Optimization of the Injection Moulding Process for ... · PDF fileDr.-Ing. Lothar Kallien....

Dr.-Ing. Lothar Kallien. Sigma Engineering GmbH, Aachen.

Optimization of the Injection Moulding Process for Thermoplasts With 3D Simulation


Dr.-Ing. Lothar Kallien

Sigma Engineering GmbH, Aachen



1


1. Introduction

The use of innovative CAE technologies has made it possibleto drastically reduce the time required for process and productdevelopment. A new simulation tool for optimization of ther-moset components has recently become available, and can beused for three-dimensional computation of the mould filling,cross-linking and internal stress buildup on a monitor.

In contrast to conventional programs, the described programoperates with volume elements deriving from the technology ofinjection moulding of plastics. The frequently three-dimension-al geometries of thermoset components are thus depicted in aphysically correct sense.

The flow algorithm for the filling simulation is based on theNavier-Stokes equations, i.e. kinetic effects such as independ-ent stream formation are predicted. Air inclusions that can re-sult from turbulent mould filling are thus detected at an earlystage in mould design and eliminated by optimization.

The mould is three-dimensionally networked and the local tem-perature distribution calculated in the new 3D program. Thus,inhomogeneous temperature zones such as corner effects andtheir influence on the local cross-linking behavior are taken in-to account. Multiple cycles can be simulated to determine thetemperature distribution in the mould during production start-up up to the quasi-stationary state.

After stripping, thermally induced internal stresses, particular-ly as a result of contraction constraints due to metallic inserts,can lead to cracking. The buildup of such internal stress can becalculated and the resultant cracking thus predicted.

2. 2D and 3D Simulation

In developing injection moulded components, simulation pro-grams are used that – based on empirical data and mathemat-ical models - can compute mould filling, the holding and thecooling phase to the point of stripping, and the extent of com-ponent deformation /1,2/. Programs used to date for simula-tion of injection moulding processes rely on geometric informa-tion that approximately describes the upper, lower and middleplanes of the actual geometry. This method of calculation isgenerally referred to as a 2?-dimensional shell model. The on-ly approximate description of the component geometry by amiddle plane can have a negative effect on the quality of theresult. This particularly applies to calculation of componentswith irregular wall thickness /3,4,5,6/. Furthermore, three-dimensional flow effects cannot be resolved, since these

programs always assume parallel laminar flow. Figure 2.1schematically illustrates zones in a plastic component in whichthree-dimensional flow effects develop /4/.

Figure 2-1: Zones of three-dimensional melt flow in injection moulding /5/

3. CAD Transference and Cross-Linking in 3D Including Mould and Inserts

Presently, volume-oriented CAD data exist for the product to becalculated in most cases. These can be imported into SIGMA-SOFT® as STL files. All types of FEM volume networks can sim-ilarly be transferred to SIGMASOFT®. The geometry of themoulding can be expanded to include the injection points orthe mould geometry using an integrated solid modeler.Separation into a three-dimensional volume network is fully au-tomatic. Depending on the complexity of the networking geom-etry, this operation takes only a few seconds to a maximum of2 – 3 minutes. In any case, the complete mould including allcooling and heating channels is networked.

4. Simulation of a Thermoset Component

A water circulation system produced at LM Plast for a Frenchautomobile was simulated in cooperation with the VyncolitCompany. The component is used in PSA-group cars such asthe 106, 206 and 306 Peugeot models and the Saxo, Xsaraand Berlingo Citroen models (Figure 4-1).

Figure 4-1: Citroen Berlingo



2

This involved replacement of a die-cast aluminum componentby a thermoset part. One of the reasons for this substitutionwas the major weight advantage: the aluminum componentweighs 614 g, and the plastic part only 344 g. Figure 4-2shows a direct comparison of the aluminum component (left)and the new thermoset part (right).

Figure 4-2: Comparison of an aluminum (left) and thermoset (right) component

The design geometry was retained essentially unchanged inthis simulation. The component is fabricated in a single-cavitymould. The data were adopted from a CAD System, and sim-ply imported into the preprocessor (Figure 4-3).

Figure 4-3: Transfer of geometry to the simulation

Networking in three-dimensional volume elements is fully au-tomatic. Figure 4-4 shows the networking geometry includingthe sprue.

Figure 4-4: SIGMASOFT® volume model

After the geometry has been entered, the process and ma-terial data must be added. These include the filling time, thevolume flow or filling pressure at the gate, the temperature ofthe thermoset material when injected, the preliminary cross-linking density, the mould temperature and information on thethermal conductivity coefficients of the involved groups of materials.

The density, thermal conductivity, heat capacity as a functionof the temperature and the cross-linking enthalpy of the ther-moset must be known. In order to calculate cross-linking as afunction of the time, cross-linking curves at a minimum ofthree different temperatures must be entered into the program.Figure 4-5 illustrates a cross-linking curve for a temperature of160°C. SIGMASOFT® approximates this process fully automat-ically using the Deng-Isayev model. The actual results and the approximated cross-linking curve are directly compared inthe figure.

Figure 4-5: Cross-linking curve at a temperature of 160°C

The cross-linking reaction during mould filling is also calculat-ed in SIGMASOFT®. This is accomplished using a Cross-Arrhenius formula that describes the viscosity as a function ofthe shear rate, the temperature and the local cross-linking den-



3

sity. If the cross-linking density exceeds a critical value in spe-cific zones, the viscosity rises sharply and flow is no longerpossible. The following formulas describe this relationship.

Alphagel is the cross-linking density at which flow is no longerpossible.

For α ≤ α gel the following term

describes the viscosity as a function of the cross-linking densi-ty, the temperature and the shear rate.

In this case

and

If α ≤ α gel then

Tb: Reference temperature [K]

B: Arrhenius constant [Pas]

τ*: Material constant [Pa]

n: Cross exponent

α gel: Cross-linking density

C1, C2: Constants

The process parameters for the component were as follows:

• Filling time: 5s

• Bulk temperature: 110°C

• Preliminary cross-linking density of the compound during filling: 5 %

• Mould temperature: 170 °C

Mould filling, the cross-linking reaction, cooling to ambienttemperature and the resultant internal stresses were calculat-ed. Figure 4-6 shows the temperature distribution at 85 %mould fill. The compound enters the heated mould at 110°C,and the temperature rises further. The local shear rate is high-est at the gate (Figure 4-7).

Figure 4-6: Temperature distribution at 85 % mould fill

Figure 4-7: Local shear rate distribution in the gate

The flow phenomena can also be visualized using tracer parti-cles. The colors of these weightless particles in Figure 4-8show the ingress age of the particles, whereas the vectors de-scribe the directions and velocities of the particles. Figure 4-9shows the temperature distribution at the conclusion of mouldfilling. The coldest melt is located at the gate.



4

Figure 4-8: Tracer particles visualize the flows

Figure 4-9: Temperature distribution at 100% mould fill

The mould filling process can also be described by the local fill-ing time (Figure 4-10). The pressure required for filling is illus-trated in Figure 4-11. The value at the front flange (arrow)could be verified by an internal pressure sensor in the mould.A pressure of 230 bars was determined at this point.

Figure 4-10: Local filling times in seconds

Figure 4-11: Pressure distribution at conclusion of filling. The arrow showsthe position of the internal pressure sensor in the mould.

Since the compound is injected into the cavity at a preliminarycross-linking density of 5 %, the local cross-linking density hasrisen to 11% at the end of the filling operation (Figure 4-12). Particularly in the vicinity of ribs, where the melt can no longer flow, the compound rapidly heats up and begins to cross-link (arrow). The local cross-linking density has increased to 55 % after 16 seconds (Figure 4-13). The effect ofmould filling is clearly apparent, since the zones that are farther away from the gate are more highly cross-linked by theelevated temperature.



5

Figure 4-12: Local cross-linking density at conclusion of mould filling. Zones such as ribs, which are not exposed to a continuous flow, heat up and cross-link more rapidly.

Figure 4-13: Local cross-linking density after 16 seconds

After 40 seconds, 7 % of the total compound is cross-linked(Figure 4-14). Zones with less than 70 % cross-linking can bevisualized in an “X-ray” view (Figure 4-15).

Figure 4-14: Local cross-linking density after 40 seconds

Figure 4-15: “X-ray” view of zones with less than 70 % cross-linking density

Following cross-linking in the mould, cooling in air to ambienttemperature is calculated. The thermally induced internalstresses outside the mould can be calculated on the basis of aplastic-elastic material model in order to obtain data on de-formation. The stress calculation can be carried out for both isotropic materials and anisotropic, fiber-reinforced thermosets.

The stress calculation assumes that the material is completelycross-linked when the mould is opened. The calculation isbased on the following temperature-dependent, thermome-chanical parameters:



6

• The isotropic elastic modulus or the elastic modulus length-wise and transverse to the fiber direction

• The isotropic coefficient of thermal expansion, or the param-eter lengthwise and transverse to the fiber direction

• The transverse contraction number

In this case, the plastic is a short glass fiber-reinforced mate-rial. The elastic modulus in such a case depends very greatlyon the fiber orientation. The fiber orientation can be three-di-mensionally calculated using SIGMASOF®. Figure 4.16 showsthe fiber orientation in a rib foot. Figure 4-17 shows the localdistribution of the von-Mises internal stresses at ambient tem-perature. Because of the previously mentioned limitation, theresults should be considered qualitative. Figure 4-18 showsthe main stresses along the y-axis. The local shifts can be cal-culated on the basis of these values.

Figure 4-16: Three-dimensionally calculated fiber orientation in a rib transition area. The vectors indicate the direction of the fibers, and the colors show the degree of orientation in the pertinent element.

Figure 4-17: Thermally induced internal (von-Mises) stresses

Figure 4-18: Thermally induced main stresses along the y-axis

Figure 4-19 shows the shifts along the y-axis. The depicted de-gree of deformation is exaggerated by a factor of 50.

Figure 4-19: Shifts along the y-axis

Figures 4.2x show a direct comparison of filling simulations.

4 Export of Results to FE Networks

Using a new interface, both the cross-linking reaction and fiberorientation results can also be exported to finite element net-works. Figure 4.20 shows the three-dimensionally calculatedfiber orientation along the xaxis for a test component. Thisresult can now be exported to a wide variety of finite elementnetworks. Figure 4.21 shows the fiber orientation after beingexported to a finite element network for further processing inABAQUS.



7

Figure 4-20: 3D-fiber orientation in SIGMASOFT®

Figure 4-21: 3D-fiber orientation in a finite element network for further pro-cessing in ABAQUS

Figure 4.22 shows a direct comparison of the filling simulationwith actual filling studies that were later performed. The simu-lation in the top picture offers an excellent view of the connect-ing seam in the component.

Figure 4-22: Direct comparison of the simulation and the result of an experi-mental filling test shows very good agreement even in details (arrow).

5. Thermoset Components With Inserts

The stress calculations are of particular interest when insertsare to be embedded. Holec Holland NV in Hengelo manufac-tures thermoset components for high-tension engineering thatare exposed to as much as 24 kV in later use. Metallic insertsare embedded in the thermoset of these components. The dif-ferent coefficients of thermal expansion of the thermoset andthe metal can lead to stress cracking that affects the operationof the component. At Holec, the SIGMASOFT® simulation pro-gram is used to predict filling, cross-linking and stress buildupduring cooling. An optimized design for the component and themould can thus be developed prior to actual component andmould construction. Figure 5-1 shows the thermoset compo-nent, and Figure 5-2 the insert. Figure 5-3 shows the temper-ature distribution at the conclusion of mould filling. The effect of mould filling on the temperature distribution is alsoapparent in this component.



8

Figure 5-1: High-tension component from Holec

Figure 5-2: Metal insert

Figure 5-3: The temperature distribution at the conclusion of mould fillingshows the effect of this operation

6. Summary

Mould filling, cross-linking, cooling and internal stress buildupduring fabrication of thermoset components by casting or in-jection moulding can be three-dimensionally calculated usingthe new simulation tool. This permits optimization of the com-ponent design and mould prior to production. SIGMASOFT®

operates on the basis of three-dimensional volume elements.The advantages of this new 3D simulation method using volu-metric elements for simulation of thermoset components maybe summarized as follows:

• Model preparation costs are eliminated since CAD data canbe utilized and automatically networked.

• Flow phenomena such as backwater areas in thick-walledzones of mouldings or at points with different wall thicknessare described in physically exact terms.

• Kinetic effects such as independent stream formation maybe predicted.

• Calculation of the cross-linking reaction takes account of thereaction enthalpy.

• Local cross-linking has an effect on mould filling.

• It is possible to take account of the back-pressure of air inthe mould.

• The fiber orientation can be calculated in three dimensions,and used for stress analysis.

• The thermally induced buildup of internal stress during cool-ing can be calculated.

• Thermal effects on the flow and cross-linking processes areaccounted for by the three-dimensionally coupled calcula-tion of the moulding, inserts and mould.

• The consideration of heating systems is three-dimensional;the local effect on the mould wall temperature is calculated.

• The cycle time can be predicted.

References

1. H. Bogensberger, Kunststoffe 85, 44 ff (1995).

2. P.F. Filz, Kunststoffe 88, 954 ff (1998).

3. B. Ohlsson, First International Thermoset Symposium in Iserlohn, MärkischeFachhochschule Iserlohn

4. P. Thienel, International Mould Construction Symposium 1999, Dr. ReinholdHagen Stiftung, Bonn

5. W. Michaeli, H. Findeisen, and T. Gossel, Kunststoffe 87, 462 ff (1997).

6. O. Altmann and H.J. Wirth, Kunststoffe 87, 1670 ff (1997).

7. A.J. van der Lelij, Kunststoffe 87, 51 ff (1997).

Optimization of the Injection Moulding Process for ... · PDF fileDr.-Ing. Lothar Kallien....

Documents

Transcript of Optimization of the Injection Moulding Process for ... · PDF fileDr.-Ing. Lothar Kallien....