Melt temperature profile prediction for thermoplastic injection molding

Melt Temperature Profile Prediction for Thermoplastic Injection Molding

CHUNHUA ZHAO and FURONG GAO*

Department of Chemical Engineering The Hong Kong University of Science & Technology

Clear Water Bay, Kowloon Hong Kong

A computer system is developed to quantitatively reveal how the melt temperature is affected by the operating conditions during the plastication, dwell and injection stages of the injection molding process. The variables considered in this study are rotation speed, back pressure, barrel heater temperatures, nozzle heater temperature, dwell time and injection velocity profile. A set of Artificial Neural Networks (ANN] has been developed to predict the effect of the operating conditions on the melt temperature during plastication. The dwell period is treated as a heat conduction problem. A free boundary model for the injection phase is developed to simulate the temperature development and melt flow due to the forward motivation of the screw. The overall prediction of nozzle melt temperature is in good agreement with Ihe experimental measurement, validating the proposed procedure combining ANNs and mathematical modeling. This work enhances the understanding of the process and provides a basis for future work on the optimization and advanced control of the process.

1. INTRODUCTION conditions. Efforts have been made to measure and

t is well recognized that melt temperature in injec- I tion molding has a decisive effect on the quality of the molded part and that melt temperature has a strong influence on important process variables such as the melt flow rate, the melt pressure at the nozzle and in the cavity, and the cooling time (1).

Given melt temperature and melt rate (or pressure) at the gate, the material status and even certain mor- phologies can be fairly well predicted by a CAD/CAE software for simulating the melt flow inside the mold. Temperature measurement at the gate is therefore an ideal process variable before the melt enters a mold cavity. However, it is difficult and uneconomical to in- stall a temperature transducer at the cavity gate for each mold. Alternatively, melt temperature measured at the nozzle exit can be a good approximation of the cavity gate temperature as all the melt has the same flow path from the nozzle exit to the gate.

Contraq to the common assumption in industry, the melt temperature at the nozzle exit is significantly different from the barrel (or nozzle) heater temperature settings. This difference is determined by the material properties, machine variables and operating

T o whom correspondence should be addressed

control of the melt temperature within the injection barrel. For example, a speedy designed thermocouple was used by Amano and Utsugi (24) to measure the polymer melt temperature in the barrel and to study its qualitative relation to some major operating conditions such as cycle time, screw revolution, barrel temperature, back pressure, and shot volume. The influence of the screw geometry was also briefly dis- cussed. A special ring-bar device was developed by Peischl and Bruker (5) to measure the melt temperature distribution in the radial direction within the barrel at a fixed barrel position, as a representation of the melt homogeneity. This measurement, however, is highly susceptible to the shearing effect. Recently, Dontula et aL (6) used an infra-red temperature transducer at the nozzle to measure the melt temperature and found that screw rotation speed and back pressure have a significant effect on the melt temperature. Different control algorithms, including conventional PID, multivariable self-tuning, f k z y logic and expert system, have been used to control the temperature of the barrel heaters to control the melt temperature in- directly (7, 8). Chandra (9) installed a thermocouple at the screw tip to measure the melt temperature and developed a PID control algorithm to control this measured melt temperature. Kamal et al. (10, l l) investi-

POLYMER ENGINEERING AND SCIENCE, SEPTEMBER 1999, Vol. 39, No. 9 1787

Fig. 1 . Melt temperature p r o m measwed at nozzle versus injection stroke.

LL"

gated the melt and barrel temperature dynamics and evaluated several alternative melt temperature control strategies, using a similar installation. In addition to these experimental approaches to melt temperature measurement and control, mathematical models have also been developed to predict the temperature distribution within the space bounded by the barrel and screw by assuming that injection plastication is a steady-state process like extrusion (12-14). Donovan et aL (15-17). Lipschitz et aL (18), Nunn and Fenner (19). and Wey (20) conducted comprehensive experimental and theoretical modeling of the reciprocating plastication phase. However, to the authors' knowledge, a systematic approach to model the melt temperature transient behavior at the nozzle during a complete molding cycle including plastication, dwell, and injection phases is yet to be developed.

In industry, the operators set the barrel heater temperatures, screw rotation speed and back pressure from experience and trial-and-error. There is no systematic understanding of the relationship between the

' operating conditions and the melt temperature. This study attempts to develop a quantitative relationship between the nozzle exit melt temperature and the operating conditions. The objectives of this study are thus 1) to investigate the melt temperature at the nozzle exit systematically and 2) to develop a quantitative system to correlate the melt temperature with process conditions.

I

2. IMPLEMENTATION RATIONALE

A nozzle melt temperature is shown to vary with the injection stroke (or time) during a typical injection as in Figure 1. This variability is contrary to the widely used assumption that there is a uniform melt temperature. This profile is determined by the following three factors: 11 the temperature distribution within the barrel in both the radial and axial directions formed in the plastication phase: 2) the heat conduc-

tion between the melt and its surroundings; and, 3) the shear heating during injection as the melt flows under pressure through the nozzle with constrained geometry.

These three factors are directly related to the three consecutive and separate phases of melt formation and movement: 1) plastication, 2) dwell and 3) injection. The prediction of melt temperature can, therefore, be based on the analysis of these separate corresponding stages as shown in Figure 2. During the plastication phase, the polymer granules go through the three zones of solid conveying, melting and meter- ing. The polymer is melted (or softened) and the temperature increases as energy is absorbed by conduction from the barrel heaters and from the polymer shearing between the barrel and rotating screw. The melt is conveyed to accumulate in front of the screw by screw rotation, pushing the screw to retract, simul- taneously. This action continues until a preset charge stroke is reached. The time that elapses between the end of plastication and the start of injection is the dwell time, during which the melt is at rest. The temperature of the melt in the nozzle and the barrel reservoir changes with time as heat is conducted to and from the surrounding. The heat transfer is dependent on the nozzle and barrel geometry, the temperature gradient distribution. and the dwell time. During the injection. the melt flows into the mold cavity through the nozzle by axial motion of the screw assembly. The temperature increases as the melt undergoes shearing. The increase due to shear heating is a function of the injection velocity, the machine geometry, and the distance the melt travels from its initial resting location to the measurement point. To summarize, in addition to the machine design and material variables, the melt temperature is determined by the following processing parameters: barrel heater settmgs, nozzle heater setting, screw rotation speed and back pressure during plastication. dwell time, and injection velocity.

1788 POLYMER ENGINEERING AND SCIENCE, SEPTEMBER 1999, Vol. 39, No. 9

Melt Temperature Pro@ Prediction

barrel barrel Nozzle heater heater heater Length of injection

velocity melt temperature profile at nozzle

back pressuse Dwell

melt temperature profile along the reservoir melt temperature

profile at nozzle

FEM model Mathematical, b

Rg. 2. Proposedprix&e to simulate the melt temperature at nozzle ewit

Once a prediction of the melt temperature at the end of plastication is available, the temperature changes taking place during the other two stages are relatively simple to predict. The temperature change during the dwell time is a heat transfer problem that may be described and solved mathematically. The temperature change during the injection is a flow problem, which may be analyzed using a free boundary model and solved by the Finite Element Method. The knowledge of the plastication parameters and their effect on the melt temperature distribution is a prior requirement for the solutions of the other two stages.

The prediction of the temperature distribution at the end of plastication is a central but difficult problem. Such a prediction can be made using a number of approaches, such as physical modeling, statistical experimental design arid the response surface method. A mathematical model based on the physical funda- mental has limited success, by deriving self-consis- tent solutions to the first principle equations, including the conservation of continuity, momentum and energy. Even if detailed mathematical modeling can be developed to correlate the melt temperature and its distribution to the process conditions, it would re- quire a large computational effort and would be time consuming. The results may not be accurate owing to mismatches in the model, material properties, and operating conditions. Furthermore, the verification for such a model is diffcult due to the lack of accurate experimental measurements of the temperature distribution. The complerity and computation effort required for such a model render it inappropriate for on-line control design and optimization purposes.

On the other hand, melt temperature at the nozzle exit can be measured The temperature measured by air shots at very low injection velocities immediately following the plastication, to a large degree, can prac-

tically represent the melt temperature distribution within the reservoir. Like the melt temperature distribution in the barrel, this temperature is affected by the plastication operating conditions, i.e., barrel temperatures, back pressure and screw rotation speed. The mathematical modeling of the relationship between the low-velocity air shot temperature and the plastication conditions is equally difficult, but measurements of the inputs and output are directly available. Based on those experimental input/output measurements, Response Surface Methods (RSM) (2 l) may be used to develop a statistical correlation model. Though no RSM application to the injection molding process is available, there are some applications to other processes (22). The RSM techniques are effective when the number of process variables is low and the relevant process is simple. In comparison to RSM as a modeling or predicting tool, Artificial Neural Network (ANN) possesses superior accuracy and requires fewer training experiments. It has been shown that the prediction capability of the neural models is superior to that of RSM for the same experimental training data (23). In this study, ANNs are adopted to model the relationship of the air shot temperature profile to the operating conditions. The melt temperature profile at the nozzle exit during injection can therefore be predicted from the operating conditions through a procedure illustrated in m e 2.

The rest of the paper is organized as follows. Section 3 describes the experimental setup. Section 4 con- cerns the development of the ANN-based model for plastication temperature prediction from the operating conditions. Section 5 is concerned with the model development for the dwell period. Section 6 develops the melt temperature model for the injection phase. The analysis and results of the combined model developed in the previous sections are presented in Section 6. Finally, conclusions are given in Section 7.


Chunhua Zhao and Furong Gao

36mm

Barrel Heater No.6 Nozzle Heater

L///////////l . & : . . .

-:- : . . F ~ J . 3. Flow channel diagram and the location of the temperature transducer of the molding machine.

3. EXPERIMENTAL SETUP

A ChenHsong JM88MKIII (88 ton) reciprocating screw injection molding machine with a n infra-red melt temperature transducer (Dymsco h4TX 935) fitted at the nozzle exit is used in this project. The installation of the transducer, together with the nozzle geometry, is shown in Figure 3. The injection barrel has six heater zones. Each zone temperature is measured by a thermocouple and well controlled by a PID controller to within t 1°C of its setpoint. The nozzle metal temperature is regulated by a PID controller. The screw rotation speed and back pressure are also separately controlled by in-house designed gain-scheduling PID controllers. The screw displacement and injection velocity is measured by an MTS Temposonics I11 sensor. All the measurement signals are properly conditioned before they are acquired by the data acquisition and computer control system that was developed in house.

4. PREDICTION OF MELT TEMPERATURE FROM PLASTICATION PARAMETERS

USING ANN 4.1: Introduction

Artificial Neural Networks (ANN), which mimic the human brain architecture, have demonstrated the re- markable ability to approximate complex non-linear relations between process inputs and outputs. A brief introduction to ANN is given below and detailed de- scriptions of ANN can be found in references (24, 25).

An ANN consists of a number of simple parallel processing units, called 'neurons'. Each neuron is inter- connected in such a way that knowledge is stored in the form of the connection weights between neurons. The weighted sum of every neuron's inputs is filtered by a nonlinear activation function and taken as the neuron's output. This allows ANN to generalize with added degrees of freedom not available in statistical techniques. The direction of ANN'S signal flow can be broadly categorized into feedforward and feedback two classes. Feedfomard ANN (FFNN) is adopted for this

project. FFNN normally consists of several layers of neurons that receive, process, and transmit information from one layer to the next, and thus it constitutes a nonlinear function mapping to model the relation- ships between input/output responses. A typical example of such a network is shown in Figure 4.

The operation of a typical ANN is divided into learr- ing and predicting two stages. The most common learning in a FFNN is error back-propagation (BP) algorithm. This is classified as supervised learning in which the functional relationship between input/output is obtained from a training set of input/output data. The network starts with a random set of weights. The output is calculated using this weight matrix for each input vector presented to the network. The output error is then used to determine the adjustment of the weights. In Figure 4, the input of each neuron can be expressed as Equation 1 .

where Wij,k is the weight between the j th neuron in layer k-1 and the i th neuron in layer k, inik is the input to the i th neuron in the k th layer, and O U $ , ~ - ~ is the output of the j th neuron in the (k-1) th layer. The summation is taken over all neurons in the (k-1) layer. The output of a given neuron is the resulting value of the corresponding activation function taking (1) as its input. This activation function is often sigmoid, as in Equation 2:

The outputs of the final layer are compared with the desired or measured output data. The squared difference between these two vectors determines the system errors (E). The accumulated error for all the input- output pairs is the Euclidean distance in the weight space that the network attempts to minimize. The accumulated error is defined in Equation 3, where n is the number of training data set, q is the number of


Melt Temperature Prom Prediction

Incomi,ng weighted outgoing weighted connections Output = f (Cinpurs) connections

neuron

Inpiat layer Hidden lavers Output layer

r k-th layer

Ftg. 4. A typical A" structure and its neuron

output neurons, 4,k is the desired output of the j th neuron in the output layer, and out,k is the calculated output of that same neuron:

, n 0

(3)

During the training stage, a mathematical optimization approach, such as gradient descent, is used to minimize the error by adjusting the weights propor- tional to the derivative of the error with respect to previous weights. One of the simplest weight update laws is given in Equation 4:

where rn is the iteration number and q is the learning rate. The gradient of the error with respect to the weights is calculated for the input-output patterns at a time. After the error goal is obtained, the learning stage is finished and the weights are determined. With the weights decided by the learning stage, ANN calculates or predicts the outputs from the inputs.

4.2: Experimental Training Samplea As previously stated, the temperature readings dur-

ing the low injection velocity (less than 5 mm/s) air shot are used to represent the melt temperature distribution in the reservoir at the end of plastication.

Nine operating variables influence the measurements. They are the settings for the barrel heaters No. 1 (close to the feed throat) to No. 6 (near the nozzle), the nozzle heater setting, the screw rotation speed and the back pressure.

The degree of influence of each individual operating variable on the melt temperature is first tested by kactional Factorial experiment design (26), with high and low two status for each variable as shown in Table 1 . This results in a total of 32 different experiments. These experimental results are analyzed using ANOVA (Analysis of Variance) (26) to reveal the degree

Table 1. Fractional Factorial Experiment Condition Settings.

Parameter Low Status High Status

barrel heater No. I -1 (1 20°C) l(140"C) (feed throat) Barrel heater No. 2 -1 (1 50°C) l(l70"C) barrel heater No. 3 -1 (1 80°C) l(200"C)

-1 (200°C) l(220"C) barrel heater No. 4 barrel heater No. 5 -1 (200°C) l(220"C) barrel heater No. 6 -1 (210°C) l(23O"C) (near nozzle) nozzle heater -1 (210°C) l(230"C) screw rotation 1(75 rpm) 1 (150 rpm) speed back pressure 15 bar 20 bar


Table 2. Parameter Settings for the Orthogonal Experiment Design With HDPE.

1 2 3 4 5

Barrel heaters 160 170 180 190 200 Nos. 2 & 3 ("C) Barrel heaters 190 200 210 220 230 Nos. 4 & 5 ("C) Barrel heater 210 220 230 240 250 No. 6 ("C ) Nozzle heater 210 220 230 240 250

70 100 130 160 Screw rotation 40

Back pressure 15 17 19 21 23

Charge stroke 40 50 60 70 80

("C)

speed (rpm)

(bar)

(mm)

of significance for each variable. These findings are used for the orthogonal experiments (26) to produce training data sets for the ANN training.

The ANOVA of these 32 experiments shows that barrel heater No. 6, which is the closest to the nozzle, and the nozzle heater have the greatest influence on the melt temperature. Of the other five heaters, barrel heater Nos. 4 and 5 are important, and barrel heater No. 1 has the least effect. The influence of a heater on the melt temperature becomes weaker as its distance from the measurement point increases, as expected. Barrel heater Nos. 4 and 5 have approximately equal influence on the melt temperature as they are both located around the plastication zone. Barrel heater Nos. 2 and 3 are located around the solid conveying zone, and they are treated as having an equal influence on the melt temperature. Barrel heater No. 1 is assigned a constant set-point value.

c .- 3

c m 2! 2

E

=J

a, P

a,

c

c

Based on the ANOVA analysis, the inputs to the ANNs are chosen as: (1) setting of barrel heater Nos. 2 & 3; (2) setting of barrel heater Nos. 4 & 5; (3) setting of barrel heater No. 6: (4) setting of nozzle heater; (5) screw rotation speed: and, (6) back pressure. To allow the ANNs to have the ability of predicting the melt temperature with different charge strokes, the charge stroke is taken as the seventh input. Five different operating levels are chosen to cover the operating range for each input, giving 78, 125 (or 57) combinations. An equal increment for each input between the two different operating values is chosen for simplicity. Table 2 shows the different operating values for each input. The Orthogonal Design method is applied to reduce the total required number of experiments to 25. This allows the most information to be obtained from a minimal number of experiments.

4.3: AllTlll Training and R e d t m

Figure 5'shows a typical melt temperature profile with a low injection velocity air shot experiment. The melt temperature profile can be described well by the defining temperature and stroke of the points shown in w e 5. The temperature points are the start temperature (TS), the maximum temperature (TH), the minimum temperature ("I,), the end temperature W), and the temperatures at the mid-stroke between two consecutive points of these four points, represented by TSH, THL and TLE. For the corresponding strokes, the start stroke is zero and the end stroke is a set operating condition; after the strokes for maximum and minimum temperature (represented by SH and SL) are determined, the other three midpoint stroke values can be calculated. The seven operating variables given in Table 2 are taken as the inputs to the ANNs while the seven temperatures defined above (TS, TH,

I I I I I 1 20 40 60 80

2251 0

injection stroke (mm) Rg. 5. A typical melt temperature prom at the nozzle exit with an air-shot at a low i@ection velocity.



nozzle heate-

barrel heater No.6

barrel heater No.4 & 5

barrel heater . No.2 & 3

back pressure

.

screw rotation speed

start point temp.(TS)

middle point temp. l(TSH) - max temp. pos. (SH)

max temp. (TH)

middle point temp. 2 (THL)

- - - min. temp. pos. (SL)

min. temp. (TL) - middle point temp. 3(TLE)

charge strok end point temp.(=)

Fig. 6. Schematic diagram of the ANNs for the melt temperature prediction dunng the plastication

TL, TE, TSH, THL, and TLE) and the two injection strokes corresponding to the maximum temperature and the minimum temperature (SH and SL) are taken as the outputs. Nine separate ANNs, each with 7 neurons in the input layer, 8-10 neurons in one hidden layer and one neuron in the output layer, are constructed as shown in Figure 6. The transfer function in the hidden layer is set to be Log-Sigmoid and the output layer transfer function is chosen to be a linear function for simplicity. The number of neurons in the hidden layer is determined so as not to make the ANNs underfit or overfit the input/output data. Adaptive back-propagation is used in the training to reduce the training time. A momentum term is incor- porated in the training algorithm to prevent the network from being trapped at a local minimum. The inputs are normalized to the range of (-1, 1) prior to training. The 25 sets experimental results are used as the training samples together with an additional 5 sets of experimental data used to avoid ovefitting to the training samples and to maintain the generalizing ability of the ANNs.

After about 10,000 iterations, the ANNs reach the set global error goal of 0.00 1. The ANNs are then used to predict the seven predefined temperatures and two stroke positions, from a given set of inputs not presented to the networks during training. A melt temperature profile is reconstructed using the Piece-Spline

method based on the ANNs outputs. The profile re- construction is divided into three steps: the profile section from the starting point to the maximum temperature point is first constructed: it is followed by the section from the maximum point to the minimum point: and, finally, the section from the minimum point to the end point is constructed.

Two experiments were conducted with the conditions stated in Table 3. The ANNs had not been previously trained with these two sets of operating condi-

Table 3. Operating Conditions for Experiments Shown in Figure 7.

Setting 1 Setting 2

Barrel heaters 160 190 Nos. 2 & 3 ("C) Barrel heaters 200 230 Nos. 4 8 5 ("C) Barrel heater 225 220 No. 6 ("C ) Nozzle heater 220 240 ("C) Screw rotation 75 70 speed (rpm) Back pressure 18 22 (bar) Charge stroke 80 80 (mm)

POLYMER ENGINEERY" AND SCIENCE, SEPTEMBER 7999, V d . 39, No. 9 1793

Flg. 7. Melt tempemture Compari- son between the ANNs prediction and the experimental measurement us@ HDPE with low velocity &-shots.

experiment measurement ANNs prediction

-

E 21 5

tions. A comparison between the actual experimental results and the ANNs predictions is given in FQure 7. It is clear that the maximum prediction error is less than 2"C, indicating a good prediction capability of the ANNs.

Theoretically, the barrel heater temperatures can be set to any value within the operating range. In reality, the barrel heater temperature interaction may prevent a large temperature variation between adjunct heaters. In practice, it is common to set the barrel heater temperature from low to high along the barrel from hopper to nozzle. A modified experimental design is carried out in which the nozzle heater is by the actual temperature and the levels for the other heaters are set as -12. -9, -6, -3, 0°C compared to the temperature of the heater located at its front. Such a setting ensures that the barrel temperatures have a gradual profile. Table 4 shows the new experimental levels for HDPE.

The detailed experimental conditions for this new design are given in Table 5 using HDPE. The similar

Table 4. New Parameter Settings for the Orthogonal Experiment Design With HDPE.

1 2 3 4 5

nozzle heater. 198 ("C) Barrel heaters -12 No. 6 ("C) Barrel heaters -12

Barrel heater -20 Nos.2 8 3("C ) Screw rotation 70 speed (rpm) Back pressure 3 (bar) Charge stroke 40 (mm)

NOS.4 & 5 ("c)

206 214 222 230

-9 -6 -3 0

-9 -6 -3 0

-15 -10 -5 0

80 90 100 110

3.5 4 4.5 5

50 60 70 80

0 20 40 60 80 injection stroke (mm)

procedure was established to obtain the experiment data, train the ANNs and verifil the predictive ability of the ANNs. The comparison of prediction and experimental results is shown in Figure 8, using the operating conditions shown in Table 6. The prediction results of the ANNs are in good agreement with experimental measurement.

A different material, PP; is used to verify the ANNs modeling approach. A comparison of the ANNs predictions with the experimental measurements using PP is given in Figure 9, following the operating conditions in Table 7. Reasonably good agreement is again obtained between the ANNs predictions and the experimental measurements. This demonstrates that the proposed ANNs approach is valid for modeling the plastication phase.

The ANNs prediction results for the plastication phase are used in the following sections for the prediction of the n d e melt temperature during the injection phase. Sections 5 and 6 present the models of the dwell period and the injection phase. These sections are presented to demonstrate the validity of the proposed procedure rather than for the detailed modeling for these two phases. Before the melt temperature profile predicted by ANNs is used in the following sections, a coordinate conversion must be carried out, because the ANNs predicted profile is along the injection stroke and the models in sections 5 and 6 need the melt temperature prome from the nozzle to the screw tip. The conversion between these two different coordinate systems is based on the volume equiva- lence (27).

8. SIMULATION OF DWELL PEASE The melt is at rest in the nozzle and reservoir during

the dwell period. The temperature changes with time by conducting heat to and from the surrounding. The low heat conduction coefflcient of the polymer allows

1 794 POLYMER ENGINEERING AND SCIENCE, SEPTEMBER 1999, Vol. 39, No. 9

Melt Temperature Prom Prediction

Table 5. Experiment Conditions for the HDPE Orthogonal Experiment Design.

HDPE

Nozzle Barrel 6 Barrel 4&5 Barrel 2&3 Rot. Sp. Back P. Charge (“C) (“C) (“C) (“C) ( R W (bar) Str. (mm)

Run Exp. No. 1 2 3 4 5 6 7 S q -

1 24 230 227 221 206 70 5 50 2 4 198 195 192 187 100 4.5 70 3 1 198 186 174 154 70 3 40 4 25 230 230 227 21 7 80 3 60 5 19 222 21 9 21 0 21 0 90 3 60 6 8 206 200 197 197 70 3.5 60 7 1 1 214 202 196 196 80 4.5 70 8 17 222 21 3 21 3 203 70 4.5 40 9 14 21 4 21 1 199 189 110 3.5 50 10 12 21 4 205 202 182 90 5 80 1 1 2 198 189 180 165 80 3.5 50 12 15 214 21 4 205 200 70 4 60 13 18 222 21 6 204 199 80 5 50 14 6 206 194 185 175 100 5 40 15 20 222 222 21 6 196 100 3.5 70 16 21 230 21 8 21 8 21 3 90 3.5 70 17 13 214 208 208 193 100 3 40 18 9 206 203 203 183 80 4 70 19 3 198 192 186 176 90 4 60 20 22 230 22 1 209 209 100 4 80 21 7 206 197 191 186 110 3 50 22 5 198 198 198 198 110 5 80 23 10 206 206 194 179 90 4.5 80 24 16 222 210 207 192 110 4 80 25 23 230 224 215 195 110 4.5 40

that the dwell period can be reasonably simplified to a one-dimensional heat conduction problem governed by.

(5)

The partial differential equation can be discretized and solved by the M i t e Differential Method (FDM) (28). The second order, central diffwence approximation is adopted for the second derivative, and the@& order, forward difference approximation is used for the first derivative, as shown in Equation 6

LTI = _ T.J+l - 2Tl. / + ‘ i . J - 1

ar2 1 , J (ArI2

aT/ Tl,j+l - Ti., - _ _

a r i , Ar

r = j . A r (6)

The boundary conditions used are,

dT - = o at r = O ar

The melt temperature profile predicted by the ANNs from the plastication phase is first converted to right coordinate, and then taken as the initial temperature profile along the reservoir. Such a profile change with the dwell time is simulated and shown in Figure 10.

6. SIMUL+ATION OF INJECTION PEASE

With results from the ANNs plastication prediction and the FDM dwell model, we now proceed to the melt temperature prediction for the injection phase. The objective is to predict the nozzle temperature profile during the injection phase for a given injection velocity profile and a nozzle pressure profile, based on the results obtained in previous sections.

The simulation of the injection phase is treated as a fluid mechanics problem. The screw is taken as a pis- ton with an equivalent cross sectional area. During injection, the screw moves forward, pushing melt out from the nozzle exit. Such simulation can be treated as a free boundary problem with a pre-determined velocity, which is its operating condition. The model is based on a continuum, non-Newtonian, incompress- ible flow. The reservoir and the nozzle are taken as axial symmetrical.

The governing equations for such a melt flow are momentum conservation and energy conservation equations, shown in Equations 8 and 9 respectively:


FQ. 8. Melt tempemture comparison behueen the AMVS prediction and the measurement using HDm with low velocity air-shots. (using the new level settings).

Table 6. Operating Conditions for the HDPE Experiments Shown in Figure 8.

N 0 c 230 a - E

- experimental measurement - ANNs prediction

-10 0 10 20 30 40 50 60 70 80 90 LVV

injection stroke (mm)

Setting 1 Setting 2 ~~~~

Barrel heaters 169 21 0 Nos. 2 8 3 (“C) Barrel heaters 1 74 21 5 Nos. 4 & 5 (“C) Barrel heater 186 224 No. 6 (“C) Nozzle heater 198 230

110 90 (“C) Screw rotation speed (rpm) Back pressure 5 4.5 (bar) Charge stroke 60 80 (mm)

Momentum Conservation

Energy Conservation (for incompressibk~

P%( $ + 9T,) = (kT,), + H (9)

Dimensionless formulation of problems has been adopted to have easier convergence. The dimensionless terms are defined in Equations 10.

t* = tU/L, p* = p/pU2,u* = u/U,P = ( T - To)/AT

= (WP, P * P ) = P(WP0.4,* = (L/u)4, . (101

Rg. 9. Comparison results using the new level settings for PP.

experimental measurement - - ANNs prediction

PP

setting1

c - - 0

220

-10 0 10 20 30 40 50 60 70 80 90 injection stroke (mm)

1796 POLYMER ENGINEERING AND SCIENCE, SEPTEMBER 1999, Vd . 39, No. 9

Melt Temperature From Prediction

Table 7. Operating Conditions for the PP Experiments Shown in Figure 9.

~~ ~ ~~~

Setting 1 Setting 2

Barrel heaters 185 226 Nos. 2 & 3 ("C) Barrel heaters 190 23 1 Nos. 4 & 5 ("C) Barrel heater 202 240 No. 6 ("C) Nozzle heater 214 246 ("C) Screw rotation 110 100 speed (rpm) Back pressure 4.5 4 (bar) Charge stroke 60 80 (mm)

In this simulation, Nine-node rectangular elements are adopted. Quadratic interpolation is adopted for velocity and temperature, and linear interpolation for pressure. The differential equations are transferred to algebraic equations using backward Euler, then solved using .an accelerated Quasi-Newton scheme. The termination criteria used are the solution vector and the residual vector for each node. The fluid domain changes with the screw forward motion at a known velocity as an operating condition. Spines method is adopted here to guide the free surface and to remesh the interior domain.

Rgure I 1 shows the flow chart of using the finite element method to solve the injection phase problem with the model structure as in Figure 12.

And the dimensionless groups used are:

, Pr=-. JLO Cp PUL Re = -- PO k

The momentum and energy conservation are then modified to Equations 12 and 13 respectively. Momentum Conservation

Energy Consentation If.r inmrnpressibk&idJ

6.1: Finite Element lyIethod

The Finite Element Method (FEM) is used to solve the above coupled energy and momentum equations. Details on the finite element method can be found in many books (29, 30).

6.2: Hodd of Injection Phame

The Cross-Experiment viscosity model is adopted with five parameters, n, Tb, p, B, 7'. Heat conduction, heat capacity and density are taken as constants in this simulation.

The boundaries of the region are set as barrel wall, nozzle wall, symmetrical line, screw surface and nozzle outlet as shown in Figure 13u The boundary conditions are:

T = Tbarreld at barrel wall T = T m & d at nozzle wall v = o at barrel wall and nozzle wall v, = 0 at symmetry p = poutletprop. at nozzle outlet V, = V, (inletmml at screw surface

The mesh determines the simulation precision and speed. In this study, the mesh is optimized by com- promising these two considerations. Figure 13b shows the mesh at the time step one. During the simulation, the velocity profile is read and the present position of the screw surface boundary is determined. The simulation region is then modified and remeshed. Figure 13c shows the mesh at time step 40. At each time

Fig, 10. Melt temperature p r o m along the reservoir at different dwell times.

220

21 6

21 4 213 212

- - 20s -

210 1 nozzle exit 209

- Screw tip I 1

0 50 1 00 150 200 distance along the reservoir (mm)


i

Initial temperature profile - (initemp.dat)

v velocity profile -b FreeBoundary (velocity .dat) Model ---*

rb of injection phase

I Creating Geometry I

temp. of the nodes ' at nozzle outlet _I+

4 l Creating Mesh

+l Problem defining

1 v

Setting Boundary Conditions

1 Reading the initial temp. along

reservoir

injection velocity

Decide the position of the screw r Solve the nonlinear equations

.I+ '0

.1 Yes

+l Result processing

Rg. 1 1. M o d e l f l o w chart for ir@ction phase.

step, material properties, velocity, temperature and pressure at each node are calculated. Thus, a temperature versus time profile can be obtained by recording the calculated melt temperature of the nodes located along the nozzle outlet boundary.

6.3. Erpsrtmeatal V d d o n of the Combined ANN6 Prediction and IUathematid Modeling

HDPE of Philips HMN 6060 with properties given in Ref. 27 is used, with the operating conditions shown

in Table 8 for a typical injection molding cycle. The melt temperature profile by plastication first predicted by the ANNs in Sections 4 and modified by the simulation of the dwell period in Section 5 is used as the initial melt temperature profile in the reservoir before injection.

The prediction is compared with the airshot experiments at high injection velocity. The injection velocity versus time and nozzle pressure versus time profile are measured and used as the boundary conditions.

Rg. 12. Model structure for injection phase.

L i z 3 pressure profile '1' 1 I I

Viscosity model I I

1798 POLYMER ENGINEERING AND SCIENCE, SEPEMBER 7999, Vol. 39, No. 9


Barrel w a1 1

Nozzle wall surface Screw

Symmetrical line

(c> Q. 13. lal Boundmy sets and the simulation region 0) M e s h plot at time step 1, (c) Mesh plot at time step 40.

Among other material status, melt temperature distribution at the nozzle exit can be obtained. According to Maier (31). the reading of infra-red temperature transducer is mostly determined by the maximum melt temperature at the nozzle exit. F‘igure 14a shows a comparison of the simulation result and experimental measurement. They correlate reasonably well.

A different material, Al3S of GE Cycolac T with properties given in Ref. 27 is used as another verification of the prediction procedure. The experimental condi-

Table 8. Operating Conditions of the HDPE Verifying Experiment.

Variables Setting

Barrel heater Nos. 2 & 3 (“C) Barrel heater Nos. 4 & 5 (“C) Barrel heater No. 6 (“C) Nozzle heater (“C) Screw rotation speed (RPM) Back pressure (bar) Injection velocity (mm/s) Dwell time (s) Charge stroke (mm)

187 197 200 206 60 3 30 10 60

tions are shown in Table 9. Comparison of the prediction result and experimental measurement can be found in mure 14b. Reasonably good agreement is again obtained. This shows that the proposed procedure combining the ANNs prediction and mathematical modeling is effective in predicting the melt temperature profile during injection.

7. CONCLUSIONS

The melt temperature at an injection nozzle exit was experimentally measured and analyzed. A systematic method for predicting the melt temperature profile was proposed by modeling the three consecutive stages, plastication, dwell and injection.

The mode- of the melt temperature during p h t i - cation can be effectively carried out by a set of ANNs. Low-injection-speed air-shot temperature measurements immediately following plastication can be used to represent the plastication contribution to the melt temperature. The temperature profile can be charac- terized by seven temperature points and two stroke positions. The good prediction capability of the ANNs has been successfully demonstrated.


Flg. 14. Melt temperature comparison between the prediction and experimental measurement during a typical injection (a) using mm, fb) usirgABs.

218

a, 216

0 5 214 ([I

0)

I3

5 212

ITI g 2 1 0

E 2 208

c

c - 0) E 206

204

202

- - - - -

- simulation - airshot with high injection velocity - - -

I I I I I

240 r 0) N N 0 c 2 3 5 ([I

2 230

a Q

g 2 2 5

a,

-

c

2 9

c c -

220

-

-

-

-

The mathematical model for the dwell period is developed and solved by the Finite Differential Method. The melt flow during the injection phase is modeled as a free boundary problem and solved by the Finite Element Method. Combining the modeling of these three stages can result in the prediction of the melt temperature. A detailed and quantitative relation between the process conditions and the melt temperature can be effecmely studied by this combined modeling system.

I I I 1 1 I 0 500 lo00 1500 2000

tirne(rns)

(b)

8. REFERENCES 1. D. V. Rosato and D. V. Rosato, Injection Molding

Handbook T h e Complete Molding Opemtion Technology, Performance. Economics, Chapman & Hall, New York ( 1995).

2. 0. h a n o and S. Utsugi, Polyrn Eng. sci, 28. 1565 (1988).

3. 0. h a n o and s. utsugi , ~olyrn Eng. sci.. 18, 171

4. 0. h a n o and S. Utsugi, Polyrn. Eng. Sci., SO. 385 (1989).

(1990).

Table 9. Operating Conditions of the ABS Verifying Experiment.

Variables Setting

Barrel heater Nos. 2 & 3 (“C) Barrel heater Nos. 4 & 5 (“C) Barrel heater No. 6 (“C) Nozzle heater (“C) Screw rotation speed (RPM) Back pressure (bar) Injection velocity (mds) Dwell time (s) Charge stroke (mm)

191 196 208 220 60 3.5 30 10 60


Melt Temperature P r o p Prediction

5. G. C. Peischl and I. Bruker. Polyrn Eng. Sci, 2B. 202 ( 1989).

6. N. Dontula, P. C. Sukanck, H. Deranthan, and G. A. Campbell, Polyrn E r g Sci 31, 1674 (1991).

7. C.-H. Lu and C.-C. Tsai, IEEE Tkans. Industry Appli- cations, 34,310 (1998).

8. R. Dubay, A. C. Bell, and Y. P. Gupta, Polym Eng. Sci, 37, 1550 (1997).

9. R. S . Chandra, SFE ANTEC Tech. Papers , 18, 831 ( 1972).

10. M. R. Kamal. W. I. F'atterson, and V. G. Gomes, Aolyrn Eng. Sci, 26, 854 (1986).

11. M. R. Kamal, W. I. Fatterson, and V. G. Gomes, Aolyrn Eng. Sci, 26, 867 (1086).

12. J. R. A. Pearson, Mcrhankal Principles of Polymer Melt Processing, Pergamori Press (1975).

13. 2. Tadmor and C. G. Gogos, Principles of Polymer Processing, John Wiley & Sons. New York (1979).

14. H. Potente and H. S. Paderborn, Kunststofe G e m Plastics, 80 (9). 40 (1990).

15. R. C. Donovan, D. E. Thomas, and L. D. Leversen, Polyrn Eng. Sci. 11, 353 (1971).

16. R. C. Donovan, Polyrn. Eng.Sci, 11, 361 (1971). 17. R. C. Donovan, Polym. Eng. Sci, 14, 101 (1974). 18. S. D. Lipshitz, R. Lavie, and 2. Tadmor, Polyrn Eng.

Sci, 14, 553 (1974).

19. R. E. N u n n and R. T. Fenner, SPE ANTEC Tech Papers,

20. W. Wey, PhD thesis, Ecole des Mines de Paris (1984). 21. G. Box and N. Draper, Empirical Model-Building and

Response Surfaces, Wiley, New York (1997). 22. M. Jenkins, M. Mocella, K. Men, and H. Sawin, Solid

State Technology, 2s. 175 (1986). 23. C. D. Himmer and G. S. May, IEEM 'Dans. o n Semi.

C o d M a n , 6, 103 (1993). 24. P. K. Simpson, Neural Networks Theory. Technology,

and Applications, New York. IEEE (1995). 25. Anonymous, Neural Network Toolbox User Guide, The

Math Works Inc.. Mass. (1995). 26. G. Taguchi, Sys tem of Expenmental Design American

Supplier Institute, Dearbom, Mich. (1991) 27. C. H. Zhao, Master's thesis, The Hong Kong University

of Science and Technology ( 1998). 28. G. D. Smith, Nume&al Solution of Partial Differential

Equations: Finite Difference M e t h o d s , 3rd Ed, Oxford University Press, Oxford, England (1985).

29. K. H. Huebner, E. A. Thornton, and T. G. Byrom. The Finite Element Method for Engineers, 3rd Ed.. Wiley, New York (1995).

30. K. J. Bathe, Finite Element Procedures, Prentice Hall, Englewood Cliffs, N. J. (1996).

31. C. Maier, Polyrn Eng. Sci, 36, 1502 (1996).

a4, 72 (1978).


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Melt temperature profile prediction for thermoplastic injection molding