Article: JMAG A to Z
Issue 4 Understanding Meshes from A to Z
JMAG continues to evolve with each passing day. There may be functions in JMAG that even those who have already been using it will learn for the first time, as well as some useful procedures that are not well known yet. Why don't we make operations more efficient by becoming familiar with new functions and operations that we don't know about?
In this series, I would like to introduce "Things that we should know" in JMAG, as well as some advantageous applications that you can try.
Most people probably feel that, out of all the operations necessary for a finite element analysis (FEA), mesh generation takes the most time and effort. People tend to worry about mesh generation because it has a big effect on calculation time and accuracy.
JMAG has developed and implemented a variety of mesh generation functions to help reduce the burden on our users. This issue introduces functions for meshes in JMAG that can help make operations more efficient. By all means, take this opportunity to try them out for yourself.
For information about the operating procedures for each function, open Help in JMAG-Designer and look at Home > Analysis > Generating Mesh (Automatic).
Running an Analysis that Accounts for Motion
In this section, I would like to introduce two functions that can be used when an analysis target like a rotating machine or actuator has a moving part. The first of these is the Slide Mesh function, which can account for motion. When using a model that cannot apply the Slide Mesh function, however, you can use the second of these features: Remesh Model at Each Step.
This function automatically generates a mesh that can handle motion in moving parts, and can be used to generate a regular mesh that can obtain motion in the gap (Fig. 1). Calculations with a mesh generated by this function are fast and stable because there are no regenerations during the calculation itself. You can set the level of detail in the gap mesh, which is vital from a calculation accuracy standpoint, by using the number of slide mesh divisions.
Fig. 1 A rotating machine mesh generated with the Slide Mesh function
Remesh Model at Each Step
Use this function to handle motion when Slide Mesh function cannot be used. It runs calculations while remeshing the model at each analysis step, and has a wide range of applications because there are no restrictions on the motion or model geometry that it can be used on. Be sure to select Semi Auto Mesh as the generation method when using this function, because it makes the meshes for the parts other than the surrounding space the same for each analysis step. The Remesh Model at Each Step function has good calculation accuracy when running calculations that account for eddy currents in particular because the mesh for the conductor does not change.
Automatically Generating a Mesh Suitable for a Rotating Machine
I would like to introduce functions that automatically generate meshes for use in a rotating machine analysis. Using these functions to generate a mesh will allow you to run accurate calculations with a small number of elements. Try using both of the following functions when analyzing a rotating machine.
Rotation Periodic Mesh
Specifying the Rotation Periodic Mesh function to run an automatic mesh generation makes it possible to reduce the accidental errors that a mesh can sometimes cause. An example of cancelling the offset in cogging torque is shown below (Fig. 2). Meshes strongly affect cogging torque calculations in particular, making them difficult to perform accurately. The magnet orientation and stator geometry in the model used in this example have been modified, and the cogging torque produced has been calculated to be extremely small. The ordinary mesh generates an offset, but it disappears when the Rotation Periodic Mesh function is used. This makes it possible to calculate the cogging torque accurately.
Fig. 2 A comparison of cogging torque analysis results
This is an automatic mesh generation function for 3D analysis. When generating a 3D mesh for a rotating machine, often times the best course of action is to have fine divisions in the in-plane direction and coarse divisions in the axial direction. The Semi Auto Mesh function used until now created fine mesh divisions in the axial direction, however, so it was often not possible to create the mesh that the user was hoping for (Fig. 3).
The Extruded Mesh function makes it possible to have coarse divisions in the axial direction for parts that have a uniform geometry. This means that you can have a low number of mesh elements without sacrificing any of the convenience that an automatic mesh provides (Fig. 4). The Extruded Mesh function produces a smaller number of elements than the Semi Auto Mesh, shortening calculation time considerably (Fig. 5).
Fig. 3 A mesh generated using the Semi Auto Mesh function
Fig. 4 A mesh generated using the Extruded Mesh function
Fig. 5 A comparison of calculation time and results
Using Hexahedral Elements
There are probably more than a few people out there who would like to run an analysis by using a hexahedral element mesh because it provides accurate calculations. However, it can be pretty tough to generate a hexahedral element mesh manually if you include the space around the analysis target.
With JMAG, it is possible to create a mesh model that uses hexahedral elements by making the mesh for the surrounding space after manually generating a mesh for the analysis target.
Generating the Analysis Target's Mesh Manually
Create a mesh by specifying its number of divisions manually with the Geometry Editor's manual mesh function. This function makes it possible to generate a triangular or quadrilateral mesh for a 2D model, or to drag a 2D mesh model and create a 3D mesh. A hexahedral element mesh can be generated by creating a quadrilateral 2D mesh model and dragging it (Fig. 6).
Fig. 6 The mesh generation procedure for the manual mesh function
Generating a Mesh for the Surrounding Space
This function automatically creates a mesh to fill in the space surrounding an existing mesh without changing the existing mesh at all. Using this function will allow you to automatically generate the mesh for the surrounding space without changing a hexahedral element mesh that has already been created manually (Fig. 7). This makes it easy to generate a mesh using hexahedral elements.
Fig. 7 Automatic generation of a mesh in a space region while maintaining hexahedral elements
Generating a Mesh That Meets Your Analysis Objective
The "optimal mesh" is different for each analysis objective. For example, when the analysis target is a sheet of laminated steel, the analysis requires a mesh that is modeled precisely in order to show the effects of eddy currents. Or as another example, you need a mesh that can express the skin effect precisely to evaluate the losses and effects from eddy currents in a conductor. In this section, I would like to introduce mesh generation functions that are suitable for these kinds of analysis objectives.
In rotating machines, axial direction components of the magnetic flux are generated in the inside edge at the top of the stator (Fig. 8). For this reason, in the laminated steel at the top of the stator there are eddy currents that flow back in the in-plane direction, in addition to the ones that flow back in the lamination direction. When examining the effects of the eddy currents that flow inside of the laminated steel, it is necessary to model each layer in the laminated steel to account for eddy currents, instead of treating it like a single block. Using this function makes it possible to look at the effects of eddy currents in the laminated steel by automatically generating a mesh that is faithful to the real article (Fig. 9).
Fig. 8 Distribution of the magnetic flux density's axial direction component
Fig. 9 Mesh generation with the Layered Mesh function
Mesh divisions that can accurately express offsets in magnetic flux distribution from the skin effect are necessary to evaluate the effects from eddy currents that flow through a conductor. The Skin Depth function can be used to generate a layered mesh of a specified thickness on the surface (face) of a certain part. This makes it possible to do two things. First, you can accurately express offsets in magnetic flux distribution caused by the skin effect, and second, you can generate a mesh capable of evaluating the effects of eddy currents (Fig. 10).
Fig. 10 Eddy current vector distribution on the surface of a claw pole
Reducing the Number of Elements and Streamlining Calculations
In order to run an accurate calculation while reducing the number of elements, it is most effective to choose a mesh generation method that is tailored to the geometry. This includes giving the mesh an appropriate density that changes where necessary and eliminating excessive detailed geometry features. In this section, I would like to introduce functions that achieve these results.
Setting the Element Size
Everyone has, at one time or another, wanted to reduce calculation time while maintaining accuracy. This requires giving the mesh an appropriate density and achieving a balance between accuracy and the time required for the calculation. JMAG has prepared an enhanced function that sets the element size to control mesh density. It can carry out the settings for edges and vertices as well, making it possible to carry out detailed density controls (Fig. 11).
Fig. 11 Mesh density control via specified element sizes
You can restrain the number of elements by eliminating excessive detailed geometry features. However, returning to a CAD software and carrying out geometry changes takes too much time and effort. To fix this problem, JMAG has a function that allows you to use its intuitive settings to eliminate detailed geometry features such as holes, fillets, and chamfers during mesh generation. Using this function to generate a mesh makes it possible to omit detailed geometry and reduce the number of mesh elements (Fig. 12).
Fig. 12 Controlling corner R with the Defeaturing function
Thin Shell Mesh
When creating a mesh for a model whose geometry includes a thin sheet, you can use the Thin Shell Mesh function (under Generating Mesh (Automatic)) to prevent the number of elements from growing too large. This function creates the thin sheet with a shell that has no thickness. By performing the Thin Shell Mesh settings for the shell and running an automatic mesh generation, you can create a part with the specified thickness in the mesh (Fig. 13). This ensures that the mesh will have a smaller number of elements.
Fig. 13 Creating a sheet coil with the Thin Shell Mesh function
Generating a Mesh Suitable for Geometry Optimization Studies
When most people hear "geometry optimization study," they probably imagine having to repeatedly change model geometry, generate meshes, and run calculations. However, if you use the automatic mesh generation function to remesh when changing geometry, the number of element divisions in the adjusted parts changes as well, greatly transforming the mesh's local division pattern. There are times when errors from the difference in mesh divisions get included in the evaluation values, making it impossible to perform an adequate evaluation.
In this section I would like to introduce the Morphing function, which can change the shape of an existing mesh.
The Morphing function is effective when you want to evaluate the effects of a small change in geometry. It changes the model geometry by moving only the nodes of the existing mesh, so that the pattern of the geometry and number divisions in the mesh do not change. Morphing does not include the errors caused by differences in mesh divisions, so you can accurately evaluate the effects of geometry changes.
In this article there is an example of geometry that has been altered by using the Morphing function (Fig. 14). This example displays changes in the width of a tooth tip. The displacement specified in the Morphing function settings becomes a variable in the parametric analysis, making it possible to evaluate the effects of geometry changes.
Fig. 14 A change in geometry using the Morphing function
In this issue, I took the opportunity to introduce JMAG's various meshing functions. Were there some functions that you will be able to use in your own work operations? By all means, take this opportunity to use them and get the maximum benefit from their application.
Next time I plan to introduce an A to Z for materials, conditions, and circuits. Be sure not to miss it.