rotordynamic analysis of a two-pole synchronous motor with sleeve

7/25/2019 Rotordynamic Analysis of a Two-Pole Synchronous Motor With Sleeve

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University of Tennessee, Knoxville

Trace: Tennessee Research and CreativeExchange

Masters eses Graduate School

5-2014

Rotordynamic Analysis of a Two-PoleSynchronous Motor with Sleeve and Pressure Dam

BearingsJustin Mahew GarrardUniversity of Tennessee - Knoxville, [email protected]

is esis is brought to you for free and open access by the Graduate School at Trace: Tennessee Research and Creative Exchange. It has been

accepted for inclusion in Masters eses by an authorized administrator of Trace: Tennessee Research and Creative Exchange. For more information,

please contact [email protected].

Recommended CitationGarrard, Justin Mahew, "Rotordynamic Analysis of a Two-Pole Synchronous Motor with Sleeve and Pressure Dam Bearings. "Master's esis, University of Tennessee, 2014.hp://trace.tennessee.edu/utk_gradthes/2710
http://trace.tennessee.edu/http://trace.tennessee.edu/http://trace.tennessee.edu/utk_gradtheshttp://trace.tennessee.edu/utk-gradmailto:[email protected]:[email protected]://trace.tennessee.edu/utk-gradhttp://trace.tennessee.edu/utk_gradtheshttp://trace.tennessee.edu/http://trace.tennessee.edu/


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To the Graduate Council:

I am submiing herewith a thesis wrien by Justin Mahew Garrard entitled "Rotordynamic Analysis ofa Two-Pole Synchronous Motor with Sleeve and Pressure Dam Bearings." I have examined the nalelectronic copy of this thesis for form and content and recommend that it be accepted in partial

fulllment of the requirements for the degree of Master of Science, with a major in MechanicalEngineering.

Trevor Moeller, Major Professor

We have read this thesis and recommend its acceptance:

Joseph Wehrmeyer, Milt Davis

Accepted for the Council:Carolyn R. Hodges

Vice Provost and Dean of the Graduate School

(Original signatures are on le with ocial student records.)


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A

D B

A Thei Peened f he

Mae f Science

Degee

The Uniei f Tenneee, Knille

Jin Mahe Gaad

Ma 2014


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Cigh 2014 b Jin Mahe Gaad

All igh eeed.


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iii

, A,

.

,

,

.


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i

I ld fi like hank m fahe, D. Glenn D. Gaad, f cnanl hing me cnine

m edcain, bee melf, and n he lea f hich f checking hi hei in i enie. Ne, I

ld like hank m cmmiee, D. Te Melle, D. Jeh Wehmee, and D. Miln Dai, J.,

f iding gidance and fheing m edcain e he ce f m Mae die. I ld al

be emi if I did n hank m cke Jeh Ca, Ga Jaell, and Dn Band f hei

menhi and hel ih ndeanding m eain and he field f dnamic. Wih

hem, I nee ld hae cnideed hi a a ible hei ic and i ha ened me a field

hich I he cnine cnibe a m caee cnine. Finall, he k eed heein a

dne a Anld Engineeing Deelmen Cmle (AEDC) n he ah n ime. Thi e a

aed f blic eleae n Mach 24, 2014 nde AEDC PA Nmbe: AEDC2014037. Diibin i

nlimied.


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A le nchn m a ecenl end f he n Kaman Ga Dnamic facili

a Anld Engineeing Deelmen Cmle, Anld Ai Fce Bae, Tenneee. Afe inalling he

end , neeced ibain amlide ee ecded ding m check. T ele hi

ie, an ineigain a iniiaed ineigae he cae f he ibain ie. The ineigain

diceed ha he iginal deign ed leee beaing ahe han ee dam beaing. A d a

fmed deemine he effec f changing he ee dam beaing back leee beaing. Becae

nl ne ae beaing hell eied, he beaing ih he highe ibain amlide a chen be

iched. A laeal dnamic anali a efmed deemine he imac f hi ich, i

efming he beaing a.

The dnamic mdel ediced ha he a eaing nea he ecnd ciical eed.

Regadle f he beaing change, he ecnd ciical eed a n imaced. Hee, he

deeminain a made change he beaing he leee beaing de ediced le ibain

amlide. Fm he m check n, he mdel edicin a eified and he leee beaing

a ke. Vibain amlide hae been edced, b ie ill emain ih he eain nea

he ecnd ciical eed. Fhe anali i eied ccefll hif he eain aa fm

he ecnd ciical eed.


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i

1.0 Indcin ............................................................................................................................................ 1

1.1 Backgnd ......................................................................................................................................... 1

1.2 Pblem Saemen ............................................................................................................................. 4

1.3 Pblem Aach .............................................................................................................................. 4

2.0 Lieae Reie .................................................................................................................................... 7

2.1 Backgnd ......................................................................................................................................... 7

2.2 Jeffc Cnibin ........................................................................................................................ 8

2.3 Jeffc MkleadPhl .............................................................................................................. 10

2.4 Lnd and Gne Peen Da....................................................................................................... 12

3.0 RBeaing Sem Mdel ................................................................................................................ 15

3.1 Beaing Anali ................................................................................................................................ 15

3.2 Sleee Beaing Mdel ....................................................................................................................... 19

3.3 Pee Dam Beaing Mdel ........................................................................................................... 26

3.4 RBeaing Mdel ........................................................................................................................ 34

3.5 R Mdel ih Pee Dam Beaing ........................................................................................ 39

3.6 R Mdel ih Sleee Beaing ..................................................................................................... 51

4.0 Eeimenal Rel............................................................................................................................. 60

4.1 Eeimenal SeU ......................................................................................................................... 60

4.2 Fi Rn Pee Dam Beaing ................................................................................................... 61

4.3 Secnd Rn Sleee Beaing Check ............................................................................................ 68

5.0 Cnclin ........................................................................................................................................... 78

5.1 Cmaaie Anali f Mdel and Eeimenal Daa .................................................................. 78

5.2 Fe Wk ...................................................................................................................................... 79

5.3 Final Dicin ................................................................................................................................. 80

Bibligah ................................................................................................................................................ 82

Aendice .................................................................................................................................................. 89

Aendi I: Beaing Eain f Min and Finie Elemen Slin ................................................. 90

Aendi II: RBeaing Sem Anali ......................................................................................... 102


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Aendi III: Elemenal Maice .......................................................................................................... 109

Aendi IV: RngeKa Mehd ....................................................................................................... 113

Aendi V: Beaing Chaaceiic ..................................................................................................... 115

Via ............................................................................................................................................................ 120


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Fige 1 Eamle f T Ple R Cncin..1

Fige 2 Reinding f T Ple R....2

Fige 3 Rankine Fee Bd Diagam.7

Fige 4 Jeffc R..9

Fige 5 SdlaGeen R and Cending Mde Shae..11

Fige 6 Sleee Beaing ...16

Fige 7 Pee Dam Beaing..17

Fige 8 Hddnamic Film in Jnal Beaing..18

Fige 9 Sleee Beaing DRBeS Sceen......19

Fige 10 Sleee Beaing DRBeS Dimeninal Anali Sceen..20

Fige 11 Sleee Beaing Jnal Eccenici Rai....21

Fige 12 Sleee Beaing Jnal Eilibim Lc.22

Fige 13 Temeae Range f Sleee Beaing...23

Fige 14 Sleee Beaing Pee Pfile a Ceneline..........................................................................24

Fige 15 Sleee Beaing 3D Pee Pfile..........................................................................................24

Fige 16 Sleee Beaing K, K, C, and C Cefficien..................................................................25

Fige 17 Sleee Beaing K, K, C, and C Cefficien..................................................................26

Fige 18 Pee Dam Beaing DRBeS Sceen...............................................................................27

Fige 19 Pee Dam Beaing DRBeS Dimeninal Anali Sceen.............................................28

Fige 20 Pee Dam Beaing Jnal Eccenici Rai....................................................................29

Fige 21 Pee Dam Beaing Jnal Eilibim Lc....................................................................30

Fige 22 Temeae Range f Pee Dam Beaing.........................................................................31

Fige 23 Pee Dam Beaing Pee Pfile a Ceneline..............................................................31

Fige 24 Pee Dam Beaing 3D Pee Pfile..............................................................................32

Fige 25 Pee Dam Beaing K, K, C, and C Cefficien......................................................33


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Fige 26 Pee Dam Beaing K, K, C, and C Cefficien......................................................33

Fige 27 Tical RBeaing Finie Elemen Aembl ....35

Fige 28 DRBeS R Mdel..........................................................................................................37

Fige 29 Undamed Ciical Seed Ma................................................................................................38

Fige 30 RPee Dam Beaing Mdel Mde N. 1....................................................................40

Fige 31 RPee Dam Beaing Mdel Mde Shae N. 1 Penial Eneg Diibin..........40

Fige 32 RPee Dam Beaing Mdel Mde Shae N. 1 Kineic Eneg Diibin..............41

Fige 33 R Pee Dam Beaing Mdel Mde N. 2...................................................................42

Fige 34 R Pee Dam Beaing Mdel Mde Shae N. 2 Penial Eneg Diibin.........42

Fige 35 RPee Dam Beaing Mdel Mde Shae N. 2 Kineic Eneg Diibin..............43

Fige 36 RPee Dam Beaing Mdel Whil Seed Ma...........................................................44

Fige 37 RPee Dam Beaing Mdel Peceinal Mde Shae.............................................46

Fige 38 Unbalance Lcain fm API 684..........................................................................................47

Fige 39 Pimi Pbe Mning .48

Fige 40 RPee Dam Mdel Mde N. 1 Unbalance Rene Bde Pl...............................49

Fige 41 RPee Dam Mdel Mde N. 6 Unbalance Rene Bde Pl...............................50

Fige 42 RSleee Beaing Mdel Mde N. 1.................................................................................51

Fige 43 RSleee Beaing Mdel Mde Shae N. 1 Penial Eneg Diibin.......................52

Fige 44 RSleee Beaing Mdel Mde Shae N. 1 Kineic Eneg Diibin...........................52

Fige 45 RSleee Beaing Mdel Mde N. 2.................................................................................53

Fige 46 RSleee Beaing Mdel Mde Shae N. 2 Penial Eneg Diibin.......................53

Fige 47 RSleee Beaing Mdel Mde Shae N. 2 Kineic Eneg Diibin...........................54

Fige 48 RSleee Beaing Mdel Whil Seed Ma........................................................................55

Fige 49 RSleee Beaing Mdel Peceinal Mde Shae.........................................................56

Fige 50 RSleee Beaing Mdel Mde N. 1 Unbalance Rene Bde Pl..............................58

Fige 51 RSleee Beaing Mdel Mde N. 6 Unbalance Rene Bde Pl..............................59

Fige 52 M Check SaU Bde Pl........................................................................................62


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Fige 53 M Check 1 Ciical Seed Secm Pl...................................................................63

Fige 54 M Check Ciical Seed Waefall Pl ES P Pbe...............................................64

Fige 55 M Check 2X Hamnic Waefall a 2100 RPM ES P Pbe..................................65

Fige 56 M Check Oeaing Seed Secm Pl...................................................................65

Fige 57 M Check Oeaing Seed Waefall Pl ES P Pbe..........................................66

Fige 58 M Check Ca Dn Bde Pl..................................................................................67

Fige 59 M Check Cadn 1800 RPM Waefall Pl ES P Pbe.................................68

Fige 60 Sleee Beaing Check SaU Bde Pl...........................................................................70

Fige 61 Sleee Beaing Check Fi Ciical Seed Secm Pl...................................................71

Fige 62 Sleee Beaing Check Fi Ciical Seed Waefall Pl WS P...................................71

Fige 63 Sleee Beaing Check Oeaing Seed Secm Pl......................................................72

Fige 64 Sleee Beaing Check Oeaing Seed Waefall Pl WS P.....................................73

Fige 65 Sleee Beaing Check Cadn Bde Pl......................................................................75

Fige 66 Sleee Beaing Check Cadn 3600 RPM Secm Pl...............................................76

Fige 67 Sleee Beaing Check Cadn Waefall Pl ES P................................................76

Fige 68 Sleee Beaing Check Cadn Waefall Pl WS P..............................................77

Fige 69 Sleee Beaing Cadn Fi Ciical Seed Waefall Pl 1800 RPM WS P..............77

Fige 70 Jnal Beaing Flid Film Mdel .....................................92

Fige 71 Jnal Saic and Dnamic Piin...93

Fige 72 Finie Elemen Meh f Sleee Beaing ..96

Fige 73 Tical Finie Elemen in Beaing Mdel .97

Fige 74 Bnda Cndiin f Film Dicnini..100


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/

A Finie elemen cecinal aea

AC Alenaing cen

AEDC Anld Engineeing Deelmen Cmle

ASME Ameican Scie f Mechanical Enginee

c Daming cefficien

c Daming cefficien, diecin

c Daming cefficien, diecin

C Radial cleaance

Cb Radial cleaance in DRBeS

Cd Pee dam cleaance

C Lbican ecific hea

DC Diec cen

e R eccenici, ObOj

em Eccenici f nbalanced ma n Jeffc

E Mdl f elaici, al knn a Yng mdl

F Flid film eacin fce

F Flid film eacin fce, diecin

F Flid film eacin fce, diecin

F, Unbalance fce, diecin

F, Unbalance fce, diecin

G Shea mdl

G Tblen fl cefficien, diecin

G Tblen fl cefficien, diecin

h Lbican film hickne


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I Aea mmen f ineia

Id Diameal mmen f ineia

I Pla mmen f ineia

k Siffne cefficien

k Siffne cefficien, diecin

k Siffne cefficien, diecin

kij Siffne mai cefficien

L Finie elemen lengh

m ma

M, Unbalance mmen, diecin

M, Unbalance mmen, diecin

Nad Nmbe f beaing ad

Ob Beaing cene

Oj Jnal () cene

Lbican ee

PLC Pgammable Lgic Cnlle

Saial cdinae

Obi adi

Rb Beaing adi

Rj Jnal () adi

Re Renld nmbe,

Time

n Time a ale n, n=0,1,2,...ec.

T Temeae

U Sface elci


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VFSS Vaiable feenc aing em

W Beaing lad, half he eigh f beaing em

Hinal cdinae

c Ceneline f finie elemen, diecin

Veical cdinae

c Ceneline f finie elemen, diecin

Aial cdinae

G Gcic mai

Siffne mai

Bending iffne mai

Shea iffne mai

Aial fce iffne mai

Tanlainal ma mai

Rainal ineia mai

Timedeenden end in dilacemen ec

Ndal aiable ec

Mde hae ec (eigenec)

Sinhil ai

Lgdecemen, daming ai f mde

Vic daming fac, diecin

Vic daming fac, diecin

Nndimeninalied cdinae f finie elemen gid geneain

Angle fm ai, beaing cicmfeenial ad angle, jnal ainal angle

h Angle meaed fm beaingjnal line f cene lcain f calclaed film hickne

Hea cndcii


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Lbican able ici

Pin ai, negaie ai f anee aial ain aicla each maeial

Nndimeninalied cdinae f finie elemen gid geneain

Deni, flid lid

Aide angle f jnal, angle beeen lad and beaing/jnal line f cene

Phae angle f nbalance fce

Tanee hea aamee

Jnal () angla elci

Damed naal feenc, diecin

n Undamed naal feenc, diecin

Damed naal feenc, diecin

n Undamed naal feenc, diecin

Ciical eed (eigenale)

Shae fncin mai


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1

1.0

1.1

The n Kaman Ga Dnamic Facili (VKF), lcaed a Anld Engineeing Deelmen

Cmle (AEDC), Anld Ai Fce Bae, Tenneee, cnain hee cnin fl ind nnel:

Tnnel A, B, and C. Pimail ed in he deelmen f enic and henic aicaf, he

nnel can be ed imlae cndiin ih fligh Mach nmbe anging fm 1.5 10 and

emeae 1440R [1]. In de me he lme f ai eied mee hee cndiin, a

nine age cme em dien b fie (18,500 hee each) elecic m i ed. Each

elecic m cnain a eel hich i machined fm ne blck f eel. The ha nn

alien le, aed in ce inding and inlaed ih G10 inlain maeial [2] beeen he

inding hich een h and ac a eaining blck f he ce inding. A ice f a

cmaable i hn in Fige 1 [3].

F 1 E C


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2

A diec cen (DC) lage i alied he ing a li ing aembl ih cabn

bhe, ceaing a magne. A aiable feenc a em (VFSS) alie an alenaing cen (AC)

a aing feenc he m a hich cae he begin in ih he alenaing

elecmagneic field f he a. A he feenc f he alenaing cen eache 60 H, hich i

he incming anmiin line feenc, he m i nchnied ih he incming line feenc

and he VFSS d ff a he nchniain beake i cled. Mliling he line feenc b 120

and diiding b he nmbe f le calclae he nchn eed f he , hich eal 3600

ain e mine (RPM) in hi cae.

Ding eain, he elecici nning hgh he ce inding cae he inding

hea , hich cae he inding eand. The inding ae deigned eand and cnac in he

li lane, hn abe in Fige 1 nning aiall ac he . Oe mlile ea; hee,

hi cnan heaing and cling can lead he ce inding binding in hei li lane

delaminaing a he end f he inding hee he a and he le. Thi ce ma ceae

h cici and can eenall lead faile f he m, hing in inceaed ibain leel

hich eenall becme nenable f m eain. T fi hi blem, he can be emed

fm eice and end ih ne ce inding, a hn in Fige 2 [4].

F 2


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3

A maj efbihmen jec a begn in lae 2009 eai he VKF m de hei age

and ie ih ibain leel n he machine ceeing ad. The m ee end and each

a balanced in a high eed balancing i ene minimal ibain ding eain. Once hi

a efmed, he m ee hen hied back and einalled in he VKF facili. Flling

inallain, m check ee efmed ene he m efmed a eeced ac i

eainal deign enele. Ding eainal check, blem ee deeced. Fi,

ibain leel ee highe han eeced and highe han ha hn in he balance i, a facili

hich n he eainal eed f balancing e afe he eind i cmleed. Secnd,

il leak fm he hddnamic beaing became feen ding hee check. An ineigain a

begn lk in he ce f hee ie.

Seeal cae ee ed a he ce f he ibain. Pi dnamic die

ggeed ha he em i nning nea he ecnd ciical eed, hich can lead inabiliie ha

make he difficl balance. The ciical eed f he i he angla elci hich ecie a

naal feenc f he hee enance cc hich can lead lage inceae in em

ibain. Al, an e in he einding ce can lead hemal eniii, a blem hich

cae he b a he emeae ie [5]. Themal eniii can be caed b

nme ie ih he einding ce, inclding hed n, cil eanin eicin,

l edge binding, and man he ie ih he inding. An ne f hee ie can make he

difficl balance hich can lead einding he .

The m ee iginall deigned e leee beaing. The cen inallain ed

ee dam beaing. Pee dam beaing ae icall me able, and eie me make il

fl in he beaing mainain he e il film. The fced feed il lbicain em f he

m beaing ee deigned f leee beaing, and he ein a aied hehe ich he

beaing e back he leee beaing.


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4

1.2

The VKF m a ffeing fm high ibain leel and il leak emming fm ime

em deign f he beaing e hich a inalled in he m. Since hee a me belief ha

he a eaing nea he ecnd ciical eed, i a deied hif he ciical eed aa

fm he eainal eed f 3600 m. One f he mehd f hifing he ciical eed i

change he beaing e. Since he beaing inalled in he m ee alead diffeen han he

iginal deign, i a decided change he beaing e back fm a ee dam a lain jnal

(leee) beaing. A dnamic anali a eied check if hi change ld affec he

eain f he m.

Thi hei eek deail and dcmen he hee maj ak emming fm he ed

beaing ich. Fi, a finie elemen anali a efmed ing a dnamic fae ackage

imlae he em ih bh beaing e, leee and ee dam. Ne, he em a

inmened and daa ee ecded ih he em eaing ih each beaing e. Finall, he

daa aken fm he indiidal n ee cmaed he edicin made ing he finie

elemen anali. Uing he mdel and he daa, a deeminain ill be made hehe kee he

leee beaing ich back he ee dam beaing. The inheen blem ha hi hei eek

ane i a fll: ill he change f beaing e fm ee dam leee el in a me

able beaing em?

1.3

Undeanding he dnamic f a beaing em i iman diagning and analing

blem ha ma aie hen eaing lage cale aing machine. Mdeling he em i

iman gain a cmehenin f h he ill defm ding ead ae nning cndiin

a ell a anien cndiin ch a a and h dn. Thi ibain ceaed b he aing


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5

machine ill need be minimied in de ene mechanical eliabili f he eimen. Thee

ae eeal iman iem ndeand ding a beaing em anali, inclding beaing

abili and efmance, ciical eed, and bi.

Vaing beaing deign ill imac he eall abili f he aing em and can inflence

ibain ih diffeen beaing iffne and daming cefficien alied he aing em. The

ha ecific naal feencie hich ae iman aid hen eaing he machine, a

hi can cae enance hich geal amlifie ibain. Thee ciical eed can be hifed

deending n he beaing iffne and daming. The bi, hing he ael f he

ceneline fm a fied lcain, can be meaed ene hee ae n mechanical fal ch a

mialignmen, beaing lbicain inabiliie ch a hil hi, an he iem f ne ha

cc ding eain f he em.

Pi efming an change a beaing em, i i deiable bild an analical

mdel ene ha he change n hif a ciical eed ad he em nning eed. Ohe

iman iem be inclded in he dnamic anali i a lk a he em behai an

nbalance, a inal anali ee if an inal naal feencie ei nea ha f he

eciing feenc (i.e. he elecical feenc f he m). Thi can be eceedingl difficl

efm b hand f ch a he m inclded in hi d, f ai ean inclding

he effec f he ce inding n he eel haf, nme haf ecin f aing diamee and

lengh, and hnkn iece ch a he inding eaining ing.

The e f a cme cde efm hi anali i a alable l. DRBeS, a fae

ackage deeled and ld b Rdn Vibain Anali, Inc. [6], i ed efm a beaing

anali ing a finie elemen baed cde efm he ak deailed abe. The and each

beaing e ae mdeled ing he DRBeS fae and he el ee analed deemine

hehe ceed ih he beaing change. Pided n maj ed flag ae een in he el, hen


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6

he ne beaing ill be machined and inalled in he machine. The mahemaical ndeinning f he

DRBeS fae and a lk a he el ill be decibed in Aendi I, Aendi II, and Chae 3,

eeciel, f hi hei.

Ding he afemenined m check, he em a inmened and a daa lgge

aed daa fm he n ih he ee dam beaing. Thi ame em a ed ecd daa

fm he check n ih he jnal beaing inalled. The be ee cnneced a Nainal

Inmen IOech dnamic ignal anale hich a cnneced a la. Nainal Inmen e

TOMAS (Tal Online Mniing and Anali Sfae) a ed ecd he daa and efm he

anali ding bh check. Afead, he daa ee cmaed he ediced el fm he

DRBeS imlain.

Wih he el in hand and he daa analed, he deeminain m be made hehe

ich fm ee dam leee beaing emanenl. If he ibain leel ae imed and he

em mdel mache he eeimenal el, hen he leee beaing ill be ke. If he ibain

leel ae imed b he mdel den mach he hical daa, hen he leee beaing ill be ke

and an ineigain in he eaknee f he mdel hld be decibed a ell a ed

imemen f fe ieain f he mdel. If he ibain leel aen imed b he mdel

edic an imemen, hen fhe ineigain i eied in eihe ible eaknee f he

mdel hehe hee i a enial hemal eniii blem ceaing he high ibain leel.


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7

2.0

2.1

Rdnamic a a field f d ha anned aimael 145 ea. In 1869, Rankine

blihed On he Cenifgal Fce f Raing Shaf [7], hich i belieed be he fi efeence

ibain in a aing em, and h he fi ae fll deed dnamic. Rankine hed

ha a a ceain angla elci, he fleible i ben, and hil and in hi ben fm.

Thi eed, defined b Rankine a he hiling eed b n knn a he ciical eed, inflenced

he deign f machine f man ea afead. Rankine belieed, incecl, ha abe hi eed

a cenifgal fce ld ecme he eing elaic fce f he , caing he hil

amlide becme nbnded. Thi edicin a de an incec eading f Rankine fee

bd diagam f he hiling , hich i deiced in Fige 3 [8].

F 3 F B D

Rankine ediced a cenifgal fce, he ma m mlilied b he ae f he angla

elci b he hil bi adi , hich ll he ad. Unfnael f Rankine and

machine deigne f he ea, hi fce de n acall ei. The ing fce k (hich i he iffne


24/136

8

f he beaing em) ac n he ma dce he cenieal acceleain, hich i he

angla elci aed mlilied b he bi adi. Becae Rankine ediced fce g

nbnded abe he ciical eed, he belieed ha i an allable n he abe hi

eed, ince hi fce ld eenall cae he fail.

The fla in hi anali a n acceed in a ideead manne f ie me ime. De Laal

and Pan indiidall deeled machine ha eaed ell abe hi ciical eed in he mid

1880. In hi a, he acice f dnamic fa eceeded he acceed he f ie me ime.

Dnkele blihed a ae in 1894 deailing he fac ha a haf ha mlile ciical eed,

celaing he naal feenc f he haf [9]. Dnkele al deeled a mehd f calclaing

he fi ciical eed. A Geman enginee, Ag Fl, hed j ne ea lae a lin

ha aeaed be alid f eed highe han he ciical (i.e. eciical) [10].

Deie hee finding, i an nil 1916 ha he engineeing cmmni began cnide

he ibili f deigning machine eae abe he fi ciical eed. Ke fnd eidence f a

ecnd ciical eed abe he fi, hich cld nl be eached b afel aing he fi [11]. Wih

he endeance f eidence iing again Rankine hhei, he Ral Scie f Lndn

cmmiined Hen Jeffc ele he dichm f Rankine aach and he eeimenal

finding f Ke and Fl. Jeffc blihed hi claic ae in ene hi cmmiin in 1919,

On he Laeal Vibain f Laded Shaf in he Neighbhd f a Whiling Seed [12].

2.2

Jeffc landmak ae eablihed ha a able eciical lin eied. Jeffc

deeled a mdel ha i feenl ed hi da decibe he baic aibe f a fleible

eaing abe he fi ciical eed. The Jeffc mdel deic an nbalanced dic lcaed n a

mmeic fleible haf, hn in Fige 4 [13].


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F 4

Becae he dik i mned in he cene f he haf, he fi fndamenal anlainal

and ainal min ae decled and can be led ing baic beam deflecin eain. Jeffc

al ed he mdel elain he effec f nbalance hen he angla elci i nea he naal

feenc f he . He hed ha ibain amlide inceae aidl in ha egin deending

n he amn f nbalance. Hi mdel inclded bh eical and hinal min f he , hich

heefe defined he bial min f he . The eain f min f he Jeffc R ae a

fll.

cos (2.1) sin (2.2)

Jeffc defined a daming fce, c, hich a inal he elci f he laeal min

f he haf. He al defined he eccenici, em, f he nbalanced ma fm he ma cene. The

hae angle f he nbalanced ma n he dik, , i defined hee b f he ingle nbalanced fce

f he iginal Jeffc ae can be e e ih l f geneali [14]. Fm hee


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eain, he ndamed naal feenc, ic daming fac, and damed naal feenc f

each diecin f he can be calclaed.

, , 1 (2.3) , , 1 (2.4)

An eciain ih a feenc ha align ih he em naal feenc ill ceae a

ae f enance. One f he m cmmn eciain fce i ha f a nbalance. When he

angla elci cincide ih he naal feenc, he nbalance ill ecie a

enance. Thi angla elci i knn a a ciical eed f he . Uing Jeffc eain f

min, he diffeenial eain hn in eain 2.1 and 2.2 can be led deic he

behai befe, ding, and afe eaching he fi ciical eed and fhe. Fm Jeffc mdel,

eeal iman el f dnamic behai ee hn. Fi, an inceae in daming el in

an inceae in he ciical eed f he . The daming i al enible f edcing ibain

amlide a he ciical eed. Secnd, a he angla elci i inceaed hgh he ciical eed,

he hae angle change. Thi can be ed edic he ciical eed. Finall, inead f he

inabili caing he amlide f ibain cnine inceaing a he ciical eed, he cene f

ma cme and inide f he hil bi, and he ae ab he cene f gai.

Fe anali ld bild ff f Jeffc mdel, fhe enhancing dnamic mdeling

caabiliie, and iding bee edicin f behai.

2.3

In 1924, Sdla [15] mmaied all f he dnamic deelmen ha in in hi

eminal k, . Sdla eened mehd f calclaing ciical eed f ih


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aiable c ecin and hed ha he eciical lin (i.e. abe he fi ciical eed)

ee abilied b cili acceleain. Sdla al a he fi inclde gcic mmen f

ha hae dik n hem ha bble, ch a fan blade m imelle. A SdlaGeen

, hn in Fige 5, i a ih an ehng dik like ha f a canilee beam and i fen ed

a a ime eamle f hee gcic effec.

F 5 G C

Mlile he ce f inabili ee fnd in he flling ea. Kimball [16] decibed

inenal daming, hich i a eciical inabili in bil beeen he indiidal

cmnen. Nekik and Tal [17] ee he fi indce he ibili f inabiliie

indced b he beaing ing he . A high eed, he il edge can becme nable

indcing il hil hich can lead il hi. Smih [18] hed fmla ha ediced hehld

in eed f e ciical inabili and hed ha he aied ih beaing iffne and ai f

inenal eenal daming. Eenal daming efe he daming fm he aina elemen f

he aing machine he , hile inenal daming i ha inegal he ielf, ch a he

maeial inenal diiain f mechanical eneg ficin fm bil n a [19].


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Wih all f hee adancemen, he anali f man aiain a made ible. Thi

ld n be neal engh flfill he need f ind. The dnamic behai f ga bine, high

eed cme, and man he ee ide f he mdeling caabiliie f a Jeffc mdified

Jeffc mdel. Fhe deelmen ee eied make dnamic anale cmmnlace.

Phl and Mklead in 1944/45 indeendenl deeled k hich led a mehd ha did j ha,

knn a he Tanfe Mai Mehd (TMM) [20,21]. Thi mehd mdel a fleible a a nmbe

(8


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cefficien nde ai lad chaaceiic. Nichla [3741] ed he finie elemen mehd le

f ee dam and iling ad beaing cefficien.

The finie elemen mehd i cenl he backbne f man cen dnamic cde.

DRBeS, he cde ed f he anali in he flling chae, e finie elemen mehd

efm beaing em anali. The cde all he e cmbine fleible haf, fleible

dik, fleible beaing, and fleible in a ingle mdel [13]. Ohe cde inclde ANSYS, XL

R, and VTFAST. In he een da, em cmbining FEM and lid mdeling echnie ae

cmbined ceae ne maj lage eaching mdel hich inclde c cling beeen

cling, fleible dik, fleible haf, fleible fndain, and fleible beaing.

Fm he 1970 nad, eeach f ai dnamic ie ha elded. Tebk

ien b me f he field eeache ch a Gne, [14], Vance [22], Ra [42], and Child [43]

ae inalable f eaching enginee ne he field ab efming dnamic anali.

Tbmachine lab a Tea A&M [44] and Viginia Tech [45] ae hing he field fhe b

eeaching magneic beaing and eemel high eed . Tea A&M h eal dnamic

mim ih ae ha ae ineigaing he cing edge f dnamic anali. The Ameican

Scie f Mechanical Enginee (ASME) Jnal f Rdnamic, Tbmachine, and Tiblg ae

hing he field fad ih ee blicain. The flling ill decibe mlile ae ien b

ai ah hich ed aiclal efl ding he ce f hi hei.

Allaie and Flack [46] decibed ai jnal beaing e and hei deign f aing

machine. Leade [47], and Zeidan and Hebage [48] al en in deh ih ai beaing deign

and beaing dnamic ih egad em. Ohe ae b He, Cld, and Bne [49] and San

Ande [50] ee al efl in egad beaing deign and mdeling. Kik [5153] e eeal

ae hich ee efl in ndeanding dnamic inabiliie. Mi [54] decibed eeal


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deign deficiencie in eiing eimen ing mden dnamic anali l. Gabeal [55]

hed ai alicain f diagning elecical machine ing ibain anali. Finall, Jdan

[56] gae a gd deciin f ha bi l h ha a eemel helfl in ineeing he daa

el hn in Chae 4.0.

Since he ime f Rankine, dnamic anali ha maed a a field f d. While a ime

acice aeaed ace he, he field i mae engh n ha m acical blem in

beaing em can be elained mdeled aiael ing he cec l and

echnie. The acice f efming a dnamic anali ha becme cmmn ha he

Ameican Pelem Inie ha ceaed a andad, API 684 [13], hich decibe he eied e

f an ne eiing machine anali. The beaing mdel ceaed in DRBeS f he e

f efming he dnamic anali i hn in he flling chae.


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3.0

3.1

The d f ficin, lbicain, and ea f ineacing face [57] ha been an iman

ne ince he beginning f he machine age. Wih a e ndeanding f he dnamic f beaing

eain, adance in aing machine ld n hae been ible. Pe beaing deign ene

eliable, able eain f all kind f machine. A ch, hi field ha een an inceaing amn f

d e he a cen, eling in mehd cmleel anale beaing eie ine in

lage cale beaing em ih mlile cmnen. The eie f ai beaing e,

ch a lain, ee dam, heelbe, flbe, and iling ad hae all been analed f ai

cnfigain.

Thi d cncen ielf ih ima beaing deign, he leee beaing and he ee

dam beaing. The leee beaing, hn in Fige 6 [50], iml cni f a lain beaing clinde f

adi Rbih he (jnal) f adi Rjaing ihin i ih a adial cleaance beeen he ,

hee hn a C. While he jnal i aing, a hin film f incmeible, Nenian lbican fill he

cleaance beeen he jnal and he beaing hell. Thi film hickne i deignaed h. The jnal

beaing cene i icall deignaed a Oband he jnal cene i Oj. The diffeence beeen he ,

e, i knn a he jnal eccenici. The jnal eccenici can change ih ime and deend n

he eenal fce n he beaing. The eccenici cann eceed he beaing cleaance, ele a

caahic faile ill cc. Finall, he aide angle, , i he angle beeen he lad (he eigh f

he he beaing i ing) and he line f cene, he line beeen he jnal cene and he

beaing cene [50].


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F 6 B

Pee dam beaing, al knn a e beaing, ae imila leee beaing ece he

hae a machined dam in he e half face f he beaing. A cecinal ie f he ee

dam beaing i hn in Fige 7 [40]. The e dce a ee ie a he dam hich ceae a

hddnamicall geneaed lad n he jnal [37]. The aificial lad inceae abili e ha f a

leee beaing. A cicmfeenial elief ack i machined in he bm half f he beaing a ell

ide fhe abili. Bh f hee k gehe indce a minimm eccenici in he beaing a

high eed l lad, hich ill be hn lae enhance he abili f he beaing.


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F 7 D B

F a gien eaing cndiin, ih jnal eed and lad W, he jnal ha a gien

eccenici and aide angle. A aic eilibim, he flid film eacin fce F and lad W ae

balanced. A =0 and a cnan lad, he jnal i a he bm f he beaing. A he eed

inceae, he jnal ie alng he jnal cene me alng he jnal eilibim lc ad

he beaing cene (e=0) a inceae infini. F cnan , he jnal i a he beaing cene

and me alng he lc nil i eache he bm f he beaing hen he lad eache infini. F

eaing ih lage ecceniciie, fll hddnamic lbicain i n eached and he film

hickne i e mall. F high and l W, he aide angle becme lage and he eccenici

mall. The angenial fce ceaed b he flid film nde hee cicmance can deabilie he

beaing em, knn a il hil and il hi.


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If he jnal and beaing ae cmleel eaaed b he lbicaing il, fll hddnamic

lbicain i bained. The lbican i dan in he hin cneging edge de he high hea

fce ceaed b he aing jnal. Thi ceae a ee ae hich i hn in Fige 8 [13].

F 8 H F B

The ee, P, bild all he lbican ecae he hin cleaance. The film ee

diibin and elci diibin ae gened b he cnini and hee dimeninal

mmenm eain. A heeical lin f an beaing eie a imlane lin f he f

eain. F a mma f he eain and hei lin ing he finie elemen mehd,

efeence Aendi I. The flling ecin ill een he el fm he leee beaing.


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3.2

Sleee beaing ae he m cmmn e f hddnamic beaing. A diced in Secin

3.1, leee beaing iml cni f a lain clinde in hich he in n a film f il hich i

ided hgh fced lbicain b il l hle in he beaing. Incmeible lbican fill he

ace beeen he beaing face and . F he VKF m, he lengh f he beaing ae eigh

inche, ih a diamee f een inche. The diameal cleaance f he beaing i 12 mil, 0.012

inche. Lking a he beaing aiall, he beaing i hn a in Fige 9.

F 9 B DB


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A dimeninal anali in DRBeS a efmed le f he eied iffne and

damne cefficien eied f he beaing mdel. The DRBeS in ceen i hn in

Fige 10. A hea balance anali a chen ih 70% f he hea geneaed b he inning

aken aa b he il. Thi effec he ici f he il, a highe emeae il i le ic. A hea

balance ih 7080% f he hea emed i ical f hee anale.

F 10 B DB D A

The lbican ed in hi d i Mbil DTE Hea Medim, an ISO ici gade 68 lbican

hich i cmmnl ed in lage indial eimen. The fced lbicain il em ide il a

100F he beaing, hi a chen a he inle emeae. The beaing lad i calclaed be


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half he eall ma f 15,200 lbm, hich ceae a fce f 15,200 lbf ha i ed b

beaing. Theefe, each beaing a lad f 7600 lbf.The lad angle i meaed

cicmfeeniall cne clckie fm he iie ai he negaie ai, hich i 270. Wih

hee in, he beaing mdel a analed fm 600 RPM 4000 RPM in incemen f 200 RPM,

hich ce he enie eainal an f he em, hich eae a 3600 RPM. F

eain beeen he incemen, a lineal inelaed ale i calclaed.

Afe nning he finie elemen anali, DRBeS een an file hich een he

beaing eaing chaaceiic a each eed incemen. Thi file i eened in Aendi V

f bh leee and ee dam beaing. The gahical eenain ill be hn in he flling

age. A he beaing cme eaing eed, he eccenici ll deceae a he

eilibim lc eache he cene f he lc, a Fige 11 and 12 h.

F 11 B E


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F 12 B E

A he beaing eed inceae, he eccenici f he beaing deceae and he eall film

hickne inceae, leading he make fl f il eied mainain he fll ee film i

inceaed. A he eaing eed f 3600 RPM, a make fl f 3.25 gm i eied. The eaing

emeae f he il eadil inceae a he jnal eed inceae. The eaing emeae

ange f he beaing i hn in Fige 13. The eeced eaing ange f he beaing a eaing

eed i and 160F.


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F 13 B

Maimm eaing emeae i and 205F. F hi alicain, keeing he beaing eaing

emeae le han 250F i deieable de he cending edcin in il ici. Thi

edcin in ici cendingl edce film hickne and can lead beaing damage.

Wih he gien ici, eccenici, and lad deailed a hn in i fige, he ee

file in he beaing can be deailed. DRBeS ffe indiidal deic he ee

file in he beaing, a dimeninal beaing ceneline ee file and a hee dimeninal

ee file hich deic he beaing a if he clindical beaing ee lled n a fla face.

The eecie ee file f he gien em a eaing eed f 3600 ae gien bel in

Fige 14 and 15.


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F 14 B C

F 15 B 3D


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Finall, he iffne and daming cefficien f each eed incemen i eened in Fige

16 f K, K, C, and Cand Fige 17 f K, K, C, and C. Thee cefficien ae eed he

DRBeS_R gam a a .bg file f e in he finie elemen anali f he beaing

em. See Aendi V f he cmlee file f he jnal beaing. A hn in Fige 17, he

c cled daming cefficien ae he ame. The ncled (al knn a diec) iffne and

daming cefficien a deending n he eed and d n aea fll an ecific end.

F 16 B , , C, C C


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F 17 B , , C, C C

3.3

Pee dam beaing, a diced in Secin 3.1, hae a machined e in he e half f

he beaing hich geneae a hddnamicall geneaed lad. Thi lad ceaed b he e, dam,

indce a minimm eccenici ha abile he , king een il hil and hi. The

ee dam beaing i geneall inended f beaing em ih eihe high eed l

lad. Thi effec i fhe enhanced b a cicmfeenial elief ack machined in he bm half f he

beaing hich deceae he face aea hich he lad i ead, inceaing he eaing eccenici

f he . The beaing i hn, ieing in he beaing aiall, in Fige 18.


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F 18 D B DB

A ih he leee beaing decibed in he ei ecin, he lengh f he ee dam

beaing eigh inche, ih a diamee f een inche. The diameal cleaance f he beaing i 12 mil,

0.012 inche. The dam i machined in he e half f he beaing a a deh f 0.07 inche 125

cicmfeeniall cneclckie fm he ceneline f he beaing. Machined ceneed a he aial

ceneline f he beaing, he idh f he dam i 4.75 inche. The elief ack machined n he bm

half f he beaing i ceneed a he aial ceneline f he beaing and i 1.75 inche ide. The deh f

he elief ack, like he dam, i 0.07 inche.

A dimeninal anali a efmed in DRBeS, efming a hea balance ih 70% f he

gien hea aken aa b he lbicaing il a in he leee beaing anali. The gien lbican a

al Mbil DTE Hea Medim and he ecified lad a 7600 lbf n he beaing. The em a


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mdeled fm 600 RPM 4000 RPM in incemen f 200 RPM. Fige 19 h he DRBeS in

ceen f he dimeninal anali ih he hea balance. The adanced feae bn i ed

define he idh/lengh f he ee dam and elief ack.

F 19 D B DB D A

Once again, he finie elemen anali a efmed and an file a ceaed b

DRBeS hich a hen eed a a .bg file f e ih he DRBeS_R gam. A a

eeced, he dam and elief ack fce cmbined een he jnal fm eaching a minimm

eccenici. The ee dam beaing eccenici ai a eaing eed i 0.62 cmaed 0.25 f

he jnal beaing, a hn in Fige 20 and fhe eemlified b he jnal eilibim lc


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hn in Fige 21, hich i mch fhe aa fm he beaing ceneline han he leee beaing

jnal eilibim lc hn in Fige 12.

F 20 D B E

Since he ee dam inceae he eccenici f he beaing, a geae il fl i eied

make f ha hich leak he ide mainain fll hddnamic lbicain. The ee dam

beaing eie 6.5 gm f il a he eaing eed f 3600 RPM, hich i dble he amn f he

leee beaing. Similal, he inceae in film hickne fm he inceaed eccenici ai f he

beaing lead il emeae hich ae le han ha een in he jnal beaing. The eaing

emeae in Fige 22 a 3600 RPM i le han 140F. Al, he maimm emeae i le han

200F. The le il emeae lead highe ici il, iding a iffe beaing.


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F 21 D B E

The elief ack in he bm f he beaing edce he eall face aea e hich he

lad can be ead. Thi ceae mch highe ee in he le half f he beaing. Inead f a

maimm ee f 258.3 i, he ediced maimm ee in he ee dam beaing i 591.4

i, a hn in Fige 24. The dam acing n f he beaing al ceae a ee fce in he

e half f he beaing ha i n een in he leee beaing. Thi effec i hn in he

dimeninal ee file f he afemenined Fige 23 and heedimeninall in Fige 24.


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F 22 D B

F 23 D B C


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F 24 D B 3D

The gien iffne and daming cefficien f each eed incemen i eened in Fige 25

f K, K, C, and Cand Fige 26 f K, K, C, and C. A ih he leee beaing, hee

cefficien ae eed he DRBeS_R gam a a .bg file f e in he finie elemen

anali f he beaing em. See Aendi V f he cmlee file f he ee dam

beaing, a ell a he leee beaing.

Fm Fige 25 and 26, i can be een ha he ncled (diec) iffne and daming

cefficien f he ee dam beaing ae in he ame de f magnide a he leee beaing.

The ccled iffne cefficien ae cnideabl diffeen f he ee dam beaing. The

ccled daming cefficien a le eed ae f a imila de f magnide f each beaing

e, b a he eed inceae he leee beaing c cled daming cefficien deceae. The

iffne cefficien Ki al cnideabl diffeen f each beaing.


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F 25 D B , , C, C C

F 26 D B , , C, C C


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Wih he finie elemen anali efmed f each beaing, he beaing efmance

cefficien in em f daming and iffne can be eed he DRBeS beaing fae

f he cmlee beaing em efmance. The ne hee ecin f hi chae ill decibe

he mdel ih he indiidal beaing el. Secin 3.4 ill een he mdel. Secin 3.5

and 3.6 ill een he el f he beaing em imlain.

3.4

If beginning a aing em deign and anali fm cach, hen i i ial cnide he

aing eimen fi and hen ie he beaing cendingl. F he blem a hand, becae

he beaing lad, aing eed, and beaing ie ee knn, he beaing cefficien cld be

calclaed fi and hen imlemened in he eall em deign. Thi ecin ill een he e

mdeling he ih he beaing and efming he laeal dnamic anali. Thi anali

ill edic he lcain f he ai ciical eed and deemine he amn f ibain eeced in

he beaing em ih each beaing e. Laeal dnamic anale ide he e ih

infmain n ciical eed, mde hae, fced ene, and beaing abili. Becae

DRBeS e finie elemen, a finie elemen aach he beaing anali ill be

eened.

R em cni f hee ima cmnen: he aing aemblie, nnaing

fleible , and male inecnnecin cmnen ch a beaing ha ide ineacing

fce beeen cmnen. Finie elemen ain ae nmbeed cneciel fm lef igh n

he haf, a hn in Fige 27. Each elemen can cni f eeal belemen, alling f

geemeic dicniniie. While each ain can cni f mlile belemen, an beaing

eal m be lcaed a he finie elemen ain. The degee f feedm f he finie elemen ain

ae cnideed mae degee f feedm.


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F 27 B F E A 36

When he eain f min f he ae aembled, hee ae ke hile he degee f

feedm f he inenal belemen ae cndened i he aembl ce [14]. Once he

dilacemen a he mae ain hae been fnd,hen he dilacemen f he belemen can

be calclaed. Pe he API andad [13], mainaining a lenghdiamee ai f le han 1.0 and

geae han 0.1 i efeed f each elemen f cmainal accac, ih an L/D f 0.5 efeed

f hee anale.

Each elemen i hmgen, ih diibed ma and elaici. The laeal min f he

elemen i decibed b anlainal and ainal dilacemen, , , , and . Each

dilacemen i a fncin f aial cdinae, , and ime, . The finie elemen anali h edce

he gening aial diffeenial eain ih infinie degee f feedm dina diffeenial


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eain ih dicee, finie degee f feedm. Each elemen can be eeed b eigh endin

dilacemen b ecifing a aial hae fncin hn b,

,,,, (3.1)hee

, , , , , , (3.2)The ima ce f hee eain i he k f Chen and Gne [14], a he hae eened he

mahemaical backgnd f he DRBeS gam. In hi inance, i he imedeenden end

in dilacemen ec. The hae fncin maice, and , ae eablihed b beam elaici

he. F fhe elanain and lin f hee eain, efeence Aendi III.

Uing hi backgnd, he DRBeS mdel a bil hich alled he ai beaing

e be imlemened. Uing manfacing daing, he a cneed in finie

elemen ain and imlemened in in he DRBeS gam. The finalied mdel cni f

32 elemen ceing he enie lengh f he . Dik ee added he imlae he

cling, cling fan, ceneing ing, and eaining ing. Beaing ee lcaed a he each eiie

ain n he . The elan finie elemen mdel i hn in Fige 28.

The eling mdel lengh i ihin ne handh f an inch f he acal meaed

lengh f he . The eigh a mached he meaed eigh f he l he gien

eigh f he cling. In de accmlih hi, eel deni, mdl f elaici,and hea

mdl ee ed f each ain eie ece he m ce ain cnaining he ce

inding and end inding. F hee ain, an eialen deni a ed mach he eigh f


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37

he cnaining he inding. F hee ain, he iffne f he inding ee cnideed

neglible, a e API cde 684, Secin 2.8.2. [13]. Theefe, cabn eel eie f mdl f

elaici and hea mdl ee ed f he m ce. F cabn eel, he mdl f elaici i

2.9107i hile he hea mdl i 1.1154107i. The deni f eel, 0.283 lbm/in3, a ed f

he iece hn in ble in Fige 28. The eialen deni, 0.17 lbm/in 3, a ed f he m

ce deiced in geen in Fige 28.

F 28 DB

Pe he API andad [13], he lengh diamee ai f each finie elemen a ened be

le han 1.0 and geae han 0.1 ene he mdel cnain fficien elin f calclaing

eie ch a ciical eed hile al eening nmeical e ha can cc beeen

adjacen elemen ih lage lengh diffeenial. A 2.5 diamee be hgh he a inclded,

hich a iginall ed f eice inecin f he fging ding cncin. Seen

indiidal dik ee ed in he mdeling f he . A he end, he cling dik ee

mdeled ing cling manface daing. Each end half he eigh f he cling

aembl. The mmen f ineia ee aken fm he daing.

Vieing he in Fige 28 fm lef igh, he dik cnaining he cling fan, ceneing

ing, and eaining ing ae lcaed he lef and igh f he m ce. Each dik a ied ing


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38

manface daing and lmed mae/ineia ee added hee ain. An ndamed

ciical eed anali a efmed deemine h nea he a he eecie ciical

eed deending n aing beaing iffne. Fige 29 h he ciical eed ma f he . Each

line eeen anhe naal feenc f he deending n he beaing feenc. The ble

line eeen he eainal eed f he , 3600 RPM.

F 29 C

Refeencing he beaing iffnee fm Fige 16 and 25, fm he ma he hld a

hgh a lea ne ciical eed hile nning eainal eed. The ecnd ciical eed

aea be eemel cle eainal eed f beaing ih a iffne ange f 106 107, a


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bh f he beaing mdel indicae. Thi ciical eed ma indicae ha edcing he beaing iffne

ill le he ecnd ciical bel eainal eed, b he hid ciical eed ld hif ad

he eainal eed a ha in. Since hee el ae incnclie, he anale ee efmed

ih he indiidal beaing mdel. The beaing cefficien ee imed fm he beaing

efmance fae f DRBeS he anali fae. Uing he ee dam beaing

eie, ai imlain f he beaing dnamic behai ee efmed, a een in he

flling ecin.

3.5

Uing he beaing cefficien deemined in Secin 3.3, eeal dnamic anale ee

efmed inclding ciical eed anale, abili anale, and ead ae ene anale. The

ciical eed ee analed deemine he eneg diibin f each mde hae, alling f an

eimain f hich a f he i he edminan ne in inflencing ha ciical eed (

naal feenc). F he fi bending mde, ing an aeaged beaing iffne he calclaed ciical

eed cc a 1547 RPM, a een in Fige 30, 31, and 32. Fige 31 and 32 h he enial and

kineic eneg diibin f hi mde hae.

Becae he enial eneg f he mde hae i e 70% haf eneg, he mde i

cnideed a fleible mde [14], a een in Fige 31. Fm Fige 32, he T eneg eeen

he kineic eneg fm ma anlainal min. R eneg eeen he kineic eneg de

a ineia. G eneg eeen he kineic eneg de gcic mmen. A a he cae ih

he enial eneg, he kineic eneg i dminaed b he haf eneg, a 69.41% f he eall

em kineic eneg i fm he haf.


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F 30 D B . 1

F 31 D B . 1 E D


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F 32 D B . 1 E D

The ne ciical eed aea a 3708 RPM, j 100 RPM and j e 3% aa fm he

eainal eed f 3600 RPM, a hn in Fige 33. Ticall, m deign eae e 10% aa

fm he ciical eed, hi mde ma infinge n he eain f he m. Thi mde i

cnideed he ecnd bending mde. A can be een in Fige 34 and 35, hi mde i a fleible

mde ha i dminaed b he haf eneg and he cling lcaed n he igh end f he haf a

hn in Fige 28. A can be een b he OeallG f Fige 35, he gcic kineic eneg (G) i

negaie. Thi limael el in he gcic effec aiing he naal feenc f he , i.e.

inceaing he ciical eed f he . Ineial (R) eneg a een in Fige 35, can le he ciical

eed [14]. The cling cnibe he geae ecenage f ineial and gcic eneg, ih he

gcic eneg haing a lage ecenage f he kineic eneg han he ineial effec.


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F 33 D B . 2

F 34 D B . 2 E D


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F 35 D B . 2 E D

The ne ciical eed cc a 4914 RPM and 7269 RPM, ell abe he eainal

eed. Thee mde ill n be cnideed. A hil eed and abili anali a an f he

beaing mdel fm a eed f 600 RPM 5000 RPM. A can be een in Fige 36, he

eeience mlile naal feencie a i cme eed. Fnael, man f hee

feencie d n effec he eain f he and ae he el f backad eceinal min

ae ignificanl damed and neal ndeecable, a ill be een.


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F 36 D B

Backad eceinal min i min in he eee diecin f haf ain. In m

dnamic anale, nl he fad eceinal mde ae cnideed f enial nchn

eciain [61]. Thee fad eciain ae ceaed b he nbalance fce hich cnain a ec in

he diecin f he ain. While die hae ineigaed he eciain f backad mde, hi

d ill iml ake in accn he mde edminaed b fad eceinal min.


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Anhe iece in deemining hich mde hae ae l iman i he lg decemen

calclain. The lg decemen, hn in Eain 3.3, e he calclaed daming f he mde

ide an indicain f hehe he mde i able.

(3.3)If hi lg decemen i geae han 0, hen he mde i able. Mde ih lg decemen ale hich

ae mch geae han 0 ma n be een hen he i eaing, a he ae fll damed. An lg

decemen ale abe ni can be cnideed ell damed. Vale f he lg decemen ha ae

cle 0 le han 0 ae neall able and nable, eeciel. Fige 37 deic he fi i

mde f he .

While hee i naal feencie ill be aed a he cme eainal eed, nl

ae eeced be ecied ch ha eain f he i affeced. The fi mde,

ccing a 1491 RPM, i he eeced fi ciical eed. Thi mde i edminanl fad

eceinal min dminaed, a 93% fad and 6% backad. An nbalance ill be ecied

b hi naal feenc, and becae he lg decemen i eal 0.0154, hich i eemel l,

hi ciical eed i n ell damed. Mde2 i n eeced be imacfl becae i i imail a

backad eceinal mde. Mde 3 i highl damed, ih a lg decemen ale f 5.8814, i

hld n imac eain. Mde 4 i al imail a backad eceinal mde and i n

eeced be an ie.

While hee i naal feencie ill be aed a he cme eainal eed, nl

ae eeced be ecied ch ha eain f he i affeced. The fi mde,

ccing a 1491 RPM, i he eeced fi ciical eed. Thi mde i edminanl fad

eceinal min dminaed, a 93% fad and 6% backad. An nbalance ill be ecied


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46

b hi naal feenc, and becae he lg decemen i eal 0.0154, hich i eemel l,

hi ciical eed i n ell damed. Mde 2 i n eeced be imacfl becae i i imail a

backad eceinal mde. Mde 3 i highl damed, ih a lg decemen ale f 5.8814, i

hld n imac eain. Mde 4 i al imail a backad eceinal mde and i n

eeced be an ie.

F 37 D B

The ne mde, 5 and 6, ae able fad eceinal mde. Thee mde cc a

3664 and 3755 RPM, eeciel, and cnain lg decemen ale f 1.7197 and 0.2121. Thee

calclaed ale lead he belief ha a 2ndciical eed hld cc mehee abe 3600 RPM


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j abe he eainal eed f he . Thi i cle engh he eed ha hee naal

feencie ma amlif ibain a eainal eed. Becae mde 6 i le damed, hi

mde ha he m imac n he eain. In de d hi imac, an nbalance ene

anali a efmed f mde 1 and mde 6.

Uing he API cede a laid in API RP 684 SP6.8.2 [13], nbalance ee laced a he

lcain hich eacebaed he mde effec and ided maimm dilacemen, a aken fm SP3

fm he API andad and edced in Fige 38. F Mde 1, 70.2 in f nbalance a laced a

Sain 18 a hn in Fige 28. The linea ead ae ene f he nbalance a n 125%

eainal eed, 4600 RPM. The effec ee hen led n Bde l hich imlae he

beaing imi be lcain eading. The eling Bde l i hn in Fige 40 f Mde N. 1.

Thi Bde l indicae a fi ciical beeen 14001600 RPM and a ecnd ciical beeen 3600

4000 RPM. Uing he ceced amlide ale hn in SP6.8.2.11 f API 684 [13], he amlide f

he ibain d n aea eceed he 12 mil f cleaance in he beaing. Hee, eain f

he aea be infinging n he ecnd ciical hich can lead nedicable ene.

Calclaing he nbalance ene f Mde 6 ill hel ge an idea f he effec f nning nea he

ecnd ciical eed, a ill be een in Fige 41.

F 38 A 684


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F amlifing Mde 6, nbalance f 35.08 in ee added Sain 13 and 24, 180 aa.

Fm Fige 41, adding nbalance a he lcain deiced in Fige 38 inceaed he ibain

amlide f he ecnd ciical 5.9 mil ibain a he EN ibain be. Thi effec h

ha an nbalance in he end inding/cling fan lcain f he can inceae he amlide f

he ibain cnideabl. Since he eainal eed i infinging n hi ecnd ciical

eed, balance f he a he ceneing ing lane i iman in ening mh eain.

Pleae ne ha n he gien Bde l hn in Fige 40 and 41, he lcain f he ibain

meaemen ae gien b he e nh (WN), e h (WS), ea nh (EN), and ea h (ES)

imi be lcaed a he beaing. The e beaing i lcaed n he lef f Fige 28 a Sain

5. The ea beaing i lcaed n he igh f Fige 28 a Sain 29. Pleae ne ha he nh imi

be, WN and EN, ae lcaed 45 fm he Xai f he beaing hn in Fige 39. The h

imi be, WS and ES, ae lcaed 135 fm he beaing Xai a hn in Fige 39.

F 39 19


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F 40 D . 1 B


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F 41 D . 6 B


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Wih he eain f he ih ee dam beaing mdeled, he ne e i mdel

he ih he leee beaing. Onl ne leee beaing ae a aailable inall in he machine,

he lcain f he highe ibain amlide a ed deemine hee he beaing a lace.

The ea beaing a changed in DRBeS a leee beaing deemine he inflence f iching

hi beaing deemine if hi ill hel ibain. Secin 3.6 ill ineigae hi eain ih

Chae 4 hing he acal n daa fm hi ich in beaing e.

3.6

Simila dnamic anale ee efmed in ineigaing he behai f he ih

he leee beaing inalled in he ea beaing. The fi ineigain a an ineigain in he

ai mde f he . Fige 42, 43, and 44 h he fi mde and i cending enial

and kineic eneg diibin. Thi mde can be een be a fleible mde. The mde cc a

1565 RPM, lighl highe han he 1547 RPM f he ih ee dam beaing. The ne

ciical eed, hn in Fige 45, 46, and 47, h ha he ediced ecnd ciical eed ih he

leee beaing i cle he eainal eed f 3600 RPM a 3641 RPM han he ee dam

ecnd ciical eed f 3708 RPM.

F 42 B . 1


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F 43 B . 1 E D

F 44 B . 1 E D


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F 45 B . 2

F 46 B . 2 E D


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F 47 B . 2 E D

F mde 2, he mde i a fleible mde ih an inceaed enial eneg diibin in

he beaing hich a changed a Sain 29. The haf inflence i le han ha een in he iginal

ee dam mdel. Al, he inflence f he cling a ain 2 and ain 32 i mch le

han he iginal mdel, ih a cending ie in he effec f he mdeled dik nea he inding

n he (cling fan, eaining ing, ceneing ing). I i heied ha hi i a el f he leee

beaing being le iff han he ee dam beaing, eling in geae ma anlainal eneg (T)

f he haf and he dik beeen he beaing ain.

Ne, a hil eed and abili anali a efmed f eed beeen 600 and 5000 RPM.

The hil eed ma h he ai naal feencie ha he ae a i cme

eaing eed. A ih he dicin in Secin 3.5, n ee naal feenc i iman elaie


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m eain. A lk a he indiidal mde hae and hei eecie eceinal min and

lg decemen/daming ale ill deemine hich ne ae eeced eie an nbalance

ene anali. Fige 48 h he hil eed ma f he leee beaing em.

F 48 B

A ediced b he ciical eed anali, he ae hgh eeal naal feencie

a i cme eed ding a a h dn. T mde f aicla inee ae he ne

and he eainal eed f 3600 RPM. The mde hae hn in Fige 49 deemine hich

ne ae ging inflence he behai.


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F 49 B

A ih he ee dam mde, Mde N. 1 and Mde N. 6 ae he mde hae eiing

fhe anali. Unlike he ei anali in Secin 3.5, he fi mde hae indicae an nable

mde ih a negaie lg decemen f 0.1193. Thi mean ha he ibain amlide ma g

aidl nle he ae hgh he fi ciical eed ickl. Mde N. 1 i eeced be een

a 1493 RPM, e cle he ee dam naal feenc ccing a 1491 RPM, and i he

belieed fi ciical mde f he . Mde N. 2 and N. 5 ae edminanl a backad

eceinal mde, hile Mde N. 3 and N. 4 ae highl damed.

Mde N. 6, ccing a 3762 RPM, i he eeced ecnd ciical eed. Wih a lg decemen

f 0.1122, he mde i lighl damed and i a able fad eceinal min mde. Thi ciical

eed i lighl highe han he ee dam mde N. 6 eed f 3755 RPM. The nbalance ene

e f bh mde ill deemine he linea ead nchn ene. Fige 50 and 51 h he

eling Bde l f he ead nchn ene f Mde N. 1 and Mde N. 6.


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F Mde N. 1, 70.2 in f nbalance a added Sain 18 f he mdel hn in Fige

28. Fm he Bde l in Fige 50, changing he ea ee dam beaing a leee beaing el

in a deceae f he ibain amlide n he ea beaing hen aing hgh he ciical eed a

and 1600 RPM and 3800 RPM. While he ciical eed cc a he ame eed, he ea beaing

damen he amlide f he ibain. Mde N. 6 a died b aling 35.08 in f nbalance

Sain 13 and 24, 180 aa a deailed in API 684 [13]. Fm he Bde l in Fige 51, he

nbalance fce ecie he ecnd ciical eed ibain amlide.

The ea beaing; hee, h ha he leee beaing ha damed he ibain n he ea

ide b edcing he ibain amlide deeced in he ea nh ibain be b half.

Unfnael, fm he l he ibain amlide in he e ha been geal eacebaed ih a

maimm amlide f 7.5 mil . Rnning he ih ibain amlide aaching 7.5 mil

ld geal edce he eeced lifean f he . The daa fm he beaing change hed

mie in iming he ibain leel f he , alhgh nning nea he ecnd ciical eed

ill lead nedicable efmance. Fm hi daa, he beaing change a aed, and hile he

ciical eed ma n change damaicall he ibain leel hld ee me imemen. The

flling chae, Chae 4.0, deail he el f he m check n, befe and afe he

beaing change.


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F 50 B . 1 B


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F 51 B . 6 B


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4.0

4.1

The VKF m ae 18,500 h m ha ae a 3600 RPM. Each ha a ma f

aimael 15,200 lbm and i ed b 7 inch diamee b 8 inche lengh beaing. The

i 203 inche lng and 165.5 inche fm he e beaing ceneline he ea beaing

ceneline. A he beaing, laeal haf min i meaed ing Benle Neada 3300 eie imi

be hich ae inalled a he 45 and 135 angle cne clckie fm he hinal lane,

eeciel, a hn in Fige 39 f he ei chae. The beaing hing li a he beaing

ceneline een inalling he imi be a he beaing ceneline, he imi be ae

aed 45 aa fm e hinal and eical.Each imi be ide ibain amlide

meaemen nceain ihin 1 mil (0.001 inch). Shaf eed i ided b a Keha be,

hich i ed mni a kea n he haf ha ide a nce e n indicain. The imi

be cmbined ih he Keha ide laeal ibain meaemen a ell a he ibain

ignal hae.

F hi e, he ibain ignal ee en a Nainal Inmen IOech 600 Seie USB

Digial Signal Anale. The digial ignal anale a cnneced a la ih Nainal Inmen

eZTOMAS fae (Tal Online Mniing and Anali Sfae) inalled. The eZTOMAS

fae ake he ignal fm each IOech channel and ide gammable file f each ignal

a ell a ime, ecm, bi, aefall, Bde, la, end, and haf ceneline anali caabiliie

[59]. Rel ided in Secin 5.0 f hi hei ae aken fm eZTOMAS fae.

Beaing ee machined a he AEDC Mdel Sh e aed daing. Beaing ee

meaed ene gien leance ee me. A Re mechanical gea m ided il he


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beaing. Oil fl he beaing a cnlled b a needle ale. Tbine flmee meaed lbe

il fl he beaing and ided a check ha e lbe il fl a geing bh beaing f

each beaing e. Oeain f he m a handled b a PLC baed cnl em. The fi f he

m check n i ceed in he flling ecin.

4.2

Afe he m efbihmen jec end he and a, check ee efmed

ene e beaing eain. Uing he eiing ee dam beaing, ibain

meaemen ee aken deemine he lcain f ciical eed and em efmance a

eaing eed. Daa ee lgged n a la laded ih eZTOMAS fae and fll Bde l,

ecm l, aefall l, and he ee ke f fhe anali. Thi ecin ill een he

el fm hi n a ell a he anali f he fi n. A ill be een, he ibain leel ae

mch highe han ne ld eec fm a fehl end hich ha ndegne balancing in a

high eed balancing i i being inalled in he VKF lan.

Fm he Bde l hn in Fige 52, i can be een ha he fi ciical eed i lcaed a

aimael 1633 RPM, 27.5 H. The mdel ediced a fi ciical a 1565 RPM, hich i a

diffeence f 2% elaie he eainal eed. Pleae ne ha he hae angle meaemen

i cnained 0 360, hen he angle hif abe 360 i a and 0 a hn nea he

ciical eed. Pe he API cde [13], hi ciical eed ha a calclaed amlificain fac f 5.41 ih

a eaain magin f 1967 RPM aa fm he eaing eed f 3600 RPM. A hi amlificain

fac and nning bel eainal eed, he eied eaain magin i 12.65% f he eaing

eed, 455 RPM. Theefe, hee i fficien eaain fm hi ciical eed he eaing

eed e API eiemen deailed in SP6.8 f API RP 684. The ecm l f he fi ciical can be

een in Fige 53.


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F 52 C B


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F 53 C 1C

A can be een in Fige 52, a he m cme eaing eed, he ibain amlide

ll begin climb, hich i m nnced in he ea beaing be, eenall eaking a 4.6

mil eakeak (). A a hn in Chae 3, he mdel ediced ha he eain a

infinging n he ecnd ciical eed. One f he ima mehd f eifing a ciical eed i

lking a he hamnic ibain eca, al knn a he 2X and 3X ibain eca. Eciain f

he 2X feenc ibain eca i ccing in Fige 54. Fige 54 i he aefall l f he

beaing em a he 1X ( ne ime he RPM) eca ae hgh he fi ciical. A aefall l

h he feenc f he ibain in he n he ai and he amlide in mil n he ai.

The feenc in he (H) can be calclaed b mliling he eed f he mliled b 1/60.

The ai hn i ime, he aefall l h he 1X (eaing eed) ibain ignae a he

cme eed and he ai hamnic (2X, 3X, ec.) ibain eca.


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Fm he Bde l in Fige 52, he ibain inceae hgh he fi ciical and deceae

a he ae hgh he fi ciical e he eed ange f aimael 1400 RPM2000

RPM. A aimael 30 H, 1800 RPM, he 2X ibain ngl inceae. Thi indicae ha a

ime he eaing eed f 1800 RPM, a naal feenc cc hich ecie he . Thi

eciain cc nil aimael 2100 RPM, a hn in Fige 55, befe he ibain leel

deceae and he eciain ceae.

Thi indicae hee i a ciical eed ccing mehee in he ange f 3600 RPM4200

RPM. While he aefall fige ae iml nah in ime f a anien een, he daa aea

mach he edicin cming fm he mdel ing he ee dam beaing. A he cme

eainal eed, he ibain leel inceae a he cme n he ecnd ciical eed.

Thi eciain i een in he ecm and aefall l f Fige 56 and 57, eeciel.

F 54 C C E


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F 55 C 2 H 2100 E

F 56 C


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F 57 C E

Once he check a efmed and he m efmance checked a ai lad, he m

anien fm he h dn ee al analed. The Bde l f he n dn f he m

check i eened in Fige 58. A can be een, fm he ca dn anien he fi ciical

aea in he fm f a li ciical eed beeen he eed f 1486 and 1338 RPM. Sli ciical ae

cmmn in genea de he inheen cncin. Thee li ciical ae he el

f diffeing hinal and eical iffnee in he . De he inding in he le genea

ce, he iffne f he i diffeen in he incial diecin [42]. While hi effec a n

inclded in he mdel, he effec f diimila iffnee can be een in he daa.


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F 58 C C D B


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Fm Fige 58, i i een ha he ibain amlide ding he check had ceeed

ad 7 mil. Eeced eain f a nel ld hld be le han ne mil. A he

caed dn fm eaing eed, he hamnic 2X feenc i ecied a hn in Fige 59, he

aefall l a he 1X feenc f 30 H (1800 RPM) . The ciical eed ill cc in he egin f

3600 RPM4200 RPM, hich a he ame a ing he n daa. Thi fheed eclain ha he

a nning nea he ecnd ciical, ha hee a me he nknn ccing ch a a

hemal eniii ie. Becae f hee finding, he ed eeimen hif he ciical eed

b iching leee beaing a aed and hee finding ill be eened in Secin 4.3.

F 59 C C 1800 E

4.3

Afe he el f he fi check ih he ee dam beaing, a al a made

ich leee beaing, hee ee he iginal em deign. Thi al a an aem

ide main daa in. Fi, he beaing ld ide a baeline bild a cae f ing he


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ee dam beaing if he ee in fac necea, a ecd f he eaning behind he hif

ee dam beaing n he m ee naailable. Al, i a belieed ha a leee beaing bil

mee iginal ecificain cld hif he ciical eed aa fm nning eed. Becae hee a

nl ne ae beaing hell aailable, i a deemined change he ea beaing fi, a ha beaing

hed he highe ibain amlide in he ee dam beaing check. The beaing cleaance

f he ne beaing a machined he ame a he ee dam beaing, 0.012 inche diameal

cleaance. The el fm hi aicla m beaing check ae eened in he flling age.

Fi be eened fm he leee beaing check i he em a. In Fige 60, he

Bde l h ha he fi ciical eed i lcaed a aimael 1680 RPM, 28 H, lighl

highe han 1633 RPM ee dam beaing ciical. The ciical eed ha a calclaed amlificain

fac f 5.79 ih a eaain magin f 1920 RPM aa fm he eaing eed f 3600 RPM. A

hi amlificain fac and nning bel eainal eed, he eied eaain magin i 13.04%

f he eaing eed, 469 RPM. Theefe, hee i fficien eaain fm hi ciical eed

he eaing eed e API eiemen deailed in SP6.8 f API RP 684.

Fige 61 and 62 een he ecm and aefall l fm he fi ciical eed. Fm he

Bde l in Fige 60, he ciical eed amlide n he ea beaing ae cnideabl me

damed, a ibain amlide ha aached 5 mil a he fi ciical eed ih he ee

dam beaing did n eceed 1 mil. The e beaing ibain amlide fm each be ae ihin

half a mil f each he fm he ee dam check. The ea imi be ee eading le

han he ee dam beaing a he ciical, b cmaing Fige 52 and 60 . Fm he Bde l, he

leee beaing ha had he iie effec f edcing he ibain amlide in he ea beaing.


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F 60 B C B


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F 61 B C F C

F 62 B C C


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Fige 62 deic he aefall l f he e h imi be, hich had he highe

amlide ding he m check. The 2X eca a ecied a he ae hgh he 1800

2100 RPM eed ange, hich al indicae a ecnd ciical eed in he ame lcain a ih he

ee dam beaing n beeen 36004200 RPM. The maimm eciain cc a and 3600

RPM, igh a he eaing eed f he machine. A eaing eed; hee, he maimm

amlide f he ibain i cnideabl le, a he beaing change damened he ibain.

The amlide f he ea ibain be ee and 1 mil a he ciical eed, hich a a

edcin in e 3 mil ibain amlide in each beaing be.

A eaing eed, he effec a een me nnced. Fm he Bde l, Fige 60, he

highe amlide ibain a een a he e h ibain be and eached le han 3 mil

eakeak. Fige 63 and 64 een he ecm l and aefall l a eaing eed. The

aefall l cnfim he edced ibain amlide a nning eed.

F 63 B C


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The efmance f he beaing em ding cadn a al ineigaed ding

he jnal beaing check. Bde l, ecm l, and aefall l ee ceaed fm hi

daa and ae hn in Fige 65, 66, 67, and 68. Thee l h ha he ea ibain ale e

he ce f he check had begn dif ad befe finall eling a 2.8 mil . The e

h ibain be amlide had deceaed, fm alm 3 mil 2.2 mil . Vibain

amlide hifing a he am ding he em check can be indicain f hemal

eniii [5] ha a he ce inding am , he eall iffne f he deceae hich

cld hif he cle he ecnd ciical eed.

F 64 B C

The ecm l and aefall l, Fige 66, 67, and 68, h he ca dn ibain a

he eaing eed f 3600 RPM. I de n aea ha he ciical eed ha been hifed aa fm

eainal eed b he ich fm ee dam leee beaing. A in he ee dam beaing


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check and he leee beaing n, he 2X hamnic i ecied a he ca dn hgh

he fi ciical eed in he ange f 16002000 RPM. Thi eciain i hn b Fige 67. The

eciain f hi hamnic eca in a neab ecnd ciical eed cle he eainal

eed f he . While each f he f be hed he 2X hamnic eciain, he e h

(WS) be a chen f Fige 67 a he highe ibain amlide ided he be indicain f

he hamnic eciain hich a ccing. The eciaed 2X eca acall indicae ha he change

in beaing e acall hifed he ciical eed cle eainal eed; hee, he ibain

amlide ae le a he ciical.

Afe he eeimen i efmed, he daa iml ha hee i a ecnd ciical eed nea he

eainal eed f he , a did he beaing mdel el hn in Chae 3.0. Chae 5.0

ill finalie hee cnclin and cmae he el fm he mdel efmed in DRBeS.

Fm he efmance check, he deeminain a made ick ih he jnal beaing

nil a bee alenaie cld be fnd. The ibain amlide ee le ac he bad afe

inalling he leee beaing in he ea beaing edeal. A ae beaing hell ill be babbied and

machined inall a leee beaing in he e beaing edeal and fe check ill cnfim he

beaing em eain ih leee beaing.


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F 65 B C C B


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F 66 B C C 3600

F 67 B C C 3600 E


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F 68 B C C 3600

F 69 B C F C 1800


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5.0

5.1

Fm he el hn in Chae 3.0 and Chae 4.0, bh mdel edic he fi ciical

eed cc beeen 15001700 RPM. A he eeimenal daa i nl aken 3600 RPM, he

eac lcain f he ecnd ciical eed i nknn, b fm he mdel an eimae f and 3700

3800 RPM i be eeced. Daa hing he eciain f he 2X ibain eca ld indicae a

ciical eed in he ange f 38004200 RPM, hee. The ich fm a ee dam leee

beaing in he ea beaing lcain did n geal affec he lcain f hee naal feencie. The

hamnic enance indicaed b he ibain eca d eem cnfim he mdel edicin f a

ecnd ciical eed nea he m eainal eed.

While he ibain amlide hn in he mdel diffe han ha aken in he field, ha i

becae he acal nbalance and nbalance lcain f he i n ecie calclable. The

mehd ed fm he API RP 684 [13] iml inend eeen he cae nbalance f a

feh fm he h. Cmaing Fige 40 Fige 52, Fige 50 Fige 60, he ene a he

fi ciical i e in he field han ediced fm he mdel nbalance ene. Since eal daa f

he ecnd ciical i n gien, i i nknn hehe he acal ecnd ciical ene ld mach

he ediced amlide f he mdel.

Regadle, he effec f he ecnd ciical eed ae alead infinging n he eain f

he a 3600 RPM, and he change in beaing de nhing imac ha el. Fm hi e, he

leee beaing ill be ke in he ea beaing hing and anhe leee beaing ill be inalled in he

e beaing hing. The leee beaing i ccefl in damening he ibain amlide in he ea

beaing. Thi el i cnfimed in bh eeimenal and mdel daa.


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5.2

While he mdel el aea clel align ih eeimenal daa, eeal knn

deficiencie ei in he mdel ha hld be ed fhe efine he mdel f fe eff. Fi,

fndainal effec, fleible beaing , can be ed me accael edic he lcain f

laeal ciical eed. Secnd, de he inheen cncin f he , he cnain diffeing

hinal and eical iffnee. Thee diffeing iffnee ee een in he ca dn e

efmed in Secin 4.2, a he li ciical eed ee aaen.

T l eeen he effec f he diffeen iffnee, a finie elemen anali f he

ih he ce and end inding inclding eaining ing and ceneing ing ill be eied. The

ce inding effec n he iffne f he ee negleced in hi anali b hld be

inclded in he finie elemen anali. Al, ne f he ima inflence f he ecnd ciical

amlide i he kineic eneg eling fm he cling. Fe k ill aem balance he

ecnd ciical amlide b ing he cling a a balance lane. Ohe balance lane ill eie

eming he fm he a and balancing in a higheed i acce he balance lane a he

ceneing ing.

Finall, hi d did n accmlih i iginal ak, i.e., hifing he ciical eed aa fm

nning eed. Smehing me daic ma be eied accmlih hi gal, and fe die ill

ineigae hee in. Tilingad beaing ma be died deemine if he can ccefll hif

he ecnd ciical eed. Siffening he beaing , hich ill be inclded in fe k, ma

cceed in ding hi. Oheie, efming a edeign f he inclding, b n limied ,

edcing he beaing lengh, iffening he , adding ma ma be eied.


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5.3

Thi d ha cnfimed i die efmed egading he eain f VKF m nea

he ecnd ciical eed. Uing DRBeS fae, he a mdeled and eeal laeal

dnamic anale ee efmed. Uing hee el, he beaing change a efmed and

daa ecded befe and afe he beaing a changed. The el f he m check cnfimed

ha he mdel indicaed, namel, ha hile he beaing ich ma ccefll edce ibain

amlide, i de n hif he eain aa fm he ciical eed.

An eeced eaain magin f 1015% (360540 RPM) fm he ciical i ical f m

deign [13]. Daa indicaed ha he ciical eed a ccing in he 38004200 RPM ange,

en b lking a he 2X ibain eca. If he ecnd ciical eed i ccing a 3800 RPM, he

eaain magin f he acal em i nl 6%. If he ecnd ciical eed i ccing a 4200 RPM,

he eaain magin i 16%. De daa ha indicae ha he i alead infinging n and

eeing he effec f eain nea he ecnd ciical eed, he cnclin i ha he beaing

em i eaing cle he ecnd ciical eed.

Wih ha being aid, he leee beaing ill be ke and anhe leee beaing inalled in he

e beaing lcain de he le ibain amlide. Fhe k ch a ha deailed in

Secin 5.2 ill aem deemine he mehd f hifing he ciical eed aa fm he

eaing eed. In he meanime, he effec f he ecnd ciical eed ill be a cnan niance in

he eain f he m. A he age, he iffne f he beaing em ill change. The

eling ciical eed ma hif lighl, eling in he ciical eed ccing a he eaing eed

f he . Theefe, ene eliable eain f he m, fhe k i necea. Cnined

ineigain in he ible change ill be made and imlemened if he mdel indicae a

miing ah.


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Rdnamic anale hae geal imed e he a 160 ea. Tl ei cenl ha

did n hen hee m ee deigned in he 1950. Uing hee l all he anal gain in

h knledge f a machine ha nl eing ided in he a. Cnideing he man ea f

eice hee machine hae ided h fa a an inegal a f fheing aednamic knledge

a he n Kaman Ga Dnamic Facili ind nnel, mainaining hee machine he ide

eliable eice i iall iman. An imemen hich can be made in accmlihing hi gal ae

h ing, a hi d achieed.


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[1] The Vn Kaman Ga Dnamic Facili Wind Tnnel.A A B.

h://.anld.af.mil/liba/fachee/fachee.a?id=12974 . Acceed:

12 Jan 2014.

[2] G10 FR4 Maeial. C . h://.

rotordynamic analysis of a two-pole synchronous motor with sleeve

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