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, 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 5.15: Two-Phase Electric Machine - Half Model, 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, 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 low- and 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 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.
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 4.14: Process Flow for a Static Cyclic Symmetry Analysis (cyclically symmetric loading) 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: