JJMIE Jordan Journal of Mechanical and Industrial Engineering

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1 JJMI Joran Journal of Mchanical an Inustrial nginring Volum 5, Numbr, c. 11 ISSN Pags init lmnt analysis for short trm O-ring rlaxation Mohamm iany*,a, Hicham Aissaoui b a Mchanical nginring pt, aculté s Scincs t Tchniqus Béni Mllal, Mghila BP 5 Béni Mllal, Morocco b lctrical nginring pt, aculté s Scincs t Tchniqus Béni Mllal, Mghila BP 5 Béni Mllal, Morocco Abstract O-rings ar us in machin vics lik th sals componnts. Thy ar inxpnsiv, an hav simpl mounting rquirmnts. In this articl, an axisymmtric finit lmnt mol is propos to stuy th O-ring rlaxation uring th first ay of its installation in th unrstrain axial loaing cas. Th rsults of th numrical mol ar compar with thos of an analytical approach bas on th classical Hrtzian thory of th contact. Th contact strss profils an th pak contact strsss ar trmin vrsus th tim rlaxation in orr to spcify th working conitions thrshols. Kywors: O-ring; contact prssur; analytical molling;rlaxation; A 11 Joran Journal of Mchanical an Inustrial nginring. All rights rsrv Nomnclatur 1. Introuction R b x rlax R b x rlax total comprssion loa (N) initial O-ring axial isplacmnt (mm) th O-ring cross-sction iamtr (mm) th O-ring man iamtr (mm) th ratio / th axial comprssion ratio th contact with btwn th gaskt an plat (mm) raial position compar to th vrtical axis of th O-ring cross-sction (mm) maximum contact prssur valu or pak contact strss (MPa) rlaxation moulus (MPa) lastic moulus for gaskt (MPa) cofficint rlaxation tim (s) total comprssion loa (N) initial O-ring axial isplacmnt (mm) th O-ring cross-sction iamtr (mm) th O-ring man iamtr (mm) th ratio / th axial comprssion ratio th contact with btwn th gaskt an plat (mm) raial position compar to th vrtical axis of th O-ring cross-sction (mm) maximum contact prssur valu or pak contact strss (MPa) rlaxation moulus (MPa) lastic moulus for gaskt (MPa) cofficint rlaxation tim (s) Th lastomric O-ring gaskts ar wily us in hyraulic an pnumatic quipmnts to nsur th saling of shafts, pistons an lis. Th corrct opration is u to th goo tightning of th oint that gnrat a contact prssurs abl to confin th fluis insi a rooms or to prvnt thir passag from on compartmnt to anothr. Svral stuis ar carri out to mol th O-ring bhaviour but without taking in account th ffct of th rlaxation an crp phnomna. Th quations vlop until toay to trmin analytically th istribution an th valus of th contact prssur ar uc from th convntional Hrtzian thory of th contact [1]. Th corrct opration of th O-ring is conition, on th on han, by th maximum valu of th contact prssur crat uring th O-ring comprssion an on th othr han by maintaining in oprating stag a minimal thrshol valu blow which th saling of th oint is blam. So th valuation of th maximum valu of contact prssur volution in tim has a primary importanc to nsur th corrct O-ring function uring its nominal lifspan. In this articl, it is propos to stuy th O-ring rlaxation uring th first hours of its installation in th unrstrain axial loaing cas, figur 1. (a) Raial position, x igur 1: Unrstrain axial loaing assmbly. (b) * orrsponing author. -mail: miany@yahoo.com

2 Joran Journal of Mchanical an Inustrial nginring. All rights rsrv - Volum 5, Numbr (ISSN ). Backgroun Svral tams wr intrst in O-ring assmbly us in various inustrial srvics. A tmporal raing of publish works on this subct can b classifi on thr catgoris. An analytical approach bas in all cass on th Hrtzian classical thory, an xprimntal part using various assmblis allowing to charactriz th O-ring itslf in traction an comprssion loas an to mol its ral bhaviour. In th thir shuttr, finit lmnts mols ar vlop to numrically simulat assmblis with th O-ring. Gorg an al. [] us a finit lmnts mol to stuy th bhaviour of th O-ring comprss btwn two plats. Th gaskt charactristics wr introuc into th program accoring to paramtr fining th total formation nrgy or by using th No-Hookan mol. Th rsults of this analysis wr compar with thos of svral xprimntal stuis an analytical approachs bas on th Hrtzian thory. ragoni t al. [] propos an approximat mol to stuy th O-ring bhaviour plac in rctangular grov. Th influnc of th grov imnsions variation an th friction cofficint was invstigat. Th work of I. Grn an. nglish [4] rviw th maority of us O-rings configurations. A finit lmnts Mols wr vlop consiring hyprlasticity bhaviour. Th rsults of ths mols wr confront with thos of mpirical stuis. Nw rlations xprssing th maximum contact prssur an th with of contact wr propos. Raparilli t al. [5] prsnt a valiation of th xprimntal rsults by a numrical mol which rgar th oint as an almost incomprssibl lastic matrial. Th ffcts of th flui prssur as wll as th friction ffct btwn th gaskt an th shaft ar stui. Th two part of th stuy wr in prfct agrmnt. In an xprimntal stuy [], th authors tri to trmin th influnc of th flui prssur on th contact prssur which nsurs of saling as wll as th aging trioration of th oint. Kim t al. [7, 8] tri to fin an approximat solution for th mchanical bhaviour of th O-ring oints in svral configurations. Th influnc of th friction cofficint is highlight. An xprimntal stuy was carri out to fin mor ralistic lastic moulus valus for lastomric O-ring. Thy compar thir rsults with thos obtain in xprimnts an by th finit lmnt analysis. Thy foun that th valus givn by th Linly [9, 1] to calculat th comprssiv forc ar similar to thos trmin by th finit lmnts mol. Th O-ring rlaxation was trat by K.T. Gilln t al. [11]. In this stuy, th O-ring graation is caus by oxiation or nuclar irraiation. Th authors scrib svral improvmnts to th mthos us in thr prvious stuis lik substituting th O-ring sgmnts for ifficult-to-prpar a mini-isk sampls. In this articl, a axisymmtric mol is vlop to simulat th O-ring rlaxation whn it is axially comprss by initial tightning btwn two rigi plans. Th ffct of th tmporal variation of th longituinal lasticity moulus as wll as th influnc of th axial comprssion ratio will b analyz. Th mol of th classical contact thory will b confront with th rsults of th numrical stuy. Th O-ring matrial bhaviour is similar to th stuffing-box packings on us to stuy th crp an rlaxation phnomna [1].. onvntional analytic Thory Most of th work icat to th stuy of th O-ring gaskt bhaviour us th sam analytical mol bas on th Hrtzian thory of th prssur contact. By aopting this classical thory, Linly [9, 1] vlop a simpl approximat formula, rlation (1), xprssing th comprssiv forc,, accoring to th ratio of initial comprss isplacmnt by th cross-sction O-ring iamtr,. ( ) (1) Th sam thory allow trmining th contact with, b, an th maximum valu of th contact strss po, accoring to th formulas () an (). b. ( ( ) 4.. ) Th contact prssur istribution accoring to th raial position on th gaskt is givn by th quation (4). x p ( x) p 1 (4) b Ths formulas o not utiliz th mchanical charactristics of th plats in contact with th oint. Only th O-ring longituinal lasticity moulus,, ar us. By consqunc, th sam quations rmain vali for th volution stuy of th O-ring bhaviour accoring to tim but using a tim varying Young moulus, call rlaxation moulus rlax. Th viscolastic bhaviour of th gaskt is givn by th moifi Maxwll mol [1], prsnt in figur. inf igur : A gnraliz Maxwll mol. Th rlaxation moulus is fin by th following quation: rlax () () ( t) (5) t

3 ontact prssur (MPa) 11 Joran Journal of Mchanical an Inustrial nginring. All rights rsrv - Volum 5, Numbr (ISSN ) 48 With an () Th rlaxation moulus of th quation (5) bcoms: t rlax( t) 1 (1 ) (7) Th initial lasticity moulus,, an th ight cofficints, call Prony sris cofficints, ar uc from th xprimntal ata of th rfrnc [14]. Th rlaxation stuy aims to valuat th variation of th contact strss vrsus tim, whn an initial axial isplacmnt,, charactriz by an axial comprssion ratio R, givn by th quation (8), is impos to th gaskt. or ach axial comprssion ratio, R, th variation of th contact prssur istribution as wll as th chang of th contact surfac with ar rcor. R 1.. (8) 4. init lmnt analysis In orr to charactriz th O-ring rlaxation, an axisymmtric finit lmnts mol, show in figur, was vlop using ANSYS softwar [15]. Th O-ring is comprss btwn two rigi plats. Uppr O_ring surfac igur : init lmnts mol. No lmnt Rigi plat Sinc th problm is axisymmtric an th mian horizontal plan cutting th O-ring in two quivalnt parts is a symmtry plan, th oint is moll by a half-isc with plan lmnts having four nos. Th O-ring matrial is rgar as viscolastic charactriz by th Prony cofficints. Th plats ar moll by rigi lmnts whos isplacmnts ar constrain in all irctions. Th gomtric an mchanic charactristics of th O-ring oint ar summariz in tabl I. In orr to chck th influnc of th O-ring rigiity two initial Young moulus valus ar consir. Th msh rfinmnt is optimiz to hav th convrgnc whil using lss mmory capacity. Tabl 1: O-ring charactristics O-ring Subscript 1 (mm).98 (mm) 1.19 (MPa) Th valu of th vrtical isplacmnt impos on th uppr surfac of th oint is calculat by th axial comprssion ratio, R, which vari btwn 7.5 an 5 % compar to th O-ring cross-sction iamtr. Thraftr, th istribution of th contact prssur is rcor accoring tim. 5. Rsults an iscussions Th suggst analytical mol calculats th maximum contact prssur, in th assmbly saling conitions, accoring to initially impos isplacmnt. In aition, th finit lmnts mol in th sam working conitions is us to invstigat th O-ring matrial propritis ffct on th contact prssur valus. igur 4 prsnts th contact prssur istribution accoring to th raial position for a comprssion ratio of 15% with various intrvals of oprating tim. It is notic that th contact prssur is maximum in th avrag iamtr position. All th curvs hav th sam apparanc an amit th mil iamtr lik a symmtrical position. Th rlaxation sp is mor important at th bginning an bcoms null aftr 18 oprating hours h 18 h Prcntag comprssion st : R=15% Raial position (mm) igur 4: ontact prssur istribution for R=15%. 1 =.8 MPa To inspct th ffct of th rigiity of th O-ring, two valus of th longituinal moulus of lasticity wr us. igur 5 compars th contact prssur istributions for th two cass. or a givn position, th contact prssur valu pns on th valu of th corrsponing lasticity moulus. Whn is largr th contact prssurs ar highr. Whn th contact prssur is ivi by th initial lastic moulus, th curvs pn only on th rlaxation tim an th comprssion ratio as illustrat in figur. onsquntly, w can conclu that th ffct of th

4 Axial comprssion ratio : R=% Maximum ontact prssur (MPa) ontact prssur for 1 (MPa) Prcntag comprssion st : 7.5% ontact prssur for (MPa) Joran Journal of Mchanical an Inustrial nginring. All rights rsrv - Volum 5, Numbr (ISSN ) gaskt rigiity os not appar whn th curv of th ratio p/o is rprsnt accoring to th raial position for svral cass..5. At t= sc Axial comprssion ratio R =.8 MPa h =4. MPa Rlativ contact strss, P/ At t= % 15% Soli lin : mol ash lin : Analytical mol Rlativ raial position igur 7: an Analytical mols comparison Rlativ raial position igur 5: ontact prssur in th two lastic moulus cass..7 1 =.8 MPa =4. MPa..7 igur 8 compars th influnc of th comprssion ratio on th sp an th valus of contact prssur u to th viscolastic rlaxation. It is clar that in all th cass th maximum contact prssur loss a grat prcntag of its initial valu with tim. This loss is vry fast in th first oprating hours. 1. p(x)/ i=1; h 1.8. Axial comprssion ratio R 7.5% 15% % 5% Soli lin : mol ash lin : Analytical mol Rlativ raial position igur : Initial lastic moulus ffct. uring th installation of th oint, th analytical mol nvisags th sam strsss istributions as th finit lmnts mol for any impos axial isplacmnt valu as shown in figur 7. Th surfac of contact an th maximum contact prssur ar largr whn th comprssion ratio or th rlaxation tim ar mor significant. Th iffrnc btwn th rsults of th two mols is rathr ngligibl an os not xc 1%. It can b affirm that th analytical mol uc from th classical thory of th contact prssur rmains vali vn for th stuy of th O-ring rlaxation Rlaxation tim (sc) igur 8: Rlaxation of maximum contact prssur in th first matrial cas.. onclusion This stuy shows that th classical thory of contact, vlop initially for stay opration, rmains vali for th rlaxation cas but with som moifications on th O- ring mchanical charactristics. In aition, th finit lmnts mol vlop proucs th sam rsults as th analytical mol. In orr to gnraliz ths rmarks, othr cass might b rgar as th raial loaing an th groovs configuration.

5 11 Joran Journal of Mchanical an Inustrial nginring. All rights rsrv - Volum 5, Numbr (ISSN ) 48 Rfrncs [1] S. Timoshnko, J.N.Gooir, Thory of lasticity. r. Nw York: McGraw-Hill; [] A. Gorg, A. Strozzi, J.I. Rich, Strss ils in a omprss Unconstrain lastomric O-ring Sal an a omparison of omputr Prictions an xprimntal Rsults. Tribology Intrnational, Vol., No. 5, 1987, []. ragoni, A. Strozzi, Thortical Analysis of an Unprssuriz lastomric O-ring Sal Insrt into a Rctangular Groov. War, No.1, 1989, [4] I. Grn,. nglish, Strsss an formation of omprss lastomric O-ring Sals. 14th Intrnational onfrnc on lui Saling, irnz, Italy, [5] T. Raparilli, A.M. Brttto, L. Mazza, xprimntal an Numrical Stuy of riction in an lastomric Sal for Pnumatic ylinrs. Tribology Intrnational, Vol., No 7, 1997, [] K. Yokoyama, M. Okazaki, T. Komito, ffct of ontact Prssur an Thrmal graation on th Salability of O- ring. JSA, No. 19, 1998, [7] H.K. Kim, S.H. Park, H.G. L,.R. Kim, Y.H. L, Approximation of ontact Strss for a omprss an Latrally On Si Rstrain O-ring. nginring ailur Analysis, No. 14, 7, [8] H.K. Kim, JH. SH. Nam, J.S. Hawong, Y.H. L, valuation of O-ring Strsss Subct to Vrtical an On Si Latral Prssur by Thortical Approximation omparing with Photolastic xprimntal Rsults. nginring ailur Analysis, oi:1.11/.ngfailanal [9] PB. Linly, omprssion haractristics of Latrally- Unrstrain Rubbr O-ring. JIRI, No. 1, 197, pp. -1. [1] PB. Linly, Loa-omprssion Rlationships of Rubbr Units. J Strain Anal, Vol. 1, No., 19, pp [11] K.T. Gilln, M. lina, R. Brnstin, Valiation of Improv Mthos for Pricting Long-trm lastomric Sal Liftims from omprssion Strss-Rlaxation an Oxygn onsumption Tchniqus. Polymr graation an Stability, No. 8,, pp [1] M. iany, A.H Bouzi, Analytical Molling of rp Rlaxation of Stuffing Box Packing. ASM-PVP onfrnc, Papr N PVP7-94, San Antonio, Txas, 7. [1] N. G. Mcrum,. P. Buckly,. B. Bucknall. Principls of Polymr nginring. Nw York: Oxfor Univrsity Prss; 4. [14] R. M. hristnsn. Thory of Viscolasticity - An Introuction. n., Nw York: Acamic Prss; 198. [15] ANSYS, ANSYS Stanar Manual, Vrsion 11.,.