## Force calculation

The VHM may be modelled by idealising the magnetic flux pattern such that the flux density under the tooth and under the slot are constant over their length and equal to Bt and Bs respectively. The equivalent magnetic circuit of Figure 4.2 represents one quarter of the machine which would give the same value of flux as modelling all the gaps and mmf sources. This model holds true for the entire phase, where there are 4 mmf sources in series with four airgap reluctances.

Branch A corresponds to the flux path through the tooth and consists of the reluctance of one magnet and the airgap under the tooth, St. Branch B represents the flux flow through the slot region and consists of a magnet reluctance in series with the reluctance of a slot, Ss. Considering just branch A, the reluctance is defined in (4.1), which gives the flux flow of (4.2) for each tooth.

V0WmL Vr V0WmL SVr + tm Vr V0 WmL

1 NI

wmL SA NIV0Vr

Noting that BA is equivalent to Bt in (3.12), substitution may now be used to relate the shear stress to the excitation current.

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