Frescos-refrigerados

The design of the permanent magnets in the machine is principally focused on the magnet pole arc and thickness in the direction of magnetisation. Whereas increasing the pole arc and magnet axial length will always tend to increase the airgap flux density and hence torque capability, the magnets in a double-sided axial field machine can constitute a significant proportion of the overall mass. Hence, there is a need through detailed analysis to establish a trade-off between machine mass and torque capability. • Magnet pole arc

The variation in the average airgap flux density as a function of magnet pole arc was investigated for the TORUS non-slotted machine. In many topologies of permanent

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magnet machine, the magnet arc is an important factor to consider due to its influence on cogging torque. However, in this slotless machine, there is no need to consider cogging torque and the pole arc can be selected solely in terms of the influence on torque capability and mass.

Three-dimensional, magneto-static finite element modelling was employed to model a range of magnet arcs from 100⁰ electrical to 180⁰ electrical for a 8 pole rotor. The coil thickness used in the model was 5mm with an additional 1mm mechanical clearance. The magnet axial length was set to 6mm. The resulting variations across one magnet pole in the axial component of flux density at the average magnet radius and at an axial position that correspond to the middle of the conductor is shown in the Figure 4. 1.

Figure 4. 1. 3D model predicted airgap flux density at average radius

As would be expected, the narrower pole arcs tend to reduce the span over which the flux density is essentially a flat-top. However, since the effective magnetic airgap is large at 6mm, inter-pole leakage is a major issue particularly in terms of the axial component of flux density towards the edge of the poles. As the magnet pole arc increased larger, and two adjacent magnet edges get closer, the benefit in the axial component of airgap flux density become less pronounced due to inter-pole leakage. Figure 4. 2shows a summary of the average value of the axial component of the airgap flux density as a function of magnet arc. For pole arcs of beyond 160⁰ or so, the rate

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of increase in the axial flux density begins to tail-off. Further increasing the magnet pole arc does not bring significant benefits in terms of airgap flux density, and there is indeed penalty in doing so. As the leakage becomes more pronounced, rather than contributing to the useful axial component of airgap flux density, the leakage flux simple increases the flux in the rotor back iron. This requires a thicker back iron to avoid the onset of magnetic saturation.

On the basis of this sensitivity study, a magnet arc of 160 was selected as this provides a good trade-off between airgap flux density and magnet mass.

Figure 4. 2. Variation in average airgap flux density with magnet arc

• Magnet axial length

Given the large effective magnetic airgap which is inevitable in a TORUS non-slotted topology, a relatively thick magnet is required in order to maintain a competitive flux density level in the airgap. Although it is important to maximise the airgap flux density, the additional mass of a thick magnet should also be taken into consideration. In the original design, to achieve a relative high airgap flux density level, a 12mm thick magnet was employed in the initial design. In this double-sided topology, the permanent magnets made up 40% of the total active mass of the machine. In order to establish the sensitivity of the torque to magnet axial length, a further series of finite element simulations were performed for a range of magnet axial length between 1mm and 20mm, with the remaining of the dimensions to be the same. All calculations were

0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 100 110 120 130 140 150 160 170 180 A ve rag e fl u x d e n si ty B z (T)

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performed with the preferred magnet pole arc of 160 and at a coil current density of 30A/mm2 _{rms. The resulting variation in torque as a function of magnet length is}

shown in Figure 4. 3. Although the 12mm thick magnets selected in the reference design in Chapter 3 provides a reasonable selection, it does not provide the optimised value as the rate of increase in torque with magnet axial length is modest. Whereas the intermittent nature of the VGV application provides the possibility of employing short intervals of very high current density, the requirement for a high magnetic loading remains important.

In order to explore the variation in torque with current density for a range of magnet axial length, a further set of three-dimensional finite element calculations were performed. Figure 4. 4. Shows the resulting variation torque with increasing current density for a series of magnet axial length. With a thinner magnet, the linearity of the increase torque with current density is inevitably reduced. Taking a 50% reduction in magnet axial length to 6mm as an example (which would reduce the active mass of the entire machine by ~20%) then for the same rms current density of 30A/mm2, the torque only drops by 19%. This torque deficit can be made up by increasing the rms current density from 30A/mm2 _to38A/mm2_{. On the basis of this analysis, the magnet axial}

length was reduced to 6mm for the preferred design at this point.

Figure 4. 3. Three-dimensional finite element predicted variation in torque at a coil current density of 30A/mm2 _{as a function of different magnet axial length}

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Figure 4. 4. Resultant rated torque variation with current density for different magnet length