Effect of aspect ratio on the performance and stability of Hydrodynamic Journal Bearings

Transcription

1 Efft of ast rato on th rforman stablty of Hydrodynam ournal Barngs anjay harma, K wasth Dartmnt of Mhanal Engnrng, hr Mata Vashno Dv Unvrsty Katra, Inda Dartmnt of Mhanal Engnrng, Bant ollg of Engnrng Thnology, Gurdasur, Punjab, Inda rtl Info rtl hstory: vd anuary 6 vd n rvsd form Fbruary 6 td Marh 6 valabl onln un 6 Kywords Hydrodynam ournal Barng, FEM, st ato bstrat Th uros of ths ar s to thortally study th fft of ast rato on th rforman of flud-flm barng systm.basd uon th dynam ynolds govrnng quaton for th dffrnt ast rato, th varous rforman aramtrs: ntrty rato, maxmum rssur, offnt of frton, mnmum flm thknss, atttud angl, drt ross-ould stffnss damng offnts, thrshold sd, whrl-frquny rato rtal mass of hydrodynam journal barngs ar valuatd. Th ast ratos () ar onsdrd.,.. for th analyss of uros. Th nflun of rato on barng rforman aramtrs for a wd rang of omrfld numbr has bn rsntd. Th rsults ould b usful to gv mor nsght to barng dsgnr for rdtng a sutabl rato for nhand stabl barng oratons.. Introduton Hydrodynam journal barng ar usful n rotatng mahnry for suortng radal loads. Ths barngs allow for transmsson of larg loads at man sd of rotaton ar sustbl to larg amltud latral vbraton du to slf xtd nstablty whh s known as ol whrl or synhronous whrl. Undr rtan unxtd dsturbans th barng systm s ron to an osllatng bhavor. If th amltud of osllaton grows too muh, t may aus th undsrd journal-barng ontat ndangr saf oraton of th whol mahn systm. Th mortant aramtrs suh as surfa roughnss, flud nrta, rhology of lubrant barng sz (ast rato) gomtry may hav an nflun on barng rforman ts stablty. Many rsarhrs [-9] hav thortally nvstgatd th rforman stablty of hydrodynam journal barngs. Owng to varous nflunng fators Zhang, t al. [] onsdrd th fft of rato sl on th stablty analyss of gas-lubratd journal barng n mro-ltro-mhanal systms (MEM). Das, t al. [] usd frst ordr rturbaton for orrsondng uthor, E-maladdrss:sanjufrnd@gmal.om; awasth.rka@gmal.om ll rghts rsrvd: htt:// dynam haratrsts of hydrodynam barng wth rst to mroolar rorty for varyng ntrty ratos ratos. Osman, t al. [] studd th stat dynam haratrsts of th magntzd journal barngs lubratd wth frrofluds. By usng fnt rturbaton thnqu, th ght-ol flm stffnss damng offnts wr dtrmnd wth rato as.. Zhang, t al. [4] dtrmnd th stffnss offnt of hydrodynam lan journal barngs lubratd wth watr. Th rlatonsh btwn th stffnss offnts th load for barng wth dffrnt rlatv laran, dffrnt ratos dffrnt rotatonal sd ar obt. nghal Khonsar [] nvstgatd th stablty of a journal barng systm, nludng th ffts of nlt vsosty. mlfd thrmo-hydrodynam dsgn harts for th rad rdton of stffnss offnts, damng offnts, thrshold sd hav bn dvlod. ang Yoon [6] rsntd analytal mthod to nvstgat th stablty of a hydro dynam journal barng wth rotatng hrrngbon groovs. Th dynam offnts of th hydro dynam journal barng ar alulatd usng th FEM rturbaton mthod. harma Krshna [7] onsdrd th fft of rato on th dynam rforman haratrsts stablty of twolob rssur dam barng. Dwvd, t al. [8] thortally 96

2 omutd th stat dynam rforman aramtrs of hydrodynam barng onsdrng short barng aroxmaton ast rato ( <.) undr dffrnt flow rgm. Mhta, t al. [9] analysd th stat dynam rforman aramtrs of a four-lob rssur-dam barng whh s rodud by nororatng two rssur dams on th ur two lobs two lobs two rlftraks on th lowr two lobs of an ordnary four- lob barng wth rato as. study of barng dynams s mortant for nhanng smooth barng lf. n undrstng on how barng sz (ast rato) nfluns barng rforman n artular barng dynams s stll not bn fully rvald. Th urrnt study has bn undrtakn wth th objtv of through undrstng about th rol of ast rato on stat, dynam stablty ast of flud-flm journal barng. Thus th urrnt study rsnts th nflun of ast rato on barng rforman for a wd rang of sommrfld numbr.. Thory Th onvntonal ynolds quaton for an nomrssbl, wtonan lubrant n th laran sa of a fnt journal barng systm s gvn blow n non-dmnsonal form as [6]: h h h h Th onvntonal ynolds Eq. () s solvd usng FEM, whh s dsrbd blow.. FEM Formulaton Th wghtd rsdual of Eq. () usng Galrkn s rtra may b xrssd as [6]: h h h h dd whr rssurs () () s th ntrolaton funton rlatng th nodal j to th rssur n th th lmnt of th dsrtzd rssur fld of fnt lmnts,.., n j j j () whr j s th lmntal sha funton n numbr of nods r lmnt of two-dmnsonal flow-fld dsrtzd soluton doman. Wth smlfatons, Eqs. () () gv th lmnt Eq. as [6]: F n n n Q n H n x X n z Z n (4) whr For an x th z ar th journal ntr vloty. lmnt, th lmnts of th abov matrs ar dfnd as follows [6]: F Q j H X Z whr n h j j d d h h h l md h d d l. m s () (6) (7) os d d (8) sn d d (9) ar th drtons osns, j, Th assmbly of Eq. (4) ovr th ntr doman of rssur fld rsults n global lnar quatons F Q x H X z Z () nvolvng two sts of nodal varabls, th rssur th flow Q.. Boundary ondtons Th boundary ondton usd for th soluton of lubrant flow fld ar dsrbd as:, at P () Eq. () an b solvd to gv both rssur flow 97

3 smultanously baus at ah nod on of th two varabls s known. Fg. shows th oordnat th shmat of a sml lan journal barng n a stady-stat onfguraton. Th stat rforman haratrsts ar omutd for th stady-stat ondton,.., x z. For th omutaton of rforman haratrsts, t s ssntal to stablsh th journal ntr qulbrum oston for a gvn vrtal load. Th soluton ross s xrssd n flow hart shown n fg.. F x F z ar omutd usng Eqs. () (4), rstvly..4 Load arryng aaty ( F ) Flud-flm raton omonnts along drtons ar rstvly gvn by [, ] F x () os d d F z (4) sn d d Thn, th rsultant flud-flm raton s xrssd as F F z x F () X Z. omnal Mnmum Flud-Flm Thknss ( Usng th omutd journal ntr oordnats ( Z h mn X ) ), th mnmum flud-flm thknss [4, ] ntrty rato ar omutd from th xrssons gvn blow: h h X os Z sn (6) Th ntrty rato s gvn by X (7) Z.6 ommrfld umbr Fg.. Dfnton of th oordnat th shmat of a sml lan journal barng.. ournal ntr Equlbrum Poston For a gvn vrtal xtrnal load W o or ntrty rato oratng gomtr aramtrs of th barng, X, Z th journal ntr oston ( ) s unqu. Ths journal ntr qulbrum oston s not known a ror s obt tratvly. For a sfd vrtal xtrnal load ( W o ), whh ats aralll to th Z-axs whn th journal ntr ous ts qulbrum ostons, th fludflm raton omonnts must satsfy th followng ondtons [6]. F F x W () z o Intally th tntatv valus of journal ntr oordnats ( X, Z ) ar fd as nut to omut th nomnal fludflm thknss ( h ) that s rqurd for th omutaton of flud-flm rssurs. Th flud-flm raton omonnts Th haratrsts n stady runnng of a journal barng of sfd dsgn ar usually xrssd non-dmnsonally as funtons of a sngl aramtr alld th ommrfld umbr [].Th ommrfld umbr an b dtrmnd as: L D (8) W.7 tttud ngl ( ) Th angl btwn th ln jonng barng, journal ntr load ln s dfnd as atttud angl. Th atttud angl, s alulatd by [6]: tan X Z (9) For dffrnt ostons of journal ntr, th xrssons to th atttud angl wll b dffrnt..8 Frton owr loss ( P L ) 98

4 Th owr loss/ torqu n a journal barng s omutd from th followng quaton [6]: P L whr n h d h () s th normalzd turbulnt outt sharng strss. journal barng systm has two dgrs of frdom to dfn th journal oston durng ts osllaton. onsdrng two dgrs of frdom systm, x flud-flm stffnss x flud-flm damng offnts an b omutd usng th xrssons gvn blow..9 Flud-Flm tffnss offnts Th flud-flm stffnss offnts ar dfnd as [6]: F j, ( q Whr, drton of for. q x, z ) () drton of journal ntr dslamnt ( q x, z ). tffnss offnt matrx wll b Fx x Fz x Fx z Fz z (). Flud-Flm Damng offnts Th flud-flm damng offnts ar dfnd as [6]: q j x, z F, ( x, z q ) () rrsnts th vloty omonnt of journal ntr ( ). Damng offnts matrx s gvn by:. rtal mass Fx x Fz x Fx z Fz z Th non-dmnsonal rtal mass xrssd as [6]: G (4) M of th journal s M () G G Whr, G G G,. Thrshold sd Th sd of journal at th thrshold of nstablty, an b obt by [, 6]: M th (6) F o Whr, F s th rsultant flud-flm for or raton h t. journal barng systm s asymtotally stabl whn th journal mass mass M (.. whn M s lss than th rtal M M ). Lkws, a systm s asymtotally stabl whn th oratng sd of th journal s lss than th thrshold sd (.. whn th ).. Whrl frquny rato Whrl frquny rato an b xrssd n smlfd form as [, 6]: K whrl M whrl (7) Whr, K K s xrssd as: Th lowr th valu of whrl, th hghr wll b stablty. Th ngatv valu of whrl mls th absn of th whrl. Th smulatd data for non dmnsonal barng rforman aramtrs hav bn gnratd lottd to gan undrstng. Th rsults hav bn dsussd n th followng aragrahs.. sult Dsusson Th rsnt rsults for hydrodynam journal barng as shown n fg. shows th varaton of ntrty rato wth rst to ommrfld numbr for varyng rato. Fgur shows that th barng wth rato of. has hghr ntrty rato than othr ratos. It s obsrvd that th nras n rato dras th ntrty rato (. nrass th load aaty). Th 99

5 Entrty rato(є) smlar rduton trnd n th valu of ntrty rato was rortd n rf. [8, ] E s lss orrsondng to rato quals to., ndat bttr stablty. ommrfld umbr () Fg. : Entrty rato vrsus ommrfld numbr Fg. 4 shows th varaton of maxmum rssur wth rst to ommrfld numbr for varyng rato. Fgur shows that th barng wth rato of. has hghr maxmum rssur than othr ratos. It s obsrvd that th valu of maxmum rssur for a sfd ommrfld numbr drass wth th nrass n rato. Th smlar rduton trnd n th valu of maxmum rssur was rortd n rf. []. Fg. shows th varaton of mnmum flud-flm thknss wth rst to ommrfld numbr for varyng rato. It s obsrvd that th valu of mnmum flud-flm thknss for a sfd ommrfld numbr nrass wth th nrass n rato. Th rduton n th valu of flud-flm thknss s qut sgnfant at lowr rato of.. Th smlar rduton trnd n th valu of h mn was rortd n rf. [8, 9] Th varaton of atttud angl wth rst to ommrfld numbr for dffrnt valus of ratos, s shown n Fg.6. tttud angl nrass wth nrass n ommrfld numbr rato. Fgur also shows that th hang n th valus of atttud angl at rato of. has mor varaton wth othr ratos. Th smlar trnd n th valu of atttud angl was rortd n n rf. [7,8]. Th varaton of frton offnt wth rst to ommrfld numbr for varyng rato s shown n fg.7 Frton offnt s nrasd wth nrasng rato. Th bhavor of offnt of frton wth dffrnt ratos s smlar as n rf.[9,]. Th rsults shows, that thr s judous nd to slt otmal rato from th vw ont of frtonal owr loss load arryng aaty of flud flm journal barng. Fgur 8, 9 shows th rsults for dmnsonlss drt stffnss offnt aramtrs ( ) wth rst to ommrfld numbr. Th barng onfguraton quals to.,... Th drt flud-flm stffnss offnts as shown n fg.8 fg.9 shows a drasng trnd wth an nras n rato. Th bhavor of drt flud-flm stffnss offnts wth dffrnt ratos s smlar as n rf.[8,]. Th fg.9 ndats that for sam valu of xtrnal vrtal load, th vrtal dformaton n flud-flm Fg. : Ovrall soluton shm

6 tttud angl (ɸ) tffnss Paramtr () Mnmum flm thknss (h mn ) tffnss Paramtr () Maxmum rssur (P max ) offnt of frton (f) ommrfld umbr () ommrfld umbr ()... Fg.4 : Maxmum rssur vrsus ommrfld numbr ommrfld umbr () Fg. : Mnmum flud-flm thknss vrsus ommrfld numbr Fg. 6: tttud angl vrsus ommrfld numbr.. L/ D. L/ D. L/ 4 ommrfld umbr () D. Fg. 7: offnt of frton vrsus ommrfld numbr ommrfld umbr () Fg. 8: Drt flud-flm stffnss offnt vrsus ommrfld numbr... Fg.9: Drt flud-flm stffnss offnt vrsus ommrfld numbr ommrfld umbr () l

7 tffnss Paramtr () Damng Paramtr () tffnss Paramtr () Damng Paramtr () Fgur, shows th rsults for dmnsonlss ross ould flud-flm stffnss offnt ( wth rst to ommrfld numbr. Th barng onfguraton quals to.,... Th dmnsonlss valu of ross ould flud-flm stffnss offnts, as shown n fg nrass wth an nras n rato Th dmnsonlss valu of ross ould flud-flm stffnss offnts ) as shown n fg drass wth nras n rato. Th ross ould flud-flm stffnss offnt trnd. shows ngatv Th smlar trnd n th valu of ross ould flud-flm stffnss offnts n rf. [8,] was rortd 4 ommrfld umbr () Fg. : ross-ould flud-flm stffnss offnt vrsus ommrfld numbr ommrfld umbr () Fg. : ross-ould flud-flm stffnss offnt vrsus ommrfld numbr Fgur shows th rsults for drt dmnsonlss damng offnt aramtrs( ) wth rst to ommrfld numbr.th barng onfguraton quals to.,...th drt dmnsonlss damng offnt aramtrs as shown n fg. fg. shows an nrasng trnd wth an nras n rato. Th valu of drt flud-flm damng offnts s onstant at lowr valu of ommrfld numbr drass wth an nras n th valu of ommfld numbr. Th bhavor of dmnsonlss damng offnt aramtrs wth dffrnt ratos s smlar as n rf. [8, ]. Fg.: Drt flud-flm damng offnt vrsus 4 ommrfld umbr () ommrfld numbr Fg. : Drt flud-flm damng offnt vrsus ommrfld numbr Fgur 4 shows th rsults for ross ould flud-flm dmnsonlss damng offnt aramtrs ( ) wth rst to ommrfld numbr. Th barng onfguraton quals to.,... Th ross ould flud-flm dmnsonlss damng offnt aramtrs as shown n fg.4 shows a drasng trnd wth an nras n rato shows ngatv bhavor. Th bhavor of ross ould flud ommrfld umbr ()...

8 Whrl Frquny ato (ω whrl ) rtal Mass Paramtr(m r ) Damng Paramtr () Thrshold sd (ω th ) flm dmnsonlss damng offnts wth dffrnt ratos s smlar as n rf. [8,] ommrfld umbr () Fg. 4: ross-ould flud-flm damng offnt vrsus ommrfld numbr Varaton of th whrl frquny rato wth ommrfld numbr wth ratos.,.. rstvly s shown n fg.. It s obsrvd that th whrl rato rmans onstant at hghr ratos drasng xonntally wth th nras n ommrfld numbr, whh ndats bttr stablty from th vw ont of whrl moton. It an b sn that th whrlng frquny rato quals to. at all ast rato. Th smlar trnd n th valu of whrl rato aramtr was rortd n rf. []. Fg.6 shows varaton of th stablty thrshold sd wth rst to ommrfld numbr wth ratos.,.. rstvly. Th valu of stablty thrshold sd s nrasd wth dras n rato. Ths s du to th varaton n th valu of rssur gradnts hangs, hn th valu of barng dynam offnt gts altrd. Thus, th barng stablty thrshold sd margn s xtd to hang. Th smlar trnd n th valu of thrshold sd aramtr was rortd n rf. [7] Fg.. Whrl rato vrsus ommrfld numbr... 4 ommrfld umbr () Fg.6. Thrshold sd vrsus ommrfld numbr Fg.7 rtal mass aramtr vrsus ommrfld numbr Fg.7 shows rtal mass aramtr, whh s also an ndator of stablty of hydrodynam journal barngs. Th lowr ur sds of ah urv orrsond to stabl unstabl rgons, rstvly. It s obsrvd that th stablty of hydrodynam journal barngs dtrorats wth an nras n rato. Th smlar trnd n th valu of rtal mass aramtr was rortd n n rf. [7, 8]. 4. onlusons. 4 ommrfld umbr () tabl. 4 ommrfld umbr ()... Ths study nvstgats th fft of ast rato on th rforman of hydrodynam barngs. Basd on rsults, followng onlusons an b drawn for a lan rular hydrodynam barng. ) Th mnmum flud- flm thknss, atttud angl, offnt of frton,, damng offnt (, ) nrass wth nras n rato. ) Th ntrty rato, maxmum rssur, drt stffnss offnt,, rtal mass aramtr drass wth nrass n rato. ) Th valu of thrshold sd s nrass wth dras n rato. 4) Th whrlng frquny rato s ndndnt of rato always quals to or aroxmat to.. Th hgh-frquny whrlng frquny rato

9 s drasng xonntally wth th nras n ommrfld numbr. ) Th stablty of hydrodynam journal barngs dtrorats wth an nras n rato. omnlatur Dmnsonal Paramtrs : adal laran, mm j D : Flud-flm damng offnts (.mm - : ournal damtr, mm : ournal ntrty, mm : ntrty rato, / F : Flud-flm raton ( F x, F z h L M, O B O j M h t, j x, z ), : Flud-flm raton omonnts n X Y drton ( h t ), : omnal flud-flm thknss, mm : Barng lngth, mm : rtal mass Mass of journal, Kg : otatonal sd, rm : ntr of th barng : ntr of th journal : Prssur,.mm - s : frn rssur,.mm - ( r r / ) : adal oordnat, : adus of journal barng, mm j b, j x, z ),.mm - W W x o : ommrfld umbr : Flud-flm stffnss offnts ( : Tm, s : load aaty, : Extrnal load, : rumfrntal oordnat : xal oordnat y X, Z : ournal ntr oordnat X Y, Z, : artsan oordnat systm : oordnat along flm thknss Grk Lttrs : Lubrant vsosty, Pa. s z : Dnsty, Kg.m - : ngular oordnat, rad : tttud angl, rad th : Thrshold sd, rad.s - : Whrl frquny, rad-s - whrl.. on-dmnsonal Paramtrs ), j F x, F z h h mn L, max j t W o j 4 r ( F, F x z s j ) h h mn ( s ) ( L, max ) s j s t s W o s X, Z ) ( X, Z ) ( r / ( X, Z ) ( X, Z) / L, th D whrl x, y) ( st rato th whrl Matrs F Q r s, d aramtr ssmbld Fludty Matrx, odal rssur Vtor, odal Flow Vtor, H olumn Vtors du to hydrodynam trms,, Global rght h sd vtors du X Z to journal ntr lnar vlots. ubsrts ursrt b max mn : Barng : ournal : Maxmum valu : Mnmum valu 4

10 x,y,z : omonnts n X, Y Z drtons. : Frst drvatv w.r.t. tm frns [] Zhang WM, BnZhou Mng, Prforman stablty analyss of gas-lubratd journal barngs n MEM, Trbology Intrnatonal ;44: [] Das, Guha K hattoadhyay K, Lnar stablty analyss of hydrodynam journal barngs undr mroolar lubraton, Trbology Intrnatonal ;8:-7. [] Osman T, ada G afar Z, tat dynam haratrsts of magntzd journal barngs lubratd wth frroflud, Trbology Intrnatonal ;4:69-8. [4] Zhang X, Yn Z, Gao G ZhngL, Dtrmnaton of stffnss offnts of hydrodynam watr-lubratd lan journal barngs, Trbology Intrnatonal ;8:7-47. [] nghal Khonsar MM, smlfd Thrmohydrodnam atblty nalyss of ournal Barngs Pro., IMhE ;9:-4. [6] ang GH Yoon W, tablty analyss of a Hydrodynam journal Barng wth otatng Hrrngbon Groovs ME r. of Trbology ;:9-. [7] harma Krshna M, Efft of ato on th Prforman of Two-Lob Prssur Dam Barng: Mroolar Lubratd, dvans n Trbology ; -7. [8] Dwvd VK, h, Py K, Efft of dffrnt flow rgm on th stat dynam rforman aramtr of hydrodynam barng, Proda Engnrng ;:-8. [9] Mhta P, attan, Bhushan G, tat dynam haratrsts of four-lob rssur-dam barngs, Trbology Lttrs ; :4. [] mth DM, ournal Barng n Turbo mahnry, haman Hall Ltd 969. [] Baluar,Valdaton of Fnt Elmnt Program For ournal Barngs tat Dynam Prorts-Thss, Unvrsty of Kntuky 4. [] harma, h an, Prforman haratrsts of Extrnally Prssurzd Orf omnsatd Flxbl ournal Barng, TLE Trbology Transaton 99;4: [] harma, Kumar V, an, nhasan ubramanan M, tudy of lot-entry Hydrostat/Hybrd ournal Barng usng th Fnt Elmnt Mthod, Trbology Intrnatonal 999;:8-96. [4] harma, an ddy MM, study of on-rssd Hybrd Flxbl ournal Barng wth Dffrnt strtors, TLE Trbology Transaton ;44():-7. [] hrawat H nhasan, tudy of tady tat Transnt Prforman haratrsts of Flxbl hll ournal Barng, Trbology Intrnatonal 988;:7-48. [6] wasth K, Th nflun of war runnng-n on flud-flm journal barng systm -Thss, Dartmnt of mhanal ndustral ngnrng,indan nsttut of thnology roork, Inda 6.