Details of Results

4.2.3.1 Electrical Excitation

If the permanent magnet regions of the FEA are replaced with air regions, then it is possible to investigate the behaviour of the VHM due to armature excitation only. Figure 4.9 shows the variation of flux linking a phase of the machine with excitation plotted on the same axis as a straight line of gradient 0.425. The good agreement of the two show that, until over 15 Amps, the iron is not becoming saturated.

Investigation revealed that varying the relative position of stator and translator had negligible (<1%) effect on the total flux flow in the absence of magnetic material.

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Figure 4.9: Variation of phase flux linkage with excitation current, no magnets.

4.2.3.2 Magnetic Excitation

Figure 4.10 shows the model flux plot when the rotor teeth are fully aligned with the magnets. Two return paths are visible, the leakage flux flowing between neighbouring magnets and the useful flux within the backiron linking the coils. Moving from left to right along each stator face, it is clear by inspection of Figure 4.10A that each aligned magnet contributes less to the flux linking the coils. The rightmost pair make a negligable contribution, with all the flux leaking between neighbouring magnets. With the translator displaced one magnet pitch to the right, as in Figure 4.10B, the pattern of leakage and driving magnets has reversed, with the leftmost pair making no useful contribution. By deduction it is clear that the leakage flux is most severe when the edge magnet has no tooth to channel the flux and so is forced to find a return path through its neighbouring magnet. Any even number of stator pole magnets will hence exhibit this effect. Calculation of the no load flux is therefore highly affected by the edge effects of the stator face, a factor not accounted for with the simple analysis used previously.

10 8

-----y=0.425x s

s'

ST

current (A)

current (A)

Figure 4.10: Flux plot for magnetic excitation. (A) zero position, (B) 12 mm position

The direction of flux flow is reversed in Figure 4.10A when compared with Figure 4.10B yet it is reasonable to assume the magnitude will be the same. From this it is clear that there will be a position of zero flux flow through the C-core between positions of full alignment with adjacent magnets. Figure 4.11 demonstrates that this occurs when the magnet and tooth are exactly misaligned and the flux return path is across the stator face.

The actual variation of flux linkage is cyclic over the rotor pitch and Figure 4.12 shows that it is a smooth function of relative tooth and magnet position.

Figure 4.11: Flux plot for the misaligned positions (A position=18 and B position=6 ), magnet excitation only.

Figure 4.11: Flux plot for the misaligned positions (A position=18 and B position=6 ), magnet excitation only.

position(mm)

Figure 4.12: Predicted no load variation of flux linkage for entire phase with position

position(mm)

Figure 4.12: Predicted no load variation of flux linkage for entire phase with position

It is now possible to investigate the accuracy of the model used to predict the emf in Equation (4.5) above. Inserting the dimensions given in Table 4-1 into equation (4.3) predicts the value of flux due to one pair of magnets interacting with one translator tooth. Multiplying this value by the number of magnet pairs per face (3), the number of faces per phase (4) and the number of turns per coil (240) gives a peak flux linkage of 3.2 Wb turns, 3.5 times greater than that shown in Figure 4.12. Even as a rough approximation, ignoring the leakage between adjacent magnets is clearly unsuitable, further highlighted by inspection of Figure 4.10.

In normal operation of the machine there will be current flowing in the coils, which will drive its own flux around the magnetic circuit in addition to that driven by the PMs. The total flux linkage may be expressed as the sum of that due to the armature excitation,^/, and the original PM driven flux, yPM, (4.13).

The direction of armature excitation with respect to remnant magnet excitation will strongly affect the reluctance and hence path of flux flow in the airgap region. Figure

4.13A and B show the flux plot in this region for a 10 Amp current flowing in either direction at the same translator-stator position. At this value of current the armature excitation dominates and an even contribution from each pair of magnets implies that end effects are less pronounced with armature excitation. When the direction of current

driven flux is opposite to that of the magnets, as in Figure 4.13 A, a path of high reluctance is enforced, with flux either travelling through the magnet in a direction opposite to its magnetisation, or being forced into the slot region of the translator. There is a danger of demagnetising the magnets in this position. The opposite is visible in Figure 4.13B, when almost parallel flux lines in the magnet and tooth regions demonstrate that the direction of magnetic remnance strengthens the flux flow, channelling it into the tooth region of the translator.

Figure 4.13: Flux plot with (A) +10A, (B) -10 A. Position = 0

Reluctance of the magnetic circuit hence varies with both position and direction of current, for example the flux linking the entire phase being 5.24 Wb turns in Figure 4.13A compared with 3.51 Wb turns in Figure 4.13B.

Flux paths have been demonstrated to be complex in this machine for both combined and magnetic only excitation. The most accurate way to model the machine is by utilising the flux-linkage map of Figure 4.14. Flux data is taken from the FEA at different coil excitations over one electrical cycle and plotted on a three dimensional flux linkage vs. position vs. current set of axes.

The symmetrical variation of flux linkage with current, present in the no load / 0 Amp condition of Figure 4.12, occurs also when the coils are carrying current. The effect of this current manifests itself in more flux being driven around the magnetic circuit and hence the entire flux vs. position curves being shifted up and down the flux axis. It is noteworthy that the plot is not symmetrical over the current range for a fixed position, for example if p=0 the resulting flux from a 15 Amp excitation is 7.5 Wb turns compared to -6 Wb turns for - 15 A. Re-inspection of Figure 4.13 confirms that this asymmetrical affect is dependent on whether the excitation current is in the same sense as the magnetisation of the aligned magnets.

Figure 4.14: Flux linkage map of entire phase

Figure 4.14: Flux linkage map of entire phase

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