An injection molding study. Part I: Melt and barrel temperature dynamics

An Injection Molding Study. Part I: Melt and Barrel Temperature Dynamics

M. R. KAMAL", W. I. PATTERSON, and V. G. GOMES

Department of Chemical Engineering McGill University

Montreal, Quebec, Canada H3A 2A7

The dynamics of the key variables in the plastication phase of injection molding were studied using a microcomputer controlled laboratory scale injection molding machine. Interfaces for the measurement and manipulation of suitable variables were developed. An approximate theoretical analysis provided a preliminary understanding of the effect of a step input in heating power on melt and barrel temperatures. Deterministic and stochastic models were derived from experimental data for the melt and the front and rear zone barrel temperatures with heater power manipulation. Experiments were performed for evaluating the effects of back pressure manipulation, heating zone interaction, and process disturbances on the melt and barrel temperatures. Experiments showed that it is desirable to directly control the melt temperature rather than the barrel temperatures.

INTRODUCTION he injection molding process involves four T phases: plastication, injection, compres-

sion, and cooling. The melt quality is largely determined by the complex thermo-mechanical history [solids conveying, melting and melt conveying) that the polymer undergoes during the plastication phase. The quality of the molten polymer obtained through plastication affects the processing performance of the other three phases. Finally, these effects are reflected in dimensional variations and quality of the molded parts.

The temperature of the plasticated polymer that is injected into the mold is an important variable in injection molding. The amount of polymer plasticated is also important; however, sufficient cushion is usually maintained to ac- commodate variations in the amount of plasticated material. The importance of the melt temperature can be evinced from the consideration that it affects a number of important process variables, such as the melt flow rate, the melt pressure at the nozzle and the cavity, and the cooling time. The effects of melt temperature on the hydraulic and cavity pressures are indi- cated in Fig. 1 (1) . These are due to the strong dependence of polymer viscosity on melt temperature, which is usually characterized by a n Arrhenius type relation. To whom all correspondence should be addressed.

The effect of melt temperature on the quality of the final product has been reported by several researchers. Harbert, et al. (2) reported a 0.07 percent increase in part dimensions in response to a temperature increase of 12K for polypro- pylene melt. Johannaber, et al. (3) reported a change of 0.052 percent in part dimensions for a change of 1 OK in polycarbonate melt temperature. These examples indicate that sufficient incentives exist for the control of melt temperature in injection molding. However, in order to develop suitable control strategies, it is neces- sary to obtain accurate measurements of the melt temperature and information regarding the dynamics of the process in response to changes in the manipulated variables and disturbances. This paper describes the development of a melt temperature measurement technique as a n alternative to conventional temperature sensors, as thermocouples on barrel metal. Subsequently, we report the results of the theoretical and empirical modeling of the dynamics of melt and barrel temperatures under a variety of conditions. The evaluation of control strategies, based on the study of process dynamics, will be discussed in the Part I1 of this work.

MEASUREMENT OF MELT TEMPERATURE Several studies are available regarding melt

temperature measurement in injection molding

854 POLYMER ENGINEERING AND SCIENCE, MID-JULY, 7986, Vol. 26, NO. 12

An Injection Molding Study. Part I : Melt and Barrel Temperature Dynamics

- t. .- '"I

Tmia*Tmb

'hold I

'ma /

,-

\ "\\ \ Time-

Fig. 1 . Effect of melt temperature on hydraulic andcauity pressures.

(2, 4-8). Van Leeuwen (10) has outlined the requirements of the sensor for this measurement: adequate strength at high temperature (about 600K) and pressure (about 70 MPa) under cyclic loads, negligible error due to heat conduction and shear heating, no distortion of the melt flow, and fast response. These criteria are difficult to satisfy simultaneously. A robust sensor will have good mechanical strength but slow and unacceptable response. A probe sup- ported on the barrel body may sustain error due to heat conduction from the barrel. A probe positioned perpendicular to the flow direction may cause melt flow distortion and cause error due to shear heating.

The following sensors were considered for the measurement of melt temperature during the present work:

0 infrared temperature detector 0 ultrasonic temperature detector 0 resistance temperature detector 0 thermocouple.

The fiber-optic infrared temperature detector has the following advantages: noncontact with the medium, fast response time and a value averaged over the viewing angle (7, 8). The disadvantages are high cost, probe size, and nonlinear characteristics. The smallest probe size (150 mm long, Vanzetti Co.) available did not provide sufficient clearance for installation at the nozzle without damaging the probe during injection. Installation on the barrel would give an average of the melt and the screw metal

temperatures. The infrared technique was, therefore, unsuitable for this application.

An ultrasonic temperature measurement technique has been reported by Herbertz (9), based on the time taken for an ultrasonic pulse to travel through the polymer melt. The advantages are similar to those of the infrared detector. The disadvantages are high cost, calibra- tion difficulties (acoustic velocity depends not only on temperature but also on the medium pressure and the type of polymer processed), and difficulty in installation due to space con- straints at the nozzle. This sensor was also disregarded.

A resistance temperature detector (RTD) and a thermocouple have approximately similar advantages and problems. Their disadvantages are: susceptibility to errors caused by shear heating, conduction from the environment, and slow response time. These problems can be eliminated, to a large extent, by the proper se- lection and installation of a sensor. The RTD, for accurate measurement, requires a four-wire configuration and is more fragile compared to a thermocouple (1 1).

In view of the above considerations, a thermocouple was selected as the sensor for the present study. The sensor configuration was decided based on the merits and demerits of earlier studies in similar situations. Harbert, et al. (2) and Schonewald, et al. (5) proposed the use of a dual thermocouple with one sensor immersed in the melt. The other sensor was employed for feedback control of the probe body temperature at a level close to that of the melt (set point). Such configurations, however, are prone to large errors (4). A thermocouple installed parallel to the flow direction is superior to the one placed perpendicular to the melt flow ( 1 0); however, a suitable support is required. Peter (6) reported on the use of a thermocouple attached to the screw-tip for the measurement of screw metal temperature and obtained satisfactory performance.

EXPERIMENTAL Equipment

The experimental work was carried out with a Danson-Metalmec reciprocating screw injection molding machine, model 60-SR, 2% oz. shot size, 60T clamping, and screw L/D of 15: 1. For both machine control and data acquisition, a 2-80 based microcomputer was used. It was equipped with the following peripherals: A Mor- row-Design Switchboard having 2 serial and 4 parallel ports, a 12-bit Burr-Brown analog-to- digital (A/D) converter, an 8-bit D/A converter interfaced to a Moog servovalve, an 8-channel input/output (I/O) module connected to the machine limit switches and solenoid valves, a Ha- zeltine 1400 terminal, and a DEC IV dot-matrix printer.

POLYMER ENGINEERING AND SCIENCE, MID-JULY, 7986, Vol. 26, No. 72 855

M. R. Karnal, W. I . Patterson, and V. G. Gornes

MANIPUULTED VARIABLES Heater Power

screw MOtOC Power SerYaVdlYe Opening

Measured and Manipulated Variables A grounded junction thermocouple (3mm di-

ameter) projecting into the polymer melt (about 7mm immersion) from the screw-tip and positioned at the center of the screw, parallel to the flow direction, was chosen for melt temperature measurement (Fig. 2). A hollow screw with a detachable screw-tip was machined to hold the thermocouple at the tip of the screw by means of a Swagelok fitting. The thermocouple signal was carried by a pair of wires through the hollow screw, which could undergo both rotation and translation during a cycle. The signal was received by the A/D converter via a slip-ring assembly at the rear end of the screw. The custom built slip-ring assembly consisted of a pair of silver rings, silver-graphite brush contacts and the assembly support with electrical insulation between the screw and rings, and the brush contacts and assembly support.

The variables suitable for measurement and manipulation were chosen after a n analysis of the variables that affect melt temperature, which is the primary measured and controlled variable of this study. Figure 3 shows a sche- matic representation of the interactions involv- ing melt temperature. The secondary variables chosen for measurement were: (a) front zone barrel temperature, (b) rear zone barrel temperature, (c) hydraulic pressure, (d) nozzle melt pressure, and (e) screw rotational speed (RPM).

The front and rear zone barrel temperatures were measured by means of two type J thermocouples, installed at approximately the mid- plane of each zone. Cold junction compensation (CJC) for the melt and barrel temperatures was provided by measuring the ambient temperature at the thermocouple termination junctions. The measurement was accomplished by an integrated circuit (Analog Devices AD 594 CD).

The transducers for the measurement of the hydraulic and nozzle pressures were installed during an earlier study (12). The screw RPM readings were taken from a tachometer installed on the screw shaft. The operation of the machine created an electrically noisy environment. This necessitated the use of several noise reduction techniques, especially for the thermocouple signals. These techniques included:

.MACHINE \ r A R I A B U - Barrel T e m p e r a t u r e screw Velocity screw RPM

ILII-I ING .11*1S~"

/

Fig. 2. M e l t thermocouple configuration.

DISTUPSANCES - POLYMER PROPERTIES MELT TEMPERIITURE

shielding and grounding, analog filtering (cut off frequency, oc = OBH,), digital filtering (a, = 0.1 HJ, and installing varistors (voltage depend- ent metal oxide semiconductor devices) across on-off limit switches on the machine.

The manipulated variables selected for the present study were: (a) barrel heater power and (b) servovalve opening. The effect of the screw rotational speed was not considered, because earlier studies (1, 5, 13) showed only a minor effect of screw speed on melt temperature. The screw rotation time is small compared to the total cycle time and the machine modification required to manipulate the screw RPM in this application, was substantial (1 4).

The heating power was manipulated by the time proportioning principle. The smallest interval ('/60th s) was derived from the 60Hz power line and a total cycle time of 4.25 s was selected. A resolution of about 0.4 percent of the maximum power was obtained by this technique. The microcomputer output signal was processed by an electronic circuit for generating appropriate control signals for the optically iso- lated solid state relays (SSR). The SSRs were interfaced to the front and rear zone heating elements and 220V, 60Hz power line (1 4). The manipulation of the servovalve opening was facilitated by a n interface to the microcomputer via a D/A converter constructed earlier [ 12).

The data, collected and stored in the microcomputer, were transmitted to the McGill main- frame computer for analysis. This was achieved by means of an asynchronous modem with a 4- wire communication link. The software to control data transmission, filtering, and error de- tection were developed during this study. Fig- ure 4 shows the integrated interface diagram between the machine and the microcomputer. Details regarding the interfaces for measurements, manipulation of control elements, and different facilities of the system are given elsewhere (14).

Material The resin used in this study was a high-den-

sity injection molding grade polyethylene (Sclair

856 POLYMER ENGINEERING AND SCIENCE, MID-JULY, 1986, Vol. 26, No. 12


M I C R O C O M P U T f R

M A I N F R A M E C O M P U l f P

Fig. 4 . Machine microcomputer interface diagram.

2908, DuPont Canada Ltd.) with a melt index of 7.4g/10 min and a density of 0.962 g/cm3.

MODELING Theoretical models were developed in this

study to gain a pysical understanding of the process. Empirical modeling was subsequently employed to yield simple yet accurate models for the synthesis of controllers, suitable for real-time implementation. The theoretical models were compared with the empirical models for a better understanding of the process dynamics.

Theoretical analysis requires the solution of the governing differential equation(s). Partial differential equations obtained from a distributed process analysis were solved for obtaining the melt and barrel temperature profiles. Em- pirical modeling involves the study of the rela- tionships between process input and output. Figure 5 shows typical process inputs employed for modeling and the corresponding responses.

THEORETICAL MODELING A complete theoretical analysis of the plasti-

cation phase is difficult, and falls beyond the scope of the present work. Therefore, the following simplified situations have been analyzed. Firstly, the heat conduction equations were solved for static heating of the melt in the absence of screw motion (Static Simulation). Step inputs in heater power were introduced

INPUT RESPONSE __

PRBS & Fig. 5. Typical inputs to a process and corresponding outputs.

and the resulting temperature distributions were calculated. This case was considered for comparison with the results obtained subsequently for step inputs in heater power during continuous molding operation (Dynamic Simu- lation).

The system was analyzed based on the following considerations: (a) the system comprises three concentric cylinders: screw, polymer melt, and barrel; (b) only the front zone is analyzed (the rear zone involves complications of additional thermal capacitance and water cooling at the hopper throat); (c) the polymer is in a molten state at the front zone at a uniform initial temperature; (d) the changes in the properties of the different materials are negligible; (e) the cylinders are in perfect thermal contact with each other: (f) the temperature distribution in the radial direction only is considered.

Static Simulation The three parabolic partial differential equa-

tions describing the temperature distributions in the three cylindrical zones can be written as follows:

d2Ti 1 dTi 1 dTi - + - - = - - dr2 r dr cyi dt

for t > 0, i =1, 2, 3

in ri < r <

where i = 1, corresponds to the screw (0 < r < a ) i = 2, corresponds to the polymer (a < r < b) i = 3, corresponds to the barrel ( b < r < c )

Initial condition: Ti = To at t = o (2) dTi Boundary conditions: - = 0 dr

(3) at r = o for i = 1

(4) Ti = T,+, at r = a, b for i = 1, 2

POLYMER ENGINEERING AND SCIENCE, MID-JULY, 7986, Vol. 26, NO. 12 a57

M . R . Karnal, W. I . Pat terson, a n d V . G. Gornes

at r = a, b dTi dTi+ 1 k . - = k . - (51 dr l + 1 dr

for i = 1, 2

at r = c for i = 3

An analytical solution was sought initially for the above equations: however, the resulting ei- genvalue problem could not be solved satisfac- torily, as described elsewhere (14). The difficulty in obtaining a realistic solution was attrib- uted to the inability to accurately identify eigen- values from a transcendental equation that required accurate evaluation of expressions in- corporating a number of Bessel functions. A similar problem for composite cylinder analysis by conventional techniques was reported earlier by Mikhailov, et al. (15).

The heat conduction equations were subsequently solved by the fully implicit finite difference scheme. Equation 6 was linearized for each time step by using the following approximation for the radiation loss term:

UFC(T;,~+I - T:) u F c ( T E , ~ . T ~ , ~ + ~ - T:) (7) Since small time steps of 5 to 10s were employed, the error due to the approximation was very small. The discretized equations, written in the matrix form, were solved by using the Tridiagonal Matrix Algorithm. The solutions obtained were reasonable and stable (1 4).

The temperature distributions over the nodal points were obtained for different step inputs in heater power: +5, +lo, and +15 percent. Figure 6 shows the calculated transient responses of the front zone barrel and melt temperatures at the location of the sensors. The barrel temperature response is suggestive of a first order process and the melt temperature shows at least a second order behavior.

Dynamic Simulation The foregoing results were obtained for a no-

molding or ‘static’ operation. The physical process is highly complex for the plastication phase during molding or ‘dynamic’ operation, because of the problems of solids conveying (including deformation), melting and non-Newtonian fluid flow in a helical channel for a cyclic process.

Previous modeling efforts have involved the use of empirical parameters, such as a single parameter to incorporate material and machine characteristics in relation to steady-state extru- sion (1 6) or data on delay in melting ( 17, 18). In the absence of satisfactory empirical data and in view of the ultimate objectives of the present work, an approximate extension of the static simulation was performed. A convective heat transfer boundary condition at the barrel-polymer interface was imposed:

0 0

0 m

L

i

a 6 aco

5 g c

w e L Y

+ o 0

0 .r

0 0

N d

THEORETICRL : FRONT ZONE lo1

0

1000 2000 3000 4000 5000 TIME. SECONDS

Fig. 6. Theoretical response to s tep input in heaterpower [static simulation).

dTi d r

ki - + h,(Ti - T,) = 0 at r = b (8)

The total cycle time was divided into two periods: screw stationary (transient heat conduction) and screw undergoing rotation and translation (transient heat conduction and convec- tion). The finite difference equations were solved with the appropriate boundary conditions for each of the periods consecutively. Fig- ure 7 shows the barrel and melt temperature responses to step inputs in the heater power of +lo, +15, and +20 percent. The responses for the dynamic simulation are similar to those obtained for static simulation, except that the changes in temperatures for the corresponding inputs are smaller and the response times are faster for the dynamic simulation.

EMPIRICAL MODELING Models can be classified into deterministic or

stochastic types, depending on the assumptions made regarding the process behavior and the technique employed for the input-output analysis. Deterministic models are most easily obtained when simple input functions, for exam- ple, steps or pulses are used. The model accu- racy can be affected by the presence of process noise and nonlinearity. Stochastic modeling techniques employ a “random” input (typically a pseudo-random binary sequence or PRBS) and statistical analysis (typically correlation) to yield a model for both the process and the noise. Both deterministic and stochastic tests were performed during this study.



THEORETICRL : FRONT ZONE lo1

TIHE, SECONDS

Fig. 7. Theoretical response to s t e p input in heater power (dynamic simulation).

Deterministic Method Step inputs were used to obtain responses of

the melt and the front and rear zone barrel temperatures, under the following conditions:

(1) Heater Power Manipulation. (a) Static Experiments: Step inputs in

heater power were introduced (5, 10, 15 percent increasing and decreasing power) with no molding operation. The purpose of these tests was to study the effect of heat transfer due to conduction from the heater to the barrel and the melt.

(b) Dynamic Experiments: The machine was operated with continuous molding under semi-automatic machine sequencing control. Step inputs in heater power (10, 15, 20 percent increasing and decreasing modes) were introduced with constant servovalve opening and screw RPM.

(2) Servovalve Manipulation Experiments. The machine was operated for molding cycles and steps in the servovalve opening (+44 and -44 percent) were introduced with constant heater power and screw RPM.

(3) Interaction Experiments. Step inputs were introduced to only one heater zone at a time, maintaining a constant power level for the other heater. These experiments were designed to provide preliminary information on the degree of interaction between the two heater zones.

(4) Pseudostatic Experiments. The machine

was switched from a no-molding steady state condition to a molding operation. The heater power and servovalve opening were kept constant. These experiments do not constitute a deterministic input in any specific variable, and their utility is lim- ited to the observation of the barrel and melt temperature responses for a disturb- ance in the operation.

Parametric models were obtained for the responses of the static and dynamic experiments, using the NONLINWOOD program (19) for fitting.

Stochastic Method The stochastic (PRBS) experiments were per-

formed with heating power input in order to derive the process and noise models for the melt and the barrel temperatures. The static experiments were performed using a PRBS length of 127 bits and a heating power amplitude of about +-5 percent. The dynamic experiments were performed using a PRBS length of 63 bits and a heating power amplitude of about 215 percent.

The Box-Jenkins time series analysis (20) was used for deriving models of the form:

(9) y(k)( l - 61B - 62B2 - - . . )

= (0, - w l B - 02B2 * - - ) x ( k - d ) + n( k )

The iterative modeling procedure consists of several steps: process model identification, initial estimation of the parameters of the model, noise model identification, final parameter estimation, and diagnostic checking.

RESULT AND DISCUSSION The experimental techniques discussed in the

previous section were applied and the results are presented in this section. The results are given in terms of temperature deviations, nor- malized with respect to normal heating power input (100 percent power = 2475 W), which were corrected for changes in the supply voltage.

Deterministic Models-Static Experiment The typical responses obtained for the melt

and barrel temperatures are given in Figs. 8a and b for +15 and -15 percent step inputs, respectively. The rear and front zone barrel temperatures were best fitted by a first order model of the form:

y( t ) = K [ 1 - exp(-t/~)] (10) The fitted parameters of the model are shown in Table 1.

The melt temperature responses were best fitted by a second order plus time delay model. It is difficult to identify higher order models from step test data. The derived model is of the form:

POLYMER ENGINEERING AND SCIENCE, MID-JULY, 1986, Vol. 26, NO. 12 859

M. R. Karnal, W. I . Pat terson, and V. G . Gornes

0 W

W

0 a L1 w - 5 m 0 14 \ ?c

- 0 3 -

cho

2 qF

2 H 3 W a ;-a m a .- 3 m

0

3 $ 0

2

w

E i N

a m w -

N H

2 0 0 4

1

960 1 8 0 0 2 3 0 0 3 6 0 0 4200

EXPERIMENTAL: FRONT ZONE

REAR ZONE

MELT

F I T T E D II0DEL:-

TIME, SECONDS

Fig. 8a. Temperature responses to +15 percent step in-put in heater power (static experiment).

Table 1. Barrel Temperature Model Parameters (Static Experiment).

Rear Zone Front Zone Power Input Gain, K 7 Gain, K 7

(%) (K/%Power) ( 5 ) (K/%Power) (s) +5.2 4.43 f 0.17 1841 f 90 5.71 f 0.27 1550 T 125

+9.3 5.26 f 0.12 2143 f 85 6.66T 0.22 1860 ? 210

+14.1 5.69 f 0.14 2194 +- 80 6.65 f 0.26 1717 2 120

-5.2 4.69 f 0.16 2020 +- 110 5.60 2 0.25 1650 f 160

-9.3 4.77 k 0.11 2082 55 5.77 f 0.24 1829 f 130

-14.9 6.06 2 0.11 2259 ? 75 6.60 f 0.28 1802 * 150

y(t) = K 1 - ___ e-(f-Dl/~i

71 - 7 2 1.2

1 ( 1 1 ) _ - e - ( t - D l / ~ z l

[ 7172 C X P C R I K N T A L : FRONT ZONE ( v )

REAR ZONE (0)

7 1

FITTED MODEL:- The fitted model parameters are given in Table 2.

A study of the model parameters for the different experiments indicates a nonlinear proc-

900 1800 2700 3600 4 5 0 0 ess. This can be explained by the following considerations:

(a) The efficiency of heat transfer between the heater and the barrel metal is affected by changes in the thermal contact resist-

I

TIME,SECONDS

Fig. 8b. Temperature responses to -1 5 percent step input in heater power (static experiment).

860 POLYMER ENGINEERING AND SCIENCE, MID-JULY, 1986, Yo/. 26, No. 12


Table 2. Melt Temperature Model Parameters (Static Experiment).

Table 3. Model Parameters from Theoretical Simulations (Static).

Power Input

+5.2 -5.2 +9.3 -9.3 +14.1 -1 4.9

("/.I Gain, K

(K/%power) 4.94 f 0.52 5.85 f 0.77 7.31 f 0.42 6.1 5 + 0.35 7.52 f 0.14 7.38 * 0.28

Time Constant(s)

T i T2

2570 f 200 306 * 46 3044 ? 320 351 f 132 3020 f 75 316 f 48 2714 f 240 404 f 82 2827 f 80 315 & 31 3096 f 27 305 f 34

Time Delay

55 f 30 60 f 35 66 f 39 50 f 33 76f18 131 +43

(s)

ance at the interface. The changes are caused by differential thermal expansion between the two dissimilar materials and the development of significant temperature gradients at the contacting surfaces. The heating and cooling processes of the barrel are governed by different heat transfer mechanisms. Heating takes place by conduction (thermal diffusivity of metal does not change appreciably with temperature), whereas cooling by convec- tion and radiation is a function of temperature. Line voltage shows fluctuations of the order of 5 percent causing heater power variations of 10 percent (Power = v2/R). Also, the drift susceptibility of the A/D converter and, to a lesser extent, quanti- zation error of the A/D converter contrib- ute to the nonlinearity of the process.

The theoretical results Gbtained -earlier (numerical solution of distributed system analysis) can be compared with the corresponding experimental results. The NONLINWOOD program was used to obtain the best fit models to the theoretically predicted melt and barrel temperature profiles (Fig . 6). The fitted model structures correspond to those obtained from experimental studies. The model parameters, given in Table 3, also compare favorably. The agreement is quite good, especially for the barrel temperatures. However, there is a definite trend in the results from theoretical analysis, that is, the gains and time constants decrease with an increase in the heat input. This is due to the increased radiation losses [proportional to T4) with higher temperatures.

Deterministic Models-Dynamic Experiment Figures 9a and b show responses to heater

power (+20 and -20 percent, respectively) during continuous molding operation. The rear and front zone barrel temperature responses were best fitted by a first order model ( E q 10). The model parameters are given in Table 4 . The melt temperature responses were characterized by a second order plus time delay model [ E q 1 1 ), and the corresponding parameters are given in Table 5.

The models for the melt and barrel temperatures show lower gains and smaller time con-

Experiments Barrel

+ 1 0%

Melt

+ 1 0%

+5%

-4-1 5%

-6%

+15%

Time Con- stant(s)

Gain, K (K/%power) T , T?

8.00 1990 - 7.05 1877 - 6.54 1767 -

7.92 2208 284 7.02 2024 292 6.51 1877 303

65 41 27

stants, in comparison to those obtained for the static experiments. These differences can be explained by the following considerations:

(a) The rapid mixing action of the polymer mass, due to the screw rotating and reciprocating motions, causes an increase in the overall heat transfer rate, resulting in a faster response time.

(b) The heat supplied is partly removed by the polymer shots during each cycle, thereby resulting in a lower steady state gain.

The theoretical results (Fig. 7) obtained earlier were fitted with deterministic models (Ta- ble 6) and compared with the experimental results. The model structures show good agreement and the parameters also are comparable. However, the time delay terms for the melt temperature show considerable difference. Fur- ther, as in the case of static simulation, the gains and time constants, in general, decrease with an increase in the step input. The simulations were carried out with a number of assumptions and the experimental data were ad- ditionally affected by process disturbances. Further, the nature of the experiments was such that the initial temperature varied with the different inputs, since it was not controlled.

Consequently, the actual heat losses incurred during the experiments do not correspond to the ones calculated for simulations, which were based on a fixed initial temperature.

Stochastic Models-Static Experiment The barrel and melt temperature responses

to a 127 bit PRBS input are shown in Fig. 10 for a sampling time, To, of 200s. The front and rear zone barrel temperature responses (To = 200s) were fitted by a mixed first order autore- gressive and moving average type (ARMA (1, 1)) process model and a second order autoregres- sive type (AR (2)) noise model. The melt temperature response (To = 160s) was fitted by an ARMA (2, 1) type process model and the noise model was fitted by an AR (1) model. The general form for the identified models can be written as:

POLYMER ENGINEERING AND SCIENCE, MID-JULY, 1986, Vol. 26, No. 12 861

M . R . Karnal, W. I . Pat terson, and V. G . Gornes

0 N

*

0 a m w . = m 0 L x \ Y

. O

z w Q .

F N E w w 0 0

w -

I-

a W e I w o I - *

0 - w PI

2

S

2

E . i a

I

a a o m r

a

a 4

EXPERIMENTAL: FRONT ZONE

REAR ZONE

MELT

rEo IIOOEL-

. 1 , ,

700 1400 2100 2800 3500 TINE. SECONDS

Fig. 9a. Temperature responses to +20 percent step input in heater power (dynamic experiment).

0 N

*

0 a m x m w ._ 0 L x . r

$ 4 0

I- - & a - w W

0 0 w - e . 3 N + a a w L E w o + *

0 - w N

-1

E a 0 O F r . 0

.. a

0

TIME. SECONOS

Fig. 9b. Temperature responses to -20 percent step input in heater power (dynamic experiment).

wo - U l B

1 - 61B - B2B2 Y ( k ) = X ( k - d )

The model parameters are given in Table 7. The stochastic model parameters can be suit-

Table 4. Barrel Temperature Model Parameters (Dynamic Experiment).

Rear Zone Front Zone Power Input Gain, K 7 Gain, K (%) (K/%Power) (s) (K/%Power) ~ ( s ) +9.6 1.95 f 0.1 7 7.66 f 130 2.86 f 0.22 689 ? 102 -9.8 1.95 f 0.05 743f 49 3.19 5 0.16 1127 f 115

-14.9 2.41 +. 0.07 1029 f 42 3.52 f 0.22 1192 f 160

-20.0 2.61 f 0.03 1007 ? 15 3.84 ? 0.20 1138 k 90

+14.9 2.49 f 0.02 708 f 25 3.67 f 0.27 986 f 32

+20.0 2.51 2 0.05 1039 f 41 4.05 f 0.10 1043 f 45

Table 5. Melt Temperature Model Parameters (Dynamic Experiment).

Power Time Constant(s) Input Gain, K Time Delay (%) (K/%Dowerl 71 72 (S)

+9.6 2.80 f 0.22 1018 f 380 364 f 142 166 ? 113 -9.8 3.30 f 0.26 1577 f 435 192 f 178 241 f 77

-14.9 3.62? 0.65 1496 f 470 388 ? 190 167 f 50

-20.0 3.53 f 0.18 1238 f 250 357 f 112 96 f 48

+14.9 3.17 f 0.42 990 f 235 284 f 172 136 f 35

+20.0 3.78 f 0.07 1258 f 80 271 f 100 128 f 62

Table 6. Model Parameters from Theoretical Simulations (Dynamic).

Time Con- stant@)

Gain, K Time Delay Experiments (K/%power) 7, 72 (5)

Barrel - +lo% 5.00 1193 -

+15% 4.51 1074 - +20% 4.31 1036 -

- -

Melt + 1 0% 4.98 1206 322 30 +15% 4.48 1072 334 23 +20% 4.29 1022 344 19

ably transformed to yield the corresponding gain and time constant terms in a deterministic model ( 1 9). Table 8 shows the average deterministic model parameters and the corresponding values calculated from the stochastic models. The agreement between the parameters for both the front and rear zone barrel is satisfactory. However, the agreement is not so good for the melt temperature, except the gain and the larger time constant. This is because of inaccurate identification due to the disparity in the two time constants of the melt temperature. An accurate identification would require a short bit interval to identify the high frequencies and a long PRBS test duration to identify the low frequencies. However, the process nonlinearity increases with very long duration experiments, due to loosening of the heater bands.

Stochastic Models-Dynamic Experiment The temperature responses and the 63 bit

PRBS input are shown in Fig. 1 1 . The barrel temperature responses (To = 1 3 6 s ) were fitted with an ARMA (1, 1 ) type process model as in

862 POLYMER ENGINEERING AND SCIENCE, MID-JULY, 1986, Vol. 26, No. 12


Table 7 . Stochastic Model Parameters (Static Experiment).

Experiments 81 82 0 0 w1 61 62 Lr2

Rear Zone 0.91 1 - 0.469 -0.01 2 0.476 0.498 0.139 Front Zone 0.900 - 0.998 0.41 8 0.797 0.173 0.181 Melt 1.349 -0.380 0.138 -0.079 0.901 - 0.188

the static experiments and AR ( 1 ) type noise model. The melt temperature response (To = 1 3 6 s ) was fitted with an ARMA (2, 1 ) type process model and an AR ( 1 ) type noise model, as in the static experiment. The model form for all the responses can be parsimoniously written as:

wo - w ~ B 1 - 61B - 62B2

Y [ k ) = X ( k - d )

The parameters of the model are given in Table 9.

The average deterministic model parameters can be compared with the corresponding calculated values from the stochastic models (Ta- ble 10). The agreement is satisfactory for the barrel temperatures, but it is not so satisfactory for the melt temperature. As noted earlier, accurate identification would require the use of longer PRBS length and longer experiment time (the 63-bit experiment took about 6 h, including 1 h to reach initial steady state values after heating). Apart from the problem of accen- tuated nonlinearity, there are the additional problems of machine malfunction during long duration experiments.

Servovalve Manipulation Experiments The step inputs in servovalve opening during

the plastication phase constitute changes in the back pressure and hence in the screw transla- tional velocity and the screw rotation period. This affects heat generation due to viscous dissipation. Therefore, the melt temperature is ex-

Y) I a' 3 i o o sboo 1b200 tisoo riooo zb too 2baoo TIIIE. SECONOS

Fig. 10. PRBS test-static experiment.

Table 8. Stochastic and Deterministic Model Parameter Comparison (Static Experiment).

Experiments

Stochastic Deterministic



Rear Zone

Front Zone

Melt

Gain, K (K/%power)

5.39 5.1 5

5.81 6.17

6.96 6.53

Time Con- stant+)

T1 12 (s)

2138 - - 2090 - -

Time Delay

1900 - - 1735 - -

2991 175 160 2879 333 73

TIME. SECONDS

Fig. 1 1 . PRBS test-dynamic experiment.

pected to be directly affected by changes in back pressure.

Indeed, Fig. 12 shows that the changes in melt temperature are greater compared to those of the front and the rear zone barrel temperatures. The temperature deviations, in general, are small (about 5 K maximum) and the speed of response is faster compared to the heater power manipulation. The small effect of heat generation by viscous dissipation and hence the small changes in melt temperature, are con- firmed by the value of the Brinkman number (about 0. l), for the average operating conditions used in this study. The Brinkman number is directly proportional to the square of the velocity, hence machines with a higher velocity, usually found in larger machines, will sustain greater temperature changes.

A deviation of 1K in temperature corresponds to a change of about 0.052 mV in thermocouple output. Hence, there is a high probability of the effect of servovalve manipulation being ob- scured by process and measurement noise. Con-

POLYMER ENGINEERING AND SCIENCE, MID-JULY, 1986, Vol. 26, NO. 12 863

M. R. Kamal, W. I. Patterson, and V. G. Gomes

Table 9. Stochastic Model Parameters (Dynamic Experiment). 0 ,

- Experiments 61 62 wo w1 41 fJ2

Rear Zone 0.861 - 0.209 -0.056 0.955 0.554 Front Zone 0.887 - 0.704 0.300 0.962 0.681 Melt 1.570 -0.600 0.145 0.037 0.951 0.731

Table 10. Stochastic and Deterministic Model Parameter Comparison (Dynamic Experiment).

Time Gon- stants(s)

Gain, K Time Delay Experiments (K/%power) ' T ~ ' T ~ (s)

Rear Zone - Stochastic 2.34 912 -

Deterministic 2.49 882 -

Stochastic 3.52 1131 - Deterministic 3.57 1029 -

Stochastic 3.47 1444 327 61 Deterministic 3.37 1263 309 155

- Front Zone

Melt

- -

01 I' L . . Z N D

I- I

a - > W

0 0

W d a a

a a I-

W e o $If

0

*

I

TEMPERATURES I FRONT I01

I

100 200 300 400 sot i' 0

TIME. SECONOS

Fig. 12. Servovalve s t e p tes t responses (+44 and -44 percent) opening.

sequently, the notion of melt temperature reg- ulation by servovalve manipulation was aban- doned.

Interaction Experiments The interaction experiments were performed

in order to determine the extent by which one barrel zone temperature is affected when the input of the other zone is changed. Figures 13a and b show responses to +20 percent in front zone and +20 percent in rear zone heater power inputs, respectively. These responses show that the front zone heater power affects the melt temperature to a greater extent than the rear

#

TEMPERATURES I FRONT I01 REAR 1.1 MELT (XI

0

ui :: 0 290 seo 870 1160 14:

TIME. SECONOS

Fig, 13a. Heater interaction test: +20 percent input to front zone.

0

u) m

0

m d

r o .t E N -. c

> w o 0

a "

W i a

a a 3 I-

W e o r . W N 6 "

9

li

TEMPERATURES 8 FRONT (.I REAR (61 MELT (XI

0

+I 290 580 870 1160 1450 TIME. SECONOS

Fig. 13b. Heater interaction test: +20 percent input to rear zone.

zone heater. Further, the front zone heater primarily affects the corresponding barrel temperature and hardly has any effect on the rear zone. Similarly, the rear zone heater primarily affects the corresponding barrel temperature and has a small effect on the front zone. Con- sequently, these experiments show that the interactions between the heater zones are weak

864 POLYMER ENGINEERING AND SCIENCE, MIDJULY, 1986, Vol. 26, No. 12

A n Injection Molding Study. Part I: Melt and Barrel Temperature Dynamics

and do not require a serious consideration for the purposes of the present study.

Pseudostatic Experiment The pseudostatic tests were performed by

switching the machine from a no-molding to a continuous molding cycle operation. The responses are shown in Fig. 14. Parametric models were not derived from these responses because these serve to demonstrate only the start-up phenomenon and are not crucial for the control objectives of this study.

The overall responses show gradual temperature decreases with time. However, the melt temperature shows an initial steep fall of the curve, which is due to the flow of fresh polymer feed into the barrel and the removal of heat from the system during molding. This phenomenon demonstrates that the disturbances that affect the melt temperature may not be reflected in the barrel surface temperature at all. Hence, better performance is expected by the direct control of melt temperature rather than through barrel temperature control.

CONCLUSIONS A thermocouple at the screw-tip of an injec-

tion molding machine was found suitable for studying the dynamic behavior of the melt temperature. The dynamics of the secondary variables, front and rear zone barrel temperatures were also studied. Numerical solutions for the governing partial differential equations relating to simplified processes were obtained to yield melt and barrel temperature profiles. Both de-

a

E l , , , , , I 0

-0 540 1080 1620 2160 2700 TIME, SECON05

Fig. 14. Pseudostatic test responses with 40 percent heater power.

terministic and stochastic models were developed for the melt and barrel temperatures, and compared with theoretical results. Difficulties associated with deterministic and stochastic modeling were evaluated. The melt temperature was only slightly affected by changes in back pressure.

The interaction between the heater zones was found to be small, and the front zone had a greater effect on the melt temperature response than did the rear zone heater. Further, pseudostatic experiments showed that the disturbances that affect melt temperature may not be observed in the barrel temperature response. Therefore, direct control of melt temperature rather than the barrel temperature is desirable. The evaluation of control strategies based on the study of the process dynamics described in this paper, will be discussed in Part I1 of this work.

ACKNOWLEDGMENTS The authors wish to thank the Natural Sci-

ences and Engineering Research Council of Canada, the Ministere de l'Education, Gou- vernement du Qukbec, and McGill University for financial support. Appreciation is extended to the staff of the machine shop at the Chemical Engineering Department of McGill University for assistance in the construction of apparatus.

NOMENCLATURE

Screw radius, m. White noise. Backward operator, By( k) = Y(k - 1). Barrel inner radius, m. barrel outer radius, m. Time delay, s. Number of lags, multiples of sampling time. Shape factor. Heat transfer coefficient at barrel-air interface, W/m2k. Heat transfer coefficient at barrel-melt interface, W/m2k. Process gain, K/percent Power. Sampling instant. Thermal conductivity at ith node. Differencing exponent. Noise. Resistance. Radius. Sampling time, s. Temperature at ith zone. Melt temperature. Time. Voltage. System input, x( k) = VnX( k). System output, y( k) = VnY( k). Thermal diffusivity at ith node, m2/s.

POLYMER ENGINEERING AND SCIENCE, MID-JULY, 1986, VOI. 26, NO. 12 865

M. R. Karnal, W. I. Patterson, and V. G. Gornes

61, 62, . ‘ . = Stochastic model parameters. & = Thermal emissivity. Cpl, Cp2, . . . = Stochastic model parameters. U = Stefan-Boltzmann constant. U2 = Variance of the residuals. 7 = Time constant, s. uo, wl, . . . = Stochastic model parameters.

Subscripts a = Ambient. i = Spatial node. j = Temporal node.

REFERENCES 1. F. Johannaber. “Injection Molding Machines”, Carl

Hanser Verlag. Munchen (1983). 2. F. C. Harbert and A. G. Forton, Proc. 2nd IFAC Confer-

ence on Instr. and Aut. in PRP Ind.. 8.1 (1971). 3. F. Johannaber and D. Schwittay, SPE ANTEC Tech.

Papers, 26, 146 (1980). 4. G. F. Turnbull, Proc. 2nd IFAC Conference on Instr.

and Aut. in PRP Ind.. 8.5 (1971). 5. R. Schonewald and P. Godley, SPE ANTEC Tech. Pa-

pers , 18.675 (1972).

6. J. W. Peter, SPE ANTEC Tech. Papers, 18.847 (1972). 7. R. T. Maher and H. T. Plant, Mod. Plast . . 51. 78 (1974). 8. S. A. Orroth, N. R. Schott, and R. H. Flynn, SPE ANTEC

Tech. Papers, 20, 56 (1974). 9. T. J. M. Herbertz. Proc. 3rd IFAC Conference on Instr.

and Aut. in PRP Ind., 349 (1976). 10. J. van Leeuwen, Polyrn. Eng. Sci. . 7. 98 (1967). 1 1. Temperature Measurement Handbook and Encyclopae-

dia, Omega Engg., Inc., Stamford, Conn. (1984). 12. M. R. Kamal, W. I. Patterson, D. Abu Fara, and A.

Haber, Polyrn. Eng. Sci., 24, 686 (1984). 13. H. Janeschitz-Kriegl, J . Schijf. and J. A. M. Telgen-

kamp, J. Sci. Instr., 40. 415 (1963). 14. V. G. Gomes, M. Eng. Thesis, McGill University, Mon-

treal (1985). 15. M. D. Mikhailov, M. N. Ozisik, and N. L. Vulchanov,

rnt. J . Heat Mass Transfer, 26, 1131 (1983). 16. R. C. Donovan, Potyrn. Eng. Sci., 11. 361 (1971). 17. 2. Tadmor, S. D. Lipshitz, and R. Lavie, Polyrn. Eng.

Sci. , 14, 112 (1974). 18. S. D. Lipshitz. R. Lavie, and 2. Tadmor. Polyrn. Eng.

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Forcasting and Control”, Holden-Day, San Francisco (1976).


Documents

An injection molding study. Part I: Melt and barrel temperature dynamics