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  • 7/26/2019 Zhou Cheng




    n J. Sne

    hief ngineer

    entritech ororation

    ouston exas

    Dana J Salamone received his B S inMechanical Engineerin in 14 and hisM S in Applied Mechanics in 1 both

    from the University of Virinia He alsoarned an MB A rom Houston Baptistniversity in 184

    He pent the rst three years o hisnineerin career a Babcock and Wlox, in Lynchbur, Virinia, where hewas responsible or seismic structuralesin, stress analysis, and rotor dynam

    ics analysis He spent two years as a Projec Enineer in theCompressor Division o AllisChalmers Corporation in ilwaukee, Wisconsin He was responsible or roor dynamicsanalysis o multistae central compressor and - initeelement tress analysis o horizontallysplit abricated casins

    r Salamone became Chie Enineer or Cenriech Corporation in Houson, Texas, in 1 He is a Bearin Desinerand Consultant to the utility, peroeum an cemical inusties or the soun o urbomachinery vibration problem

    He has several publications on rotor dynamics withASE , the Turbomachinery Symposium and the VibrationIntiute

    Mr Salamone is a member o ASE ASLE he VibrationInstitute, and the National Society o Proessional EnineersHe is an associate member o Sima Xi and a reisteredprofessional enineer in the State o Texas

    ABTATA review of several dierent types of hydrodynamic jour

    nal bearings that are commonly found n turbomachinery ispresented Emphasis is placed on the key geometric designparameters of each type The discussion covers plain journalaxial groove pressure dam oset splt lemon bore multlobeand titling-pad bearings

    The application of the critical speed map and some basicnon-dimensional bearing parameters as tools for preliminarybearing selection and comparison are dscusse These toolsare applied to two case studies which demonstrate the properapplcation of diferent bearing designs to industrialturbomachnery

    INTOTIONIndustral turbomachinery such as steam turbines gas

    compressors pumps and motors contan a variety of dierenttypes of hydrodynamic journal bearings The types of bearingsmost commonly found in turbomachinery include

    plain cylindrcal axial grove pressure dam lemon bore


    oset pivot three-lobe four-lobe tilting-pad

    The reason for such a large selection of bearngs is tat ac ofthese types has unique operatonal characteristics tat renderit more suitable for one application than anoter [145]

    The ndamental geometric parameters for all ournalbearings are diameter pad arc angle length-to-diametr ratioand runing clearance For the bearing types consisting ofmultple pads there are also variation in the number o padspreload pad pivot oset angle and orientation of te earing

    (on or between pads) In addition to the geometric paretersthere are several important operating parameters e keyoperating parameters are oil viscosity oil density rotatingspeed gravity load at the bearin and applied externl loadsVolute loads in pumps and mesh loads in gear boxs areexamples of external loads

    The plain journal bearing shown in Figure 1 is t mostbasic hydrodynamic journal bearing As the name imlis thisbearing has a plain cylndrical bore A shaft rotating in plainjournal bearing is illustrated in Fgure The eccentric rotatingsha wll develop an oil lm pressure prole as shon in thegure If ths pressure prole is ntegrated around th aringa net resisting force to oppose the imposed load rsultsThe postion at which there s a balance between the iposedload and the hdrodynamic force is called the eqlirum

    position The shaft ecentrcity e is te distanc beten thedisplaced shaft at equilibriu and te bearing center Inhoriontal turbomachinery the imposed bearing loads re dueto the gravitational weight of the rotor In addition to thegravity load there can be external bearing loads as preiouslymentioned

    Fiure 1 Plain Journal earin

    The four axial groove journal bearing [6 7] illstrted inFigure 3, is another variation of a plain journal bearin Thisdesign incorporates four axial grooves 90 apart c arenormally located at 45 degrees from te vertical axis This

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    180 OD O OY YO

    design is more stable tan te plain journal bearing for someapplications [6].


    o' C

    o H


    M U p

    igure 2. Hyroynamic Bearin Pressure Prle.

    Fiure FourAxial Groove ournal Bearin

    e pressure dam journal bearing [8 9 10] is sown inFigure 4 is bearing is also similar to te plain bearing

    except tat it incorporates a circumferential relief scallop witdept d in te top alf. e relief ends abruptly in a step atsome angle from te orizontal split line as sown in tegure. e pressure dierential before and after te stepcreates a net loading tat forces te journal down into tebottom alf of te bearing and can signicantly increase stability [8]. Anoter variation of tis bearing incorporates a circumerential relief groove in te bottom alf. is groovereduces te unit area of te bearing and terefore increases thebearin unit loading.

    e bearing designs described could be classied as variations of te plain journal bearing because te babbitt bore is

    Fiure 4 Pressure Dam Journal Bearin

    concentric wit te journal wen te journal is centered in tebearing. e rest of te bearing designs to be discussed aremore complex because tey consist of two bores (te bearingset bore and te pd macines bore. e combination of teseo bores determines a non-dimensional parameter known aspreload. A bearing pad wit a macined bore radius Rp centered at O and a set bore radius Rh centerd at te truebering center O is sown in Figure 5. IfO is coincident witO ten Rp = Rh and te preload is zero. In tis case if tejoural is centered in te bearing te pad arc will be concentric wit te journal surface. If te pad bore is larger tan teset bore te centers of curvature will be oset as sown in tegure. e set bore radius is te distnce from te true bearingcenter to te pad surface at te point of minimum clearancefrom te centered saft. e set bore radius can also bedescribed as te radius of te largest mandrel tat could beinserted into te assembled bearing. If te pad macined boreis eld at a xed value te preload is increased by moving tepad radially inward toward te s. e extreme value ofpreload results wen te pad contacts te saft. In tis condition te set clearance is zero and te preload is unity. Preloadforces te oil to converge at eac pad because of te reducedclearance at te mid point of te pad were te clearancesized mandrel would make contact. e result is an oil wedge


    Fiure 5 Bearin Preloa





    Cb Rb Rj

    M , - -b , PRELOADp

    e lemon bore (elliptical bearing [] is a two-pad-xedgeometry bearing wic is preloaded in the vertical directionas sown in Figure 6. is bearing can be manufactured byinserting a sim in te split line before born. Wen te simis removed te vertical clearance w be less tan te orizontal clearance. ote tat te centers f curvature of te top andbottom alves are not coincident it te rue bearing centerin te gure.

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    O O O O 181

    Figure 6. Lemon BoreJornal Bearing.

    The oset spt bearing [11] is shown in Figure 7. Thisbearing is preloaded in the horiontal direction. It is manufactured by osetting the halves before nish boring such thatwhen the halves are matched the pad centers will be oriontally oset. In this bearng the horiontal clearance is smallerthan the vertical clarance. The vertical clearance equals thepad machined clearance. The horiontal diametral clearance isequal to the pad machined diametral clearance minus twicethe radial oset.

    Figure. Offset Split Jornal Bearing.

    Three-lobe (Figure 8 and four-lobe (Figure 9) bearingsbelong to a class of bearing called multiobe bearings[11, 12,13, 14, 15, 16]. These bearings are similar in concept tothe lemon bore bearings (i.e. there is a separate pad machinedbore and bearing set bore). Note that the centers of pad ac foreach of the lobes form a circle referred to as a preload circle.herefore a wide range of preloads is possible by changing thepad and set bores.

    Figure8 Three-obe Journl Bearng.

    Figure For-oe Journal Bearing.

    Up to this point the discussion has addresse severalstyles of xed geometry or xed pad bearings. Eac o thesebearings has specic avantages in dierent applications butthey all have a characteristic calle cross-couple stiesswhich creates an out-of-phase force to the displacemnt ancouples the equations of motion for the lateral egrees ofeedom. Under certain conditions this cross-copling cancause the bearing to be unstable and an oil whirl ill rsult.

    The tilting-pad journal bearing [17,18,19,20,1,2,23]consists of several individual journal pads which can pivot inthe bore of a retainer. The tilting pad is like a mltilobebearing with pivoting lobes o pads. The same conept ofpreload applies to the tiltig-pad bering. The pas hae amachined bore and these pads can be set into a retiner toachieve a particular bearing set bore. The primary avantage ofthis design is that each pad can pivot independently to velopits own pressure prole. This independent pivoting aturesignicantly reduces the cross-couple stiess. In ct if padpitch inertia is neglectd and the bearing is symmetri aboutthe vertical axis the cross-couled stiffness terms areeliminated [17]. The number o pads tilied in the tiltng-padbearing can be three four ve or seven. However te mostcommo tilting-pad bearing arrangements have fr or vepads. The rocker pivot and the spherical pivot arrangmentsare illustrated in Figures 1 and 11, respectively. The rockerdesign has a line-contat pivot beteen the pa nd thebearing retainer. As the name implies the spherical esign hasa semispherical surface-contact pivot. Both of these esignsallow the pads to pitch in the conventional manner. oeverthe spherical design has the additional ability to accommodatesha misalignment.

    Figure 10 Rocker Pivot Tilting-Pad Journal Bearing.

    EY EIGN PAAETEThe discussion of preloa broht out the istinction

    between two dierent bearing bores Tese are a mchined

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    18 OD O OY YO

    Figre11. Spheical Pivot TiltingPad ornal Beang.

    bore and bearing set bore ote that the plain journal axialgroove and pressure dam bearings have only one bore (the setbore is the same as the pad bore The dierence between thepad machined bore radius and the journal radius is the padmachined clearance The dierence between the bearing setbore radius and journal radius is the bearing set clearance Theset clearance is the same as the running clearance which isoften specied as a clearance ratio of mils (milli-inches perinch of journal diameter Some typical values of clearance ratio

    are between 15 to 0 mils/in Obviously there are someapplications where these values do not apply The manufacturer will speci the recommended clearances for the particularbearing application

    Slenderness ratio is also referred to as D ratio This isthe ratio of the bearing length to the sht diameter This ratiotypically varies between 0 and 10 However some plainjournal bearings have slenderness ratios above 1 0 The bearing length aects the stiess and damping characteristics ofthe bearing In the selection of a bearing length one mustconsider the bearing unit loading The unit load is the bearingload divided by the product of the bearing length and the shdiameer therefore the units are psi Typical values of unitloading are between 150 and 50 psi

    NAPE ITIAL PEE APAn example of a typical critical speed map for a rotor

    supported between two bearings is depicted in Figure 1 Thisis a plot of the undamped critical speeds as a nction of thebearing stiess The map illustrates the eect of bearingstiess on the rotor critical speeds In the exible bearingregion the shaft is sti relative to the bearings Thereforebearing stiness can signicantly aect the critical speedsbecause the criticals increase as the bearing stiness is increased In the sti bearing region the critical speeds becomeasymptotic to an upper limit as which the bearings are rigidrelative to the rotor shaft Hence they are called the rigidbearing critical speeds

    In order to control sh dynamics a designer must selecta bearing with stiess and damping qualities that are compat

    ible with the rotor If the bearings are too sti the eectiveness of the bearing damping will be limited regardless ofthe theoretical damping coecient value Three undampedcritical speed curves are shown on the map in Figure 1 Thesemodes are the rst three natural equencies of the rotorbearing system

    The combination of dierent bearing types geometriesand imposed operating conditions provides a broad selection ofdierent stiess and damping properties Therefore somebearings will be better than others for a particular applicationWhen the actual bearing stiness is plotted on the criticalspeed map the intersections indicate the undamped critical






    Figre 12. Typical Undamped Citical Speed Map.

    speeds It should be noted that the stiess of an actualhydrodynamic bearing is a complex quantity

    K=K+i (1where the subscripts u and v denote the principal lateral

    directions x or yThe real term K is the stiess coecient The imaginaryterm c is the product of the damping coecient and theangular speed Therefore the undamped critical speeds fromthe map are only an approximation of the actual dampedcritical speeds


    In addition to the critical speed map the designer can usesome basic non-dimensional quantities to compare dierentbearing designs The relationships presented here were developed by Barrett Gunter and Allaire[4] based on thesingle-mass rotor The single-mass rotor on damped elasticbearings is illustrated in Figure 13 This model commonlyreferred to as te Jecott model [5] has been equently usedby researchers to investigate rotor dynamic behavior Thesebasic single-mass rotor relationships can then be applied asapproximations to determine complex industrial rotor characteristics provided that the major masses of the complex rotorsuch as wheels are mounted between the bearings and provided there is a relatively symmetric mass distribution

    L 2

    Figre 1. SingleMass Rotor.

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    O O O O 183

    Te eective s stiess can be calculated from the-

    igid bearin critical speed and te modal mass of te rotor byusing te equation:

    s = Wcr mwee Wcr = te igid bearing critical speed (rad/sec

    = te eective sa stiess (lb/in


    m = te rotor modal mass on rigid supports(lb-sec/inapproximatelywrotor12g

    Te total critical bearing damping can also be calculated

    Ccr = mWcrTe stiess ratio [4] is te total bearing stiess divided

    by te rotor stiess or:

    K = bl + bwere b and K are te stiness for eac of the bearings. Itis recommended tat tis atio be limited to six or less.

    Te damping ratio [4] is te total actual bearing dampingdivided by the total critical damping or:

    act = Cbl + Cbz/Ccrwhee bl and b are te damping values for eac of te

    bearings. Te optimum damping ratio can be approximatedom te stiess ratio as:

    opt = (1 + K /Tese ratios can be calculated for bot te oriontal and

    vertical directions. However te gravitational roto load normally causes te bearing stiess to be ige in te eticaldirection tan in te horiontal direction. Tus the verticalstiess is usually most important.

    Two case studies will be presented in order to demonstrate the application of tese bearing design concepts. Itshould be empasied tat te rules of tumb and designcriteria applied here are not universal-design rules tat applyin all cases. They are simply guidelines tat can assist tedesigner in the pursuit of te optimum bearing design.

    AE TIESeven-Stage Centifgal Compesso

    A seven-stage centifugal compesso as sown in Figure14, wic ad exibited ig vibration in te eld gured inte rst case. Tis was a 1942 lb rotor wit a 744 in bearingspan. Te rotor was supported in two 3.6 in diameter journalbearings. A critical speed map for the compressor showing test three modes is depicted in Figure 15. Note tat te rigidbeaing critical was 3685 rpm and the opeating speed was69 rpm. Also note te atness of te rst mode curve wichis typical of a long exible rotor. Te stiess of this saft isonly 37 X 1 lb/in.

    Fige 14 Seven-Stage Centgal Compesso

    HIR MO

    SCO MO


    IRS MO

    1 -




    Fige 15 Undamped Citical Speed Map fo Seve-StageCentgal Compesso.

    Te original bearing design sown in Figure 16, was adouble-land plain cylindrical journal bearing wic consistedof a pair of .0 in lands. Therefore te slendeess U ratioof eac land is 0.55. Te diametral bearing clearance range was6 to 8.0 mils whic represents 1.6 to mils per inc ofjournal diameter (an 80 mil clearance will be assumed in this

    Fige16 Doble-and Plain Cylindical jonal Beaing.

    case. As sown in Table 1, tese bearings ad an acceptablestiess ratio of 36, but te logaritmic decrement value of41 indicates tat te rotor was unstable. Te data measured on te macine conrmed tat tis instability predictionwas correct. In an attempt to increase stability tese bearings were modied to a pessure dam design. A pressure da and arelief groove wee cut into eac of te lands as sown in igure17 Te reason for modiing bot lands is not known but itcould ave been simply to preserve symmetry. Te damwidts were475 percent of eac land widt te radial clearance in te dam step was 4.5 times te bearing radial clearance te dam angle was 13 degrees om te split line andthe relief tack widths wee 21 percent of eac land widt. Tismodication did improve te rotor stability to a marginally

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    Figure 17. Dule-ad Pressure Dam Bearig

    Tale1 Bearig Stfess ad Dampig Ratis fr Seve-StageCetrifugal Cmpressr






    AINJURNA 3.6


    I A




    - UNAB



    stable logarithmic decrement value of +0. 13. However theresulting bearing stiness was too high as indicated by thestiess ratio of 14.6 in Table 1. The critical speed map alsoindicated this problem because the vertical stiess wasshown to ntersect the rst mode curve in the rigid bearing region Therefore the pressure dam modication wasunacceptable

    Based upon the previous discussion two major objectivesneeded to be met in considering a design alternative First thebearing stiess had to be reduced to the exible bearingrange and the rotor stability needed improvement Thesecriteria were met with the ve shoe tilting-pad bearing conversion shown in Figures 18 19 and 20. The new design had 2.5in pads 25 percent preload 6. 0 mil diametral set clearanceand load-between-pad orientation With these redesignedbearings the stiess ratio ws reduced to5. 8 and the logarithmic decrement was increased to a very stable value o +0. 45.The resulting horiontal and vertical stiess curves for thenal tilting-pad bearing design are shown in Figure 15. Sincethe bearing retrot this compressor has been opeating successlly in a renery for several years

    18,000 Hrsepwer Steam Turie

    A two-stage 18,000 horsepower steam turbine shown inFigure 21 was the principle gure in case number two [26.This was a 913 l rotor wich was operated at 1,30 rpmOriginally the rotor was supported by two 4. 0 in diameter

    tilting-pad joural bearings conssting of ve rocker-pvotshoes with a length of 1. 6 in preload of 0. 0, and load-on-padorientation

    igure 18 New Tiltig-Pa Jural Bearig Hardware rlet Ed f Cmpressr Jural Pad Remved t ShwSpherical Pivt

    Figure19 New Tiltig-Pad Jural ad Thrust Bearig Hard ware fr Discharge Ed f CmpressrView it Tp Ha

    Figure 20 New Jural ad Thrust Bearig Hardware frCmpressr Active ad iactive thust earigs i fregrud shw d irected luricati zzle mald s etweethe pad s

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    O O O O 185

    Figue 21 18,000 HP Steam Tubine.

    In te plant tis rotor ad exibited sycronous vibratio amplitudes as ig as 5.0 mils at te bearings. Tis level ofvibration is unaccetable; particularly wen a typical 40 inbearing as a diametral operating clearance of oly 6.0 to 8.0mils. ese ig vibration amplitdes yielded oticable distress in te bearing babbitt linig. Tis babbitt fatigue failure isillustrated in Figures and 3. Oe of te bearigs sowed

    Figue22 Oiginal iltinga ournal eang or urbinePad s have babbitt fatigue amage

    igure23 Original iltinga ournal earing Note aifatigue d amage towad one end of beaing which ind icatesmisaligment

    babbitt fatigue in four out of ve pads. e fatigue toard oneed of te bearing in Figure 3 indicated a possible misalignmet condition.

    An undamed citical speed map sowing te orizontalad vertical stiesses for te origina tilting-pad jornal bearings assuming a diametral running (set clearance of 7.0 mils issown in Figre 4. Te gure sos tat te orizontalstess line intersects te tid mode curve at te runningspeed. Terefore te undamped criticl speed ma indicated

    a potential critical speed proble. In ddition to tese problems tere was suspicion of bearing sell looseness de totermal case distortions.

    R BRG B/

    BRG KY

    - - - ORG IG BRIG

    - W IIG BRIG

    X = HOROY = VRC

    Figure 24 Undampe Citical Speed Map for TwoStage

    Steam Tubine Showing Oiginal and ew Beaing Stnesses

    I order to illustrate te dirent caracterstics tat canbe obtained for various bearing geometries te rbine criticalspeed map containing speositions of te vertical rincipalstiess crves for eigt dierent bearing designs is presentedin Figure 5. Tese eigt bearings ere elected only forillustation puposes. Nuerous geometic combinations areossible for eac bearing type. Tis ilustration emasizes teimportance of rotor dynamics optimization tecnqes as abasis for seecting te best bearing desgn from te large realof possibilities. All of te bearigs referred to n Figure 5 ave4.0 in journal diaeters slenderness ratios (D of 1.0 anddiaetral rning clearances o 0.006 nces. Te lbicantligt tbine oil was ISO 3 ad e bearing load was 450 lb.

    Te plain and axial groove bearings are sel explanatory.Te pressure dam bearing as a radil earance in te dastep tat is 3.0 ties te radial bearing clearce [8]; te damwidt is 80 percet of te bearing widt; te dam angle is 135degrees om te split lne; and tere is no relief groove in tebotto alf. Te lemo bore bearing s a 50 ercent reloadad te oset bearing as a 50 pecent oset. Te tilting-padbearing as ve soes 80 percent preload nd load-betweenpad orientation.

    Te nal bearing design ardware is son in Fige ad 7. Te ew desig is also a ve pad tilting-ad bearngbut e pad legt is iceased by 56 ercnt te reload is

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    Figre 25 Undamped Critical Speed Map of Two-Stage Trbine howing Comparison of Stfnesses for Derent earingDesigns

    igre 26. New Tilting-Pa ornal earing Harware orTrbine ornal pa is remove to show spherical pivot

    increased by 50 percent and orientation is canged to oadbetween-pads Te new bearing oi stiness in botdirections was greater as te rotor speed increased as indicated in Figure 4 Terefore te tird undaped criticaspeed was raised because te bearing stiess curves weresied relative to te tird ode curve of te rotor A coparison of te stiess and daping ratios for te origina andnew bearing designs is presented in Tabe Note tat teoriginal and new designs ave te sae vertica stiess anddaping ratios at te rst rigid critica speed even toug tenew design is uc stir at iger speeds Tese new designcaracteristics were obtained sipy by canging te geoetric paraeters of te titing-pad bearing

    Te sperica pivots beind te pads f te new bearingare sown in Figure 6. Tis pivot arrangeent eped accoodate isaignent Te new design aso incuded integraspring-oaded pads on te outside of te bearing se as

    sown in Figure 7 ese pads sef-adjust to od te setigt witin te case Since te bearing retrot te easuredvibration at te bearings is less tan 10 mi

    igre2 New earing Harwreor Trine pnglodepad is remove from otsid e of shell to show belleville springarrangement

    Table2 earing Stiness an Damping Ratios for Two-Stage

    Steam Trbine







    16 13 09 69

    16 13 0.9 69


    AA review of a nuber of ydrodynaic bearing types and

    two case studies were presented to iustrate bearing appications to industria turbomacinery e concusions reaced intese case studies regarding preference of one bearing typeover anoter soud not be overy generaied For exapein case nuber one te odication of te pain bearing to apressure da bearing was an unacceptabe aternative for tisparticuar acine It is iportant to note tat te addition of apressure da to a pain journa bearing design as been aneconoica cure for any bearing instabiity probes in tepast However te pressure da and reief groove can signicanty aect te stiness and daping of te bearing especiay for a doube-and bearing In tis case te odicationincreased te tota bearing vertica stiness and dapingnear te rst critica speed by 30 percent and 50 percentrespectivey

    In case nuber two te origina bearings were te titingpad type Tis retrot did not require canging te bearingdesign type Instead te new design required a titing-pad

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    O O O O 187

    bearig wit lger pads, larger preload ad lad-betwee-padorietati. Tis gemetry cage produced te same uidlm ertical caracteristics ar te rst critical speed. Howeer, at ter speeds, tese caracteristics were sigicatlydieret. I particular, te icreasig bearig stiess caracteristic at eleated speeds raised te tird critical speed.

    Te case studies illustrate te eectieess of te criticalspeed map ad te stiess and damping ratis as tools tatca assist a desiger i prelimiary bearig selectio. Howe

    er, tese basic tols are oly approximate and tey sould otbe substituted for te more complete ubalace respose[27,28] ad damped stability aalyses [29,30,3].

    EEENEl Allaire, P. E. ad Flack, R. D., "Desig of Jural Bear

    igs fr Rotatig Maciery, roceedings of the TenthTurbomachinery

    Symposu Turbmaciry Labratries, Texas A& Uiersity, College Stati, Texas, pp.25-45 (1981).

    2. Abramitz, S., "Fluid Film Bearigs Fudametals adDesig Criteria ad Pitlls, roceedings of the SixthTurbochinery Symposium Gas Turbie Laboratries,Texas A&M Uiersity (1977).

    3. Raimdi, A. A. ad Byd, J., "A Sluti r te FiiteJoural Bearig ad Its Applicati t Aalysis ad Desig I, II, I, ASLE (1957).

    4. Lud, J. W., "Rotr-Bearig Desig Teclgy; Part III Desig Hadbok for Fluid-Film Bearigs, MecaicalTeclgy Icrprated, Tecical Reprt N. AFAPLT-65-45 (1965).

    5. ippe, H. C., "Cast Brnze Bearig DesigMaal,"

    Cast Broze Bearig Istitute, Ic. (1971).

    6. Eirma, R. G., "Stability Aalysis ad Trasiet tif Axial Gre, Multilbe ad Tiltig Pad Bearigs,M.S. Tesis, Uiersity of Virgiia


    7. Adams, M. L., "Axial-Grooe Joural Bearigs, MachineDesign pp. 120-123 (April 1970).8. Niclas, J. C. ad Allaire, P. E.,"Aalysis f StepJoural

    BearigsFiite Legt, Stability, Tras. ASLE (2),pp. 197-207 (1980).

    9. Niclas,J. C., Allaire, P. E. ad Lewis, D. W.,"Stiessad Dampig Ceciets r Fiite Legt Step JouralBearigs, Tras. ASLE, (4), pp. 353-362 (1980).

    10. Allair, P. E., Niclas,J. C. ad Barrett, L. E.,"Aalysisof Step Jural BearigsInfiite Legt, Iertia Effects, Tras. ASLE, (4), pp. 33-341 (1979).

    11. Lud, J. W. ad Tmse, K K "A Calculati Metdad Data for te Dyamic Coeiciets of Oil-Lubricat dJural Bearigs, Topcs in Fluid Film Bearings andRotor Bearing System Design and Optimization ASEBok N. 100118, pp. 1-28 (1978).

    12. Kirk, R. G., "Te Iuece f Maufacturig Tleraceo Multi-Lbe Bearig Permace i Turbomaciery,Topics in Fluid Film Bearing and Rotor Bearing SystemDesgn and Optimization ASME Book N. 100118, pp.108-129 (1978).

    13. Falkeage, G. L., Guter, E. J. ad Sculler, F. T.,"Stability ad Trasiet Moti of a Vertical Tree-LbeBearig System, Jural f Egieerig fr Idustry,Tras. ASE, Series B, (2), pp. 665-677 (1972).

    14. Falkag, G. L., "Stability ad Transiet Motion of aHydrdyamic Horizotal Tree-obe Bearig System,Te Sock ad Vibratio Digest, (5) (1975).

    15. Lud, J. W., "Rotor-Bearig Dynamics Desig Tecology, Part VI: Te Tree-Lobe Bearig ad Floatig igBearig, Mecaical Tecology ncorporated, T chicaprt No. AFAPL-TR-64-45 (1968).

    16. Pikus, 0, "Aalysis ad Caracteristics f te TreeLbe Bearig, Joural of Basic Egieerig, Tras.ASME, pp. 49-55 (1959).

    17. Lud, J. W., "Sprig ad Damping Coeiciets for teTiltig-Pad Joural Bearig, Tras. ASLE, (4), pp. 342-352 (194).

    18. Nicolas,J. C., Gunter, E. J. ad llaire, P. E., "Stiessad Dampig Coeciets for te Fie Pad Tiltig PadBearig, Trans. ASLE, (2), pp. 113-124 (1979).

    19. Sapiro, . ad Colser, R., "Dynamic Caracteristics fFluid-Film Bearings, roceedings of the Sxth Turbochinery Symposium Gas Turbine Laboratories, TexasA&M Uiersity, College Statio, Texas (1977).

    20. Jes, G. J. ad Marti, F. A., "Geometry Eects iTiltig-Pad Jural Bearigs, ASE Preprit N. 78-AM-

    2A-2 (1978).21. Ettles, C. M. McC., "Te Aalysis ad Perrmace of

    Pioted Pad Joural Bearigs Considerig Termal andElastic Eects,Joural f Lubricatio Tecology, Tras.ASME, ASME Paper N. 79-LUB-31 (1979).

    22. Abdul-Waed, M. N., Free, J. and Nicolas, D., "Analysis of Fitted Partial Arc ad


    Jural Bearings,ASLE Preprit No. 78-AM-2A-3 (1978).

    23. aimdi, A. A. ad Boyd, J.,"A alysis of te PiotedPad Jural Bearig, Mecaical Egieering, p. 380-386 (193).

    24. Barrett, L. E., Guter, E. J. ad Allaire, P. E., "ptimm Bearig ad

    Support Dampig fr Ubalace Respse ad Stability of tatig Machi ry," Journal of

    Egieerig fr Poer, Tras. ASME, (1), pp. 89-94(1978).

    25. Jett, H. H., "Te Lateral Vibratio of Loaded Sas inte Neigbrood of a irlig SpeedTe Eect ofWat f Balace, Pil. Mag., Series 6, p. 304 (1919).

    26. Salame, D. J., "Bearig eplacmts for Turbomaciery, VbrationInstituteroceedingsMachineryVibration Monitoring and Analsis pp. 57-60 (April1981).

    27. Lud, J. . ad Orcutt, F K "Calculatios and xperimets o te Ubalace espose of a Flexible otor,Jural of Egieerig fr Idustry, Tras. ASME, SeriesB, (4), pp. 785-796 (1967).

    28. Salame, D. J. ad Guter, E. J., "Eects f Saftarpad Disk Skew o te Sycronous Ubalace Responseof a Multimass Flexible otor in Fluid Film Bearings,Topics in Fluid Film Bearing and Rotor Bearing SysemDesign

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    29. Guter, E. J., "Dyamic Stability of tor-Baring Systems, NASA SP-1 13, Oce of Tecnical Utilization, U.S.Goermet Pritig Oce, asigto D.C. (196).

    30. Lud, J. ., "Stability ad Damped Critical Speeds of alexible otor i Fluid Bearings, Joural of Engineerngfr Idustry, Tras. ASME, Series B, :2, pp. 509-517(1974).

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    31. Gunter E. J. and rumler P. R. "e Inuence ofInternal Friction on te Stabilty of ig Seed Rotorswit Anisotroic Suorts Journal of Engineering forndustry rans. ASME Series B 4 . 1105-118(1969.

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    Bernard S Herage s Presdent andTechncal Drector of C entrtech C orporaton He s a regstered professonal engneer n the State of Texas Hereceved h s B.S M degree fromBradley Unversty where he was also amemer of the honorary fraternty ofengneers Ta Sgma

    The frst ten years of Mr Herage'sengneerng career were spent wth AllsChalmersnne years of whch were n

    the Mechancal Desgn Secton of the Steam Trne and argeGenerator Department and then one year as Spervsoryngneer n the Research Dvson d evelopng new proctsDrng ths perod Mr Herage concentrated a consderale

    amont of hs tme n the d esgn applcaton and testng ofhgh capacty thst and ornal eargs

    Aftr hs AllsChalmes experence he contned t prse hs nterest n ld lm Bearngs y movng to WakeshaBearngs Coporaton workng n vaos postons as Chengneer General Manager and VePredent Thee heworked wth vrally every maor hgh speed rotatng machnery manfactrer n the d esgn and aplcaton of lmthst and ornal earngs

    Centrtech Coporaton fonde n 171, s a hghlysccessfl growth orentated compay specalzng thed esgn and manfactre of d fl earngs d lmseals and layrnth seals wth emphass on endser problemsovng of tromachnery often reqng the applcatonof nhose rotor d ynamc capalty

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