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How Choice of Mesh Type Affects Analysis Outcomes
Computer-aided engineering (CAE) simulation of injection molding is a mathematical representation of a physical manufacturing process. As such, there are assumptions and limitations inherent in the software that users must understand in order to obtain the most accurate results. One crucial area is that of mesh type. There are several meshing options available in Moldflow’s Design Optimization Solutions – Moldflow Plastics Advisers® (MPA®) and Moldflow Plastics Insight® (MPI®) products. In particular, there are four basic types of mesh used to represent the different geometry components for injection molding simulation. These four mesh types are:
- Beam (1D) mesh elements
- Midplane (2.5D) mesh elements
- Dual Domain™ mesh elements (also referred to as modified 2.5D and MPI/Fusion meshes)
- True three-dimensional (3D) elements.
Not every mesh type is available in every Moldflow product or even appropriate for use in every analysis. Let’s take a detailed look at these four mesh types to gain a better understanding of each.
Four Basic Mesh Types
Beam Mesh
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| Figure 1. Beam (1D) mesh schematic. |
Beam elements are simple, one-dimensional lines that connect two nodes and have an assigned, cross-sectional area shape. They are used in Moldflow Plastic Advisers (MPA®) and Moldflow Plastics Insight (MPI®) software, usually to represent melt-delivery systems (cold and hot runners) and cooling lines. Further, in MPI software, beam elements have the additional functionality to represent part geometry that is “beam-like” in nature, such as a boss. In beam elements, flow is assumed to be symmetrical about the axis. The length of a beam element should be two to three times its diameter. Also, a gate should have at least three elements defining its length.
Midplane Mesh
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Figure 2. Midplane mesh schematic. |
A midplane (or shell) mesh represents a three-dimensional part with a two-dimensional planar surface at the center of the thickness. A thickness property is assigned to this planar surface, hence the terminology “2.5D.” Midplane elements are used in MPI software.
Using a midplane mesh works best when the part being modeled is a traditional, thin-walled injection molding application. To reduce computation time in the simulation, this mesh type relies on the assumption that the flow length of a section is much greater than the wall thickness; this is known as the Hele-Shaw approximation. Care should be taken when working with midplane mesh models of parts that are not considered thin-walled, otherwise significant error may be introduced. As a minimum, the average of the length and width of any local region should be greater than four times the local thickness (see Figure 3). This guideline is sometimes referred to as the “4 to 1” rule.
Average of Length (25) and Width (15) = 20
Thickness (3) < 1/4 Average (5)
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Figure 3: Minimum thickness guideline for thin-wall analysis assumption in midplane mesh models. |
A more conservative rule is that the width should not be less than ten times the thickness of a particular section. The more a midplane mesh model deviates from these guidelines, the greater is the potential for error in analysis calculations. This is a particular problem for square-shaped, “beam-like” geometry such as connecting ribs, housing vents or grills.
Dual Domain Mesh
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Figure 4. Dual Domain mesh schematic. |
Dual Domain mesh is a patented technology that represents a three-dimensional part with a boundary or skin mesh on the outside surfaces of the part obtained from a common CAD translation model such as STL or IGES format. A Dual Domain mesh is very similar to a midplane mesh, but this boundary shell mesh has aligned and matched mesh on both corresponding outside surfaces (Figure 5). Dual Domain mesh is utilized in both MPA and MPI analyses.
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Figure 5: Unmatched mesh (left) compared to matched mesh (right) in a Dual Domain mesh model. |
The distance between the mesh surfaces defines the part thickness. Mesh density plays a key role in determining the thickness of varying geometry such as drafted ribs or living hinges. Best results are obtained by maintaining at least three rows of elements across a dramatic change in thickness so the thickness effects are not averaged out. In the MPI environment, the initial thickness is automatically determined when meshing the model. The same thickness ratio limitations that apply for midplane mesh models also apply to Dual Domain mesh models – that is, the Dual Domain mesh is most appropriate for thin-wall parts. Although MPI modeling tools allow users to change element thickness manually, the initial element match interpretation influences analysis results, so it is important to have overall high mesh matching ratios (greater than 80 percent at minimum).
3D Tetrahedral Mesh
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| Figure 6. 3D mesh schematic. |
A 3D mesh technology is available in both MPA and MPI software and consists of four-node, tetrahedral elements meshed through the part volume, which gives a true three-dimensional representation of the part. 3D mesh can be used with thin-wall geometry but particularly works well with “thick and chunky” parts such as electrical connectors or thick structural components that violate the thin-wall thickness limitations described previously. This is because 3D analyses use the full 3D Navier-Stokes equations, rather than the Hele-Shaw approximations that apply specifically to thin-wall parts.
Total Analysis Time:
It is important to consider the total solution time when choosing a mesh type for analysis. Total solution time includes model preparation (e.g. mesh clean up) and analysis run time. These components are highly dependent on model complexity, element count and user selected analysis options. As such it is difficult to predict but in general, Dual Domain mesh offers the best compromise between preparation and analysis time for most models.
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Total Analysis Time |
Research: How Does Mesh Type Affect Analysis Results?
With so many mesh types to choose from, you may ask, “Am I using the best mesh type for my particular part geometry? And how do I know when to use one mesh type over the other? Or how severe are the consequences if I choose the wrong one?”
Since many Moldflow customers have been asking these very questions of the Moldflow technical support group, I wanted to conduct a study to research these issues. While working as Moldflow’s US technical support manager, I have also been pursuing a Masters of Science degree in Plastics Engineering at the University of Massachusetts/Lowell. One of the requirements for this degree is to successfully write and defend a thesis topic. I chose to use this opportunity to research the different mesh types and how they can affect analysis results; it is intended that Moldflow customers can take advantage of this research as a guide to selecting and using the correct mesh type to achieve the most accurate filling analysis results on their particular part geometry.
Experimental study
This study compared actual moldings of an injection-molded plastic comb with the flow patterns resulting from simulations on models using beam, midplane, Dual Domain and 3D mesh types. Short shots of a polypropylene material were taken strategically at different shot volumes and a comparison was made between reality and simulation to demonstrate how the assumptions related to the different mesh types can affect the accuracy of filling analysis results for this particular part geometry. Filling pattern was chosen for comparison because if this analysis result was not accurate, then the rest of the analysis results, such as predicted pressure values, also would be suspect.
The comb mold is a two-plate, four-cavity mold with an unbalanced cold runner system. The layout of the comb mold is shown in Figure 7. It should be noted that because of variations in the tool and the scope of this study, the experimental results focus on the filling pattern of a single comb cavity, as indicated in the figure.
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Figure 7. Comb mold layout |
Meshed models used to simulate the comb geometry are shown in Figure 8. All simulation work was conducted using MPI 4.1 build 03203.
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Figure 8. Close-up views of comb models used in simulations: (a) beam elements for teeth and midplane elements for rim, (b) midplane mesh with horizontal teeth representation, (c) midplane mesh with vertical teeth representation, (d) Dual Domain mesh, and (e) 3D tetrahedral mesh. |
The Dual Domain mesh model in this study (Figure 8(d)) had to be manually altered because the thickness in the rim area was not interpreted correctly. It is extremely important to double-check Dual Domain thickness interpretation compared with the original CAD model to ensure an accurate model geometry representation.
Results and Discussion
Experimental and numerical results are compared in Figure 9 for beam, midplane, Dual Domain and 3D mesh types at a fill time of 1 second. It can be seen from the simulation trends that the predicted filling pattern of the midplane mesh with horizontal teeth representation (Figure 9(c)) is not very accurate in the teeth sections for this particular part, while the beam elements (Figure 9(b)), midplane mesh with vertical teeth representation (Figure 9(d)), Dual Domain mesh (Figure 9(e)) and 3D mesh (Figure 9(f)) simulate the filling pattern more accurately. The inaccuracy or success of filling pattern prediction can be attributed to the assumptions made for each mesh type.
Figure 9: Comb short shots (1.0 sec fill time) obtained by experiment and
various mesh simulation results: (a) experiment, (b) beam mesh result,
(c) midplane
mesh result with horizontal teeth representation,
(d) midplane
mesh result with vertical teeth representation,
(e) Dual Domain mesh result and (f) 3D mesh.
For the midplane horizontal mesh model (result shown in Figure 9(c)), the teeth of the comb are interpreted as a collapsed surface from top to bottom as described schematically in Figure 10(a). The side edges of each tooth are ignored as sources of heat transfer and flow resistance. The negative impact this assumption has on the analysis results is visually apparent in Figure 9(c). The simulation predicts an easier flow through the teeth of the comb as there is virtually no hesitation in the teeth.
A better result is achieved when the teeth are meshed in the vertical or side-to-side direction, as indicated schematically in Figure 10(b). This results of this method are seen in Figures 9(d) and 9(e), the midplane mesh with vertical teeth representation and the Dual Domain mesh, respectively. The simulation error is significantly minimized but does still exist.
For this part, the best results are obtained by modeling the teeth as beam elements (result in Figure 9(b)) as shown schematically in Figure 10(c), or by meshing the model with 3D elements (result in Figure 9(f)).
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Figure 10. Thickness interpretation comparison for comb teeth. Dark lines represent where heat transfer is considered; dashed lines represent collapsed midplane surface. |
Conclusions and Future Considerations
Because the great majority of injection molded parts are thin-walled, using a midplane or Dual Domain mesh model in most cases provides accurate simulation results because the thickness assumptions that are inherent in the CAE analysis reflect the typical part geometry.
However, as demonstrated in this study, there are some “thick and chunky” part geometries where these assumptions do not result in optimal solution accuracy. In these cases, using a combination of mesh types such as midplane and beam elements or using 3D elements should improve the accuracy of results.
This study also demonstrated that the orientation of the midplane mesh can have a significant effect on the accuracy of the simulation. To minimize simulation error, it is suggested to consider how the part is going to fill and choose the most significant midplane orientation direction when creating the analysis mesh.
If a given part geometry has several features that require different mesh types, the user will have to make an educated decision on which mesh type to use based on the analysis options required and the mesh types available. This will mean selecting a mesh type that will most accurately describe the majority of the part geometry. For example, if a part is mostly “thick and chunky” in nature and violates the thickness guidelines in many areas, then a 3D mesh should be used.
As seen with the results of the combined midplane and beam mesh model of the comb mold, some mesh types can be combined and used successfully in a flow analysis, but use this technique with care. Mixed mesh types in a single model may not be supported in other advanced analyses such as cooling or warpage simulations, so user discretion is advised. Consult the training documentation, on-line help or your local technical support office for specific details on the limitations of combining mesh types for Moldflow analyses.
Utilizing a 3D mesh for all simulations is just not feasible today from an analysis time/benefit perspective. Moldflow products offer a wide range of software solutions to our customers so they can obtain accurate results in the shortest period of time. However, a fundamental understanding of the assumptions and limitations that govern each is necessary to achieve the most accurate possible analysis results.
For more information about Moldflow Plastics Advisers and Moldflow Plastics Insight solutions, visit www.moldflow.com.
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