7.3.6. Solving a Magnetic Cyclic Symmetry Analysis

Most magnetic analysis problems can be defined with flux parallel and/or flux normal boundary conditions. With problems such as electrical machines, however, cyclic boundary conditions best represent the periodic nature of the structure and excitation, and have the advantage of being able to use a less computation-intensive partial model, rather than a full model.

You can analyze only one sector of the full model to take advantage of this kind of symmetry. The full model consists of as many sectors as the number of poles. In Example Magnetic Cyclic Symmetry Analysis (p. 216), the number of sectors is two; the analysis can be done on a half model.

The cyclic boundary condition is between matching degrees of freedom on corresponding symmetry faces. The studied sector is bounded by two faces called the low edge and high edge, respectively. In Figure 7.29: Two-Phase Electric Machine – Half Model (p. 217), the low edge face is the y = 0, x >= 0 plane; the high edge is the y = 0, x <= 0 plane.

The simplest case is when the node-matching interface of the low edge is the same as the high edge. In this case, for every node, there is one and only one matching node on the high edge; moreover the pertinent geometry and connectivity are the same. In this case, the cyclic boundary condition for the edge formulation could be formulated as

Az(low entity) = - Az(high entity)

This is an anti-symmetric condition which is called ODD symmetry.

The analysis could be carried out on a 360/p sector (where p is the number of poles), in which case the cyclic condition would be:

Az(low entity) = + Az(high entity)

which is a symmetric condition called EVEN symmetry.

In Example Magnetic Cyclic Symmetry Analysis (p. 216), the ODD model is smaller and thus more practical. For some problems, depending on geometry and excitation, EVEN symmetry may be more practical. The program supports both ODD and EVEN cyclic symmetry.

In a more general case, the mesh on the low and high end may be different. In this case, more general cyclic symmetry conditions can be established by interpolation on the pertinent faces. The program handles this process automatically via the CYCLIC command.

The geometry of the lowand high-end cyclic faces may be more general than a simple plane surface. Thus, for example, a skewed slot of an electric machine may constitute the cyclic sector modeled.

Cyclic Modeling (p. 164) discusses cyclic modeling in detail.

The following restrictions apply to a magnetic cyclic symmetry analysis:

•Cyclic conditions can be restricted to specific degrees of freedom (DOFs) via the DOF option. DOF restrictions may be useful, for example, in cases involving circuit-/voltage-fed solenoidal edge elements

.

•Multiphysics coupling must use the same EVEN/ODD condition.

•Circuit coupling is not supported for cyclic symmetry except solenoidal SOLID97.

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•Harmonic and transient analyses are not supported.

•By default, plotting displays the partial solution only. To see the full model solution, issue the /CYCEXPAND command. For magnetic cyclic symmetry, the /CYCEXPAND command produces contour plots but not vector plots.

Figure 7.9: Process Flow for a Static Cyclic Symmetry Analysis (Cyclic Loading) (p. 177) shows the process for a cyclic symmetry analysis. The process is virtually identical for a magnetic cyclic symmetry analysis; simply disregard the step for a large-deflection solution.

Magnetic cyclic boundary conditions can be applied to the following element types:

•Nodal magnetic vector potential elements: PLANE13, PLANE53, SOLID97

•Magnetic scalar potential elements: SOLID5, SOLID96, SOLID98

•Electrostatic elements: PLANE121, SOLID122, SOLID123

7.3.7. Database Considerations After Obtaining the Solution

At the conclusion of the cyclic symmetry solution, exit the solution processor via the FINISH command.

If you intend to exit the program at this point (before postprocessing), save the database (Jobname.DB). The saved database allows you to perform postprocessing on the analysis results at a later time.

7.3.8. Model Verification (Solution)

The cyclic solution reports the number of constraint equations generated for each harmonic index solution and information about how they were created. The information should match what you already know about the analysis model; if not, try to determine the reason for the discrepancy. The following extracts (from a batch output file or an interactive output window) are typical:

MAX NODE LOCATION ERROR NEAR ZERO)

Meaning: 124 constraint equations are created, used, and then deleted to enforce cyclic symmetry conditions between the lowand high-edge nodes. Every node on the low edge is precisely matched to a corresponding node on the high edge, representing the best possible situation.

MAX NODE LOCATION ERROR = 0.73906E-02)

Meaning: 124 constraint equations are created, used, and then deleted to enforce cyclic symmetry conditions between the lowand high-edge nodes. Every node on the low edge is matched to a corresponding node on the high edge within the current tolerance setting, but not all matches are precise. The largest position mismatch is 0.0073906.

Meaning: 504 constraint equations are created, used, and then deleted to enforce cyclic symmetry conditions between the lowand high-edge nodes. At least one node on the low edge does not match any node on the high edge within the current tolerance setting, so the program uses the unmatched nodes algorithm.