Evaluation of gas pressure dynamics for gas-assisted injection molding process

Pergamon

Int. Comm. Heat Mass Transfer, Vol. 26, No. 1, pp. 85-93, 1999 Copyright © 1999 Elsevier Science Ltd Printed in the USA. All fights reserved 0735-1933/99/S-see front matter

PII S0735-1933(98)00124-9

EVALUATION OF GAS PRESSURE DYNAMICS FOR GAS-ASSISTED INJECTION MOLDING PROCESS

Sher-Meng Chao, Shih-Ming Wang and Shia-Chung Chen* Mechanical Engineering Department Chung Yuan University Chung-Li, Taiwan 32023, R.O.C. Furong Gao Chemical Engineering Department Hong Kong University of Science & Technology Kowloon, Hong Kong

(Communicated by J.P. Hartnett and W.J. Minkowycz) ABSTRACT This study presents the development of gas pressure dynamic model that may be useful for the study and design of gas-assisted injection units. The model was derived theoretically and its dynamic characteristics on injected gas pressure variation was verified via experimental measurements using a laboratory injection unit operated under a microprocessor-based control system. The agreement between the simulations and the measured results indicates that the present dynamic model predicts the gas pressure dynamic behaviors of the system adequately. The present model is not only useful for process parameters investigation but also practical for the control system design of gas injection unit. © 1999 Elsevier Science Ltd

Introduction Gas-assisted injection molding (GAIM) process, being an innovative injection molding process, has recently become a popular technology in the thermoplastic injection molding industry. Previous studies [1-5] have shown that the conventional injection molding could achieve some advantages by corporation with gas-assisted injection during the process. These advantages include: (1) molding of larger and thinner parts with projected areas or cross-sectional geometry is permitted; (2) creating hollowed voids the gas to reduce part weight, hence saving thermoplastic materials, reducing cycle time and lowering production cost; (3) reducing clamping tonnage because of the significant reduction in injection pressure; (4) minimizing warpage and sink marks and improving part 85

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dimension's accuracy and surface finishes and (5) producing parts of higher stiffness-to-weight ratio, etc.. Although gas-assisted injection molding could provide the mentioned advantages, it also introduces additional processing parameters in the process and makes the application much more critical.

tim Melt

Filling

(70-98%)

...... Assisted

(c}

Filling

u a~-Assisted P a c k i n g

FIG. J. Schematic of Gas-assisted injection molding process

Basically, gas-assisted injection molding process consists of three major phases: first to partially fill the mold cavity with polymer melt; then to inject inert gas to assist melt filling, and finally to pack melt with the gas. Schematic of GA1M is illustrated in Fig. 1. Compared with conventional injection molding, volume of the polymer melt, starting time of gas injection, speed and/or pressure of injected gas are new gas-related processing parameters. To significantly improve the injection process, it requires the accurate monitoring and control of the process parameters. Among the mentioned process parameters, the gas injection pressure shows strong effect on gas bubble formation and packing degree that affects final product characteristics. Thus the development of an accurate dynamic model that can describe the gas pressure during the process becomes an important issue at the initial design stage. Theoretically, the dynamic model can be derived through the fundamental laws and equations governing the flow of gas. Unfortunately, since the gas dynamics during the manufacturing process is quite complicated, non-equilibrium and highly nonlinear. It is difficult to be solved analytically. In this paper, some assumptions were made to simplify the model derivation and numerical solutions were conducted to evaluate the model by comparing the experimental results.

Dynamic modeling

For the sake of simplicity meanwhile without losing the generality, this paper assumes that the gas used in deriving the mathematical model of the system behaves as ideal gas. The working temperature of the gas is constant everywhere under processing and heat transfer to the environment

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GAS PRESSURE DYNAMICS FOR MOLDING PROCESS

is negligible. In addition, assumption is made that the inertia of the gas is negligible under unidirection flow. The used gas injection unit is basically a pressure regulation system as shown in Fig. 2. Relevant process variables on the system were also defined there. Since the tank volume is much larger than the volume of the charging chamber, the pilot inlet pressure, Pi=7.679 bars, and the supply pressure, Ps =300 bars, are considered as constants. Let Vt be the volume of the pipe connecting the nozzle and the pressure regulator valve.

ir

Computer exhaust valve

inlet valve Pilot pressure inlet Pi Actuator ~aphragmHigh pressure nitrogen tank -] Pressure regulator

Sensor l I

v

I i~l--'--'-]

I

J _ ~ l R e g u l a t o r sensor

Manual shut-off valve cavity

Vent Sensor 2

FIG. 2 Schematic of gas pressure regulation and injection.

If the nozzle is blocked, Vt can be considered as a fixed volume chamber. The pilot valve contains two normally closed solenoid valves that are used to adjust the control pressure, Pa, of the actuator diaphragm. This simple on/off type of control simulates the action of a true proportional valve. When there is no feedback signal to the pilot valve, the control pressure, Pa, will increase until it reaches the maximum limit, 6.891 bars and can be described by the following equation:

d/'a

- ick ~

(1)

dt

where ic is command current to the pilot valve and kl, proportional gain of pilot valve. The difference in area between the actuator diaphragm and the regulator sensor determines the ratio of the regulate pressure, Pt, and the control pressure, P,. The force balance equation of the pressure regulator can be

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written as follow:

d2x , dx P~a1 = Pla2 + m v ~ - + 0.. -dt + k,.,x

(2)

where a~ is the area of the actuator diaphragm, a2, area of the regulator sensor, my, total mass of the spool and associate moving parts, by, damping coefficient of the spool and associate moving parts, kv, spring gradient and x, spool travel. Let the linearized flow equation of the pressure regulator valve is

W = xKq

(3)

where W is gas weight flow rate through the pressure regulator valve orifice and Kq, constant depend on the valve opening x, the gas supply pressure, and the valve geometry. To determine pressure in a closed chamber subjected to a given weight flow rate, the following dynamic equation is considered.

W = kRTdTt rl

(4)

where k is the ratio of specific heat of the perfect gas, R, the gas constant, T, the gas temperature and g, the acceleration of gravity. Then equations (2), (3) and (4) can be solved simultaneously to obtain input-output relationship between P, and P,. +

alP, = a2P,

g~

(

d3

k~T~q lng ~

d2

d/

+ b,. ~l 2 + k~ 7

P'

(5)

Since the values of kv is relative larger than my and b,., the first and second terms in the parenthesis in the right hand side of equation (5) can be neglected. Thus the input-output dynamic equation of Pa and Pt can be approximated by:

p.k, = r dP' .

, ~-t

+ P,,

(6)

where k2=aJa2 is the area ratio and xt=gVtk,./(kRTkqa2), time constant of pressure regulator valve. To correct the linearized assumption of pressure-flow characteristic of the pressure regulator valve, the following equations can be further considered when investigating the gas flow characteristics. 1

Ps ( 2 )k-S1 [ 2k W=CdAg~(~) ~ k +1 f

Ve-

VPsJ

if Pt / Ps <0.528

(7)

k +1//k

"~

V sJ

"

where Cd is the discharge coefficient of the orifice and, A, effective orifice area of regulator valve. Because the orifice size of the pressure regulator valve is not available, the effective area of the orifice can be approximately calculated from Cv, coefficient of the pressure regulator valve. C,.

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GAS PRESSURE DYNAMICS FOR MOLDING PROCESS

(slpm/bar) is the flow coefficient indicating the flow capacity of a flat edge orifice under wide open conditions at specific inlet, outlet pressure and temperature. It was developed to size the liquid control valves and has been adapted to gas flow use. The converting equation can be written as:

Os = c ~x g ~I ~ ( P s~ + P~b~)

(9)

where Qs is the gas flow in liters/sec at 1 bar, 20 °C. Kg iS the units converting factor, 114.5, AP, the pressure drop between inlet and outlet pressure, G, specific gravity of gas, 1 for air. And Pabs is atmospheric (absolute) pressure. Rewrite equation (7) and (8) in the form of volumetric flow.

Qs=ll.34CdAPs~T 3

tf

0o)

Pt/Ps < 0.528

//'-,143 / pt/1.71 =43.8642C~AP~ 2 ~ 7 3 / / ~ - /

-

ifPt/P s >

0.528

(11)

The maximum orifice area of the regulator valve then can be calculated from equations (9) and (11) given that Ps = 689.1 bars and AP=275.64 bars. Fig. 3 shows a block diagram represents the nonlinear model of the gas injection system under the blocked nozzle situation that just derived.

Input

I ~'s

B=kRT/g ]

~

~ [ - - - - ]

]lT~J dt ~"~[Pt ]

i

cl = 0 " 6 8 5 C d A g / ~ c 2 = 2.646C d Ag / ~

f ( u ) = 4u IA3 - u

1"71

where u = Pt//~ps

FIG. 3 Simplified non-linear model )'or gas injection dynamics. It is noted that the orifice area given by equations (9) and (11) is the maximum opening that the gas can flow through. Since the actual orifice opening is dependent on spool travel x and control pressure Pa. TO correct this deviation, the following equation that represents the orifice opening change

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dynamic was proposed.

The corresponding constants Ta, at different input currents were estimated based upon the weight flow equation given Pt solved by equation (4). Simulations were carried out by computer program written in Simulink, a toolbox of Matlab. The results are shown in Fig. 4.

;>

3ool

,00t

200

7~ ¢r

7;m

14.4

0 0

0.2

0.4

0.6

0.8

1

1.2

114

1.6

1.4

1,6

00 2mA

0.04

r-" ©

0.02

~

0o, 0

0

0.2

0.4

~

0.6 0.8 1 TIME - s e c o n d s

7.2 mA

1.2

1

FIG. 4

Non-linear model simulation of gas injection dynamics.

Regulator p output

r

e

~ @ L ~

8~[~ Cavity pressure

Clock

FIG. 5 Simplified non-linear model for gas dynamics within the mold cavity. The charging dynamic behavior of the mold cavity is then easy to described. Using the same

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GAS PRESSURE DYNAMICS FOR MOLDING PROCESS

augments, the block diagram for the non-linear model of the charging dynamic for the mold cavity is shown in Fig. 5. The orifice diameter of the gas inlet is 0.3048 mm (0.012 in) and the volume of the mold cavity is 65.548

cm 3

(4in 3 ). Simulations were also conducted by computer program written in

Simulink.

Experiments Several tests have been conducted in order to verify the validity of the theoretical model. Note that the regulator valve starts to open at 4 mA, and fully open at 20 mA. The corresponding pressure can be calculated by (input current - 4 ) x 6.25 x 100 × 0.06891 bar. Open-loop step tests of input currents 7.2 mA and 14.4 mA were performed. The pressure responses measured from pressure sensor 1 are used for the purpose of model verification for the gas injection pressure. The pressure responses recorded by pressure sensor 2 are then used to investigate the gas pressure in the mold cavity. These analog signals were sampled at interval 0.055 seconds with 16-bit analog-digital converters, converted to floating point format, and stored

Results and discussion Fig. 6 presents the model simulated results with different control input currents and experimental results of gas injection pressure, respectively. As we can see from the test results, the model shows reasonable predictions. A better correlation between the model and experimental data can be obtained by developing detail component's dynamic model and knowing all the necessary parameter's values in the models.

350 300

~

~

~

.z,

250 200 150 i

100 50

/z~ ~

* ~

y 0

~"

' 0.2

i 04

input 14.4 mA non-linear model prediction i 0.6

i 0.8

i 1

TIME - seconds FIG. 6 Open-loop step response of gas injection pressure.

1.2

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To investigate the pressure responses in the mold cavity, simulations were conducted and comparing to the test data taken from the last test. Fig. 7 shows the predictions match the actual pressure dynamic responses in the mold cavity. It is found that increases the speed of gas injection before the nozzle has little affect to the settling time of cavity pressure for both cases. This is because the gas flows at its maximum rate almost all the time during gas injection, as shown in Fig. 8. However, a slightly increase in pressurized speed for the cavity is expected when charging gas flow faster in the beginning.

350

,I

fo

~

250

'10oi

g

j

0

/

j7

35° I

l,

t

]

: ; actual test data

- ~lp~ion

2

4

6

8

10

5°oy-

,

,,

0

2

4

lnput,current = 14"4mA

FIG. 7 Step response of gas pressure in the mold.

10 -3 5

14.4 mA

g3 ~2

g, 0 4 TIME

6 - seconds

6

11rv~- seconds

11ME-seconds

- - 1 0

FIG. 8 Predicted weight flow rate in the mold cavity.

8

l0

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GAS PRESSURE DYNAMICS FOR MOLDING PROCESS

93

Conclusions

In this study, a non-linear dynamic model of gas injection system was developed for a gasassisted injection unit. The dynamic model can fairly predicts the gas pressure variation performances as verified by experiments. The slight disagreements between the simulations and the experimental results are caused by the errors of model parameters that are calculated based on insufficient information. Due to the assumption of constant gas volume and neglecting the dynamics of the melting polymer in the cavity, the predicted errors are expected but acceptable for practical application. To correct these errors, further study is required to investigate the gas pressure-volume correlation and the pressure relationship between the injected gas and the polymer melt. In general, a complete and reasonable modeling process has been successfully proposed and has shown very useful in practical implementations.

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2.

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7.

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8.

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9.

L. Lj ung, System Identification Toolbox - User's Guide, The mathworks Inc. (1991). Received June 10, 1998