Summary

In EMSolution, we have provided PHICOIL (Potential Current Source). Here we explain the definition of PHICOIL in the case of rotational z-anti-mirroring symmetry.

Explanation

EMSolution provides a rotational z-anti-mirroring symmetry (CYCLIC=3). This symmetry is mainly used in the analysis of claw motors, etc. As shown in Fig. 1, this symmetry is applied when the magnetic field or current is considered cyclic if it is rotated by a certain angle q (45 degrees in this case) and flipped upside down. The figure shows the case of SYMMETRY=0. The magnetic flux density at the position where the rotation is reversed remains the same in the z direction, but the directions in the r and q directions are reversed. For a double angle (2q), this can be viewed as normal cyclic symmetry, but with half the computational domain compared to that. (The analysis in Fig. 1 can be analyzed with mirror symmetry at 0 and 45 degrees, but when rotations, etc. are introduced, it is necessary to consider it as cyclic

Fig.1　Analytical model of rotation z-anti-mirroring symmetry(Contour lines represent magnetic flux density intensity distribution.)

In the case of this rotational z-anti-mirroring symmetry, if a coil that goes around a full revolution as shown in Fig. 1 is defined by PHICOIL, the gap plane is defined by a surface element as shown in Fig.2. The gap plane is defined by cutting one more element outward from the coil conductor element. The direction of the coil current coincides with the direction of the gap surface element. Fig. 2 shows the current density distribution with this definition. The gap face should be defined on the side with the smallest angle of cyclic symmetry. The direction of the coil current coincides with the direction of the gap surface element. This gap surface property number is shared by the gap surface and PHICOIL definitions. Fig. 2 shows the current density distribution with this definition.　Since EMSolution ver10.1.1 (April, 2007), it is no longer possible to define a gap plane on a periodic boundary plane. Gap surfaces should be created so that they do not coincide with the periodic boundary.

Fig.2 Definition of PHICOIL in the case of periodicity

A coil with translational (CYCLIC=1) or rotational (CYCLIC=2) cyclic symmetry with current flowing across the plane of symmetry can be defined in the same way. Note that PHICOIL has a non-uniform distribution of current density for curved coils.