NEAR NET SHAPE FORGING USING THE BACKWARD DEFORMATION METHOD

Transcription

1 VII Internatonal Conference on Computatonal Platcty COMPLAS 2003 E. Oñate an D. R. J. Owen (E) CIMNE, Barcelona, 2003 NEAR NET SHAPE FORGING USING THE BACKWARD DEFORMATION METHOD Bglar F. R. *, Abrna K. **,Ghaem H. **, Nkbn K. M., an O Dow N.P * Mechancal Engneerng Department, Amrkabr Unverty of Technology, Hafez Ave., Tehran, Iran bglar@cc.aut.ac.r ** Mechancal Engneerng Department, Unverty of Tehran, Amrabaa, Tehran, Iran cabrna@ut.ac.r Mechancal Engneerng Department, Imperal College Lonon, Lonon SW7 2AZ, UK k.nkbn@mperal.ac.uk, n.oow@mparal.ac.uk Key wor: Fnte element, perform, backwar eformaton, platc tran. Abtract. A new metho preente for the egn of preform e hape n a multtage forgng proce. The metho ncorporate a backwar lnear Lagrange nterpolaton cheme nto the fnte element metho. In the backwar eformaton metho, the fnal component hape taken a the tartng pont an the e move n the revere recton. The noal coornate n the backwar recton are nterpolate ung the lnear Lagrange nterpolaton metho, whch can pecfy the locaton of the noe n each backwar tme ncrement. The metho alo ue the contant volume concept n conjuncton wth geometrcal feature, uch a backwar e/workpece overlap attrbute, to etermne the hape of the perform e. 1

2 1 INTRODUCTION Forgng one of the mot economcal procee for the manufacture of engneerng component. Materal cot an mportant fracton of the total manufacturng cot o any reucton n materal lo urng the forgng operaton ha a rect effect on the prce of the fnhe prouct. Wth recent mprovement n engneerng egn metho an metal formng technology, flahle or near net hape forgng metho have been evelope, whch reult n almot no materal watage urng forgng. For near net hape forgng of complex hape, one or more ntermeate preform tage may be requre to acheve the fnal hape of the prouct. The optmum egn of thee perform e then become an mportant part of the egn proce. A well a mnmzng materal watage, the ue of optmum hape n the ntermeate tage can lea to mprove qualty of the forge component, ue to, for example, a reucton n local peak reual tree n the component, an an extene lfe of the e themelve, ue to a reucton n the frcton energy expene at the e/workpece nterface urng forgng [1]. In a conventonal forgng e egn proce, the egner requre to etermne the number of ntermeate forgng tage a well a the perform hape. Th normally one by expermental tral an error. However, toay, wth the upport of computer ae egn tool, the total manufacturng an tool egn cot can be reuce [2]. In aton, n recent year, the applcaton of the fnte element metho ha become a major tool n connecton wth perform e egn e.g. [3]. The backwar tracng metho wa evelope by Hwang an Kobayah [4] to revere the formng proce n a rollng operaton n orer to egn preform rollng pae. Later, th metho wa ue to obtan the preform e hape n the forgng of axymmetrc hape [3, 5]. Park et al. [6] evelope a new metho bae on the backwar tracng metho an apple t to preform egn of a hell nong. Granh et al. [7] ntrouce the optmum control egn algorthm nto proce parameter egn of the forgng proce. The optmum ram velocty for mantanng the pecfe tran rate n the bllet, for an othermal k forgng, wa generate through th approach. Thee analye were all carre out ung the fnte element metho wth a rg vcoplatc materal formulaton. Degn contrant on tran rate an temperature varaton are mpoe to acheve the ere forgng conton. To ate backwar formng ha been tue n axymmetrc an plane tran cae the author are unaware of any three menonal analye of the backwar formng proce. Bglar et al. [8] propoe a fuzzy-econ makng approach, whch wa evelope to pecfy new bounary conton for each backwar tme ncrement, bae on geometrcal feature an the platc eformaton of the workpece. In th paper a new approach evelope by ncorporatng the Lagrange nterpolaton metho [9] wthn the backwar eformaton metho to etermne the backwar eformaton path of the bounary noe. Th replace the more computatonally ntenve teratve proceure ue n [6-8]. The metho ha been ncorporate wthn a non-lnear rate epenent fnte element framework [10] an reult are preente for the cae of a plane tran an an axymmetrc forgng egn. 2

3 2 BACKWARD LAGRANGE INTERPOLATION In fgure 1, the ue of the lnear Lagrange nterpolaton metho llutrate n the egn of ntermeate forgng e hape. In the backwar mulaton, the tartng hape taken a the fnal e tage (the nvere of the hape of the fnhe component n flahle forgng) an backwar geometrcal nterpolaton conucte n orer to revere the eformaton. At the tartng pont the e an workpece are n contact an the noe at the e/workpece nterface are graually releae a the eformaton revere. The lnear Lagrange nterpolaton between two pont can be efne by takng the fnal hape an the ntal bllet hape a two extreme pont where the nterpolaton requre an vng t nto M nterpolate coornate pont a hown n fgure 1. Th can be expree by X = 0, X,2 X,3 X,...,( N 1) X ] (1) [ Y = f (0), f ( X ), f (2 X ),..., f (( N 1) X )] (2) [ where X an Y are the bounary noal coornate of the fnal hape an N number of noe on the e bounary urng an teraton an X = 0, X,2 X,3 X,...,( N 1) X ] (3) [ Y = g(0), g( X ), g(2 X ),..., g(( N 1) X )] (4) [ where X an Y the bounary noal coornate of the ntal hape (ntal bllet). Durng each nterpolaton tep, X an Y wll approach X an Y repectvely an the whole proce of nterpolaton conucte n M teraton a ecrbe n the next ecton. In aton to efnng the path of the bounary noe, t alo neceary to pecfy when the e urface come nto contact wth the workpece (or when bounary noe are releae n the backwar eformaton proce). The releae of noe from contact wth the e may be controlle by proce aumpton, relate to the geometry of the component, an other feature, uch a a nee to mnmze varaton n platc tran. Thee ue are cue further n [8]. In the current work the proce aumpton are lte a follow. 1. Snce, n forwar moton, the noe between the workpece/e nterface (eep n the e cavte) an e eparaton lne come nto contact at the en of formng proce, n the backwar mulaton they houl be releae at the begnnng of backwar proce. 2. In forwar mulaton, the workpece noe near the lne of ymmetry normally come nto contact wth the e at the tart of formng, therefore n the backwar mulaton they houl be releae from the e urface at the en of the backwar nterpolaton. 3. Volume contency urng all backwar nterpolaton ncrement mut be enure. 3

4 The mplcaton of pont 3 above that throughout the backwar eformaton the volume of the eformng bllet reman contant an equal to the fnal component volume. (Note that th gnore the effect of elatc eformaton urng the eformaton proce, whch expecte to be neglgble.) 2.1 Interpolaton Proce Bounary Conton The proce bounary conton pecfe at the tart an en of the proce. In orer to etermne the ntermeate noal coornate, the lnear Lagrange nterpolaton approach ue. Therefore, n tep k X k = X f k = 0 then (5) Yk = Y X k = X f k = M then (6) Yk = Y where k = 0 an k = M mean begnnng of tep 1 an the en tep M repectvely. X an Y are the noal coornate electe on the bounary of the bllet an X an Y are the noal coornate pecfe at the e urface. Note that the tance between neghbourng noe on the e an bllet bounare equal at the begnnng of the nterpolaton proce ( X = X ). For an ntermeate tage, the X coornate gven by, an the Y coornate by, k k X k = X 1 + X (7) M M k k Yk = Y 1 + Y (8) M M The volume contency conton then enforce at each backwar nterpolaton tep, uch that the volume of the fnal hape equal to the volume of the workpece. The pecfcaton of th conton cue n ecton 4 an 5, a t epen on the geometry of the forgng (whether plane tran or axymmetrc). 3 MATERIAL PROPERTIES AND CONSTITUTIVE MODEL The workpece a low carbon teel wth yel tre of 700 MPa an Young moulu of 200 GPa. The conttutve moel ue accommoate rate epenent eformaton wth von Me yel crtera an otropc harenng. The platc tran rate expree a: D ε pl j 3 pl j = D ε (9) 2 σ 4

5 where S j the evatorc part of the tre tenor, σ the equvalent (von me) tre, an D pl ε the equvalent platc tran rate, efne by the flow rule: n pl σ εd = D 1 (10) σ 0 where D an n are materal parameter an σ 0 the yel tre. The materal parameter n th mulaton were choen a D = 40/ an n = 5. The above materal formulaton for mall eformaton theory. For a large eformaton analy a ue n th cae, the equvalent platc tran rate D ε pl replace by the p ymmetrc part of the rate eformaton tenor, L,where pl where F the platc part of eformaton graent, F, [10]. = ( ) p PL pl 1 L FD F (11) 4 PLANE STRAIN CASE In a plane tran cae the volume contency n each nterpolate tep can be acheve by atfyng the area contency conton. The area can be calculate ung Smpon crete ntegraton rule a follow: S = N = 1 f ( X + X ) X (12) Before the applcaton of the volume contency conton the area of each ntermeate hape, etermne from the Lagrange nterpolaton, fferent from the fnal hape. Therefore a volume/area correcton factor C efne a C = where S k the nterpolate hape area an S the fnal hape area. To obtan the correcte coornate of the ntermeate hape the volume/area correcton factor ue a follow: S S k X k k (13) X ( Mofe) = C (14) Y ( Mofe) = C (15) k Y k Fgure 2 an 3 how the forwar an backwar mulaton repectvely, ung the fnte element metho, of a forgng proce uner plane tran conton. Due to ymmetry only half of the forgng geometry moelle. In Fgure 3, the tartng hape the fnal component hape an enng hape a quare bllet. Fgure 4 llutrate the two tage forgng proce ung two et of preform an fnhng e. The comparon of accumulate platc 5

6 tran for the forgng mulaton hown n fgure 2 an fgure 4 llutrate n fgure 5. A can be een here a more unform platc tran ha been acheve ung the propoe ntermeate preform hape. 5 AXISYMMETRIC CASE In the axymmetrc cae, the area agan calculate ung Smpon rule a follow: an the volume S = f ( r + r ) r (16) V = N = 1 S 2π r (17) where r the rau for any S n cylnrcal coornate. The volume correcton factor for nterpolate hape are thu obtane from V C = V where V k the volume of the nterpolate hape an V the fnal hape volume. The correcte coornate of the ntermeate hape are then obtane from equaton (14) an (15). Fgure 6 an 7 how forwar an backwar mulaton, repectvely, of the forgng proce for an axymmetrc analy. Fgure 8 llutrate the analy of a two tage axymmetrc forgng ung two et of preform an fnhng e. The comparon of accumulate platc tran for the forgng mulaton hown n fgure 6 an 8 llutrate n fgure 9. It clear that more unform platc tran ha been acheve ung the propoe axymmetrc preform hape. 6 CONCLUSIONS A new metho ha been preente for the egn of preform hape for multtage forgng. The lnear Lagrange nterpolaton metho, n conjuncton wth the fnte element metho, ha been ue to etermne the noal coornate that form the bounary hape of ntermeate hape n the backwar mulaton metho. A number of mulaton were conucte to elect the hape of the workpece at each Lagrange backwar proce. The reultant bounary hape can then be ue a the preform e n a forwar mulaton analy. Example of the forgng for plan tran an axymmetrc workpece were tue. More unform platc tran wa reporte through the ue of th metho for complex geometre compare to ngle tage formng. REFERENCES [1] G.B. Yu an T.A. Dean, A practcal computer-ae approach to moul egn for k 1 3 (18) 6

7 axymmetrc forgng e cavte. Internatonal Journal of Machne Tool Degn an Reearch 25 pp. 1 13, (1985). [2] T.A. Dean, Concept an practce n the precon forgng, 7th Internatonal. Col Forgng Congre, 15 23, (1985). [3] S.M. Hwang, S. Kobayah, Preform egn n k forgng, Internatonal Journal of Machne Tool Degn Reearch, 26 (3), , (1986). [4] S.M. Hwang, S. Kobayah, Preform egn n plan-tran rollng by the fnte element metho, Internatonal Journal of Machne Tool Degn Reearch, 24 (4) , (1984). [5] S.M. Hwang, S. Kobayah, Preform egn n hell nong at elevate temperature, Internatonal Journal of Machne Tool Manufacturng, 27 (1),1 14, (1987). [6] J. Park, N. Rebelo, S. Kobayah, A new approach to preform egn n metal formng wth the fnte element metho, Internatonal Journal of Machne Tool Degn an Reearch, 23(1), 71 90, (1983). [7] R.V. Granh, H. Cheng, S.S. Kumar, Optmum egn of forgng proce wth eformaton an temperature contrant, ASME Avance n Degn Automaton, 2, , (1993). [8] F.R. Bglar, N.P. O'Dow an R.T. Fenner, Optmum egn of forgng e ung fuzzy logc n conjuncton wth the backwar eformaton metho, Internatonal Journal of Machne Tool an Manufacture, 38, , (1998). [9] G. Ptre, Moellng, nterpolaton an contourng proceure. In Terran moellng n urveyng an cvl engneerng. Ete by G. Ptre an T.J.M. Kenne. Whttle, Lonon, (1990). [10] ABAQUS, Veron 5.8. HKS Inc, Pawtucket, RI 02860, U.S.A., (1998). 7

8 (Fnal e hape) Bounary noe wth coornate X an Y Bounary noe N Bounary noe 1 noe 2 X tep k Lnear Lagrange nterpolaton n M tep Bounary noe wth coornate X an Y (Intal bllet hape) Fgure 1: Intermeate perform hape egn bae on lnear Lagrange nterpolaton. 8

9 Fgure 2: Forwar FE mulaton of one tage forgng (plane tran cae). 9

10 Fgure 3: Backwar mulaton of forgng proce ung lnear Lagrange nterpolaton (plane tran cae). 10

11 Fgure 4: Forwar FE mulaton of two tage forgng (plane tran cae). 11

12 (a) PEEQ VALUE +4.73E E E E E E E E+00 (b) PEEQ VALUE +2.86E E E E E E E+00 +INFINITY (c) PEEQ VALUE +1.15E E E E E E E+00 +INFINITY Fgure 5: Plane tran analy of a forgng operaton (a) Accumulate platc tran n one tage forgng, (b) Frt tage of forgng for a two tage operaton (c) Secon tage of forgng. 12

13 Fgure 6: Forwar FE mulaton of one tage forgng (Axymmetrc cae). Fgure 7: Backwar mulaton of forgng proce ung lnear Lagrange nterpolaton (Axymmetrc cae). 13

14 Fgure 8: Forwar FE mulaton of two tage forgng (Axymmetrc cae). 14

15 (a) PEEQ VALUE +2.82E E E E E E E E+00 PEEQ VALUE +1.76E E E E E E E+00 +INFINITY (b) PEEQ VALUE +2.80E E E E E E E+00 +INFINITY (c) Fgure 9: Axymmetrc analy of a forgng operaton (a) Accumulate platc tran n one tage forgng, (b) Frt tage of forgng for a two tage operaton (c) Secon tage of forgng (Axymmetrc cae). 15