Journal of Chemical and Pharmaceutical Research, 2014, 6(7): Research Article

Transcription

1 Avalabl onln Journal of Chmcal and Pharmacutcal Rsarch, 214, 6(7): Rsarch Artcl ISSN : COEN(USA) : JCPRC5 Rsarch on fatgu damag of suckr rod basd on damag mchancs Ru-fn Zhou, Mng-x Fng, Mn-zhng Jang and Kang-xng ong Mchancal Scnc and Engnrng Collg, Northast Ptrolum Unvrsty, aqng, Hlongang, Chna ABSTRACT Fatgu falur of suckr rod can occur undr th ffct of altrnatng load, and rsults n falur of suckr rod. In ths papr, th damag mchancs thory s appld to th fatgu damag of suckr rod on th study, stablsh th fatgu damag voluton quaton of suckr rod, and th damag mchancs-fnt lmnt mthod s adoptd to solv fatgu damag of suckr rod, obtan chang law of strss fld, stran fld and fatgu damag fld of suckr rod, and carry out fatgu damag cycls of suckr rod. Th study has a crtan thortcal sgnfcanc and practcal sgnfcanc on th ratonal us of suckr rod, th dcras of suckr rod fractur accdnt and th mprovmnt of ovrall conomc bnfts n olfld dvlopmnt. Kywords: suckr rod; damag mchancs; falur; fnt lmnt INTROUCTION Undr th altrnatng load for a long tm, coupld wth borhol lqud corroson and up-and-down opraton, th suckr rod wll fractur, whch mak th rod strng can't work normally. In th fractur accdnt of suckr rod, falur s causd by fatgu damag fractur, and fractur occurs mostly n suckr rod upsttng sgmnt and thradd conncton scton[1,2]. Th study of suckr rod fatgu damag s start wth mtallography[3]. At prsnt, th rsarchrs tnd to adopt th mthod of fractur mchancs to study fatgu damag lf of mtal matrals and componnts. Th dfcts ar quvalnt to cracks n fractur mchancs, and study propagaton ruls of cracks undr th altrnatng load, thr ar a larg numbr of dsprsd mcro dfcts nsd th ngnrng matral, damag wll gradually b volvd undr th acton of xtrnal factors(such as xtrnal forc, tmpratur). Cntralzd dvlopmnt of th damag lads to dstructon of th matral, macroscopc dfcts (such as cracks) wll b formd vntually. Aftr th formaton of macroscopc dfcts, mcrocosmc dfcts wll b volvd contnually, and promot th dvlopmnt of macroscopc dfcts. In th xpanson procss th rgon nar th macroscopc cracks s th hghly concntratd ara of macroscopc dfcts[4,5]. Th man rsarch obct of damag mchancs s dsprsd dvlopng voluton of mcrocosmc dfcts nsd th ngnrng matral, whras fractur mchancs gnors th damag stag whch s bfor th formaton of macroscopc cracks, th damag around macroscopc cracks s also gnord, consdrng only th dal macroscopc dfcts. In vw of th fact that fractur damag of pumpng wll suckr rod s srous, usng damag mchancs thory to rsarch th fatgu damag of suckr rod, whch has a vtal sgnfcanc on th ratonal us of suckr rod, th dcras of suckr rod fractur accdnt, th lowr producton costs of ol producton and th mprovmnt of ovrall conomc bnfts n olfld dvlopmnt[6]. THEORETICAL ANALYSIS SECTION In th procss of suckr rod damag analyss, th frst stp s to slct approprat damag varabl and dtrmn ts voluton quaton, and thn consttut damag dfnt soluton or varatonal problm of suckr rod wth th condton of qulbrum, gomtry and physcs, and us fnt lmnt dscrt structur to solv strss, stran fld and damag fld of suckr rod, fnally, accordng to th crtcal condton of damag, udg th damag dgr of suckr rod and ts saf workng lmts. 1394

2 Ru-fn Zhou t al J. Chm. Pharm. Rs., 214, 6(7): Blow s th couplng thory of fatgu damag of suckr rod. Th basc quatons of th thory ar as follows: Gomtrc Equaton Rlatonshp btwn small dformaton dsplacmnt and stran s statd by th followng quaton: ε 1 u u = + 2 x x (1) whr u s an quaton of dsplacmnt componnt, and ε s a rang of stran componnt. Equlbrum Equaton Undr th condton of small dformaton, th rlatonshp btwn stran and body forc s dfnd as x + B = (2) whr s a rang of strss componnt, and B s a rang of body forc. Consttutv Rlaton For damagd matrals, th rlatonshp btwn strss and stran s xprssd as ( 1 ) = C ε (3) kl kl whr C kl s lastc constant, and s damag dgr of mtallc matral, whch s rgard as a scalar, th rang of damag dgr s from to 1. amag Evoluton Equaton Equvalnt strss s dfnd as 3 = ss (4) 2 whr s s strss dvator componnt, ts valu s 1 s = δδ rs rs (5) 3 Accordng to damag voluton quaton of unaxal loadng, th damag voluton quaton of suckr rod can b xprssd as d α 1 1 q ( ) ( p 1) 2 p 2 2 p 1 2 (.5 β )(2 p = R + + 2) M + (1 ) + + (6) P+ P+ dn p + 1 (2 E) 1 ( ) whr N s cycl numbr, R s strss rato, M s quvalnt strss whn matrals bars th maxmum load, s strss thrshold whn matrals s wthout ntal damag, E s Young's modulus of matrals, β, α, p ar th paramtr of damag mchancs of matrals, whch ar dtrmnd by th curv of fatgu proprts of matrals. Whn damag mchancs mthod s appld to solv th problm of fatgu, thr wll b two problms. On s to analyz strss fld, dsplacmnt fld and stran fld of suckr rod whn th damag fld s known; th othr s to analyz damag voluton fld and stmat lf of cracks whn strss fld and damag fld ar known. Bcaus of th complxty of suckr rod, t s dffcult to calculat th damag of suckr rod and stmat th dgr of damag as a whol. Consquntly, th fnt lmnt mthod whch dsprss suckr rod modl to many unts and calculats 1395

3 Ru-fn Zhou t al J. Chm. Pharm. Rs., 214, 6(7): strss fld and stran fld s adoptd, ths s undrstandabl also for calculatng th damag of vry unts, th damag procss of suckr rod s smulatd to th damag procss of unts, thus, th lf whch th frst unt damagd s th crack ntaton lf of cracks, th lf whch from th damag of th frst unt to th complt damag of suckr rod s crack propagaton lf. amag mchancs and fnt lmnt mthod ar combnd, and fnt lmnt s utlzd to forcast th lf of suckr rod. Strss Analyss Thory of Known amag Fld Expand quaton (3) to obtan th followng quaton = Cklε kl Cklε kl (7) Supposng that voxl strss s If f thr s no damag, that s = C ε, th quaton (7) may b rwrttn as kl kl + = C ε. kl kl = (8) Puttng quaton (8) n balanc quaton (2), th followng quaton can b obtand x + B + B = (9) whr B s addtonal body forc causd by damag, ts xprsson s B = (1) x Puttng quaton (1) n quaton (7) of statc boundary condtons, th followng quaton can b obtand l p p S ) (11) = + (On th P whr p addtonal surfac forc causd by damag, ts xprsson s p = l (12) For th strss analyss problm whch damag fld s gvn, th quaton (9) and (11) ndcat that th problm can b solvd n no damag crcumstanc wth ntroducng addtonal body forc and addtonal surfac forc. Th Addtonal Load Addtonal Load of Strss Analyss wth Known amag Fld Accordng to strss analyss thory of known damag fld, th fnt lmnt soluton- addtonal load fnt lmnt mthod whch corrspondd wth th thory s gvn. For th dsgnat fnt lmnt, lmnt stran can b xprssd as ε = B (13) { } [ ]{ } whr { ε } s lmnt stran array, { δ } s lmnt nodal dsplacmnt array and [ ] matrx. δ B s lmnt gomtrc From consttutv quaton (9) th lmnt strss can b xprssd as = E B δ + (14) { } [ ][ ]{ } { } whr { } s lmnt strss array, [ E ] s lastc matrx of matral, { } s lmnt strss array causd by damag, that s whr s lmnt damag dgr. { } [ E][ B]{ δ } = (15) 1396

4 Ru-fn Zhou t al J. Chm. Pharm. Rs., 214, 6(7): Accordng to vrtual work prncpl, lmnt nodal forc can b xprssd as whr { f } s lmnt nodal forc array, [ ] xprssd as whr } { f } [ K ]{ } { f } = δ (16) K s lmnt non-damag lastc stffnss matrx, and t can b T [ K ] V [ B] [ E][ B] = (17) V s lmnt volum, { f s lmnt addtonal nodal forc array causd by damag, that s { f } = [ K ]{ δ} (18) If { δ } s ovrall dsplacmnt array, th rlatonshp btwn lmnt dsplacmnt array and ovrall dsplacmnt array can b bult wth th condton of dsplacmnt coordnaton: { δ} = [ A ]{ δ} (19) whr [ A ] s coordnat matrx. Furthr, accordng to vrtual work prncpl, th ovrall forc can b xprssd as { f } = [ K ]{ δ} { f } (2) whr { f } s ovrall forc array, [ K ] s ovrall non-damag lastc stffnss matrx, and t can b xprssd as = (21) [ K ] [ A ] T [ K ][ A ] whr { f } s ovrall addtonal xtrnal forc array, that s T [ f ] ( [ A ] [ K ][ A ]){ δ} = (22) Th followng quaton can b gt from quaton (1) to quaton (2) K δ = f + f (23) Thus, aftr mportng addtonal xtrnal forc array { } [ ]{ } { } { } f, th problm of dsplacmnt analyss whch ts damag fld s gvn, can b translat nto th problm of non-damag dsplacmnt analyss. amag Analyss, Crack Formaton and Propagaton Lf Forcast wth Known Strss Fld If damag dgr of crtcal lmnt ( x) and ts ncrmnt ar xprssd by ( ) and ( ), damag dgr of som lmnt x and ts ncrmnt ar xprssd by ( x) and ( x), th quaton (24) can b obtand accordng to th quaton (6). 2 p+ 2 q( p+ 1) ( ) (1 R) M x 1 x ( x) = ( ) 1 ( x) q (1 ) ( p+ R 1) M 1 p p ( ) ( ) (.5+ β )( 2 p+ 2 ) 2 p+ 2 p ( ) ( ) (.5+ β )( 2 p+ 2 ) (24) d dn s absolut damag voluton rat of lmnt, thn ( d dn ) ( ) If / / 1 s rlatv damag voluton rat of lmnt. In a damag fld, f rlatv damag voluton rat of on lmnt s bggr than rspons valu of all th othrs, thn damag voluton of ths lmnt must b fastst, and ths lmnt s crtcal lmnt. Thrfor, th crtron of crtcal lmnt can b xprssd as [ ] ( ) ( ) ( d / dn ) 1 1 max 1 n (25) whr n s th numbr of lmnt that dvdd by componnt. 1397

5 Ru-fn Zhou t al J. Chm. Pharm. Rs., 214, 6(7): For th vry ncras of crtcal lmnt damag dgr, th cycl numbr of corrspondng load as th followng quaton (26) can b calculat wth quaton (24), ( P+ 1) α 1 1 ( ) ( 1 ) q p+ 2 p+ 2 2 p+ 2 (.5 + β )(2 p+ 2) N = 1 R 2 2 M (1 ) P+ (26) ( p + 1) 2E ( 1 ) that s, whn fatgu cracks growth lf s stmatd, th Calculaton bgns from crack formaton, to obtan th whol damag fld of suckr rod. APL languag s usd to carry out scondary dvlopmnt for ANSYS, th procdur of fatgu damag of suckr rod s wrttn, thn strss fld, stran fld and dsplacmnt fld of suckr rod s obtand on th procss of cyclc loadng, and addtonal load s usd to calculat th damag valu of vry lmnt, th calculatd addtonal forc s addd to strss whch suckr rod bars, damag cycl numbr and fatgu damag law can b obtand wth crculatory calculaton. RESULTS AN ISCUSSION In formng procss of suckr rod, thr wll b dfcts (such as ncluson and mcro cracks) nvtably n suckr rod, consquntly, accordng to basc prncpl of rgd-vscoplastc fnt lmnt mthod, th larg-scal fnt lmnt softwar EFORM-3 s usd to smulat th upsttng formng procss of suckr rod, thn th ntal damag and ntal strss of suckr rod ar obtand, and ths ar for ntal condtons of fatgu damag of suckr rod, to mak fatgu lf forcast of suckr rod mor ralstc. Th Foundng of Fnt Elmnt Modl of Suckr Rod For th common suckr rod CYG19 n ol fld, th lngth of ts had s 18 mm, th gnratd nodal lmnt from EFORM smulaton s as shown n Fg.1. Fg.1 grd chart of suckr rod Th fnton Procss of Ral Constant and Matral Modl By EFORM softwar usd n th unt of lngth s mm, so th unt of lastcty modulus s MPa, th unt of dnsty s tons pr cubc mllmtr. Th lmnt attrbuts n th papr ar adoptd as th followng Tab 1. Tab 1: Constant of suckr rod Elastcty modulus(ex) Posson rato(prxy) nsty (ENS) 2.1E E-9 Th Load Paramtrs of Suckr Rod Th damtr of suckr rod: φ19mm; Th damtr of ol wll pump: φ44mm; Strok: 3m; Strok tm: 6 stroks pr mnut; Mostur contnt:.9; Th lngth of suckr rod: 1m; Submrgnc: 4m; Maxmum load: 37.7kN; Mnmum load: 13.8kN. Th trmnaton Procss of amag Mchancs Paramtr of Suckr Rod Matral Th S-N fatgu curv forφ19 suckr rod s shown n Tab 2. In th tst data, fatgu data t 1 R =.33. K =, strss rato 1398

6 Ru-fn Zhou t al J. Chm. Pharm. Rs., 214, 6(7): Tab 2: th tst data of S-N fatgu curv of suckr rod Proct Th strss thrshold valu for md-valu fatgu curv, of md-valu fatgu curv s ( ) th paramtrs p and max MP ( a ) N(pr) E E E E E+7 = 231MP, th coordnat away from th farthst pont thm a 498,8, and β =.5. Accordng to th offrd xprmntal data ponts, K m ar fttd by th last squars mthod: p =.644, K m = Furthr calculatd: 14 m =.7175, K = , = , α = On nd of suckr rod s fxd and th othr nd s loadd, n on strok th strss nphogram and th damag nphogram of suckr rod can b obtand by th calculaton mthod of transnt nonlnar, th nphograms ar shown n Fg.2 and Fg.3. As shown n Fg.2, th maxmum quvalnt strss of suckr rod occurs n upsttng sgmnt and wrnch sgmnt. Fg.3 shows th damag locaton of suckr rod, th maxmum damag occurs nar th upsttng of suckr rod. 9 Fg.2 Mss strss nphogram of suckr rod Fg.3 amag nphogram of suckr rod had By analog computaton, undr th crcumstanc of dffrnt ntal strss and dffrnt ntal damag, th cycl numbr whn vry crtcal lmnt s brokn can b sn as Tab 3. Tab 3: th cycl numbr whn suckr rod lmnt damag Th numbr of lmnt damag Cycl numbr In Tab 3 th frst crtcal lmnt damag s for th longst tm, t xplans th formaton of cracks s a long procss, and s not nstantanous, at th sam tm th frst crtcal lmnt damag, othr crtcal lmnt also bgn to damag, aftr th frst crtcal lmnt damag, th cracks bgn to form. From th formaton of cracks to crack propagaton, lmnts ar n th damag contnuously. Wth th ncrasng damag valu, th damag lmnts ncras contnuously, whn th damag lmnts rach 16, th cycl numbr ncrass no longr, th lmnt damag don n an nstant, thn fractur occurs. 1399

7 Ru-fn Zhou t al J. Chm. Pharm. Rs., 214, 6(7): CONCLUSION In th papr, fatgu damag voluton quaton of suckr rod s stablshd, th addtonal load-fnt lmnt mthod s usd to carry out scondary dvlopmnt for ANSYS, APL languag s usd to wrt subroutn, fatgu damag modl of suckr rod upsttng sgmnt s bult, n th procss from th formaton of cracks to crack propagaton, th cycl numbr s obtand whn vry crtcal lmnt damag and th whol componnt damag. In th papr, th thory of damag mchancs s usd for th frst tm n rsarch of suckr rod fatgu damag, th rsarch mthod of suckr rod fatgu s prfctd. Th papr provds a nw thory to prdct th fatgu lf of suckr rod. Acknowldgmnt Proct supportd by Scnc and Tchnology Rsarch Proct of Hlongang Provnc partmnt of Educaton: Optmzaton sgn of Scrw Pump Ol Producton Systm n Horzontal Wll (NO ). REFERENCES [1] Zhou Rufn; Ba Ln; Gao Yuan, Scnc Tchnology and Engnrng, 21, 1(26), [2] Zhou Rufn; Jang Mnzhng; ong Kangxng, Chmcal Engnrng & Machnry, 211, 4(38), [3] Sun Wuan, J. Chm. Pharm. Rs., 213, 12(5), [4] Zhang Hongyuan; Xng Jan; Guo Chang, J. Chm. Pharm. Rs., 213, 9(5), [5] Fan Shan; Wang M, J. Chm. Pharm. Rs., 213, 11(5), [6] Gu Juzhang; Ca Yuanxao; Qng Tan, J. Chm. Pharm. Rs., 213, 12(5),