Simulation of the injection molding process with a special capillary rheometer.

When injection molding rubber compounds, adequate mold filling is an essential requirement. Mold filling depends on pressure, temperature, mold geometry and the flow behavior of the compound. The overlapping of flow and scorching during the injection phase is a particularly crucial factor in determining the degree of mold filling.

This article sets out to investigate the possibility of obtaining reliable information about the injection molding process by means of laboratory tests, mainly using the Gottfert Rheovulkameter (ref. 1). This would reduce the amount of valuable time lost when tests are carried out on production machinery. The scope of this investigation was restricted to two target functions: degree of filling and injection time.

As far as is known, the Rheovulkameter has so far mainly been used for comparative tests on various compounds. To date no simulation tests for production machinery have been carried out (ref. 2).

Machinery and equipment

Laboratory equipment

The following items of typical laboratory equipment were selected: Mooney viscometer; High-pressure capillary rheometer; Curemeter.

The Rheovulkameter consists basically of a laboratory-scale model of an injection molding machine without a screw. Function-wise, it consists of a capillary rheometer with a cylinder, piston and capillary plus a mold into which the crosslinkable rubber compound can be injected.

A spiral mold was used. A two-channel recorder which measures the piston stroke can be used to record the volume and speed of the material during the injection process. These data are also displayed in digital form as maximum values. The main target function - the degree of mold filling - can be determined by means of volume measurements or by weighing the molding. This will eliminate any losses caused by reverse flow at the piston. The volume curve can also be used to determine the injection time.

The set-up parameters consist of pressure and temperature in three zones (the piston, the nozzle and the mold).

Production machinery

Practical trials were carried out on two production machines. These were: A Desma 962 (clamping force 80 kN, injection pressure 1,500 bar, shot volume 400 [cm.sup.3]; spiral mold; and a Werner and Pfleiderer GSP 400 (clamping force 426 kN, injection pressure 1,900 bar, shot volume 3,900 [cm.sup.3]; axle boot mold.

Test compounds

An injection molding compound based on an acrylonitrile butadiene rubber was taken as a starting material and its viscous behavior was systematically modified by varying the polymer. The recipes are given in table 1.

Table 1 - recipes for the test compounds

                     K101B   K102B   K103B   K104B
NBR (28% ACN,         100      -       -       -
 Mooney 31)
NBR (28% ACN,          -      100      -       -
 Mooney 47)
NBR (28% ACN,          -       -      100      -
 Mooney 67)
NBR (28% ACN,          -       -       -      100
 Mooney 92)
Carbon black N-660    60      60      60      60
Ester plasticizer     30      30      30      30
Colophonium            3       3       3       3
IPPD                   2       2       2       2
ZnO                    5       5       5       5
Sulfur                2.4     2.4     2.4     2.4
CBS                    1       1       1       1
TMTD-80%              0.25    0.25    0.25    0.25

Using Mooney (ML 4 (Mooney viscosity [ML (1 + 4) 100 [degrees] C], MR [Mooney relaxation]) and curemeter (ML[minimum torque], MH [maximum torque], [t.sub.10], [t.sub.50], [t.sub.90] [time taken to reach 10, 50 and 90% crosslinking]) measurements under standard conditions (Mooney 100 [degrees] C; curemeter 160 [degrees] C), these four compounds were first characterized and displayed in figure 1 normalized to a reference compound. Normalized means that the values for a reference compound (no. K 102 B) are shown as 100% or 1.0, and all other values are referred to this. It is clear from the diagram that this polymer variation only affects the viscous test values ML 4, MR and ML. The crosslinking rate remains unchanged. These differences in flow behavior would lead one to expect corresponding differences in the injection molding process.

In addition to these standard measurements, measurements were also carried out over a wide range of shear rates and temperatures in the HCR. It was only possible to measure the dependence of viscosity on temperature up to about 120 [degrees] C in the HCR, because at higher temperatures the material begins to scorch in the capillary. Additional measurements therefore have to be obtained in the MDR when determining the energy of activation (e.g. at 160, 180, 200 [degrees] C).

The family of curves shown as an example in figure 2 illustrates the dependence of viscosity on shear rate and temperature.

Injection trials with the Rheovulkameter

The Rheovulkameter has a number of advantages over larger machines in terms of the amount of material required, temperature control and handling. It was therefore decided to use the Rheovulkameter to analyze the fundamental behavior of an injection operation and to determine the main influencing parameters. The spiral mold used had the following dimensions: length of spiral channel: 60 cm; cross section: 2.5 x 4 mm; volume: 7 [cm.sup.3] (= 100% degree of filling). The spiral is open at the end to allow filling in excess of 100 %. In the diagrams these areas are crosshatched.

Dependence of the degree of filling on mold temperature

All the compounds were run at various mold temperatures with the pressure set at the maximum safe limit of 95 bar (= 280 bar at the injection piston). The tests were continued until volume equilibrium was obtained.

At low temperatures, however, this leads to extremely long test cycles. In this fundamental study, interrupted flow processes of the sort obtained in injection molding technology by pre-setting of injection speeds and times would have prevented the expected relationships from emerging so clearly. In order to ensure reliable evaluation, injection time was defined as the time taken for 95% of the attainable volume to be filled.

Figure 3 shows the degree of filling for each of the compounds as a function of mold temperature with the piston and nozzle temperatures at a constant 100 [degrees] C. The result is a typical family of bell-shaped curves, each of which passes through a maximum. The left-hand section of the curve is characterized by viscous flow because flow resistance in the mold becomes less as the temperature increases. Thus, longer spiral flow paths are covered and ever greater degrees of filling result. The right-hand section of the curve reflects a decline in the degree of filling caused by the onset of scorching.

As figure 4 shows, the same test carried out on a compound containing no crosslinking agents results in increasing degrees of filling with an asymtotic curve, The absence of sulfur additionally causes a lower level in the degree of filling.

Influence of pressure

Figure 5 shows the influence of pressure on the degree of filling. With the temperature at 140 [degrees] C, setting different pressures resulted in a linear correlation between the degree of filling and the pressure. Thus, varying the pressure represents a simple method of adjusting the degree of filling (to 100%), provided the equipment has sufficient pressure reserves available. However, pressure also affects the position at which the bell-shaped curve reaches its maximum. As the pressure increases, injection times become shorter and the position of the maximum tends to shift towards higher mold temperatures.

Influence of capillary diameter

There is always a correlation between the influence of capillary diameter (i.e., gate design) and the geometry of the entire mold.

Figure 6 shows that the difference in the degree of filling between the standard diameter of 2 mm and the smaller diameter of 1 mm is greater than that between the standard diameter and the large diameter of 4 mm, which roughly corresponds to the cross section of the spiral channel. No change is observed in the position of the maximum degree of filling, however.

Pretreatment

The Rheovulkameter does not utilize a screw, so an attempt was made to simulate the effect of a screw by premastication of the compound on a laboratory mill. However, this produced no significant differences. Pre-heating the compound with hot air also has practically no effect.

Temperature of the injection piston and the capillary

The last influencing parameter to be investigated was the temperature of the injection piston (piston temperatures 60 [degrees] C and 100 [degrees] C). Although the position of the maximum does not shift, there is a slight change in the level of the degree of filling.

Injection molding trials on production machines

Computer-controlled production machines enable different programs to be run. Speed or time-determined methods of operation with maximum pressure settings are often used.

To ensure a reliable comparison with the Rheovulkameter, however, we wanted to carry out injection molding trials at a constant pressure and measure the injection time and degree of filling. This method of operation could only be achieved on these machines through manual control, however. Heat losses through radiation from the moldings were so great that corrections based on surface measurements had to be made even when setting the mold temperature. The temperature of the injection piston was set at a constant 60 degrees] C, because the long-drawn-out flow trials made lengthy screw dwell times inevitable. After preliminary trials, the pressures were set so as to ensure an adequate differentiation between the individual "degree of mold filling" curves (Desma: 67 bar hydraulic pressure = 312 bar piston pressure; GSP: 30 bar hydraulic pressure = 235 bar). For technical reasons, the trials on the Desma machine were run for a maximum of 200 s (figure 7).

The bell-shaped curves from this test reach their maximum at about 140-160 [degrees] C. These flow trials were unfortunately interrupted by the machine before they were complete - particularly those carried out at lower temperatures. By bypassing the installed software, however, the trials on the GSP 400 were continued for a maximum of eight hours, until the flow processes had really come to an end figure 8).

This diagram shows that the maxima have undergone a significant shift to lower temperatures.

Unlike the Rheovulkameter, the molds used on the production machines have no outlet at the end, so degrees of filling in excess of 100% are unobtainable in practice.

Scale-up and application

Experimental and qualitative scale-up

In terms of scaling up the laboratory results to production machinery, one positive factor is the marked similarity between the "degree of filling" curves. The gradations of the different types of polymer, as shown in the Rheovulkameter, are also reflected - at least qualitatively - in the families of curves for the production machines (refs. 7, 13 and 14).

An area of processability exists wherever the degree of filling curves touch or cross the 100% line.

The pressure on the Rheovulkameter cannot be set higher than 100 bar, which means that the curves plotted at 95 bar represent the practical upper limit for this piece of equipment. On the production machines the pressure was set sufficiently low to ensure an adequate differentiation with all the compounds.

This increase in pressure means, of course, that even the harder compounds can attain a 100% degree of filling. It is nevertheless conceivable that there

may be molds with a higher flow resistance which could not be completely filled even at the highest pressures.

An initial scale-up can be effected by plotting the degree of filling/temperature functions of the relevant compounds and taking a standard setting in the Rheovulkameter as a starting point.

For practical purposes the temperature range above the maximum degree of filling is sufficient, because lower temperatures preclude economical processing on account of the lengthy cure times.

Similar trials are to be carried out on the production machine, with the optimum pressure being experimentally determined. An unknown compound, for example, could be run in the Rheovulkameter to determine its position in the existing family of curves, which can then be transferred to a corresponding position in the family of curves for the production equipment.

Given the large amount of testing involved in this qualitative, empirical procedure, one would be justified in asking whether it would be possible to use a theoretical method in order to reduce the number of measurements.

Theoretical scale-up

The bell-shaped curves shown in figure 3, for example, are produced by the overlapping of two influences which have an opposite effect. These are: viscous flow, which is dependent on temperature and shear rate, in the low temperature range, and the onset of the crosslinking process, which is determined only by temperature, in the high-temperature range.

Viscous flow

Viscous flow can be described in terms of the expanded Newtonian equation

T = N [Y.sup.n] and In T = In N + n [multiplied by] InY where T = shear stress at the capillary wall; N = viscosity; Y = shear rate; n = flow index.

Taking the logarithm shows that a double logarithmic plot yields straight lines. This is a well-known form for representing HCR flow curves (figure 2).

The simplified form of the Arrhenius equation (ref. 3) gives:

v = [e.sup.-A/RT] and In v = -A/RT [multiplied by] I/T where: v = reaction rate; A = activation energy; R = general gas constant; and T = temperature (absolute).

Taking the logarithm yields descending straight lines in a semi-logarithmic form In v = f (I/T) (plotted as an Arrhenius function).

Figure 9 shows that the dependence of the viscosity of rubber compounds on temperature can also be represented as straight lines in an Arrhenius plot. From the measurement point of view, this means that two measuring points per compound are sufficient.

Scorching

DIN Standard 53 529 (ref. 4) shows in some detail that the dependence of curing times on temperature can also be illustrated very clearly with the aid of an Arrhenius equation.

Analysis of the bell-shaped curve

If an entire bell-shaped curve (e.g., compound no. 102, figure 3) is plotted as an Arrhenius function with respect to its reciprocal injection times, the result is a set of straight lines with a kink in the middle (figure 10). The section on the left which is determined by crosslinking (high temperatures) follows a virtually identical path to that of the scorching times of the curemeter [t.sub.10]. The kink indicates the maximum, while the right-hand section (low temperatures) represents viscous flow.

Flow resistance of the mold

Reciprocal injection times can be calculated from the HCR measurements by taking into account the particular temperatures and shear speeds for the capillary (minus mold) of the Rheovulkameter:

I/t = [pi]/128 [multiplied by] P/V [multiplied by] N [multiplied by] [D.sup.4]/l (Hagen-Poiseuille, ref. 5) where: p = pressure; D = diameter of the capillary; I = capillary length; V = volume; N = viscosity.

These values, which represent only viscous flow, yield a straight line which runs parallel to the second half of the bell-shaped curve. If this straight line is shifted by parallel displacement to cover the bell-shaped curve, the flow resistance of the entire mold is obtained. The flow resistance for the Rheovulkameter spiral can be estimated by calculation if the rectangular cross section of the spiral channel is reduced to a circular cross section having the same area, and an assumed uncurved section of 65 cm length. For the geometry factor

[D.sup.4]/l = 1.2 [multiplied by] [10.sup.-4] [cm.sup.3] and from the curve shift you then get a similar value of 1 [multiplied by] [10.sup.-4] [cm.sup.3]. The error of approximately 20% is acceptable for such a rough estimate. Since calculation is difficult with complex molds, this provides an empirical means of determining the flow resistance of injection molds.

Analysis of practical trials

The GSP and Desma values for compound 102 are also plotted as an Arrhenius function in figure 11. Although these measurements are not as accurate as those obtained with the Rheovulkameter, similar relationships can be discerned. In the high-temperature area the curves can clearly be seen to deviate from the [t.sub.10] line. These deviations were explained by insert a probe into the rubber compound to measure the internal temperature at the end of flow time. Figure 12 shows a difference in temperature of approximately 40 [degrees] C at 200 [degrees] C, for example. A broadly similar error is also found with the Rheovulkameter, but not until a temperature of 220 [degrees] C has been reached. The temperature therefore needs to be corrected.

Processing window

If a curve of constant degree of mold filling is determined instead of the bell-shaped curve at constant pressure, and if this curve is plotted as an Arrhenius function, taking compound 101 with a 40% degree of filling as an example, the path followed is similar to that of the normal curve. If constant degrees of filling are to be achieved, the pressure must be varied, and in this example we find a pressure minimum at 100 [degrees] C. In principle, a curve of this sort is also conceivable for a 100% degree of filling, but at present this cannot be measured on the Rheovulkameter, because the pressure is inadequate.

In the Arrhenius plot shown in figure 13, this line represents the limit for possible processing, because any shift to the left in the direction of higher temperatures would mean that filling was no longer adequate. The area of processability is therefore situated on the right-hand side of this curve and is further defined by a differently angled line for viscous flow which is calculated for the maximum pressure of the machine, and a vertical temperature line to the right, resulting in a triangle.

In technological terms, this limiting temperature is determined by curing times (e.g., [t.sub.90]) which can still be considered cost effective.

This processing window (crosshatched area) can be constructed simply on the basis of measurements made with the curemeter and the HCR, plus at least one low-temperature flow trial on the production machine.

This window gives the possible area of processability with respect to injection time and temperature. Since there is no strict correlation between injection time and degree of filling, some production machine trials still have to be carried out to confirm that the degrees of filling are adequate. In this respect the experimental, qualitative scale-up method described earlier helps to reduce the number of trials required.

Summary and further measures

In an experimental study, comparative injection molding trials were carried out on four rubber compounds with different viscosities using two production machines and one Rheovulkameter. In addition to these measurements, the standard laboratory methods of cure testing and high-pressure capillary testing were also used. With respect to two target functions which are crucial for injection molding, namely degree of mold filling and injection time, similar relationships were obtained on all three machines. These were represented by the dependence of the degree of mold filling on mold temperature.

The various compounds yield a family of bell-shaped curves whose level is determined by the flow resistance of the mold and the viscosity of the compound, but whose position is determined by the flow rate and by pressure. It is therefore advisable to carry out preliminary trials on the Rheovulkameter if using unknown compounds.

By analyzing the bell-shaped curve with the aid of the Arrhenius equation, a triangular processing window identifying possible areas of processability for injection time and temperature can be constructed in the Arrhenius plot. This evaluation also indicates a way of determining the flow resistance of complex molds.

These trials are to be continued using various other compounds, concentrating particularly on types with different crosslinking rates. The conclusions drawn from the construction of the processing window need to be confirmed by further experiment.

References

[1.] Gottfert, O., "The Rheovulkameter, a test device for providing a rapid assessment of the processing characteristics of rubber compounds" Kautschuk + Gummi, Kunststoffe, no. 10, vol. 35. Jg. (1982), pp. 849-857. [2.] Kilthan, G. and Wiegang, N., "Comparison of test methods for monitoring the processing characteristics of rubber compounds, " VDI-K (1981), SpritzgieBen technischer Formteile, VDI-Verlag. Moos, K.H., "Rheovulkameter, " Intern. Polymer Processing III 1982) 2, pp. 86-90. Ehrend, H., "Rubber compounds which can be injection molded," VDI-Kunststofftechnik (1988) pp. 25-50, VDI Verlag. Bouton, J., "Rheometry as a guarantee of the quality of rubber compounds. Caoutch. Plast. 65 (1988) 682, p. 99. [3.] Arrhenius, S., "The rate of reaction in the inversion of cane sugar by acids." Z.F. Phys. Chem. 4 (1989), p. 226, Leipzig. [4.] DIN-VDE (paperback), Kautchuk u. Elastomere 1, Phys. Prufverf., (1988), Beuth-Verlag, Berlin. [5.] Schwarzel. F.R., "Polymer technology," Springer-Verlag (1990), p. 42.