84 J. Mate. Sci. Technol., Vol. No., 006 Analysis of the Intenal Pessue in Tube Hydofoming and Its Expeimental Investigation Hongyang LI 1), Zhongen, WANG ), Qibin MIAO ), Shijian YUAN ) and Xiaosong WANG ) 1) Depatment of Plasticity Technology, Shanghai Jiao Tong Univesity, Shanghai 00030, China ) School of Mateials Science and Engineeing, Habin Institute of Technology, Habin 150001, China [Manuscipt eceived Januay 19, 005, in evised fom Apil 11, 005] The intenal pessue of the pocess was studied theoetically and expeimentally. The extenal load chaacte and intenal stess chaacte of tube hydofoming wee discussed fist. Then, accoding to the chaactes, the function and classification of intenal pessue wee pesented in geneal. Base on the stess analysis, its effect on the yield citeion and calculation fomula wee also eseached and deived. To veify the coection of the theoetical analysis and deived fomula, expeiments with diffeent intenal pessues wee caied out and the esult was compaed and discussed. It demonstates that intenal pessue plays an impotant ole in tube hydofoming and theoy and fomula discussed and deived by this pape ae feasible in pactice. KEY WORDS: Tube hydofoming; Intenal pessue; Stess state; Yield citeion 1. Intoduction Tube hydofoming is a kind of soft-tool foming technology and developed apidly in the past decades. Fo taking tubes as pocessing blanks and liquid as flexible punch, it is moe suitable fo manufactuing special tubula components, such as diffeent kinds of hollow shafts, dischage pipe of automobile & aeoplanes, sectional pipe and so on [1 4]. Figue 1 is the schematic diagam of the pocess. Tubes wee placed in the die and sealed on the end fist. Then unde the co-action of compessive axial foce and intenal pessue, it is foced to defom fom elastic stage to plastic stage. With the inceasing of the applied load, the defomation inceased coespondingly. Finally, unde the extemely high pessue, the tube assumed the intenal contou of the die pecisely. Compaed with taditional pocessing technology, tube hydofoming always manufactues components at one step. So it can enhance pat quality, such as tighte toleance and incease igidity, and lowe poduction costs, such as eduction in poduction cycle and fewe dies. With the special advantages, since 1990 s, tube hydofoming begins to attact damatic attention fom scientist to enginees and developes apidly. A seies of semina and academic congess had been oganized in USA & Euope, and special manual has even been published in Gemany. Many commecial finiteelement softwaes have taken it as a main function of the codes and a lage numbe of foundations fom the govenment had been appopiated fo it. Especially in automobile industy, most of the famous automotive copoations, such as DAIMLER BENZ and GM, ae adopting it as a potent means in stengthening thei competitive powe in the maket [5 10]. Howeve, with the apid development, thee Pof., Ph.D., to whom coespondence should be addessed, E-mail: lihongyang@sjtu.edu.cn. Fig.1 Schematic diagam of tube hydofoming ae some poblems still puzzling eseaches and enginees. Such as tibological mechanism between the blank and the die, stess and stain distibution of the tansition egion and defomed egion, and pocessing paametes selection duing the diffeent defomation stages, which ae all hindeing the futhe development of the pomising pocess seveely. In this pape, aimed at the poblem of paametes selection, the action of intenal pessue duing the pocess was investigated theoetically and expeimentally. By establishing the elationship between micoscopic stess state and macoscopic defomation, the effect of intenal pessue was discussed and analyzed. Based on the theoetical discussion, expeiment was caied out coespondingly. The esult demonstates that theoy and fomula pesented in this pape ae ational in theoetical analysis and it is impope in-
tenal pessue that induced winkle defect and cicumfeential tensile destabilization.. Mechanical Backgound J. Mate. Sci. Technol., Vol. No., 006 85.1 Chaacteistics of the extenal load Tube hydofoming is a kind of plastic foming technology, the defomation of the blank and the mechanical chaacte of the pocess ae all detemined by the extenal load. It is the extenal load chaacte that detemined what shape will the blank be assumed if the component can satisfy the design citeion. Fom the discussion of Fig.1 we can find, in fact the extenal load of tube hydofoming consists of thee pats, axial compession foce, intenal compession pessue and fiction between the die and the blank. The diffeent combination of the foces ceated diffeent shape of the components and the diffeent extenal foce plays diffeent oles and assumed diffeent chaacte duing the pocess. Axial compession foce is mainly used to seal intenal liquid and povide axial supplement, so it is the fist extenal foce that act on the blank and the last foce to withdaw. With the development of the pocess, it assumed a n-shape cuve, taking the lagest value duing the pocess of axial supplement. Intenal compession pessue povides the foce fo bulging and pesents quasi-linea shape. It acts on the blank afte the axial seal and then inceases monotone until the completion of the pocess. Of couse, with the end of a poduction cycle, the intenal compession pessue also deceases and stats subsequently in the next poduction cycle. Of all the thee extenal loads, fiction is the only one that is not an active load. It acts on the blank with the stating of axial supplement and inceases with the inceasing of the intenal pessue. It just acts on the pat of the blank that contact with the die and disappeaed when thee ae no elative shift between the die and the blank. Theefoe its tibological mechanism is vey sophisticated and up to now thee ae still no satisfied theoy to unpuzzle its mechanics. Fo it is not an active load on the blank and compaing with othe two extenal loads its influence is elatively low, accoding to eseach convention, it is ignoed to be consideed in this pape.. Chaacteistics of intenal stess Stess state is detemined by extenal load. Accoding to the extenal load chaacte, the stess state of tube hydofoming is thee-dimensional. Axial compession foce gives ise to axial compession stess and intenal pessue ceats cicumfeence tensile stess and adial compession stess. The blank was unde the state of two compession stess and one tensile stess state and Fig. is the coesponding stess state diagam. Axial compession stess is always emaked as σ z = F S, whee F is the quotient of axial compession foce S and the action aea of the axial foce. Fig. Stess state of tube hydofoming Cicumfeence tensile stess and adial compession stess ae always denoted as σ θ = P R t and σ t =P, whee P, R and t ae the intenal pessue, adius, thickness of the blank, espectively [11]. 3. Function and Classification of the Intenal Pessue Intenal pessue and axial compession foce ae the two impotant extenal active loads of the pocess and play diffeent oles duing the pocess. Intenal pessue povides the load of bulging and has special chaacte when compaed with axial compession foce. 3.1 Function The main function of intenal pessue is to geneate cicumfeence tensile stess and adial compession stess. It is the souce of the defomation along the adial diection and the eason of cicumfeence tensile stain and adial displacement. On the one hand, it pushes the blank to bulge in ode to empty out moe space fo the axial supplement duing the initial stage, and on the othe hand it pesses the blank to assume the intenal contou of the die pecisely duing the ultimate stage. In geneal, the stain of the blank of tube hydofoming can be summaized as axial compession stain and cicumfeence tensile stain, which ae mainly geneated by intenal pessue. 3. Classification Accoding to the function of the intenal pessue, intenal pessue of tube hydofoming can be divided into two stages o two classifications, initial stage and ultimate stage. Duing the initial stage, the function of the intenal pessue is mainly to empty out space fo axial supplement and avoid the geneation of winkle, so the pessue is elatively low and it is always called as initial low pessue stage. Duing the ultimate stage, to guaantee the blank to stick to
86 J. Mate. Sci. Technol., Vol. No., 006 the die pecisely the pessue is elatively high, so it is always defined as ultimate high pessue stage. Although the value and the time of the two stages vaied with diffeent components, all of the loading path of tube hydofoming consists of the two stages. 4. Effect on the Yield Citeion Duing plastic defomation stage, the defomation of the mateials is contolled by yield citeion flow stess. The action of intenal pessue on the pocess is also though the yield citeion flow stess. Equation (1) is the expession of Mises yield citeion, which is the most geneal yield citeion of plasticity. (σθ σ t ) + (σ t σ z ) + (σ z σ θ ) = σ s (1) whee σ θ, σ t, σ z ae the pimay stess components sepaately, and σ i and σ s ae the equivalent stess and yield stess of the blank, espectively. The expession shows that, thee ae two stesses, σ θ and σ t ae detemined by intenal pessue. The inceasing of the intenal pessue gives ise to not only the inceasing of σ t but also σ θ, any vaiation of the intenal pessue all affects the yield citeion doubly. To to make it convenient fo analyzing, accoding to the classification of the intenal pessue, Eq.(1) was simplified as Eqs.() and (3) and discussed espectively as follows: (σ θ + (σ z) + (σ z σ θ ) = σ s () (σθ σ t ) = σ s (3) Duing the initial stage, σ t is elatively low, so it is omitted in the fomula. By substituting it with zeo, Eq.(1) was simplified as Eq.(). The expession of Eq.() shows that, duing the initial stage, σ θ and σ z ae the main stesses which influence the defomation of the blank, and they pesent invese elation duing the pocess. With the intenal pessue inceasing, σ z deceased coespondingly and vice vesa. That means, duing this stage, if the intenal pessue is elatively highe, the axial supplement can be finished unde a elatively low compession foce. And if the intenal pessue is elatively low, the plastic defomation will need elatively high axial compession foce. The highe the axial supplement foce, the moe dange of folding is. So lowe intenal pessue will give ise to winkle defect duing the initial stage. Duing the ultimate stage, with the inceasing of the pessue, σ z begins to be the second pimay stess and equal to the value of σ θ. Thus Eq.(1) is simplified as Eq.(3). That means, any inceasing of the intenal pessue will geneate double effects and it is the intenal pessue that influences the defomation in this stage. Fig.3 Schematic diagam of a cut cell cube 5. Calculation Intenal pessue affects the defomation of the blank by yield citeion and it is contolled by extenal load. But in pactical pocess, fomula of the intenal pessue calculation is moe valuable. Fo the blank of tube hydofoming, the stess should satisfy the equilibium diffeential equation and unde the cylindical coodinates it can be expessed as Eq.(4). σ τ θ τ z + 1 + 1 τ θ σ θ τ θz + τ z + τ zθ + σ σ θ + τ θ (4) + 1 + σ z + τ z Consideing the symmetical chaacte of the blank, and if the component is also symmety, it can be simplified as Eq.(5). σ τ z + τz + σ σ θ (5) + σ z + τ z Fo the thickness of the blank and the component that is always elatively thin, if cut a cell cube fom the blank as Fig.3 and set up the equilibium equation, Eq.(5) can also be simplified as Eqs.(6) and (7) σ dθdz σ θ dθtdz (6) σ θ P (7) t Equation (7) is an equation about the pessue and intenal stess, so it is just the calculation fomula of intenal pessue. Howeve, as a fomula deived unde hypothesis, coesponding expeiments wee necessay to see whethe the fomula is coect in pactical applications. 6. Expeimental Investigation 6.1 Component and blank To make the expeiment moe epesentative, hydofoming thee-stepped shaft was adopted as expeimental component and Fig.4 is the geometical pototype of the component and blank.
J. Mate. Sci. Technol., Vol. No., 006 87 Fig.4 Geometical pototype of expeimental thee-diamete shaft and blank: (a) thee-diamete shaft, (b) blank Table 1 Mechanical popeties of expeimental blank E/GPa µ n σ s/mpa σ b /MPa σ s/σ b δ/%.05 0.3 0.1 45 410 0.6 Table Main technical paametes of the equipment Pessue of Pessue of Open height of Open height of Maximal Maximal axial oute slide/kn inne slide/kn inne slide/mm inne slide/mm pessue/mpa foce/kn 6000 4000 700 700 400 1500 The whole length of the shaft is 50 mm and the width of stages ae all 80 mm. Fom the left to ight, the diamete of each stage is 80, 90 and 70 mm, espectively. Accoding to the dimension of the shaft, tube with 60 mm in diamete was adopted as blank and table 1 shows its mechanical popeties. 6. Equipment and paametes Equipment plays an impotant ole in tube hydofoming and the expeiment of veifying the above discussion was caied out on a special tube hydofoming equipment at Habin Institute of Technology, China. Table shows the main technical paametes of the machine. Accoding to Eq.(7), the calculated value of the intenal pessue is 3.7 MPa. To be moe convenient fo contolling and analyzing, the ound numbe 30 MPa was selected as theoetical pessue and 0 and 40 MPa initial pessue was selected as check sample, espectively. 6.3 Results and discussion Figue 5 is the loading path of sample with diffeent pessues and Fig.6 is thei coesponding pictue. Fom the pictue we can find that, with 0 MPa initial pessue, the blank is bulged a little but winkled seveely in the middle. The winkle assumes an aow shape and some mateials wee pushed into the inne of the othe side. Fo too many mateial winkles in one place, the heavy cinkle cannot be unfolded by succeeding high pessue, so expeiment was stopped in half stage and the loading path is only a staight line, without the ultimate high pessue stage. When the intenal pessue inceased to 30 MPa, component and loading path changed geatly. The loading path begins to consist of initial low pessue stage & ultimate high pessue stage and the component assumed the designed shape popely. With the intenal pessue futhe inceasing to 40 MPa, the pocess degaded again; the middle of the blank bulged obviously and the blank busted duing the pocess. Fo the expeiment stopped with the busting, the same as the loading path of component with 0 MPa intenal pessue, the loading path tuns to a staight line again. The expeimental esults demonstated that, duing the pocess of axial supplement, the cicumfeence tensile stess geneated by 0 MPa intenal pessue is not lage enough to empty out sufficient space. So the mateial was pessed heavily along the axils and filled up into the die with only a little cicumfeential tensile bulging and geneated winkle. With the intenal pessue inceasing to 30 MPa, the cicumfeential stess inceased coespondingly. With the filling up of the mateials, blank bulged in synchonism, stess state tends to be ational and stain state becomes homogeneous, so the component was fomed successfully. When the intenal pessue inceasing to 40 MPa, the cicumfeential stess inceased ulteioly and gave ise to thinning. Mateials filled up in the die by axial supplement cannot compensate the thickness decease in time. So the thickness deceased geatly and cicumfeential destabilization happened finally. 30 MPa is the theoetical initial pessue of Eq.(7),
88 J. Mate. Sci. Technol., Vol. No., 006 Fig.5 Loading path of the sample with diffeent intenal pessues: (a) loading path with 0 MPa intenal pessue, (b) loading path with 30 MPa intenal pessue, (c) loading path with 40 MPa intenal pessue Fig.6 Photogaph of the sample with diffeent intenal pessues: (a) sample with 0 MPa intenal pessue, (b) sample with 30 MPa intenal pessue, (c) sample with 40 MPa intenal pessue so the esult also demonstates that Eq.(7) is eliable in the calculation of the intenal pessue, excessive low pessue will induce winkle and excessive high pessue povokes busting. 7. Conclusions (1) Intenal pessue geneates cicumfeence tensile stess and adial compession stess, which is the eason of cicumfeence tensile stain and adial displacement. () Duing the pocess, intenal pessue always expeienced two stages, initial low pessue stage and ultimate high pessue stage. (3) Of the initial stage, it is mainly to fill mateials up to the die popely and duing the ultimate stage it is mainly to pess the blank to assume the intenal contou of the die. (4) The action of intenal pessue on the pocess is though the yield citeion and yield citeion can be simplified as diffeent styles duing the diffeent stages. (5) The calculation of the initial intenal pessue can efe to fomula (7), and it is ove-low intenal pessue that geneates the winkle defect and excessive high pessue povoked busting. Acknowledgements This wok is suppoted by the National Natual Science Foundation unde gant No. 5997501, which was gatefully acknowledged. At the same time, the autho also thanks Pof. P.Zeng of Tsinghua Univesity fo his kind assistance which is also indispensable in the accomplishment of this pape. REFERENCES [1 ] F.Dohomann and Ch.Hatl: J. Mate. Pocess. Technol., 1996, 60, 669. [ ] S.H.Zhang: J. Mate. Pocess. Technol., 1999, 91, 36. [3 ] Sungtae Kim and Youngsuk Kim: J. Mate. Pocess. Technol., 00, 18, 3. [4 ] H.Y.Li, S.J.Yuan, K.Dai, L.H.Lang and Z.R.Wang: J. Mate. Sci. Technol., 001, 17(1), 158. [5 ] L.P.Lei, J.Kim and B.S.Kang: Inte. J. Mech. Sci., 00, 44, 1411. [6 ] L.P.Lei, J.Kim and B.S.Kang: Int. J. Mach. Tool. Manu., 000, 40, 1691. [7 ] M.Ahmetoglu, K.Sutte, X.J.Li and T.Altan: J. Mate. Pocess. Technol., 000, 98, 4. [8 ] M.Stano, S.Jiatheaanat, S.G.Sh and T.Altan: J. Mate. Pocess. Technol., 004, 146, 130. [9 ] Q.C.Hsu: J. Mate. Pocess. Technol., 003, 14, 367. [10] D.Schmoeckelm, C.Hielsche and M.Pie: Advanced Technol. Plasticity, Poc. of the 6th ICTP, 1999,, 1171. [11] H.Y.Li, X.S.Wang, S.J.Yuan, Q.B.Miao and Z.R.Wang: J. Mate. Pocess. Technol., 004, 151, 345.