ISSN (1897-331 0) Volume 8

Special lssue 112008

1. Introduction

FUUII~IN qUalLmIJ ,,= VIYeII mIIUII w ~ ~ ~ ~ ~ ~ ~ ~ I ofthe Pofiih Academy olscbnces

Cognisable effects of model investigations of die casting processes

J. Da6ko "*, R.Daliko ', J. stojckb' a Faculty of Foundry Engineering, AGH Univcrsity of Sciencc and Technology , Reymonta 23,30-059 Krakdw, Poland

Faculty of Mechanical Engineering, AGE1 Univcrsi ty of Scicnce and Technology . Mickiewicza 30,30-059 Krak6w. Poland *Corresponding author. E-mail address: jd@agh.edu.pl

Receivcd 06.03.2008: acccpted in revised form 06.04.2008

Abstract

Analysis of hchaviour of thc strcam of thc modcl liquid (of various viscosity) during thc 1st and IInd phase of the process was achicvcd on thc basis OF invcstigations performed in Ihc hydraut ic modcl of thc system: shot slccvc - mou Id cavity. 7hrce versions of thc filling sysrcrns and various degrccs of a cavity filling were applicd. Thc comparison of rcsul ts, obtaincd by rncans of filming thc proccss with ~ h c rcsiilts schicvcd by sirnula~ion calculazions pcrlorrncd hy thc Magmasoft sokwarc. was donc.

Kcywortls: Dic-cawing; Mold filling; Alloy dispersion; Air occlusion: Modcl rcscarch,

First works concerning thc thcory of filling a casting mould with mcial in dic casting proccsscs wcre p c r f o d in ycars 1930- 1950 by I,. h m r n c r 141. who - as ths first scientist - developed thc thcorctical hasis of a liquid rnctal rnovcmcnt in a die casting. Latcr works, oftcn mutually contradictins, constituted a trial of an experimcn~al verification or t hc Frornrner's Ihcory. Finally his theory was iscopni7cd as thc first svcccssful test of dcrcrmining the isolhcrmal modcl of fi [ling thc mould with molten metal.

Thc main ~cchnotogic;ll prohlcm of dic casring arc difficulties with the complcrc rcrnov;ll of a gas phasc from a mould cavity, under condizions of a total lack of pcrrncnbility of thc rnctal mould and a very short tirnc (a fraction nf a sccand) of its filling. Undcr such conditions. thc subsurf;lcc pnscous porosi~y of a metalIurgical origin - rclatcd to thc cmission of gascs dissolved in a solidifying alloy - can superirnposc itsclf ovcr the occPusion phenomcnon in thc shot slecvc. Thc dic casting porosity results in a worse air-tightness, surfacc dcfccts af~cr n hcat trcatmcnt, no possibility of wclding and coating by powdcr-iurnacc techniques as well as limiting the work tcrnperaturc. This si~nificant dcfcct

mechanisms and paramctcrs of machines. Thc following proccdurcs arc applicd: dic casting in vacuum, application of multiphasc or phasc-lcss injcction systcrns cnabling high pressurc moulding (c.g. up to 900 MPa), shorrcning rhc time of pressure build-up in thc Illrd or IVth phasc nT rhc final pcessurc rnouIding of alloy (approximntcl y 10 11s) as wcll as passing into the catcgory of low-prcssurc dic casting systcms.

lntcrcsling investigations of rhc numcrical modelling of the process of a mould cavity fi [ling were pcrfomed in thc rniddlc of thc ninaies by 13. Skocrylas [ 5 ] . who uscd thc SOM-VOF method describing thc liquid Tm: sudacc in numcrical solutions of equations by the Finitc- Diffcrcncc Mcthod. Thc rraclion of liquid phasc E is the main paramctcr in thc applicd rncthod. This fraction is equal unity in a spacc fillcd with liquid. cqual zcm in an empty space and has inrcrmcdiate valucs in difk'crentinl elerncnts via which the frce surface passcs.

Widely recognised model invcstigations of dic casting processes are included in the cumnt rcscsrch topics carricd out by rhc tcam of scientists from thc Chair of Proccss Automatisation and the Chair of Casling Pmccsscs Engineering, AGII - Univcrsity of Scicnce and Technology.

of dic castings can bc rcstrictcd hy ir&rovcmcnts of

A R C H I V E S of FOUNDRY E N G I N E E R I N G Vo lume 8. Spec ia l Issue 112008, 57-62

2. Test stand for modcl investigations of thc dic casting proccss

The laboratory tcst stand hcing thc physical modcl of thc dic casting machinc was dcsigncd and construclcd for thc ealisation of the rcscarch program.

T h e following scts arc within thc tcst stand: Physical modcl o f a dic mould, Physical modcl o f a shot slccvc, Elcctm-hydraulic control system. Hydraulic fcedcr.

Physical modcl o f rhc dic mould asscmbly comprises oS(Fig. I): Shot sleeve model (horizooral visualisation chambcr), Die mould d c l (vcriical visualisat ion chnmhcr), t lydraulic servo-motor bcing thc piston drivc, Fixing clcmcnrs and mcasuring acccssarics.

Pig. I. Schcmc of thc laboratory stand showing the mnst important clements: 1 - Shot slccvc modcE (horixontal visualisation chamber). 2 - Die mould modct (vmknl visualisarion chamber), 3 - Hydraulic servo-motor. 4 - Scrvo- valvc. 5, 6, 7 - hcssure convcrtcrs, 8 - Lincar vctocity convcrtcr, 9 - Lincar displaccmcnt convcncr. I0 - Measuring disk

Exnrnplc of thc configuration of the mcasuring and contro! stand for thc flow phcnomcna testing during ~ h c proccss of casting mould filling in thc die mould machinc i s presented in Figure 2. Modcls of die moulds o f various shapcs and dimensions wcrc appl icd in invcsiigations pcrrormcd in thc cxpcrimcntal stand. Thc main pan nf ressarch was pcrforrncd on thrcc vcrsions o f moulds of thc shapc: of thc rectangular cavity and thc following dimensions: 2R0 mm (bcight) x I90 mrn (width) x I0 mm (depth). Mdcls of dic moulds with 3 vcrsions o f thc working cavity wcn: consrmctcd:

- Rectangular cavity without nny clcmcnts insidc - markcd version I, - Rcctmgutar cavity with 2 circular clcmcnts insidc - markcd vcrsion [I,

Rcaanplar cavity with 2 clcmcnts in a shape of semi-rinp insidc - markcd version 111.

mould 1 <TDK computer

pressure converter 0

converter

velocity converter 0

Fig. 2. Configunlion of thc rncasuring and control systcrn o f thc stand for thc flow phcnomcna wst ing during the proccss of casting mould filling in thc dic mould machinc

At1 vcrsions had mould vcnts locntcd on thcir uppcr surracc. Thc following markings and venting modcs of mould cavitics wcrc uscd in the presented hereby lcsts: - 0-0-0 - Full vcnting - total surfacc OF vcnting holcs 52

mm2. - Z-0-Z - rcduccd vcnting - rota1 surfacc of vcnting holcs X mm2.

Figurc 3 prcsents sbapcs and basic gcornctrical dimensions of mndcls - prcparcd by rncans of the Solid Works 2005 Program.

Thc prcscntcd bclow cxpcrimcnts wcrc pcrformcd for IWO rnodcl liquids:

- Modcl liquid o f a kinematic viscosity o f 1.39 rnrn'ls) ( 1.38 cSt) - markcd ,,LIQUID 7%, which corrcspnds approximately lo the aturninium alloy viscosity at dic casting, - ModcI liquid of a viscosity of 9.46 mm2ts (9.46 cSr) - markcd .,LIQUID 80%'. which can wprcscnt thc viscosity of orhcr aluminium alloys in thc statc of n partial crystallisalin~~ nr casting.

A R C H I V E S of FOUNDRY ENGINEERING Vo lume 8 , Specia l Issue 1 1 2 0 0 8 , 57 -62

I.. !

",. ., , ." ."' ", "a' .&, :, , ,+

" . ; ,* ;, &," >,, ,;,, < < < <,, <, , : , > , ,. +<,><: ,> 7 , , , , < ' " , T '

A , ,: %,> : a ,, ; < " ;,'T':b',,';, 2;;: , ! ,.$ CCn ,-.-. * . ,,, < I I ,,

. , , -,, , : . " . " . Y C :,:

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3. Invcstigations at the test stand

Thc mwmh pmgram present4 in the hereby papcr was ,zr follows: I. Dctcrrnina~ion of the influcncc or thc prcssing piston vclocity on thc

3. Dctmninaiion of rhc inffucnce of fhc pssin,c piston vclocity on rhc filling dcgrcc of thc cavitics or thc rrdcl cx~ ing moulds (vcrsion I <and 111);

4. Numerical simulation of rhc proms of fillins thc cavity of thc mde l casting mould (vcrsion 1 and n pressing piston vcIocity of 0.2ds) with thc application of the Magmxwfi softwnrc:

5. Comparison of rcsults obraincd from simulation calculations with thc results of cxpcrimcn!~ at thc tcst stwd.

Thc graphical picturc of thc dcpmdcncc of thc avmgc ac~ttal ntc of filling on thc vclocity of twa kinds or d c l liquids in thc gatc holc of rnodcl moulds (vcssion I - I I I with tk ing into account thc vcnting modc) is givcn in figure 4 ;~t the hxkgmund of thc thmmical mtc d filling (mi-stmight linc). The dcpndcncc of thc diffcrcncc bctwccn thc avc~gc vduc of 2hc actual mtc of filling and 111c thcomicdly cdtlculatcd one on the vclocity of liquid in thc gatc holc- undcs thc samc axpcrimcnlal conditions - m pmscnrorl in Figurc 5. Thc ohtaincd rcsults hmdlcd smistically hy inc,ms of thc Exccl progmm providc empirical dcpcndcncics. which can constitute thc basis for forccaqting thc avcmgc actual n tc of filting of rhc d c l liquid of n dctcrmind viscosity (being insidc rbe rcstcd v,ui;lhility mgc) undcr ~ h c known conditions of thc mould filling.

lip +pal. bob I.?. m O H lrpu~d +LIOUID l2 Hnl lng -dm ODD, ~ d u r n d u r n - r n a ! m holm 4 7 m a a l lhquld -LIQUID W4 wnung md. 0&0. meurn varue +ga!. balm 4 7, m a a l lhqv80-LIPUID 1- wnhnp - d l 2 0.2 mOd#vmvliu. -qaf* holm 1 7, m o ~ l lhquma_~1CUID 83-.vonf#ngrnod. 2.0.2. m r e ~ u m u s r ~ -Calculated ralsol all~lrg 01m1 -

-I -

fig. 4. The depmdcncc of the a v m p m u d r;uc of filling on thc liquid vclociry h the gate holc (Tor rhc gale: 4.7 x 48 mm) at various vcnling modes and mrious viscosities of thc d c l liquid

volumetric ntc of tifling of the d c l liquid - achicwcd hy tncans Fg. 5. Thc dcpcndmcc of thc dilfcrcncc hctwccn thc avcngc vduc of of filming thc p m s s : ~ h c actual mtc of filling and thc cdculaicd onc on rhc liquid vclnciry in

2. Prcssurc mcasu~mcnis in thc shot slccvc ;:md in thc d c l cxting thc patc holc (For tlic gate: 4.7 x 48 mm) m v;lriws vcnling d c s and inot~ld; vmious vixositics nf thc modct liquid

A R C H I V E S o f F O U N D R Y E N G I N E E R I N G Vo lumo 8 , S p e c l a ! l s s u o 112008 , 5 7 - 6 2 59

Fressun: murcmcnts wcrc used Tor determining the prcssurc changcs in the shot sIccve and in the mould dcpd ing on the conditions of thc p e s s realization. h s u n : curvcs wcrc m d y d in cornlation with characteristic phascs of the prcssing piston displaccmenz. The timc of filling thc mould cavity with model liquid z wcll as thc votumetric mtc of filling wcrc dctmincd on this basis. Thc following data were detcrmind: - Maximum pressure in the shot stccve [ppr. mu.) and in the dic

mould (pf. rnax.) (Fig. 6 and 7). - Difference of thc maximum prcssurc in thc shot slceve and in h c

die mould (ppr. max. - pf. ma.), - Work prcssurc in be shot slccvc (ppr.) and in the dic mould @I) during the muld filling. i I

L "-

; t.4

U r)

E '3 z

5 ',D s c e e G n o 2 : g E o* 'n

K a 4 - rn

'C 0,2

3 0 0

0 1 1 3 5 u 7

Aclual In)ectro* valotIty01 model IlquU, mls

Fig. 6. The depndencc of the maximum pressure in thc shot slccw (ppr, max.) and in the mould (pf, max.) on the liquid vclocity in rhc gare Me. .LIQUID RO%, for a hole: 4.7 x 48 mm". 0-0-0 vcnting d c .

Analysis of graphs confirms the exp tcd correctness conccrning rhc pressure distribution in the shot slecve and in the mould, which is refated to mis t ice of a Iiquid flow via the gate hole and vents. At the theoretically constant vcnting surface (0-0-0 vcnting m d c ) thc maximum pressure changes exponentially wih the increase of the liquid vclocity in thc gatc holc. Highcr pmalrc values b t h in the shot slccw and in the mould arc obtnind For gatc holcs of a smdlcr surfacc area and for higher viscosity of model 1 iquids.

a l 2 1 4 5 I I

M u a l Inbclbn velocity or model llquld mlr

Fig. 7. The dqmdmce of h e maximum pressure in the shot slcevc (ppr. max.) and in thc mould (pf. max.) on thc liquid velmity in the gate hole. ,LIQUID 7% for a hole: 4.7 x 48 mm", 0-0-0 vcnting mode.

A comparison of data conccrning thc volumtric ntc of filling - dctcrmined from the analysis of thc film and from [he pressure - indicates quite significant discrcpancics whcn thc piston vctocity c x d s 0.1086 d s (vdocity in thc gatc holc 4.7 x 48 mrn - 1.96 nds and 3.07 trls - in thc gatc holc 3 x 48 mm). Volumetric rates of filling arc much highcr and highly variablc d p d i n g on thc vcrsion of lhc mould and the Iiquid vimsity. Law rqxatnbility of milts in individual measuring scrim nllows to consider them on1 y as thc approximate oncs. However, monitoring of the prcwrc fluctuations is uscrul for thc interpretation of Lhf, filling process in thc caw whcn thc process is not rccordcd by filming. The d e w of fitling of the model mouId cavity was estimatd by measuring the surfacc trtkcn by liquid during thc filIing proccss. This estimation was done by using h c LEICA QWin v. 2.2. pmgtxrn for automatic picture analysis. It was possible due to the previously pcfirrnod thc filting proccss recording by mans of filming. Thc sclcctcd frames (for each mould version) werc andysorl in order to compare the pcrccntagc filling of thc cavity of the muld rcdised at various injection vclocitics of thc mdcl liquid. Thc applicabili~y of thc E I C A QWin v. 2.2. prugmm for thc automtic piaurc ,malysis was vcrit'id morc prcciscty lor vcrsion I of thc model muld since - in this casc - thc pmcess of cavity [iIling \mq not additionally dislurberS by the influcncc of inscrts in rhc s h a ~ of circles and rings.

The results of measuring thc surface area by m a s of thc LEICA QWin v. 2.2. microscope arc prcsmtcd in Figurrs 8.9 and t O. Thc dza analysis indicates much mom intensive surfacc dcvclopmcn of thc stream of liquid of a lower viscosity (.LIQUID 7W3, as c o m p d to thc onc of a higher viscosity (,UQUID go%'?. which indimly cxplains its highcr mobility and tcndcncy to a dtstuFbcd flow. Continuous lines illustrate the cavity filling proccss at the hll vcnting area (0-0-0). whilc broken lines at the roduccd venting ,ma GO-2) . Morc significant inffuencc of a vcning modc on thc dcgcc of thc cavity filling with the model liquid of a towr viscosity -can hc s m .

Fig. 8. Surface m a s taken up by .WQUID 80%': calculatcrl hy mans of thc LElCA QWin v. 2.2 m i c m s c o ~ Vcrsion I of thc muld.

= g 7D -

$ 0 - 0

A R C H I V E S of F O U N D R Y E N G I N E E R I N G Vo lume 8 , S p e c i a l Issue 1 1 2 0 0 8 , 57 -62

.... that pelon Y e k * V=D.OB WL mnl~ng mod. O-PO

- m o r p a l o n ~ s c n y Y=&i83+vmt1ng m& m 0 - - 6 h t prrlon valacny V=Q OB m l b uenllnp mode 2--2 rhot pmlon vehcrly V=183 ma Mnlnng mode Z.Gt

0.5 t 1.5 2 2 6

Fig. 9. Surfacc arcas takcn up by ,LIQUID 7%': calc~zlarcd by mans of the LEICA QWin v. 2.2 micrnscopc. Vcrsion 1 of the mould.

t g 2 0 -

1D -

Fig. 10. Liist and data handling for t hc calcular ion - pdormcd by means of the LElCA QWin v. 2.2 microscope- of the surfacc am t&cn up by ,UQUID 80'*, version I olthc rnarild.

. - __..' .... Shot plalon nlocsly v=O 08 nus. wnang mar 040 - Snm plslon voloc4y V=O 153 mh. wnl8ng mode 00.0

ShM olslon v 1 1 ~ 1 l y V=O 08 mrs mnang mr#o Z O Z - S ~ M plslon valwlly '41163 mrr. wmlng mode 2-0-2

4. Simulation investieations

0 * 0 0 5 1 1 5 2 2,5

Fllllna tlme. r

Thc comparison of mdts conccming the degrcc of tilling hc model mould cavity obtainccl as thc rcsult of simulation md as thc mult of surface m a measurements by means 01" rhc E I C A mimscopc and program - is givcn in Table 1 .

Table 1. Comparison of numerical calculations - concerning the d c p x of filling thc d c l mould cavity - with the rcsults ot expximcnts

mould caully

" 1 I 74-18 95-12 100 determined by the

slmulatlon. %- Fllllno ol tne model

mourd cavlty detarm~ned by the 82.67 84,49 91.32

audaca area measureents,*A

Tlme,s C O , Z 6 s 0.53 a O,E3 a I,% S

The rcsults of simulation dctcrminations pxforrncd by mans of thc MAGMASOFT software and h c adual mults obtincd by filming thc filling pmess arc c o r n p d in thc photographs bcrow (Fig. t t).

On thc grounds of the list givcn in Tahlc 1 i t can hc slated that in thc first, lcss atrhulcnt, p h m or thc cavity filling lhc results ohtnincd by both types of mc,lsurcmcnts arc consisted with cach o~lrcr. It cni k d.m noticd that vducs or thc dcgrcc of filling ob~nind by simnln~ion calculations arc sIightly s~nallcr, Thc situation chnngcs in thc Iinnl phm of the p m s s , which is cnliscd by thc tiihulcnt hchnviour or n litp~id insidc thc m d c l mou!d cavity - not suKcicntly tAcn intn accounl in the calculating d u l c . I11 Ihc ctw of thc ~nodcl 'Lcsts at tlhc cnd of tIlc cwiry filling with a two-phxc mixtun: (liquid and air buhhlcs) ccrtnin mount of liquid is forcod through thc vcaing holes info thc ova-flow tank Thcrcforc thc crw~ivc voli~~nctric ratcs of filling ,m srndlcr lllm

thc ones appxing from rhc mlcs cdciilatcd on thc hzis of thc pmduct oFrhc movcmcnt vcIoci~y md thc prcssing pisfon surfacc.

Cras 0,28 s

Czas 0.83s

Fig. 1 1. Comparison orrhc filling of thc rnnrlcl mould cavity - ohtaincd by filming thc phcnomcnon - with lhc vclocity vcctors o h ~ a i n d hy mcans or the Magmxoft mnwarc

Analysis of picturcs of displaccmcnt of the liquitl 5IKilm inside thc mould cavity obtained by mcims or thc MAGMASO17r wfiw;~rc iuld thc ones m r d c d by camen shows g d visunl cornpatihilily. Ihis compatibility conccms somctimcs quitc dclnilcd pmhlcms is c . ~ 'protrusion' sccn -on thc righr hmld side - it1 rmnt of a Iic~uir I slrcam (Fig. 1 E , t i ~ne 0.53 s.). which is vcry ortcn ~isihlc in picturcs aflcr Ihc

A R C H I V E S of F O U N D R Y E N G I N E E R I N G Vo lume 8 , Spec ta l I ssue 1!200B. 5 7 - 6 2 61

tmfmcnt pxformcd by m,ms or the E I C A QWin v. 2.2 progmm for gascous bubbics occludcd by liquid is highcr for liquids or a low nulomfi~ic ,and ysis. viscosity.

5. Conclusions

Thc p m ~ d krchy considcmtions indicalc that such p m c t c r s as the gmmctry of thc ptc systcm and thc injcction velwity influcncc thc The authors wish to express heir gmtirudc to Dr h g . Rys7,ud

d c l tiquirl c h w c t , which c o m p n d s to the quality of rhc obtained Skoczytx of thc KOM-ODLElV Company. Cornputcrisd bginccring Systems I.I.Compy (Komptcrowc Systcmy In@nicrskic Sp, a o. o.) dic castings. Gcnmd rccornmcndf ions givcn in the refmnccs [14].

concerning thc p ~ c holc shapc md its hydraulic resistance are only from K d o w for pdorming calculations hy incnns of lhc

imwnmt whcn ~ h c rclinblc md cxtlcrimcnidly vcrificd chm~1cristics MAGMMOFT soRwarc.

nf. ~olumctric or mass ntcs of fillini i~ available. The fnllowing mnclusions can Ix dnun on thc M s of rhc photographed - in an actual timc - thc flow phcnomma ad on thc mcmuEmcnu of the ratc of filiing: 1. Dimcnsions and Fcomctrq. or thc gat systcm of the m l d as wclt

as the liquid velocity have a dccisivc bcaring on thc chamctcr of the liquid flow during thc mould filling. At ~ b c consmt fining vclocity thc characariaic of flow dcpcnds mrc on thc dcpth or thc gate systcm than on f s width. thus thc criticat filling vctociry is invcrscly propnional to rhc p r c h l c dcpth.

2. At an mymmctric plxcmcnt o l inwits insidc thc mould cavity rhc axid intduction o l thc d c l liquid dms not pmvidc condi~ions of mwld filling, which would climinatc air voids, md in mnscqucnce rhc time ncccswy for thc total stahilisiat ion of inodcl liquid movcmt is prolongerl.

3. Thc m l t s ohtaincd From expcrimcntal tcsts confirm thc oncs cnlculnrcd on the basis of the Reynolds n~unbcr. At Zhc pmsmtly spplicd technology of dic casting, whcrc gate sysfcms arc of a dqth trp to 10 mm. thc gatc vclocity of h c m g c 0.34.5 mk is consirlcd thc p r o p unc for maintaining Ihc now of thc xssud ckuxtcr. In thc c;m. whcn the prcssing pmm is pxformccl in thc stntc crf p;ulial ~ I - y ~ l d l i ~ a t i ~ I I the gate vclocity can bc onc odcr highcr without champing thc flow from laminar to thc i n r c d i a r c one.

4. Tllc stationsuy now pmccsscs of thc modcl Iiquid in a mwld -or ,my shapc o f thc cavity -,m morc cmily obtainhtblc whcn the liquid uscd IS of a hlghcr viscosity. wh~lc !Rc vclocity or renwval of

Rcscarch financed by Statc Committcc for Scientific Rcscnrcb in 2005-2007. Projcct No 3T08B 025 28

[I] . Bintobrzcski A,: Odlcwnictwo ciinicnio~r.~. Maszyny, urzqdren ia i tcchnologis. Warsmrva, P\W. 1 992.

[2]. Dafiko J., Lucarz M.: Analim porb\vna\vcm zalchoSci do obliczania przckroju szczclin wlcwowych w odlcwach ciSnienio\vch. Polska Mctnlurgia w latach 1998-2002. Komitct Mctalurgii Polskicj Akadcmii Nauk. t. 2. 103-1 09.

[3].Dahko J.: Masqny i um.qd;rsnia do odlclvnnia pod ciinie- niem: podsrawy tcorii, konstrukcja. pmiary i cksploatncja. Wydawnictwa AGH. Knk6w 2000.

[4].Skoczylas R.: Dadania modcloivc proccstl zapclninnia wncki formy. Krzepniecie Metnti i S1op6w. Nr 23, 1995, PAN- Oddzial Katowicc, PL ISSN 0208-03R6,65-70.

[5 ] . Badania modclowe wlaSciwoSci liydrodynnmicznycli strugi rnetalu E zapelnianisl form w ci9nicniowvycli inasqnncli zimnokomor~wych. Projckt badawczcgo KBN ar 31'0813 025 28 (kicrownik J. Dahko).

Efckty poznawczc badah modelowych procesu sdlcwania ciinicniowcgo

S treszczenie

W oparciu o bdania p c p r o ~ ndzone na mdclu hydmul icmym uk tadu komora pmmvania-~\nqka r m y pmpro\rdmno nnaliq nclio\cmin siq stmniiunia decc rnodeIo~\.c.j Q r62nc.i 1cpkoSci w mkcic 1 i 11 T n q pmccsu. 2astoso\vano ~rzy pmyl;lh\\r \vcrsjc ttkl;~ditiv dopmuxlmjqj;lcych cicm modclotq do ~vnqki formy o m rrimc jc j wypclnicnic. Dakonmo ponhvnmia pzebicgbw uq&m!rh na dralzc f i lmo~~~ai in pmcrsu z annliq malogicmych qaivisk ot~rnnnych pntz oblic/tnin symulac~Jnc 7a pomocq pmgmmu qmulaqjncgo MagmwCt.

A R C H I V E S 0 1 F O U N D R Y E N G I N E E R I N G V o l u m e 8 , S p e c l a l l ssus 112008. 57 -62