1. November 26, 2024 1
Permanent Magnet materials Minor hysteresis loop and recoil
line Magnetic Characteristics Permeance coefficient Principle
of operation Types Magnetic circuit analysis EMF and torque
equations Commutation Power Converter Circuits and their
controllers Motor characteristics and control Applications.
PERMANENT MAGNET
BRUSHLESS D.C. MOTORS
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PMBLDC MOTORS
Magnetic circuit analysis, Magnetic
characteristics and Permeance
coefficient
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MAGNETIC CIRCUIT ANALYSIS
The basic calculation method of a magnetic circuit is the same
as is used in a basic electrical analysis using Ohms Law.
The total magnetic flux 淡 (analogous to electric current),
magneto-motive force F (analogous to voltage), and magnetic
reluctance R (analogous to electrical resistance) are related
as shown in below.
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In magnetic circuit calculations, it is more common to use the
magnetic permeance P, which is the reciprocal to reluctance
R.
Using permeance instead of reluctance, the total flux
equation is changed as shown in below.
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The permeance P is a function of the magnetic circuit length
L, magnetic circuit cross sectional area A, and magnetic
permeability 亮.
This means that when the length is shorter and the magnet
area and permeability are greater, the permeance is greater.
Conversely the reluctance is reduced.
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Magnetomotive force loss coefficient f
The magnetomotive force loss coefficient f is the ratio of the
total magnetomotive force Ft and the magnetomotive force in
the air gap Fg for a given magnetic circuit.
The total magnetomotive force Ft in the magnetic circuit is
determined as the product of the magnetic field strength Hd
at the operating point, and the length of the magnet Lm.
(4)
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The magnetomotive force in the air gap Fg is given as the
product of the magnetic field strength of the air gap Hg, and
the length of the air gap Lg.
Thus equation (4) becomes as follows
(5)
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Leakage coefficient ()
The leakage coefficient is the ratio of the total magnetic flux
淡t generated from the magnet in a given circuit and the flux
found in the air gap 淡g.
The total magnetic flux generated in a magnet 淡t is given as
the accumulation of flux density at the operating point Bd
over the cross sectional area of the magnet Am and the
magnetic flux in the air gap 淡g is given as the accumulation of
flux density Bg over the area of the air gap Ag.
(6)
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Permeance coefficient (Pc)
The permeance coefficient is used to design a permanent
magnet application with a B-H curve.
This is defined as the ratio of flux density Bd and magnetic
field strength Hd of the operating point, and equation
becomes:
(8)
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The permeance coefficient in a magnetic circuit can be
rewritten from equations (5) and (7), and then they are placed
back into equation (8).
Equation (5) therefore
Equation (7) therefore
(9)
(10)
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Equivalent Circuit and General Equations
The per phase equivalent circuit is shown in Fig.1 as following,
where 了m is the flux linkage of stator winding per phase due
to the permanent magnet.
For steady state conditions, assuming v and e are sinusoidal at
frequency , the equivalent circuit becomes the one shown in
Fig.2, where X=L, and V, I, E, and 了m are phasors with rms
amplitudes.
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The steady state circuit equation can be written as
Assuming that L << R, For a maximum mechanical power at a
given speed, I and E are in phase.
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A brushless dc motor has position feedback from the rotor via
Hall devices, optical devices, encoder etc. to keep a particular
angle between V And E, since E is in phase with rotor position,
and V is determined by the inverter supply to the motor.
Assuming that L << R, when I is in phase with E, V will also be
in phase with E. Thus the circuit can be analyzed using
magnitudes of E,V, and I as if it were a dc circuit.
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But first note that when E and I are in phase, the motor
mechanical power output (before friction, windage, and iron
losses) i.e. the electromagnetic output power is
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COMMUTATION
Brushless motors rely on semiconductor switches to turn
stator windings on and off at the appropriate time.
The process is called electronic commutation
Commutation with electronics has large scope of capabilities
and flexibility.
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In this motor, the mechanical "rotating switch" or commutator
is replaced by an external electronic switch synchronised to
the rotor's position.
Brushless direct current electric motors, or BLDC motors for
short, are electronically commutated motors powered by a DC
electric source via an external motor controller.
Put simply, commutation is the process of switching the
current in the motor phases to generate motion.
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BLDC Motor commutation
Before dwelling too far into feedback options for BLDC
motors, it is important to understand why they are necessary.
BLDC motors come in single phase, 2-phase, and 3-phase
configurations; the most common configuration being 3-
phase.
The number of phases matches the number of windings on
the stator while the rotor poles can be any number of pairs
depending on the application.
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Because the rotor of a BLDC motor is influenced by the
revolving stator poles, the stator pole position must be
tracked in order to effectively drive the 3 motor phases.
Hence, a motor controller is used to generate a 6-step
commutation pattern on the 3 motor phases.
These 6-steps, or commutation phases, move an
electromagnetic field which causes the permanent magnets
of the rotor to move the motor shaft.
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This is where feedback technology becomes important; for the
controller to maintain accurate control of the motor, it must
always know the exact position of the stator in relation to the
rotor.
Any misalignment or phase shift in the expected and actual
position may result in undesirable behavior and a decline in
performance.
There are many ways to achieve this feedback for the
commutation of BLDC motors, but the most common are Hall
effect sensors, encoders, or resolvers.
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Position feedback
Since the inception of the brushless motor, Hall-effect sensors
have been the workhorse for commutation feedback.
For 3-phase control, only three sensors are required, Hall
sensors are embedded into the stator of the motor to detect
rotor positon, which is used to switch the transistors in the 3-
phase bridge to drive the motor.
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The three Hall-effect sensor outputs are commonly noted as
the U, V, and W channels.
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The commutation sequence is shown in the following video
url
https://www.youtube.com/watch?time_continue=4&v=6ELRk
eEwlDw
(Students are advised to go through the video link for greater
clarity and understanding)
