Analytical and Numerical Analysis of Free Bulge Tube Hydroforming

Transcription

1 Amercan Journal of Appled Scences 5 (8): , 8 ISSN Scence Publcatons Analytcal and Numercal Analyss of Free Bulge Tube Hydroformng F. Djavanrood, M. Ghesary and H. Zogh-shal Department of Mechancal Engneerng, Iran Unversty of Scence and Technology, Tehran, Iran Abstract: Free bulge hydroformng smulaton was analysed to nvestgate the baxal behavor of extruded alumnum tubes. A fnte element model was constructed to smulate the hydroformng process and asses the nfluence of frcton between de walls and tube, tube materal propertes and sprngback of formed tube. It was found that materal hardenng coeffcent had the most sgnfcant nfluence on formablty characterstcs durng bulge hydroformng, the smulated model also revealed that de radus and tube thckness had great effects on sprngback and hence changed tolerances of formed tube. Also an analytcal model for free bulge formng was proposed and t was shown that for β =.5(β = ε /ε ), good correlaton between expermental and analytcal model was obtaned. It was also shown that for β = ( ), formablty of tube ncreased and lower pressure s needed for formng the tube. Key words: Free bulge formng, tube hydroformng, frcton coeffcent, stran hardenng INTRODUCTION Tube hydroformng has emerged as one the desrable manufacturng processes n automotve and aero ndustres due to t s capablty of creatng complex shapes n a sngle step. It also offers further advantages such as mproved structural strength and stffness, lghter products and more effcent materal usage. Open de hydroformng s one of the popular methods used to obtan baxal behavor of extruded and welded tubes []. Although the applcaton of nternal pressure s the fundamental mode to acheve the desred expanson of the tubes, the end condtons used n these tests can be prmarly classfed nto three categores, as llustrated n Fg.. Nelsen [], Harl [] and Sgret [3] studed dfferent methods, advantages, Lmtatons and equpments n Tube Hydroformng Process. Altan [4] optmzed Forceend tube Hydroformng process by usng expermental and smulaton data. Frcton coeffcent and materal propertes nfluences were shown n hs study. Krdl [5] used axs symmetrc model and plan stran assumpton to smulate Force-end tube hydroformng wth ABAQUS. It was shown that wth hgher de radus lower thckness varaton obtaned. Fan [6] studed formng of T-branch tubes and used expermental and smulaton to get to Formng Lmt Dagram (FLD) to optmze Process. It was shown that sequental method s much better than batch method to acheve Formng Lmt Dagram (FLD). Batalha [7] smulated Tube hydroformng (both free end and forced end) wth Ls- Dyna and optmzed FLD for force end tube hydroform. Imannejad [8,9,] showed that stran hardenng had the most nfluence on Formablty of the tube, so that wth hgher coeffcents, lower nternal pressure needed. Also frcton coeffcent effects, ansotropc of welded tubes and load path optmzaton n force end tube Hydroformng (THF) studed n these artcles. It was shown that to obtan to optmze thckness dstrbuton; the majorty of the end feed should be appled after the tube materal yelded under nternal pressure. Asnaf [] calculated optmzed load path n force end tube Hydroformng (THF) by expermental, analytcal and numercal technques. He used stroke controlled method to analyze tube Hydroformng (THF). Asnaf [] also, studed sprngback on doublecurved autobody panels. Yasar [3] has analyzed the sprngback behavor of alumnum cylndrcal cups obtaned by gas detonaton formng process. Palanswamy [4] has studed the sprngback effect on an axsymmetrc concal part manufactured by flex formng. In ths study, a fnte element model was constructed to smulate the hydroformng process and asses the nfluence of frcton between de walls and tube, tube materal propertes and sprng back of formed tube. Correspondng Author: F. Djavanrood, Department of Mechancal Engneerng, Iran Unversty of Scence and Technology, Tehran, Iran 97

2 Am. J. Appled Sc., 5 (8): , 8 a) b) c) Fg. : (a-c) schematc llustraton of the end condtons used durng hydroformng [8]. (a) Free-formng (b) Fxed-end (c) Forced-end Where And σ α = (4) σ β = ε / ε (5) The tangental and radal strans, ε and ε, can be denoted as: ε = Ln( ) (6) Fg. : The stress actng on an element at the mddle of the tube Also an analytcal model for free bulge formng was proposed and t was shown that when β =.5 (β = ε /ε ) good correlaton between expermental and analytcal model can be obtaned. ANALYTICAL SOLUTION Yeldng: Consder a tube that s subjected to an nternal pressure p (Fg. ). For an element at the mddle of ths tube, the followng equlbrum can be wrtten [] : t ε = (7) Ln( ) t Where and s ntal and fnal tube wall thckness and t s nstantaneous tube wall thckness. The levy-mses flow rule yelds (assumng volume constancy): Or α = (β + ) /( + β ) (8) β = (α ) /( α ) (9) Combnng Eq., and 4 gves: σ σ P + = t () σ t α = + ( α + α ) () Von Mses yeld crteron (plane stress) and the equvalent stran can be wrtten as: And σ = ( α + α ) σ () ε = (4( + β + β ) /3) ε (3) At the nterface between elastc and plastc deformaton, t can be assume that: = (d t )/ () = () t = t (3) 973

3 Am. J. Appled Sc., 5 (8): , 8 Orgnal tube Shape durng hydroformng Combnng Eq. () and () yelds: p = t σ (d t ) α + α () If Fg. 3: The plastc deformaton ( = ) σ = σ (4) y Where d s ntal (outer) tube dameter and σ y s yeld stress of the tube materal. Substtutng Eq. -4 nto Eq., yelds: σ t (5) y y (d t )( α + α ) = Eq. (5) can be used for determnng the yeld lmt. Eq. (6) can be used to obtan the stroke n yeldng pressure (L s ntal tube length): νσ / E y Sy = L ( e ) β.5 β (6) sne n free bulge formng S =, yeldng pressure s: P Yeld t = σy D t (7) Plastc deformaton: Assume that that the tube expands n the fashon shown n Fg. 3. Ths assumpton means that =. Wth ths assumpton, Eq. can be wrtten as: Combnng σ P = t d t (8) = (9) d s nstantaneous tube dameter (outer dameter), wth Eq. 8: tσ p = d t () n σ = k( ε ) () Combnng Eq. 3 and wth Eq., one obtans: n tkε p = ( 4( + β + β ) /3) (d t ) α + α Substtutng n ε = Ln( ) = Ln[(d t )/(d t )] And Eq. 9 nto Eq. 3 yelds: t d t p = k( ) ( α + α ) (Ln ) d t α d t Assume now that: n n n (3) (4) (5) ε + ε + ε 3 = (6) Combnng Eq. 5, 7 and 9 wth Eq. 6, we can wrte: d t = t [(d t ) /(d t )] t ( ) (7) ( +β) ( +β) d FEM Analyss: A D element wth four node blnear ax-symmetrc quadrlateral wth the explct method was used for smulaton. For des, rgd analyss was selected and the tube assumed to have Isotropc behavor. After mesh verfcaton (Max bulge heght and Von-Msses maxmum stress are output parameters), expermental [8] and smulated results were compared. Materal used for the analyss was alumnum alloy 68-T4. Mechancal and physcal propertes and tube dmensons are shown n Table and Fg. 4. Frcton coeffcent s assumed to be.5(µ =.5) [7,8,]. In order to confrm the accuracy of modelng a comparson has been made wth the expermental data [8], results are shown n Table and Fg. 5. As t can be seen a good agreement between expermental and numercal results has been acheved (average error<%). 974

4 Am. J. Appled Sc., 5 (8): , 8 Table: Alumnum alloy 68-T4 characterstcs [8].7 Densty,,(g/cc) 7 Young Modulus, E, (Gpa).3 Posson Coeffcent () 49 Strength Factor, K (Mpa).3 Stran Hardenng exponent, (n) 6 Yeld Stress, (MPa) Table : Expermental and smulaton results Error Max. bulge heght Max. bulge heght Pressure (%) (Smulaton) (Experments) [8] (Mpa) Fg. 4: Tube and de dmensons RESULTS AND DISSCUSION Analytcal results: Solvng equatons 5 and 7 smultaneously, maxmum bulge heght and thckness varaton (n max bulge heght poston) can be obtaned. These results are compared wth smulaton data n Fg. 6. As llustrated, for β =.5, a good correlaton between smulaton and analytcal results has been acheved. It s also evdent that for β = ( ), formablty of tube ncreased and lower pressure s needed for formng the tube and thckness varaton wll ncrease. Numercal analyss results Stran hardenng coeffcent (n): To nvestgate the effect of hardenng coeffcent (n) on the formablty of the extruded tube, pressure assumed to be 49.7Mpa and the value of n were vared between o. to.3 and the correspondng bulge heghts were compared. The resultng tube expanson s shown n Fg. 7. As llustrated, a larger hardenng coeffcent results n a hgher expanson. Moreover, for a gven ncrement n n a greater ncrease n formablty was seen at hgher n value. Max Bulge Heght (mm) Expermental Smulato (wthout sprng back rato) Smulaton wth sprng back Rato Pressure(Mpa) Fg. 5: Expermental [8] and smulatng befor and after sprng back correcton These results are n agreement wth the known formablty characterstcs based on power law consttutve model for sheet metals [4]. It can be concluded that materal wth hgher hardenng coeffcent are always desrable so as to maxmze the allowable expanson. Influence of frcton: Frcton plays an mportant role n the majorty of formng operatons. A low frcton coeffcent s often desrable for formng process. To study the effect of frcton between the de and tube surfaces, dfferent frcton coeffcents between. and., were consdered n the FE smulaton. The power law consttutve model was employed and the resultng bulge heghts and thckness varaton plotted aganst the frcton coeffcent n Fg. 8. As one can see, a hgher frcton coeffcent leads to a lower expanson and more thckness varaton. In other words, decreasng the frcton wll result n an ncrease n the formablty of tubes. 975

5 Am. J. Appled Sc., 5 (8): , 8 Outsde Dameter (mm) ß = ß = -.5 ß = -.7 Smulaton Internal Presssure(Mpa) (a) Thckness (mm) ß = ß = -.5 ß = -.7 Smulaton Internal Pressure(Mpa) (b) Fg. 6: Analytcal results, (a) nstantaneous outer dameter (at the top of the bulge), (b) Thckness varaton (top of the bulge) Thckness(mm) Stran Hardenng (a) Max Bulge Heght (mm) Stran Hardenng Exponent (n) (b) Fg. 7: Influence of hardenng coeffcent on formablty of tube, (a) Max bulge heght, (b) Thckness varaton Sprng back: Better shape accuracy on formed tubes has been requred and dscussed n many years. It s, therefore, essental to clarfy the factors governng tolerances on the formed tube. Sprngback after formng processes, has the sgnfcant nfluence on the dmensons and tolerances of the formed tube. Sprngback wll occurr after removng nternal pressure (formng tool). When the formng force s removed, hgher yeld Stress, hgher elastc stran and lower module of elastcty ncrease sprngback value. For a specfed metal wth specfed stran, sprngback value ncrease wth hgher wdth-thckness rato. Moreover, Heat treatment method, alloy components, de radus, bendng angle and real stress-stran dagram (contact module) show ther effects on tolerances of fnal formed tube []. As pressure ncreases, plastc zone expands n the center of the tube and remander of the tube remans elastc, when pressure s removed, maxmum sprngback appears on the maxmum bulge heght. 976 As frcton between de walls and tube ncreases, t creates a bead force on the contact surface and expand plastc zone, so ncreasng frcton coeffcent would lead to a reducton n sprngback value. Ths s shown n Fg. 8. As llustrated n Fg. 9 ncreasng module of elastcty (E), wll lead to a faster yeldng of the surface of the tube, thus sprngback would decrease. The effect of yeld stress on sprngback value s shown n Fg.. It s clear that as yeldng stress ncreases, the rato of plastc/elastc deformaton becomes sgnfcant e. Elastc part ncreases and hence larger sprngback value. For low yeld stress plastc deformaton s much larger than elastc deformaton and sprngback values decreases. Thckness ncrement, ncreases bendng moment and so ncrease bendng stran n external warps and therefore decrease sprng back on the formed tube. Ths s shown n Fg.. De radus s one the most mportant parameters and has sgnfcant effects on sprngback and accuracy.

6 Am. J. Appled Sc., 5 (8): , 8 Thckness (mm) Frcton Coffcent (a) Max Bulge Heght (mm) Frcton cofftent (b) Sprng back (%) Frcton Coeffcent (c) Fg. 8: Influence of Frcton coeffcent on formablty of tube, (a) Max bulge heght, (b) Thckness varaton, (c) Frcton nfluence on sprngback percentage Sprng Back (%) Module of Elastcty Fg. 9: Elastcty module effects on sprngback (%) Small radus cause local ntensve deformaton and so plastc zone ncrease n the contact surface sgnfcantly, ths wll cause the elastc deformaton to be reduce, therefore sprngback rato decrease (Fg. ). Sprng Back (%) Yeld Stress (Mpa) Fg. : Yeld stress nfluen Fgure 4 shows the combned effect of thckness and de radus on sprngback rato (specmen angle after r formng/de angle Fg. 3), for = the sprngback t α rato s = α 977

7 Am. J. Appled Sc., 5 (8): , 8 Sprng back (%) Sprng back Rato Thckness (mm) Fg. : Thckness nfluences on sprngback Sprngback Rato R/t (De Rads/Thckness) Fg. : De radus/thckness rato effects on sprngback (%) Fg. 3: De radus and bendng angle n free bulge formng Table 3: Results after usng correcton coeffcent on smulaton data Error Max. Bulge heght Max. bulge heght Pressure (%) (Smulaton) (experments) (Mpa) 3.% % % % R/t(De Radus/Thckness) Fg. 4: Sprngback correcton factor effect on smulaton, (a) R/t.5, (b) R/t >.5 Introducng sprngback correcton factor n to fnte element analyss would lead to a lesser error (<%8) as shown n Table 3 and Fg. 5. CONCLUSION Based on the above expermental, FE smulaton and theoretcal analyss results and subsequent dscussons, the followng concluson are drawn: Stran hardenng coeffcent has the sgnfcant nfluence on formablty of the tube, so that for formng materals wth hgher n, Low nternal pressure s needed, but thckness varaton n these materals s hgher than others wth lower stran hardenng coeffcent. As frcton between de walls and tube ncrease, t causes rentent force on the contact surface, so maxmum outer dameter decrease and thckness varaton ncrease. As llustrated n ths study, f tght tolerances are necessary on fnal formed tube, sprng back should be controlled n the process. Wth hgher frcton, hgher elastcty module, hgher ntal thckness, lower de radus and lower yeldng stress, tghter tolerances can be achved. When sprngback rato correctng coeffcent were used ( r t = ) ( α =.9375 ), better α correlaton could be acheved between expermental and numercal results. Theoretcal analyss showed that thn walled cylnder equatons were sutable to solve tube hydroformng process. It was shown that when β drawn on ( ) (Thn walled sphere), lower nternal pressure was needed to form. In β =.5, there s better correlated between smulaton and analytcal results. 978

8 Am. J. Appled Sc., 5 (8): , 8 REFERENCES. Nelsen, K.B., 4. Hydro Formng Hghlghts: Sheet Hydro Formng and Tube Hydro Formng. J. Mater. Processng Tech., 5: Hartl, Ch., 5. Research and Advances n Fundamentals and Industral Applcaton of Hydro Formng. J. Mater. Processng Tech., 67: Sgeret, K.,. Recent Development n HydroFormng Technology. J. Mater. Processng Tech., 48: Altan, T., 4. Optmzaton Tube Hydro Formng Usng Process Smulaton and Expermental Verfcaton. J. Mater. Processng Tech., 46: Krd, G.T., 3. Investgaton of Thckness Varaton and Corner Fllng n Tube HydroFormng. J. Mater. Processng Tech., 33: Fann, K., 3. Optmzaton of Loadng Condtons for Tube HydroFormng. J. Mater. Processng Tech., 4: Batalha, G.F., 5. Expermental and Numercal Smulaton of Tube Hydro Formng. J. Mater. Processng Tech., 64-65: Imannejad, M., 4. Expermental and Numercal Investgaton of Free-Bulge Formaton Durng HydroFormng of Alumnum Extruson. J. Mater. Processng Tech., 47: Imannejad, M., 4. Influence of End-Condtons Durng Tube Hydro Formng of Alumnum Extruson. Int. J. Mechancal Sc., 46: Imannejad, M., 5. Loadng Path Optmzaton of Tube Hydroformng Process. J. Machne tools and manuf., 45: Asnaf, N.,. Theoretcal and Expermental Analyss of Stroke-Controlled Tube Hydro Formng. J. Mater. Sc. and Eng., A79: Asnaf, N.,. On Sprng Back of Double- Curved Autobody Panels. Int. J. Mechancal Sc., 43: Yasar, M., 4. Gas Detonaton Formng Process and Modelng for Effcent Sprng Back Predcton. J. Mater. Processng Tech., 5: Palanswamy, H., 4. Optmzaton of Blank Dmensons to Reduce Sprngback n the Flexformng Process. J. Mater. Processng Tech., 46: Deater, G.E.,. Mechancal Metallurgy. 979