SENSORLESS FIELD ORIENTED CONTROL OF BRUSHLESS ...

present analysis). When this is true, the motor in Figure 2.12 can be “unwrapped” into a linear
version that is qualitatively equivalent (called the developed view) as shown in Figure 2.13. Like
cross-section detail views, developed views are rarely drawn to scale; in particular, the airgap
length and slot sizes are usually greatly exaggerated for clarity.
Figure 2.13 – Developed view showing only ideal rotor flux density.
The angle θ is measured beginning at zero and increasing as the airgap is traversed counter-
clockwise. It is worthwhile to mentally verify that the flux paths are equivalent between the two
figures. The graph below the developed view shows the “impossibly ideal” air gap flux density B
(which cannot be attained in practice due to fringing effects, rotor leakage flux, and core
nonlinearity).
Now that the magnetic structure has been introduced, the magnetic circuit will be developed. This
will lead to some important observations about how the magnet sets up flux in the airgap, the
meaning of flux linkage, and the meaning of inductance.
When the rotor is fixed in the position shown in Figure 2.12, the magnetic circuit can be modeled
schematically as shown in Figure 2.14 ([68], [42]), which ignores leakage flux (flux that links
only the stator or only the rotor, but does not cross the airgap). S R , R R , and R ag represent the
effective reluctances of the stator, rotor, and airgap, respectively. The magnets are represented as
a source of flux in parallel with a reluctance R m , as in a Norton current source. R m is shown as a
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