## Vernier Hybrid Machine VHM

The VHM has a significantly more conventional machine structure, and a two dimensional flux pattern [65, 68]. Figure 3.10 shows four stator pole faces supported on two opposed C-cores each carrying two coils. The stator mounted PMs interact with the purely iron toothed rotor, in order to produce the flux path shown. This two dimensional path links all four coils, four magnets and four airgaps. A similar topology has been proposed, [66], which had the magnets on the moving part and the stator face toothed. If the rotor moved one magnet pitch, equal to half a rotor pitch, in either direction, it can be seen that the teeth would fully align with the opposite poles to those shown, and hence the flow of magnetic flux would be completely reversed.

Figure 3.10: The VHM

Because of the slots in the rotor the flux density is not constant throughout the width of the airgap. The flux pattern will resemble that shown in Figure 3.11, with a higher density being observed under the tooth region than under the slot region. Due to the magnets being alternatively magnetised, the greatest force is reacted when the magnets and teeth are exactly misaligned and hence the equivalent current carrying coils are in the area of highest flux density. As shown, the flux under the slot region causes a force which opposes that under the teeth.

Figure 3.11: Flux pattern of VHM

The peak resultant force per tooth pitch, Fnet, will be the difference of these opposing forces, given by (3.10).

Where Bt = flux density under the tooth (T)

Bs = flux density under slot region (T) Using the ratio of flux densities Bt and Bs, calculated using a conformal mapping technique given in [65] and (3.11), and substituting IPM from (3.5), it is possible to obtain a relationship for the force of one magnet from (3.10), or the general shear stress in terms of the maximum flux density under the tooth, (3.12).

## Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

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