Axisymmetric Strain Stability in Sheet Metal Deformation

Transcription

1 Intenational Jounal of Nonfeous Metallugy, 3,, -5 doi:.436/ijnm.3.36 Publised Online July 3 (ttp:// Axisymmetic Stain Stability in Seet Metal Defomation atjana V. Bovman ve State ecnical Univesity, ve, ussia bovman@mail.u eceived Decembe 3, ; evised Febuay 7, 3; accepted Febuay 8, 3 Copyigt 3 atjana V. Bovman. is is an open access aticle distibuted unde te Ceative Commons Attibution License, wic pemits unesticted use, distibution, and epoduction in any medium, povided te oiginal wok is popely cited. ABSAC Poduction of axisymmetic pieces by tecnology of seet metal dawing is widespead nowadays. So te calculation analysis of capacity and foces necessay fo defomation is of special inteest. e lengt of cylindical pieces wit axisymmetic defomation is limited by loss of stability and buckling due to te development of side stains. A new tecnological pocess is based on making consideable numbe of folds 8-6 wit te amplitude of mm befoe te defomation o immediately afte te patial one. at educes te stiffness of billets and pevents fom development of lage size buckles. A new tecnological pocess is developed fo poducing a long un of ig-quality poducts. Keywods: Plastic Axisymmetic Defomation; Loss of Stability; Side Stain Development. Intoduction Axisymmetic defomation of seet metal blanks ae widely used in te manufactue of cylindical pieces made of flat metal seets. Suc poducts as vaious vessel bodies, nozzles, connecting pipes ae made of low cabon steels as well as of coppe, bass, magnesium alloys and ote metals. is pape examines only te defomation of te poducts wit axial symmety, wic ae inceasingly used in industy. egulaities of plastic defomation ae studied in eseac papes [-4]. ey demonstate tat unde te pessue of a cylindical die on te cente of te wokpiece wic was initially saped like a disk, te plane stess is developed, wit only two of te six tenso components being nonzeo. Due to tensile adial stess and compessive tangential stess [,] te buckling of defomable wokpiece accompanied wit folds is possible. Usually tis leads to waste metal and teefoe it is necessay to limit te lengt of a poduct, to use dawing wit subsequent additional defomation (seconday dawing opeation, olling). o pevent te occuence of folds te blank oldes ae used, but tis significantly inceases te defomation stain to an extent of te occasional ovedawing occuence in a defomable wok piece. Sometimes dawing wit te billet o its edge pats eating (nea te maximum diamete) is used. Fo some metals billet eating can incease te allowed lengt of a poduct by.5 -. times. Magnesium alloy seets ae tougt to be used fo deep dawing only wit te billet eating. But as te tickness of a seet metal to be defomed is small (up to - 3 mm) and is exposed to cilling it as to be eated diectly on a die. at complicates te design of te equipment, enances significantly powe consumption and makes it difficult to ensue safety conditions. In tis pape we discuss some featues of te seet blanks axsymmetic stain. A new dawing tecnique wic allows to impove te tecnology and to expand significantly te ange of poducts is poposed and investigated.. Kinematically Admissible Velocity Fields by Dawing Defomation e gapic patten of dawing defomation is illustated in Figue, wee one can see matix, defomed billet wit oute adius and inne one, tickness and punc 3 wic moves along axis Z wit constant velocity V z = V. Kinematically admissible velocity field detemines te uppe limit of defomation ca capacity N and te associated moving die foce P. Suc a velocity field is to satisfy: a) te incompessibility condition, b) velocity bounday conditions, c) te condition unde wic te defomation capacity is positive []. e volume of a defomable billet can be divided into two pats. One of tem aving a cylindical sape wit inne adius

2 . V. BOVMAN moves wit velocity V z = V togete wit moving die 3 [,3]. In tis zone V is equal to (te coodinate axes location is sown in Figue ). As tis pat of a billet moves like a igid body, its capacity of plastic defomation is equal to zeo [3]. e second zone includes te pat of a billet wic as a sape of a ing wit tickness limited by adius = + and =. Some featues of tis defomation ae consideed in pape [4]. In tis aea te kinematically admissible velocity field could be V V ; Vz () wit te stain-ate tenso components V ; V ; z (te ote tenso components ae equal to zeo). Value V is velocity unde and te second invaiant of stain-ate tenso is equal to H V is velocity field can be assumed as kinematically admissible only if tee exists suface z() sepaating te two selected defomation zones. On tis suface te nomal ate components ae to be equal, (tangential components may diffe and tei diffeence detemines te capacity of te sea). Suc a suface exists and is a paaboloid [5]. As a esult, it is possible to detemine te defomation capacity N Hd 4kVln wee k is yield point in sea, and sea capacity ove te suface of paaboloid is dz N kkv d d wit paaboloid equation: z Figue. Dawing Sceme. () dz d tangential components beak at te bounday of two zones wit sea capacity dz dz V V N d d kv, Full capacity wit povision fo fiction load at te suface of lowe die is N PV N N V P, wee is coefficient of sliding fiction. Moving die foce is N N P V If te defomation is caied out wit te use of blankolde, wit foce, te fiction load inceases and foce P is equal to Usually P N N P V and te foce is k ln k 3 If te steel seet defomation is caied out witout te use of blankolde, as sown in Figue (wit Т =, 8 mm, 96 mm,. ; = mm, = МН МН., 3, k 73 ), te value of foce m м accoding to (5) is P=.3 MN. As usual, te kinematically admissible velocity field detemines te uppe limit of foces (i.e., ovestated values of P). Accoding to expeimental data, in case of dawing tis ovestatement amounts to % - 5%. is is acceptable fo te coice of equipment in most cases. 3. Wokpiece Buckling in te Dawing Defomation (3) (4) (5) In te pocess of deep dawing a seet saped initially

3 . V. BOVMAN like a disk undegoes tangential compessive stess tat can lead to loss of stability. eeby folds occu on te pat of a suface, as sown in Figue. Pape [] indicates tat te location and numbe of folds depends on te metal anisotopy, fo example fo some alloys te numbe of waves is fou, wit te location being at an angle of 45 to te olling diection of a seet. But te numbe may come up to six []. Usually, te fold occuence, i.e. wavy suface wit amplitude of up to - mm, leads to inability to output poducts and to ejected mateial. Fom Saint-Venan condition end equation of equilibium d (6) d and condition of plasticity k it is clea tat stess is k ln kln k (7) wee te integation constant is detemined by te condition of wit. angential stess wit is equal to k. e minimum allowable value, (unde wic folds occu) is detemined by paametes:,,,, Е Т wit te dimensions: m (fo te fist tee) и МН/m fo yield limit and plastic defomation d adening modulus E. Hee E is a value caacteizing metal adening in plastic defomation. d Out of tese five vaiables it is possible to fom tee dimensionless paametes: E A, A and A 3 As well as to detemine appoximately stain-adening caacteistic E В, wee В is ultimate stengt. Accoding to teoem te elationsip between te above-mentioned paametes must take te following fom f A, A, A 3. Having solved it fo A, we get f A, A3 (8) Based on te data of many defomation expeiments wit cabon steel seets of.5 mm,. mm,.5 mm and. mm ticknesses te gaps f A, A3 wee plotted as given on Figue 3. e elationsip (8) can be detemined wit te empiical fomula fo a maximum pemissible (minimum) value E.5 min (9) o povide te seet stability te following condition sould be fulfilled: min () Since te maximum possible upset lengt is equal to l, it follows fom (9) tat te maximum possible lengt of wok is l E.9 () max Fo example, fo a steel seet of = mm tickness Figue. Development of Folds. Figue 3. Gap of Function.

4 . V. BOVMAN 3 MN MN wit 5, 49 B, m m E ; mm.. 5 ac- coding to Fomula (9) we get 9.4 mm ; l = 8.6 mm. Fomula (9) can be applied if E.94, min.4 and te expeimental data spead is consideable wic is seen fom Figue 3. e dotted line ee divides te data span into two pats. Below te dottedline tee is a zone fo specially selected samples wit tickness diffeences of no moe tan. mm. e ige te gage intefeence, te moe often te buckling failue and buckle development appen. eefoe it is impotant to incease te dimensional accuacy of seets used fo deep dawing. Empiical fomula (9) gives tat if E,. It confoms to te test wic min sows wat sould be applied fo metal (alloys) dawing B wit ig adening: te ige is, te easie te defomation can be made, and te lage wok lengt can be poduced wen dawing. Metals wit mino adening wit gap of function being close to a pefectly plastic body gap (i.е. wen const. ) ae unfit fo deep dawing. Steel seets wit up to.5% -.5% tempe and not moe tan - 3 µm gain size wit extension stain of no less tan 4% ae often used fo dawing. Accoding to te above-mentioned te olde allows to incease l value and decease paamete. How- eve, te ing cack wastage inceases as sown on Figue 4. ee can be seen ing cacks being te easons of up to % and moe incease of waste numbe wic aggavates te manufactues economic indexes signifycantly. 4. New Metod of Dawing Based on te eseac conducted a new tecnological dawing pocess as been suggested (see Patent Application of ussian Fedeation 374/, MPK 7ВD / fom 8 June ). e metod consists in foming a seies of waves (idges) along a ing on a disk-fom billet, see Figue 5. e amplitude of te waves is small (usually not moe tan (/)) but tei quantity is lage up to 6-8 waves located along te ing as can be seen on Figue 5. All te deepenings (waves) ae easonable to be made simultaneously wit one die ten te billet sould be uptuned and defomed by dawing, te cleaance between te seet being defomed and te punc sould exceed te waves amplitude.5 -. times in ode to avoid seet jamming. Wit dawing defomation te buckled seet compessive defomation elieves (its adness is educed). Expeiments wee made wit samples of diametes 7 - mm and eigt 8-4 mm of low cabon steels. e waves may be located not along te billet edge as sown on Figue 5(а) but in its middle as on Figue 5(b). Even making.5 - mm amplitude waves on a billet paallel potion gives a positive esult afte patial dawing defomation. Vaious wave vaiants ae also sown on Figues 5(c) and (d), e. e dept fo.5 mm seets of cabon steel was.5 mm, te numbe of waves being 8-6. e loss of stability wit lage wave fomation, e.g. sown on Figue, does not occu and tee is a possibility of manufactuing poducts wit a lengt - 3 times ige te admissible lengt of a conventional dawing. e defomation is sue to esult in inceasing te wave amplitude, sometimes.5 times (tee occus tei compession wit wave sotening sometimes in - 3 times), but te new waves of lage amplitude do not emege (e.g. as tose sown on Figue ). Figue 4. Blanks wit Cacks. Figue 5. New Metod of Dawing.

5 4. V. BOVMAN e main idea of te metod consists in making a lage numbe (8-6) of waves of small amplitude on a seet (disk) in advance in ode to avoid te potential of emeging 4-8 waves (buckles) of lage amplitude (up to - mm). It deceases te igidity of a defomed billet, wit te amplitude being able to eac.5 mm afte dawing, wic does not lead to sap canges of te wole poduct patten (it usually appens wit te stability loss) and allows to manufactue te equied poduct of ig quality. Figue 6 sows te samples manufactued at OAO sbp (te town of ve, ussia) wit te new metod used. ese Filte Casing Blanks wee made fom low cabon steel (st.8 accoding ussian standat 5-88). Quality of Cabon was.5% -.5%. Pat of filte Casings was made of semi-killed steel (st.3). Diametes of tese Casing Blanks wee 96 mm and tei eigt was 9 mm. Atificial waves wee made wit lengt 8 mm and amplitudes mm. Quanlity of Filtes was good and eject was deceased twice till.75%. e atificial waves (idges) ae cetain to emain on te poduct. e metod is sue not to be used in cases wen even small waves on te poduct cannot be allowed. But in many cases suc waves wit amplitude of less tan mm do not at all make te poduct quality wose and teefoe ae possible. So te above-mentioned ve plant manufactued moe tan tousand filte casings (Figue 6) of ig quality. An analogy may be dawn to te case of ba pessing (see Figue 7). Wen a staigt cantileve ba is compessed wit stess P (Figue 7(а)), accoding to Eule fomula (a) Figue 7. Sceme of Stability unde Defomation J Fl it loses stability wen being subject to compessive defomation, (wee F is an aea of ba section, J is its moment of inetia, l is a ba lengt). Wit fute compession a ba loses its configuation, wit te deflection inceasing apidly up to.5 l and moe. If a ba can be manufactued as sown on Figue 7(b), it keeps its wole configuation in ige defomations,3. Its igidity is a consideably less tan tat of a staigt ba but no sap canges of te wole fom occu. (Bot te ings and defomable bodies of Figue 7(b) can cetainly buckle but, as a ule, in cases wen te defomation is seveal times moe tan value fo a staigt ba). In some cases te manufactued igidity eduction of te billet being dawn can be ational. 5. Conclusions e following conclusions can be deduced fom te above-said study: ) e axially symmetic seet blank defomation unde dawing as been examined. e kinematically admissible velocity field fo foce uppe limits as been built. ) A new metod of dawing wic included making idges-waves of small amplitude on a blank befoe dawing as been poposed and studied. But te numbe of suc waves sould be consideable and it gives te possibility to avoid te fomation of moe significant fom distotions of a billet. 3) e metod was used fo poducing oil filte casings and getting a ig-quality poduct. Moe tan tousand filte casings of good qualities of cabon steel wee poduced wit use of new metod. (b) Figue 6. Filte Casing Blanks Poduced wit New Metod. EFEENCES []. Hill, Matematical eoy of Plasticity, Claendon Pess, Oxfod Univesity Pess, 95, 47 pages. [] L. A. Sofman, eoy and Calculation of Cold Fom-

6 . V. BOVMAN 5 ing, Macine-Building, Moscow, 964, 375 pages. [in ussian] [3] M. Ja. Bovman, Application of te eoy of Plasticity in olling, Metallugiya, Moscow, 99, 65 pages. [in ussian] [4] H. Vegus and. Soweby, e Pue Plastic Bending of Laminated Seet Metals, Jounal of Mecanical Sciences, Vol. 7, No., 975, pp [5]. V. Bovman, Seet Stamping Foces Calculation, Vestnik Masinostoyenia, No. 3, 4, pp [in ussian]