Fig.1 shows a permanent magnet bistable actuator operated by switching the current in alternate directions. It is characterised by long air gaps, and, for mechanical reasons, the cross‐section of the moving part (armature) is much smaller than those of other parts. These features make the magnetic field problem essentially 3‐dimensional, although the main flux path is confined to the longitudinal (x,y) plane. The amount of detail requires a 2D mesh of about 3000 elements in this cross‐section and about 500 elements in the transvers cross‐section, so that a full 3D solution would require a substantial calculation. The dynamic force characteristic requires a magnetic field distribution for each level of current in the coil and each position of the armature, thus creating strong incentives to use 2D approximations.
Carpenter, C.J. and Affane, W. (1992), "TWO‐DIMENSIONAL APPROXIMATIONS TO THREE‐DIMENSIONAL FIELDS IN AN ACTUATOR", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 11 No. 1, pp. 117-120. https://doi.org/10.1108/eb051766
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