SERBIATRIB th International Conference on Tribology. Kragujevac, Serbia, May 2011

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1 Srbian Triblgy Scity SERBIATRIB 11 1 th Intrnatinal Cnfrnc n Triblgy Kragujvac, Srbia, May 11 Faculty f Mchanical Enginring in Kragujvac EFFECT OF CHANGES OF VISCOSITY OF MINERA OI IN THE FUNCTION OF PRESSURE ON FOWING THROUGH A ONG RADIA CEARANCE Dark Knžvi, Alksar Milašinvi, Zdravk Milvanvi, Vladimir Savi 1 Faculty f Mchanical Enginring Banja uka, BiH RS darkkn@blic.nt; acm@blic.nt, mzdravk@urc.rs.ba, Faculty f Tchnical Scinc Nvi Sad, Srbia; savicv@uns.ac.rs Abstract: Radial claranc in hydraulic cmpnnts (but als in mtr vhicls, tc) has multipl rls: it allws rlativ mvmnt f lmnts t achiv th givn functins, prvids th saling functin btwn th spac with diffrnt lvls f prssur, als srvs as hydrstatic r hydrdynamic baring accrding t th frcs within th cmpnnt. Cmmn valus f radial claranc is apprximat in th rang frm 1 m (minimum valus fr srv valvs) t 5 m (maximum valu fr axial pistn pumps). It is cmmn that whn calculating th flw rat f minral il thrugh clarancs, cnstructrs calculat with a cnstant valu f viscsity fr givn wrking tmpratur. In this papr is analyzd th rrr bcaus f accptanc f such assumptins. Kywrds: prssur, viscsity, radial claranc, vrlap, vlumtric flw rat 1. INTRODUCTION Minral ils ar th mst cmmn typ fluid usd in th hydraulic systms (vr 9% f th ttal us). T b abl t achiv th prjctd functins, in th hydraulic systms ar usd many cntrl rgulatry cmpnnts in which thy appar radial clarancs. In th analysis f th hydraulic systms ar usually nt takn int accunt chang f viscsity f minral il with a chang f prssur, bcaus that chang is far smallr than chang f viscsity with changs in tmpratur. Hwvr, as th wrk f wll-dsignd hydraulic systm usually taks plac at apprximatly cnstant prating tmpratur f wrking fluid, this nglct may lad t significant rrrs in calculatins. In practical calculatins, it is cmmn that th vlumtric flw rat f fluid thrugh radial claranc is calculatd using th fllwing frmula r d c p Q, (1) 1 d diamtr; c r radial claranc; p prssur drp; dynamic viscsity at th atmsphric prssur; lngth f vrlap. Exprimntal masurmnts shw that th vlumtric flw rat thrugh radial claranc calculatd by frmula (1) is diffrd frm th masurd valus.. PRESSURE DEPENDENCE OF VISCOSITY OF MINERA OI Viscsity f il is incrasd with grwth f prssur. Chmical cmpsitin gratly influncs n viscsity-prssur charactristics f a hydraulic fluids. Th bst knwn quatin, which dscribs viscsity-prssur bhavir f minral hydraulic fluids, is Barus quatin: [1], () p dynamic viscsity at th prssur 'p' [Pas]; 1 th Intrnatinal Cnfrnc n Triblgy Srbiatrib 11

2 dynamic viscsity at th atmsphric prssur [Pas]; - prssur-viscsity cfficint, which dpndnc f prssur tmpratur [1/Pas]. T adpt xprimntal data by a mathmatical mdl, th s-calld "Mdulus Equatin" was usd. "Mdulus Equatin" is basd n Barus quatin. Th mdl cmpriss th prssur, p [bar], tmpratur, T [ C], dpndnc f th dynamic viscsity [] pt, p a1atb1btp. (3) Dpndnc prssur-viscsity cfficint,, f prssur tmpratur is givn by quatin ln ln 1 (4) pt,. p p a a T b b T p a 1 1 Th paramtrs a 1, a, b 1, b rprsnt th il bhavir hav t b calculatd frm xprimntal data. In accrdanc with th data givn by th minral il prducrs ([3]), by using mthd f idntificatin unknwn paramtrs f mathmatical mdl, ar calculatd cnstants frm quatin (4). Tabl 1. Paramtr valus fr prssur-viscsity cfficint, [4] p 1 35 bar, T 4 C.98 bar, valus f dynamic viscsity, ar calculatd by using f frmula (3): p35 bar, T.5 C.3375 p 35 bar, T 4 C.8. Valu f dynamic viscsity, at prssur f 35 bar tmpratur f.5 C (4 C), is fr.3375 (.8) tims highr thn valu f dynamic viscsity at atmsphric prssur th sam tmpratur. Figur shws valus f dynamic viscsity f sm hydraulic il at 5 C, fr diffrnt valus f wrking prssur. Minral il f paraffinic bas structur a 1 [bar] a [bar/ C] b 1 b [1/ C] Figur. Chang f viscsity f sm minral hydraulic ils with th chang f prssur (tmpratur 5 C) [4] 3. FOW OF MINERA OI THROUGH ONG RADIA CEARANCES Figur 1. Prssur-viscsity cfficint f minral il paraffinic bas structur: a) p = p a ; b) p = 5 bar; c) p = 1 bar; d) p = bar Exampl: Fr th prssur f 35 bar tmpraturs f.5 4 C, valus f prssur-viscsity cfficint, ar calculatd by using f frmula (4): 1 p35 bar, T.5 C.46 bar Undr th lng claranc is undrstd such claranc whs lngth vrlap (th lngth f lakag path) is such that th hydraulic fluid is slightly warmd at flwing thrugh th claranc. [4] In this cas, chang f stat f minral il at flwing can b cnsidrd isthrmal. Such cass flw thrugh th claranc is prcssd in th litratur, but with n flaw: thy ignr chang f viscsity f il with a chang f prssur. This nglct can lad t th calculatd flw rat is up t 5% highr than th actual flw rat (dpnding n valu f wrking prssur in th hydraulic systm ). 1 th Intrnatinal Cnfrnc n Triblgy Srbiatrib

3 As trajctris f fluid particls straight paralll, fluid flw thrugh radial claranc can b sn as flw btwn flat paralll surfacs which width ar, th distanc btwn thm is c. r Figur. Flw f hydraulic fluid thrugh lng radial claranc Th flw f fluid thrugh radial claranc can b dscribd by th Navir-Stks quatins. Fr stady flw f incmprssibl fluid, taking int accunt th chang f viscsity alng claranc, th vctr frm f ths quatins is Dv f gradp v. (5) Dt D v - inrtial frc pr unit vlum n lmntary Dt particl f fluid; gradp - prssur frc pr unit vlum n lmntary particl f fluid, - viscus frc pr unit vlum n v lmntary particl f fluid. Fllwing analysis will b carrid ut fr symmtrical radial claranc bcaus f in ral cnditins at flwing f il thrugh th radial claranc within th hydraulic cmpnnt, prssur sks t hld pistn in cncntric (caxial) psitin in rlatin t th cylindr. Crss sctinal ara thrugh which fluid flws thrugh th claranc is 378 d1 d A, (6) 4 d - innr diamtr f cylindr, d 1 - diamtr f pistn. Figur 3. Symmtric radial claranc Figur 4. Th flw f fluid btwn paralll plats Can b writtn d1 d cr, (7) d d cr. (8) Substituting quatins (7) (8) in quatin (6), w gt A d cr wc r, (9) whr w is dfind as th width f rctangular pning. During stady rctilinar paralll flw thr is nly lngitudinal cmpnnt f vlcity u, whil cmpnnts v w ar qual zr. Prfil f vlcity fr this cas f flw ds nt chang alng claranc. Cntinuity quatin in diffrntial frm is givn by u v w. (1) x y z As v w qual zr, frm quatin (1) fllws u x, why u f( z). Sinc th influnc f mass frcs (f) ar ngligibl, th Navir-Stks quatins ar rducd t frm 1 th Intrnatinal Cnfrnc n Triblgy Srbiatrib 11 dp d u. (11) dx dz Dynamic viscsity f fluid that flwing thrugh claranc, fr th spcific prating tpmratur, is givn by th Barus's quatin (). As prssur is functin f lngitudinal crdinat x, th dynamic viscsity dpnds n prssur, thn th dynamic viscsity is functin f crdinats x, s w can writ

4 p dp d u. (1) dx dz As th lft sid f quatin (1) dpnds nly f x th right sid quatin (1) dpnds nly f z, it fllws that bth sids f th quatin (1) must b qual t a cnstant C. Gnral slutin f quatin (1) is C u z C z 1 C. (13) Th cnstant C can b dtrmind frm th bundary cnditins fr prssur: fr x, p p, (14a) fr x, p. (14b) Frm th cnditin that th lft sid f quatin (1) is qual t cnstant C, i. p dp C, (15) dx putting p dp 1 d p dx dx. (16) quatin (15) can b dirctly intgratd, w gt p Cx C. (17) Incrprating th bundary cnditins (14) in quatin (17), w gt C 3 1 p 3, (18) p 1 C. (19) Using quatins (16) (19), frm quatin (15), w can gt th law f chang f prssur alng claranc 1 p 1 p ln p x. () As an xampl, in Figur 5 is shwn th chang f prssur thrugh th claranc that lngth f vrlap is 1 mm wrking prssur 35 bar. In Figur 5 is givn an vrviw f changs f prssur thrugh th claranc: at nglct f influnc f prssur n th valu f dynamic viscsity, curvs f prssur chang which ar calculatd by frmula (), fr diffrnt prating tmpraturs ( C 5 C). Th wrking fluid is a minral hydraulic il HM 46. Figur 5. Chang f prssur alng th claranc Th bundary cnditins fr vlcity ar: fr z, u, (1a) fr z c, u. (1b) r Substituting cnditins (1) in quatin (13), w gt C, () C C1 c r. (3) Incrprating th cnstants C 1 C in quatin (13), w gt xprssin fr th vlcity prfil in th crss sctin f claranc p 1 u r c z z. (4) Vlumtric flw rat thrugh claranc is p 3 1 d c Q r. (5) 1 4. ORIENTATION (BASED ON RESUTS OF EXPERIMENTS) CRITERIA FOR THE DIVISION CEARANCES BETWEEN SHORT AND ONG CEARANCES Basd n th xprimntal rsults, it was dtrmind brdr lngth g fr applicatin f th frmula (5) [4] cr g 9.5cr, (6) ln.9 1 th Intrnatinal Cnfrnc n Triblgy Srbiatrib

5 - cfficint dtrmind frm xprimntal data. Fr th lngths f vrlap that ar gratr than g, flw rat thrugh th radial claranc is calculatd using th frmula (5). Cficint can b dtrmind frm xprssin ([4]): p. (7) 5 Viscsity-tmpratur cfficint can b calculatd frm quatin ([4]) 1 ln. (8) T whr - T T T [ C] - tmpratur incras, - - valus f dynamic viscsity at tmpratur T T, at atmsphric prssur, - p wrking prssur. In Figur 6 ar givn th valu f th cfficint fr sm ils usd in xprimntal rsarch. [4] Figur 6. Tmpratur-viscsity cfficint f hydraulic il: a) HM 68; b) HM 46; c) HM 3; d) HM 5. EXPERIMENTA VERIFICATION OF THEORETICA MODE In this papr is givn an xampl f chck thrtical mdl at masurmnt f flw rat thrugh th radial claranc siz c r 17 m diamtr f th pistn d 1 mm. Wrking prssur was 35 bar. It was usd minral il HM 46 [4] Figur 7. Thrtical curvs: a) vrlap mm, b) vrlap 6 mm; a) vrlap 8 mm; a) vrlap 1 mm Tabl. Th numrical valus f th xprimntal rsults in Figur 7 crrspnding valus calculatd by th thrtical mdl (Equatin 5) Vlumtric flw rat [l/min] T [ C] Exprimnt Thrtical [mm] mdl It shuld b ntd that this xampl prvids an illustratin. Th masuring f th flw rat was carrid ut fr diffrnt diamtrs f pistns, varius sizs f radial claranc varius kinds f minral ils. Rsults f masurmnts wr shwd gd agrmnt btwn xprimntal rsults ths btaind using th thrtical mdl. 6. CONCUSION As th fficincy f cmpnnts with nncntact saling clarancs dpnds n th cnstructin, typs charactristics f wrking fluid, wrking prssur tmpratur, th rsults f this study hav th fllwing scintific cntributins: - In this papr is prsntd a dtail dscriptin f chang f viscsity in functin f chang f prssur fr minral ils (spcially minral hydraulic ils). It is shwn that th prcis mathmatical mdling f th fluid prprtis ar ncssary fr rsarch phnmna within 38 1 th Intrnatinal Cnfrnc n Triblgy Srbiatrib 11

6 cmpnnts in which thr ar radial clarancs; - It is givn mathmatical mdl f flw thrugh lng radial clarancs, taking int accunt chang f viscsity minral il with chang f prssur, fr givn wrking tmpratur; - Th drivd frmulas can b applid fr flw thrugh radial clarancs with th lngths f vrlap that ar gratr than ths givn frmula (6), fr radial clarancs whs siz is largr than 1 µm. Fr radial clarancs whs siz is lss than 1 µm, thr is th ffct f blitratin, which is nt analyzd in this papr. REFERENCES [1] JUGOMA Grup f Authrs, ubricants ubricatin, Th Unin f Yugslav Scitis fr Applicatin f Fuls ubricants, Zagrb, [] Schmidt A., Viscsity-Prssur-Tmpratur Bhaviur f Minral Synthtic Oils, 1th Intrnatinal Cllquium Triblgy., Stuttgart, Grmany,. [3] Fraunstin M., Guid fr Fluid Undr Prssur fr Cnstructrs, Mbil Oil, [4] Knžvic D., PhD Thsis, Influnc Clarancs Gmtry in Hydraulic Cmpnnts f Autmatin Cntrl n Efficincy f Hydraulic Systms, Nvi Sad, 7. 1 th Intrnatinal Cnfrnc n Triblgy Srbiatrib