill be equal t o

the ra dial bearing cleara nce Cb, plus a n a dditional Dropdue to the pad pivot.

I t should be noted tha t t h is Droponly occurs in the static shaft conditiondepicted in Fig. 4-13. During machine operation, the diametrical bearing clear-

a nce is tw ice the radia l bea ring cleara nce Cb, and the s ta t ic Dropdoes not occur.

However, if bea ring clea ra nce is t o be extra cted from t he sta tic journal L i f t , the

pa d Dropmust be subtra cted. St a ted in another wa y, if a dial indica tor is used to

measure the to tal vert ical L i f t of the sha ft w ithin the bearing, the indicator read-

ing will exceed the bearing clearance. Clearly, the L i f t va lue must be reduced by

the pad Dropin order to determine the a ctua l diametr ica l bea ring cleara nce.

Fig. 413 Total Vertical Clearance In A Five Pad LBP Tilting Pad Journal Bearing

Fig. 414 Shaft Drop In ARadial Tilting Pad BearingDue To Pad Pivot

Cb

Cb+ Drop

Bearing

CenterlineShaft CL

Shaft CL

Drop

Cb

Cb


21/50


A direct approach for determining bearing clearance from shaft L i f t w a s

presented in the 1994 papers by Nicholas 5, p lus Zeidan and Paquette6. These

a uthors used dia gra ms simila r t o Figs. 4-13 a nd 4-14 to expla in th is chara cteris-

tic of radial tilting pad bearings. Specifically, within Fig. 4-14, the dotted line

describes the radia l bea ring cleara nce Cb, and is the angle between the vert ica lcenterline and the pad pivot point. The trigonometric relationship within this

right t ria ngle is as follows:

From Fig. 4-13, the total shaft L i f t for t h is t i l t pad bearing is the summa-

tion of the movement in the top half plus the bottom half of the assembly. This

ma y be sta ted an d combined with t he la st expression as :

The dia metrical cleara nce Cdmay be determined by solving the last equa-

tion for the ra dial bearing clea ra nce Cb, and multiplying by 2 to yield:

(4-9)

A sub-subscript odd ha s been a dded to the dia metrical clea ra nce solution of

equa tion (4-9). This identifi es the fa ct th a t this solution is for a tilt pad bea ring

with an odd number of pads. The assembly diagram shown in Fig. 4-13 repre-

sents a load between pad (LBP) configuration. However, if this bearing was

tur ned upside down , a load on pad (LOP) a rra ngement w ould be depicted. Thus,

equation (4-9) is correct for either a LOP or a LBP tilt pad bearing with an odd

number of pads. For an even number of pads with LOP configuration, = 90 ,

5

J ohn C. Nicholas, Tilt ing Pa d B earing D esign, Proceedi ngs of the Twenty-Th ir d Tur boma-chinery Symposium, Turboma chinery La borat ory, Texas A&M U niversity, College St at ion, Texas(September 1994), pp. 179-194.

6 Fouad Y. Zeidan, a nd D onald J . Pa quette, Applicat ion of High S peed a nd H igh P erforma nceFluid Film Bearings In Rotat ing Machinery, Proceedi ngs of the Twenty-Th ir d Tur bomachin erySymposium, Turboma chinery La borat ory, Texas A&M U niversit y, College St at ion, Texas (Septem-ber 1994), pp. 209-233.

cosCb

Cb D r o p +----------------------------

=

or

Cb D r o p +Cb

cos------------

=

L i f t T op H a l f Clea rance( ) Bo t tomH a l f Clea rance( )+=L i f t C b( ) Cb D r o p +( )+=

L i f t C b( )Cb

cos------------

+ Cb 11

cos------------+

= =

Cdod d2 Cb 2

L i f t 1

1

cos------------+

---------------------------= =


22/50

170 Chapter-4

a nd t he cosine of 90 is equa l to 1. Thus, equa tion (4-9) ma y be simplifi ed a s:

(4-10)

The fina l common confi gura tion for a r a dial tilt pa d bearing would be a L B P

wit h a n even number of pads. This bear ing t ype would display excessive clear-

a nce or Dropin both t he upper, and t he low er halves, a nd th e total L i f t w ould be:

Once more, the diam etrical clea ra nce Cd

may be determined by solving for

the ra dial bearing cleara nce Cb, and multiplying by 2 to produce:

(4-11)

For symmet rical tilting pad bearings w ith a n odd number of pa ds, the a ngle

between th e vertica l centerline an d t he pad pivot point is fi xed. The followin gvalues a re typica lly used for this bearing a ngular dimension:

3 Pads ..................... = 60

4 Pads ..................... = 45

5 Pads ..................... = 36

6 Pads ..................... = 307 Pads ..................... = 25.7

8 Pads ..................... = 22.5

For purposes of simplification and easy reference, the developed equations

(4-9) and (4-11) are combined with the standard bearing pad pivot angles, and a

diam etrical clear a nce to lif t r at io ca lculat ed for ea ch configura tion. These results

a re summ a rized in Ta ble 4-3, a nd t he tr ivia l case represent ed by equa tion (4-10)

Table 43 Tilt Pad Bearing Diametrical Clearancea Based On Shaft Lift Measurements

a Dia metrical Clearan ce = Numerical Factor x L i f t

Load 3 Pads 4 Pads 5 Pads 6 Pads 7 Pads 8 Pads

LB P 0.667xL i f t 0.707xL i f t 0.894xL i f t 0.866xL i f t 0.948xL i f t 0.924xL i f t

LOP 0.667xL i f t L i f t 0.894xL i f t L i f t 0.948xL i f t L i f t

CdL OP ev en 2 L i f t

11

cos------------+

---------------------------2 L i f t

11

1---+

--------------------2 L i f t

2-------------------- L i f t = = = =

L i f t T op H a l f Clea rance( ) Bo t tomH a l f Clea rance( )+=L i f t C b D r o p +( ) Cb D r o p +( )+=

L i f t Cb

cos------------

Cbcos

------------ +

2 C bcos

----------------= =

CdL B P even 2 Cb

2 L i f t cos2

---------------------------------------- L i f t cos= = =


23/50


ha s a lso been included. If the sha ft L i f t in a r adia l t i l t pad bearing is measured

w ith a dial indicat or or a proximity probe, the measured L i f t ma y be converted t o

a dia metr ical cleara nce based upon the fa ctors in Ta ble 4-3 for t he specifi c bea r-

ing configuration. For example, if a L i f t of 14 Mils was measured, and the bear-ing was a five pad assembly, the diametrical bearing clearance is determined

from Ta ble 4-3 a s follows :

Ta ble 4-3 ma y a lso be a pplied t o the situ a tion w here a lift check of the jour-

na l with in the bearing is not physica lly possible. In these ca ses, a separ a te ma n-

drel may be used to measure the allowable motion within the bearing (i.e. , the

L i f t ). The shaft bearing journa l diamet er must be a ccura tely measur ed as previ-

ously discussed, and a suitable mandrel cut on a precision lathe to exactly the

same dimensions. Depending on the bearing configuration, the mandrel and

assembled bearing may be mounted either vertically or horizontally. Typically,

the ma ndrel is fixed, and t he bea ring housing is physica lly moved back and fortha cross the pa ds. For a fi xed mandr el, a dial indicat or is used to measur e the over-

a ll motion of the bearing housing about t he ma ndrel.

Conversely, if the bearing housing is m ounted in some rigid fi xture, the fa b-

ricat ed mandr el may be moved between pads, and t he overall motion of the ma n-

drel measured with the dial indicator. In either case, care must be exercised to

insure that the stat ionary e lement remains fixed, and that the mandrel and

bearing h ousing a re collinea r (i .e., the a xial centerline of th e ma ndrel is par a llel

to the bea ring a xial centerline). In addition, a n a ccura te dial indicator reading t o

tenths of a Mil should be used for these measurements. The resultant Shi f tor

L i f t ma y t hen be multiplied by t he a ppropria te geometric fact or from Ta ble 4-3 to

determine the diametr ica l bea ring cleara nce of the tilt pa d bearing.

When checking tilt pad bearing clearances with a mandrel and an assem-

bled bearing, it is desirable to check clearances in more than one direction. Forinsta nce, a four pa d bear ing should be checked at orthogona l diam eters. Tha t is,

the updow n, and t he leftright pa ds should be measured to verify th a t uniform

clearances exist in both directions. For a five pad bearing, a total of three posi-

tions should be checked to insure that clearances are measured with respect to

each pad. Obviously, the sa me concept ma y be extended to bea rings w ith a lar ger

number of pads.

This d iscussion of bea ring L i f t checks w a s predica ted upon the a ssumption

that a ver t ica l L i f t or Shi f tmeasurement could be made directly at the bearing.

Obviously, this is a n ideal condition. In ma ny inst a nces it is physically impossi-

ble to both mount a dial indicator next to the bearing housing, and position the

indicator on top of the shaft. A more common condition is shown in Fig. 4-15.

This diagram depicts a three stage rotor, horizontally supported between two

ra dial journal bea rings. In th e sketch a t the t op of Fig. 4-15, a vertical dia l indi-

cat or is locat ed close to the coupling end of the rotor. The a xial d ista nce betw een

the adjacent bearing and the indicator is identified as Zb-i. The spa n or a xia l dis-

ta nce betw een bear ing centerlines is specifi ed as Zb.

Cdod d0.894 L i f t 0.894 16 Mils 14.3 Mils 14 Mils= = =


24/50

172 Chapter-4

In addition, a vertical proximity probe is located on the outside of each

bearing in Fig. 4-15. If an upward vertical force is applied at the coupling end of

this r otor, the sha ft w ill move towa rds t he top of the coupling end bearing. I t is

assumed tha t t he le ft end shaf t rema ins reasonably sta t ionar y a t t he bottom of

the outboard end bearing. This may be verified by another dial indicator at the

outboar d bearing, or t he DC ga p of the proximity probe a t t his bearing.

If no interference occurs, and if the rotor remains rigid, a straight lif t

should occur between the zero motion pivot point at the outboard end of the

rotor, and the lifting point. This elevated rotor position is shown in the middle

sketch of Fig. 4-15. Additionally, th e vertica l chan ge in sha ft cent erline a long the

length of the rotor is presented a t the bottom of Fig. 4-15. In t his dia gra m, the

vertical axis is expa nded for clarity. I t is noted tha t a series of similar r ight t ria n-

gles a re present in t his ideal lif t diagra m. By simple proportion of these right t ri-

a ngles, the follow ing expression evolves:

Fig. 415 Field Lift CheckOf Coupling End BearingOn A Horizontal RotorMounted Between TwoJournal Bearings

Zb-i

Zb

Vertical Force

ProximityProbe

DialIndicator

Rotor in Bottom of Bearings

Rotor withCoupling End Elevated

Bearing Bearing

AssumedPivotPoint

ProximityProbe

Coupling

Lift @ Dial Indicator

Lift @ Proximity Probe

Lift @ Bearing

Lifti

Zb-i

Zb

Liftp

Liftb

L i f t bZb

---------------L i f t i

Zb Zb i+--------------------------=


25/50


This equa tion of proport ions ma y be solved for the bea ring L i f t b, as follow s:

(4-12)

Thus, the bear ing sha ft L i f t bmay be determined based upon a dial indica-

t or L i f t iobta ined at a different a xial locat ion on the sha ft. Next, the bea ring dia-

metrical clearance may be determined by applying the appropriate correction

factor from Ta ble 4-3 for a tilt pad bearing, or by equa ting t he L i f t to the vertical

clearance for a fixed pad bearing. If a vertical proximity probe is mounted adja-

cent to the bearing (e.g., Fig. 4-15), the change in DC gap voltages may also be

used t o determ ine the lift a s show n in equa tion (4-13):

(4-13)

In many cases, the vertical shaft lif t measured by a proximity probe L i f t pmay be very close to the shaft shift within the bearing L i f t b. This is due to the

short a xial dista nce betw een t he bearing a nd t he probe location (e.g. , the confi gu-

ra tion show n in Fig. 4-15). In fa ct, it is highly d esira ble to compar e the corr ected

dial indica tor rea dings from equa tion (4-12) with the differential probe gap r ead-

ings comput ed w ith equa tion (4-13). This logic a lso a pplies t o th e opposite end of

the machine. For instance, in Fig. 4-15, the outboard bearing is the assumed

pivot point for lifting the rotor. At this location a vertical dial indicator should

show zero motion as the shaft is lif ted. In many cases, this non-motionis ta ken

for granted, and an indicator is seldom positioned at the bearing opposite the

unit subjected to lift check. However, proximity probes are often installed, andthese probes should be monitored to verify that the shaft is not moving at the

opposite end of the rotor. In pra ctice, the DC ga ps at th is opposite bea ring sh ould

not change as t he shaf t is ra ised.

On ma ny inst a llat ions, the ma chinery is equipped wit h th e preferable com-

binat ion of X-Y proximity probes. Often t hese tra nsducers a re mounted a t 45

from the vert ica l centerline, and a true vert ica l proximity probe does not exist. In

this situa tion, the dista nce cha nges w ith respect t o each probe should be vectori-

a lly summed to determine the overall sha ft lif t a t t ha t loca tion. The specifi c steps

a re outlined in t he follow ing case history 7.

L i f t b

Zb

L i f ti

Zb Zb i+---------------------------

L i f t i

1Zb i

Zb-------------+

----------------------------= =

L i f t p 5.0Mils

Volt-----------

DCGa prest DCGa pe leva ted{ } Volts=


26/50

174 Chapter-4

Case History 7: Expander Journal Bearing Clearance

A 5,000 HP hot ga s expa nder operat es at 8,016 RP M w ith 4.00 inch diame-

ter journals mounted in tilting pad bearings. The bearings are four pad with aload between pad (LBP) configuration. This machine is equipped with X-Y prox-

imity probes a djacent t o each bearing a t 45 from vert ica l. A dial indicat or wa s

mounted 11 inches from the bearing, and the distance between bearing center-

lines wa s measur ed to be 53 inches. The shaft wa s lif ted with a pry ba r, and t he

indicator showed a vertical lift of 10.5 Mils. The probe gap voltages measured

durin g th e lift a re summ a rized in Ta ble 4-4:

The lift a t t he bea ring ma y be ca lculat ed based upon th e externa l lift m ea-

surement, and the axial distances between bearings and indicator position.

U sing equa tion (4-12), it is easily determined t ha t:

This mecha nical result should now be compar ed wit h t he lif t measur ements

obtained with the shaft proximity probes. Applying equation (4-13) for eachtra nsducer, the sha ft sh ift detected by each probe may be computed in t he follow -

ing manner:

The negative signs indicate that the shaf t movement was towards the

probes. If a sta nda rd coordinat e system is used, the t rue horizonta l axis w ould bea t 0 , and true vert ica l would be at 90 . Within t his coordinat e system t he X-Axis

probe would be located a t 45 , an d t he Y-Axis tra nsducer a t 135. I f t he measur ed

shifts are considered as vectors towards each probe, the overall motion may be

Table 44 Summary Of Probe Gap Voltages During Lift Check

Shaft Physical Position Y-Axis X-Axis

P robe Loca t ion 45 Left of Vert ica l 45 Right of Ver t ica l

At Rest - B ot t om of B ea r ing -10.73 Volt s D C -9.69 Volt s D CE leva t ed - Top of B ea ring -9.96 Volt s D C -8.51 Volt s D C

L i f t b

L i f t i

1Zb iZb

-------------+ ----------------------------

10.5 Mils

111 Inches

53 Inches---------------------+

------------------------------------

10.5 Mils

1 0.208+( )--------------------------- 8.69 Mils= = = =

L i f t pY Ax i s 5.0

Mils

Volt-----------

10.73( ) 9.69( ){ } Volts 5.20 Mils==

a n d

L i f t pX A xi s 5.0

Mils

Volt-----------

9.96( ) 8.51( ){ } Volts 7.25 Mils==


27/50


expressed as the following two vectors:

The sum of horizont a l vector components a re det ermined w ith (2-31):

Sim ila rly, th e sum of vertica l vector components a re comput ed w ith (2-32):

From these shaft position changes it is noted that the shaft did not come

straight up in the bearing. The horizontal shift of nominally 1.5 Mils indicates

that the shaft moved sideways. This is not a surprising result since the pry bar

used for t he lif t w a s not completely level, an d some horizonta l force wa s probably

applied to the rotor. For bearing clearance purposes, the vertical lift of 8.8 Mils

should be used for further calculations. However, before addressing the bearing

clearances, it is desirable to conclude the vector addition computations of the

shifts measured by the proximity probes. If equation (2-33) is used to determine

the combined ma gnitude shift, th e follow ing result is obta ined:

Note that the vector sum of 8.9 Mils is very close to the vertical shift of 8.8Mils determined in the previous group of calculations. Finally, the angle of the

shaft lift is determined from equation (2-34) as:

Ideally, the lif t angle should be 90. Since some horizontal shift was

imposed, a slight variation in angles does occur. If the lift angle is between 75

a nd 105 t he tota l vertical lif t error w ill be less tha n 4%. In ma ny ca ses, it is

more convenient to add t he shift vectors on a ha ndheld ca lculat or rat her tha n go

thr ough t he deta il required in t he previously outlined steps. For t his a pplica tion,

the diagnostician should make sure that the calculator is capable of easily per-

forming vector a ddit ion (e.g., HP 48SX).The vertical lift readings based upon the dial indicator should be close to

the values measured by the proximity probes (assuming that the probes are

mounted next to the bearing). If the deviat ion betw een th e tw o values is great er

than approximately 5 to 10% then there is something wrong, and the entire

Vy A 5.20 Mils 135= =

Vx B 7.25 Mils 45= =

Vad dh o r i z A cos B cos+=

Vad dh o r i z 5.20 135cos 7.25 45cos+ 3.68 5.13+ 1.45 Mils= = =

Va d dve r t A sin B sin+=

Vad dve r t 5.20 135sin 7.25 45sin + 3.68 5.13+ 8.81 Mils= = =

Va d d Vad dh o r i z ( )2 Va d dve r t ( )

2+ 1.45( )2 8.81( )2+ 79.72 8.93 Mils= = = =

ad dVad dve r t Va d dh o r i z

------------------------

a t a n8.81

1.45----------

a t a n 6.076( )a t a n 80.6 81= = = =


28/50

176 Chapter-4

measurement scenario should be re-examined. In this case, the calculated lift

from the X-Y probes (8.8 Mils) should be compared with the mechanical lift as

measur ed wit h t he dial indica tor (8.7 Mils). Since the probes a re mounted out-

boa rd of the bear ing, the indica ted vertical lif t from the probes is slightly gr eat ertha n th e mecha nical lif t corrected to the center of the bea ring. I t is reasona ble to

conclude tha t t he vertical bearing lift is equa l to 8.7 Mils. Ba sed on t his informa -

tion, Ta ble 4-3 or eq ua tion (4-11) may be used t o determine t he vert ical dia metr i-

cal bearing cleara nce as follows:

The final step is to verify the general validity of this measurement. Typi-

cally, a bea ring clea ra nce rat io (BCR)is calcula ted a s follow s:

(4-14)

Since this expa nder ha d 4.00 inch journa ls, the BCRis simply:

A clearance to diameter ratio of 1.6 makes good sense for this bearing con-

figuration in a horizontal machine. Table 4-5 describes the general behavior of

key para meters as t he BCRis varied. Most bearing designers agree that a BCRof 1.0 is generally on t he tight side. Sma ll bearing clea ra nces result in high oil

film stiffness, and this is accompanied by low shaft vibration, and potentially

high bea ring temperat ure. If the BCRis increa sed to 2.0, the st iffness a nd da mp-ing will decrease, vibration will increase, and the bearing would probably run

cooler. In addition, the machine with larger bearing clearances would be more

susceptible to a variety of instability mechanisms. In most horizontal industrial

ma chines, the BCRis seldom less than 1.0, and it generally does not exceed 2.0.In specia lized a pplica tions, with exotic mecha nical designs a nd met a llurgy, these

traditional limits may be extended. However, in most cases, the BCR runs

betw een 1.0 an d 2.0.

On lar ge vertical ma chines, the ra dial bear ing loa ds a re low, a nd th e weight

of the rotating element is supported by a massive thrust bearing that is usually

located at the top of the machine. On these units, the radial bearing clearances

Table 45 General Trends Of Key Bearing Parameters With Variations In Bearing Clearance

Ratio (BCR) For Horizontal Machines Mounted In Fluid Film Bearing

Bearing Clearance Ratio(BCR)

Oil FilmStiffness

Oil FilmDamping

ShaftVibration

BearingTemperature

1.0 Mil/Inch Increa ses Increa ses D ecrea ses Increa ses

1.5 Mi ls/In ch Nom inal N om inal N om inal N om inal

2.0 Mils/Inch D ecrea ses D ecrea ses Increa ses D ecrea ses

CdL BP ev en L i f t cos 8.7 45cos 8.7 0.707 6.2 Mils== = =

BCRB ear i ng Di ametr i calClea ranceMils( )

J o u r n a l Diame te rInches( )-----------------------------------------------------------------------------------------------------------=

BCRB ear i ng Di ametr i calClea ranceMils( )

J o u r n a l Diame te rInches( )-----------------------------------------------------------------------------------------------------------

6.2Mils

4.00Inches------------------------ 1.6 Mils/Inch= = =


29/50


a re much t ight er, and Ta ble 4-5 is not a pplica ble. For these vert ical ma chines,

the bearings are basically a flooded oil bath, with diametrical clearances that

genera lly va ry betw een 10 a nd 20 Mils (0.010 and 0.020 inches). These a re t ypi-

cally referred to as gui de bear in gs, and t heir fundament a l function is to keep thesha ft r unning in a vertical position. The cleara nce of these bearings a re normally

obtained by physically swinging the rotor back and fourth in orthogonal direc-

tions (e.g., North-South and East-West). In this case, the upper thrust bearing

becomes th e pivot point, a nd bear ing cleara nce is mea sured wit h dia l indica tors

a t ea ch bear ing. For vertical ma chines equipped w ith t ilt pad bearings, the indi-

vidual pads are often radially adjustable in position to provide the capability to

change the overall bearing clearance. On fixed geometry bearings, the proper

cleara nce ha s to be built int o the bea ring ba sed upon a ctua l diameter.

In any lift measurement on assembled machines, consideration must be

given to physical configurations or conditions that could cause measurement

errors. For instance, close clearance seals, or a long balance piston might restrict

the r otor lif t , an d a ppea r a s reduced bear ing cleara nces. On gea r boxes, if an ele-

ment is partially supported by a mating gear, the lif t check will be erroneous

since the starting point will not be at the bottom of the bearing. Similarly,

installed couplings, governor drive gears, and engaged turning gears will all

inhibit the shaft lif t , and may be incorrectly interpreted as reduced bearing

clearances.

Conversely, excessive cleara nces in other ma chinery pa rt s a ssociat ed wit h

the bearings may look like large clearances. Loose hold down bolts, or housing

attachment bolts can produce inordinate shaft lif t readings. On electric

ma chines such a s motors or generat ors, the bearings a re norma lly insula ted wit h

some type of non-conducting material. This electrical insulation isolates the

rotor volta ge from passing to ground t hrough t he ma chine bearings. These insu-

lat ing blocks a re usua lly insta lled w ith zero cleara nce. However, cleara nces can

expand with time and excessive vibration, with an overall reduction in supportstiffness. The same argument applies to the fit between the bearing assembly

and the housing. Although wide variations may be encountered for this dimen-

sion, most m a chines opera te somewhere betw een a n int erference fit , or crush, of

1 or 2 Mils; and a clea ra nce of 1 or 2 Mils. Clea rly, excessive crush can d istort th e

bearing assembly resulting in premature failure, whereas excessive clearance

will reduce the support stiffness. This stiffness reduction may allow a rotor reso-

na nce tha t n ormally resides above operat ing speed to creep back into the opera t-

ing speed domain. When this occurs, shaft vibration increases, and the

propensity t owar ds early fa ilure of the bearing increases.

It is generally advisable to refer to the OEM specifications for guidance in

establishing the proper clearances between the bearing assembly and the bear-

ing cap. If this informat ion is not a vaila ble, then a zero to 1 Mil cleara nce should

be used as a reasonable starting point. Determination of this clearance may bedifficult due to the possibility of a zero clearance. If Plastigage or lead wire in

installed between machine parts that have essentially no clearance, the mea-

surement media becomes smeared, and essentially useless. The solution to this

situa tion resides in providing a n initia l, or r eference, cleara nce at the split line.


30/50

178 Chapter-4

For exam ple, a 5 Mil shim ha s been insta lled a t t he housing split line shown in

Fig. 4-16. This shim elevates the entire upper half of the bearing cap by 5 Mils,

a nd a llows t he use of B lue Pla stiga ge (4 to 9 Mil range) to measure t he remain-

ing cleara nce. If the P last igage shows a 4 Mil cleara nce, then subtra ction of the 5

Mil shim reveals a n int erference fit of 1 Mil. Conversely, if the P last igage indi-

cates a 6 Mil cleara nce, then subtr a ction of the 5 Mil split line shim results in a

bearing t o ca p cleara nce of 1 Mil. For cleara nces t ha t exceed t he measu rement

ra nge ava ilable from Pla stiga ge, lead wire ma y be used. In either ca se, wh en the

measur ement checks a re completed, the P last igage (or lea d w ire) remna nts, plus

the split line shims mus t be removed before fi na l a ssembly of the housing.

If excessive ca p to bearing cleara nces a re encountered, the best perma nent

solution is to re-machine the offending stationary element(s) to restore properclearances. In some cases, this is not a viable option due to production or mainte-

nance demands. In this situation, a temporary stainless steel shim may be

insta lled betw een th e ca p and the bear ing to tighten up t he assembly. If this cor-

rection technique is used, then the machine history records should clearly indi-

cate the insta llat ion of this shim.

In all cases, the success of the lift check is highly dependent upon the

method used to mechanically lif t the shaft. For light rotors, a simple pry bar is

quite adequate for this task. For heavier rotors, a screw jack, or an overhead

chain hoist might be used. On very heavy r otors, a hy dra ulic jack may be neces-

sary to lif t the rotor. I t must be recognized that this is a potentially dangerous

practice. Rotors have been permanently bent, and bearing housings have been

cracked or broken due to the aggressive use of a hydraulic jack. This type of lift

should be performed carefully, and with full knowledge of the expected clear-ances. Multiple dial indicators might be installed axially on the shaft to verify

tha t a linea r (stra ight line) lif t is occurring. This informat ion w ould help to mini-

mize potentially bending the shaft. I t might also be desirable to mount a sepa-

Fig. 416 Typical ClearanceMeasurement BetweenBearing Liner And Bearing

Housing

Shaft

Blue Plastigageor Lead Wire

Bearing5 MilShim

Bearing Pedestal


31/50

Bearing Supports Measurements and Calculations 179

rate dial indicator on the outboard end of the bearing housing. This vertical

indica tor w ould be used to reveal an y tendency towa rds a vertical lif t of the hous-

ing. This informat ion w ould help to minimize any da ma ge to the bea ring housing

from the vertical hyd ra ulic jack under the sha ft.

BEARING SUPPORTS MEASUREMENTSAND CALCULATIONS

The previously discussed bearing characteristics are associated with the

properties of the oil film between the rotating shaft, and stationary bearings of

different configurations. This is an acceptable description of the rotor support

system if the bearings are rigidly supported. Industrial machines with heavy

cases, and light rotating elements fall within this category. Barrel compressors

with internal bearings, rigid gear boxes, high pressure pumps, and many older

pieces of equipment operate with structural stiffness that are substantially

greater t han the o il fi lm st i f fness.

However, this is not the case for many other machines that have flexible

supports a nd/or founda tions. U nits s uch as induced dra ft or forced dra ft fa ns,

steam or gas turbines, horizontally split centrifugal compressors, and pumps

with external bearings are just a few examples of machines that operate with

fl exible supports. For these ty pes of ma chines th e rema inder of the mechanical

syst em must be included. In a genera l case, the effective support st iffness for a

typical rotor on a flexible support may be defined by equation (4-15) that

describes the relat ionship a s a group of springs in series:

(4-15)

where: Keff = Effective Rotor Support Stiffness (Pounds/Inch)

Koil = Oil Film (Bearing) Support Stiffness (Pounds/Inch)Khsg = Bearing Housing Support Stiffness (Pounds/Inch)

Kbase = Baseplate Support Stiffness (Pounds/Inch)

Kfnd = Foundation Support Stiffness (Pounds/Inch)

This expression will be subjected to substantial modification if the support

structure is in a resonant condition, or if the support is highly flexible. However,

th ese ar e ra re occurrences, a nd t he a bove equa tion (4-15) is considered t o be gen-

erally representat ive of the norma l rotor support para meters.

Quan tifi cat ion of the str uctura l support t erms in equa tion (4-15) is a formi-

dable technical feat. The calculation of these individual stiffness terms is diffi-

cult at best, and in some cases it is virtually impossible. The most reas

Documents

Chapter 4 Bearings