EE6703

SPECIAL ELECTRICAL
MACHINES
UNIT-IV
PERMANENT MAGNET BRUSHLESS
DCMOTORS
UNIT IV PERMANENT MAGNET BRUSHLESS DC MOTORS

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.
UNIT IV PERMANENT MAGNET BRUSHLESS DC MOTORS

PART-A QUESTIONS

1.Explain the construction and working principle of PMBLDC motor.

2.Discuss about minor hysteresis loop and recoil line.
3.Discuss about the magnetic characteristics and magnetic circuit
analysis of PMBLDC motor.
4.Drive the expressions for the EMF and torque of PMBLDC motor.
5.Draw and explain the operation of electronic commutator.
6.Explain the operation of power converter circuit for PMBLDC motor.
7.Explain the closed loop control scheme of PMBLDC motor.
8.Draw and explain the torque-speed characteristics of PMBLDC
motor.
PERMANENT MAGNET BRUSHLESS DC MOTORS

When the functions of commutator and brushes

were implemented by solid state switches,
maintenance free motors were realized
These motors are known as Brushless DC
Motors
The function of magnets is the same in both
brushless motor and the DC commutator motor
The motor obvious advantage of brushless
configuration is the removal of brushes
PERMANENT MAGNET BRUSHLESS DC MOTORS

Brush maintenance is no longer required, and

many problems associated with brushes are
removed
An advantage of the brushless configuration in
which the rotor inside the stator is that more cross
sectional area is available for the power or
armature winding
 PERMANENT MAGNET MATERIALS

NdFeB – Neodymium – iron – boron has the

highest energy product of all commercially
available magnets at room temperature
It has high remanence and coercivity in the motor
frame size for the same output compared with
motors using ferrite magnets. But it is costlier
Stated magnets are sensitive to temperature and
care should be taken for working temperature above
100˚C
For very high temperature applications, alnico or
rare earth cobalt magnets must be used
 PERMANENT MAGNETIC CHARACTERISTICS
BH Hysteresis loop of hard permanent magnet material
 PERMANENT MAGNET MATERIALS

X – axis – Magnetizing force or field intensity H

Y – axis – Magnetic flux density B in the material
An un-magnetized sample has B = 0 and H = 0 and
therefore starts out at the origin
Curve OA
If it is subjected to a magnetic field, magnetic
fixture (an electromagnetic with shaped pole pieces
to focus flux into the magnet), then B and H in the
magnet follow the curve OA as the external ampere
– turns are increased
 PERMANENT MAGNET MATERIALS
Curve AB
If the external ampere – turns are switched off, the
magnet relaxes along AB
The operating point (H, B) depends on the shape of
the magnet and permanence of the surrounding
magnetic circuit
If the magnet is surrounded by a highly permeable
magnetic circuit, then its poles are effectively
shorted together
So that H = 0 and then the flux density is the value
at point remanence Br
 PERMANENT MAGNET MATERIALS
Permanence
Maximum flux density that can be retained by the
magnet at a specified temperature after being
magnetized to saturation
Curve BC
External ampere turns applied in the opposite
direction cause the magnets operating point to follow
the curve from B through the second quadrant to C
Curve CD
If the ampere – turns are switched off at c the
magnet relaxes along CD
 PERMANENT MAGNET MATERIALS
Permanence
Maximum flux density that can be retained by the
magnet at a specified temperature after being
magnetized to saturation
Curve BC
External ampere turns applied in the opposite
direction cause the magnets operating point to follow
the curve from B through the second quadrant to C
Curve CD
If the ampere – turns are switched off at c the
magnet relaxes along CD
 PERMANENT MAGNET MATERIALS
It is now magnetized in the opposite direction and
the maximum flux density it can retain when B r
To bring B to zero from negative remanence point
D, the field +Hc must be applied
The entire loop is usually symmetrical and be
measured using instruments such as hysteresis graph
Soft PM
Soft PM materials have Knee in the second quadrant
such as Alnico
 PERMANENT MAGNET MATERIALS
Alnico magnets have very high remanence and
excellent mechanical and thermal properties
But they are limited in the demagnetizing field
they can withstand
These soft PM are hard when compared with
lamination steels the hysteresis loop of typical non
oriented electrical steel is very narrow when
compared with Alnico
 PERMANENT MAGNET MATERIALS
Demagnetization curve
 PERMANENT MAGNETIC CHARACTERISTICS
In the absence of externally applied ampere-turn,
the magnets operating point is at the intersection of
the demagnetization curve and the load line.
The slope of the load line is the product of μ 0 and
the permeance co efficient of the external circuit.
Relationship between B and H is

H -flux density that would exist if the magnet were

removed and the magnetizing force remain at the
value H
J-contribution of the magnet to the flux-density
within its own volume
 PERMANENT MAGNETIC CHARACTERISTICS
If the demagnetization curve is a straight line, and
therefore its relative slope and there by the μrec is
unity, Then J is constant
J-Magnetization of the magnet, unit T Tesla
Hard magnets have μrec>= 1,J decreases as the -Hc
increases
The magnet can recover or recoil back to its
original flux density as long as the magnetization is
constant
The coercive force required to permanently
demagnetize the magnet is called the intrinsic
coercivity and it is Hci
 PERMEANCE COEFFICIENT
Apply Ampere’s law to a closed flux line, and since there is
no current enclosed by flux line, we have

Hm lm + Hg lg = 0 ……………………(1)
Hm lm =- Hg lg ………………………..(2)
Neglecting the fringing flux,
Am Bm = Ag Bg ………………………...(3)
Bm/Hm = -(Bg Ag lm)/ (Hg Am lg)………(4)

Bm/Hm = -(Bg Ag lm)/ (Hg Am lg)………(5)

CONSTRUCTIONAL FEATURESB OF BLPM MOTORS
 CONSTRUCTIONAL FEATURES OF BLPM MOTORS

STATOR
The stator of the BLPM dc motor is made up of
silicon steel stampings with slots in its interior
surface
These slots accommodate either a closed or opened
distributed armature winding usually it is closed
This winding is to be wound for a specified
number of poles
This winding is suitably connected to a dc supply
through a power electronic switching circuitry
(named as electronic commutator)
 CONSTRUCTIONAL FEATURES OF BLPM MOTORS

ROTOR

Rotor is made of forged steel. Rotor

accommodates permanent magnet.
The rotor shaft carries a rotor position sensor.
This position sensor provides information about
the position of the shaft at any instant to the
controller which sends suitable signals to the
electronic commutator.
 CONSTRUCTIONAL FEATURES OF BLPM MOTORS

Merits
There is no field winding. Therefore there is no field
cu loss.
The length of the motor is less as there is no
mechanical commutator.
Size of the motor becomes less.
It is possible to nave very high speeds.
It is self-starting motor.
Speed can be controlled.
Motor can be operated in hazardous atmospheric
condition.
Efficiency is better.
 CONSTRUCTIONAL FEATURES OF BLPM MOTORS

Demerits

Field cannot be controlled.

 Power rating is restricted because of the maximum
available size of permanent magnets.
A rotor position sensor is required.
A power electronic switch circuitry is required.
PRINCIPLE OF OPERATION OF BRUSHLESS
PM DC MOTOR
When DC supply is switched ON to the motor the
armature winding draws a current.
The current distribution within the stator armature
winding depends upon rotor position and the devices
turned ON.
An EMF perpendicular to the permanent magnet
field is set up.
Then the armature conductors experience a force.
The reactive force develops a torque in the rotor.
If this torque is more than the opposing frictional
and load torque the motor starts.
PRINCIPLE OF OPERATION OF BRUSHLESS PM DC MOTOR
It is a self-starting motor.

Dynamic equilibrium
As the motor picks up speed, there exists a relative
angular velocity between the permanent magnet field
and the armature conductors.
As per faradays law of electromagnetic induction,
an EMF is dynamically induced in the armature
conductors.
This back EMF as per lenz‘s law opposes the cause
armature current and is reduced.
PRINCIPLE OF OPERATION OF BRUSHLESS PM DC MOTOR

As a result the developed torque reduces.

Finally the rotor will attain a steady speed when the
developed torque is exactly equal to the opposing
frictional load torque.
Thus the motor attains a steady state condition.

Electromechanical transfer
When the load – torque is increased, the rotor
speed tends to fall.
As a result the back EMF generated in the armature
winding tends to get reduced.
PRINCIPLE OF OPERATION OF BRUSHLESS PM DC MOTOR

Then the current drawn from the mains is increased

as the supply voltage remains constant.
More torque is developed by the motor.
The motor will attain a new dynamic equilibrium
position when the developed torque is equal to the
new torque
Power drawn from the mains is V*I
Pm=2πNT/60
Various losses in the motor and in the electronic
switching circuitry.
PRINCIPLE OF OPERATION OF BRUSHLESS
PM DC MOTOR
Magnitude of the developed torque
Te= K1s r sin 
Where,
s --Stator field flux
r –Rotor field flux
 - Torque Angle
K1 Torque Constant
PRINCIPLE OF OPERATION OF BRUSHLESS
PM DC MOTOR
When A Phase is energised
Tea= Kiasin 
Where,
ia –Stator current in Phase A

When B Phase is energised

Teb= Kibsin (-120º)
When C Phase is energised
Tec= Kicsin (-240º)
PRINCIPLE OF OPERATION OF BRUSHLESS
Phase CurrentsPM DC MOTOR
ia= imsin 
ib = im sin (-120º)
ic = im sin (-240º)

Phase Currents
Tea= Kimsin 2
Teb= Kimsin2 (-120º)
Tec= Kimsin2 (-240º)
Resultant Torque
TeR= Tea + Teb + Tec
PRINCIPLE OF OPERATION OF BRUSHLESS
PM DC MOTOR
Resultant Torque
Te= 3/2 K im
 CLASSIFICATION OF BLPM DC MOTOR
BLPM dc motors can be classified on the basis of
the flux density distribution in the air gap of the
motor. They are
(a). BLPM Square wave dc motor [BLPM SQW DC
Motor]
(b).BLPM sinusoidal wave dc motor [BLPM SINE
WAVE DC Motor]

BLPM Square wave motor

These are two types:
180 º and 120º pole arc
 CLASSIFICATION OF BLPM DC MOTOR
180º pole arc
Air gap flux density distribution in 180º BLPM SQW
motor is
 CLASSIFICATION OF BLPM DC MOTOR
120º pole arc
Air gap flux density distribution in 120º BLPM SQW
motor is
 CLASSIFICATION OF BLPM DC MOTOR
BLPM Sine wave DC Motor

Air gap flux density distribution BLPM DC sine

wave motor
 EMF EQUATION OF BLPM SQW DC MOTORS
Let
‘p’ be the number of poles
‘Bg’ be the flux density in the air gap in wb/m2
‘Bk’ is assumed to be constant over the entire pole pitch in
the air gap (180º pole arc)
‘r’ be the radius of the air gap in m
‘l’ be the length of the armature in m
‘Tc’ be the number of full pitch turns per coil
‘ωm’ be the uniform angular velocity of the rotor in
mechanical rad/sec.
ωm =2πN/60 where N is the speed in rpm.
EMF EQUATION OF BLPM SQW DC MOTORS
 EMF EQUATION OF BLPM SQW DC MOTORS
Let at ωmt=0, the flux enclosed by the coil per pole is given
by
Bg = m/A ……………………(1)
m = Bg *A …………………(2)
A= (2πrl)/p …………………(3)
Equation (2) implies
m = Bg * (2πrl)/p ……………………(4)

Flux linkage of the coil

c= m *Tc……………………(5)
c= Bg * (2πrl)/p *Tc……………………(6)
 EMF EQUATION OF BLPM SQW DC MOTORS
Let at ωmt= π/p, the flux enclosed by the coil per pole is
given by
d  /d t = (Final flux linkage –initial flux linkage)/(Final time

=0- (Bg * (2πrl)/p *Tc )/ (π/m P)-0…………………(7)

– initial time)

= - (Bg * (2rl) *Tc m…………(8)

Induced EMF in the coil a1 A1
ec1=- (d/dt) …………………(9)

= (Bg * (2rl) *Tc m…………………(10)

FLUX DENSITY AND FLUX LINKAGE
FLUX LINKAGE AND PHASE VOLTAGE
 EMF EQUATION OF BLPM SQW DC MOTORS
EMF induced per phase in a coil
eph1= 2Bg rlTphm…………………(11)

EMF induced per phase in a coil a2 A2

eph2= 2Bg rlTphm…………………(12)
Resultant EMF induced per phase in a coil
eph1 +eph2= 4Bg rl Tphm…………………(13)
PHASE VOLTAGES
CONSTRUCTION OF MECHANICAL COMMUTATOR
COMMUTATOR SEGMENT

Commutator is made up of specially shaped

commutator segments made up of copper.
COMMUTATOR SEGMENT

These segments are separated by thin mica sheets

(ie) Insulation of similar shape.

 The commutator segments are tapered such that

when assembled they form a cylinder.

These segments are mechanically fixed to the shaft

using V – shaped circular steel clamps

Isolated electrically from the shaft using suitable

insulation between the clamps and the segment.
MECHANICAL COMMUTATOR AND BRUSHES
ARRANGEMENT
COMMUTATOR SEGMENT

It represents a case with 2 poles and 12

commutator segments.
To start with the brush X contacts with CSI and
brush Y with 7.
A DC supply is connected across the brushes X and
Y.
The DC current I passes through brush X, CSI,
tapping 1,tapping 7and brush Y.
There are two armature parallel paths between
tapping‘s 1 and 7
COMMUTATOR SEGMENT
Allow the armature to rotate by an angle in a
counter clockwise direction
Then the brush X contacts CS2 and the tapping‘s a
and the brush Y
The DC current passes through the tapping‘s 2 and
8 there are two parallel paths.
Now the MMF set up by the armature winding is
form tapping 8 to 2 along the brush axis YX
Thus the armature MMF direction is always along
the brush axis YX, even though the current
distribution in the armature winding gets altered.
(i) 2 – 3 – 4 – 5 – 6 – 7 – 8
(ii) 2 – 1 – 12 – 11 – 10 – 9 – 8
 ELECTRONIC COMMUTATOR
The armature winding which is in the stator has
12 tapping‘s.
Each tapping is connected to the positive of the DC
supply node and through 12 switches designated as
S1 ,S2,….S12 .
Negative of the supply at node Y through switches
S‘1,S‘2,…….S‘12.
ELECTRONIC COMMUTATOR
ELECTRONIC COMMUTATOR
 ELECTRONIC COMMUTATOR
When S1 and S‘1 are closed the others are in open
position, the DC supply is given to the trappings 1
and 7
There are two armature parallel path.
(i) 1 – 2 – 3 – 4 – 5 – 6 – 7
(ii) 1 – 12 – 11 – 10 – 9 – 8 – 7
After a small interval S1 and S‘1 are kept open
and S2 and S‘2 are closed. then DC current
passes from tapping 2 to 8 sets up MMF in the
direction 8 – 2.
 ELECTRONIC COMMUTATOR
Thus by operating the switch in a sequential
manner it is possible to get a revolving MMF in the
air gap.
 The switches S1 to S12 and S‘1 to S‘12 can be
replaced by power electronic switching devices such
as SCR‘s MOSFET‘s IGBT‘s, power transistor etc.
 TORQUE- SPEED CHARACTERSISTICS OF
BLPM SQM DC MOTOR
Let the supply voltage V be constant

Permissible region of operation in T-ω m plane

The continues current should not exceed the
permissible current limit In (i.e) Torques should not
exceed Kt In.
 TORQUE- SPEED CHARACTERSISTICS OF
BLPM SQM DC MOTOR
The maximum permissible supply voltage = V n.
The speed should not exceed ωmn.
 TORQUE- SPEED CHARACTERSISTICS OF
BLPM SQM DC MOTOR
Line AB
 Parallel to X-axis represents maximum permissible torque
line which corresponds to maximum permissible current In.
The speed should not exceed ωmn.
Line FG
It represents T-ωm characteristics corresponding to
the maximum permissible Vn.
Line DH
It represents constant maximum permissible speed
line (i.e) ωmn is constant.
The area OABCDO is the permissible region of
 TORQUE- SPEED CHARACTERSISTICS OF
BLPM SQM DC MOTOR
 To obtain a particular point P corresponding to
given load-torque and speed condition the only
way to operate the motor at P is by suitably
adjusting the supply voltage fed to the motor.

 As the load torque is increased, the speed drops

and the drop is directly proportional to the phase
resistance and the torque.

 The voltage is usually controlled by chopping or

PWM.
 TORQUE- SPEED CHARACTERSISTICS OF
BLPM SQM DC MOTOR
 The boundaries of continuous and intermittent
limits are shown.
 Continuous limit - determined by the heat transfer
and temperature rise.
 Intermittent limit – determined by the maximum
ratings of semiconductor devices in circuit.