t1025-45_ lobe design factors

8/11/2019 T1025-45_ Lobe Design Factors

1/22

DESGN OF JOURALBEARGS FOR ROANG MACHNERY lae

ssociate rofessor

and lackssociate rofessoreartent of ecanica an erosace ngineerigniversit of irginiaarottesvie irginia

Dr. Pal E. Allaire is crrentlyworking on the analysis of ows inpmps compressors and trbines. Theemphasis is on rotating achinery vib rations cased b y these ows. Dr. Allairehas also worked extensively in the area bearing a nalysis and finite elementanalysis. He has developed a nmber ofcompter programs for bearings whichare widely sed in the United States tocalclate bearing statc and dynaicproperties.

Dr. Ronald D. Flack is an associateprofessor in the Departent of Mechanical Engieering at the University of irginia. i research areas are in experiental bearing lbrication id owsin trbomachines and rotor dynamics.He has pblished papers in these areas

He received B.S.M.E. MS.M.E adPh.D. derees from Prde Uiversity i1970 1973 and 1975 respectively andwas employed by Pratt and Whitney Ai rcraft from 1970 throgh 1971 He is an active ebe ASLE A SME ASEE and other societies.

ABSTRACT

Roang machney s ofen subec o vbaons due occa speeds, unbaance, an sabty Usuay the easexpesve modcaon of a machne o ake s he beang Awde vaey of beangs have been deveoped o comba someof he deen ypes o f vbaon pobems Ths pape ds cus-

ses he geomey and heoeca and expemena esuswhch have been oba ned fo a numbe of beang ypes Thehee man beang ypes dscssed n hs wo ae muo bepessue dam, and ng pad beangs A beang summaycha ndcang some of he advanages nd dsadvanages ofhese beang ypes as we as ohes s cuded n he pape

INTRODUCTION

I s ofen he case n dusy hat a oan machne sdesged fom he po of vew of he pessue o be de-veed, he ow ae o be deveed, the oque equed ofhe elecc moo, n othe facos whch ae epend en of

vbaon consdeaons Nea he end of he desgn ocesshe vbaon chaacescs of he obeang syse aeconsdeed f vbaon pobems ae encoueed ethe ne desgn sages o esng sages s vey du oedesgn he ene oo a hs po Th eass cha ne o

mae s ofen a beang change Thus he desgne and u se ofoa ng mach ey sho d be acqan e d wh he d am e -as of he vbaon su ppesso chaacess of a u be ofden ud fm beangs

Roang machnes ae commony suppoed ud mydodyamc beags They have eatvey ow ionaes sance o nng bu mo e po any pode s cousdampng o ece aea vbaons n hese aches f agve mache conguaon wee spp ed n on e eme beangs ahe han he ud m beangs genaly hevbaon woud be so age as o oay peven opeaton ofe machne e o vbaon Rong eeme beans po-vde he sess necessay o supp the weh f hemachne bu ae essenay z eo damg o shoc abs bngcapabes

numbe of causes of age vbaos n oag ah-ey exs These ae descbed d ea n ohe efence s andw ony be enoned hee They ncde machne unba-ance hydodynamc joua beangs hemseves eaconwh he wog ud n a machne seas n ang mach nes con ubs, a nena con due o sess vesas nshunon pas Noay a excep he s caegoy ue omachne unbaance poduce a age aplude of vbaton ne machne whch occus a a deen fequency fom h a ofhe oag feqency The esung dynamc sh oncaed an nsaby occus a a fequency ess han ha f heoa ng speed an d s ca ed sub synchono us v ba on any ofhe beangs descbed n hs ace have been eveopedspecfcay o comba oe o anohe of the caus es of ns ayndcaed above Usay f a beang has good dampn pop-

ees such ha w suppess oe of he causes of nsa, wl aso geaty modeae the ohe causes as we ypca vbaon paen o an ndusal compsso

wh vbaon pobems [ 1] s shown n he waefa dagam nFgue 1a A subsynchonou s vbaon st occus a a unnn gspeed of 10800 RP The fequency f hs whl mon snea 4000 RPM , whch s a so he machne s cca seed A he opeang speed of 13500 RP, shows synchnousvbaon a 1500 RP alon he dod ne of 1N PM,sbsynchonous vbao a appoxmael y 4000 RP , andsupesynchonous vbaon a 2700 RP a 2N h svaue of subsynchonous vaons s casd b machn sea


2/22

CEEDIS F THE TET TUBCHIE SYSIU

foces, nena aeodnamc cosscoupng, and nadequaedampng a he beang saons Ths shoud be emnaed bcangng he sea geoey and he beang sess anddampng caacescs The synconous vbaons a N canbe mpoved b a bee baancng of he s sem Fna, esupesynchonous baon a 2N can be mpoed b a beeagnmn of he compesso o he dng machne

6

FRQUNCY SPCRM VS SPD

NNSHRNOS WIRL

1

/

V

6 8 6UEN SPETRM (PM)

FU SPEM P VS SP

I SZ FIL M AM-SABILIZ SSTM

2"

8 = =7 =e 6 4= *' - .

8 FQENC SP M Fx 10

3P

Fire 1. Indstrial Compressor with ibration Problemsa) Beore Fixb) Aer Fix

Fgue b shos ha baon paen foong hesempovemens excep agnmen can be see n ha ee s nosbsnchonous vbaon, a sm a sychonou s vbaon, an ds e o mes supesnchonous v baon The machne sno unnng pope and h s been fo que s ome yeas

an of e bengs hch ae dscusse n hs papehave been deveoped pncpa o comba one o anohe ofhe causes of vbaon. s founae fo desgs of oagmacne a a beang hc hs good s es s nd amngpopes such ha w suppess one f e causes ofvbaon usua modeae one of he ohes as we shoud be noed, owee, ha he ange of be ang popeesdue o e deen geomec eecs s s o a ge ha one mu sbe eavey cae o choose he beang h he popechacescs fo he pacu causes of vbaon fo a gvenmachne. n ohe ods, hee s no one be ang ch fxeve machne

BERING TYPES ND OMETRY

Fixed Pad Non-Preloaded jonal Bearing

Fou pes of beangs ae shown n Fg ue 2 hch ae asomeha sma o he pan ouna beang The panouna beang has been dscussed n gea ea eseheePaa ac beangs ae a pa of a ccua ac, as shon nFgue 2b, whee a cena oaded 150 paa ac s pe-sened f he shaf has adus R he pad s aufacued wadus R + c An axa goove beang, d agae d n Fgue

2c, as axa gooves machned n an o ese c cua bea-ng Te oang bush beang has a ng hch oaes some acon of h sa angua veoc of hese aecaed nonpeoaded beangs because he pad sufaces aeocaed on a cce h adus R + c Peae d beangs aedscussed n de ae n hs secon

PLAIN JOURNL

OIL

SUPLY

GROOVE

F XAGROVE BEG

FOTIG USHBEAING

Figre 2 Types o Fxed Pad on-preloaded jornal Bearings.

Paa ac beangs ae on used n eave o speedappcaons Te y educe poe oss by o h avng he uppepad, bu ao age veca vb aons Pla unal and algoove beangs ae ae pefecy ccua shape Excepn a vey few cases , such as age nucea wae pump be angswch ae ade of cabon, hese ae cushe o de o maeh e bea ng s gh nonccu has been ud o ve ma n


3/22

DESI J BEI TTI CHIEY

ears f praca use of suc bearns ha nser a sm orsome her means of decreasg he cearance sg i hera dreon mes he machne run uch be C-drca an ourna bearngs are subec o a phenomenonnon as o hr hc curs a haf of e opeang seedof he bearg Thu s ae haffrquenc hr xagroo bearngs ha a nuber of axa grooes cu n hfae hh prode or a beer o supp and aso suresshr a reae sma degree Foang ush rnrdue he poer s s copared o an equaen paurna bearn bu are so sue o o h of eebearns hae he mor aaae f beg o os andea o make

Fxd Pd Prloadd orl barns

gure sos e pca oe af and hee and r-obe bearns hh are dren from he pur ndrabeans n ha he cene rs f uraure f eah of he pas arno a e ae pn Each pa moed n ard e ner

f he arn e an f he pad eran n rder a d hness re cnern an der n nnar hn us n h an r axa r oa banTe er f uraue s n daed b a r naese rns od uppreson f na ese bu n be u bnchno br peds rae anure of es arns s n aaseas o ban

) EPTCA OR EMOO EARG 0.50m 04)

c REE OE EG\050 m 04)

b) OE A EARG

125 m04)

OUR OE EARG(a 050 m 040)

r 3 Tys f Fxd Pa P ld al Ba s

A e paraeer usd n drbn hse bearn s haon f nrng ad fu pad enh a a ad hose faor s

Ose FacorConergn Pad Lengh

Pad Ar Lenh

The epca bearng shon n Fgure a ncaes ha heo pad ceners of uraure are mo ed aong he axs Thscreaes a pad hch has each m hcness hch s onehafcnergng and onehaf dergng f he shaf ere cen eredesodg o an ose facor a 0 The os hafbean n Fgure b onsss of a oaxa rooe bearneae he boo ha has hgh horzona sne ss ho era ness s essen a no more d cu o m aehan ax re bearn Genera he braon c hara-erscs of hs ng are such as o aod he preousmenoe o

whihc ca n dr e a ma ch n e u ns ab e The

ose af arng ha a ure onergng pa h pad arenh an he o oppose he ener of cuaure a10 Boh he hree e ur obe e arns shon ha anose cor o 0

The fraon o p nce hh h ads are brn s e h rad r Le h barn earan he pad n nss h h ha r dned b q Fure a hs ha h ar shf b aed h en ha C T h rr

s n ra f C

Preoad Faor C

A ra or f r rrd h f anr f urar n h r f r he a ra cor of rrn pads un he ha Fr n 4 se as r h af rads n d ran r nsan

) ARGET HAT WHT EARG

TO O EG EOA m 00 RGTAT R+c ERG

ARACE cb c

b) TWO OE ARGWIH REO ARGET HAT R

ERG CECE

Fr Effct of Prlad n To Lo b B arn

Fxd Pad oral Ba s th S ts ams or Pocts

Pressure dam bearngs shon n Fgure a ar coose dof a pan ourna or o axa rooe bea rn g n hch a da s


4/22

CEEDIS F THE TETH TUBCHEY SYSIU

cut n the tp pd If the dm heght s c the rdus f theberng n the dm regn s R + c + c As the ud rttesnt the dm regn lrge hydrdynmc pressure s creted tp f the shft The esultg hydrdymc fce dds tthe stt ld the ber ng mkg the shft pper t weghmuch mre th t ctull des Ths hs the eect f mkgthe berng pper much mre hely lded nd thus m restble Pressure dm bergs re extremely ppulr wthmchnes used n the petrchemcl ndusty d re ftenused fr replcemet berngs ths dustry It s esy tcnert ne f the xl gre r ellptcl berng types ert pressure dm berng smpl by mllng u t dm Wthprper desgn f the dm these begs c reduce brtnprblems n wde rnge f mchnes Generll ne musthe sme de f wht the mgtude d drect f theberg ld s t pperly desg the dm

RERE AM EAR

ME AMOBE BEARG

OR A YROABEARG

Fgre 5 Fed Pad jornal Bearngs wth Steps, Dams orPockets

Sme mnufcturers f rttng mchner he tred tdesg sngle beng whch cn e used ll r lmst ll ther mchnes n reltely rutne fshn An exmple s

th mul tple xl gre r multlbe beng shwn n Fgure5b ncprtes numbe f fetures f ther berngshch re desrble

Hydrsttc berngs shwn Fgure 5b re c mpsedf set f pckets surrundng the sh thugh whch hghpressure lu brct s suppled Clerly the use f hydrsttcberng requres n externl supply f hgh pre ssure lubcntwhch my r m nt be lble n prtculr mchneThe berngs ls tend t be reltely st s cped wthther hydrdynmc berngs They re nrmlly used n hghprecs rtrs such s grdng mchnes r nuler wterumps fr hgh stess

No-Fxed P ad jornal B earngs

The lst ctegry s the nly n nxed pd jnl berngwhch s wdely used n ndusty It s clled te tltng pdberg nd e ch f the pds whch nmlly ry nywherem three up t seen re free t tlt but pt pntsndcted Fgure 6 Ech pd s pted t p nt behnd thepd whch mens tht there cnnt b e ny m me t n the pdhe pd tlts such tht ts cet er f curture sh wn n Fgure

6b mes t crete strngly cnegng pd lm thcknessThe pt pnt s set nywhee rm nehlf the length f thepd t ely ll the w t the tlg edge f the pd Thefrct f the dstnce frm the ledng edge t the pd ptpt dded by the dstnce frm the pd ledn g edge t thetrlg edge s clled the set ctr smlr t the setfctr fr multlbe berngs set fctrs ry frm 05 t1 0 An set fctr less thn 0 5 crete s sgncnt frctn fdergg wedge whch s unde srble If there s ny ps sbl-ty tht the bergs wll rtte n the dr ectn pp ste t thedesgn drectn n set f 05 shuld be used An set f05 ls ds the prblem f the pd beng nstlled bck-wrds whch hs bee knwn t ccur mcnes

PAD

PIVOT

FOU R ILING A

P CEE

CURVAURE =PA LGL

BM SHW N IL

POSII WI CNVR M

ICKSS

Fgre 6 Tltg Pd B earng eoetry

Anther mjr desgn cnsdetn fr tltng p er-ngs s the rdl lctn f te pd pt pnt It my med s tht the pd centers f curture d n t cncde t pt t the cente the beng Ths s reld ct


5/22

DESI F J BEAIS TTI HIEY

essentlly the sme s descrbed be fr ellptcl nd three-nd furlbe berngs A preld fctr less thn zer (pdcenter f curture between the pd nd the berng centercretes pd hch wll tend t dg the ledng edge nt theshft Ths s smetmes clled pd lckup. Lckup cn bepreented by plcng smll beel n te pd ledng edgewch prduces smll c nergng wedge eect but negteprelds shuld be ded.

Tltng pd berngs re ery wdely used t stblzemchnes whch he subsynchrnus brtns . Becuse thepds re free t fllw the shft the frces prduced n theberng re nt cpble f drng the shft n n unstblemde. Ther dsdntges nclude hgh cst s retrtnblty t be retrtted n sme m chnes hgh hrsepwerlss nd nstlltn prblem s.

ULTILOBE BERINGS

In the preus sectn the gemetres f multlbe ber-ngs were descrbed In ths sectn sme typcl theretclnd expermetl studes whch demnstrte the pertngchrcterstcs f multlbe berngs re present

Linearized Stability Analysis for Mltilobe Bearins

Ths sect nestgtes the prblem f the lner stbtynd the nnlner behr f sngle ms s rgd rtr [2 3] the fur multlbe berng cngurtns shwn n Fgure (n ellptc lem shped berng b n et elptclberng (c threelbe berg nd (d furlbe berg.All f the bergs he length t dmeter rt f 05preld ctr d et fctr f 0 5 except the et berngr whch the et s 10 Stess nd dmpg cecetsre gen elsehere d d nt ge much f bss frcmprng rus berg desgs wth e ther Thelerzed stbty threshld s fte used r ths purpse. It

uo LBE

OS .5

.

LB

60 LBE

OFFST 1.

e

+ jFS .

.

Figre 7 Mltilobe Bearing Geometry

shuld be emphszed tht the lnrzed stblty teshldssumes tht the rtr s rgd whch s usully nt cect. All rtr stblty nlyss wt bth rtr nd ber prperts mus t be cnducted fr ny m hne

Snce multlbe berns d exhbt selfexctd whrlbrtn under certn speed nd ldng cndtins thedesgners re fced th the prbl em f selectng th erngwhch wll be the mst s tble r he the lwest frce l els fr gen pplctn. Sm etme s erngs re clsse s mrestble smply becuse they re s ter A typcl nstbil ty tkesthe frm f hlffrequ ency wh rl ccurr ng t shft ttnlspeed f pprxmtely tw tme s th resnnt frequ ncy f rtr system. The str berng s desgnted m stblebecuse be rng stess ncrese s th n turl frequen whcheectely rses the stblty threshl d speed t whc erngnduced whrl wll ccur In ths study ll the bengs rerented wth the weght f the jurnl drectly n the nter fthe bttm lbe The mbent d cttn presures retken t be zer Flm rupture s ssue d t ccur fr n gtepressures (the hlf Smme rfeld cndt The Reynld s equtn s sled wth the pressure t the le dng nd trln g edgef ech berng sectr s well s the sdes ssumd t bezer. The hydrdymc pressure s ntegrted nly er theregn n whch the pressure s pste

The equts tht led t the determ nt f te ber ng linerzed stblty fr rgd rtr re presete [2]Fgure 8 shws the stblty threshld speed pltte gnstthe Smmeld umber r the ur berg types w Fgure Ech f the 45 strght lne wth pste s lpe ndcstnt crss the gures ges the l cus f the p tn f berg wt xed gemetry s t bru ght up r w nspeed The berng prmeter T s dned s

S LD

j 8Wr

(

shuld be nted tht s ndependent rtr spd ds n tself sucet fr the descrpt f certn erggemetry n stblty grph. s berng ncreses n pee dt l prceed l g ne f cnstt T nd becme unstbles t eters the ustble regn by crssg the stblt curem belw

3wwww


6/22

30 C EEDINS THE TETH TUB CH INEY SI

Figure 8 ma e separated roug into tree regionsight d a/or cse cearance ( 0 1 to 1 0 eraeoa an/o moderate cearace = 0 01 to 0 1 and heaoad ad/or pn earace ( = 0 01 to 00 It is obsredat der a perating conditions threobe bearing isconitent mre stabe than the fouobe baring except at = 0 1 whee the earins hae about sae stabitthreshod A the other stabii cures aso appear to intersectrough at this same point indicating itte dierence betweenthe stabiit characteristics of the bearings in this area ofoperation

At ght oad and/or cose cearanc operations the o setbearing i the most stab he threeobe bearing s betterthan the four oe bearing b a sma margin whe te e iptica emon bearng is te east desirabe ithi this regionthe stabiit a be muc improed b reducing the obecearanc or eectie ncreasing th bearing parameter

nder moerat oad condiions te oset haf bearingoses its superirit cmpete he most sabe bearing in thisregio is the e iptica bearing foowed b t theeobe thefourobe and te oset cindrica bearig Impoment inthe stabiit performance increasing obe cearance or decreasing is ot substantia on the ig side witin thisgion

At hea oad and/or open cearanc opations the orderof inreasing stabiit is te urobe bearing the oetbearing the threeobe bearings and th eiptica beaingIncreasing obe cearance or deceasing i drastica improe the stabiit threshod for a of te bearings

Whie the oset bearing is superior in stabiit r ightoad operation the eiptica bearing appears to be mo st stabefor a wid ran e from hea oad d to reati igt oadedappications

to the throbe bearing oes not hae the beststabi it oers good era perrmanc under a oadcondiions It is se cond on to the most stabe bearing in eachregion

e rato of th whir spee to the rotor spee is gien b

te diensioness imaginar art of e unstabe compexeienaues 2] At the stabiit thresod t rea part of theroot i zero ad the wir atio ma conenient becompued

Figure 9 shs the ariation of the whir ratio ith teSommefed nu mbe r fr te four bearing tpes at the thre shodof instabiit t is een that a nie retion exists beteenthe stabit and th whir ato in a a that te ore stabeearing distinc whirs t oer speed ratio

Wh te exception of the eiptica bearing a bearingshir at speds ess than 0 48 of the rotor spee he osetearing atains maximu whir raio of 0 44 a a So mme rfednumber of about 0 4 and decreases to a stead ue of 0 35 athiger Sommered numbers Tis obserat ion corresponds to te superior stabiit with the ose bearing at high

seed and ight oad opertionsThe wir rtios with the threeobe and he fourobebearings share s imiar characteristics he both rise sharp atow S omerfed n umbers and remain fair constant for mo stportions of the cures Asmptotic whir ratios of 04 and048, respectie, are reached at high Sommerfed numbersIn comparison to the fourobe bearing, th e threeobe be aringawas has the ower hir ratio

he eiptica bearing which is the east desirabe foright oaded appications is see n to hae a hir ratio in exce sso 0 5 aboe a Somm erfed num ber of 1 3 Whir ratios aboe05 ae been obseed b oter authors as we he highest

Figre 9. Whirped atio Verss omeld mber

whir ratio of0 6 is reached asmptotica at hig omme rfednumbers

A the cures in Figure 9 drop er rapid when thebearings are operated near the teep ertica region of thstabiit cures en a bearing is inite sae the whirratio aproacs zero

sing a singe mass exibe rotor it can be sown that theexibe rotor stabiit threshod is gien b [2]

where wr is the roto critica speed on rigid bearings Becausethe s tabiit threshod for a exibe rotor i s awas ower thanthat for a rigid rotor Figure 9 shou d be i ewed as the highestpossibe stabiit that can be achieed in these bearings

On of he ajr cocerns in this inestigation is thestabiit of te mutiobe berings in ight oa apicationsTe oinear charateristic of the bearings xmin d n thissetion are to hae the bearing paraeter T = 3 Insofar aspossi be eneraiation of the res us throu gout this paper isproided the use o dimensioness parameters instead ofparticuar beaing specicatons and operating coitions Anexampe be aring with = 03 is

381 mm (15 in

62 mm (30 in

c 0 152 mm (0006 inW 168 3 N (38 b

689 0 N sm ( 1 0 10 bs/in Fo r comparison to the transient anasis, the inear stabii

t threshods, orresponding Somerfed nubers, and hirspeed ratios or the four bearing tpes at T = 03 aretabuated in Tabe 1 The journa speeds or e ach o the ourbearing tpes at the threshod speeds of instabiit are asoshown he orde o iesin tabiit is the e itica bearing, he fourobe bar, te threeobe bearing, an theoset bearing


7/22

DEI F JU BEIS TI CIEY 3TBLE 1 TBILITY THRE SOD ND HIRL RTIOS FOR RIOU BERIN TYPE ITH BE RIGPRMETER = 0arg Typ Sfld

Ellptcal4ob

3Lobst

umr

1 1 515

1832

For-Lobe Bearins on a Sinle ass Flexible Rotor

I this scto a xbl rotor scrbd pdx as outd a st of four lob b args typca fourlobbarg s show Fgur 10 Dyamc bhaor ad thstablty thrshold was s tat from sral coguratos (for mor dtal s s rfrc [ 4] ll paramtrs rhld costat r all tsts th th xcpto of th alu of tload agl For a four lob barg = Sm all cags

ths param tr r s to cha t damc rsposcosdrably Th spccatos of th to bargs ar su

marzd Tabl 2 Th sm two bargs wr usd r all ofth tsts ths scto

END OVERNPOI FPAD

= cb/Rp-l = +c

a= c= -R

.OURNALIF CETEED

IN BANG

Fire Typical For-Lobe Bearin

TBLE 2 FOURLOE BERING SPECIFICTIONS

Shaft Damtr (mmMimum Raal Clarac Cb(mmPrload Factor mPad gl Barig Lgth L (mmOst Factor a

25 3/25 342*0041/00580/0063/63122/1422050/050

* ubl lu l b pl

rl Stablt Brato Thrshold (P

W49 382 9 25245 508 1230

40 6 21 15 01361 120 2923

Th rst ortato to b dcussd s = 15 Fgur shows th syhroous moti o total moto a phasagl rsposs for roor ruup for th X2 prob I tsgur th o mst mportat fatrs ar th rsposs att rotor rst crcal spd ad at gh spds Frst th rotors s to rma stabl for all sds Th maxm um spdtat th otor was ru was apprxmatl 12500 RP adthr th total or s chroous oto of th rotor d sp lada larg lmt cycl brato Th oral moto dd hwr gradual td to cras as th spd crasd abo

6000 PM Scod th moto o f th rotor at th crtcal s pds s to cras

OO

g

PHASE ANGE

TOTL RON

X2 MOTION 9=-15

c_0.041mm

Cp 0178 m 077L, W 28\ 54

C 0058mmc013

m 070L/05 05

OTT

9 9

Fire Toal and Syncono 2 oton Rn- r=

Th class c phas shft obsrd at a crtcal spd s 180 Hor a o rall phas shft o 360 was osrd a t X2Ths phas shft bhaor s attrbut d to th bow of th ro tor

Th atrfall frquc spctms ar prstd fr thX2 moo Fgur 12 Such gur complmts thschroous rspos plots wll or xampl th suprs

croous xctato of th rotor crtcal spd ca sly bs lso th 2x ad 3x compots that cotrbut to thtotal obsrd moto ca asl b s For rotatoal s dsgratr tha 600 RP M th schr ous X2 moto s s tocras th sp d as as also s i Fgur 1 1 La st ly osubsychrous m oto was s a t ay tm th opratorag Ths rotorbarg sstm ws thus ry stbl thrughout this tst

Th scod coguratio discss is = 30 h X2total ad sychroous moto ad phas agl rsposs arprstd for rotor ruup Figur 13 Th rotor wtustabl ry rapdly at 6600 RP as dcatd by th total


8/22

CEEDIGS F THE TETH TUBACHIEY SYSIU

0.041m c0058 c

078 c,-o.t93

07 2 00 L/559 N X63'

L

05

0000ni\ _

000'

n L

000 l 000 J 000 000

!

\

)

000

1

000

0001 000

A

T

L

0 000 000 000 000 0000 000

Figre 12. Wateall Freqency Spectrm 2 Motion for6 1.

. -- -_,3- 75 .\-

Q5 12.5 - Ji -P A_E

A_G>

L

E

-

1o.o I

5

50

004mm 08 m 077L 3 3cmW 28N 254

i TOTAL RESPONSE

{ SYNCHRONOUS RESPONSE

2.5 v

0.058mmC1093 mmm 070L/005!9

i

0

.

_ ROTATIONAL SPEED, RPM

9 -9 :

Figre 1 Total and Synchronos 2 Motion Rnp) for6 .

t u rtt t r 45 r t tl ptrdud t tlty trld by r t 5900 RPM . O

rud t rtr ld utl dt wl rvd r prur d r wtrll quy ptru r 6 30 (X2

t ruup) prtd ur 14 . ur prtd t dtrt t rquy t w t rtr wvbrt dur t utl dt rquy t t rtl pd t rtr (pprxtly 3000RPM) Otr urt utl l lltd t t rquy d t rtr w vr tdtrt y rquy l rl u trtrr yt dtrtd y tlt t dt wp ppd t wrl

:

550 50 000 5000 400 00 2006 000:

_

[

J

{

I

X2 MOTIO = 30" 0041mm 0058m 0178 m Cp093 mm

m '077 =00 5334cm L/D=0559 8N ) 63" 254 em =0.5

f

I 0 2000 400 00 0 00 20

Figre 1. Watell Feqency Spe ctm or X2 Mot ion for6

U t rult prtd v t rult tr tt t tlty trld pd rrltd tt ulr pt t rv lt prtd ur 15. Al plttd ur 15 t t ytrtt wp rudw. A r t ur tptu lt t rv r vlu r t 0 r 7 t 90 wrt = 30. t tr d t d p rud t t tr t lvl rd t 5800 d400 RPM r ll t yt t utl Tpl tt t r rtr tlty trld tlr t rtr ll dtrt p dur rud rvt w l d r prur d r

1000 13000 1000 11000 10000

;

NSABY HRESH* AU SPEE- SABE ARGINALY SABE E F WHIPN RUDWN

* * 055 3 050m077 m070

5 -30 -5 0 15 30 5 GRVE LAN, EGREEFe 1 Smmay o Coelation o Insbly ThresholdSeed h


9/22

DSIN F JUNA BINS F TTIN CHINY

Te experimea daa i ex rreaed wih ereiapredii. Fr hi ei, ie eeme were uiized auae e beari eie r he urbe beariued here. A, he exibe rr wa mdeed ui umpedrr ae [5] Ti mde wa he ued wi e bearieie predi e abiiy e rrbeari yem.Ti abii red wa auaed r variu vaue 'gad he ereia predii are preeed i Fiure 5 Aa be ee, iia dieree exi bewee he experi

mea daa ad ereia predii r e iabiirehd rai rm 40 RPM a

'g= 30 ver 400

PM a " = 0 Neee, he experimea ad ereia reu are i emiquaiaive areeme ie e pimum vaue 'g i e ame r b 'g = 5 r 75Te dieree bewee e ereia ad experimeaiabii red r a beari ype are aribued er a mbiai ve ee. The reaive aiude ee ave bee deermied Tey are: iauraebudary dii (eier a Smered r Reyd) ie beari auai; variai eperaure ad,u, viiy wii e uid m e beari; 3 marbia mi e a wii e beari reui iraie variai e ie ad dampi beari haraerii; 4 ai ee e uirade i; ad 5redued i e di due dampi i ehadi

die are preey bei paed par

iay expai deree. e ha i bei irueedu a preure wii e beari a be meaured admpared ereia predii deerie e auray e uid m beari budary dii.

Two Axial Groove Bearings on a Three ass Flexible Rotor

Axia rve beari have ee eed i a hree maexibe rr i a imiar maer e udie de i epreviu ubei [6] Te apparau i imiar e iea exibe rr ad i deribed i Appedix B. epeiai e beari are preeed i Tabe 3 Fr

TABLE 3 TWO AXIAL GROOVE BEARINGS.Sa Diameer, D (mm)Cearae, (mm)Pad Ae, XLeh, L (mm)Pead, m

5 375 3870037/0045/57070000000

breviy, y e ummary rap i preeed here (Fiure 6 A a be ee, he iabiiy red i ideraby werr ee beari a r e urbe beari i he iema rr. There are w rea r hi. Fir ad mimpray, he pread r ee beari i zer. Sed,

TABLE 4 BEARING SPECIFICATIONS.

Se N. 3 4

iiu Radia 0340043 0034/0043 00380043Cearae, (mm)Pread, 004 33 0 55 56 0 7560 73Oe Far, 0500/0500 0550505 04840484Pad Ae, X 66 33 55

JJ((J(

AXIAL GROOVE BEARNGS

LD= 55 R 55

7rpmQ

LOAD 5

ROOVE CTIN, DEREE

Figre 16 Smmary of Correlat ion of Instabi lity Treshol dSpeed with

'hi apparau i mre exibe due e aer diaeer. e iabii red de vary wih he ad e ade pimu vaue 'g i e aai pprxiae 5

Fr hi ye e ereia iabiiy red waapprxiae 4700 RPM, rearde ad ae. Te dieree bewee ery ad experime are aribued he verea diued abve.

Three-Lobe Bearings on a Three ass Flexil Rotor

Seve e hreebe beari ae bee ee i eame ree ma rr a deried i Appedix B [] Thepeiai are derbed i Tabe 4 ad e variabe are heame a deed r a urbe beari. A a be ee hepread ar ad e ar were yemaiay vried.

Typia ummary p are preeed r ree eaie i Fiure 7 hru Te uary diara r e = 50 m 04 i Fiure 7 w he exprieaiabiiy rehd, ih aried rm 63 50 P a" = 7500 RPM a 'g = 30 Thery w amiimum iabiiy 4600 RPM a 'g = ad ireaeup 5500 RPM a 'g = 30 Auh e maiue eiabiiy rehd are he ae, he experima daaw e ereia red.

5 6 7 8

00380043 00380046 0038/043 38/00

0 7470 73 0 7660 73 0 747/073 0 6/030770677 0 33/0 33

66 9 6


10/22

EEDI TE TEH TCIE SI

1

ooog 6

THREELOB EAINGS. (SET NO2)

LD 05/.cb/R = 0.027/034

m 09/.39a = 55

96 HRH

F HP O -OECA AT

TR

-

3 GOOV OO GFigur 1 Summary of stabiiy hrshod ad d ofhip Cyc with 'for Barig St 21

1 8


11/22

DESI F JUR BI FR RTI: CHIERY 3

to inacurat bearin calculations ather than incuraeoto odin n efenc 1] h ath foun haneithr te alSmel no Renlds boundar codioneice psse ros ic er n ood agreentit eperieta masurees lac an Alar [1] undhat expimetal oeain cntricities fo threelobe be-ings ere loe (b as much as percent an edtd heieences betee the thoretial and eeimntl insabili-t thresholds for all earing ts are atributed to cmbin-tion of e ects dri earlier n this apr

o mmarize te expermtal behai o the insilithresold aiatio ih prload facto and oset fctor ig-urs 0 nd 1 are pesnte igure 0 shos t dependcof he experimental nsabilit treshld at the timum loadangl fo bearing sets throug 4 esus the prelad factorit an oset facor 05 his gur shs the maximminstaili hesol increasing from 6700 RM ith m = 00(t axial gooe o 7500 RPM ith m = 044/0393 (3oese to 150 RPM ith m = 0 756/0 3 (set

! I

I

I LD /e 9 HREE LBE BEAN SES AIAL RE BEARINS / - _< e

! -!

< I < !

RELAD ARFigur 20. xprimta Summary of stabiity hrsho d atOptimum Load A g wih Proad Factor

>:: :

= 77

HREE OBE BERGE 7 8

FF FO

8

Figur 21 xprimta Summary of stabiity hrsho d atOtimum Load Ag with Ost Factor

igue 1 ho the deendne of the mxiu eei-enal ntail thsold rss it ; 0 hemaxim istabiit hresol 150 RP ith = 0 set 4 and ae do to 500 P tp = 0 91 (et 6

rm rsults in iure 1 e bearings th tesmallest o factos pruce t ost table sstem Her th igs in tis ste e lihtl oade ese th sma eultig positie reue egins in bears tt oset factos les than 0 te load carring capaceasmall s a rsult i hih loads ae apli th barigs failprematel or te lght loded ssem esribd ee eains oerated hu pblms oeer si sucbeangs o a heai lade sstem is ot recommended

DA BAINGS

Liraizd Stabiity Aaysis for Stp arigs

Pressure am or step journal bearings hae lon beesed to impo h sabilit of ratin machinr he canrepace plain jounal o axial gooe bearings in a hineoperating at hih seeds and increase the stabilit threshld Astep or dam is cu in the uppe half surce of te earing

producing pessure is near the step and a hdrodyamcloa on the journlAt high speeds and/or light loads the step crtes a

loading tha maintains a minimum operating eccenticit hatis as sped is incrased the bearing eccentricit des notapproach zro a i old for plain jounal or to axial rooebearings he eccenicit appoaches some minimum lue orma een incease ith increasin speed due to the steploading hus a properl designed step beaing ould peraea a modeate eccentricit een at high Somerld nbes113 14]

Conside a nite length step bearing as shon in igures and 3 Man industrial bearings hae to oil spplgrooes in the horintal plane and a step located in the secondquadran ith counterclocise shaft rotation A ectaular

UY

hhh

Figur 22 Prssur am Schatic Sid Viw


12/22

CEEDIGS F THE TETH TUB.!CIE SSIU

rt2 l .

U

I )

d L L > d l l l U _

- '

M

Figur 23 Prsr Dam Schwt c o ad Bottom Pads

am s sa s A crcmrna rf groo or r ck ssoeimes groo n h boom haf of h arng Boh ofhs cs am an rf

r ck combn o ncas hopang ccnrc

of

h be ring whn comar o apl i

jorna o wo aa goov be ringany gomrc ri les aJc h peform nce of prs-

sr a bangs For ll of he sp jona barngs anassn hs papr wo 0 oil n gooes wr oca a = 0an = 0 Aso h am aa lengh rao was

hed

cons n a Tu = 0 7 >r a cass o s h cs of hmanng aabs on o n w as chang while h ohrsrman h sam Ohr paramrs n:

LD 10R 10, 1K 30L 05hs scon anayzs h n ngh pressre am ar-

ng ngcng spineri

cs b nng h cs ofurbunc or h nr barng srfac Barng sabhrsho curs for varos prss am barng gomrsar compar o

pl in jon l,

wo aa groo an grooowr haf barngs h cs on h saby hrsho of

m hcnss rao am ocaton an ohr gomcpaamrs ar consr Opmm barng sgns ar sg-gs to pov vorab saby characrscs

Fgur 4 compars h sabty characrscs of hpan journa wo aa goov an groo ow haf barngsto o yps of prssur am barngs h sab hrshosp , w , s po agans h Somm nmber, S Asonca at th top s h barng ccntrc rao h for aoov bans rspctvy No ha at hgh

Sommerld

numbs th sab curs for ach barng approach asmp-totc vaus of w = 3 pan journa) an w = 0 woa oov)

tA L - 73 66 . 4 7 . 2 92 A X I A L 82 7 2 3 4 rGROVE

O A M # 3 7 5 6 8 . 5 5

D A M 4 75 . 5 5 4 3 3 3 A M " 5 5 6 7

( )

-: ;

T

4

2 7 6

5 . 5 5

F

igure 2. S t ab l i ty Aap C o m p a r n g Prssu re Da Be arings

toPla n Journal andTwo Axial Crooe B e a r i n g s .

Be ring mbr is h groov owr haf barng hsbarng is simp a wo xi roo be ring th a crcum-ni l rf r ck o groo c n h lower h l In hscas h rf

r ck xi l lengh rao Figure ) s L = 0 (he f r ck s ' of h boom pa) A consider blencras n h innie sab gon s nt Tha s hpl in jona barng s hoca sab a a sps owa

Somme d nmber of 048 wh h groov owr hafbarng ncrass hs rang of nn s biltv b a cor ofhr o S 0.17. h rf rack mos p ; i h banglo d carrng src h boo pa hrb llowingbarng nm r 3 o e c 0 8 cnrc a a hghr Som-mrf

nber han h panourn l

arng Arondb = 0 8 K changs sgn prong h vorab s bilicharacrscs

Esseni lly no ncras n s biliy s sn ahgh Sommr numbrs

Bang nmbr 4 s a prssr am barng whK = 3 0 am caranc hr ms as arg as

the

barngcle r nce) an L = 00 no rf r ck) For hs cas hstab is ncras compa o h journa barng at hghSommerld nmbrs

while h region of innie saby sss As

discssed arr a hgh Sommrf nmbrs hsp forcs h jorna o opra a a mora ccnrctFrom h op of Fgur 4 bang numbr 4 opras a anccnrcy rao of h = 05 a S = Ths moraccnrcy pros h orab saby characrstcs a

hgh Sommr numbrs for hs stp jorn l barngCombining h two cs of a rf groov n h owr

haf an a sp n h upp haf barng nubr s a ambarng wh K = 0 an 0 For ths cas hst biliy s ncras for h ntr rang of Sorf num-brs compar o h journa barng Th two sparat ctsof a prssur a

be ing ar shown cay n Fgur 4 Thrf track rcs barg to oprat at hgh ccn-tcs hrby ncasng h rgon of nnt s bilty ham oas up th jorna a hgh Sommrf nubrs pro-ng a morat opang ccntrct an hhr stabtythsho


13/22

DES F JU BEIS F TTI CHIE 3

The eect of rying the m thickness atio K' onsbiity ws crried out but is not shown hee Refeence [4]concudes tht the optimum (s fr s od capcity is con-cered) is pproximatey K' = 3.0. A bering with mthickness rtio ofK' = 6.0 is ony sighty ess supeior (a 0decrese t S = 0.0). A 40 decrese in stbiit is evidentfor step bering with K' = 2.0 when compared to theK' = 3.0 berins t S = 0.0.

The importnt geometic parmetes in pressure dmbering design e the m thickness ratio K' nd the dmoction , Steps shoud be octed at aound , = 45 or50, whie K' vues of between 3.0 and 6.0 ae rcom-mended

Fom Sommefed numbers bove S = 2.0, step journberings dsignated with near optimu m step oction nd sizecn increse the igid rotor s tbiity parmeter by fctoof ten or more over pin journ bering Additionay thepressure dm bering woud operte t moderate eccenticityrtio (beteen Bb = 0.25 nd Bb = 0.5) even though theoding is ight nd/or speed high Howeer fo Sommerfednumbes beow S = 2.0, step beaing wi increase onysighty (b a facto of round .5) over pin joun beaingven if the optimum dm height and oction were used

Stp Barigs o a Sig ass Fxib RotorExpeimenta resuts re given fo dieent step cong-

urtions on simi experiment exibe otor described inAppendix A Fo these tests the rotor was a constnt diametersft (2.54 m) A theoreticexperimenta compaison of theinstbiity onset speed for the simpe exibe roto is presented[9 5]. Five dient step be aring geometies nd two xigrooe beaing are considered The pessure dm beringsempoyed have dieent step heights nd ocations Optimumnd ooptimum designs re used Instbiity onset speeds redetermined both theoreticy nd expeimentay nd a com -prison is mde to determine the accucy of the thoreticanysis

A six pais of berings considered hve two xia oisuppy gooves octed t the horizont spit (Figure 22).

These grooves e 20 in arc ength mking the arc ength ofboth top nd bottom pds 60. The step berings do notcontin cicumferenti reief groove in the bottom pd Thetwo xia groove berings re identic to the pressure damdesign with h = h in Figure 22. The ength to dimeterrtio for ech bering is .0 with = 2.54 m

Ide ech bearing was to hve 5.08 x 0 (2.0m) radi cernc However due to dicuties in nufc-tuing the rdi cernce nged from 4.57 to6.35 0 m ( 8 to 2.5 mis) The cernce w me-sued cod with di m icrometer Severa redings we tkenand the averge ue used

The important geometric prmetes in step beg de-sign re the m thickness ratio K ' and the dm octin , The rtio of m thcknesses is dened s h/h wn the

shft is centered in the bering (Figure 22). Thus K' = h/hnd K = h/c whee h is th centered cernce ind e thepocket The dm oction nge is m esured with ttionfrom the positive x (horizonta) xis Optimum ves forforabe stbiity re ound K' = 3.0 and = 5 to50. Othe pameters re the dm xi engt rtio = / (Figure 23) nd the reief groove xi enth rtio = / For cses = 0.0 since the bott pddoes n ot hve a circumferenti relief groove

A sum mry of thes e prmeters is iste d in be for six sets of berings Note that step bering sets nd 2epesent the ne optimum design with m thickne rtiosbetween 2. nd 2.8. Sets 3 and 5 re ooptimu m desi s withrger K' vues between 6.6 nd . 7. The otimumnguar ocation is represented by set 4 with , = . Thedu numbers in the Tabe refer to the eft (motor) nd ightends of the test rotor respectivey

Figue 25 iustrtes the tot rotor respons with t xigroove berings The subsynchronous component rst persat bout N = 6600 RPM s the system goes unstbe

Qu

Figur 25 ota Rspos, o Axia Groov Barigs

TABE 5. SUM MARY OF GEOMETRIC PARAMETERS FOR THE SIX BEARING S ETS

Bring Type K , c cSet No (m x 0) (mis)

A Two Axi .0 4.57 .8Groove .0 5.08 2.0

Step 2. 45 5.59 2.2 .75

2.4 6.35 2.52 Step 2.8 40 6.35 2.5 75

2.6 6.35 2.53 Step 6.6 50 6.0 2.4 .75

8.6 6.35 2.54 Step 3.3 6.0 2.4 75

2. 6.0 2.45 Step .7 40 5. 33 2. 50

8.3 6.0 2.4

ommon to berings: .0 0.0 X 60


14/22

CEEDIGS F THE TETH TUBCIE SSIU

he total response for a ear optimum step bearing design(et number 1 is shon in Fige 6 ith a orrspondingequen spetrum in Figure 7. This de sign feature s a ste at = n lm thkness ratios of .1 an .. The rooras run up t mxium speed ithout a lare subsnhronouscomponent appearing Hoer to small eaks appar inFigure 6 at around 100 R ad 1000 R Figure shos a sliht onsnhroous bum at 1000 RPM Ippers that te rotor m be on the instailit theshold at

1000 R}M

U t14 5

t, Z C o 6 IOlcf fK Z 1 K'V

RdtR SPED RPM

Figur 2 ot Rspo Stp Barig t u aptium Dsigs

1400

120 10[19.6%3.7%

0.6%.%0.0%


15/22


16/22


17/22

F J S H

FI PA RE OA ES

Bering Type

Elliptil

Oset lf itHrizontl Split)

ree nd Fu-be

dntges

Es t mke2 t3 Gd mping t riticl

speeds

Ecellet suppresin firl ig speeds2 t3 s t mke

Gd s upressin f wirl2 Orll d perfornc3 Mer t st

isdntes

Subject t oil wirl t higspeeds

2 od direction must beknn

Fir suppressin f hirl tmoderte speeds od diection must b

knwn

Some tpes cn be epen-sie mk prprly2 Subjet t wirl t highspeeds

3 Ges unstble with littlewrning

4. ery high ibrtn leelsduring instbility

TABE FIX P OURA BEARIGS ITH STEPS AMS OR POKETSering Type

Pressur mSingle m

Mlti m

Ail Grer Mutilbe

yrosttic

dntges

God s upressin f wirl2 t3 Gd dmping t riticl

speeds4 Esy t mke

ms re reltiely esy t

ple in eisting berings2 Gd sppres sin f whirl3 Reltiely lw cst4 Gd verll perfrmne

ide rnge f designprmeter

2 Mdrte cst3. Gd ld pit f lw

speeds

TABE 8d OIXE PA OURA BEARIG

Bering Type

Tling Pd

Adntgs

ill nt use irl nrsscupg)

2 ide rnge esigprmeters

3 Originl cst but e smes ter berings

isdntges

Ges unstble wth littlewrning

2 m my be subject t werr buildup er time

3. d direction m ust beknwn

4 es nt suppress whirl frery eible rtrs

Cmple bering reuiring

detild nlysis2 y nt suppress whirl ue

t nnbering cuses

Por dmping riticlspeeds

2 Reuires crel esign3 Reuires high presre lu-

brint supply

isdtges

Hig replcement st uires crel design3 Pr mping riticlspeeds4 Hrd t determine tul

clees g sepwr lss

mens

Probl mst widel usedberng t lw r mertespeds

s ig rizntl stesnd ertil stiess myeme ppu use ut-s id e U S

urentl used b s me nu-ftrs s stndr bringdesin

mments

r pulr wit tr-cheicl industry Es t n-ert ellitil er t prssurd

se stndrd desin by

sm mnuftures

Geerll ig tiess prp-ertis ued fr hig prisinrtrs

mments

iel us ed bering tbilieine it srnusnrig eittins


18/22

4 PREEDIS OF HE EH RHIERY SYPSI

ACKNOWLEDGEMENTS

The ork escrie in this pper hs lrgely ben pu-lishe elsehere s incte in the referenes. This pper isntene s s mpler of ieren t orks crrie ou t for severlbering types in orer to provie n introuction to beringesign for the user of turumchinery.

Vrous phses of the ork reporte in this pper hvebeen supporte in prt y . . Deprtment of Energy Con-

trct No. DEC79ET3 5, N Leis Reserch Con-trct No. NG377 Engineering Foundation Grnt No.RC77. The uthors lso cknolege support from theInustril upporte Progrm for the Dynmic nlysis ofTurbomchinery n the Rotting hinery n Controls(ROMAC) Inustril eserch Progrm, oth t the niversityof Virgini.

REFERNCES

. Gunter, E. J . , B rrett, L. E. , n llire, P . E . , "Designn ppliction of queeze Film Dmpers for Tur-omchinery Stailization," Proceedings of the FourthTurbomachiney Symposium, Texs &M niversity,College ttion, Texs, 7, pp. 898.

. llre, P. E., n Flck, . D., "Journl B aring Design

for High pee Rottng Mchinery, Invite pper pre-sente t 980 MELE Interntionl

Lbrcation

Conference, ugust 8, 980, n Frncisco, Clir-na, in Bea ng DesigHistoica Aspects esent Technoogy, and Future Probems, ME publction No.H000, pp. 59.

3. Li, D. F . , Choy, C. , n llire, P. E . , "tbility nTrnsient Charact ristics oFour Multiloe Jornal Ber-ng Congurtions, Jounal o Lubrication Technoogy,Trns. ASME, Vol. 0, No. 3 (July, 980), pp. 999.

4. Leer, M . E . , Flck, . D. , n Leis, D . "nExp rim ntal Determntion of the I nstbility of Flex-ible Rotor in Four-Lob Berings, Wear, Vol. 8. No. (1980), pp. 3547.

5. Lun, J "tilty n Dmpe Critcal pees of Flexible Rotor n FluiFilm Berings, Journa of Engieering for In dusty, Trns. ME , Vol . 9, No. My974), pp. 50957.

. Lnes, R. F., Flck, R. D., n Leis, D. "Experi-ments on the tlity n Response of Flexible Rotor inThree Types of Journl Berings, ccepte for publctionin ASLE Transactions, in press, Preprint No. 8E .

7. Lnes, . F. , n Flck, R. D . , " Eects of Three LoeBering Geometries on Fle xile Rotor tility, cceptefor publiction in ASLE Transactions, in press .

8. Flck, R. D. , n Lnes, R. F . , " Eects of Three LoeBering Geometries on Rigi Rotor tility, ccepte

for publiction in ASLE Tansactions, in press, PreprntNo.8ME .

9. Nichos, J. C., Brrett, L. E., n Leer, M. "E-permentl

Th or tical

Comprson of Instility Onsetpee s for Three Ms s Rotor upporte y tep JournlBerngs, Journa o echanica Design, Trns. ME,Vol. 0, No. pril 980), pp. 33435.

0 . Flck, R. D. , Leer, M . E. , n llre, P . E. , "nExpermentl n heoretcl Inv estigtion of Pressures nourLobe Berings, Wear; Vol. , No. June ,980), pp. 334.

. Flack, R. D. , and Allaire, P. E . , "n Eerim ental andT h or

tical Examnation of the Static haracteri stics ofThreeLobe Bearings , accepted for pulication in ASLETransactions, in press, PreprntNo . 807C .

. llre, P . E. , Nichols, J . C. , n Brrett , L. E . , "nly-sis of tep Journl Berings Innte ength, Iner tEects, ASLE Trans , Vol. , No. 4 Octoer, 979) , pp.3334.

3. Nichols, J . C. , n llire, P . E. , "nlyss of tep Jour-nl Berings Finite Length, tility, SLE Tas ,Vol. 3, No. pril, 980), pp. 970.

4. Nichols, J . C. , llre, P . E. , n Leis, D. "t-nes s n Dmping Coecents for Fi nit Length tepJournl Berngs, ASLE Tans , Vol. 3, No. 4 Octoer,980), pp. 3533.

Leer, E . , Flck, R. D . , n llir, P . E . , "Eperi-mentl tuy of Three Journl Berings ith Fl xilRotor, ASLE Tras. , Vol. 3, No. 4 Otoer, 980) , pp.33.

16 . Flack, H. E . , Leader , M . E . , and Allare, P. E . , " Experi-mental and

T h or t

ical P r

s su r s in Step Journal Bar-n g s , " ASLE Trans . , Vol. 2', No. 3 (J

l y 1981) , pp . 316

3.

D SIGLE MASS FLEXIBL ROTOREXPERIMETAL APPARUSThe Test otor

The testrotor consistsof a exible sha withthreecloselymounteddisks locatedmidway between twobearing supports(F

ig r A-1) . The combined wight of the shaft and centralmasses is 1 3.5 g. Thethree masseswere mounted onto thesh ymeansof a cone ndneoprene "rn which

s c u r

ly

fastened the disks to the sh withoutadding any appreciablestiess . Each disk has 24 bala

n c holes, each 15 apart. The

three disks weremounted suc that succssive balance holeswere ncremented by . The sh was n o

m ina l l

y 2.54 m indiameter wit 2.22 m diamter undercuttings such that thedi sks could be removedor moved easily. This rotor system hasa rst rotor critical speed of 300 HPM .

TRST

PD

2 . 54 e m f- 9 e

FLEX IBLE

COUPLING

1 5 2 e l A I SKS

2 . 2 2 e I A

THRUST

PD

53 3 em

Figue 1 Sh at ad oto sseb

The rotor s rven y one horsepoer DC motorthrough eltpulley n ele couplng. ulley rtio of5 . 5 s use n the mxmu spee of the m otor is proi-mtely 400 RPM. The torque n spee of th system reelectroniclly controlle n oertor justle. ny rotorspee eeen 00 n 3, 00 PM cn e otne n hl


19/22


20/22

4 PCEEDNGS F TE TENT TBACNEY SYPS

PP THREE MSS FLEXIBLE ROTOR APRTUSIn this Appendix he three mass exible rotor is

descrbed. The rg is nerly identical to that described inAppendix A with the xeption of the shaft diamete r andmass locations. The instruentation to redue the data isidentical. The specicatons are shown in Figure B-1.

' " ..Figure 1 Rtr Dimesis d Pre LctisNOMENCLAURE

imesio Qutities

Cx, Cxy Cx, CyyD

'

m m NNO O O

ering rdil lene number oneberng number o berig (Linimum lm hikess for enere

shf (LSep heigh (L)Lobe lerne (LBeing dmpig oeiens (FTBering dim (L)

ering eenrii (LBering ore in he x nd direions (F )Grviinl elerion ()Film hikess before fe sep enredbering (h = (LBering siess oeiens (F

h h - = - Fm hkness roh Berg lengh (LSp berng il dm lengh relief rkxil leng (L Roo mss ()Sh roionl speed (P) (RPSBering journl pd ener

Rdus of s (ournl (L)Lobe rdius L)

x

X

i bering lod (FJournl posiion in he x nd oordines(LJourl velo i in he x nd oordines(LTJounl aelerion in h nd oordi-nes (TGroove loion (degrees

Pd il ngle (degreesFluid visosi (FT/L)Roor hil fequen (/Journl roionl speed (/Roor iil speed on igid suppor (/TGoove loion (degreesLoion of sep mesured ih roionfrom posiive xxis (degrees Lobe lengh

N-Dimesio Qutities

S

Sbscrits

bdg

x

D i m e n s i o n l d m p i n g o e f i i e n s xx = Cxx(j/W)D i m e n s i o n l s i f n e s s o e f f i i e n s

xx = Kxx(/W

)LL LL S ep bering il dm lenghrio elief rk xil lengh ioPrelod in m ulilobe berigsRoo mss lm/\Renolds number for sep ering

1

7

L

D

(R

) v

Sommeld number

I

:

L

D (R

,S ommefeld number

Bering prmeer

Whirl fequen rio /Roor speed meer Vm/\' Ror sped pee horizonl roor

Rigid roor sbili hreshldFlexible roo sbili hresold

Ose fore/ Bering eenrii io

BeringDmGrooveJounlxiu gniudePd or lobe


21/22

r

x y1

DESG F JOURA BEARGS FOR ROAG CHERY

Rlai o quiliium poiinSpacHozonal and ca dionsBaings 1 and n xrimnal oor


22/22

4 PROCEDGS OF THE TETH TURBOMCHERY SYMPOSUM

t1025-45_ lobe design factors

Documents