## A

By calculating the values of flux density at points along the airgap of the machine it is therefore possible to predict the attractive forces between the rotor and the stator. In a two sided machine with an equal airgap between each half of the stator, the net force on the rotor will be zero, it being equally attracted in two opposite directions. The forces present between the rotor and any one side of the linear machine are given in Figure 4.16. As with the tangential force above, the force is cyclic over the 24 mm pole pitch at high currents, yet cyclic over the 12 mm magnet pitch at zero current.

Figure 4.16: Attractive forces between rotor and stator

Figure 4.17 shows the normal force for a positive and negative 15 Amp current, demonstrating that current direction dictates the phase with respect to the position and not the amplitude. This figure demonstrates the high frequency cyclic load which the support structure has to withstand.

+15 Amps — -15 Amps

position (mm)

10 15

position (mm)

Figure 4.17: Comparison of normal forces for ± 15 Amps

Figure 4.17: Comparison of normal forces for ± 15 Amps

Figure 4.18: Point force along stator. The stator faces correspond to 24-96 and 240-312 mm positions.

A breakdown of the force distribution across the stator airgap for these two currents in the two alternative aligned positions is given in Figure 4.18. As expected, there is no force felt by the majority of the translator, only regions under pole face. Comparison of the upper and lower graphs reveals that the position of the force is dictated not by the location of the rotor tooth, but by that of the magnet in phase with the armature field. When the tooth region is under the in phase magnet, a large 'smooth' force is observed, corresponding to the dashed upper and solid lower graph lines of Figure 4.18, the flux pattern of Figure 4.13B and the peak of Figure 4.17. When it is the slot region which is aligned with the in phase magnet, a smaller force is observed.

Figure 4.19 shows the variation of force with a current of 10 Amps flowing in the coils, when the rotor and stator are at the 6 mm position. It demonstrates that the attractive forces are highly dependant on the chosen size of airgap. The gradient of the force vs. gap size graph, effectively the stiffness of the magnetic attraction, increases slightly with current, from 1.49 MNm-1 at 5 Amps to 2.2 MNm-1 at 20 Amps.

Figure 4.19 shows the variation of force with a current of 10 Amps flowing in the coils, when the rotor and stator are at the 6 mm position. It demonstrates that the attractive forces are highly dependant on the chosen size of airgap. The gradient of the force vs. gap size graph, effectively the stiffness of the magnetic attraction, increases slightly with current, from 1.49 MNm-1 at 5 Amps to 2.2 MNm-1 at 20 Amps.

Figure 4.19: Normal force on stator, p=6

### 4.3.1.3 Co-Energy Model for Electromagnetic Force

Electromagnetic force in a linear machine can be calculated by determining the rate of change of co-energy with position. Using the flux linkage vs. mmf diagram as a visual tool to analyse co-energy in switched reluctance motors is well established [76] and it has recently been used to characterise a doubly salient permanent magnet motor [77]. Total mmf is obtained by the product of current flowing and number of turns for an entire phase, whereas the instantaneous flux linkage is calculated from FEA results. Both of these quantities are a function of translator position and coil current, giving a closed trajectory for each electrical cycle as shown in the typical Y-mmf graph of Figure 4.20.

in c

 § i 3 ^co-energy X z} / iL / w mmf (A-T) - portion

Figure 4.20: Example flux linkage-mmf trajectory

Figure 4.20: Example flux linkage-mmf trajectory

Figure 4.21A shows a typical magnetisation curve, with the field energy and co-energy, corresponding to (4.15) and (4.16) respectively, labelled.

## 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.

Get My Free Ebook