A theoretical analysis for tube bulge forming using elastomer medium

Transcription

1 AIJSTPME ( 5(4: 7- A theoetical analyi fo tube bulge foming uing elatome meium Ramezani M. an Neitzet T. Cente of Avance Manufactuing Technologie (CAMTEC, School of Engineeing, Aucklan Univeity of Technology, Aucklan, New Zealan Abtact A new theoetical moel i peente in thi pape fo bulge foming of tubula component with oli bulging meium. The moel i bae on the eult of the fiction moel which wa evelope peviouly by one of the autho fo ubbe/metal contact an take into account the effect of local contact conition. E imulation uing commecial oftwae ABAQUS ae caie out fo an axiymmetic tube bulging opeation uing the efine fiction moel. The compaion of the eult of the theoetical moel an the E imulation clealy how that the newly evelope theoetical moel i uitable fo peicting foming peue an te in the tube. The effect of key poce paamete uch a the fiction between the tube an the ie, the tube initial thickne an the length of the ealatomeic o on the eult ae invetigate uing theoetical an E moel. Keywo: inite element imulation; iction; Theoetical analyi, Tube bulging. Intouction In ecent yea, tube bulge foming technique have been ue in poucing a wie ange of tubula component. Thi i mainly ue to the quet to eceae pouction cot an to optimize pouction technology. Thi technique i ue fo poucing bicycle fame backet fom mil teel bulging an to manufactue the ea axle cating fo automobile. The poce i alo wiely ue in foming coppe pipe fitting fo ometic wate an ga upplie []. The bulge foming of pipe can be one by implementing the intenal hyotatic peue via a meium. The peue meium i uually a liqui (hyaulic flui o wate o oli elatome (ubbe o polyuethane. By etaining the pipe in ie with iffeent geometie, component with eie hape can be pouce. Exceive thinning ue to the high intenal peue i the main limitation of thi poce. To ovecome thi poblem, compeive axial loaing i applie to the en of the tube togethe with the intenal peue. In the bulge foming of tube with oli meium, an elatome o inie the tube applie lateal peue to expan the tube cicumfeentially, while imultaneou axial feeing of the tube i ecue by the fictional taction on the tube a the elatome o efom elative to the tube. The ue of elatomeic meia ha futhe avantage. The nee fo an elaboate contol ytem to cooinate the axial compeion with the hyaulic peue i eliminate. ictional foce between the tube an the elatome ae ue to geneate the axial compeion, an the flexible meium applie a lateal peue to the tube cauing it to expan within the ie. Moeove, the fiction acting on the tube ha an avantage in elaying the onet of tenile intability. When bulging with oli meium, ealing poblem an the poibility of leakage of the highpeue liqui employe in hyaulic bulging ae eliminate. The cot of poucing the component i much le than uing a pecialize machine equie fo hyaulic bulging. The nee fo the filling an emoval of oil o the cleaning of the bulge tube of oil afte foming i eliminate. The inetion of the elatome o i both quick an convenient an the o can be e-ue again []. Many expeimental tuie concening bulge foming ae available in liteatue [-4] an in ecent yea a ignificant numbe of finite element imulation tuie have been etaile out [5-8]. Diffeent theoetical moel have alo been evelope fo the poce [9-]. Mac Donal an Hahmi [5] evelope a thee-imenional imulation of the 7

2 Ramezani M. an Neitzet T. / AIJSTPME ( 5(4: 7- manufactue of co-banch component uing a oli bulging meium. The effect of vaying fiction between the bulging meium an the tube wa examine in thei pape an the hitoy of evelopment of the bulge an te conition in the fome component wee invetigate. Hwang an Lin [7] popoe a theoetical moel to examine the platic efomation behavio of a thinwalle tube uing the bulge hyo-foming poce in an open ie. They coniee non-unifom thinning in the fee-bulge egion an ticking fiction between the tube an ie. The analyi wa followe by finite element imulation of the poce uing DEORM an the elationhip between the intenal peue an the bulge height of the tube wa achieve. Yang et al. [8] invetigate the effect of the loaing path on the bulge hape an the wall thickne itibution of the tube uing theoetical an E moel. Uing thei moel, a eaonable ange of the loaing path fo the tube bulge hyofoming poce wa etemine. Thiuvauchelvan [9, ] evelope a theoetical moel bae on the expeimental fiction analyi pefome by akua an Yamaguchi []. Uing thi moel he coul etemine the initial yiel peue an the final foming peue neee to bulge a tube. Boumaiza et al. [] icue the platic intabilitie of elato platic tube ubject to intenal peue an evelope a local necking citeion bae on a moifie Hill aumption fo localize necking. In all thee tuie, the E an theoetical analyi bae on a compehenive analytical fiction moel which take into account the local contact conition have been mie. Ramezani et al. [] evelope a fiction moel fo ubbe-metal contact in tube bulge foming poce uing oli meium. They howe in thei pape that the newly evelope fiction moel i vey effective in poucing eliable E imulation compae to a taitional Coulomb fiction moel. In the peent wok, thi fiction moel i ue in theoetical analyi of tube bulging poce to examine it efficacy in eveloping analytical moel fo ubbe foming pocee. Bae on the eult of a fiction moel evelope by Ramezani et al. [, ] an an analytical moel evelope by Thiuvauchelvan [9], an analytical analyi i pefome fo the cae of tube en bulging with polyuethane meium, followe by finite element imulation of an axiymmetic tube bulging opeation uing ABAQUS oftwae. To evaluate the influence of the new fiction moel, theoetical an E imulation eult have been compae with each othe an with expeimental eult fom [4]. Static fiction moel When two oli ae queeze togethe they will in geneal not make atomic contact eveywhee within the appaent contact aea an contact happen only on peak apeitie of uface [4]. To moel the contact between ough uface, it i neceay to etemine the contact paamete between the pai of apeitie caying the loa [5]. o two elatic pheical apeitie which ae loae by a nomal foce n, Hetz theoy [6] i the baic theoy fo pecifying the aiu of the contact cicle, the peue an the nomal appoach. o the cae when a tangential foce t i ubequently applie, the tangential iplacement of apeitie an the hea te within the contact can be etemine by Minlin theoy [7]. He coniee a tick egion in the cente of contact between a pai of apeitie uoune by an annulu aea of mico-lip aco the ege of the contact. Johnon [8] peente a olution fo thi mico-lip egion. Rubbe mateial exhibit both elatic an vicou eitance to efomation. The mateial can etain the ecoveable (elatic tain enegy patially, but they alo iipate enegy if the efomation i maintaine []. Vicoelatic mateial behavio can be moele uing ping an ahpot connecte in eie an/o in paallel. A ahpot i connecte in paallel with a ping in igue. Thi i known a a Voigt element. If efome, the foce in the ping i aume to be popotional to the elongation of the aembly, an the foce in the ahpot i aume to be popotional to the ate of elongation of the aembly. In thi moel, if a uen tenile foce i applie, ome of the wok pefome in the aembly i iipate in the ahpot while the emaine i toe in the ping. A ahpot i connecte in eie with a ping i hown in igue (b. Thi i calle a Maxwell element. In thi aembly, if a uen tenile foce i applie, it i the ame in both the ping an the ahpot. The total iplacement expeience by the element i the um of the iplacement of the ping an the ahpot. The epone of ubbe to change in te o tain i actually a combination of element 8

3 Ramezani M. an Neitzet T. / AIJSTPME ( 5(4: 7- of both mechanical moel (ee, igue (c. The epone i alway time-epenent an involve both the elatic toage of enegy an vicou lo. The Stana Linea Soli (SLS moel (igue (c give a elatively goo eciption of both te elaxation an ceep behavio. Ste elaxation i the time-epenent eceae in te une contant tain at contant tempeatue. o the SLS moel the genealize Hook equation can be witten a g g g ( g g. ( whee g, g ae the elaticity of ping, i the vicoity of the ahpot, i the tain an i the te. By making the te contant an equal to in Eq. ( an olving the iffeential equation with epect to the tain, we aive at the ceep compliance function (t a follow: ( t t ( t [ exp( ] ( g g T whee T i the etaation time. g Similaly, the te elaxation function (t can be obtaine by taking the tain contant an equal to in Eq. (, eulting in ( t g ( t t [ g g exp( ] ( g g T whee T i the etaation time. ( g g Suface oughne can be moele a a compoe et of pheical apeitie which have the ame aiu an thei height following a tatitical itibution, a fo intance a Gauian itibution (ee, igue. Thee paamete ae commonly ue to ecibe a anom ough uface moel. The tatitical paamete of the apeitie ae: the aveage apeity aiu (pheical hape apeitie, the apeity enity n, an the tana eviation of the apeity height. Accoing to expeiment epote by Geenwoo an Williamon [9] mot uface how a value in the ange of.-.5 fo the pouct n. Hui et al. [] evelope a theoy fo vicoelaticigi contact une eveal loaing conition uch a contant loa tet, loa elaxation tet an contant iplacement ate tet. In thi theoy, an exponentially itibution of apeitie i coniee an then an analytical olution i evelope fo the eal contact aea an the total nomal loa. In thi pape, the cae of a vicoelatic ough uface which i nomally loae againt a igi uface i coniee.. Nomal loaing of vicoelatic/igi multiapeity contact o a cetain epaation h the numbe of apeitie in contact, the eal contact aea an the total loa caie by the apeitie can be calculate uing the following equation. The numbe of apeitie in contact at a cetain epaation i given by n c An n ( (4 h whee A n enote the nominal contact aea, / i the nomalize apeity height, h h/ i the nomalize epaation, an ( i the nomalize Gauian height itibution which can be obtaine a ( e (5 Then, the eal contact aea i given by: A An n ( h ( (6 h The total nomal loa can be obtaine a the um of all nomal loa caie by the apeitie in contact. 8 n An n ( h ( ( t h (7 9

4 Ramezani M. an Neitzet T. / AIJSTPME ( 5(4: 7-. Tangential loaing of vicoelatic/igi multiapeity contact Conieing the multi-apeity contact intouce in Section. to be ubequently loae by an inceaing tangential loa, an appoach i peente in thi ection fo a vicoelatic ough uface pee againt a igi flat. At a cetain epaation an fo a tangential loa malle than the foce neceay to initiate macoliing, o-calle maximum tatic fiction foce, the multi-contact inteface will be compoe of micocontact which ae in the patially-lip egime an mico-contact which ae totally liing. Macoliing will occu if all contacting apeitie ae in the fully liing egime [7]. A conition ha been et fo an elatic multi-contact inteface by Bueau et al. [] which povie a citical apeity height above which the micocontact ae patially liing. In thei appoach, a contant local coefficient of fiction i coniee fo all mico-contact. Uing Bueau metho, a citical apeity height fo a vicoelatic multi-contact inteface can be eive. ( tv n whee t ( ( [ ( t n t ] (8. tv i the peliminay iplacement; i the Poion atio; an i the local coefficient of tatic fiction. Reaanging the facto in Eq. (8, we aive at: ( tv t ( t (9 n ( t (. n The ight-han ie of Eq. (9 i a poitive eal numbe fo. tv ( t n ( t ( t n, thu: ( The inentation epth of the apeity n can be eplace by ( z h. Then, the inequality ( become t z tv ( h ( ( om Eq. ( it can be infee that the apeitie which have the height t tv ( c h ( ( ae in the fully liing egime becaue they cay a tangential foce which i equal to o lage than the maximum tatic fiction foce. The mico-contact of which height atify the elation z c ae in the patially-lip egime. The total tangential loa caie by the multi-contact inteface can be witten a: t tick lip ( whee tick component i calculate a the um of all tangential loa caie by the mico-contact which ae not fully liing. That mean that thei contact aea ae compoe of tick an lip egion. Delai [] peente the following equation fo tick component: c tick ( t A ( h n n 8 ( t t ( h ( ( (4 The lip component i taken a the um of all tangential loa caie by the mico-contact which ae fully liing an i calculate with equation lip ( t A n n 8 ( t c ( h ( h (5 Having obtaine the tangential loa caie by the multi-contact inteface, the maximum foce equie to initiate maco-liing (o maximum tatic fiction foce can be etemine a the um of all tangential loa cauing go liing of all mico-contact []. When thi conition i obeye, the patially liing

5 Ramezani M. an Neitzet T. / AIJSTPME ( 5(4: 7- component tick become zeo an the conition can be witten a: if (6 t max lip tick So, the tatic coefficient of fiction can be calculate a: t max (7 n By giving the mico-geomety, the nominal aea of contact an the mateial popetie, the eal aea of contact, A an the nomalize epaation, h can be obtaine fom Eq. (6 an (7. Next, auming a tangential iplacement, the citical height, c can be calculate fom Eq. (. Then, the tangential loa caie by each mico-contact ae obtaine fom Eq. (4 an (5. If the patially tick component of the tangential foce i not zeo, the tangential iplacement houl be inceae until all mico-contact ae fully liing. Thi maximum tangential iplacement coeponing to the occuence of maco-liing i taken a the global limiting iplacement. At thi tage, the maximum tatic fiction foce i eache an o, the tatic coefficient of fiction i etemine fom Eq. (7.. Calculation of fiction coefficient An Alicona imaging infinite focu micocope (IM. wa ue to meaue the uface paamete of polyuethane. Suface paamete in tem of enity of apeity n, mean aiu of apeity, an tana eviation of the apeity height ae the input paamete of the fiction moel. igue how the oughne pofile along a electe line in the uface. The geometical paamete mentione above can be obtaine by thee meauement uing the Alicona micocope. The vicoelatic mateial paamete in tem of ping elaticity g, g an ahpot vicoity of the SLS moel ae the othe input paamete of the fiction moel. The value of vicoelatic mateial paamete ue in the calculation of the fiction moel ae obtaine fom a te elaxation tet of ubbe. In a te elaxation tet a compeive tain at a contant ate within a vey bief peio of time i applie on an uncontaine cyline an the te equie maintaining the compeive tain i ecoe in time. The tet i pefome accoing to ASTM D 648 tana. Ste elaxation moulu a a function of time (ee, Eq. fo polyuethane of Shoe hane A 95 i hown in igue 4. Accoing to Eq. ( an (, fo t we obtain ( ( g an fo t we have g g ( (. The value of input g. g paamete fo calculation of the coefficient of fiction a a function of contact peue ae peente in Table. igue : Mechanical moel epeenting the epone of vicoelatic mateial: (a Voigt moel, (b Maxwell moel, (c SLS moel. igue : Roughne pofile fo polyuethane. igue : Contact moel of ough uface. Uing the value of paamete in Table a input value fo the fiction moel peente in Section, we calculate the coefficient of fiction between polyuethane an coppe tube a a function of contact peue (ee, igue 5. It can be een fom igue 5

6 Ramezani M. an Neitzet T. / AIJSTPME ( 5(4: 7- that an inceae in contact peue eult in eceae in coefficient of fiction. At low peue thi eceae i moe ignificant than at highe loa when the coefficient of fiction eache a quite table level. Thi i compaable to the obevation mae by Benaballah [] whee expeimental wok on ome themoplatic againt teel an aluminum howe imila effect. loa, an hence, the fiction foce an fiction coefficient inceae with eceaing nomal loa. om igue 5 the following equation fo the vaiation of coefficient of fiction with peue P i cuve-fitte P (8 igue 4: Ste elaxation moulu a a function of time fo polyuethane ubbe. Table : Value of the input paamete fo fiction moel. Paamete n ( m Value.7 ( m. 54 ( m. 8 g (Pa 7 8. g (Pa 8.89 ( Pa igue 5: Coefficient of fiction (fo polyuethane/ coppe contact a a function of contact peue. The phyical explanation fo the inceaing fiction coefficient at lowe peue i that the effect of the aheion foce become moe ignificant at lowe nomal loa [4]. High aheion foce eceae the epaation h, at a given nomal loa an bing moe apeitie into contact epecially when the nomal loa i mall, enabling uppot fo lage tangential Theoetical moel The chematic of tube bulge foming i hown in igue 6. A can be een in the figue, the tube an the polyuethane o ae ivie into two zone (i.e. - an - to implify the theoetical analyi. The tube i in full contact with the ie wall in zone - an thee i no platic efomation of tube in thi egion. Howeve, the tube i not containe cicumfeentially in zone - an can efom platically until taking the hape of the ie. The theoetical moel peente in thi ection i bae on the wok of Thiuvauchelvan [9]. Mathematical fomulation fo the peue in the polyuethane o an te component in the tube ae evelope fo each zone an ae peente below. Zone -: Accoing to igue 6, the equilibium equation fo polyuethane o at zone - can be expee a p p x (9 4

7 Ramezani M. an Neitzet T. / AIJSTPME ( 5(4: 7- Subtituting Eq. (8 into Eq. (9 an implifying the eult, we aive at p 4 p x By integating Eq. (, we will have p. x C. 6 ( x C ( Accoing to igue 6 at x we have p p an o. p C. Theefoe x 6.. p p. ( igue 6: Schematic of tube bulge foming poce. On the othe han, the compeive axial loa on the tube exete by the polyuethane fictional foce can be expee a x ( p p ( 4 A the tube i agge to the ie uface, the fictional foce exete on the tube fom the ie i x p x Integating Eq. (4 lea to x.. p x x (4.. p p (5 whee i the coefficient of fiction between the ie an the tube. The axial compeive te an the hoop te on the tube wall in zone - can now be eaily eive fom Eq. (, ( an (5 by uing the following equation: x x T.95 T p 4T p. p... p.6 x (6 p...6 x p (7 T T A the tube i completely uoune by the ie wall at zone -, the hoop te i mall an may be neglecte. o thi egion an by neglecting the lateal peue p, the Teca yiel citeion i x., whee te of the tube mateial. Thu x p 4T.95 T Zone -: i the initial yiel ( p.... p p..6 x (8 The axial equilibium equation fo the polyuethane o at zone - can be expee a ( D D D ( p P p 4 4 px D (in co co (9 By neglecting highe oe tem of Eq. (9 an eaanging the equation, we have

8 Ramezani M. an Neitzet T. / AIJSTPME ( 5(4: 7- D ( p D Dp 4 p (tan ( tan Conieing x D / tan, we have D p p ( D pcot.78.9 p cot Integating Eq. ( lea to 5 ln D p.9 cot. C ( Accoing to igue 6 at D we have p p.7. an o ln p C. Theefoe cot D cot.. p p.6 ln ( Neglecting the effect of bening at point, the equilibium equation nomal to the conical uface of the tube at zone - i co p p T (4 whee i the tenile hoop te. Auming contant thickne, the equilibium equation along the axi of the tube i ( T co ( p p p cot p cot (5 Combining Eq. (4 an (5 lea to cot ( p p T co (6 whee an ae tenile an compeive tee epectively. Uing the moifie Teca yiel citeion. an combining Eq. (4 an (6 lea to cot. m ( cot coec.78 (.695 p p T (7 m whee m i the aveage yiel te of the tube mateial. By integating an manipulating Eq. (7, we aive at the following expeion fo the compeive meiian te in ection ( : D ( cot.695 coec ( cot T ( D / coec ( cot T ( D / cot. m cot D p p Calculation poceue:...6 cot ln.6 cot ln ( cot ( cot ( cot (8 om the above calculation, the peue at ection an ae given by Eq. ( an (, epectively. p p.. p.6.. p L D.6 ln cot (9 Alo, the compeive meiian tee at ection an can be achieve by Eq. (6 an (8, epectively. 4T.95.. p p p p T (4 ( cot ( cot cot. m D cot D coec. ( cot p.6 cot ln ( cot T ( D / 4.55 coec. ( cot p.6 cot ln ( cot T ( D / (4 The initial peue exete on the top of the polyuethane o to bulge the tube, p can be obtaine fom E imulation an ubequently, the value of p, p an, can be calculate uing Eq. (9-4. 4

9 Ramezani M. an Neitzet T. / AIJSTPME ( 5(4: 7-4 inite element imulation Numeical tuie wee caie out to eveal the efomation patten of the tube an to veify the theoetical analyi. A ange of foming paamete can be ue in the finite element imulation an the optimal value can be peicte at low CPU cot. ABAQUS finite element coe wa ue to imulate the poce an peict the mateial efomation uing foming. Due to the axiymmetic chaacte of the foming, only a -D moel wa ue to euce computation time. igue 7 how the hape at the lat tage of the tube bulging uing a oli bulging meium. A polyuethane o of Shoe Hane 95A an iamete 8mm wa ue to bulge an anneale coppe tube of iamete 4mm an wall thickne of.mm. The bottom plate of the ie wa not moele, intea the noe at the bottom of ie, tube an flexible meium wee containe in the appopiate iection to imulate the peence of the ie bottom plate. igue 7: E imulation of the poce at the lat tage of bulge foming. Die tool mateial wa aume to be teel, an the tube wa moele uing CAX4R (a 4-noe bilinea axiymmetic quailateal, euce integation, hougla contol element. The polyuthane o wa moele uing CAX4RH element. Penalty contact inteface wee ue to enfoce the intemittent contact an the liing bounay conition between the blank an the tooling element. The Coulomb fiction moel with vaiou value of coefficient of fiction i ue fo contact uface between the tube an the metallic ie. The coefficient of fiction between the polyuethane an the tube change with contact peue bae on the moel peente in ection. The contact peue epenent coefficient of fiction ae implemente into the moel though the contact popety option of the ABAQUS pogam. Thi option i ue to intouce fiction popetie into the mechanical uface inteaction moel. The imulation begin with the tube in contact with the ie an the polyuethane o. The flexible o then move own to bulge the tube. The inteface between the ie an the tube, an between the tube an the flexible o ae moele uing an automatic uface to uface contact algoithm. The foming loa wee applie on the polyuethane o in tem of iplacement on the top uface of the o. The iplacement wa aigne to be equal to the iplacement of the o meaue uing the expeimental tet pefome by Gia et al. [4]. The contitutive behavio of the tube i ecibe by an elatic platic moel. o the elatic pat, Young' moulu of GPa an Poion' atio of.4 i ue. o the platic pat, the haening moel i aume to be iotopic ecibe by the powe law appoach: n K (4 whee i the tue te (MPa, i the total tue tain (imenionle, K i the tength coefficient (MPa an n i the tain-haening exponent (imenionle. o the anneale coppe in thi eeach, K 5 MPa an n. 44 ae being ue an the aveage yiel te of the anneale coppe i MPa. m 97 Rubbe i mae of iotopic, non-linea, hypeelatic, incompeible, tain-hitoy-inepenent mateial. Hype-elatic mateial ae ecibe in tem of a tain enegy potential W which efine the tain enegy toe in the mateial pe unit of efeence volume (volume in the initial configuation a a function of the tain at that point in the mateial 5

10 Ramezani M. an Neitzet T. / AIJSTPME ( 5(4: 7- [5]. Among eveal fom of tain enegy potential available in ABAQUS, Ogen (N= tain enegy [6] i ue fo ubbe moeling. The Ogen mateial moel ha peviouly been ue with ucce to peict the behavio of hype-elatic mateial at high tain ate (ee, e.g. [7]. The fom of the Ogen tain enegy potential i: W ij (4 ij W N i N i i ( i i ( J D el i i i i (44 whee W i the tain enegy pe unit of efeence volume; i ae the eviatoic pincipal tetche / which can be efine by i J i ; i ae the el pincipal tetche; J i the total volume atio; J i the elatic volume atio; an i, i an Di ae tempeatue-epenent Ogen contant. Compeibility can be efine by pecifying nonzeo value fo D i, by etting the Poion' atio to a value le than.5, o by poviing tet ata that chaacteize the compeibility. We aume a fully incompeible behavio fo ubbe with.4997 an Di equal to zeo an o the econ expeion in Eq. (44 can be eliminate. To etemine the tain enegy enity W, ABAQUS ue a leat-quae fitting algoithm to evaluate the Ogen contant automatically fom expeimental ata. 5 Reult an icuion To valiate the E moel evelope in Section 4, the final thickne of the tube afte bulging i compae with expeimental eult peente by Gia et al. [4] an i hown in igue 8. A emontate in the figue, the thickne itibution obtaine fom the E moel an the expeiment agee vey well with each othe with the eo le than 6%. A hown in the figue, the maximum thinning happen at the en of the tube, whee the tube ha the maximum expanion. The unefome pat of the tube oe not how any euction in thickne. The peue P at the top of the polyuethane o obtaine fom E imulation with iffeent value of coefficient of fiction between the ie an the tube i hown in igue 9. A can be een in the figue, highe peue ae neee fo bulging with highe fiction coefficient to ovecome the fictional eitance between the ie an the tube. igue 8: Thickne itibution of the bulge tube obtaine fom E imulation. igue 9: Peue at the top of the polyuethane o obtaine fom E imulation. The vaiation of peue at point an (ee igue 6 of the o ae illutate in igue an. The value of P an P ae calculate uing Eq. (9. Accoing to the figue, the eult of E imulation an the theoetical moel coelate with each othe. The maximum eo fo peicting P i 6

11 Ramezani M. an Neitzet T. / AIJSTPME ( 5(4: 7-4.6% which happen at the coefficient of fiction of.. The eo inceae to 4.9% fo peiction of P. in igue 4 an 5. It can be een that the te component ten to inceae with inceaing the coefficient of fiction. Thi i ue to the highe foming peue exete to the tube fom the polyuethane o at highe fiction. The theoetical moel peict thi inceae quite linealy. The compaion between the theoetical an E imulation eult how goo coelation. The maximum peiction eo at i % fo. an 8.% fo. The E imulation ten to peict the tee highe than the theoetical moel. igue : Vaiation of P with coefficient of fiction. igue : Vaiation of peue at iffeent point of the polyuethane o with tube thickne. igue : Vaiation of P with coefficient of fiction. The effect of tube initial thickne an length of the o on the itibution of peue at iffeent point of the polyuethane o i calculate uing the theoetical moel an peente in igue an. A can be een in the igue, highe peue ae neee to bulge the tube with thicke wall. igue how that a length of the o in contact with the containe pat of the tube inceae, the peue neee to bulge the tube inceae. Howeve, the calculation how that the effect of o length i not a ignificant a the tube thickne. The effect of coefficient of fiction between the tube an the ie on the vaiation of tee an at point an of the tube (ee igue 6 i hown igue : Vaiation of peue at iffeent point of the polyuethane o with the length of the o. Effect of initial tube thickne an polyuethane o length on the te at point of the tube ae calculate uing the theoetical moel an ae hown in igue 6 an 7. A emontate in igue 6, 7

12 Ramezani M. an Neitzet T. / AIJSTPME ( 5(4: 7- the te at point inceae haply with eceaing the initial tube thickne which make it ifficult to bulge vey thin tube. Accoing to igue 7, the inceae in the o length oe not have a emakable effect on the te at point. thee i a hap eceae in axial te at point at the en tage of the bulge foming poce. igue 6: Effect of initial tube thickne on te. igue 4: Vaiation of te with coefficient of fiction. igue 7: Effect of polyuethane o length on te. igue 5: Vaiation of te with coefficient of fiction. The hitoy of aial te at point an uing the E imulation i hown in igue 8. A hown in the figue, the compeive aial te inceae contantly uing the poce an make it poible to expan an bulge the tube en. The value of tee at point an ae quite imila which i ue to the hyotatic natue of the bulge foming uing an elatome bulging meium. The vaiation of axial te at point an of the tube with imulation time i hown in igue 9. A can be een in the figue, the axial tee inceae with time, howeve igue 8: Raial te hitoy at point a of the tube uing bulging imulation. 8

13 Ramezani M. an Neitzet T. / AIJSTPME ( 5(4: 7- igue 9: Axial te hitoy at point a of the tube uing bulging imulation. 6 Concluion In thi pape bulge foming of tubula component wa invetigate uing an analytical moel an E imulation. A new fiction moel bae on local contact conition wa ue in the E imulation of the poce an bae on the eult of thi fiction moel, a theoetical moel fo bulge foming wa evelope. The main concluion of thi eeach ae a follow: An inceae in contact peue eult in eceae in coefficient of fiction between ubbe an metal. The coefficient of fiction eache a nealy contant value at highe nomal peue. Highe peue ae neee to bulge the tube with thicke wall. The te at the en of the tube inceae haply with eceaing the initial thickne of the tube, which may caue uptue at the en of the tube with vey thin wall. The effect of the length of the elatomeic o on the peue an te itibution i negligible. Compeive axial an aial tee at the tube inceae contantly uing the poce which make it poible to bulge the tube. Refeence [] Mac Donal BJ, Hahmi MSJ ( Nea-nethape manufactue of engineeing component uing bulge-foming pocee: a eview. J Mate Poce Technol :4 47. [] Ramezani M, Ripin ZM, Ahma R (9 A tatic fiction moel fo tube bulge foming uing a oli bulging meium. Int. J. Av. Manuf. Tech. 4 ( 4:8 47. [] Kim J, Kim SW, Pak HJ, Kang BS (6 A peiction of buting failue in tube hyofoming poce bae on platic intability. Int J Av Manuf Technol 7: [4] Gia AC, Genie YJ, Mac Donal BJ (6 Numeical imulation of axiymmetic tube bulging uing a uethane o. J Mate Poce Technol 7: [5] Mac Donal BJ, Hahmi MSJ ( Theeimenional finite element imulation of bulge foming uing a oli bulging meium. inite Elem Anal De 7:7 6. [6] Pipan J, Koel ( Numeical imulation of otational ymmetic tube bulging with inie peue an axial compeion. Int J Mech Sci 44: [7] Hwang YM, Lin YK ( Analyi an finite element imulation of the tube bulge hyofoming poce. J Mate Poce Technol 5 6:8 85. [8] Yang B, Zhang WG, Li SH (6 Analyi an finite element imulation of the tube bulge hyofoming poce. Int J Av Manuf Technol 9 (5: [9] Thiuvauchelvan S (994 A theoy fo the bulging of aluminum tube uing a uethane o. J Mate Poce Technol 4:. [] Thiuvauchelvan S (994 A theoy fo initial yiel conition in tube bulging with a uethane o. J Mate Poce Technol 4:6 74. [] Boumaiza S, Coeboi JP, Bunet M, Nefui G (6 Analytical an numeical tuy on platic intabilitie fo axiymmetic tube bulging. Int J Mech Sci 48: [] ukua M, Yamaguchi K (974 On the coefficient of fiction between ubbe an metal une high peue. Bulletin of JSME 7 (: [] Ramezani M, Ripin ZM, Ahma R (9 Compute aie moelling of fiction in ubbepa foming poce. J Mate Poce Technol 9 (: [4] Ramezani M, Ripin ZM, Ahma R (8 Moelling of kinetic fiction in V-bening of ulta-high-tength teel heet. Int J Av Manuf Technol 46 (-4:-. [5] Ramezani M, Ripin ZM ( A fiction moel fo y contact uing metal-foming pocee. Int J Av Manuf Technol 5 (-4:9-. 9

14 Ramezani M. an Neitzet T. / AIJSTPME ( 5(4: 7- [6] Hetz H (88 Übe ie Beühung fete elatiche Köpe. J. Reine. Angew. Math. 9:56 7. [7] Minlin RD (949 Compliance of elatic boie in contact. ASME J. Appl. Mech. 6: [8] Johnon KL (985 Contact mechanic. Cambige: Cambige Univeity Pe. [9] Geenwoo JA, Williamon JBP (966 Contact of nominally flat uface. Poc. Roy. Soc. Lonon, A 95: 9. [] Hui CY, Lin YY, Baney JM ( The mechanic of tack: vicoelatic contact on a ough uface. J Polym Sci, B: Polyme Phyic, 8: [] Bueau L, Caoli C, Baumbege T ( Elaticity an onet of fictional iipation at a non-liing multi-contact inteface. Poc. Roy. Soc. Lonon, A 459, 8: [] Delai EL (6 Static fiction in ubbe metal contact with application to ubbe pa foming pocee. PhD thei, Univeity of Twente, The Nethelan. [] Benaballah HS (7 Static fiction coefficient of ome platic againt teel an aluminum une iffeent contact conition. Tibol. Int. 4:64 7. [4] Yu N, Pegane SR, Polycapou AA (4 Static fiction moel fo ough uface with aymmetic itibution of apeity height. ASME J Tibol 6: [5] Ramezani M, Ripin ZM, Ahma R (9 Numeical imulation of heet tamping poce uing flexible punch. Poc. IMechE, B: J. Eng. Manuf. (7: [6] Ogen RW (97 Lage efomation iotopic elaticity on the coelation of theoy an expeiment fo incompeible ubbelike oli. Poc. Roy. Soc. Lonon, A 6: [7] Ramezani M, Ripin ZM ( Combine expeimental an numeical analyi of bulge tet at high tain ate uing plit Hopkinon peue ba appaatu. J. Mate. Poce. Tech. (8:6-69.