Numerical simulation of sand mould manufacture for Lost Foam Casting process

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1 Numercal smulato of sad mould maufacture for Lost Foam Castg process J. Rojek 1,, F. Zarate, C. Agelet de Saracbar, M. Chumet, M. Cervera, P.M. Hagh 3, C. Glboure 3, P. Verdot 4 1 Isttute of FudametalTechologcal Research, Swetokrzyska 1, Warsaw, Polad URL: e-mal: jrojek@ppt.gov.pl Iteratoal Ceter for Numercal Methods Egeerg, CIMNE, J. Groa 1-3, Barceloa, Spa URL: e-mal: zarate@ cme.upc.es; agelet@ cme.upc.es 3 Castgs Techology Iteratoal, 7 East Bak Road, Sheffeld, UK URL: e-mal: c.glboure@castgstechology.com 4 Huttees-Albertus Frace, BP 30309, Z.I. de Pot Breoulle, 6073 Pot Sate Maxece, CEDEX, Frace e-mal: Hateccom@aol.com ABSTRACT: Ths paper presets a umercal model of mould maufacture for the lost foam castg process. The process of mould fllg wth sad ad sad compacto by vbrato are modeled usg sphercal ( 3D) or cyldrcal ( D) dscrete elemets. The moto of dscrete elemets s descrbed by meas of equatos of rgd body dyamcs. Rgd partcles teract amog oe aother wth cotact forces, both ormal ad tagetal drectos. Numercal smulato predcts defects of the mould due to suffcet sad compacto aroud the patter. Combg the dscrete elemet model of sad wth the fte elemet model of the patter allows us to detect possble dstorto of the patter durg mould fllg ad compacto. Results of umercal smulato are valdated by comparso wth expermetal data. Key words: lost foam castg, mould maufacture, dscrete elemet method 1 INTRODUCTION Lost foam castg (LFC) s a type of metal castg process that uses a sad mould wth a polystyree foam patter remag the mould durg metal pourg. The foam patter s replaced by molte metal, producg the castg. Ths process gves ear et shape castgs of hgh qualty ad defto ad provdes a desg flexblty ot gve by other castg techologes, but o the other had the techology of LFC poses serous dffcultes, producto of a good mould beg oe of them. The producto of moulds for LFC process volves three steps. It s started wth the placemet of the patter the mouldg box. Next, the patter s covered wth dry ad uboded sad. The the compacto of the sad s acheved by a vbrato process. Oce the compacto s complete, the mould s ready to be poured. Vbratory compacto s oe of the most mportat phases of the LFC process ad t may be crtcal to obta a good qualty cast product. Vbrato should esure uform ad proper compacto, by fllg all the cavtes wth the sad ad packg sad to maxmum desty aroud the patter. There s o smple relatoshp betwee sad parameters ad vbrato process parameters, therefore the compacto process s ofte desged a purely emprcal tral ad error maer. Other defects occurrg the LFC process are the shape defects due to deformato of patter uder sad pressure durg fllg ad the vbrato process. Ths pheomeo has also bee studed our umercal model. BASIC ASSUMPTIONS The objectve of the computatoal model developed s to provde a more ratoal way to desg the fllg ad compacto process. The ma physcal pheomeo cosdered s the flow of graular materal (sad) aroud a rgd or deformable

2 obstacle (mouldg box, patter) uder gravty or vbrato. Numercal models of sad compacto adopted the preset study are based o the dscrete elemet method (DEM) whch s wdely recogzed as a sutable tool to model graular materals [1, ]. Wth the DEM, t s assumed that the castg sad the LFC process ca be represeted as a collecto of rgd partcles (spheres or balls 3D ad dscs D) teractg amog themselves the ormal ad tagetal drectos, due to frcto. The materal model cosstg of rgd sphercal elemets has bee cosdered the most sutable to model the flow ad re-arragemet of the sad gras duced by vbrato. It would be dffcult to capture properly the ma characterstcs of such a process usg a cotuum formulato. Obvously, t s ot teded that each partcle used the DEM represets a sad gra, but t s assumed that the ma characterstcs of the (loose) sad behavour durg fllg ad sad compacto ca be macroscopcally represeted usg the DEM. O the other had, t s also obvous that a large umber of partcles wll lead to a better approxmato of the results provded by the umercal method used, but a hgher computatoal cost, terms of computatoal tme ad computatoal resources, s ecessary. Dfferet gra szes were troduced to our computer model wth the sze dstrbuto beg a fucto of the sad graulometry. To allow us to predct the cellular foam patter deformato durg mould fllg ad compacto the Dscrete Elemet Method s combed wth the Fte Elemet Method. A geeral model cossts of dscrete elemets represetg sad ad fte elemets dscretsg a deformable patter. 3 DISCRETE ELEMENT FORMULATION The DEM scheme usg sphercal rgd elemets has bee troduced by Cudall [1, 3]. Our study s based o our ow mplemetato of the DEM the fte elemet explct dyamc code Smpact [4]. The traslatoal ad rotatoal moto of rgd sphercal or cyldrcal partcles s descrbed by meas of Newto-Euler equatos of rgd body dyamcs. For the -th elemet we have m u I ω F T (1) where u s the elemet cetrod dsplacemet a fxed (ertal) coordate frame X, ω s the agular velocty, m s the elemet (partcle) mass, I s the momet of erta, F s the resultat force ad T s the resultat momet about the cetral axes. F ad T are the sum of all forces ad momets appled to the -th elemet due to exteral load, cotact teractos wth eghbourg spheres ad other obstacles, as well as forces resultg from dampg the system. The form of the rotatoal equato (1) s vald for spheres ad cylders ( D) ad s smplfed wth respect to the geeral form for a arbtrary rgd body wth the rotatoal ertal propertes represeted by the secod order tesor. Equatos of moto (1) are tegrated tme usg the cetral dfferece scheme. Tme tegrato operator for the traslatoal moto at the -th tme step s as follows: F u (3) m u 1/ u 1/ u t (4) 1 1/ u u u t (5) The frst two steps the tme tegrato scheme for rotatoal moto are detcal as those gve by (3) ad (4): T ω (6) I ω 1/ ω 1/ ω t (7) Rotato s defed by the vector of cremetal rotato : θ 1 1/ θ ω t (8) Explct tegrato tme yelds hgh computatoal effcecy. Its kow dsadvatage s the codtoal umercal stablty mposg the lmtato o the tme step. Cotact forces F are obtaed usg a costtutve model formulated for the cotact betwee two rgd spheres. The cotact terface our formulato s characterzed by the ormal ad tagetal stffess k ad k T, the Coulomb frcto coeffcet, ad the cotact dampg coeffcet c. The ormal cotact force F s decomposed to the elastc part F e ad to the dampg part F d. The elastc part F e s proportoal to the ormal stffess k ad the peetrato of the two partcles u r :

3 F k u (9) e r The cotact dampg force s assumed to be of vscous type F c v (10) d r proportoal to the ormal relatve velocty v r of the cetres of the two partcles cotact. The tagetal cotact force F T s brought about by frcto opposg the relatve moto at the cotact pot. Frcto s modelled usg regularzed Coulomb law. The sldg frcto caot provde ay resstace to the movemet of the sphere (cylder) rollg o a rough surface f there s o relatve tagetal velocty at the cotact pot (v rt = 0). The rollg resstace ca be smulated umercally by assumg some eccetrcty of the ormal reacto ad applyg the resstg momet proportoal to ths eccetrcty. Cotact dampg, gve by Eq. (10), dsspates ketc eergy of cotactg partcles. There s also dampg whch s appled to o-cotactg partcles as well. It ca be of vscous or o-vscous type. agle values ragg from 6 to 36, wth lowest value correspodg to the cerabead (Fg. 1a), a artfcal sad characterzed by perfectly rouded gras. The repose agle obtaed D smulato, 5, s close to the expermetal results. It agrees especally well wth the value for the cerabead sad. 4. Sad flow to horzotal tubes A metal test pece cosstg of a seres of three tubes of dfferet dameters (Fg. ) was placed the sad box. The box was flled wth sad ad vbrated the vertcal drecto, wth vbrato frequecy beg 50 Hz ad accelerato ampltude of 1.5 G. Mgrato of the sad to the horzotal tubes has bee vestgated (Fg. a). Numercal smulato of ths test has bee carred out usg D model of 64,000 partcles wth the tube of largest dameter cosdered oly. Partcle dameters raged from 1 to 4.5 mm ad sze dstrbuto was take accordg to the graulometry of the real sad. A good correlato of the umercal results (Fg. b) wth the expermetal oes ca be see. 4 NUMERICAL EXAMPLES 4.1 Repose agle test a) a) b) Fg. 1.Repose agle: a) expermet for cerabead, b) smulato Smple expermets of emptyg a small hopper have bee carred out to obta the repose agle of dfferet sad types. Expermets yelded the repose b) Fg.. Sad flow to horzotal tubes after 40 s vbrato: a) expermet, b) smulato

4 4.3 Test wth a L-shaped patter Dstorto of a smple L-shaped patter durg fllg ad vbrato has bee studed expermetally ad umercally. Expermetal results show that the fllg process dstorts the patter (Fg. 3a) ad that a area of low sad desty exsts below the horzotal secto. The patter dstorto although slghtly reduced s stll observed after vbrato (Fg. 4a). Durg vbrato the sad flows to the cavty below the horzotal part of the patter. Smlar dstorto of the patter durg fllg ad compacto has bee predcted by umercal aalyss, cf. Fgs. 3b ad 4b. The patter has bee dscretzed wth 4-ode pla stra elemets wth elastc propertes assumed. chemcal bder. Fgure 5a shows a secto through the sad block revealg the test patter ad sad layers. Smlar sad flow aroud the patter has bee obtaed umercal smulato (Fg. 5b). Ths example demostrates the computatoal effectveess of the umercal model ad the possblty to treat large models ths case early 180,000 partcles have bee used. Fg. 5. Sad layers, a) expermet, b) umercal smulato 5 CONCLUSIONS Fg. 3. Deformato of the foam patter after mould fllg: a) expermet, b) umercal smulato The umercal model developed s sutable to model mould maufacture, sad fllg ad compacto of sad by vbrato. The model gves the possblty to take to accout deformato of the foam patter durg fllg ad vbrato. Expermetal valdato tests show good correlato of umercal results wth practce. ACKNOWLEDGEMENTS Fg. 4. Deformato of the foam patter after vbrato: a) expermet, b) umercal smulato 4.4 3D test of mould fllg ad compacto Expermetal study ad 3D umercal aalyss of mould fllg ad compacto have bee carred out for a smple dsc shape wth a sde bracket. The desg was chose as beg able to characterse basc problems ecoutered dustral LFC processes. Sad was flled layers ad vbrated durg fllg. I order to valdate the smulato of sad flow aroud the patter, expermetal trals were performed usg coloured sad cotag a Facal support of the Europea Commsso through the Growth Europea Project GRD (FOAMCAST) s gratefully ackowledged. REFERENCES 1. P.A. Cudall ad O.D.L. Strack, A dscrete umercal method for graular assembles. Geotechque, (1979) C.S. Campbell, Rapd graular flows. Aual Revew of Flud Mechacs, (1990) P.A. Cudall, Formulato of a Three Dmesoal Dstct Elemet Model Part I. A Scheme to Detect ad Represet Cotacts a System of May Polyhedral Blocks. It. J. Rock Mech., M. Sc. & Geomech. Abstr., 5 (1988) J. Rojek, E. Oñate, F. Zarate ad J. Mquel, Modellg of rock, sol ad graular materals usg sphercal elemets. d Europea Coferece o Computatoal Mechacs ECCM-001, Cracow (001).

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