Automotive Engineering - May 2021 - 21

ELECTRIFICATION | SIMULATION FEATURE

PMM magnetic flux density distribution (shown at left) and air-gap MFF wave.

BOTH IMAGES: COMSOL

also increased coherently with rotor motion. In contrast, for asynchronous machines such as induction
motors, stator windings produce a rotating magnetic
field, which induces currents in the rotor. These currents interact with the stator field, producing a
torque, which is a function of lag between the rotating stator field and the motion of the rotor.
It will be useful to understand how the stator coils
are excited to produce rotor motion. Imagine a case
where a rotor magnet is aligned with a particular stator tooth. In simple terms, the magnetic field of a stator tooth has to be such that it repels the rotor magnet away, causing a tangential push. A tangential force
is what constitutes a torque for producing rotation.
The magnitude of the stator field should be highest
when there is a maximum alignment between the stator tooth and rotor magnet for producing the highest
value of force.
The rotor magnets are arranged with alternating
polarity (north and south poles) along the rotor periphery. Therefore, when the rotor magnet moves
ahead and the next rotor magnet follows, the stator
field has to flip to produce a repulsive push again,
along the same tangential direction. This ensures that
the torque is unidirectional and the rotor continues
rotating in the same direction.

Magnetic field distribution
In designing electrical machines, the magnetic field
distribution along the air gap periphery is a very crucial factor. Also referred to as the air gap magnetomotive force (MMF) wave, it is basically the plot of the
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radial component of the magnetic field along the circumference of
the air gap. The voltages induced in the stator coils directly depend
on the shape of the MMF wave. If the wave has a sinusoidal shape,
the stator phase will have a pure sinusoidal voltage. If there is a nonsinusoidal MMF wave, higher-order harmonics will be present in the
induced stator voltages. For a generator, the presence of harmonics
will result in poor power quality supplied to the power system, while
for a motor any higher-order harmonics imply wasted power and
therefore reduced efficiency.
From the COMSOL simulation of the PMM, we obtain the magnetic
field distribution and the air gap MMF wave. Simply by inspecting the
MMF wave in this case, we know that there will not be a purely sinusoidal voltage induced in the stator phase.

Investigating electromagnetic torque
A closer look at the model, in terms of generating maximum electromagnetic torque, shows many approaches we can use for exciting stator windings in a PMM with a specific slot/pole configuration. The pattern in the motor's schematic details one way that we
can drive a 12-slot, 10-pole PM motor. By adjusting either the initial
rotor position or phase of the stator coil excitation, we can apply
the maximum torque to the rotor. We give the rotor an initial angular displacement and vary the angle over an angular span of a rotor
magnet. We can then calculate the average torque value over the
entire range.
We choose the initial angular displacement corresponding to the
maximum average torque as the rotor's initial position. Therefore,
it is easy to visualize the relative positions of the stator and rotor
that produce the maximum torque. This study illustrates the use of
parametric sweep in COMSOL Multiphysics to vary the motor's design parameters and analyze their effects on the motor performance with ease.
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Automotive Engineering - May 2021

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