Release 11.0 Documentation for ANSYS
www.kxcad.net Home > CAE Index > ANSYS Index > Release 11.0 Documentation for ANSYS
When should you use a 2-D model or a 3-D model? What are the differences between the scalar and vector potential formulations? How do the edge-based and nodal-based formulations for 3-D magnetic analyses differ? The next few topics provide some answers.
A 3-D analysis uses a 3-D model to represent the geometry of the structure being analyzed. A 3-D model is the most natural way to represent a structure. However, 3-D models usually are more difficult to generate than 2-D models and usually require more computer time to solve. Therefore, you should first consider using a 2-D model for your analysis.
The magnetic scalar potential (MSP) formulation is recommended for most 3-D static analysis applications. The scalar approach allows you to model current sources as primitives rather than elements; therefore, the current sources do not need to be part of the finite element mesh. The scalar method offers the following:
Brick, wedge, pyramid, and tetrahedral element geometries
Current sources defined by primitives (coils, bars, and arcs)
Permanent magnets
Linear and nonlinear permeability
Node coupling and constraint equations
In addition, modeling of current sources (current conducting regions) is simpler with the scalar formulation. This is so because you can simply specify current source primitives (coils, bars, and so forth) in the proper locations to account for their magnetic field contribution.
The magnetic vector potential (MVP) formulation is one of the two nodal-based methods for 3-D static, harmonic, and transient analyses which the ANSYS program supports. (The scalar potential formulation is the other nodal-based method.)
The MVP formulation has more (three) degrees of freedom per node than the scalar method: AX, AY, and AZ, the magnetic vector DOFs in the X, Y, and Z directions. Voltage-fed or circuit coupled analysis may add up to three additional degrees of freedom to the magnetic vector DOFs: current (CURR), electromotive force drop (EMF), and electric potential (VOLT). You must use the MVP formulation for a 2-D static magnetic analysis; doing so results in a single magnetic vector potential degree of freedom, AZ.
With the MVP formulation, you model current sources (current conducting regions) as an integral part of the finite element model. However, the MVP formulation runs more slowly than the scalar formulation because of the added DOFs.
You can also use the MVP formulation for 3-D static, harmonic or transient magnetic analysis. If you do, however, you should be cautious when including permeable materials in the model due to a loss of accuracy using the 3-D MVP formulation. (The solution has been found to be inaccurate when the normal component of the vector potential is significant at the interface between elements of different permeability.)
You can include both 3-D MSP and 3-D MVP formulations in the same model by using the INTER115 interface element.
The edge formulation is similar to the MVP formulation. It associates degrees of freedom (DOFs) with element edges rather than element nodes. The method offers 3-D static and dynamic solution capability for low frequency electromagnetics. You perform 3-D edge-based analyses using essentially the same procedures you use for 3-D nodal-based analyses. The edge-based analysis is not available for 2-D models.
The Theory Reference for ANSYS and ANSYS Workbench discusses the edge formulation in more detail.
The edge formulation is more accurate than the nodal-based formulations in cases where both methods share the same functionality, particularly when models contain iron regions. Edge-based analysis also is more efficient than the nodal-based methods in terms of the active degrees of freedom.
The edge formulation is the recommended method for most 3-D harmonic and transient electromagnetic analyses. However, currently the methods do not support identical capabilities. You should use the MVP formulation in these situations:
When your model requires motion effects and circuit coupling
When your model requires circuit and velocity effects
When you are analyzing a model containing no iron regions.
You can solve most 3-D static problems using the MSP formulation or a MVP or edge formulation. In accuracy critical applications, it is a good idea to solve your problem using both MSP and MVP or edge formulations. The difference between the MSP and MVP or edge solutions is your best measure of accuracy.
Except for coil regions, you can generally apply the same mesh for MSP and MVP or edge formulations. To switch from MSP formulation to MVP or edge formulation, you switch element type.
You must also switch boundary conditions (flux-normal-flux-parallel).
The following are important additional points to remember about accuracy:
Energy is the most accurate quantity.
The finite element method is a variational procedure minimizing or maximizing the energy stored in the studied domain. Thus, energy is the most accurate single number characterizing a solution. Monitoring the convergence of energy is a prudent way to check accuracy.
The MSP and MVP or edge formulations converge monotonously to the exact energy from above and below, respectively. Therefore, without knowing the exact energy, you can obtain a good accuracy measure by checking the energy difference between MSP and MVP or edge solutions. If you refine the mesh, this energy difference must theoretically decrease.
The LMATRIX command macro computes the inductance matrix of a coil system based on the stored energy. Therefore, the difference between MSP and MVP or edge inductance coefficients is also a good accuracy measure.
In accuracy critical applications, rely on centroidal field values.
Field quantities are less accurate than nodal solutions because they are obtained from derivatives of the potential solution. The derivatives are first evaluated at the element integration points then extrapolated to corner nodes. Consequently, integration point field values are more reliable than corner data. Centroidal field values are averaged integration point values.
The finite element variational procedure converges in the energy space. In most situations the energy convergence implies convergence of local field values. However, field values at special locations, like corners and edges, may not converge.
Continuity conditions are a reasonable measure of solution accuracy.
The satisfaction of continuity conditions is a reasonable measure of solution accuracy. The MSP and MVP or edge formulations must satisfy continuity of tangential magnetic field, Ht, and normal flux density, Bn, respectively. Therefore, the difference in Ht and Bn continuity is a good measure of MSP and MVP or edge convergence, respectively.
MMF and flux are better accuracy measures than continuity conditions.
Although the difference in Ht and Bn is a reasonable measure of the accuracy of a magnetic finite element solution, these values contain differentiation and extrapolation errors, especially when evaluated at element nodes. Integration can smooth these fluctuations.
MMF (magnetomotive force) is the closed loop integral of Ht. When MMF is evaluated over various loops enclosing the same current, according to Ampere's law, the loop integral should theoretically be equal to the enclosed current. Therefore, the difference in MMF values over different loops enclosing identical current is a good measure of MVP or edge solution accuracy. See the MMF macro for a convenient way to evaluate magnetomotive force.
The flux is the surface integral of Bn over a closed loop. Since there are no magnetic poles, the flux crossing the surfaces of a flux tube is constant. In general, it is impractical to predict a flux tube. However, for accuracy check purposes, you can select elements on opposite sides of a surface to obtain two faces of a flux tube. The flux difference crossing the same surface is a good measure of MSP solution accuracy.
In accuracy critical applications, tighten the Biot Savart tolerance for MSP solutions.
In MSP solutions, ANSYS applies the Biot Savart integration procedure to evaluate source magnetic field values exited by SOURC36 current source elements. The accuracy of the Biot Savart calculations is most critical at corners and edges. The default tolerance value is satisfactory for most applications. However, in accuracy critical applications, you may need to tighten the tolerance (SOURC36 element real constant EPS).
For MSP solutions, apply a pseudo iron material around iron domains.
To avoid cancellation errors, the MSP formulation applies certain physical assumptions in the iron region. These assumptions may not prove to be good approximations where iron regions are heavily saturated (for example, near corners and edges). Sometimes air regions may behave similar to iron. Violated assumptions may degrade accuracy.
ANSYS differentiates air and iron regions by the relative permeability. A material with a relative permeability larger than one is considered to be iron. To avoid a violation of the air-iron behavior assumptions, apply a couple layers of pseudo iron material around iron domains. Set the relative permeability to slightly above one (for example 1.0001).
Make sure that elements occupying the air space of coils are "real" air elements (that is, the relative permeability is exactly one).