f Analyss for th Man barng of Arcraft Engns Png n a, Xaolng Zhang a, png H a, anglang Dng a a School of Mchancs, Elctronc, and Industral Engnrng, Unvrsty of Elctronc Scnc and Tchnology of Chna, Chngdu, Chna Emal: lpngh@ustc.du.cn ABSTRACT: f of man barngs n a arcraft ngn drctly affcts th rlablty, safty and fasblty of arcraft ngns. In ordr to optmz and mprov th prformanc of th xstng arcraft ngns, as wll mt th nds of a nw gnraton of arcraft ngns, ths papr analyss and stmat of man barng s lf of arcraft ngns by takng th dp groov ball barng as an xampl. Frstly, th D modl of dp groov ball barngs s stablshd by usng Pro-E softwar and thn convrtd nto a fnt lmnt modl. Scondly, such faturs as stffnss, strngth and fatgu lf of th dp groov ball barng ar nvstgatd by ANSYS softwar, whch rsult n som thortcal ar dscusson and som rlvant masurs that nabl mprovng th srvc lf of man barngs of th arcraft ngn. Kywords: arcraft ngns, dp groov ball barng, srvc lf, rlablty, fnt lmnt analyss. INTRODUCTION Th barng of man shaft s a major componnt of arcraft ngn. Wth th dvlopmnt of arcraft ngns, th dmand of workng condton has bn ncrasng rapdly. Snc lf and rlablty of man barng drctly affct th lf and rlablty of th ngn, falurs of man barng would lad to dsastrous consquncs. As th loadng support and movmnt connctng componnt, barng can transform th sldng frcton nto th rollng frcton. So man barng plays a vtal rol n th arcraft ngn, t s opratng tmpratur s 00 C, th valu of DN (barng damtr (mm) spd (r/mn)) s largr than 2. 0 6. Manwhl, as th ngn barng unt, arcraft ngn man barng also bar th statc load, th axal concntrcty causd by statc and dynamc load, manuvrng load, stady vbraton load, rotor hot bndng, th comprssor dynamc load, tmpratur load and so on. As th ky componnt of th arcraft ngn, ts advancd rsarch and dvlopmnt has bn concrnd n hom and abroad. Such as NASA of Amrca, t bgan a "spd barng rsarch and dvlopmnt program n th 959[2]. But w hav a larg gap n th rsarch of man barng of arcraft ngn, spcally n th dsgn. In ordr to mt th nds of arcraft dvlopmnt, w should dvlop and apply advancd dsgn and analyss tchnqus of barng. Accordng to study of Chn[2],Tang[] and Zhao[4], w tak a n-dpth rsarch about th rcnt progrss of th currnt fnt lmnt analyss mthod for fatgu lf prdcton n ths papr. ot of study has bn don about th lf prdcton of arcraft ngn n th world. In th prsnt papr, w tak th dp groov ball barngs as an xampl, whch manly composd of outr rng, cag, Probablstc Safty Assssmnt and Managmnt PSAM 2, Jun 204, Honolulu, Hawa
rollng lmnts and nnr rng. Snc fatgu falur gnrally dos not occur on th rtanr, th barng lf s manly dcdd by th lf of th outr rng, nnr rng and rollng lmnts. Accordng to th undbrg-palmgrn barng lf thory, th lf of th barng outr rng, nnr rng and rollng lmnts ar a srs of random numbrs subjctd to Wbull dstrbuton. So th lf of barng can b stmatd through th lf of th barng outr rng, nnr rng and a rollng lmnt.th man work of th prsnt papr shown as follows: () In scton 2, w ntroducd th basc thory and modls for fatgu lf prdcton of th dp groov ball barng, and analyzd th basc procdur of fatgu lf prdcton. (2) Establshd paramtrc modl and loadd th approprat boundary condtons by usng th statc analyss modul of ANSYS, thn obtand th barng strss and dformaton undr statc load. () Got th fatgu lf of th dp groov ball barng wth fatgu modul of ANSYS, and compard t wth th thory valu n th nd, and proposd a srs of masurs to mprov th barng s lf. 2. COMPUTATIONA BASIS OF MAIN BEARING MODEING Fatgu lf of rollng barngs s whn th rar barng starts runnng, ncludng any part on th nnr and outr rng or rollng, bfor matral fatgu causd by th damag, th total numbr of barng rotaton or a fw hours. Contact fatgu s th major falur mod of rollng barng, so fatgu lf s an mportant ndcator of barng s dsgn and applcaton. Th xprnc shows that th -P modl s smpl and has a suffcnt accuracy for th barng lf assssmnt. Thus w us t to calculat th fatgu lf n ths papr. For th partcular barng matrals, th gratr spac of strss and mor cycls can mak th matral fatgu falur probablty ncrasng, thrfor gvs th followng mprcal formula: ln S () c 0 NV h Z0 Whr 0 s th maxmum altrnatng shar strss; Z 0 s th maxmum dpth of altrnatng shar strss s locatd; c,, h ar dtrmnd by th ndx data barng tst V s th volum by strss. Assum that th wdth of contact llps strss valu 2a, dpth Z 0, th racway lngth s l, thn w obtan V az l (2) Manwhl, th numbr of strss cycls s proportonal to th fatgu lf,.. N In th cas of pont contact, wth th Hrtz thory of lastc rollng contact, thr xsts a () Tak Eq. (), (4), (5) nto Eq. 0 (4) 0 Z0 (5) Probablstc Safty Assssmnt and Managmnt PSAM 2, Jun 204, Honolulu, Hawa
ch2 ln (6) S Whr s rollng load Whn a crtan barng s gvn, S s a constant probablty of survval, w can gt: ch2 =constant (7) If c dscrbd as th rollng loads (.., rollng dynamc load ratng) whn = (.., runnng on mllon rvolutons), thn gt: In cas of ln contact, w gt ch2 ch2 c (8) c ch2 (9) 2 0 (0) Consdrng that th rollr s lngth s qual to a, w gt Z0 2 () Tak Eq. (0), () nto th Eq. (2) c c ch2 2 P (2) () Whr for th pont contact P ( c h 2) for th ln contact P ( c h 2) 2 Whr P s dtrmnd by th xprmntal data. and P =, so c Eq. (4) s th basc formula for fatgu lf calculaton of th dp groov ball barng Th fatgu lf of nnr and outr rngs can b dscrbd as c (5) c (4) (6) Whr c c ar nnr and outr rngs of th dynamc load ratng ar nnr and outr rngs of th contact load ratng Th fatgu lf of th barng s th ntrscton of th fatgu lf of nnr and outr rng. Probablstc Safty Assssmnt and Managmnt PSAM 2, Jun 204, Honolulu, Hawa N w b w w, j=,2,, Nb (7) j j
Whr w s th Wbull slop and w 0 / 9 In th Eq. (7), w only consdr th fatgu damag of th nnr and outr rngs. In th actual projct, rollng fatgu spall also accountd for a consdrabl proporton. Thrfor, t s ncssary to consdr th mpact of fatgu lf for rollng lmnt barng. Rollng lmnts wth th nnr and outr contact fatgu lf can b dscrbd as b b (8) b Whn consdrng th mpact of rollng lmnts, barng fatgu lf can b dscrbd as Whr, b (9) N w b w w w w b b,(,2,, b) (20) j j j N ar th fatgu lf of th nnr and outr rng. b, b ar th fatgu lf of th rollng lmnts contact wth th nnr and outr rng. Th calculaton procss for fatgu lf, s shown as Fgur. start start Boundary condtons nnr matral paramtrs Structural paramtrs Outr matral paramtrs Innr dynamc load ratng Outr dynamc load ratng Innr rng quvalnt load Innr rng ratd load Outr rng ratd load Outr rng quvalnt load Barng nnr lf Barng outr lf Barng lf End Fgur Th calculaton procss of man barng s fatgu lf. CONSTRUCTION OF FINITE EEMENT MODE Fnt lmnt mthod s a way that taks th contnuous gomtry nto fnt numbr unts, whch st a fnt numbr of nods n ach unt. As th succssv body s rgardd as a st of unts aggrgats whch connctd only n nod, w can convrt contnuous nfnt dgrs of frdom nto a fnt Probablstc Safty Assssmnt and Managmnt PSAM 2, Jun 204, Honolulu, Hawa
dscrt-dof doman, ths way wll gratly smplfy th problm... Dscrptons of fnt lmnt modls. A thr-dmnsonal modl Usng Pro/E stablsh th dp groov ball barng 627 D modl, th outr damtr D s 50mm, damtr d s 85mm, th thcknss s 28mm. And mport t nto ANSYS workbnch softwar moduls. W can s Fgur 2. 2. Dfnton of matral proprts Aftr mportng th sold modls of dp groov ball barng succssfully, w dfn matral proprts and choos th lastc modulus (2.07 0Pa)and Posson's rato (0.).. Mshng Usng fr msh, nnr and outr rngs of th grd cll sz of 2mm, rfnng th grd of dffrnt lvls to th contact ara, th grd rollng contact ara s mor rfnd than th nnr, outr rng racway grd. W can s Fgur. Fgur 2 D modl Fgur Fnt lmnt modl 4. Contact pars To stablsh th contact btwn nnr rng racway, outr rng racway and th rollng lmnts, dtrmn th nnr and outr rng racway and rollng lmnts ar flxbl contact, th outr rng racway surfac and th nnr rng racway surfac ar th targt surfac, th rollng lmnt surfac as th contact surfac. Contact lmnt typ as th nod contanng ght nods quadrlatral lmnt CONTA 74. Targt surfac contact lmnt typ as thr-nod whch hav no-mddl-nod unt TARGEl70, In ach pck up on, st rollng wth th nnr and outr racway frcton coffcnt MU = 0.00, normal contact stffnss factor FKN = 0., th ntal nar factor ICONT = 0.0. Each contact wth th rollng lmnt and nnr and outr rngs, crat two contact pars. Thr ar 0 rollng lmnts, cratd 20 pars of contacts rght. In ordr to nsur th accuracy of th calculaton and rduc th amount of calculaton, th occurrnc of th contact ara may us a dnsr mshng styl; th modl conssts of,42 lmnts and 26,97 nods, shown as Fgur..2. Dtrmnaton of boundary condton. Impos boundary condtons () Smulaton barng sat: Constrant all frdom dgrs of th outr surfac of th barng outr Probablstc Safty Assssmnt and Managmnt PSAM 2, Jun 204, Honolulu, Hawa
rng; (2) Smulaton th rtanr: Constrant th crcumfrntal (UY) and axal (UZ) dsplacmnt of all nods n th nutral plan quator of rollng. () Frdom of th nnr surfac of couplng load: Th couplng of all nods on th nnr crcl of th radal surfac (UX) and crcumfrntal (UY) dgrs of frdom. (4) Smulaton flangs: Constrant th UZ dsplacmnt of th sd of th barng rng body. (5) Apply radal load: Applyng a radal nod radal forc s appld n th form of th avrag radal forc to ach nod on a straght ln, can b drctly loadd n th drcton UX. (6) Applyng a cntrfugal forc: Barng rotary nrta forc n ANSYS structural statc analyss can b usd to smulat th dynamc condtons mposd by way of nrtal load ) Add Rotatonal Vlocty, th Dfn By opton nto Componnt. 2) Th actual angular vlocty s appld n th global Cartsan Z-axs. 2. Solvng st () Tm-stp control: Analyss Sttngs undr Statc Structural, th Numbr of Stps to stp 8. (2) Analyss of control: Contact analyss du to th larg local stran, w choos larg dsplacmnt statc, and opn th lnar sarch. 4. APPICATION OF IFE PREDICTION FOR MAIN BEARINGS 4.. Fnt lmnt analyss Consdrng th mpact of th numbr of rollng lmnts, th rollng lmnt damtr and groov curvatur coffcnt, to gt rsult of th contact strss bfor th fnt lmnt analyss of barng lf. Thn analyss th varous factors on th barng contact strss and dformaton, study for th nxt stp varous factors affctng barng lf and mprov barng lf masurs provd an mportant bass for th analyss and th analytcal rsults mor rasonabl. W gt th concluson as followng: () Th maxmum quvalnt strss and quvalnt stran occurrd n th radal forc at th bottom ln s contact pont, that s man barng th rsk of fatgu damag part s th rollng lmnt and racway contact ponts. And th shap of th contact ara s approxmatly llps. (2) Maxmum rollng contact strss occurs n th radal forc bnath ln whr rollng contact wth th racway. () Ovrall radal dsplacmnt occurs whr th nnr rng bar th radal load. 4.. Rsults and Its Analyss Fgur 4 shows th ffct of th numbr of rollng lmnt barngs for barng contact strss and dformaton curvs. Th damtr of th rollng lmnt barngs can b sn D w = 6.5, th nnr and outr groov curvatur coffcnts wr f 0.505 and f 0.5. Fgur 5 shows th ffct of th damtr of rollng lmnt barngs for barng contact strss and dformaton curvs. As th numbr of ts rollng s 0, th nnr and outr groov th curvatur coffcnts wr f 0.505 and f 0.5. Fgur 6 shows th ffct of th nnr and outr groov curvatur coffcnt of rollng barngs for Probablstc Safty Assssmnt and Managmnt PSAM 2, Jun 204, Honolulu, Hawa
barng contact strss and dformaton curvs. Th numbr of rollng barngs n = 0, th damtr of th rollng lmnt barng D w = 6.5mm, dffrnc n coffcnt of curvatur of th nnr and outr groov f f 0.005. Accordng to th fgurs and data w obtand abov, w can know th rsults as follows:. Aftr gttng a dp groov ball barngs, w know that th outr contact ara s approxmatly llptcal, th contact ara of th contact strss dstrbuton; th nnr and outr rac on contact strss wll dcras whn th numbr of rollng ncras, th nnr and outr rac on contact strss wll dcras whn th rollng damtr ncras, th nnr and outr rac on contact strss dcras whn nnr and outr curvatur coffcnt s f 0.5, f 0.55 ;and ts wll ncras whn f 0.5, f 0.55. 2. Th radal dformaton wll dcras whn th numbr of rollng ncras and th rollng damtr ncras, but t wll ncras whn th nnr and outr curvatur coffcnt ncras. Fgur 4 Th mpact undr th chang of th numbr of rollng lmnts Fgur 5 Th mpact of th chang of th rollng damtr Probablstc Safty Assssmnt and Managmnt PSAM 2, Jun 204, Honolulu, Hawa
Fgur 6 Th chang of th curvatur coffcnt of nnr and outr rac 4.2. Fatgu lf analyss In trms of numrcal smulaton of th fatgu lf,th artcl wll consdr th ffct of th numbr of rollng of barngs, rollng damtr and curvatur coffcnt of nnr and outr rac and othr factors, and us th nomnal strss mthod for fatgu lf of dp groov ball batng through numrcal smulaton. Wth th hlp of ANSYS softwar fatgu analyss modul, th fatgu lf of barng s smulatd, and th nflunc dscpln of varous factors on th batng fatgu lf s obtand, th rsults wth th thortcal fatgu lf of -P rsults ar compard, and dscuss dffrnc rason btwn th two rsults;fnally t propos th tchncal masurs to mprov barng lf.w also gt th dagram whch dscrbs th changs of th fatgu lf of th barng. Th rsults show that th fatgu dangrous parts of dp groov ball barngs appars at th contact pont of btwn rollng unts and racway;barngs fatgu lf wll ncras whn th numbr of rollng ncras, fatgu lf wll ncras whn rollng damtr ncras, fatgu lf wll ncras whn nnr and outr curvatur coffcnt s f 0.5, f 0.55, and t wll dcras whn f 0.5, f 0.55. Smulaton mthod of fatgu lf for dp groov ball barng can calculat th complx workng condtons of barng and th fatgu lf prdcton has a hgh rlablty. Fgur 7 th chang of th fatgu lf Probablstc Safty Assssmnt and Managmnt PSAM 2, Jun 204, Honolulu, Hawa
4.. Masurs to mprov th fatgu lf for barngs Basd on th analyss abov and rfrncs [8]-[2], n ordr to mprov th fatgu lf of dp groov ball barngs, th followng stps can b usd n th dsgn.. An ncras of th numbr of rollng lmnts Whn ncras th numbr of rollng lmnts, ach rollng lmnt xposd th radal load s dcras, th contact load for ach rollng lmnt s also smallr, so fatgu lf of mprov. 2. An ncras of th damtr of th rollng Rollng damtr ncrass, th quvalnt barng structur ncrass barng capacty ncrass, so th rollng lmnt barng lf ncrass wth th damtr ncrasd.. Rasonabl assgnmnt of rollng lmnt and racway contact paramtrs. For dp groov ball barngs, nnr groov curvatur coffcnt f 0.52, outr groov curvatur coffcnt of th barng f 0.5. It should also b notd btwn f and f matchs. In addton, you can also rduc th ptch damtr of th barng, th barng dos not slp undr th prms of guarantd mnmz prload, at hgh spd, rollng cramc matral nstad of stl matrals. 5. CONCUSION. Th rsults ndcat that th outr contact ara of th dp groov ball barngs s approxmatly llptcal, also th contact strss dstrbuton of th contact ara s obtand. Bsds, w also gt th concluson that th nnr and outr rac on contact strss wll dcras whn th numbr of rollng ncras, th nnr and outr rac on contact strss wll dcras whn th rollng damtr ncras, th nnr and outr rac on contact strss dcras whn nnr and outr curvatur coffcnt s f 0.5, f 0.55,and t wll ncras whn f 0.5, f 0.55. 2. Th radal dformaton wll dcras whn th rollng numbr and th rollng damtr ncras, but t wll ncras whn th nnr and outr curvatur coffcnt ncras. Th rsults of th smulaton of th fatgu lf ndcat that th fatgu dangrous parts of dp groov ball barngs appars at th contact pont of btwn rollng unts and racway, barngs fatgu lf wll ncras whn th rollng numbr ncras, fatgu lf wll ncras whn rollng damtr ncras, fatgu lf wll ncras whn nnr and outr curvatur coffcnt s f 0.5, f 0.55, and t wll dcras whn f 0.5, f 0.55.Th smulaton mthod of fatgu lf for dp groov ball barng can smulat th complx workng condtons of barng and has a hgh rlablty for fatgu lf prdcton. In ordr to shortn th tst cycl, rduc cost and mprov th accuracy of lf prdcton, th numrcal smulaton mthod usd to smulat th fatgu lf of th barng calculaton n prsnt papr s vry ffctv. Acknowldgmnts Probablstc Safty Assssmnt and Managmnt PSAM 2, Jun 204, Honolulu, Hawa
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