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# Modeling Techniques

This chapter describes geometry modeling techniques for the part and melt-delivery systems as well as the mold cooling systems. These techniques are mainly intended for injection molding and gas-assisted injection molding applications. You'll also find helpful information on special-purpose modeling techniques for blow molding and thermoforming, transfer molding for microelectronics encapsulation, and structural-reaction injection molding.

# Injection Molding

## General Procedures for Injection Molding

This section describes the general procedures for geometry modeling using C-MOLD Modeler. The major task in geometry modeling is to describe the part (e.g., Figure 3-1) by a finite-element mesh (e.g., Figure 3-2) that carries the proper dimension and attribute information.

Figure 3-1. Geometry of an injection-molded part, including sprue, runner, and gate.

Figure 3-2. Finite-element mesh of a single cavity, plus cooling channels. Counterpart is modeled by specifying connector multiplicity factor.

### Attributes

This section describes several of the attributes and how they are utilized in modeling. For an introduction to attributes, see "Attributes Editor" in Chapter 2; for a description of individual attributes, see Chapter 5, "Command Reference," and for a complete list of attributes and their default values, refer to Appendix A.

#### Diameter and shape factor

Diameter and shape factor are 1-D element attributes used to incorporate the actual geometry features. The diameter is specified as the actual diameter for a circular cross section of the element, and the shape factor is equal to 1. The diameter of a baffle or a bubbler is the diameter of the hole drilled in the mold.

Figure 3-6. Definition of equivalent diameter and shape factor of a rectangular tube.

When 1-D elements are used to model a section of sprue, runner, or gate, the shape factor should always be equal to 1 (circular) or greater than 1 (non-circular). Allow exceptions, however, when 1-D elements are used in conjunction with the triangular elements for modeling gas channels in the parts. The shape factor can be less than 1, depending on the geometry, as detailed on page 3-55. For the same equivalent diameter, a larger shape factor means the cross section is more irregular and has more cooling effects from the wall, as well as greater flow resistance from the cross section. C-MOLD analyses automatically adjust these two effects for 1-D elements, based on their respective shape factors. Table 3-1 lists the equivalent diameter and shape factor for several commonly used 1-D geometries.

#### Thickness and shape factor

Thickness and shape factor are attributes for triangular elements, similar to diameter and shape factor used for 1-D elements. When a surface has a regular cross-section (flat on both sides), the thickness is specified and the shape factor is equal to 1. However, surface patterns are frequently used in plastic part designs for appearance and functional reasons. There are two ways to model parts with surface patterns: use elements that are smaller than the feature in the surface patterns, or use elements with an equivalent thickness and a shape factor to correct for the additional cooling and flow resistance from the surface patterns. The first method could result in a very large number of elements for models with small features in the pattern. The second method is a more efficient way to solve practical problems.

The shape factor for a triangular element is defined as the ratio of the actual contact surface to that of the equivalent flat surface. A slab-like surface is shown in Figure 3-7. The equivalent thickness and shape factor are calculated from one basic unit of the pattern, which is repeated.

Figure 3-7. Equivalent thickness and shape factor of a slab-like surface.

There are two ways to model geometries with grills, depending on the relative dimensions of the grill and the mesh size. If the length of a grill segment is larger than the mesh size, as in Figure 3-8(a), the grills should be modeled by 1-D elements with the proper equivalent diameter and shape factor, as described above. But, if the grill size is small in relation to the mesh size, the total grid area should be modeled as triangular elements with an equivalent thickness and shape factor, as shown in Figure 3-8(b).

Figure 3-8. Modeling geometries with grills. (a) Grill size is larger than mesh size. Use 1-D elements with equivalent diameter and shape factor to model the grill. (b) Grill size is much smaller than mesh size. Use triangular elements with equivalent thickness and shape factor to model the grill.

#### Initial Fill

The initial fill condition is used to determine whether or not a part element is filled with polymer at the beginning of the injection cycle. Its purpose is to differentiate between hot and cold runners. A part element is `Empty` (= 0), unless otherwise specified with this element attribute. Two more conditions can be specified for a part element. `Filled At Inlet Melt Temp.` (= 1) indicates that the element is initially filled with polymer at inlet melt temperature. `Filled At Hot Runner Mnfld. Temp`. (= 2) indicates that the element is initially filled with polymer at its wall temperature. Note that the initial fill condition applies to both 1-D plastic elements and triangular plastic elements. C-MOLD Modeler automatically assigns `Empty` to all triangular elements, cold runners, and part runners, and assigns `Filled At Inlet Melt Temp.` to all hot runners.

#### Hot Runner Manifold ID

When creating a hot runner, C-MOLD Modeler requests a hot runner manifold ID, which points to the hot runner manifold control specified as one of the process conditions. C-MOLD analyses use the temperature specified in the associated hot runner manifold control as the wall temperature of a hot runner.

#### Connector Multiplicity

A special element type called a connector is available for convenience when modeling symmetric parts or multi-cavity molds. The connector, which connects two nodes in the finite-element mesh, can be used in three applications: to include symmetrical branches without modeling all of them (the connector is considered to be a multiplier); to better represent runner/runner or runner/cavity connections to avoid significant volume overlapping that may cause inaccuracy in overall volume calculation and numerical problems for mold cooling analysis; and to model valve (shut-off) gates that open and close at different times.

Figures 3-9 and 3-10 indicate the applications of connectors for multi-cavity systems and symmetric parts. The numbers next to the connectors are the multiplicity factors; the arrows indicate the directions in which the number of cavities should be multiplied. That is, a connector has an orientation when its multiplicity factor is greater than 1.

In most cases, the orientation of a connector should be along the polymer flow, from upstream to downstream. There are exceptions, as indicated in Figure 3-10(c), where a connector with a multiplicity factor of 2 at the merging point is oriented against the flow direction. This is because there are two identical branches from upstream, meeting at the merging point.

Figure 3-9. Use of connectors to model multi-cavity systems.

Figure 3-10. Use of connectors to model symmetric parts.

### General Modeling Tips

#### Tips for Surface Creation

All surfaces in C-MOLD Modeler must be topologically equivalent to a rectangle (i.e., they must be bounded by four edges). Degenerate cases will fail to mesh. For example, revolving a 90 degree arc around a line that shares an end point with the arc to create a hemisphere creates a degenerate case (one edge of the equivalent topological rectangle collapses to a single point). A bounded surface consisting of three curves that form a triangular patch would be another illegal surface. Note that creating geometrical surfaces is a different issue from creating surface regions, which do not have to map to rectangles.

When creating a revolved surface, the position on the axis of revolution where you pick with the mouse is important. The line chosen to be the axis is considered a directed line, whose starting point is the end point closest to where you picked. The right-hand rule of rotation is then applied, using this directed axis (Figure 3-11).

Figure 3-11. Creating a revolved surface.

The starting point is the end point of the entity closest to where you picked. The curves generated to complete the lofted surface will go from starting point to starting point, so if you pick, for example, two lines at "opposite ends," the resulting surface will be "twisted" and any mesh generated from it would be illegal (e.g., Figure 3-12).

Figure 3-12. Creating a lofted surface.

C-MOLD Modeler will not attempt to extend one entity to meet another.

This occurs because C-MOLD Modeler smoothly interpolates control points for the surface boundary, whereas the entity used might not have such smoothing. (This is most likely to happen when using splines as boundaries). While displays could show some discrepancy as a result, mesh nodes along the boundary are guaranteed to lie along the original entity.

#### Tips for Surface/Surface Intersection

A simple instance of this case is two cylinders of equal diameter whose axes of revolution are coplanar (i.e., an X-joint pipe piece). Another simple case is two cylinders that touch each other: the intersection would be the common tangent line. If you really need such a tangent point or curve for your model, form the surfaces such that the tangents fall on the boundary curves of both surfaces (i.e., split the cylinder into four "swept arc" surfaces), as shown in Figure 3-13.

Figure 3-13. Surface/surface intersection.

#### Tips for Projecting Entities to Surfaces

The entity must not extend beyond the edge of the surface, nor can it cross the surface's seam, if any. If you need to do such a projection, first create a swept surface; use the entity to be projected such that the intersection of the swept surface with the original surface will be the desired projection of the original entity. (Note that such a swept surface intersection will then be subject to the limitations noted above). Then intersect the surfaces to create the desired curve.

C-MOLD Modeler assumes that the intersection set is a finite set of points, which is not the case when the entity lies on the surface.

#### Tips for Surface Region Generation

Use the command Edit Geom.; Break Edges; Break Edges on Surfaces to pick two curves on the same surface. The order in which you pick the curves is not important (both entities get broken), but the position where you pick on the curves is. You need to pick close to the intersection point where you want the curves broken, because C-MOLD Modeler breaks at only one intersection point, and uses the pick location to decide where to break. Then, before creating a surface region, you might want to delete superfluous entities on the surface. Do not delete entities that form the boundary edges of the surface.

The auto. search for region generation will occasionally be unable to determine what constitutes a region. We haven't isolated any hard-and-fast rules to warn you when this might occur; if it does, turn off Auto. Search and pick all the edges manually, in sequential order of the desired region.

## Part and Delivery System in Injection Molding

This section discusses the general geometric modeling techniques for the part and delivery system. These modeling techniques provide basic guidelines for constructing finite-element meshes of typical injection molded parts. The objectives are to yield more accurate predictions, as well as to allow more efficient computation. These techniques are applicable to any geometry modeler and mesher.

#### Model the part on the mid-surfaces; model runners along the axes.

There is no need to create a solid model (a model with part thickness). C-MOLD analyses use two-dimensional, triangular elements, and 1-D elements with the attributes of thickness and diameter, respectively. To maintain correct spatial relationships, triangular elements should be modeled on the mid-surfaces and one-dimensional elements should be modeled along the axes of a part and its delivery system.

#### Define major surfaces first, then add the details.

Elaborate reproduction of geometric details is not necessary. Don't labor over the small details of the geometry, such as round corners or small holes (e.g., Figure 3-14); for modeling, these details require many small elements, even with a variable mesh density, but do not influence the overall melt-front and pressure predictions. They can, therefore, be simplified by using a square corner to approximate a round corner, and so on. Care should be taken to match the volume of the modeled part and the actual part as closely as possible.

Figure 3-14. Details smaller than the mesh size on the part can be omitted in modeling

### Using 1-D Elements for the Delivery System

A delivery system can be described by using runners and/or connectors. To create a runner, supply the runner attributes and two points to define the runner. Runner attributes include runner type, starting diameter, tapered half-angle, and shape factor.

Figure 3-15. Geometrical definition of a tapered runner.

To modify runner attributes, see "Attributes Editor" in Chapter 2. For convenience in modifying a tapered runner, you can specify the ending diameter, instead of using a tapered half-angle.

If the volume of a delivery system is significant in the overall mold design, it is important to conserve the runner volume in the model. We strongly suggest that connectors be used for this purpose. In Figure 3-15(b), connectors are used between a sprue and a primary runner, and between a primary runner and a secondary runner, to avoid overlapping. We also suggest you use connectors to model naturally balanced multi-cavity systems or symmetric parts, as discussed in "Connector Multiplicity" on page 3-15.

Figure 3-16. Modeling of delivery system, where (a) runner volume is not conserved, and (b) runner volume is conserved.

#### Pin gates

Pin gates are modeled by a small section of a cold, solid runner.

Figure 3-17. Pin gate, shown with hidden element lines.

#### Submarine gates

Submarine gates are modeled by tapered runners.

Figure 3-18. Submarine gate, shown with hidden element lines.

#### Tab gates

Tab gates are modeled as regions with a small gate thickness. Connectors are used to ensure the tab gate entrance nodes have the same conditions as at the end of the runner.

Figure 3-19. Tab gate, shown with hidden element lines.

#### Fan gates

Fan gates are modeled as regions. If the thickness of the fan gate varies, two or three regions should be used, each with a different assigned thickness.

Figure 3-20. Fan gate, shown with hidden element lines.

#### Valve gates

Valve (shut-off) gates are modeled as solid runners with an equivalent diameter and shape factor. A connector must be attached to the end of a valve gate to control the delayed opening in sequential process control, as discussed earlier.

Figure 3-21. Valve gate, shown with hidden element lines.

#### Edge gates

Edge gates (film gates) are an extension of the part and are designed to fill uniformly across the width of the part. They should be modeled by cold runners with connectors to the film-gate region. The runner length should be equal to the desired mesh size in the film gate, so a connector can be placed at every node in the runners to connect to the film gate.

Figure 3-22. Edge gate, shown with hidden element lines.

#### Ring gates

Ring gates are modeled by cold runners and linked to the cavity with connectors. Similar to edge gates, the runner length should be equal to the desired mesh size in the ring gate. Connectors are placed between nodes in the runners and the cavity.

Figure 3-23. Ring gate, shown with hidden element lines.

### Tips for Modeling the Part and Delivery System

The aspect ratio of triangular elements is important to the accuracy of the solution, especially in sensitive areas such as gates, or gas channels in a gas-injection simulation. The rule of thumb is that the average aspect ratio of triangular elements should be less than 5. Triangular elements with an aspect ratio greater than 10, as reported by the analysis, should be modified.

The aspect ratio of a triangular element is defined in Figure 3-24. Triangular elements with smaller aspect ratios are more suitable for the analyses. The minimum aspect ratio is equal to 1 and occurs with an equilateral triangle.

Figure 3-24. Aspect ratio of a triangular element.

The flow calculation in a triangular element considers only the drag force and heat conduction from the top and bottom surfaces. The side wall effects are not included in the flow calculation in these elements. Decreasing the element size gives a better definition in terms of melt-front advancement, but at the expense of more CPU time. In contrast to the element aspect ratio, as described above, the element size-to-thickness ratio (Figure 3-25) does not change the accuracy of the solution, or the fact that the side wall effects are not considered. Such effects are important in certain geometries, and are discussed in later sections.

Figure 3-25. Element size-to-thickness ratio does not change the accuracy of the solution

The thickness of a triangular element or the diameter of a one-dimensional runner element has a significant influence on flow resistance and heat transfer. In isothermal filling (without considering the cooling of polymers), the sensitivity of the flow resistance to the thickness or diameter is given by:

###### (3.2)
where t is the thickness of the triangular element, and d is the diameter of the one-dimensional runner element. Reducing the thickness of triangular elements by 10 percent results in a 37 percent increase in flow resistance.

###### (3.4)
Reducing the thickness of triangular elements by 10 percent results in about an 18 percent increase in the pressure drop. If cooling effects are included, however, the increase of the pressure drop is even greater. Note that the pressure drop is more sensitive to the diameter of runners than to the thickness of triangular elements.

###### (3.6)
Reducing the thickness of triangular elements by 10 percent results in about a 19 percent saving in cooling time. The cooling time of a runner is proportional to a value between the diameter and the square of the diameter. Since there is no simple expression for this correlation, the average exponent, 1.5, is used as a good approximation in Equation 3.6.

Thickness (diameter) and shape factor have major affects on the pressure and cooling time predictions; thus, correct dimensional information must be specified in the model to obtain accurate predictions. Surfaces with different thicknesses or with surface patterns should be modeled as different regions with the appropriate information assigned to each region, as shown in Figure 3-26. For large parts with variable thickness, divide the surface into several regions and specify the average thickness and shape factor over each region.

Figure 3-26. Modeling a surface with different thicknesses.

Pins that extend from a surface can be modeled as part runners. Bosses with a diameter smaller than or equal to the mesh size can also be modeled as part runners. The equivalent diameter and shape factor can be found in Table 3-1. Bosses or cylindrical surfaces with a diameter larger than the mesh size can be modeled as surfaces, with the actual wall thickness assigned to triangular elements.

In the case of a thin cavity, the shear region from the side wall affects only a small portion of the flow, about two times the part thickness as shown in Figure 3-27(a), and can be disregarded. Triangular elements should be used to model this kind of geometry, and the shear and cooling from the side walls is thus neglected. However, if the thickness-to-width ratio of a flow channel is in the order of 1 to 4, the shear and cooling from the side walls become important and can affect the calculation significantly. In this case, part runners should be used, as shown in Figure 3-27(b), so the shear and cooling from all the contact surfaces are considered.

A typical example can be seen on computer housing grills, where the width of a grill is the same as the thickness. Part runners should be used to model the flow in this region. It is still possible to model such one-to-four ratio flow channels with triangular elements, as shown in Figure 3-27(b). The shear and cooling effects from the side walls can be corrected with an equivalent thickness (t) and shape factor (). The total number of elements in the model increases, however, if triangular elements are used instead of part runners.

Figure 3-27. (a) Triangular elements for thin cavity surface. (b) Part runners or triangular elements for flow channels with thickness-to-width ratio of 1 to 4.

## Mold-Cooling System in Injection Molding

Figure 3-28(a) illustrates a typical cooling system in a molding plate. The cooling system consists of two circuits connected to the supply and collection manifolds using hoses. The coolant first enters these circuits at the connection to the supply manifold, flows through the cooling channels and baffles (where the flow rate, or pressure drop, is controlled), and leaves the circuits to a collection manifold. The collection manifold takes the coolant to the temperature controlling unit, where the coolant temperature is regulated. This temperature controlling unit is then connected to the supply manifold by a pump.

The cooling system required for C-MOLD Cooling analysis specifically includes the components between the supply and collection manifolds. A manifold is identified by an ID number and has unique coolant entrance and exit nodes, as shown in Figure 3-28(b). All channel elements in a manifold must be connected. The coolant temperature at the entrance is controlled, and either a total flow rate or total pressure drop is specified at the entrance.

"Channel Element Types" on page 3-39 details the cooling channel elements that are used for modeling. Then, cooling system modeling techniques are described. The objectives of these modeling techniques are to obtain more accurate predictions, and to achieve more efficient computation.

Figure 3-28. Schematic of (a) a typical cooling system and (b) model of a coolant manifold for C-MOLD Cooling analysis.

### Channel Element Types

Cooling channels are modeled in C-MOLD Modeler as 1-D elements with an assigned channel type. There are four types of cooling channel elements: regular cooling channels, baffles, bubblers, and hoses. Hose elements contribute only to the pressure drop calculation. The other three participate both in the pressure drop and heat transfer calculations. Note that a connector element cannot be used in modeling cooling channels.

#### Regular cooling channel

A regular cooling channel is defined by two end points and a diameter that is the size of the drilled hole in the mold. Both circular (shape factor = 1) and non-circular cooling channels are allowed. Circular cooling channels are the most commonly used.

#### Baffle

The coolant enters a baffle through the entrance node, flows up through the semi-circular region, then bends around the baffle plate and returns to the exit, which coincides with the entrance node in the model, as shown in Figure 3-29. A baffle is defined by at least two nodes: one for the coolant entrance, and the other(s) for the top free end(s) where the coolant changes direction. The size of the drilled hole is used as the outer diameter of the baffle, and the shape factor equals 1.

Figure 3-29. Schematic of a baffle and its model

#### Bubbler

The coolant enters a bubbler through an inner tube and returns through the annular region between the inner tube and the outer channel surface. A bubbler is defined by at least two nodes: one for the coolant entrance, and the other(s) for the top free end(s) where the coolant changes direction. Similar to a baffle, the size of the drilled hole should be specified as the outer diameter.

Figure 3-30. Schematic of a bubbler and its model.

#### Hose

Hoses are external connecting channels, which account for pressure drop in the coolant flow, but assume no heat loss. A hose element is defined by two end nodes and a diameter.

### Tips for Modeling the Cooling System

The mesh size of the cooling channels should be properly selected to obtain accurate results for mold cooling analysis. The rule of thumb is that the mesh size for the cooling channels give an aspect ratio (mesh size/channel diameter) of 2 to 3. For cooling channels that are very close to the mold cavity surface or other cooling channels, use an aspect ratio of about 1. (A distance of less than the channel diameter is considered close.)

If a baffle (or bubbler) is very long compared to its diameter (Figure 3-31), it can be modeled and meshed as more than one element to give an aspect ratio of about 2 to 3. Two or more baffle elements can be used to model this baffle, with the same diameter assigned to each baffle element.

Figure 3-31. Modeling a long baffle with two connecting baffle elements.

Use a hose element to connect two cooling channels of different diameters, as shown in Figure 3-32. The hose element contributes only the pressure drop of the coolant flow and does not participate in the heat transfer calculation. Note that a connector element cannot be used in modeling cooling channels.

Figure 3-32. Connecting cooling channels with diameter changes.

Just as small features can be ignored when modeling the part, channels that have small surface areas can be ignored as well. The channel connectivity must be maintained, though. Figure 3-33(a) shows a small end feature in a channel element that can be ignored in the model. If the channel to be neglected leads to constriction of the coolant flow, then it can be modeled by using a hose element, which still accounts for the pressure losses due to a small dimension, as shown in Figure 3-33(b).

Figure 3-33. (a) Cooling channel to be ignored, and (b) cooling channel to be modeled by hose element.

Each element can be part of one (and only one) coolant manifold. The cooling system model shown in Figure 3-34 is illegal because one element is shared by two coolant manifolds.

Figure 3-34. Model of coolant manifolds is illegal because of shared element.

It is occasionally necessary to use hose elements to consolidate multiple coolant entrances and exits when modeling the cooling system, as shown in Figure 3-35. In the model, each coolant manifold can have only one entrance node and one exit node, with all the associated channel elements defined in between. Also, entrance and exit nodes can be connected to only one channel element. In other words, an entrance node connected to two hose elements, as shown in Figure 3-35 (second iteration) is illegal.

Figure 3-35. Consolidating multiple entrances using hose elements.

Isolated elements that cannot be reached from any manifold entrance node (Figure 3-36) will cause C-MOLD Coolant Flow analysis to stop. The program reports a list of such isolated elements before stopping execution. If this occurs, check the element connectivity.

Figure 3-36. Isolated channel causes C-MOLD Coolant Flow to stop execution.

For part surfaces that are in close proximity, choose a smaller mesh size to ensure the accuracy of surface integration used in C-MOLD Cooling, but not too small compared with the channel diameter. It is occasionally necessary to use variable mesh densities for different regions and cooling channels.

The example in Figure 3-37 shows six regular channel elements with nodes that are not shared by more than one channel element. Nodes corresponding to the free end of these elements are called dead ends. In reality, such elements are plugged, so coolant cannot pass through them. Since stagnated flow in the cooling channels does not contribute to removing heat from the mold, dead-end nodes and elements can be ignored in the model. C-MOLD Coolant Flow searches for and reports all such dead-end nodes in a warning message. The analysis continues without calculating the heat transfer in these elements.

Figure 3-37. Dead-end nodes and elements should be ignored in the model.

Overlapping regions or surfaces in the geometry model will introduce numerical problems for C-MOLD Cooling. When building the part model, check for overlapping regions or surfaces and delete them. The analysis checks for overlapping and intersecting elements before any heat transfer calculation begins. If these exist, an error message is given and the program stops execution. Figure 3-38 illustrates geometries that are illegal because of overlapping and intersecting elements.

Figure 3-38. Illegal geometry due to overlapping and intersection.

# Special Procedures for Gas-Assisted Injection Molding

Gas-assisted injection-molded parts are similar to traditional injection-molded parts, except they typically have a network of heavy-sectioned gas channels to guide gas penetration. Gas channels are modeled in the same way as any other plastic element. Whether to use triangular elements or part runner elements depends on the aspect ratio of the gas channel cross section. The rules discussed in this section are applicable for the modeling of gas channels only. Because of the dynamic nature of the gas-assisted injection-molding process, accurate modeling of gas channels is critical to the numerical prediction of gas penetration.

## Tips for Modeling Gas Channels

When the width of the gas channel is greater than four times its thickness, shear and cooling effects from the side walls can be neglected. This kind of gas channel should be modeled as a region with the proper thickness and shape factor, and meshed with triangular elements as shown in Figure 3-39. It is important that the mesh size over and adjacent to the gas channel be kept small to ensure numerical accuracy and better resolution of the gas-penetration display. The rule of thumb is that the mesh size should allow at least two layers of triangular elements across the width of the gas channel.

Figure 3-39. Gas channel modeling when the channel width is greater than four times the thickness.

One way to achieve small elements adjacent to the gas channel is to use variable mesh density. Specify a finer local mesh size in the gas channel regions, as well as neighboring regions. Another way is to create lines parallel to the gas channels and to create additional regions in the neighboring thin-section areas. As shown in Figure 3-40, these additional lines constrain the elements adjacent to the gas channel from the mesher. This mesh configuration also reduces the artificial zigzag gas penetration resulting from the mesh configuration when the predicted gas penetration is displayed.

Figure 3-40. Confine the mesh size adjacent to the gas channel.

When the flow width of the gas channel is less than four times the thickness, shear and cooling effects from the side walls cannot be neglected. The gas channel should be modeled as illustrated in Figure 3-41. First, separate the thin plate from the gas channel, which is to be modeled as a part runner with an appropriate equivalent diameter and shape factor. Then restore connectivity by using the connectors.

Refer to Table 3-1 on page 3-10 for the derivations of the equivalent diameter and shape factor for the part runner that is used to model the gas channel. Note in Table 3-2 on page 3-55 that the cross-sectional area (A) and the perimeter (C) are derived from the detached gas channel. In particular, the perimeter does not include the edge that is in contact with the thin part.

For simplicity, the part runner can be merged with the thin section, as shown in Figure 3-41(d), thereby eliminating the extensive use of connectors.

Figure 3-41. Gas channel modeling when the channel width is less than four times the thickness.

Table 3-2 shows the commonly used geometries for gas channels, with the corresponding models with connectors, and the simplified models without connectors. The cross-sectional area and perimeter are also illustrated; they are used to calculate the equivalent diameters and shape factors.
Note that the perimeters (heavy curves) exclude the edges in connection with the thin sections because such boundaries do not contribute to the cooling of gas channels. However, the simplified model introduces extra volume that is embedded within the gas channels.

# Blow Molding & Thermoforming

C-MOLD Blow Molding and Thermoforming analyses require modeling that is very different from that used for other C-MOLD analyses.

## Element Attributes

The thicknesses of the topologies that correspond to mold surfaces are not used by C-MOLD Blow Molding and Thermoforming. However, thicknesses would have been specified in order to create the topology using C-MOLD Modeler.

## Nodal Attributes

The polymer domain must be adequately "clamped." This means that free edges must be fixed, in order to prevent them from moving freely during mold closing or pressure application. If the polymer domain is not clamped adequately along its free edges, instability in the computations performed during the simulation may result. To clamp a node or edge, assign to it the attributes Nodal X Displacement, Nodal Y Displacement, and Nodal Z Displacement. Assign a value of 0 to each of these x, y, and z displacement boundary attributes. As a result, these entities will not be allowed to move during the simulation.

## Mold Meshing

A crude mesh can be used on the mold surfaces if the mesh output from C-MOLD Blow Molding and Thermoforming is not directly used for structural analysis. In this case, the mold elements need to be fine enough only to the extent needed for a reasonable representation of the mold geometry, because the mold surface mesh would not be part of the computational domain, and would be used only for enforcing contact conditions with the polymer.

## Type of Elements

In C-MOLD Blow Molding and Thermoforming, one-dimensional elements (runners) and two-dimensional triangular elements cannot be used in the same mesh. Two-dimensional elements can be used for a 3-D analysis and 1-D elements can be used for analyzing two-dimensional (plane strain or axisymmetric) cases. If the input mesh has both 1-D and 2-D elements, C-MOLD Blow Molding and Thermoforming will exit, and provide an error message.

## Parting Plane Modeling

In blow molding analysis, when mold halves close in on the parison/preform from both sides, the mold surfaces that comprise the parting plane must be modeled and meshed. In C-MOLD Blow Molding and Thermoforming, contact is computed between polymer nodes and mold elements; hence, if the parting plane surfaces are not modeled, there is a possibility of mold surfaces that are "perpendicular" to the parison or the preform surface passing through polymer elements without contact being detected.

# Reactive Molding: Microchip Encapsulation

C-MOLD Reactive Molding filling and curing simulation for reactive materials can be applied to transfer molding in microchip encapsulation. But since the chip device and leadframe are inserted inside the multi-cavity mold, special modeling techniques are required. Figure 3-42 is a schematic of a typical multi-cavity transfer mold. Figure 3-43 shows the cross-sectional view of the transfer pot and the flow of the molding compound in a cavity.

Figure 3-42. Schematic cavity and runner layout of a transfer molding tool for microelectronic encapsulation.

Figure 3-43. Cross-sectional views of the transfer pot and the flow of the molding compound in a cavity.

## Tips

Connectors can be used to model symmetric geometry to reduce redundancy and CPU time. For example, the system shown in Figure 3-42 can be modeled using connectors with appropriate direction and multiplicity factor, as shown in Figure 3-44. The identical branches and cavities have been modeled using connectors (indicated by arrows) with corresponding multiplicity factors (indicated by numbers).

Figure 3-44. Modeling the runner system shown in Figure 3-43.

The transfer pot can be modeled as a hot runner and is initially filled with molding compound, as shown in Figure 3-44. The initial fill condition in the transfer pot can be either `Filled at Inlet Melt Temp.` (=1) or `Filled At Hot Runner Mnfld. Temp.` (=2). The hot runner manifold temperature for the transfer pot is given in the hot runner manifold control specified in the process conditions file (filename.prc). If the Initial fill condition is set to 1, the pre-heated temperature is given as the inlet melt temperature specified in the process conditions file (filename.prc). The rest of the runners can be modeled as cold runners with the wall temperatures given in the coolant manifold control, which will also be used as the cavity wall temperatures.

For modeling individual cavities, refer to Figure 3-45. Each cavity is further divided into two sub-cavities by the leadframe. The spacing of the leadframe is assumed to be small throughout the cavity, except at the opening adjacent to the gate that actually allows material to flow through. In this way, the permeation of molding compound through the leadframe for the rest of the cavity is ignored. Each sub-cavity has an attribute of thickness that includes the presence of the paddle as shown in Figure 3-45. In other words, the molding compound divides into two streams flowing above and below the leadframe across the cavity. The two sub-cavities are linked by a connector at the leadframe opening. The distance between these two sub-cavities (or the length of the connector) has no affect on the simulation results, because there is no flow resistance in the connector.

Figure 3-45. Cavity with leadframe and paddle is modeled by two sub-cavities with a connector.

The flow resistance across the leadframe opening can be approximated to predict the "lead-lag" phenomenon of melt fronts in these two sub-cavities. The pressure drop, P, of a Newtonian fluid through a rectangular opening, with dimensions of width, w, and height, h, is estimated by:

###### (3.7)
where µ is the viscosity, and Q is the flow rate.

There are two ways to incorporate the flow resistance of the leadframe opening. The first way is to replace the connector in the model shown in Figure 3-45 by a part runner. The part runner should have dimensions that provide an equivalent pressure drop as in Equation 3.7. The diameter of the part runner should not be too large, to avoid contributing excess volume that does not really exist. On the other hand, the diameter should not be too small, or considerable shear heating will be generated by the flow.

###### (3.8)
where L is the length, and d is the diameter of the tube.

###### (3.9)
The resulting model is shown in Figure 3-46, where the part runner has a diameter, h, and length, L, given in Equation 3.9.

Another way of incorporating the flow resistance of the leadframe opening is to first perform the flow analysis with the model in Figure 3-45. From the output displays, estimate the flow length from the gate that has the same pressure drop as given in Equation 3.7. Modify the geometry so the end of the connector is away from the gate for the estimated flow length, as shown in Figure 3-47. Run the analysis with the modified geometry. The flow will not branch into the second sub-cavity until the melt front reaches the end of the connector.

Figure 3-46. Modeling the flow resistance of the leadframe opening with a part runner.

Figure 3-47. Modeling the flow resistance of the leadframe opening with an off-set connector.

# Reactive Molding: RTM and SRIM

Resin-transfer molding (RTM) and structural-reaction injection molding (SRIM) are two important processes for manufacturing composite parts using thermoset resins and fiber mats. In RTM and SRIM, resin is forced to flow through a cavity in which reinforcing fiber mat (also called preform) is present. The flow type, characterized by the properties of the fiber mat, can be isotropic or anisotropic, depending on the network of the mat. Although there are some fundamental differences (such as resin used, machine configuration, and cycle time) in these two processes, the geometry modeling techniques for both processes are the same.

## Element Attributes

### Fiber Mtl ID

The Fiber Mtl ID, which is represented by an integer, is a parameter that associates the fiber mat in the geometry model with the Fiber mat porosity and permeability data set (TCODE 3920) specified in the material property file (filename.mtl), as shown in Figure 3-48. The Fiber mat porosity and permeability data set consists of

For unreinforced (i.e., empty) regions, there is no need to specify the Fiber Mtl ID. The use of Fiber Mtl ID makes C-MOLD Reactive Molding analysis uniquely capable of simulating the resin flow through more than one kind of fiber mats, as shown in Figure 3-48. Detailed descriptions on the Fiber mat porosity and permeability data set can be found in the C-MOLD Reactive Molding User's Guide.

Figure 3-48. Schematic representation of a simple cavity that contains an isotropic fiber mat, an empty region, and an anisotropic fiber mat. Note that the associated Fiber Mat IDs of the fiber mats point to the corresponding Fiber mat porosity and permeability data set in the material property file (filename.mtl).

Keep in mind that the same Fiber Mtl ID can be assigned to different regions (or surface regions) over which the same fiber mat is used, and that the ID number does not have to be continuous, as long as it matches the ID in the Fiber mat porosity and permeability data set in the material property input data.

## Nodal Attributes

### Fiber Mat Orientation Node for the Anisotropic Fiber Mat

The structure of a directionally stitched/woven fiber mat is not uniform. In terms of the pore area distribution, it shows a maximum in one direction and a minimum in the other direction that is orthogonal to the former. When the resin flows through such a fiber mat, the flow in the direction of maximum pore area will have longest flow length because of the least flow resistance. If the pore area distribution is smooth, the in-plane melt front exhibits an elliptic pattern, as shown in Figure 3-49. The shape of the ellipse depends on the maximum and the minimum pore areas, which can be characterized by "the permeabilities of the principal directions." One of the primary principal directions corresponds to the major axis of the ellipse. This direction has the largest pore area (and, thus, the largest permeability) and is denoted as the principal direction 1. The other principal direction, the principal direction 2, corresponds to the minor axis of the ellipse, as shown in Figure 3-49.

Figure 3-49. A schematic representation of a cavity showing elliptic melt-front pattern for resin flowing through an anisotropic fiber mat. Principal directions 1 and 2 of the fiber mats are determined by the major and minor axes of the ellipse.

#### Defining the fiber mat orientation before mesh generation

When the mesh is generated, nodes will be created on those two points, which carry the nodal attribute Fiber Mat Orientation (TCODE 20050). Figure 3-50 illustrates how the fiber mat orientation is defined by selecting the two points that determine the principal direction 1.

Figure 3-50. A schematic representation of a cavity geometry model showing that the principal direction 1 can be defined by selecting two points (P1, P2).

#### Defining fiber mat orientation after mesh generation

When the mesh is saved, these two nodes will carry the Fiber Mat Orientation nodal attribute (TCODE 20050). Figure 3-51 illustrates how the fiber mat orientation vector is defined by selecting the two nodes that determine the principal direction 1.

Figure 3-51. A schematic representation of a cavity finite element mesh model showing that the principal direction 1 can be defined by selecting two nodes N1, N2).

#### Using the same fiber mat in a cavity with varying thicknesses

The same fiber mat preform can occasionally be placed on areas with different thicknesses, resulting in different porosities and permeabilities. This kind of situation can be handled by creating different regions that carry the corresponding thickness in a normal way, and assigning the same Fiber Mtl ID to those regions that use the same fiber mat, as shown in Figure 3-52. As a result, these regions will share the same Fiber mat porosity and permeability data set. If the cavity thickness at molding is different from the reference thickness specified in the Fiber mat porosity and permeability data set, the porosity and permeability used in the simulation will be internally modified by the analysis. Keep in mind that this automatic modification of the fiber mat porosity and permeability is based on the assumption that the thickness variation in the cavity is not too large from the reference thickness and that the porosity is within 0.4 and 0.7; otherwise, errors in the predictions could be introduced due to the improper values of the fiber mat attributes.

Figure 3-52. A schematic representation of a cavity with a single fiber mat but different thicknesses. Different regions corresponding to various thicknesses have been created, but they carry the same Fiber Mat ID.

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