SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

Figure 5.15 – Rotor types: (a) nonsalient (surface magnet); (b), (c) salient (interior magnet).
The amount of rotor steel along the d and q axes is different for each rotor type. High quality
magnets have a relative permeability of approximately unity. Therefore the reluctances in the d
and q directions are the same for the nonsalient rotor (Figure 5.15-a) which has been the subject
of discussion throughout the report. Inductance is inversely proportional to reluctance, and the
reluctance itself is directly proportional to length of the airgap through non-ferrous material. For
the salient rotor where the d axis is through steel (Figure 5.15-b), the reluctance in the d direction
is lower than that in the q direction, thus the d-axis inductance is larger than the than of the q-
axis. The opposite is true for the other salient rotor (Figure 5.15-c), in which the d axis passes
through less steel than the q axis. For the majority of interior magnet BPMS motors, Ld Lq
[43,
p.756].
If the magnetic material in each rotor was replaced with plastic, only the salient rotors would
produce torque with the stator field; this is the reluctance torque mentioned above. The different
ratios of these inductances cause the torque function (for a concentrated full-pitch winding) to be
different. Figure 5.16-a shows the torque produced as a function of the torque angle. The black
line indicates the mutual torque which varies as the sine of the torque angle [77, p.349]; it is the
familiar torque-angle curve for a synchronous machine and is shown for both the braking and
motoring directions. The two double-frequency components are those due to the different
reluctances of the salient rotors; they are shown in only the motoring direction for clarity. The
curves are combined in Figure 5.16-b. It is clear that for the rotor in Figure 5.15-b, the ideal
torque angle is less than 90° [30, p.260], whereas for the rotor in Figure 5.15-c the ideal torque
angle is greater than 90° [42, p.509].
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