Page 619 - Mechatronics with Experiments

ELECTRIC ACTUATORS: MOTOR AND DRIVE TECHNOLOGY 605
torque generation capability per unit current. This is accomplished by commutating
the stator current (mechanically or electronically) as a function of the rotor position.
3. Stepper motors (permanent magnet (PM) type) work on basically the same principle
as brushless DC motors, except that the stator winding distribution is different. A
given stator excitation state defines a stable rotor position as a result of the attraction
between electromagnetic poles of the stator and permanent magnets of the rotor. The
rotor moves to minimize the magnetic reluctance. At a stable rotor position of a step
motor, two magnetic fields are parallel.

The torque generation, that is the electrical energy to mechanical energy conversion process,
in any electric motor can be viewed as a result of the interaction of two magnetic flux density
vectors: one generated by the stator ( ⃗ B ) and one generated by the rotor ( ⃗ B ). In different
r
s
motor types, the way these vectors are generated is different. For instance, in a permanent
magnet brushless motor the magnetic flux of rotor is generated by permanent magnets and
the magnetic flux of stator is generated by current in the windings. In the case of an AC
induction motor, the stator magnetic flux vector is generated by the current in the stator
winding, and the rotor magnetic flux vector is generated by induced voltages on the rotor
conductors by the stator field and resulting current in the rotor conductors. It can be shown
that the torque production in an electric motor is proportional to the strength of the two
magnetic flux vectors (stator’s and rotor’s) and the sine of the angle between the two vectors.
The proportionality constant depends on the motor size and design parameters.

T = K ⋅ B ⋅ B ⋅ sin( ) (8.1)
r
m
s
rs
where K is the proportionality constant, and is the angle between the ⃗ B and ⃗ B , and T
rs s r m
is the torque.
Every motor requires some sort of current commutation by mechanical means as in
the case of brush-type DC motors, or by electrical means as in the case of brushless DC
motors. Current commutation means modifying the direction and magnitude of current in
the windings as a function of rotor position. The goal of the commutation is to give the
◦
motor the ability to produce torque efficiently, that is to maintain = 90 .
rs
The design of an electric motor seeks to determine the following:

1. the three-dimensional shape of the effective magnetic reluctance of the motor by
proper selection of materials and geometry of the motor,
2. the distribution of coil wires, coil wire diameter, and its material (i.e., copper or
aluminum)
3. the permanent magnets (number of poles, geometric dimensions and PM material).

The engineering analysis is concerned with determining the resulting force/torque for
a given motor design and coil currents. In addition, we also need to examine the flux
density and flux lines in order to evaluate the overall quality of the design so that there
is no excessive saturation in the flux path. These results are obtained from the solution
of Maxwell’s equations for electromagnetic fields. Modern engineering analysis software
tools are based on the finite element method (FEM) to solve Maxwell’s equations and used
for motor design (examples include Maxwell 2D/3D by Ansoft Corporation, Flux2D/3D
by Magsoft Corporation, and PC-BLDC by The Speed Laboratory).