POLYMER PARTS PRODUCTION SIMULATION FOR DOMESTIC REFRIGERATORS

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1 POLYMER PARTS PRODUCTION SIMULATION FOR DOMESTIC REFRIGERATORS N.O. Moaga, C.A. Salaza, R.A. Molina Depatamento de Ingenieía Mecánica, Univesidad de Santiago de Chile, Alameda 3363, Santiago, Chile Abstact Numeical simulation based on finite numeical methods is used to pedict the poduction pocess by injection molding of two polymes pats used in low cost domestic efigeatos. The Hele-Shaw fluid mechanics model along with the volume of fluid method ae used to calculate velocity and pessue fo nonnewtonian polyme flows duing the injection pocess using finite elements. The enegy equation, with tansient, convective, diffusive and viscous dissipation tems, descibing the cooling pocess of the heated polyme while being injected in the cold mold, is solved by the finite diffeence method. Results fo the time evolution of polyme font, pessue and tempeatue distibutions duing injection of Polystol 495F in the mould cavity to poduce the feeze doo, obtained fom two diffeent non-newtonian fluid models, thee mold tempeatues and two thickness ae pesented. The effects of the location of the injection point and heat tansfe coefficient between polyme flow and mould cavity on the pediction of weld lines and time histoy of tempeatue distibution in the Polystol 143E eggs cabinet ae veified by expeimental evidences. Weld lines location, time histoy of both tempeatue distibution and polyme font time evolution ae found to be well pedicted by eithe the Coss-LWF o the second ode fluid models. Keywods: Polyme pats poduction. Numeical simulation. Mathematical modeling. Domestic efigeatos poduction. 1 INTRODUCTION One of the tendencies in moden technologies is the substitution of metals and alloys by polymes, caused by the cost eduction obtained. Powde injection moulding, PIM, based on the use of polymes is the pope method used to ensue the poduction of big quantities of high quality pats, with complicated shapes and small sizes. The PIM poduction pocess equies an injection machine that feed the polyme into cavities, with the shape of the pat being poduced, into a mould. Wate is pumped though the cooling channels, built in the mould in the vicinity of the cavities, to allow the polyme solidification. Cost and quality ae majo issues in moden poduction technologies. The selection of optimized molding conditions and appopiate moulds ae the two main souces of defects in the manufactuing. The use of mathematical models and numeical simulation of polyme injection, cooling and solidification ae useful tools used in mould design and selection of adequate paametes fo industial poduction, [1-4]. The moving flow font duing polyme injection is calculated using a volume of fluid, VOF, method, based on the Hele- Shaw model, [5]. This appoach coupled to the dono and accepto flux appoximation, has been solved by the finite volume method, with the SIMPLER algoithm, to pedict mold filling and solidification, [6]. Numeical simulation analysis to investigate the polyme injection moulding has been studied with thee commecial codes: C-Mould, Moldflow and PoCAST. Expeimental data obtained fo a flat model with a complex shape wee used to compae with the obtained esults. Weld lines and tempeatue pedictions by the thee pogams wee found to be in good ageement with the expeimental esults, while C-Mould gave the best pediction fo pessue, [7]. The pape objectives ae: a) to descibe the use of fluid mechanics, heat tansfe and solid mechanics mathematical models and b) to evaluate the numeical simulation, by commecial pogams based on finite numeical methods, on the pediction of the fabication pocess of domestic efigeatos plastic components by polyme injection and moulding. 2 PHYSICAL AND MATHEMATICAL MODELS The injection pocesses studied included the industial poduction of two components of a one doo low cost domestic efigeato: the feeze doo suppot and the egg cabinet. Figue 1 shows the efigeatos and the two pats investigated. Figue 1: Feeze doo and egg cabinet of efigeato. The manufactuing pocedue fo the Polystol 495F, BASF, doo suppot was pefomed in a 125 tons Po Yuen me-125 injection machine, with a 45 mm diamete scew, a hydaulic pessue of 14 MPa, maximum injection flow ate of 160 cm 3 /s, injection tempeatue of 240 ºC and a mold tempeatue of 40ºC. The paametes used to fabicate the Polystol 143E, BASF, egg cabinet, in a Po Yuen me-250 injection

2 machine, wee: 250 tons, 45 mm diamete scew, P h max = 18 MPa, mmax =160 cm 3 /s, T inj = 245ºC, T m = 40ºC. The fluid mechanics mathematical model was built based on the continuity and linea momentum equations fo non Newtonian fluid in lamina flow Dρ D + ρ ( v ) = 0 ; = + v (1) Dt Dt t Dv ρ = p + τ + ρ b (2) Dt The stess tenso was calculated in tems of the shea ate tenso D fo non Newtonian fluids by τ = 2η & γ D (3) ( ) The dynamic viscosity fo polymes was descibed in tems of pessue and tempeatue by using the Coss-William- Landel-Fey five constants model η0 η = η & 0 γ 1+ τ * with 1 n ( T* ) ( *) A1 T η0 = D1 exp A% 2 + D3p+ T T And T* = D + D p NUMERICAL SOLUTION The fluid mechanics model was solved by using the finite element method, while the enegy equation, which included heat convection and diffusion, was solved by the finite diffeences method. The Hele-Shaw appoximation was used to combine continuity and linea momentum equations into one equation, witten in tems of the divegence of the fluidity times the pessue gadients in two diections, [1]. A volume of fluid method, VOF, was used to pedict the polyme font. Solution pocedue was based on the use of the Moldflow commecial softwae. Discetization fo the feeze doo suppot was accomplished by using thee meshes with 145,898; 179,542 and 286,460 tiangula elements. The time step was equal to 0.01s and equivalent to the time needed to fill 1% of the cavity volume. Convegence citeia wee fo tempeatue and fo velocity and pessue. (4) Thee meshes with 25,454; 33,460 and 50,294 elements wee investigated to pefom the fluid mechanics and heat tansfe calculations duing the injection poduction pocess of the egg cabinet. The iteative pocess ended when a convegence citeia equal to 0.02 was satisfied fo tempeatue and pessue. A time step of s was used (5) (6) to calculate the polyme acceleation and the ate of change of the intenal enegy. Calculations wee pefomed in an Intel Pentium IV pesonal compute with 2.4 GHZ, 1GB of RAM and 20 GB of Had disk. CPU times equied anged fom 63.5 to 74.7 hous. A volume of fluid, VOF, model was used to tack the moving font duing the injection pocess F + Fu = 0 (7) t Heat tansfe duing injection was calculated by solving the enegy equation with tansient, convective, diffusion and viscous dissipation tems, fo the non-newtonian polyme. The values of the themal popeties fo the two types of polymes used in the calculations ae given in Table 1. Table 1: Popeties of Polystol 495F and 143E polymes 4 RESULTS The influence of non-newtonian model fo Polystol 495F polyme, mould tempeatue and wall thickness on the simulation of the injection industial pocess to fabicate a feeze doo suppot is analysed fist. Next, numeical simulations ae used to assess the effect of the location of the injection point on the industial poduction of the Polystol 143E eggs cabinet by injection. 3.1 Feeze doo suppot The geomety of the feeze doo suppot, with details of the two injection channels and the discetization used in the calculation pocedue ae shown in Figue 2. Plastic Density ρ, g/cm 3 Specific heat C p, J/kgºC Conductivity k, W/mºC 286 mm 495F E The values of the constants needed to calculate the dynamic viscosity, fo each one of the polymes, along with the Coss-WLF method wee D 2 = 373.2, D 3 = 0, A 2 = Table 2 gives the values fo the fou emaining paametes. Espeso e 96 mm M S S 50 mm 100 mm D1 D2 3 mm 6 mm Table 2: Paametes to calculate dynamic viscosity A Polyme D 1 A 1 τ * n 495F 1.91 x E 3.01 x B Figue 2: Geomety of feeze doo suppot.

3 The esults fo the instantaneous location of the melt font, at the left hand side and pessue distibution, at the ight hand side, duing the feeze doo suppot injection ae shown in Figue 3. Results, at times equal to 0.379, 0.74, 1.65 and 2.09 s, shown fom top to bottom of figue 3, wee calculated using the mesh with 179,542 elements, that wee within 1% of the injection time obtained with 286,460 elements. Numeical simulations wee accomplished in 63.5 hous, with the coase gid, instead of in 73.2 hous, when the moe efined gid was used. t, s Vista A-A 0,33 0,74 1,14 1,47 1,68 1,93 2,09 Figue 4: Unsteady tempeatue distibution, doo suppot. Numeical simulations wee pefomed using two diffeent models in ode to calculate the fluid stess I tems of the shea ate (ate of defomation) fo the polyme. The diffeence between the unsteady pessue at the injection point, calculated with Coss-WLF and with the Second Ode non Newtonian models, needed to poduce the Polystol 495F feeze doo suppot, is shown in Figue 5. A lowe enegy equiement in the manufactue pocess can be anticipated when the simulation is based on the use of the Second Ode non-newtonian model P, MPa Figue 3: Melt font and pessue fo doo suppot at times: 0.379; 0.74; 1.65; 2.09 s. As a esult of the lack of symmety in the suppot geomety one of the cones of the cavity equied moe time to be filled. A low pessue calculated in the last potion being injected could patially be used as an agument to explain failues obseved in the industial fabication pocess. Tansient evolution of tempeatue distibution in the feeze doo suppot injection pocess pedicted ae shown in Figue 4, at seven time instants, fom 0.33 to 2.09 s. Polyme inlet tempeatue is constant and equal to 210ºC. Duing injection tempeatue is athe unifom until 1.47s. At the end of the injection pocess lowe tempeatues can be noticed at both ends and in the cental egion of the doo suppot. Simulations pefomed with the Coss-WLF non Newtonian model gave 10ºC lowe tempeatues than the values calculated using the second ode non-newtonian mathematical model fo the polyme ,5 1 1,5 2 Figue 5: Unsteady pessue at injection point. t, s Coss - WLF Segundo oden The influence of the mold tempeatue in the clamp foce equied in the injection pocess to fabicate the feeze doo suppot was also investigated. Numeical simulations wee pefomed at thee values of the mold tempeatue: 30ºC, 40ºC and 50ºC. A 10% eduction in the clamp foce can be possible to achieve by inceasing the mold tempeatue fom 30ºC to 50ºC. 3.2 Lateal balcony A top and a side view of the lateal balcony with the cental injection channel ae shown in Figue 6. Holes located in the base ae used to incease the cooling pocess of foods by heat convection in the efigeato and to educe the amount of polyme.

4 Moldflow Plastic Insight has a vey useful tool named gate location that can be used to change the location of the injection point to achieve an impoved injection pocess. Figue 9 depicts the gate location ecommended afte the simulation. Figue 6: Geomety and discetization of lateal balcony The evolution duing the injection time of the polyme font in the cavity and pessue distibutions at thee time instants ae shown in Figue 7. Figue 9: Impoved gate location in balcony Results fo melt font and unsteady pessue distibution obtained afte a new simulation of the injection pocess with the displacement of the gate location suggested by the commecial pogam ae shown in Figue 10. 0,35 (s) 0,7 (s) 1,15(s) 1,5(s) 1,83(s) 2,18(s) Figue 7: Melt font and pessue distibution in balcony. The pesence of holes in a side of the bottom wall of the balcony causes a delay in the injection pocess. The polyme is foced to bifucate in the egion nea the hole and the two steams of polyme being fomed ecombine in one main steam afte each hole. This dynamic fluid mechanics phenomenon is vey impotant fo the balcony quality. Fast polyme flow will cause weld lines at the two steams meeting location and two types of failues can be anticipated. Fist, because the polyme is tanspaent weld lines can be noticed by the naked eye causing a negative visual impact. Second, a low stength of mateial can be calculated in the weld egion and theefoe the balcony will fail when mechanical and themal extenal chages ae applied. 2,63(s) Figue 10: Melt font and pessue in balcony with impoved gate location Validation of the esults obtained fom the simulation was patially accomplished in two ways. Fist, a sequence of poduction pocesses in the industy was pefomed with less than the equied polyme mass. The lack of polyme avoided that the cavity could be filled at the end of the pocess and hence that the pedicted instantaneous

5 location of the melt font could be compaed with the expeimental data. Figue 11 shows a good ageement between expeimental and simulation esults of fou tests pefomed, that ae defined in the poduction pocess by the name of shot shots. Expeimental 1,5(s) 1,9(s) Pedicted Figue 12: Simulated and expeimental balcony weld lines 4 CONCLUSIONS Numeical simulations based on commecial pogams have been pefomed to pedict the injection pocess to fabicate pats fo domestic efigeatos. Fluid mechanics and polyme font movement wee calculated with the finite element method while heat tansfe was evaluated by finite diffeences. As a fist conclusion, the size of the mesh ecommended to descibe the injection of Polyme 495F to fabicate an evapoato doo is 179,542 elements and 33,450 elements to poduce a efigeato balcony by injection of Polystol 143E. Accuate pedictions of size and location of weld lines and of the instantaneous location of the melt font duing polyme injection wee found afte expeiments to fabicate a efigeato cabinet wee pefomed. Optimal design of the injection pocess and of the molding conditions fo poduction of high quality polyme components of efigeatos can be detemined in a cost effective way by using numeical simulations based on finite numeical methods. 2,5(s) 2,63(s) Figue 11: Expeimental and simulated balcony melt font A second patial way to validate the esults fo the injection pocess of the tanspaent Polystol 143E polyme to poduce the lateal balcony was using a Photoelastic polaiscope. Incident light fom the polaiscope on the balcony gave lines of diffeent colos that could be compaed with the pedicted weld lines. Both location and magnitude of weld lines calculated wee simila to the expeimental esults. 5 ACKNOWLEDGMENTS This wok was patially suppoted by CONICYT/Chile though Fondecyt No poject and by CORFO/Chile though Innova No poject. 6 REFERENCES [1] Chiang H.H., Hiebe C., Wang K.K., A Unified Simulation of the Filling and Post Filling Stages in Injection Molding. Pat I: Fomulation, and Pat II: Expeimental Veification, Polyme Eng. Sci., 1991, 21, [2] Bilovol V.V., Kowalski L., Duszczyk J., Numeical Simulation of the Powde Injection Moulding Pocess fo Optimization of Mould Design and Pocess Paametes, Adv. Eng. Mat., 2000, No.2, [3] Dantzig J.A., Tucke III, C.L., Modeling in Mateials Pocessing. Cambidge Univesity Pess, Cambidge, [4] Hwang C.J., Kwon, T.H., A Full 3D Finite Element Analysis of Powde Injection Molding Filling Pocess including Slip Phenomena, Polyme Engineeing and Science, 2002, 42, [5] Kietzmann C.V.L, Van de Walt J.P., Mosi Y.S., A Fee-Font Tacking Algoithm fo a Contol-Volume based Hele-Shaw Method, Intenational Jounal fo Numeical Methods in Eng., 1998, 41, [6] Mok J., Hong C.P., Lee J., Development of a New Simulation Method of Mold Filling and Solidification based on the SIMPLER Algoithm, ISIJ Intenational, 2003, 43, [7] Bilovol V.V., Mould filling simulation duing powde injection moulding, Ph.D. Thesis, Delft Univesity of Technology, Delft, Nethelands, 2003.