INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN

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1 INTERNTIONL JOURNL OF DVNCED RESERCH IN Inenaional Jounal of dvanced Reseach in Engineeing and Technology (IJRET), ISSN 976 ENGINEERING 648(Pin), ISSN 976 ND 6499(Online) TECHNOLOGY Volume 3, Numbe (IJRET), July-Decembe (), IEME ISSN (Pin) ISSN (Online) Volume 3, Issue, July-Decembe (), pp IEME: Jounal Impac Faco ():.778 (Calculaed by GISI) IJRET I E M E MTHEMTICL MODELING ND NLYSIS OF HOOP STRESSES IN HYDROFORMING DEEP DRWING PROCESS BSTRCT D.R.Uday Kuma ssisan pofesso, Dep.of Mechanical Engineeing Mahama Gandhi Insiue of Technology, Gandipe, Hydeabad ndha Padesh. India. Cell No# This pape pesens evaluaion of hoop sesses of magnesium alloys hough mahemaical fomulaions in hydofoming deep dawing pocess. In hydofoming deep dawing pocess, applying he hydaulic pessue on blank peiphey in adial diecion. I is obained hough he punch movemen wihin he fluid chambe, which is povided in punch and die chambes. These wo chambes ae conneced wih he bypass pah and i is povided in he die. Duing he pocess punch movemen wihin he fluid chambe he pessue is geneaed in fluid and i is dieced hough he bypass pah o blank peiphey, he fluid film is ceaed on he uppe and lowe sufaces of he blank and subsequenly educes ficional esisance and is o educe ensile sesses acing on he wall of he semi dawn blank. The blank is aking a cene place in beween blank holde and die suface wih suppoing of high pessuized viscous fluid. The hoop sesses ae poduced in he blank in cicumfeenial diecion due o punch foce applied on i, he shea sesses aced by viscous fluid on he boh sides of blank, so apply viscosiy phenomenon o his analysis. The blank holde pessue is conolled by he adial pessue of fluid and hese ae equal fo unifom defomaion of blank o obained equied shape and also eliminaion of failue of blank in defomaion. The hoop sesses ae deemined in ems of viscosiy of caso oil, blank geomey and pocess paamees fo magnesium alloys. Keywods: hoop sess, viscosiy, shea sess, deep dawing pocess, hydo foming. INTRODUCTION Hydofoming deep dawing is one of shee meal foming pocess o poduce seamless shells, cups and boxes of vaious shapes. In his foming pocess, an addiional elemen such as fluid pessue is o be conibues posiively in seveal ways. mongs he advanages of hydaulic pessue foming deep dawing echniques, inceased deph o diamee aio s and educes 43

2 Inenaional Jounal of dvanced Reseach in Engineeing and Technology (IJRET), ISSN (Pin), ISSN (Online) Volume 3, Numbe, July-Decembe (), IEME hickness vaiaions of he cups fomed ae noable. pa fom ha, he hydaulic pessue is applied on he peiphey of he flange of he cup, he dawing being pefomed in a simulaneous push-pull manne making i possible o achieve highe dawing aio s hen hose possible in he convenional deep dawing pocess. In deep dawing a shee meal blank is dawn ove a die by a adiuses punch. s he blank is dawn adially inwads he flange undegoes adial ension and cicumfeenial compession []. The lae may cause winkling of he flange if he daw aio is lage, o if he cup diamee-o-hickness aio is high. blank-holde usually applies sufficien pessue on he blank o peven winkling []. Radial ensile sess on he flange being dawn is poduced by he ension on he cup wall and hoop sesses ae induced by he punch foce. Hence, when dawing cups a lage daw aios, lage adial ension ae ceaed on he flange and highe ensile sess is needed on he cup wall. Bending and unbending ove he die adius is also povided by his ensile sess on he cup wall. In addiion, he ension on he cup wall has o help o ovecome ficional esisance, a he flange and a he die adius. s he ensile sess ha he wall of he cup can wihsand is limied o he ulimae ensile sengh of he maeial, in he field of hydo fom deep dawing pocess he special dawing pocesses such as hydo-foming [3], hydo-mechanical foming [4], coune-pessue deep dawing [5], hydaulic-pessue- augmened deep dawing [6]. The pocess is an auomaic co-odinaion of he punch foce and blank holding foce, low ficion beween he blank and ooling as he high pessue liquid lubicaes hese inefaces and eliminaion of he need fo a complicaed conol sysem [7-]. The pessue on he flange is moe unifom which makes i easies o choose he paamees in simulaion. The pessue in he die caviy can be conolled vey feely and accuaely, wih he appoximae liquid pessue as a funcion of punch posiion, he pas can dawn wihou any scaches on he ouside of he pa and also obained in good suface finish, suface qualiy, high dimensional accuacy and complicaed pas. In he hydofoming deep dawing pocess he pessuized fluid seves seveal puposes ae suppos he shee meal fom he sa o he end of he foming pocess, hus yielding a bee fomed pa, delays he on se of maeial failue and educes he winkles fomaion. In his pape he hoop sesses ae evaluaed in ems of viscosiy of fluid, blank geomey, and pocess paamees fo magnesium alloys and sudied using above pocess heoeically. The viscosiy phenomenon is consideed fo evaluaion of he pocess.. NOTTION p Radius of punch cp cone adius on punch d adius of die opening cd cone adius on die hickness of blank j adius of blank σ adial sess σ ө hoop sess dθ angle made by elemen a job axis P h blank holde pessue P adial pessue of fluid Shea sess acing by he fluid on each side of elemen Toal Shea sess aced by he fluid on he Elemen d widh of elemen adial disance of blank elemen fom job axis σ o yield sess σ Radial sess a die cone. d C cleaance beween die and punch d p (dy) disance beween uppe suface of he blank elemen and blank holde 44

3 Inenaional Jounal of dvanced Reseach in Engineeing and Technology (IJRET), ISSN (Pin), ISSN (Online) Volume 3, Numbe, July-Decembe (), IEME (dy) disance beween lowe suface of he blank elemen and die suface dy disance mainained by blank elemen fom boh blank holde and die suface shea sess aced by fluid on uppe suface of he blank elemen shea sess aced by fluid on lowe suface of he blank elemen du velociy of he blank elemen elaive o blank holde and die suface µ dynamic viscosiy o absolue viscosiy o Viscosiy of fluid, he oal shea sess acing by he fluid on he blank elemen h heigh of he gap hickness of fluid 3. MTHEMTICL MODELING 3. Evaluaion of Hoop Sess The Hydofoming deep dawing Pocess as shown in fig.. In his dawing Pocess, a high pessue is poduced in he fluid by he punch peneaion ino he fluid chambe. This pessuized fluid is dieced o he peipheal suface of he blank hough he bypass holes and also his high pessue fluid leak ou beween he blank and boh he blank holde and die. This ceaes a fluid film on uppe and lowe suface of he flange and subsequenly educes ficional esisance. Duing he pocess he shea sesses ae acing by fluid on he boh sides of semi dawn blank a a gap, which is povided beween he blank holde and die suface and he semi dawn blank is aking place a middle of he gap. The heigh of he gap is moe han he hickness of he blank. The adial sesses ae geneaed in he blank in adial diecion and hoop sesses ae poduced in he blank in cicumfeenial diecion due o punch foce applied on i. So hese sesses ae geneaed in cicula blank maeial duing in he hydofoming deep dawing pocess. The vaious sesses acing on he blank elemen duing he pocess is shown in fig.. Fo mahemaical modeling and evaluaion of hoop sesses, le us conside a small elemen of blank d in beween blank holde and die suface in adial diecion a a disance fom he job axis of he cicula blank wih in he fluid egion (fig..). The viscous fluid conac on he boh sides of blank elemen, due o his, he viscous foce is aced by fluid on he boh sides of he blank elemen. The oal shea sess acing by he fluid on he elemen (i.e. shea sess is acing by he fluid on he each sides of elemen and i is same).then shea foce F is given by, F x c Whee c fluid conac aea of elemen Bu c d d dθ + ddθ 45

4 Inenaional Jounal of dvanced Reseach in Engineeing and Technology (IJRET), ISSN (Pin), ISSN (Online) Volume 3, Numbe, July-Decembe (), IEME Fig. Hydofoming Deep Dawing pocess pply he equilibium condiion adial diecion equal o zeo. s σ, θ + F ( σ σ θ )d + dσ d () σ ae he wo pinciple sesses, he equaion is obain by using Tesca s yield cieia σ Fig.. Sesses acing on he elemen duing Dawing pocess in adial diecion, i.e. Ne foces acing on he elemen in he σ () σ σ + dσ dσ Combining eq. (), (3) and eq.() + d σ d + dσ + d d Dividing by σ onn boh sides, we ge (3) dσ d dσ σ d (4) Inegaing dσ d dσ σ d 46

5 Inenaional Jounal of dvanced Reseach in Engineeing and Technology (IJRET), ISSN (Pin), ISSN (Online) Volume 3, Numbe, July-Decembe (), IEME σ Whee C is consan, i is obained fom bounday condiion. Tha bounday condiion : a j, σ and σ Q µ coefficien of ficion beween blank and boh he blank holde and die suface The bounday condiion is sub. in eq. (5 ) we ge, C j + σ ln Componen C is sub. in eq.(5) σ ln j This equaion (6) epesens mahemaical modeling and disibuion of hoop sesses in he blank duing he hydofoming deep dawing pocess. 4. PHENOMEN OF VISCOSITY In his hydofoming deep dawing pocess, he blank is ineacion wih he fluid, hen he viscosiy is comes ino he picue. Duing he pocess he shea sesses andd shea foces ae acing by he fluid on he blank in he gap, which is he egion beween blank holde and die suface. Duing he hydofoming deep dawing pocess, he blank is aking place a middle of he gap. The effec of viscosiy phenomenon in his pocess as shown in below fig.3. Newon s law of viscosiy is inoduced o his pocess fo evaluaion of hoop sesses in ems viscosiy, hen he sudy of effec of viscosiy of influence on hese sesses is incopoaed. Le us conside a small elemen of blank in beween blank holde and die suface wih in he fluid egion i.e gap. as shown in fig.3.. dy, becausee he blank elemen is aking place a middle of he gap Bu ( ) ( dy) ( j [ ln ] + ) + C ( ) (5) whee µ is he j (6) Fig.3.The blank elemen beween blank holde and die suface wihin he fluid egion ( dy ) ( dy) bu ( dy) dy h 47

6 Inenaional Jounal of dvanced Reseach in Engineeing and Technology (IJRET), ISSN (Pin), ISSN (Online) Volume 3, Numbe, July-Decembe (), IEME Because, ccoding o Newon s law of viscosiy µ, µ Le us The oal shea sess acing by he fluid on he blank elemen + Bu µ, Whee du u u µ 4µ u h µ u h 4µ u h Now we have o deemine he hoop sesses in ems of viscosiy and hen he sudy of effec of viscosiy of influence on hese sesses is incopoaed. (7) 5. HOOP STRESSES EXPRESSED IN TERMS OF VISCOSITY We know ha hoop sesses disibuion in magnesium alloys blanks duing he pocess is given by eq.6. j σ ln ( j ) and subsiue componens fom eq. ( 7 ) we ge j 4µ u j σ ln (8) h The equaion (8) epesens he effec of viscosiy of fluid on he mahemaical modeling and disibuion of hoop sesses in he blank duing hydofoming deep dawing pocess. 6. DESCRIPTION OF MGNESIUM LLOYS Magnesium is he highes of he commecially impoan meals, having a densiy of.74 gm/cm 3 and specific gaviy.74 (3% highe han aluminum alloys and 75% lighe han seel). Like aluminum, magnesium is elaively weak in he pue sae and fo engineeing puposes is almos always used as an alloy. Even in alloy fom, howeve, he meal is chaaceized by poo wea, ceep and faigue popeies. Sengh dops apidly when he empeaue exceeds C, so magnesium should no be consideed fo elevaed empeaue sevice. Is modulus of elasiciy is even less han ha of aluminum, being beween one fouh and one fifh ha of seel. 48

7 Inenaional Jounal of dvanced Reseach in Engineeing and Technology (IJRET), ISSN (Pin), ISSN (Online) Volume 3, Numbe, July-Decembe (), IEME Thick secions ae equied o povide adequae siffness, bu he alloy is so ligh ha i is ofen possible o use hicke secions fo he equied igidiy and sill have a lighe sucue han can be obained wih any ohe meal. Cos pe uni volume is low, so he use of hick secions is geneally no pohibiive.fo engineeing applicaions magnesium is alloyed mainly wih aluminum, zinc, manganese, ae eah meals, and ziconium o poduce alloys wih high sengh o-weigh aios. pplicaions fo magnesium alloys include use in aicaf, missiles, machiney, ools, and maeial handling equipmen, auomobiles and high speed compue pas.on he ohe posiive side, magnesium alloys have a elaively high sengh-o-weigh aio wih some commecial alloys aaining senghs as high as 3 MPa. High enegy absopion means good damping of noise and vibaion. While many magnesium alloys equie enamel o lacque finishes o impa adequae connecion esisance, his popey has been impoved makedly wih he developmen of high puiy alloys. Fo his analysis wo ypes of Magnesium alloys consideed namely Z3B-O and Z6-F Magnesium alloy Z3B-O : composiion (%): 3.5 l,.6 Mn,.Zn and Tensile sengh 4MPa, Yield sengh 5MPa. Magnesium alloy Z6-F: composiion (%): 6.5l,.Zn and Tensile sengh 48MPa, Yield sengh Mpa. 7. RESULTS & DISCUSSION 7. Hoop sess The hoop sess disibuion in he blank duing he hydofoming deep dawing is given by eq.8 j 4µ u j σ ln h The following pocess paamees and yield sess values of magnesium alloys ae consideed fo evaluaion of hoop sesses of magnesium alloys wih given fluid fo successful fomaion of cup in hydofoming deep dawing pocess. p 3 mm, cp 4mm, d 35mm, cd 4mm, BH 4 mm, c 5 mm, Radial pessue of fluid P, Punch speed (velociy of blank) u mm/sec, h 4 mm, hickness of blank 3mm, adius of blank j 5mm, ype of maeials used: Magnesium alloys ype of fluid used: caso oil, viscosiy µ.985n sec/ m Yield sess values ( σ ) of magnesium alloys: Z3B-O σ 5 x 6 N/m Z6-F σ x 6 N/m The evaluaion of values of hoop sesses ( σ θ ) in he blanks of magnesium alloys wih a given fluid a a adial disance fom job axis fo a given adius of blanks a consan hickness of blanks as follows. Subsiue he above values in above equaion we ge genealized equaion fo evaluaion of hoop sesses duing he pocess wih espec o diffeen adial disance of blank fom job axis fo blanks of magnesium alloys wih caso oil medium ae a consan hickness of blanks 3mm. j 5mm 5 σ ln [ ]

8 Inenaional Jounal of dvanced Reseach in Engineeing and Technology (IJRET), ISSN (Pin), ISSN (Online) Volume 3, Numbe, July-Decembe (), IEME The hoop sesses of magnesium alloys ae pesened in fig. 4 a 3mm wih adius of blanks j 5mm wihin he ange of adial disance 65mm o 95mm. Fom he figue, due o viscosiy of fluids, he shea sesses and shea foces ae aced on he blank suface duing he hydofoming deep dawing pocess..x 8.x 8 Z3B - O Z6 - F Hoop sess ( N/m ).8x 8.6x 8.4x 8.x 8.x 8 8.x 7 6.x Radial disance fom job axis (mm) Fig.4. Hoop sess disibuion in Magnesium alloys a j 5mm So he Hoop sesses ae inceases wih inceasing of he adial disance of he blank fom he job axis. Hoop sesses ae also depends up on pocess paamees, yield sess of alloys and fluid pessue. Fom fig.4. he magnesium alloys a j 5mm wih caso oil viscosiy, he ange of adial sesses of Z6-F is N/m N/m and Z3B O is N/m N/m, he ode of hoop sesses of magnesium alloys as Z3B-O < Z6-F.mong hese alloys, fo a high adial disance fom he job axis of blank is 95mm, he hoop sess is highe value in Z6-F and lowes value in Z3B-O 8. CONCLUSIONS The Hoop sesses ae he funcion of pocess paamees, yield sess of magnesium alloys and viscosiy of caso oil. The hoop sesses ae inceseses wih inceasing of he adial disance of he blank fom he veical job axis. These effecs ae due o viscosiy of caso oil aced on he blanks of magnesium alloys duing he foming pocess. The adial pessue of fluid acing on blank suface of alloys is equal o blank holding pessue is o fo unifom defomaion of blank duing he pocess. The winkling is educed in blank due o he blank suppoed by high pessuized viscous fluid. Hoop sesses of magnesium alloys ae deemined wih in he ange of is 65mm 95mm wih caso oil. Fo j 5mm, a 95mm he highes value of hoop sess occued in Z6-F is N/m, lowes value occued in Z3B-O is N/m. The inceased amoun of adial sesses in magnesium alloys wih in he ange is 65-95mm, in Z3B-O is N/m and in Z6-F is N/m. So among he ode of incease moun in hoop sesses of magnesium alloys as Z3B-O < Z6 F. The hoop sesses ae in he magnesium alloys ae high a is 95mm, low a is 65mm.So he hoop sesses ae diecly popoional o he adial disance fom job axis wee obained. The hoop sesses ae depends on he viscosiy, fluid pessue and pocess paamees. The highe values of 5

9 Inenaional Jounal of dvanced Reseach in Engineeing and Technology (IJRET), ISSN (Pin), ISSN (Online) Volume 3, Numbe, July-Decembe (), IEME hoop sesses ae gives he minimizing he dawing ime and highe in foming limis. These hoop sesses ae used o ge bee esuls of fomabiliy of magnesium alloys. CKNOWLEDGEMENT One of he auhos (D.R.Uday Kuma) hanks he managemen, dieco and pincipal of Mahama Gandhi Insiue of Technology fo encouaging and ganing pemission o cay ou his wok. REFERENCES [] J.M. lexande, n appaisal of he heoy of deep dawing, Me. Rev. 5 (9) (96) []D.F. Eay, E.. Reed, Techniques of Pess-woking Shee Meal, penice-hall, New Jesey, 974, pp. 7. [3]W. Panknin, W. Mulhause, Pinciples of he hydo fom pocess, Mileilungen de foschungges Blechveebeiung 4 (957) [4] B. Lasen, Hydomechanic foming of shee meal, Shee Me.Ind. (Feb. 977) [5] K. Nakamua, Shee meal foming wih hydaulic coune pessue in Japan, nn. CIRP 36 () (987) [6] S. Thiuvaudchelvan, novel pessue augmened hydaulic-deep-dawing pocess fo high daw aios, J. Mae. Poc.Technol. 54 (995) [7] K. Lange, Handbook of Meal foming, McGaw-Hill, New Yok, 985, pp...4. [8] S. Yossifon, J. Tiosh, on he pemissible fluid-pessue pah in hydofoming deep dawing pocesses analysis of failues and expeimens, Tans. SME J. Eng. Ind. (988) [9] S. Thiuvaudchelvan, W. Lewis, noe on hydo foming wih consan fluid pessue, J. Mae. Pocess. Technol. 88 (999) [] K. Obelande, The hydomechanical deep dawing of shee meals-ii, Blech Rohe Pofile 4 (98) [] D.Y. Yang, J.B. Kim, D.W. Lee, Invesigaions ino he manufacuing of vey long cups by hydomechnical deep dawing and ioning wih conolled adial pessue, nn. CIRP 44 (995) [] S.H. Zhang, J. Dancke, Developmen of hydo-mechanical deep dawing, J. Mae. Pocess. Technol. 83 (998)