356 Motor Design Finiteelement Modelling

3D finite-element modelling (FEM) was not required, as the topology of the machine in x-y plane is the same along the axial length, except at each end where the end turns winding exists. However, a 2D finite-element model has been employed for the machine to calculate and analyse the flux distribution in it, Fig. 3.10. This is done to facilitate the rotor movement relative to the stator, so that the characteristics of interest such as the flux modulation due to slot ripple effect on the magnet and the rotor hub can be examined. To carry out this kind of analysis, several meshes have to be created, one for each rotor position, and then each solved in turn. The software program has a facility for coupling meshes, using Lagrange multipliers. This technique has been used to join the independent rotor and stator meshes at a suitable interface plane, a sliding Lagrange interface being placed in the middle of the air gap. The view at (a) shows a close-up view of the joined meshes for the machine, and in (b) is the rotor of the machine at 45° from base (half of the rotor mesh is missing for clarity).

Fig. 3.10 Finite-element modelling: (a) the coupling meshes; (b) rotor at 45o from base; (c) air gap flux waveforms; (d) contour and vector flux.

The stator winding flux linkage waveforms of the machine have been calculated from the time transient solution, as the rotor speed is dynamically linked to the program, at 20 000 rpm. The experimental phase flux linkage has been deduced by integration of the phase EMF generated from the machine at no-load. These EMFs are shown to be within 8% difference, the value calculated by FEM being the higher. The flux in the air gap was measured using a search coil that is inserted on the stator side. From this search coil, a flux waveform was recorded and it is shown together within the flux calculated from FEM in (c). The flux plot, as contours and vectors at 0° rotor position for the machine, is shown at (d).

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