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All meshes are not created equal
November 1, 2004
8 Min Read
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Editor’s note: Matthew Jaworski, U.S. technical support manager for Moldflow’s Design Solutions division, believes that users need to understand the assumptions and limitations of mesh types to get the most accurate results. In this excerpt from Jaworski’s white paper, titled, “A Mesh by Any Other Name,†he explains the benefits and caveats inherent in each of four common mesh types, and then shares a study he recently conducted as a part of his thesis for a Masters of Science degree in Plastics Engineering at the University of Massachusetts Lowell.
CAE simulation of injection molding uses mathematical models to represent the physical process. Choosing correctly from among these models, commonly referred to as finite-element meshes, can determine whether the outcome is on target or out of the ballpark. Users have several meshing options in moldfilling analysis programs, and generally there are four basic types of mesh used to represent the different geometry components for simulating the molding process:
Beam (1-D) mesh elements.
Midplane (2.5-D) mesh elements.
Dual Domain mesh elements (also referred to as modified 2.5-D and MPI/Fusion meshes).
True 3-D elements.
Not every mesh type is available in every product or even appropriate for use in every analysis.
Four Basic Mesh Types
Beam elements are simple, one-dimensional lines that connect two nodes and have an assigned, cross-sectional area shape (Figure 1). Typically used to represent melt-delivery systems (cold and hot runners) and cooling lines, beam elements can also 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.
A midplane (or shell) mesh represents a 3-D part with a 2-D planar surface at the center of the thickness (Figure 2). A thickness property is assigned to this planar surface, which gives rise to the term 2.5-D. This type of mesh works best when the part being modeled is a traditional, thin-walled application. To reduce a simulation’s computation time, midplane meshes rely on the assumption that the flow length of a section is much greater than the wall thickness, known as the Hele-Shaw approximation.
Be careful when working with midplane mesh models for parts that are not considered thin-walled—there is an opportunity for significant error here. At the minimum, the average of the length and width of any local region should be greater than four times the local thickness, a guideline sometimes referred to as the “4 to 1†rule (Figure 3). A more conservative rule is that the width should not be less than 10 times the thickness of a particular section.
To the extent that a midplane mesh model deviates from these guidelines, it has 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 grilles.
Dual Domain mesh is a Moldflow-patented technology that represents a 3-D part with a boundary or skin mesh on the outside part surface obtained from a common CAD translation model such as STL or IGES format (Figure 4). A Dual Domain mesh is similar to a midplane mesh, but includes an aligned and matched mesh on both corresponding outside surfaces.
The distance between the mesh surfaces defines the part thickness. Mesh density plays a key role in determining the thickness of geometry such as drafted ribs or living hinges. For best results, maintain at least three rows of elements across a dramatic change in thickness so that the thickness effects are not averaged out. 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-walled parts.
3-D meshes (Figure 5) can be created with several kinds of elements such as voxel, pyramid, prismatic, hexahedral, or four-node, tetrahedral elements meshed through the part volume. The 3-D part mesh 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 3-D analyses use equations that solve for results in all three directions, rather than the Hele-Shaw approximations that apply specifically to thin-wall parts.
Real-world Study
With so many mesh types to choose from, users tend to ask, “Am I using the best mesh type for my particular part geometry? How do I know when to use one mesh type over the other? How severe are the consequences if I choose the wrong one?â€
Moldflow conducted a study to research these issues, comparing actual moldings of an injection molded plastic comb with the flow patterns resulting from simulations on models using beam, midplane, Dual Domain, and 3-D 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, would also be suspect.
The comb mold is a two-plate, four-cavity mold with an unbalanced cold runner system (Figure 6). 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 shown in the figure. Meshed models used to simulate the comb geometry are shown in Figure 7. All simulation work was conducted using MPI 4.1.
The Dual Domain mesh model in this study had to be manually altered because the thickness in the rim area was not interpreted correctly. This illustrates an important caveat: To ensure accurate model geometry representation, always double-check the Dual Domain thickness interpretation against the original CAD model.
Making Sense of Results
Experimental and numerical results are compared in Figure 8 for beam, midplane, Dual Domain, and 3-D 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 (8c) is not very accurate in the teeth sections for this particular part, while the beam elements (8b), midplane mesh with vertical teeth representation (8d), Dual Domain mesh (8e), and 3-D mesh (8f) 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.
For the midplane horizontal mesh model (8c), the teeth of the comb are interpreted as a collapsed surface from top to bottom as shown schematically in Figure 9a. 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 8c. 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 9b. The results of this method are seen in figures 8d and 8e, 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 (8b) as shown schematically in Figure 9c, or by meshing the model with 3-D elements (8f).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 3-D elements should improve the accuracy of results. 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 this technique should be used with care. Mixed mesh types in a single model may not be supported. Consult the training documentation, online help, or your local technical support office for specific details on the limitations of combining mesh types.
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, consider how the part is going to fill and choose the most significant midplane orientation direction when creating the mesh.
If a given part geometry has several features that require different mesh types, the user will have to make an educated decision about 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.
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