COLD STRANGLING HOLLOW PARTS FORCES CALCULATION OF CONICAL AND CONICAL WITH CYLINDRICAL COLLAR

Transcription

1 COLD STANGLING HOLLOW PATS OCES CALCULATION O CONICAL AND CONICAL WITH CYLINDICAL COLLA Lucian V. Sevein, Taian Lucian Sevein,, Stefan cel Mae Univesity of Suceava, aculty of Mechanical Engineeing, Mechatonics and Management, omania, sevein@fim.usv.o, sevein.taian@fim.usv.o Abstact. This pape pesents an application of the enegy method to solve the poblem of detemining the foce to stangle cave o hollow pats by cold plastic defomation. Analytical elationships have been established fo the calculation of the total foce of conical tapeed and conical with cylindical colla of cave pats. These elationships show that the total foce of stangling affects by physical and mechanical chaacteistics of the mateial blank, defomation semi-angle stangling cone, adius stangling mould and fiction coefficient between the die and the blank mateial. Keywods: stangling foce, stangling conical tapeed, conical with cylindical colla stangling, stangling mould.. Intoduction Machining stangling belongs in the categoy of pocesses by moulding and can be defined as educing the coss-sectional size of the hollow pieces, hollow o solid cylindical pofiles by pessing the mateial in the adial diection fom the outside. Machining pocess stangling is applied to obtain by cold plastic defomation of pats of diffeent type metal packaging, tubes wa catidges, muff, pats fo installations, etc. Stangled pats can be tubula o hollow with cone shape (fig., a), conical with cylindical colla (fig., b), tooidal (fig., c) and tooidal with cylindical colla (fig., d). Chaacteistic pocessing by moulding pats cave is changing the low wall thickness, so it can be consideed fom the pespective of engineeing, pat thickness emains the same and afte To obtain a diamete d though the of hollow o tubula pats pocessing of diamete D, by the coefficient mgi it is estimated, which is the invese of the degee of defomation, and is defined by the elationship: d D m g () whee d is the aveage diamete of the piece section by stangling and D is the aveage diamete of the fist section piece blank. This stangling facto mg must be geate than the allowable value mga. The facto mga is function to the physical and mechanical popieties mateial blank, the elative thicknesses of the walls, s/d, the geometic shape of the stangled zone, the design of the mould suppoting wall piece, fiction between the blank and the mould suface [,. ]. The knowing of the tapeed foce by cold plastic defomation is an impotant paamete of the stangling pocess, and both in tems of choice of pessing machine, but especially in tems of stability piece wall duing pocessing 8

2 a b c d igue. Stangled cave pats foms. Calculation of stangling conical foce In conical cold defomation by stangling of pats, the active tool of mould acts with N foce on the blank to defom blank walls (figue ). Mould-blank at the inteface, due to fiction with the fiction coefficient, fictional foce f occus which acts on the suface the wall and acts against the walls. By composing the two foces and esulting foce. The N f vetical pojection of the esultant foce will be the foce equied to be applied to the die necking, fomed by two components, tgc coesponding foces pojections N and f. As shown in figue, can be witten: () tg gc fv whee the vetical foce gc is only equied fo plastic defomation of walls and is the vetical component of fiction fv foce. f om geometic consideations we can wite: cos () fv f in which f N and N gc sin (4) Taking into account the elations () and (4) the elationship () becomes: tgc ctg (5) gc Plastic mateial defomation the foce equied size igue. Conical stangling foces system gc, can be calculated using the enegy method, by equating the extenal stangling foces wok with the intenal tensions wok duing defomation, as follows: Le L i (6) The elementay wok of intenal tensions Li, detemined the elationship []: dli cidv (7) whee: c is yield stength of the blank mateial; point M; dv-defomed volume element by elementay mechanical wok, dl i in the vicinity of M (figue ). The intensity of the defomations can be calculated by the elation [4]: i - intensity of defomations at the 9

3 i z z (8) whee, and defomations, to diection cos z ae the main, and z (fig.). If the point M is witten elationship of constant volume at cold plastic defomation defined by elation: z () and it is consideed that, because the stetch defomations of wall at stangling cave pat ae elatively small, esults: () z The size of the specific defomation of the wall thickness, is defined by the equation: s s (4) s In equation (4) taking into account the elation () it follows: z tg s s (5) Elementay volume dv coesponding to figue is defined by the equation: igue. Defomations scheme at conical stangling The main defomations in the cicumfeential diection, coesponding to figue, is defined by the equation: z (9) whee: z z tg () If substitute elation () in (9) esults: z tg () dv da s (6) whee: da z d (7) cos By substituting da in () and taking into account the elations () and (5) gives: z tg d dv s (8) cos If you take into account the elations () and (), the intensity of defomations defined by equation (8) will have the following calculation expession: z i tg (9) By eplacing elation (8) and (9) in equation (7) is obtained by calculating fomula elementay mechanical wok of intenal tensions, dli, as follows: z z tg d dli cs tg () cos At conical stangling the mechanical wok of intenal tensions, Li, is obtained by integating the elation (), as follows:

4 h z z tg tg Li cs d () cos Afte the calculation esults: 4 h h sin Li cs tg 4 () cos The wok of extenal foce defomation Le, to stangle cone has the expession []: L h () e whee: gc, because duing pocessing gc inceases fom to the maximum value []; h- size displaced fo defomation. Afte equalizing the elationship () to () gives: 4 h sin gc cs h tg (4) cos The defomation stoke h is appoximately equal to the geneatix of the cone, and has the value: h (5) sin By substituting the elationship (5) in (4) we obtain: 4 gc cs (6) cos cos o gc csd d cos cos (7) Anothe fom is obtained if in (7) to take account of the elationship (): gc csd d m g cos cos (8) In equation (8) using equation (5) gives the expession fo calculating the total foce of tapeed stangling unde the fom: tgc cs cos D d m ctg g (9) The total foce of stangling pocess will be slightly highe if it neglects tem defined by the cos elationship esulting: tgc cos m g and 5, s D d ctg () c cos safety. Calculation of conical with cylindical colla stangling foce. Getting the conical stangling pats with cylindical colla utilizing hollow cylindical o tubula wokpiece is in fact a continued of mould stangling moving afte conical stangling completion fom so that the cylindical colla diamete d is obtained (figue 4). Analysis of wall defomation highlights in this case that afte the stangling to diamete d m cos the mateial continues to defom, moving on the adius m mold, educing the diamete to the value d. On connection aea with a adius m the mateial blank continues to stangle to the diamete d, but simultaneously bend until mid angle then staightening, foming cylindical suface diamete d. The total foce of stangling tg in this case, using ovelapping effects, it will consist of the total foce of stangling of the conical suface tgc and pulling foce fo bending and staightening plastic mateial piece walls of the mold adius m, as follows: tg () tgc The amount of foce î tgc î on the is detemined by the elation () and bending and staightening foce fo using the enegetically method of the wok of the extenal foce î to moving blank acoss m with that of intenal tensions. Thus we can wite: M î Le î m ; L i M î î () m The inne stain bending moment is detemined by integating the elemental momentum necessay bending a stip with bm

5 aveage width, along cicumfeence of colla, as follows: î dm î M () 8, s î m g d If ae eplaced î m cos (9) as defined by (9) and tgc obtained by equation () in () esults the total foce t of the conical with cylindical colla stangling, following fom: t 5, cs D d ctg d 8, s cos m cos mg (4) 4. Conclusions igue 4. Cconical with cylindical colla stangling scheme The amount of elemental moment is given by [4]: dbm s dmî, 5 (4) 6 whee the value of bm is given by expession d m cos dbm d (5) By substituting dbm in (4) and pefoming the integation, it follows: d m cos s Mî, 5 6 (6) The thickness s is detemined by the ate of stangling, mg [,5] s s (7) m g elation (7) is substituted in (6) and this one gets () to fom: d m cos s î, 5 m 6 g m (8) In geneally, the stangling pocessed pats have a good plasticity mateial, and if adopted 4%, equation (8) will take the following fom: Shown that pocessing of the stangling tubula o hollow pats ae a complex pocess, ove which it exets influence of seveal factos. The conical stangling total foce inceases with physical and mechanical chaacteistics of the mateial wokpiece, hollow blank diamete, the degee of defomation, cone semi-angle, initial thickness of the blank walls and fiction coefficient between the die and stangled cave o tubula blank. Expession of calculating the conical with cylindical colla stangling foce shows that it is highe than the conical stangling total foce. This incease is due to bending and staightening walls fo foming cylindical zone of pat. As against conical stangling, the conical with cylindical colla stangling besides othes also viewing ae added mentioned influence factos the initial thickness of the walls of the squae, and the adius of the cylindical colla connection with conical mould suface. With the gowth of these, incease total stangling foce of conical with cylindical colla of hollow pats 5. efeences. [] Zguă, Gh., Ciocâdia, C, Bude, G., Pelucaea metalelo pin defomae plastică la ece. Editua tehnică, Bucueşti, 977;

6 [] Sevein, L.,V., Iacob, D., Tehnologia pesăii la ece. Pelucăi pin defomae plastică la ece. Editua Univesităţii Suceava,. [] Teodoescu, M., Al., Tehnologia pesăii la ece. Editua didactică şi pedagogică, Bucuşti, 98; [4] Ponomaiov, S., D., ş.a., Calculul de ezistenţă în constucţia de maşini. Editua tehnică, Bucueşti,96. [5] Iliescu, C., Tehnologia pesăii la ece. Editua fidactică şi pedagogică, Bucueşti, 984.