The study on polymer melt front, gas front and solid layer in filling stage of gas-assisted injection molding

ht. Comm.HeatMassTramfe~Vol. 28, No. 1, pp. 139-148, 2001

Copyright 8 2001 Elsevier Science Ltd Printed in the USA. All rights reserved 07351933/01/$-see front matter

Pergamon

PII: SO7351933(01)00221-4

THE STUDY ON POLYMER MELT FRONT, GAS FRONT AND SOLID LAYER IN FILLING STAGE OF GAS-ASSISTED INJECTION MOLDING

Y.K. Shen LungHwa Institute of Technology Department of Mechanical Engineering 300 Wanshou RD., Secl Kueishan, Taoyuan County Taiwan, ROC 333

(Communicated

by J.P. Hartnett and W.J. Minkowycz)

ABSTRACT The algorithms are developed to predict the polymer melt front, gas front and solid layer in gas-assisted injection molding. The simulation of two-dimensional, transient, non-isothermal and high viscous flow between two parallel plates with the generalized Newtonian fluid is presented in detail. During solidification while an injection mold tills, a solid-liquid interface moves and a two-phase zone exists; an enthalpy model is used to predict this interface in the two-phase flow problem. The model takes into account the three-phase flow including the effects of the gas front, solid layer and polymer melt front. Q 2001 Elsevier Science Ltd

Introduction Gas-assisted injection molding is an innovative process of multi-component injection molding recently developed. In this process, polymer melt is first injected to partially fill the mold cavity. Gas is then introduced through the runner or the cavity to assist filling of the polymer melt. Gas-assisted injection molding has increasingly become an important process in industry, due to its flexibility in the design and manufacture of plastics parts. Gas-assisted injection molding can produce parts incorporating both thick and thin sections with less residual stress and warpage, and a better surface finish. It requires a 139

:

Vol. 28, No. 1

Y.K. Shen

140

lower clamping force than the conventional injection molding process. Chcn [l-3] developed and discussed the primary and secondary gas penetration, skin melt thickness in gas-assisted

injection

gas-assisted

molding.

[4-51 compared

the interface

shape

for Co-injection

and

injection molding. Tumg [6-71 studied the automotive hood panel and indicated the design

guid-line in gas-assisted implement

Lanvers

injection molding. Khayat [8] used Eulerian boundary

the three dimensional

simulation of the primary gas penetration

element approach to

stage of the gas-assisted

injection molding process. In this paper, finite element method is used to solve the gas front, gas-liquid interface (solid layer) and polymer melt front for gas-assisted injection molding.

Mathematical Modeling The governing

equations to simulate of the non-isothermal,

generalized

Newtonian

fluid in x-z

plane are the equations of conservation of mass, of momentum and of energy.

au&v

-+-_=o

ax

(1)

a2

au

au

au

P(dr+Yax+W-)=--+-+_ a2

aw

aw

ap

&

32

aH

aH

at

ax

c3H

ax

az

as,

as,

ax

(2)

(3)

ax

a2H a2H au -+-)+5,(-_)+r,(-_)+r,(-+-_) 2

a2

as,

as,

ax

aw

P(-g+u,+w-)=--+-+-

-+?A-+w--=a(

ap

ax

a2

ax

aw

auaw

a2

a2 ax

(4)

Vol. 28, No. 1

i

GAS-ASSISTED

-

k,+k,

-

a=-,k=-

.p=

ps+pl -,c

2

@P

INJECTION MOLDING

141

cps+cp~

=

2

p

(5)

2

H is the enthalpy function. For the Stefan Problem the enthalpy is defined as (Fig. 1) PI-

H = pscps CT- Tref I+ d [vs-

-

T(%lp 1$,&r

+ T < T,

4 -

a{

o1

aT

(6)

j[v -T(-_)pI$>fir+T~Tm

H=P~c~~(T~-T~~~)+P,~+P~~~~(T-T,)+

(7)

volume

v=-

(8)

mole

The final terms in above equations are pressure correction terms, which are important for the large pressures at the packing stage in gas-assisted

injection molding; however

they are insignificant

and

negligible during the tilling stage of gas-assisted injection molding. For a generalized Newtonian fluid the viscosity

7 depends on the shear rate (p ) and temperature

(‘0. rl

=

jj

.

e-W-W

, p 111-l

(9)

(10) The boundary conditions are as following (Fig.2): 1). On DE

u(x,+h) = 0,w(x,+h) = 0,H(x,fh)

= H,

(11)

2). On AF W(X,O) = O,$+,O) 3). On EF

= 0

(12)

Y.K. Shen

142

Vol. 28, No. 1

(13) 4). On AD (14) (15) 5). At the gas-liquid interface (On BC)

(P-P,)=~,,

8s

(16)

ai?

6). For polymer, On AD u = --&(S)[l-

(f,“f,

(17)

For gas, On AC u =

(18)

Him,et = Hin

(19)

FIG. 1 The enthalpy function.

GAS-ASSISTED

Vol. 28, No. 1

143

INJECTION MOLDING

Calculation Domain ;$................. .............................-.-...** E ..a. %_

FIG. 2 The calculation domain.

Numerical Methods The model has a) four independent variables: two velocities, one pressure and one enthalpy b) one dependent variable: viscosity. In this paper, the author used Galerkin method to derive the finite element equation for the governing ehuations. The continuous problem becomes the following set of first order differential equations: Forflowjield

(20)

bw~~ + [~Ivo = IFI

Where M

U and 0

represent the acceleration and the velocity of finite element nodes. The matrix

is the mass matrix. K is the diffision

matrix and

parts: the viscosity term and the pen&y term.

F

is the force vector.

K

is composed of two

Vol. 28. No. 1

Y.K. Shen

144

For thermalfield

(21)

Where

MH

I?

and H

represent the rate of enthalpy and enthalpy of finite element nodes. The matrix

is the mass matrix for enthalpy.

KH

is the diffusion matrix for enthalpy and

FH

is the force

vector for dissipation. The viscosity of melting polymer is highly temperature dependent, the flow and heat transport equations are strongly coupled. The solution procedure follows the repeated sequence of a) solving the flow field with given enthalpy H and b) solving the thermal field with solved velocity u and w [9]. In the numerical simulation, the process conditions are shown in Table 1 and the HDPE properties are shown in Table 2.

TABLE 1 Process Conditions.

Tmoldwoll Tr?I H.In H

moldwall

Volume flow rate

303OK 385.5” K 455.884

J /g

23.53 J / g 2ocm

3 / s

Vol. 28, No. 1

GAS-ASSISTED

INJECTION MOLDING

145

TABLE 2 HDPE Properties.

Parameter

Value

/J

cPl

3.04

cPs

1.09 /J

g°K g°K

2.7. 1O-3 /.Jcm

rOK

4.8. 1O-3 /.Jcm

s,,K

0.84 /g

3 Cm

0.9 /g

3 cm

282OOPa.s" 399.5K 0.2781 O.O24K-1 135.3 J

/ g

I

I

Numerical Results and Discussion Fig.3 show the various position of gas-liquid interface * polymer melt front and solid layer profile in filling stage of gas-assisted

injection molding.

The results indicate the distance between

gas-liquid

interface and polymer melt front is more closer is gas-assisted injection mold filling. The coating layer is defined as the layer between the gas bubble and mold wall. From Fig.3, the coating layer is 0.29 in this

146

Y.K. Shen

Vol. 28, No. I

study case.

Fig.4 show the various position of gas front 8 polymer melt front and solid layer in filling stage of gas-assisted injection molding. It shows the gas front is an exponent function vs. time scale. The result shows the gas front accelerates in the filling stage. It also shows polymer melt front and solid layer is a linear function vs. time scale. The result shows the velocity of the polymer melt front and solid layer is constant in the filling process.

Conclusions A comprehensive mathematical model for the non-isothermal filling of parallel plates cavity has been developed in gas-assisted injection molding. Numerical results in this paper indicate the gas-liquid interface accelerates on gas-assisted injection mold tilling. The Hele-Shaw model for the commercial software has been developed to simulate the gas-assisted injection molding. This model traces the polymer melt front very well. This model can’t trace the gas-liquid well because it lacks of the transient term in the momentum equation, In this paper, the author introduced the numerical results to the reference on the gas-assisted injection molding.

GAS-ASSISTED

Vol. 28, No. 1

INJECTION MOLDING

FIG. 3 The gas front, polymer melt front and solid layer profile during the filling process in gas-assisted injection molding. (The filling time is 0.375s, 0.436s and 0.441s.)

-

.I

4-

I-

I

PolYmer lrod Goi lmnt

--C-

Solld layer

3-

2-

l-

0

0.1

0.2 0.3 Time (Se)

0.4

5

FIG. 4 The gas front, polymer melt front and solid layer position during the filling process in gas-assisted injection molding. (The filling time is 0.375s, 0.436s and 0.441s.)

147

Vol. 28, No. 1

Y.K. Shen

148

Acknowledement The author thanks the National Science Council of the Republic of China (contract No.NSC-88-2216-E-158-001)

for support.

References 1. S.C.Chen,N.T.ChengandK.S.Hsu,Intem.Comm.HeatandMassTrans.,22,319(1995). 2. S.C.Chen, K.F.Hsu and K.S.Hsu, J. Applied Polym. Sci., 58,793 (1995). 3. S.C.Che.n and N.T.Cheng, Intern. Conun. Heat and Mass Trans., 23,215 (1996). 4. A.Lanvers and W.Michaeli,ANTEC,

1796 (1992).

5. A.Lanvers, Eng. Plastics, 17,223 (1994). 6. L.S.Tumg, ANTEC, 452 (1992). 7. L.S.Tumg,Adv.

Polym. Tech., 14, 1 (1995).

8. R.E.Khayat, A.Derdouri and L.P.Hebett, J. Non-Newtonian

Fluid Mech., 57,253 (1995).

9. Y.K.Shen, Intern. Comm. Heat and Mass Trans., 24,295 (1997).

Received November 21. 2000