- Email: [email protected]
Simulations of gas penetration in thin plates designed with a semicircular gas channel during gas-assisted injection molding
Pergamon
Im J Mech SoL VOI.38, No. 3, pp. 335
34.8,1996 Copyright ~" 1995ElsevierScience Ltd Printed in Great Britain. All rights reserved 0020 7403/96 $15.00+ 0.00
0020-7403(95) 00051-8
S I M U L A T I O N S O F GAS P E N E T R A T I O N IN T H I N P L A T E S D E S I G N E D W I T H A S E M I C I R C U L A R GAS C H A N N E L DURING GAS-ASSISTED INJECTION MOLDING SHIA CHUNG CHEN', NIEN TIEN CHENG and KE SHENG HSU Mechanical Engineering Department, C h u n g Yuan University, Chung-Li, Taiwan 32023, R.O.C. (Received
10 N o r e m b e r 1994: a n d in revised lorm 21 M a r c h 19951
Abstract Numerical simulations and experimental studies concerning gas and melt flows during gas-assisted injection molding of a thin plate designed with a gas channel of semicircular cross section were conducted. Distribution of the skin melt thickness along the gas penetration path was measured. Melt and gas flows in a gas channel of semicircular cross section were approximated by a model which uses a circular pipe of equivalent diameter superimposed on the thin plate. An algorithm based on the control-volume/finite-element method combined with a particle-tracing scheme using a dual-filling-parameter technique was utilized to predict both melt front and gas front advancements during the mold filling process. Simulated distribution of gas penetration shows reasonably good coincidence with the experimental observations
NOTATION B
viscosity constant, Eqn (13)
Bi
b
= Y: - Yk
half gap thickness
Ci
Cr D~k {G} [K] k L n P {P} Q qi R r S T Tb u u v f w g' x y z
~ x k -- x j
specific heat of polymer melt influence coefficient, Eqn (14) column matrix of Eqn (19) coefficient matrix of Eqn 119) thermal conductivity of polymer melt length of runner element viscosity constant, Eqn l l2l pressure column matrix for pressure volumetric flow rate net flow rate of node i, Eqn 1141 radius of runner radial direction of pipe fluidity, Eqn 16) and Eqn II 1I temperature reference temperature, Eqn 113! velocity in x direction average velocity along z direction for u velocity in y direction average velocity along z direction for v velocity in axial direction of runner average velocity along r direction for w planar direction planar direction gapwise direction of cavity or axial direction of runner
Greek symbols
A r/ ~0 ",; p r*
area of a triangular element viscosity viscosity constant, Eqn 1121 shear rate density of polymer melt viscosity constant. Eqn (12)
*Author to whom correspondence should be addressed.
336
.... ~ , ~. :., ,i b ~ : ~ ~ ,;!
Subscripts t
k gas melt
Superscripts / /.
d e s i g n a t i o n c ° local he,de m d c x m a n c i c m e n l designanon, !ocal n o d e m d c ~ m a n e i e m e ~ d e s i g n a t i o n ,.~ ~ocai n o d e :nde* :r! a n c t e m ~ n " d e s i g n a t i o n o~ :,.as-related p a r a m e t e ~ d e s i g n a t i o n ol r",ett-related p e r a m e { e ~
d e s i g n a t i o n o f / t h adoacenl e k : m e ~ d e s i g n a t i o n of / th ciemer~ ~ ",:~R')I}L'¢
FION
In gas-assisted rejection Inoiding, the n'oid cawty is partially filled with polymer melt followed by the injection of inert gas into the core of the polymer melt [1 4]. A schematic of this molding process is illustrated in Fig l This new molding technology, being an innovative injection molding process, can substantially reduce operating expenses through reductions in material cost, clamp tonnage and cycle time for thick parts. In addition, residual stress and warpage within molded parts can be minimized and part quality can be improved. Despite the advantages associated with the process compared with conventional injection molding, molding window and process control become more critical and difficult since additional processing parameters are im, olved. These new gas-related processing parameters include amount of melt injection, gas pressure, delay time of gas injection and gas injection time, etc. During the rejection stage the gas usually takes the path of least flow resistance to catch up with the melt front. In order to guide gas flow to the desired location and/or the designed distribution, part design using thick ribs as gas channels also plays a dominant role in the successful application of the process. In general, due to the complexity' of the gas channel design, process control as well as different flow characteristics between gas and melt, computer sinmlation is expected to become an important tool to assist in both part design and process evaluation in future. For nearly a decade a simulation model based on the Hele-Shaw type of flow has been developed to describe the polymer melt flou in thin cavities during conventional injection moldings. Two typical types of control volume,finite element formulations were employed [5, 6]. These simulatmns provide acceptable predictions from the engineering application point of view. Now. the existing models meet it new challenge and must be adapted to handle both gas and melt flows in cavities of non-uniform thicknesses. Although a complete three-dimensional analysis ma..~ be the final solution, the computational cost is too expensive to be implemented at the present s~age for engineering design purposes. At present the
iiiiiiNiiiii•i•iiii•i•iiii•iiiigN•iiiiiiiiii•iii•ii
Partial Meh
i
Fdlmg
i1
..................................................
i................ ii
C, a s - A s s l s t e d
Filling
.....................................................iii~~iiiil....................................................................
ii~~i~ 2
{{
H{{{~ Gas-Assisted Packing
.%g 1 Schetham_ ,~t the gas~assisted i n j e c t i o n m o l d i n g p r o c e s s .
tJa~,
9t:t~ctratltm
11"1 t h i n
plate
v, I t h g.a~ t. i a a n n e l
337
t/niform Velocity
Material
Frozen Melt
Gas/Mtql Interface
Skin ~,|elt Front
Fig 2. Schematic view of the gas penetration ahmg a gapwlse direction. process requires a numerical scheme which includes a particle-tracing algorithm for the simulation of both gas and melt front advancements. It also requires an appropriate model describing the coating melt thickness existing between the solidified melt and the gas/melt interface (Fig. 2) as a function of processing parameters, material properties and/or flow geometry. For parts laid out with gas channels, which are usually of pipe-like flow leaders, the flow algorithm should also be adjusted to describe these mixed 1-D and 2-D flow characteristics. In the present stud), we first utilized a circular pipe of equivalent diameter and a superposition approach [7] to represent the mixed 1-D and 2-D flow characteristics for the melt and gas flow in the gas channel of a non-circular cross section. Then a numerical algorithm based on the control-volume, finite-element method combined with a particle-tracing scheme using a dual filling parameter technique was developed to simulate both the polymer melt and gas flows during the filling process in the gas-assisted injection molding. This particle-tracing scheme was modified from the algorithm concept successfully applied to the calculation of the skin and core melt front advancements during the coinjection molding process [8]. The present numerical algorithm and the associated simulations were first employed in a gas injection-molded spiral tube which involves a purely one-dimensional flow. The predicted results and the simulation scheme were verified by experiments. Finally. a thin plate part laid out with a gas channel of semicircular cross section was gas-assisted injection molded. The coating melt thickness was investigated and measured along the gas penetration path. The gas penetration length in the primary penetration period which occurs during the gas-assisted melt filling stage was identified. Simulated results for the advancements of both melt and gas fronts during the filling process are illustrated and discussed. The predicted distribution gas penetration is compared with the experimental observation.
It has bccn generally accepted that the Hele Sha~ type of flow model provides a reasonably accurate description on the polymer melt flow m a three-dimensional thin cavity. As a result the relevant governing equations for the inelastic, non-Newtonian fluid flow under non-isothermal conditions are similar to those used in the conventional injection molding [-5, 93: (=
(x-?=~ 8P
~y
? -- (ht~) +
8-, pC~
,
+u-=
('\
-
?'
: c:
(1)
'll ( 'l ii,2: } L
".
,
? =-{b() = 0 ~)'
(3)
+ t ~ , , v , = . = k = ; + ,/;'" /
(2)
('2
(4)
338
Shia Chung Chen
et al.
where P, T, u and v represent pressure, temperature and melt velocities in the x and y directions, respectively. The half thickness of the mold cavity in a gapwise direction, z, is designated by b. Correspondingly, ti and 6 designate gapwise averaged velocities for u and v. In addition, f, r/, p, Cp and k represent shear rate, viscosity, density, specific heat and thermal conductivity, respectively, for the polymer melt. Equations (1) and (2) can be substituted into Eqn (3) and become the form of
ts n_-0
(5)
with S=
fb£ dz.
(6)
3o7 The governing equations for the 1-D melt flow in the delivery system (runner) can also be written in a similar way but in cylindrical coordinate by ~-4n R- @) = 0
(7)
C2
az - rar r ~-&r pC,, 7~ + " az / = L; ~ \
W/J + "~Y)
(8) (9)
where w is the velocity in the axial direction, z and r the radial direction, ff the averaged velocity of w along the radial direction and R the radius of the runner. Equations (7) and (8) can also be formulated into an integrated form described by
af
aP\
(lO)
with S = f0Rr3 ~dr.
(11)
Non-Newtonian characteristics of the polymer melt viscosity is described by a modified Cross model [5] with Arrhenius temperature dependence, that is, r/o(r) q(T, f} - 1 + (rlo~/r*) 1-"
(12)
~toiT) = B exp -~-
(13)
with
where T~, B, rlo, r* and n are constants.
3 NUMERICAL ALGORITHM 3.1. Algorithm lbr melt front advancement during melt injection (A) M elt flow in the conventionally injection-molded thin cavities. For solving the pressure field during the melt injection period, Eqn (5) and Eqn (10) of the elliptic form are discretized using the standard Galerkin finite element method [10]. The control volume formulation can also be employed directly to obtain the same discretized form [5, 9]. The net flow q(/i that enters its control volume centered at node A (Fig. 3) from an adjacent element g can
Gas penetration in thin plaa, with gas channel
Middle Point of Side
339
E l e m e n t Centroid
i
"*~,, ",,
"
' /
/ / Fig. 3. Schematic of a control v o l u m e centered at node A. The control volume is constructed by c o n n e c t i o n s of the centroids of all the adjacent finite elements a r o u n d node A.
be represented by 2
3
or
q'/' = S"'- ~
O(i ', Pi',
(14)
k=l
where i is the local index for node A in element / and i = 1, 2, or 3 for triangular elements and i = 1 or 2 for rod-like elements. Subscript k denotes the local node index in element ( and n(r) is the influence coefficient of the nodal pressure to the net flow in element {. Linear interpolation functions are used for both types of elements. Values of DI~ ) are equal to
D,,l *~
BiBk ± (',C~ =
"-" - - - 4 - N " - ' - - -
t 15)
k=l
and I )
D{ ,k = i - ll'
. ~.
2i~"'
(16)
for the triangular element and the rod-like element, respectively. N'~ is the area of triangular element d, and L (r) is the length of the rod element. B~ - Y2 - )'3 and Cx = x3 - x2, where x and y are planar coordinates of the nodes in the triangular element. The other coefficients are obtained by cyclically permuting the subscripts. At the entrance the net flows from all adjacent elements must satisfy the following relationship:
y .i
1,71
/
where Q is the total volumetric flow rate of the polymer melt. For the interior nodes the net flows from all adjacent elements obey the conservation law of mass and are equal to zero, i.e.
~,q', /,
- -
0.
(J8)
Equations (17) and [18) can be tinally integrated and described by the matrix form
[ K ] 'LP', = ',G',
(19)
where [ K ] is the element coefficient matrix. IP} the column matrix associated with pressure, P, and {G} the column matrix for the variable, G,,. G,. = Q/2 if m, represented in the global node index number, is the entrance node of the polymer melt, Otherwise, G,, = 0. In solving Eqn (19), boundary conditions at the melt front boundary, the cavity side wall and the melt inlet region must also be specified. At the melt-front nodes the nodal pressures
340
Shla C h u n g Chen et al.
are equal to zero (guage pressure), i.e. P = o.
(20)
Along the cavil3, side wall where melt is impermeable, the boundary condition is specified as
?P - - = 0. ?n
(21)
Since in deriving Eqn (18), the melt flow rate across the cavity side wall is assumed to be zero for nodes located on the cavity side, the boundary condition in the form of Eqn (21) is automatically satisfied. Near the melt entrance region boundary conditions are specified according to the operation conditions of the melt and gas injection systems. If the pressure is prescribed, then
t'I~., .....
=
Pinjection
(22)
and P~,j,~,ion is the injection pressure at entrance. If the volumetric flow rate is defined, then the boundary condition is expressed by 'i
- S cZnn d s = 5
where C is any closed contour lying in the melt-filled region and enclosing the melt entrance. In the present study, the melt flow rate, Q, is determined from the filling speed during the melt injection period whereas the gas pressure is defined during the gas injection stage. In the former case gqn {23) is automatically satisfied when applying Eqn (17). To verify the numerical convergence in every step of the analysis, mass conservation at the melt entrance expressed by Eqn (17) is also checked once the pressure and the flow rate q~e) in each sub-element are obtained. When the gas pressure is prescribed during the gas injection period, the flow rate at the materials entrance is treated as unknown and a variable rearrangement in the matrix described by Eqn (19) is required. To distinguish the entrance node and the interior nodes from the melt-front nodes, a filling parameterfme~, is defined and calculated during all analyses. For the entrance node and the interior nodesfme~t is equal to 1, whereas 0
Entrance ;
(a)
Melt f r o n t n o d e O< fmelt< I
Empty node fmelt:O
-a
~:-"
i
' i Entrancel
Melt I n t e r l o r n o d e fmelt= l, fgas =0
~-!~-'s~: ' . . . .
Gas i n t e r i o r
node
fgas =1, fmelt=0
= :-_-_-:-.-_-- -_-_-_t-.-.- .-.-.-
Empty node frnelt:O,f gas =0 ~
'
Gas f r o n t n o d e Melt f r o n t n o d e 0
Fig. 4. (a) Schematic of filling parameters used to identify the location of the melt front during melt injection. (b) Filling parameters used to identity the gas front nodes as well as gas interior nodes in the gas injection stage.
Gas penetration in thin plate ~lth ga~ ~hannel
341
J i,lLli',, ~/Icnl Diz4melcr:
•)
=\ :7 I~- +4l-; + 8 R t
I)eq
I I
Using Circular t ' i p c t)t [{qui,,~tlem Diameter and Shape [:actt]r
-)
" i
::
-
=/l ~ Vl¢ + 2t ...... ;7])uct
Fig. 5. Circular pipe of equal cross section area is used to represent lhe gas channel with a semicircular cross section and the connecting portion of the plate. Form ulations of equivalent diameter as well as the shape factor are also g~ven.
neighboring elements which are filled with melt can be computed• The analysis interval is chosen so that only one melt-front node is filled per step. Once the pressure field is solved, the gapwise velocity profile and the associated shear rate values can be calculated. At the melt fronts a uniform profile for the temperature and the gap-averaged velocity is assumed to account for the fountain flow effect. In solving the temperature field, the same method reported previously [5, 9] is used. The calculation of the nodal temperature is basically weighted from the sub-volumes of all adjacent elements. However, the convection term considers only the contribution of the upstream elements. An implicit method is used for the conduction term, whereas the convection and viscous-heating terms were evaluated at the earlier step. The iteration criteria and algorithm are also similar to those in conventional injection molding [5, 9]. All the detailed numerical formulation and numerical solution have been reported [5, 9, 11]. (B) Melt flow in a flow-leader type gas channel q]non-utrcular uross section. The geometry of the gas channel of a semicircular circular cross section together with the connection portion in the thin part is approximated by a circular pipe of an equivalent diameter Deq. Deq can be computed according to the description in Fig. 5 for a gas channel cross section of semicircular shape. A shape factor is defined and used to correct for the excess heat transfer caused by the extra area in using an equivalent diameter pipe. Once the shape factor value is obtained, it is combined with the thermal conductivit} of the polymer melt to take the excess heat transfer into account. Then the gas channel is modeled as a linear, two-node element which is superimposed on the part shell mesh consisting of triangular elements. The modeling approach is depicted in Fig. 6. During the simulation, a true volumetric flow rate is obtained from the real part volume. In solving the temperature field, the same methods used tk~r the regular, thin part is employed. However, the energy equation in the cylindrical coordinate system is used to calculate the temperature whenever the triangular part element node is superimposed on by the rod-like node representing the gas channel. A verification of the present approach by experiments has been reported for the melt front advancement within a rib-type flow leader of semicircular cross section during a conventional injection molding [7]. 3.2. Algorithm for yas and melt JJ'ont advancements durm,q gas in)ection Once the gas is injected into the mold, either through the runner or any location in the cavity the domain filled with gas is assumed to be of uniform pressure. The pressure at the gas injection node is assumed to be the injected gas pressure and the total flow rate of the melt is treated as unknown. Once the melt flow rate is calculated, the gas front advancement around a gas injection node is determined by the melt flow rate in each sub-element of the control volume around the node. When the gas front advances, it is necessary to introduce the second filling parameter, ./~.... lo identify the gas flt~nt qodes and the gas interior nodes
342
Shia Chung Chen et al. ~
.
.
.
.
.
,
-
beam
element
2-D triangular
element
Fig. 6. A schematic for the superimposition of a triangular shell element mesh and a two-node beam element mesh representing the thin part and the gas channel, respectively.
among the melt interior nodes filled with melt at previous instants, as specified in Fig. 4(b). The algorithm is similar to particle-tracing scheme developed for both skin and melt front advancements in the coinjection molding process reported recently [8]. However, for the gas front nodes whose sub-elements contributed to the corresponding nodal control volume involving both melt-filled elements and gas-filled elements, the mass conservation law must be derived considering the coating melt thickness. In calculating the temperature of the coating melt within the gas-filled region, a transient heat conduction equation discretized by the finite difference method is used. The convection term and the viscous-heating term in the energy equation can be neglected. A convective boundary is assumed at the gas/melt interface using 30 W/m 2 °C for the heat transfer coefficient of gas. Due to the small time interval of the gas injection, heat transfer from the coating melt to the gas is negligible. 4
EXPERIMENTS
A 75-ton Battenfeld 750/750 coinjection molding machine and a Airmold system were used for the present experiments. Melt temperature for PS resin was 230°C and mold temperature was 40°C. A spiral tube part considered as one-dimensional flow was first gas injection molded to provide experimental verification for the present simulation scheme. Then, a thin plate designed with a gas channel of semicircular cross section geometry was also gas injection molded. In all cases coating melt thickness along the gas penetration direction was measured. Primary gas penetration which occurs during the melt filling period was identified. Detailed experimental procedures have been described elsewhere [123. For polystyrene (CHI M E I / P G 3 3 ) the material constants in the modified-Cross viscosity model are n = 0.2838, r * = 1.791E + 04 Pa, B = 2 . 5 9 1 E - 0 7 P a . s and Tb = 11680°K. The density, specific heat and thermal conductivity of PS are 940 kg/m 3, 2100 J/kg" °K and 0.18 W/m- K , respectively. 5. R E S U L T S A N D D I S C U S S I O N
5.1. Case oja straight circular tube [numerical test for convergence) In order to verify the convergence of the present numerical algorithm, a straight circular tube 20 cm long first filled with 70% of a Newtonian fluid under an isothermal condition followed by the injection of gas at 100 bar pressure was assumed for the test. Assuming a 25% coating-melt thickness ratio, the theoretical gas penetration length is expected to be 10.67 cm long under an incompressible assumption for melt. The simulated result is 10.5 cm. Numerical accuracy is within 2%.
Fig. 7 (a) A gas-assisted injection molded spiral tube. Fig. 9. Short-shots (73.7% and 94% strokes) of the injection molded plate showing the melt front advancements during the melt injection period. The final short-shot corresponds to a melt front location immediately in front of the gas injection. Fig 11 Experimental results of the ga~ penetration in the gas-assisted injection molded plate.
Gas penetration in thin plate with gas channel
S a m p l e N~,.
G S~
71a)
Melt T e m p e r a t u r e " ~_30 °C Mold "K'uq~ermur~" 40 ~'C Filling T i m e t F u l l S I l ~ k c }: 1.40 see
343
Gas penetration in thin plate with gas channel
//~
Simulation f),(1) gas 2),(II) gas 3),(Ill) gas
I
(I)
(II)
345 (III)
~/~ RefeTred °rigin ~
Results of Gas and Melt Front Locations: and melt fronts at beginning of gas injection and melt fronts after 0.075 seconds of gas injection and melt fronts after 0.09 seconds of gas injection
Fig. 7(b). Predicted and experimental rcsults of thc gas front locations in a gas-assisted injcction moldcd spiral tube.
~
Unit:
m m
Section A-A
Fig. 8. Mold geometr? tot the thin plate cavity with a gas channel of semicircularcross section. 5.2. Case of the spiral tube [one-dimensional flow) The second test example is a gas-assisted injection molded spiral tube, as shown in Fig. 7(a). The distribution of the coating melt thickness in the molded tube was carefully measured along the gas penetration path 1-12, 13]. The skin-melt thickness ratio measured from the experiments was about 0.36. Using this coating-layed ratio, simulated results for the gas front advancement are shown in Fig. 7(b). Experimental observation of the gas front location is also indicated. The simulated result shows reasonably good consistency with the experimental observation. The result is also consistent with the theoretical value calculated from the injected volume of gas. 5.3. Case of the thin plate with a 9as channel of semicircular cross-section (mixed character-
istics of one-dimensional and two-dimensional flow) The geometry of the mold, which includes a thin plate of 3 mm uniform thickness and a rib-type gas channel of semicircular cross section (of a diameter 6.91 mm), is shown in Fig. 8. This part geometry represents mixed l-D and 2-D flow characteristics for both melt
346
Shla ('hung Chen etal. "'i
~ I
I
i I
I I
l I
....
1 1
1 I
• I
i I
1 1
~ ~
I ,
[ |
I i
Experiment Simulation '[ '
tt
1
I
I
l
I
I
J'
~
I
I
1.05secf#~.31 sec//~j~'~ Fig. 10. Simulated results of the meh front locations during and at the end of the melt-injection process. Observed melt front locations from the experiments are also shown.
o O.SO
k m
0.70 1 0.60
~-----..~....,
0.50 I
0.40 o
0.30
o~ 0.20
Tm=230"C Tw=40*C . . . Fillin i Time(Full St~oke)=l.4 sec Melt I n j e c t i o n S b r o k e = 9 4 9K Gas Pressure= 35 b a r
.~ 0.1o I0
0.00
Sccondar~ Penctnltion
P r i m a r y Gas Pcnctration
"~",
0
f
,
u
,
I
~
T
,
~
~
i
'
I
*
,
U
I
I
,
I
r
I
I
T
I
I
1
I
]
!
I
I
1
150 lflO Position along gas penetration direction(mm) 30
60
90
.
120
Fig. 12. Distribution of the thickness ratio for the hollowed core along the gas channel. The primary gas penetration and the secondar3 gas penetration corresponding to the filling and the post-filling stages, respectively, are identified.
and gas. Short-shot experiments corresponding to a 73.7% and a 94% of the full melt injection stroke are shown in Fig. 9. From these short-shot experiments the final melt front location prior to gas injection can be identified. Based on the formula given in Fig. 5, the calculated equivalent diameter D,q for the semicircular gas channel is 12.18 mm and the value of the shape factor is 0.928. Simulated results of the melt front locations during and at the end of the melt-injection process, corresponding to a 73.7% and a 94% of the full injection stroke, respectively, are shown in Fig. 10. The predicted melt front locations, although slightly behind the observed results, are in fairly good agreement with observed positions. After 94% melt injection ( 1.316 s of melt injection), the gas is injected at a pressure of 140 bar. The gas injection molded plate associated with gas penetration can be seen in Fig. 11. The gas-assisted-injection molded plates were then cut along the gas flow direction and the solidified skin melt thickness was measured with calipers within an accuracy of ___0.05 mm. Distribution of the coating melt thickness ratio along the gas channel is shown
(}as p e n e t r a t i o n in thin plate v
347
Skin p o l y m e r fractioll at T i m e : I ~7 sec
0.88 /'2~/"
0 759
/,
. . . . . . . . . . . . .
H
,-
>4
G a s fiont l o c a t i o n
H
!!o 52
/ Z
/
//
04 Fig. 13(al. S i m u l a t e d result at the g a s f r o n t locatJml after 0.06 s of gas injection.
Skin p o l v n ] e r fiaclion at T i m e
1 4 " ',co
:[:]"1
.q g5:8
075q
0 6z:
(I ':,7: i_l l
Fig. 131bl. Simulated result at the gas penetrauon at the end of the gas-assisted filling process. in Fig. 12. From the area of the cored out section and the total area of the cross section (the area enclosed by the tube with an equivalent diameter, Deq), the estimated ratio for the hollowed core thickness is about 0.60. From the variation profile of the hollowed core thickness ratio, the estimated length for the primary gas penetration is 11,3 cm (within an error range of about 5%), corresponding to the gas front location shown in Fig. 11. The calculated value for the melt shrinkage from the pressure, volume-temperature ( P - V - T ) state equation is 6%, corresponding to a 44 m m length for the secondary gas penetration. The estimated length for the secondary phase of gas penetration is also consistent with that found from the variation profile of the hollowed core thickness ratio in Fig. 12. Details of the identification of the primary and the secondary gas penetration have been reported [12, 13]. Simulated results for both gas and melt front advancements after 0.06 s of gas injection and at the end of the filling stage {0.16 s after gas injection) are shown in Figs 13(a, b), respectively. The simulated gas penetration length in the primary phase is 10.6 cm. Again, the predicted result of the final gas front location is also in good agreement with the observed location.
348
Shia Chung Chen et al. 6 CONCLUSION
A numerical algorithm based on the control-volume/finite-element method combined with a particle tracing scheme was developed to simulate both gas and melt front advancements during a gas-assisted injection molding process. Melt and gas flow in the gas channel of a semicircular cross section were approximated by a flow model which superimposes a circular pipe of equivalent diameter on the thin plate. The simulated melt front locations before the gas injection were in reasonably good consistency with the observed results from short-shot experiments, indicating that the present approach used to approximate the melt front advancement in a semicircular channel cross section is appropriate. Simulation of the primary gas penetration was also conducted employing a dual-filling-parameter technique for tracing the advancements of both melt and gas fronts. The predicted gas penetration length during the primary stage is also in good agreement with the experimental results. The present research results indicate the applicability of the current numerical scheme for the simulation of primary gas penetration in a gas-assisted injection mold filling process. Acknowledgement--This work was supported by the National Science Council under NSC grant 83-0425-E933033R. REFERENCES 1. K. C. Rush, Gas-assisted injection molding--a new technology is commercialized. Plastics Enors 35, July (1989). 2. S. Shah, Gas injection molding: current practices. SPE Tech. Papers 37, 1494 (1991). 3. L. S. Turng, Computer-aided engineering for the gas-assisted injection molding process. SPE Tech. Papers 38, 452 (1992). 4. S. Shah and D. Hlavaty, Gas injection molding: structural application. SPE Tech. Papers 37, 1479 (1991). 5. 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. Engno 7, 21 (1986). 6. A. Davidoff, S. C. Chen and H. Bung, PROCOP: a stress and flow analysis package for injection molding. SPE Tech. Papers 36, 393 (1990). 7. S. C. Chen and K. F. Hsu, Simulation of the melt front advancement in injection molded plate with a rib of semicircular cross section. Numerical Heat Transfer, Part A, 28, 121 (1994). 8. S. C. Chen and K. F. Hsu, Numerical simulation and experimental verification of melt front advancements in coinjection molding process. Accepted by Numerical Heat Transfer (1995). 9. S.C. Chen, P. Pai and C. Hsu, A study of finite element mold filling analysis in application. Annual Tech. Paper SPE 34, 250 (1988). 10. K. H. Huebner and E. A, Thornton, The Finite Element Method for Engineers, Chap. 4 & 5. John Wiley, New York (1982). 11. P. Kennedy, Flow Analysis Reference, Chap. 7, 8 & 9. Moidflow Pry. Ltd., Australia (1993). 12. S. C. Chen, M. C. Jeng, K. S. Hsu and K. F. Hsu, Study of gas-assisted injection molding process and its computer integrated manufacturing technology. Progress Report of NSC (1994). 13. S. C. Chen, K. S. Hsu and J. S. Huang, An experimental study of gas penetration characteristics in a spiral tube during gas-assisted injection molding. Ind. E~gnO Chem. Res. 34, 416 (1995).
Im J Mech SoL VOI.38, No. 3, pp. 335
34.8,1996 Copyright ~" 1995ElsevierScience Ltd Printed in Great Britain. All rights reserved 0020 7403/96 $15.00+ 0.00
0020-7403(95) 00051-8
S I M U L A T I O N S O F GAS P E N E T R A T I O N IN T H I N P L A T E S D E S I G N E D W I T H A S E M I C I R C U L A R GAS C H A N N E L DURING GAS-ASSISTED INJECTION MOLDING SHIA CHUNG CHEN', NIEN TIEN CHENG and KE SHENG HSU Mechanical Engineering Department, C h u n g Yuan University, Chung-Li, Taiwan 32023, R.O.C. (Received
10 N o r e m b e r 1994: a n d in revised lorm 21 M a r c h 19951
Abstract Numerical simulations and experimental studies concerning gas and melt flows during gas-assisted injection molding of a thin plate designed with a gas channel of semicircular cross section were conducted. Distribution of the skin melt thickness along the gas penetration path was measured. Melt and gas flows in a gas channel of semicircular cross section were approximated by a model which uses a circular pipe of equivalent diameter superimposed on the thin plate. An algorithm based on the control-volume/finite-element method combined with a particle-tracing scheme using a dual-filling-parameter technique was utilized to predict both melt front and gas front advancements during the mold filling process. Simulated distribution of gas penetration shows reasonably good coincidence with the experimental observations
NOTATION B
viscosity constant, Eqn (13)
Bi
b
= Y: - Yk
half gap thickness
Ci
Cr D~k {G} [K] k L n P {P} Q qi R r S T Tb u u v f w g' x y z
~ x k -- x j
specific heat of polymer melt influence coefficient, Eqn (14) column matrix of Eqn (19) coefficient matrix of Eqn 119) thermal conductivity of polymer melt length of runner element viscosity constant, Eqn l l2l pressure column matrix for pressure volumetric flow rate net flow rate of node i, Eqn 1141 radius of runner radial direction of pipe fluidity, Eqn 16) and Eqn II 1I temperature reference temperature, Eqn 113! velocity in x direction average velocity along z direction for u velocity in y direction average velocity along z direction for v velocity in axial direction of runner average velocity along r direction for w planar direction planar direction gapwise direction of cavity or axial direction of runner
Greek symbols
A r/ ~0 ",; p r*
area of a triangular element viscosity viscosity constant, Eqn 1121 shear rate density of polymer melt viscosity constant. Eqn (12)
*Author to whom correspondence should be addressed.
336
.... ~ , ~. :., ,i b ~ : ~ ~ ,;!
Subscripts t
k gas melt
Superscripts / /.
d e s i g n a t i o n c ° local he,de m d c x m a n c i c m e n l designanon, !ocal n o d e m d c ~ m a n e i e m e ~ d e s i g n a t i o n ,.~ ~ocai n o d e :nde* :r! a n c t e m ~ n " d e s i g n a t i o n o~ :,.as-related p a r a m e t e ~ d e s i g n a t i o n ol r",ett-related p e r a m e { e ~
d e s i g n a t i o n o f / t h adoacenl e k : m e ~ d e s i g n a t i o n of / th ciemer~ ~ ",:~R')I}L'¢
FION
In gas-assisted rejection Inoiding, the n'oid cawty is partially filled with polymer melt followed by the injection of inert gas into the core of the polymer melt [1 4]. A schematic of this molding process is illustrated in Fig l This new molding technology, being an innovative injection molding process, can substantially reduce operating expenses through reductions in material cost, clamp tonnage and cycle time for thick parts. In addition, residual stress and warpage within molded parts can be minimized and part quality can be improved. Despite the advantages associated with the process compared with conventional injection molding, molding window and process control become more critical and difficult since additional processing parameters are im, olved. These new gas-related processing parameters include amount of melt injection, gas pressure, delay time of gas injection and gas injection time, etc. During the rejection stage the gas usually takes the path of least flow resistance to catch up with the melt front. In order to guide gas flow to the desired location and/or the designed distribution, part design using thick ribs as gas channels also plays a dominant role in the successful application of the process. In general, due to the complexity' of the gas channel design, process control as well as different flow characteristics between gas and melt, computer sinmlation is expected to become an important tool to assist in both part design and process evaluation in future. For nearly a decade a simulation model based on the Hele-Shaw type of flow has been developed to describe the polymer melt flou in thin cavities during conventional injection moldings. Two typical types of control volume,finite element formulations were employed [5, 6]. These simulatmns provide acceptable predictions from the engineering application point of view. Now. the existing models meet it new challenge and must be adapted to handle both gas and melt flows in cavities of non-uniform thicknesses. Although a complete three-dimensional analysis ma..~ be the final solution, the computational cost is too expensive to be implemented at the present s~age for engineering design purposes. At present the
iiiiiiNiiiii•i•iiii•i•iiii•iiiigN•iiiiiiiiii•iii•ii
Partial Meh
i
Fdlmg
i1
..................................................
i................ ii
C, a s - A s s l s t e d
Filling
.....................................................iii~~iiiil....................................................................
ii~~i~ 2
{{
H{{{~ Gas-Assisted Packing
.%g 1 Schetham_ ,~t the gas~assisted i n j e c t i o n m o l d i n g p r o c e s s .
tJa~,
9t:t~ctratltm
11"1 t h i n
plate
v, I t h g.a~ t. i a a n n e l
337
t/niform Velocity
Material
Frozen Melt
Gas/Mtql Interface
Skin ~,|elt Front
Fig 2. Schematic view of the gas penetration ahmg a gapwlse direction. process requires a numerical scheme which includes a particle-tracing algorithm for the simulation of both gas and melt front advancements. It also requires an appropriate model describing the coating melt thickness existing between the solidified melt and the gas/melt interface (Fig. 2) as a function of processing parameters, material properties and/or flow geometry. For parts laid out with gas channels, which are usually of pipe-like flow leaders, the flow algorithm should also be adjusted to describe these mixed 1-D and 2-D flow characteristics. In the present stud), we first utilized a circular pipe of equivalent diameter and a superposition approach [7] to represent the mixed 1-D and 2-D flow characteristics for the melt and gas flow in the gas channel of a non-circular cross section. Then a numerical algorithm based on the control-volume, finite-element method combined with a particle-tracing scheme using a dual filling parameter technique was developed to simulate both the polymer melt and gas flows during the filling process in the gas-assisted injection molding. This particle-tracing scheme was modified from the algorithm concept successfully applied to the calculation of the skin and core melt front advancements during the coinjection molding process [8]. The present numerical algorithm and the associated simulations were first employed in a gas injection-molded spiral tube which involves a purely one-dimensional flow. The predicted results and the simulation scheme were verified by experiments. Finally. a thin plate part laid out with a gas channel of semicircular cross section was gas-assisted injection molded. The coating melt thickness was investigated and measured along the gas penetration path. The gas penetration length in the primary penetration period which occurs during the gas-assisted melt filling stage was identified. Simulated results for the advancements of both melt and gas fronts during the filling process are illustrated and discussed. The predicted distribution gas penetration is compared with the experimental observation.
It has bccn generally accepted that the Hele Sha~ type of flow model provides a reasonably accurate description on the polymer melt flow m a three-dimensional thin cavity. As a result the relevant governing equations for the inelastic, non-Newtonian fluid flow under non-isothermal conditions are similar to those used in the conventional injection molding [-5, 93: (=
(x-?=~ 8P
~y
? -- (ht~) +
8-, pC~
,
+u-=
('\
-
?'
: c:
(1)
'll ( 'l ii,2: } L
".
,
? =-{b() = 0 ~)'
(3)
+ t ~ , , v , = . = k = ; + ,/;'" /
(2)
('2
(4)
338
Shia Chung Chen
et al.
where P, T, u and v represent pressure, temperature and melt velocities in the x and y directions, respectively. The half thickness of the mold cavity in a gapwise direction, z, is designated by b. Correspondingly, ti and 6 designate gapwise averaged velocities for u and v. In addition, f, r/, p, Cp and k represent shear rate, viscosity, density, specific heat and thermal conductivity, respectively, for the polymer melt. Equations (1) and (2) can be substituted into Eqn (3) and become the form of
ts n_-0
(5)
with S=
fb£ dz.
(6)
3o7 The governing equations for the 1-D melt flow in the delivery system (runner) can also be written in a similar way but in cylindrical coordinate by ~-4n R- @) = 0
(7)
C2
az - rar r ~-&r pC,, 7~ + " az / = L; ~ \
W/J + "~Y)
(8) (9)
where w is the velocity in the axial direction, z and r the radial direction, ff the averaged velocity of w along the radial direction and R the radius of the runner. Equations (7) and (8) can also be formulated into an integrated form described by
af
aP\
(lO)
with S = f0Rr3 ~dr.
(11)
Non-Newtonian characteristics of the polymer melt viscosity is described by a modified Cross model [5] with Arrhenius temperature dependence, that is, r/o(r) q(T, f} - 1 + (rlo~/r*) 1-"
(12)
~toiT) = B exp -~-
(13)
with
where T~, B, rlo, r* and n are constants.
3 NUMERICAL ALGORITHM 3.1. Algorithm lbr melt front advancement during melt injection (A) M elt flow in the conventionally injection-molded thin cavities. For solving the pressure field during the melt injection period, Eqn (5) and Eqn (10) of the elliptic form are discretized using the standard Galerkin finite element method [10]. The control volume formulation can also be employed directly to obtain the same discretized form [5, 9]. The net flow q(/i that enters its control volume centered at node A (Fig. 3) from an adjacent element g can
Gas penetration in thin plaa, with gas channel
Middle Point of Side
339
E l e m e n t Centroid
i
"*~,, ",,
"
' /
/ / Fig. 3. Schematic of a control v o l u m e centered at node A. The control volume is constructed by c o n n e c t i o n s of the centroids of all the adjacent finite elements a r o u n d node A.
be represented by 2
3
or
q'/' = S"'- ~
O(i ', Pi',
(14)
k=l
where i is the local index for node A in element / and i = 1, 2, or 3 for triangular elements and i = 1 or 2 for rod-like elements. Subscript k denotes the local node index in element ( and n(r) is the influence coefficient of the nodal pressure to the net flow in element {. Linear interpolation functions are used for both types of elements. Values of DI~ ) are equal to
D,,l *~
BiBk ± (',C~ =
"-" - - - 4 - N " - ' - - -
t 15)
k=l
and I )
D{ ,k = i - ll'
. ~.
2i~"'
(16)
for the triangular element and the rod-like element, respectively. N'~ is the area of triangular element d, and L (r) is the length of the rod element. B~ - Y2 - )'3 and Cx = x3 - x2, where x and y are planar coordinates of the nodes in the triangular element. The other coefficients are obtained by cyclically permuting the subscripts. At the entrance the net flows from all adjacent elements must satisfy the following relationship:
y .i
1,71
/
where Q is the total volumetric flow rate of the polymer melt. For the interior nodes the net flows from all adjacent elements obey the conservation law of mass and are equal to zero, i.e.
~,q', /,
- -
0.
(J8)
Equations (17) and [18) can be tinally integrated and described by the matrix form
[ K ] 'LP', = ',G',
(19)
where [ K ] is the element coefficient matrix. IP} the column matrix associated with pressure, P, and {G} the column matrix for the variable, G,,. G,. = Q/2 if m, represented in the global node index number, is the entrance node of the polymer melt, Otherwise, G,, = 0. In solving Eqn (19), boundary conditions at the melt front boundary, the cavity side wall and the melt inlet region must also be specified. At the melt-front nodes the nodal pressures
340
Shla C h u n g Chen et al.
are equal to zero (guage pressure), i.e. P = o.
(20)
Along the cavil3, side wall where melt is impermeable, the boundary condition is specified as
?P - - = 0. ?n
(21)
Since in deriving Eqn (18), the melt flow rate across the cavity side wall is assumed to be zero for nodes located on the cavity side, the boundary condition in the form of Eqn (21) is automatically satisfied. Near the melt entrance region boundary conditions are specified according to the operation conditions of the melt and gas injection systems. If the pressure is prescribed, then
t'I~., .....
=
Pinjection
(22)
and P~,j,~,ion is the injection pressure at entrance. If the volumetric flow rate is defined, then the boundary condition is expressed by 'i
- S cZnn d s = 5
where C is any closed contour lying in the melt-filled region and enclosing the melt entrance. In the present study, the melt flow rate, Q, is determined from the filling speed during the melt injection period whereas the gas pressure is defined during the gas injection stage. In the former case gqn {23) is automatically satisfied when applying Eqn (17). To verify the numerical convergence in every step of the analysis, mass conservation at the melt entrance expressed by Eqn (17) is also checked once the pressure and the flow rate q~e) in each sub-element are obtained. When the gas pressure is prescribed during the gas injection period, the flow rate at the materials entrance is treated as unknown and a variable rearrangement in the matrix described by Eqn (19) is required. To distinguish the entrance node and the interior nodes from the melt-front nodes, a filling parameterfme~, is defined and calculated during all analyses. For the entrance node and the interior nodesfme~t is equal to 1, whereas 0
Entrance ;
(a)
Melt f r o n t n o d e O< fmelt< I
Empty node fmelt:O
-a
~:-"
i
' i Entrancel
Melt I n t e r l o r n o d e fmelt= l, fgas =0
~-!~-'s~: ' . . . .
Gas i n t e r i o r
node
fgas =1, fmelt=0
= :-_-_-:-.-_-- -_-_-_t-.-.- .-.-.-
Empty node frnelt:O,f gas =0 ~
'
Gas f r o n t n o d e Melt f r o n t n o d e 0
Fig. 4. (a) Schematic of filling parameters used to identify the location of the melt front during melt injection. (b) Filling parameters used to identity the gas front nodes as well as gas interior nodes in the gas injection stage.
Gas penetration in thin plate ~lth ga~ ~hannel
341
J i,lLli',, ~/Icnl Diz4melcr:
•)
=\ :7 I~- +4l-; + 8 R t
I)eq
I I
Using Circular t ' i p c t)t [{qui,,~tlem Diameter and Shape [:actt]r
-)
" i
::
-
=/l ~ Vl¢ + 2t ...... ;7])uct
Fig. 5. Circular pipe of equal cross section area is used to represent lhe gas channel with a semicircular cross section and the connecting portion of the plate. Form ulations of equivalent diameter as well as the shape factor are also g~ven.
neighboring elements which are filled with melt can be computed• The analysis interval is chosen so that only one melt-front node is filled per step. Once the pressure field is solved, the gapwise velocity profile and the associated shear rate values can be calculated. At the melt fronts a uniform profile for the temperature and the gap-averaged velocity is assumed to account for the fountain flow effect. In solving the temperature field, the same method reported previously [5, 9] is used. The calculation of the nodal temperature is basically weighted from the sub-volumes of all adjacent elements. However, the convection term considers only the contribution of the upstream elements. An implicit method is used for the conduction term, whereas the convection and viscous-heating terms were evaluated at the earlier step. The iteration criteria and algorithm are also similar to those in conventional injection molding [5, 9]. All the detailed numerical formulation and numerical solution have been reported [5, 9, 11]. (B) Melt flow in a flow-leader type gas channel q]non-utrcular uross section. The geometry of the gas channel of a semicircular circular cross section together with the connection portion in the thin part is approximated by a circular pipe of an equivalent diameter Deq. Deq can be computed according to the description in Fig. 5 for a gas channel cross section of semicircular shape. A shape factor is defined and used to correct for the excess heat transfer caused by the extra area in using an equivalent diameter pipe. Once the shape factor value is obtained, it is combined with the thermal conductivit} of the polymer melt to take the excess heat transfer into account. Then the gas channel is modeled as a linear, two-node element which is superimposed on the part shell mesh consisting of triangular elements. The modeling approach is depicted in Fig. 6. During the simulation, a true volumetric flow rate is obtained from the real part volume. In solving the temperature field, the same methods used tk~r the regular, thin part is employed. However, the energy equation in the cylindrical coordinate system is used to calculate the temperature whenever the triangular part element node is superimposed on by the rod-like node representing the gas channel. A verification of the present approach by experiments has been reported for the melt front advancement within a rib-type flow leader of semicircular cross section during a conventional injection molding [7]. 3.2. Algorithm for yas and melt JJ'ont advancements durm,q gas in)ection Once the gas is injected into the mold, either through the runner or any location in the cavity the domain filled with gas is assumed to be of uniform pressure. The pressure at the gas injection node is assumed to be the injected gas pressure and the total flow rate of the melt is treated as unknown. Once the melt flow rate is calculated, the gas front advancement around a gas injection node is determined by the melt flow rate in each sub-element of the control volume around the node. When the gas front advances, it is necessary to introduce the second filling parameter, ./~.... lo identify the gas flt~nt qodes and the gas interior nodes
342
Shia Chung Chen et al. ~
.
.
.
.
.
,
-
beam
element
2-D triangular
element
Fig. 6. A schematic for the superimposition of a triangular shell element mesh and a two-node beam element mesh representing the thin part and the gas channel, respectively.
among the melt interior nodes filled with melt at previous instants, as specified in Fig. 4(b). The algorithm is similar to particle-tracing scheme developed for both skin and melt front advancements in the coinjection molding process reported recently [8]. However, for the gas front nodes whose sub-elements contributed to the corresponding nodal control volume involving both melt-filled elements and gas-filled elements, the mass conservation law must be derived considering the coating melt thickness. In calculating the temperature of the coating melt within the gas-filled region, a transient heat conduction equation discretized by the finite difference method is used. The convection term and the viscous-heating term in the energy equation can be neglected. A convective boundary is assumed at the gas/melt interface using 30 W/m 2 °C for the heat transfer coefficient of gas. Due to the small time interval of the gas injection, heat transfer from the coating melt to the gas is negligible. 4
EXPERIMENTS
A 75-ton Battenfeld 750/750 coinjection molding machine and a Airmold system were used for the present experiments. Melt temperature for PS resin was 230°C and mold temperature was 40°C. A spiral tube part considered as one-dimensional flow was first gas injection molded to provide experimental verification for the present simulation scheme. Then, a thin plate designed with a gas channel of semicircular cross section geometry was also gas injection molded. In all cases coating melt thickness along the gas penetration direction was measured. Primary gas penetration which occurs during the melt filling period was identified. Detailed experimental procedures have been described elsewhere [123. For polystyrene (CHI M E I / P G 3 3 ) the material constants in the modified-Cross viscosity model are n = 0.2838, r * = 1.791E + 04 Pa, B = 2 . 5 9 1 E - 0 7 P a . s and Tb = 11680°K. The density, specific heat and thermal conductivity of PS are 940 kg/m 3, 2100 J/kg" °K and 0.18 W/m- K , respectively. 5. R E S U L T S A N D D I S C U S S I O N
5.1. Case oja straight circular tube [numerical test for convergence) In order to verify the convergence of the present numerical algorithm, a straight circular tube 20 cm long first filled with 70% of a Newtonian fluid under an isothermal condition followed by the injection of gas at 100 bar pressure was assumed for the test. Assuming a 25% coating-melt thickness ratio, the theoretical gas penetration length is expected to be 10.67 cm long under an incompressible assumption for melt. The simulated result is 10.5 cm. Numerical accuracy is within 2%.
Fig. 7 (a) A gas-assisted injection molded spiral tube. Fig. 9. Short-shots (73.7% and 94% strokes) of the injection molded plate showing the melt front advancements during the melt injection period. The final short-shot corresponds to a melt front location immediately in front of the gas injection. Fig 11 Experimental results of the ga~ penetration in the gas-assisted injection molded plate.
Gas penetration in thin plate with gas channel
S a m p l e N~,.
G S~
71a)
Melt T e m p e r a t u r e " ~_30 °C Mold "K'uq~ermur~" 40 ~'C Filling T i m e t F u l l S I l ~ k c }: 1.40 see
343
Gas penetration in thin plate with gas channel
//~
Simulation f),(1) gas 2),(II) gas 3),(Ill) gas
I
(I)
(II)
345 (III)
~/~ RefeTred °rigin ~
Results of Gas and Melt Front Locations: and melt fronts at beginning of gas injection and melt fronts after 0.075 seconds of gas injection and melt fronts after 0.09 seconds of gas injection
Fig. 7(b). Predicted and experimental rcsults of thc gas front locations in a gas-assisted injcction moldcd spiral tube.
~
Unit:
m m
Section A-A
Fig. 8. Mold geometr? tot the thin plate cavity with a gas channel of semicircularcross section. 5.2. Case of the spiral tube [one-dimensional flow) The second test example is a gas-assisted injection molded spiral tube, as shown in Fig. 7(a). The distribution of the coating melt thickness in the molded tube was carefully measured along the gas penetration path 1-12, 13]. The skin-melt thickness ratio measured from the experiments was about 0.36. Using this coating-layed ratio, simulated results for the gas front advancement are shown in Fig. 7(b). Experimental observation of the gas front location is also indicated. The simulated result shows reasonably good consistency with the experimental observation. The result is also consistent with the theoretical value calculated from the injected volume of gas. 5.3. Case of the thin plate with a 9as channel of semicircular cross-section (mixed character-
istics of one-dimensional and two-dimensional flow) The geometry of the mold, which includes a thin plate of 3 mm uniform thickness and a rib-type gas channel of semicircular cross section (of a diameter 6.91 mm), is shown in Fig. 8. This part geometry represents mixed l-D and 2-D flow characteristics for both melt
346
Shla ('hung Chen etal. "'i
~ I
I
i I
I I
l I
....
1 1
1 I
• I
i I
1 1
~ ~
I ,
[ |
I i
Experiment Simulation '[ '
tt
1
I
I
l
I
I
J'
~
I
I
1.05secf#~.31 sec//~j~'~ Fig. 10. Simulated results of the meh front locations during and at the end of the melt-injection process. Observed melt front locations from the experiments are also shown.
o O.SO
k m
0.70 1 0.60
~-----..~....,
0.50 I
0.40 o
0.30
o~ 0.20
Tm=230"C Tw=40*C . . . Fillin i Time(Full St~oke)=l.4 sec Melt I n j e c t i o n S b r o k e = 9 4 9K Gas Pressure= 35 b a r
.~ 0.1o I0
0.00
Sccondar~ Penctnltion
P r i m a r y Gas Pcnctration
"~",
0
f
,
u
,
I
~
T
,
~
~
i
'
I
*
,
U
I
I
,
I
r
I
I
T
I
I
1
I
]
!
I
I
1
150 lflO Position along gas penetration direction(mm) 30
60
90
.
120
Fig. 12. Distribution of the thickness ratio for the hollowed core along the gas channel. The primary gas penetration and the secondar3 gas penetration corresponding to the filling and the post-filling stages, respectively, are identified.
and gas. Short-shot experiments corresponding to a 73.7% and a 94% of the full melt injection stroke are shown in Fig. 9. From these short-shot experiments the final melt front location prior to gas injection can be identified. Based on the formula given in Fig. 5, the calculated equivalent diameter D,q for the semicircular gas channel is 12.18 mm and the value of the shape factor is 0.928. Simulated results of the melt front locations during and at the end of the melt-injection process, corresponding to a 73.7% and a 94% of the full injection stroke, respectively, are shown in Fig. 10. The predicted melt front locations, although slightly behind the observed results, are in fairly good agreement with observed positions. After 94% melt injection ( 1.316 s of melt injection), the gas is injected at a pressure of 140 bar. The gas injection molded plate associated with gas penetration can be seen in Fig. 11. The gas-assisted-injection molded plates were then cut along the gas flow direction and the solidified skin melt thickness was measured with calipers within an accuracy of ___0.05 mm. Distribution of the coating melt thickness ratio along the gas channel is shown
(}as p e n e t r a t i o n in thin plate v
347
Skin p o l y m e r fractioll at T i m e : I ~7 sec
0.88 /'2~/"
0 759
/,
. . . . . . . . . . . . .
H
,-
>4
G a s fiont l o c a t i o n
H
!!o 52
/ Z
/
//
04 Fig. 13(al. S i m u l a t e d result at the g a s f r o n t locatJml after 0.06 s of gas injection.
Skin p o l v n ] e r fiaclion at T i m e
1 4 " ',co
:[:]"1
.q g5:8
075q
0 6z:
(I ':,7: i_l l
Fig. 131bl. Simulated result at the gas penetrauon at the end of the gas-assisted filling process. in Fig. 12. From the area of the cored out section and the total area of the cross section (the area enclosed by the tube with an equivalent diameter, Deq), the estimated ratio for the hollowed core thickness is about 0.60. From the variation profile of the hollowed core thickness ratio, the estimated length for the primary gas penetration is 11,3 cm (within an error range of about 5%), corresponding to the gas front location shown in Fig. 11. The calculated value for the melt shrinkage from the pressure, volume-temperature ( P - V - T ) state equation is 6%, corresponding to a 44 m m length for the secondary gas penetration. The estimated length for the secondary phase of gas penetration is also consistent with that found from the variation profile of the hollowed core thickness ratio in Fig. 12. Details of the identification of the primary and the secondary gas penetration have been reported [12, 13]. Simulated results for both gas and melt front advancements after 0.06 s of gas injection and at the end of the filling stage {0.16 s after gas injection) are shown in Figs 13(a, b), respectively. The simulated gas penetration length in the primary phase is 10.6 cm. Again, the predicted result of the final gas front location is also in good agreement with the observed location.
348
Shia Chung Chen et al. 6 CONCLUSION
A numerical algorithm based on the control-volume/finite-element method combined with a particle tracing scheme was developed to simulate both gas and melt front advancements during a gas-assisted injection molding process. Melt and gas flow in the gas channel of a semicircular cross section were approximated by a flow model which superimposes a circular pipe of equivalent diameter on the thin plate. The simulated melt front locations before the gas injection were in reasonably good consistency with the observed results from short-shot experiments, indicating that the present approach used to approximate the melt front advancement in a semicircular channel cross section is appropriate. Simulation of the primary gas penetration was also conducted employing a dual-filling-parameter technique for tracing the advancements of both melt and gas fronts. The predicted gas penetration length during the primary stage is also in good agreement with the experimental results. The present research results indicate the applicability of the current numerical scheme for the simulation of primary gas penetration in a gas-assisted injection mold filling process. Acknowledgement--This work was supported by the National Science Council under NSC grant 83-0425-E933033R. REFERENCES 1. K. C. Rush, Gas-assisted injection molding--a new technology is commercialized. Plastics Enors 35, July (1989). 2. S. Shah, Gas injection molding: current practices. SPE Tech. Papers 37, 1494 (1991). 3. L. S. Turng, Computer-aided engineering for the gas-assisted injection molding process. SPE Tech. Papers 38, 452 (1992). 4. S. Shah and D. Hlavaty, Gas injection molding: structural application. SPE Tech. Papers 37, 1479 (1991). 5. 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. Engno 7, 21 (1986). 6. A. Davidoff, S. C. Chen and H. Bung, PROCOP: a stress and flow analysis package for injection molding. SPE Tech. Papers 36, 393 (1990). 7. S. C. Chen and K. F. Hsu, Simulation of the melt front advancement in injection molded plate with a rib of semicircular cross section. Numerical Heat Transfer, Part A, 28, 121 (1994). 8. S. C. Chen and K. F. Hsu, Numerical simulation and experimental verification of melt front advancements in coinjection molding process. Accepted by Numerical Heat Transfer (1995). 9. S.C. Chen, P. Pai and C. Hsu, A study of finite element mold filling analysis in application. Annual Tech. Paper SPE 34, 250 (1988). 10. K. H. Huebner and E. A, Thornton, The Finite Element Method for Engineers, Chap. 4 & 5. John Wiley, New York (1982). 11. P. Kennedy, Flow Analysis Reference, Chap. 7, 8 & 9. Moidflow Pry. Ltd., Australia (1993). 12. S. C. Chen, M. C. Jeng, K. S. Hsu and K. F. Hsu, Study of gas-assisted injection molding process and its computer integrated manufacturing technology. Progress Report of NSC (1994). 13. S. C. Chen, K. S. Hsu and J. S. Huang, An experimental study of gas penetration characteristics in a spiral tube during gas-assisted injection molding. Ind. E~gnO Chem. Res. 34, 416 (1995).