Simulation and verification of the secondary gas penetration in a gas-assisted-injection molded spiral tube

Pergamon

International Communications in Heat and Mass Transfer, Vol. 22, No. 3, pp. 319-3280 1995 Copyright © 1995 Elsevier Science Ltd Printed in the USA. All rights reserved 0735-1933/95 $9.50 + .00

0735-1933(95)00023-2

S I M U L A T I O N AND V E R I F I C A T I O N OF T H E S E C O N D A R Y GAS P E N E T R A T I O N IN A G A S - A S S I S T E D - I N J E C T I O N M O L D E D S P I R A L T U B E S. C. Chen, N T. Cheng and K. S. Hsu Mechanical Engineering Department Chung Yuan University, Chung-Li 32023, Taiwan, R.O.C.

(Communicated by J.P. Hartnett and W.J. Minkowycz) ABSTRACT This paper presents both experimental investigation and numerical simulation on the characteristics of the secondary gas penetration in a spiral tube during the gasassisted injection molding. The primary and the secondary gas penetration phases, corresponding to the filling and the post-filling stages of the molding process, respectively, were identified from the skin thickness distribution along the gas penetration path. Numerical scheme based a dual-filling-parameter technique is first used to simulate the gas front advancement in the primary gas penetration period. Simulation for the secondary gas penetration is developed assuming an isotropic melt-shrinkage model combined with the control-volume/FEM employed on a gapwise layer basis. Simulated result shows good coincidence with the experimental observation.

Introduction In the gas-assisted injection molding process the mold is first partially filled with polymer melt followed by the injection of the inert gas through nozzle or any designed locations in the mold cavity [1-2]. In the primary gas penetration period the injected gas hollows out the melt core and pushes the melt to complete the cavity filling. During the post-filling stage the gas continues to penetrate as a result of melt shrinkage and exerts uniform pressure on the molded part until the part is sufficiently solidified and ejected. A schematic of the gas penetration is shown in FIG. 1. This new molding technology can substantially reduce operating expenses through reduction in material cost, reduction in clamp tonnage and reduction in cycle time for thick parts. In additions, part qualities can also be greatly improved by reduction in residual stress, warpage, sink marks and shrinkage. Although the gas-assisted injection provides many advantages, it also introduces new processing parameters in the process and makes the 319

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application of this new technology more critical. One of the key factors that determines the successful application of this new process is the design of gas channels which guide the gas flow to the desired locations. In addition to the design parameters introduced by gas channels, other processing parameters such as the numbers as well as the locations of gas injection points, the amount of polymer melt injection, delay time, injected gas pressure and holding time for gas injection, etc., are also important in obtaining good injection-molded parts. Due to the complexity of the gas channel design, the processing control, as well as the different flow characteristics between the gas and the melt, a design/molding guideline, particularly using CAE simulation software, is expected to become an important and a required tool to assist in part design, mold design and process evaluation in the coming age.

P r i m a r y Gaa P e n e t r a t i o n

S e c o n d a r y Gas Penetration

/

tSolidified Me~t During Filling Stage

Melt Solidifica/tion During P o g t - F i l l i n g Stage

FIG. 1 Schematic of gas penetration during gas-assisted i~ection molding process.

For nearly a decade a simulation model based on the Hele-Shaw type of flow has been developed to describe polymer melt flow in the thin cavities. These simulations provide acceptable predictions for the melt flow in thin cavities from the engineering application prospective. Now, the existing models meet the new challenge and must be adapted to handle both gas and melt flows in the thin part laid out with gas channels. This requires a numerical scheme which includes a particle-tracing algorithm for the advancements of both melt and gas fronts. An appropriate model suitable for the gas and melt flow within the thick ribs used as gas channels [3] must also be established. Although studies on the numerical simulations are now in progress [4-6], attentions have been focused only on the gas and the melt front advancements during the primary gas penetration period. Significant gas penetration occurs during the postmold-filling stage as result of melt shrinkage. Characteristics of gas penetration in the primary phase and in the secondary phase are quite different, resulting in a different distribution profile in the skin melt thickness formation. A special algorithm is also required for the simulation of the secondary gas penetration. In additional to the requirement of all these numerical algorithms,

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it is of equal importance to establish a general model or empirical formula describing the thickness variation of the coating melt existing between the gas/melt interface and the solidified melt near the cavity wall (FIG. 1) as a function of processing parameters, melt properties and/or flow geometry. The correlation of the coating melt thickness to all contributing parameters by a mathematical model is quite a complicated issue. A recent experimental results showing the effects of melt temperature, mold temperature, gas delay time as well as gas pressure on the coating melt thickness were reported [6-7]. Identification of the primary and the secondary gas penetration can also be achieved from analyzing the distribution profile of the coating melt thickness and the unfilled volume of the cavity prior to gas injection. Details have been described elsewhere [7]. In the present research, spiral tubes of a uniform diameter were gas-assisted-injection molded. Then the primary and the secondary gas penetration phases were identified. Gas penetration length in the primary phase was simulated using a dual-fillingparameter scheme capable of tracing the advancements of both gas and melt fronts. Simulation for the secondary gas penetration is developed assuming an isotropic melt-shrinkage model combined with the control-volume/FEM employed on each gapwise layer. Both simulation results on the primary and the secondary gas penetration were compared with the experimental observations.

Modeling and Formulation The relevant governing equations for the inelastic, non-Newtonian melt flow under nonisothermal conditions in a tube of circular cross section are based on the Hele-Shaw flow model and can be written in cylindrical coordinate by 0p ~ z ( p W ) = 0 Ot

(1)

S) P -]l ~r[ or ( r l z~

(2)

0T ~T 10 0T ~w 2 pCp(-~-t + w - ~ z- ) = [ r ~ r (rk --~-r)J + rl(~rr)

(3)

where P and T represent pressure and temperature, w is the velocity in the axial direction, z, r is the radial direction. In addition, 1"1, p, Cp and k represent viscosity, density, specific heat and thermal conductivity for the polymer melt, respectively. Viscosity of the polymer melt is described by a modified-Cross model with Arrhenius temperature dependence, that is, rl(T'4/) =

rl0(T) . , 1-n 1 + (rlo~'/'c)

and

ri0(T) = B exp ( T b )

(4a,b)

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During the post-filling process, gas continues to penetrate as a result of melt shrinkage. Calculation of melt shrinkage is based on the P-V-T equation of state proposed by Tait [8] in the form of Vo(T ) - V ( T , P ) : C gn ( l + ~ P )

Vo(T)

(5)

B(T)

where B(T) = b 1 exp(-b2T), Vo(T) = Vg + b3(T-Tg), C = .0894 (universal constant), V and Tg are specific volume and glass transition temperature of the polymer melt, respectively. Eq. (1) and Eq. (2) can be integrated into a form described by G P T oP + ~ S oP ( , ) ~ - ~zz( - ~ z ) = F ( P T )

and

S=J0

p

r dr

R r3 2--~dr

(6,7)

where G(P,T) =

C

(8)

[B(T) + P][1- Cfn(1 + B--~)] l and

FP'T!t-Cb2Pp b3 I_Cgn[I+B~]

V0(T) ~ 0 t

Details was reported previously [9]. During melt filling stage, polymer melt is assumed to be incompressible, As a result, F and G are equal to zero.

Numerical Algorithm (1) Algorithm for the Advancements of Melt Front and Gas Front During the Filling Stage For solving the pressure field during melt injection, the control-volume/finite-element approach used for conventional injection molding by Wang, et. al. [10] and Chen, et al. [11] is employed directly. In order to trace the melt front advancement, a filling parameter, fmelt, is introduced to distinguish the entrance node and the interior nodes from the melt-front nodes. For the entrance node and interior nodes fmelt is equal to 1, whereas 0 < fmelt < 1 for melt-front nodes. When fmelt is 0, the node is designated as an empty node. Once the pressure field is solved, radial velocity profile and the associated shear rate values can be calculated. At the melt fronts, a uniform profile for temperature and radial-averaged velocity is assumed to count for the fountain flow effect. In solving for temperature field, the same method reported previously is used [ I0-11 ]. Once the gas was injected into mold, domain filled with gas is assumed to be of uniform pressure. Pressure at the gas front is assumed to be the injected gas pressure and the

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total flow rate of the melt is treated as unknown. Once the melt flow rare is solved, gas flow rate and the associated gas front advancement are determined and the filling parameter is updated. To calculate the gas front advancement, it is necessary to introduce the second filling parameter, ~as, to identify gas front nodes and gas interior nodes in each analysis interval. The algorithm is similar to our particle-tracing algorithm developed for the skin and core melt front advancements in coinjection molding reported recently [ 12]. Schematic of the dual-filling-parameter technique for node identification is depicted in F I G . 2.

Melt I n t e r i o r N o d e f melt = 0

Melt F r o n t N o d e 0
E m p t y Node f melt = 0

Melt :::::::::5:::::5::: ::::::::::::::':::::::5::::::::::: ::::::::::::::::::::::::':::::::::

(a) Melt F i l l i n g S t a g e Melt I n t e r i o r

Node

Melt F r o n t Node E m p t y N o d e 0 < f m e l t <1 fmelt =0

::::.:.:: :.:.:-:i.: ? :-:.:. : :.:-.::.:.:. .::.:.:7:.7:.:.:-::::::.::::::::::::::::::::::::::::::::::::7:::::::i:::::::::::::::::::::::::::::::::::: :::::::::::::::::::::: i

|

.................................................... , ::.:.:-:):........ i)i:i:i)i:i:i),)i)i)i)i:i:i /.-. , . . I . . , .....f ,...-~:,<:+:~ t :::::::::::::::::::::::::: . . . . . . ¢:-:.:-:-:.:.:-i:.:+:.: ...... :7/

t

Gas Interior Node

f g a s =1 f m e l t =0

Gas Front Node

Melt Interior Node

0
~,

fmelt=l f g a s =0

(b) Gas I n j e c t i o n

Stage

FIG. 2 (a) Melt filling parameter defined tor the node identification during melt injection period.(b) Gas filling parameter defined for the node identification during gas injection period.

(1) Algorithm for the Advancements of Gas Front During the Post-Filling Stage To. solve the pressure and the temperature field during this period. The mathematical model and numerical scheme used for the post-filling simulation in the conventional injection molding were implemented. Gas-filled domain is assumed to be of uniform pressure. Gas is assumed to penetrate toward the melt-filled-only region. An isotropic shrinkage model, which allows to melt to shrink along both the axial and the radial directions, is assumed. To trace the gas front advancement, the gas filling parameter, fgas, is now extended to each gapwise layer on the same control-volume/finite-element basis. A schematic is depicted in F I G . 3. During each analysis step, the available volume in each gapwise layer resulting from melt shrinkage is calculated from the temperature and the pressure values using P-V-T relationship described by Eq. (5). Along the radial direction, ten gapwise layers were implemented. The analysis continues until the gas is released and the part is ejected.

Experiments and Simulations

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A 75-ton Battenfeld 750/750 coinjection molding machine and an airmold system were used for the present experiments. Melt temperatures for PS resin were 230 °C. Mold temperature was 60°C. One of the molded spiral tubes of 6 mm diameter was shown in F I G . 4. Gas was injected after 82% of full injection shot (corresponding to a filling time of 0.45 seconds) at a pressure of 100 bar. Distribution of the coating melt layer thickness is investigated. For polystyrene (CHI MEI/PG33), the material constants in the modified-Cross viscosity model are n = 0.2838, "~* = 1.791E+04 Pa, B = 2.591E-07 Pa.s and Tb = 11680°K. Density, specific heat and thermal conductivity of PS are 940 Kg/m 3, 2100 J/Kg.°K and 0.18 W/m.°K, respectively. Constants in Tait P-V-T equation can be found elsewhere [8]. Mold

Wall

i

Skin Melt Thickness .l/

(;as Front at t,,+l

J

Gas Front at tn

f k k,

AV

,

i

_

. . . . . . .

i

tR i

Element l

AL FIG. 3 Schematic of the isotropic melt-shrinkage model used to simulate the secondary gas penetration. Results

and

Discussions

It has been found that the skin melt thickness is relatively uniform behind the gas front. The measured coating melt thickness ratio in the primary gas penetration period was about 0.36, as shown in F I G . 5. Using this measured ratio the gas front advancement at different stages of primary gas penetration period were simulated. The secondary gas penetration during postfilling phase was also simulated using the pressure, the radial temperature profile and the P-V-T equation of state. Simulated distribution of the skin melt thickness ahead of the primary gas front location is shown in F I G . 6. Experimental observation of the gas front location (27 cm) at the end of filling process is indicated in F I G . 7. Simulated result of the primary gas

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penetration length (27.2 cm) shows reasonably good consistency with experimental observation. The final gas front located at a distance of 36.5 cm away from the referred origin. The simulated gas penetration length for the secondary phase is 10.1 cm corresponding to a final gas front location at a 37.3 cm away from the referred origin. The consistency between the predicted value and the experimental result is also very good. This indicates that the present numerical algorithm provides a good methodology for the simulation of the gas penetration during gas-assisted injection molding in a one-dimensional flow geometry. Moreover, the concept of the algorithm can be extended and applied to the three-dimensional thin part laid out with gas channels [6]. However, processing effects on the coating layer ratio are remained to be investigated from variety of experiments such that coating melt thickness does not have to be known as apriori during simulation. Conclusions

Both experimental investigation and numerical simulation on the characteristics of the secondary gas penetration in a spiral tube during the gas-assisted injection molding were implemented. The primary and the secondary gas penetration phases, corresponding to the filling and the post-filling stages of the molding process were identified from the skin thickness distribution along the gas penetration path. A numerical algorithm based on the controlvolume/finite-element method combined with a dual-filling-parameter particle-tracing scheme developed previously was used to simulate the advancements of both gas and melt front in the primary stage of gas-assisted injection molding. Simulation for the secondary penetration is developed assuming an isotropic melt shrinkage model combined with the control-volume/FEM employed on a gapwise layer basis. Simulated results on both the primary gas penetration length and the secondary gas penetration show good coincidence with experimental observations. Nomenclature

B

viscosity constant, Eq. (4b)

b

temperature-dependent coefficient, Eq. (5)

Cp

specific heat of polymer melt

k

thermal conductivity of polymer melt

n

viscosity constant, Eq. (4a)

P

pressure

R

radius of tube

r

radial direction of tube

T Tb

temperature reference temperature, Eq. (4b)

326

V

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specific volume of polymer melt

Vo

specific volume of polymer melt at one atmosphere pressure

w

velocity in axial direction of tube

z

axial direction of tube

rI rl0

viscosity viscosity constant, Eq. (4a)

~'

shear rate, Eq. (4a)

p

density of polymer melt

"1:*

viscosity constant, Eq. (4b) References

1. K. C. Rush, "Gas-assisted Injection Molding - A New Technology is Commercialized", Plastics Engineers, July, 35 (1989). 2. S. Shah, "Gas Injection Molding: Current Practices", SPE Tech. Paper, 37, 1494 (1991). 3. S. C. Chen and K. F. Hsu, "Simulation of the Melt Front Advancement in Injection Molded Plate with A Rib of Semicircular Cross section", Submitted for publication. 4. A. Lanvers and W. Michaeli, "CAE for Co-Injection and Gas-Assisted Injection Molding", SPE Tech. Papers, 38, 1796 (1992). 5. L. S. Turng, "Computer-Aided-Engineering for the Gas-Assisted Injection Molding Process", SPE Tech. Papers, 38,452 (1992). 6. S. C. Chen, K. S. Hsu and M. C. Jeng, "A Study of the Gas-Assisted Injection Molding Process and Its Computer Integrated Design and Manufacturing Technology", Progress Rept. of NSC, (1994). 7. S. C. Chen, K. S. Hsu and J. S. Huang, "An experimental Study on Gas Penetration Characteristics in A Spiral Tube During Gas-Assisted Injection Molding", accepted by Industrial & Eng. Chem. Res. (1994). 8. Wang, V. W., and Hieber, C. A., "Post-Filling Simulation of Injection Molding and Its Application", SPE Tech. Paper, 34,290 (1988). 9. S. C. Chen and N. T. Cheng, "Simulation of Post-Filling Process Considering the Cooling Effect of Mold Cooling System", Int. Comm. Heat & Mass Trans, 18,833 (1991). 10. V. W. Wang, C. A. Hieber and K. K.Wang, "Dynamic Simulation and Graphics for the Injection Molding of Three-Dimensional Thin Parts", J. Polym. Eng., 7, 21 (1986). 11. S. C. Chen, P. Pai, and C. Hsu, "Study of Finite Element Mold Filling .Analysis in Application", SPE Tech. paper, 34, 250 (1988). 12. S, C. Chen and K. F. Hsu, "Numerical Simulation and Experimental Verification of Melt Front Advancements in Coinjection Molding Process ", submitted for published (1994).

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GAS-ASSISTED-INJECTION MOLDED SPIRAL TUBE

FIG. 4 A gas-assisted injection molded spiral tube.

.2 o.ao Tw=60"C Tm=230°C Pg=lOObar . . . . . delay t i m e =0.0 8ec

h

~

°~

>'

0.60

0 Ca

I 0.40

£

Secondary penetratior ( 7.92% | - Shrinkag~

0.20 0

<

Primary penetration

spiral t u b e of 6ram d i a m e t e r 0.00

,

0

i

,

J i

i

l

i

r i

,

I00

i

i

,

4 ,

i

i

i

r i

200

i

,

i

i

i

,

i

r

i

l

300

i

i

r i T'I

Fp']

]Vl"1

400

P o s i t i o n along gas p e n e r a t i o n d i r e c t i o n ( r a m ) FIG. S Distribution of the skin-melt thickness ratio along the gas penetration path.

327

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S.C. Chen, N.T. Cheng and K.S. Hsu

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Primary Penetration

(Gas Seconda~'Penetr2~n)-~>

i0 1 cm

Tw=60°C .

Tm=230°C

m c~

~

P~=1oMp~

~

Delay tirne=O.Osec

2,0

[..-,

~

1.0 ~

1

a

s / M e l t I n t e r f a c e Location

4 ~/Gas

~-"

0,0

i

0.0

i

i

:

i

fornt ~ I

i

~

-

I

2.0

location ~ I

E E ~11

I I

at the I

I

I

'

~

4.0

Penetration

6.0

e n d of f i l l i n g s t a g e I

I I I

I I

I

I

I

~ b IT~--~l

8.0

[

L

lO.O

D i s t a n c e (ern)

FIG. 6 Simulated result on the skin melt thickness distribution along the gas penetration path during secondary, penetration period.

hserved Gas Front {36.5em) of secondary penetration) Cend

(a)

i) I 10bserved Gas Front (27cmJ_~xL \\ (end of primary \%"J-

I1 ] I

Simulation Results of Gas and Melt Front Locations: 1),(I) gas and melt fronts at the h e ~ g of gas injection 2),[If) gas and melt fronts after 0.075 seconds of gas injection ~).(~) ~a. ~ d melt ~ront~ after 0.09 ....~d. of gas i~je~Uo~ gas f r o n t at t.he eRd of the secondary penetration 4)

FIG. 7 Comparison of the simulated and experimental results of the gas front locations during primary, and secondary gas penetration. Received November 15, 1994