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UNIT V
SINGLE PHASE INDUCTION MOTORS AND
SPECIAL MACHINES
Constructional details – Double revolving field theory
– Equivalent circuit – Starting methods – Role of
induction motor in industries and household
appliances – Reluctance motor - Servo motor -
Stepper motor - Universal motor - Switched
reluctance motor - Linear induction motor – Linear
Synchronous motor.
Single-Phase Motors
These motors, have output less than one horse-power
or one kilowatt, hence are called fractional horse-
power or fractional kilowatt motors.
AC single-phase, fractional kilowatt motors perform
variety of services in the homes, offices, business
concerns, factories etc.
Almost in all the domestic appliances such as
refrigerators, fans, washing machines, hair driers,
mixer grinders etc., only 1-phase induction motors are
employed.
Classification of Single-phase Motors
1. Single-phase induction motors
(i) split-phase type (ii) capacitor type
(iii) Shaded-pole type
2. AC series motors or universal motors
3. Repulsion motors
(i) Repulsion-start induction-run motors
(ii) Repulsion-induction motors
4. Synchronous motors
(i) Reluctance motors
(ii) Hysteresis motors.
Single-phase Induction Motors
A single-phase induction motor is very similar to a 3-
phase squirrel cage induction motor in construction.
• Similar to 3-phase induction motor it consists of two
main parts namely stator and rotor.
1. Stator: It is the stationary part of the motor. It has
three main parts, namely.
(i) Outer frame (ii) Stator core and
(iii) Stator winding.
(i) Outer frame: It is the outer body of the motor. Its
function is to support the stator core and to protect
the inner parts of the machine.
• Usually, it is made of cost iron.
• To place the motor on the foundation, feet are
provided in the outer frame as shown
(ii) Stator core:
• The stator core is to carry the alternating magnetic field which
produces hysteresis and eddy current losses.
• To minimise these losses high grade silicon steel stampings are used
to build core.
• The stampings are assembled under hydraulic pressure and are keyed
to the outer frame.
• The stampings are insulated from each other by a thin varnish layer.
• The thickness of the stamping usually varies from 0.3 to 0.5 mm.
• Slots are punched on the inner periphery of the stampings to
accommodate stator winding.
(iii) Stator winding:
• The stator core carries a single phase winding which
is usually supplied from a single phase AC supply
system.
• The terminals of the winding are connected in the
terminal box of the machine.
• The stator of the motor is wound for definite
number of poles, as per the need of speed.
2. Rotor: It is the rotating part of the motor.
• A squirrel cage rotor is used in single phase
induction motors.
• It consists of a laminated cylindrical core of some
high quality magnetic material.
• Semi-closed circular slots are punched at the outer
periphery.
• Aluminium bar conductors are placed in these slots
and short circuited at each end by aluminium rings,
called short circuiting rings
• Thus, the rotor winding is permanently short
circuited.
The rotor slots are usually not parallel to the shaft but
are skewed. Skewing of rotor has the following
advantages:
(a) It reduces humming thus ensuring quiet running of
a motor
(b) It results in a smoother torque curves for different
positions of the rotor
(c) It reduces the magnetic locking of the stator and
rotor
(d) It increases the rotor resistance due to the
increased length of the rotor bar conductors.
Nature of Field Produced in Single Phase Induction Motors
The field produced in a single-phase induction motor can be explained by
double revolving field theory which is given below:
•This theory is based on the “Ferraris Principle” that pulsating field produced
in single phase motor can be resolved into two components of half the
magnitude and rotating in opposite direction at the same synchronous speed.
•Thus the alternating flux which passes across the air gap of single phase
induction motor at standstill consists of combination of two fields of same
strength which are revolving with same speed
•one in clockwise direction and the other in anticlockwise direction. The
strength of each one of these fields will be equal to one half of the maximum
field strength of the actual alternating field
•Let 𝜑𝑚be the pulsating field which has two components each of magnitude
𝜑𝑚
2
.
• Both are rotating at the same angular speed 𝜔𝑠rad/sec but in opposite
direction
•The resultant of the two fields is 𝜑𝑚cos𝜃. This shows that resultant field
varies according to cosine of the angle𝜃.
Mathematically:
• where two magnetic fluxes each of magnitude
𝜑𝑚
2
are
revolving in opposite direction.
• At any instant t, the two fluxes have been rotated through
angle𝜃(𝜃 = 𝜔t).
• To determine the resultant value at this instant, resolve the
flux vectors along x-axis and y-axis
• Total value of flux along x-axis =
𝜑𝑚
2
cos 𝜔t +
𝜑𝑚
2
cos 𝜔t
=𝜑𝑚cos 𝜔t
• Total value of flux along y-axis =
𝜑𝑚
2
sin 𝜔t −
𝜑𝑚
2
sin 𝜔t =0
• Resultant flux, 𝜑 = 𝜑𝑚cos 𝜔t2 + 0 = 𝜑𝑚cos 𝜔t
• Thus an alternating field can be represented by the two
fields each of half the magnitude rotating at same angular
(synchronous) speed of 𝝎𝒔 radians/sec but in opposite
direction.
Torque Produced by Single-phase Induction Motor
• The two revolving fields will produce torques in opposite
directions. Let the two revolving fields be field No. 1 and field
No. 2 revolving in clockwise and anticlockwise direction.
• The clockwise field produces torque in clockwise direction,
whereas, the anticlockwise field produces torque in
anticlockwise direction.
• The clockwise torque is plotted as positive and anticlockwise
as negative.
• At stand still, slip for both fields is one. At synchronous speed,
for clockwise direction, the field-1 will give condition of zero
slip but it will give slip = 2 for field No. 2.
• At synchronous speed in a counter clockwise direction, will
give condition of zero slip for field -2 but slip = 2 for field No.
1.
• The resultant torque developed in the rotor is shown by the
curve passing through zero position as shown in Fig.
• The resultant torque it is observed that the starting
torque (torque at slip = 1) is zero. And except at
starting there is always some magnitude of
resultant torque,
• At position 1-1’, the torque developed by field-1 is
dominating, therefore, motor will pick-up the speed
in clockwise direction.
• At position 2-2’, the torque developed by field-2 is
dominating, therefore, motor will pick-up the speed
in anti-clockwise direction).
• This shows that if this type of motor is once started
(rotated) in either direction it will develop torque in
that direction and rotor will pick-up the required
speed.
• The above analysis shows that single phase
induction motor with single winding develops no
starting torque
• but if the rotor is rotated in any direction by some
auxiliary means in will develop torque in the same
direction and will start rotating in that direction.
• So the problem is to find out the auxiliary means to
give the starting torque to the motor.
Equivalent Circuit of Single-phase Induction Motor
• The equivalent circuit of a single-phase induction motor may be drawn on
the basis of two revolving field theory.
• Accordingly, each of the field is producing emf in the rotor by induction.
• A single-phase induction motor may be imagined to have common stator
but two rotors revolving in opposite directions.
• Where, each rotor has resistance and reactance half the actual rotor values:
R1 be the resistance of stator winding
X1 be the leakage reactance of stator winding
Xm be the total magnetising reactance
Rm be the total magnetising resistance
R2’ be the resistance of rotor referred to stator
X2’ be the reactance of rotor referred to stator
• While developing the equivalent circuit, it is considered that the stator is
having only one winding.
• The equivalent circuit can be developed under stand-still (at start) and
running (operating) conditions.
At Standstill Conditions
• At standstill, the motor is considered simply as a
transformer with its secondary short-circuited.
• The only difference is that in this case, two fields are
considered revolving in opposite direction.
• Therefore, for each field rotor resistance and reactance
is considered to be half the value, i.e., 𝑅2
′
/2and 𝑋2
′
/2.
Moreover, each rotor is associated with half the total
magnetising reactance and resistance i.e., Xm/2 and
Rm/2 respectively.
• The equivalent circuit of a single-phase induction motor
at standstill is shown in Fig. 11.5(a),
• Its simplified circuit is shown in Fig. 11.5(b) where core
loss component Rm has been neglected.
At Running Condition,
• At running condition, if the rotor is rotating in the
direction of the forward revolving field with the
• slip S, the rotor current produced by the forward
field will have a frequency Sf.
• At the same time the rotor current produced by
the backward field will have a frequency (2-S)f.
Accordingly, the equivalent circuit of single-phase
induction motor at running condition is drawn
• it is simplified in Fig. 11.6(b) where core loss
component Rm has been neglected
Input power 𝑃𝑖𝑛 = 𝑉𝐼1 cos 𝜑
Airgap power due to forward field 𝑃𝑎𝑔 =
𝐼1
2𝑅2
′
2𝑠
Methods to make Single-phase Induction Motor Self-starting
• A single-phase induction motor inherently is not self-starting.
• To make it self-starting, some method is required to be evolved to produce a
revolving magnetic field in the stator core.
• This may be obtained by converting a single-phase supply into two-phase
supply which can be achieved by using an additional winding (this additional
winding may be or may not be disconnected once the motor starts and picks-
up the speed) or by creating another field (by induction) using a short
circuiting band or ring.
• Accordingly, depending upon the method used to make a 1-phase induction
• motor self-starting, single-phase induction motors can be classified as:
1. Split-phase motors: These motors are started by employing two-phase
motor action through the use of an auxiliary winding called starting winding.
2. Capacitor motors: These motors are started by employing two-phase motor
action through the use of an auxiliary winding with capacitor.
3. Shaded-pole motors: These motors are started by the interaction of the
field produced by a shading band or short circuiting ring placed around a
portion of the pole structure.
Split Phase Motors:
• The outer frame and stator core of a split-phase motor is similar to
the outer frame and stator core of a 3-phase induction motor.
• It is provided with an auxiliary stator winding called starting
winding in addition to main winding. These windings are placed in
the stator slots.
• Both the windings are put in parallel. The purpose is to get two
different currents sufficiently displaced from each other so that a
revolving field is produced.
• The main winding which is highly inductive is connected across the
line in the usual manner. The auxiliary or starting winding has a
greater resistances and lesser reactance as compared to main
winding.
• The current in the starting winding Is lags the supply voltage by
lesser angle 𝜑𝑠
′
• whereas the current in the main winding Imbeing highly inductive
lags the supply voltage by greater angle 𝜑𝑚.
• The two currents have a phase difference of 𝜃°electrical. Thus, a
revolving field is set-up in the stator and a starting torque is
developed in the rotor.
Split-phase induction motor
Consequently rotor starts rotating and picks up the speed. A centrifugal
switch which is normally closed is incorporated in series with the
starting winding. When the motor attains a speed about 75% of
synchronous speed, the centrifugal switch is opened automatically with
the help of centrifugal force and puts the starting winding out of circuit.
It is important that the centrifugal switch should open otherwise the
auxiliary winding being made of thin wire will be over heated and may
damage.
Performance and Characteristics
the starting torque is about twice the full load torque. The current at
start is about 6 to 8 times. The speed falls with increase in load by only
about 5% to 7% otherwise it is a constant speed motor. Speed is
governed by the relation
NS =
120𝑓
𝑃
𝑅𝑃𝑀
Actual speed is less than synchronous speed NS. For the same weight its
rating is about 60% to that of the poly phase induction motor. It has
lower p.f. and lesser efficiency. P.f. is about 0.6 and efficiency is also
about 60%.
The direction of rotation of a 1-phase (split phase) induction motor can
be reversed by reversing (interchanging) the connections of either
starting winding or running winding.
Capacitor Motors
• It is also a split phase motor. In this motor, a
capacitor is connected in series with the starting
winding. This is an improved form of the above said
split phase motor.
• In these motors, the angular displacement between
IS and Im can be made nearly 90º and high starting
torques can be obtained
• since starting torque is directly proportional to sine
of angle 𝜃. The capacitor in the starting winding
may be connected permanently or temporarily.
Accordingly, capacitor motors may be
1. Capacitor start motors. 2. Capacitor run motors.
2. Capacitor start and capacitor run motors.
Capacitor start motors
• In the capacitor start induction motor capacitor C is of
large value such that the motor will give high starting
torque since torque T𝛼sin 𝜃.
• and in this case, the phase angle between Im and ISis
made near to 90.
• Capacitor employed is of short time duty rating.
• Capacitor is of electrolytic type. Electrolytic capacitor C
is connected in series with the starting winding along
with centrifugal switch S.
• When the motor attains the speed of about 75% of
synchronous speed starting winding is cutoff.
• The construction of the motor and winding is similar to
usual split phase motor.
• It is used where high starting torque is required such as
refrigerators.
Performance and characteristics:
Speed is almost constant with in 5% slip. This type of
motor develops high starting torque about 4 to 5
times the full load torque. It draw low starting
current.
The direction of rotation can be changed by
interchanging the connection of either starting or
running winding.
Capacitor run motors (fan motors):
• A paper capacitor is permanently connected in the
starting winding. In this case, electrolytic capacitor
cannot be used since this type of capacitor is
designed only for short time rating and hence
cannot be permanently connected in the winding.
• Both main as well as starting winding is of equal
rating.
Performance and characteristics.
• Starting torque is lower about 50 to 100% of full
load torque.
• Power factor is improved may be about unity.
Efficiency is improved to about 75%.
Capacitor start and capacitor run motors
• In this case, two capacitors are used one for starting
purpose and other for running purpose.
• For starting purpose an electrolytic type capacitor (Cs)
is used which is disconnected from the supply when
the motor attains 75% of synchronous speed with the
help of centrifugal switch S.
• Whereas, a paper capacitor CR is used for running
purpose which remains in the circuit of starting
winding during running conditions.
• This type of motor gives best running and starting
operation.
• Starting capacitor CS which is of higher value than the
value of running capacitor CR.
Performance and characteristics:
• Such motors operate as two phase motors giving
best performance and noiseless operation.
• Starting torque is high, starting current is low and
give better efficiency and higher p.f.
• The only disadvantage is high cost.
Shaded Pole Motor
Construction
• Shaded pole motor is constructed with salient poles
in stator.
• Each pole has its own exciting winding
• A 1/3rd portion of each pole core is surrounded by
a copper strip forming a closed loop called the
shading band
• Rotor is usually squirrel cage type.
• When a single phase supply is given to the stator
(exciting) winding, it produces alternating flux.
• When the flux is increasing in the pole, a portion of
the flux attempts to pass through the shaded
portion of the pole.
• This flux induces an emf and hence current in the
shading band or copper ring.
• As per Lenz’s law the direction of this current is such
that it opposes the cause which produces it i.e.,
increase of flux in shaded portion. Hence in the
beginning, the greater portion of flux passes
through unshaded side of each pole and resultant
lies on unshaded side of the pole.
• When the flux reaches its maximum value, its rate of
change is zero, thereby the emf and hence current in
the shading coil becomes zero.
• Flux is uniformly distributed over the pole face and the
resultant field lies at the centre of the pole.
• After this the main flux tends to decrease, the emf and
hence the current induced in the shading coil now
tends to increase the flux on the shaded portion of the
pole and resultant lies on the shaded portion of the
pole
• Hence, a revolving field is set up which rotates from
unshaded portion of the pole to the shaded portion of
the pole as marked by the arrow head
• Thus, by electromagnetic induction, a starting torque
develops in the rotor and the rotor starts rotating.
• After that its rotor picks up the speed.
Split Phase Capacitor
Start
Capacitor run Capacitor
start and run
Shaded pole
Characteristi
cs
Low and
medium
starting
torque
High Starting
torque
Medium
torque
High starting
torque
Low starting
torqu
Starting
torque
100% to 250%
of rated value
250% to 400%
of rated value
100% to 200%
of rated value
200% to 300%
of rated value
40% to 60%
of rated value
Braking
torque
Upto 300% Upto 350% Upto 250% Upto 250% Upto 10%
Power
factor
0.5 to 0.65 0.5 to 0.65 0.75 to 0.9 0.75 to 0.9 0.25 to 0.4
Efficiency 55% to 65% 55% to 65% 60% to 70% 60% to 70% 25% to 40%
Rating 0.5 to 1 HP 0.125 to 1 HP 0.125 to 1 HP 0.125 to 1 HP Upto 40W
Applications Fans,
blowers,
Centrifugal
pumps,
washing
machines
Compressors,
Pumps,
Conveyors,
Refrigerators,
AC and
Washing
Machines
Fans,
blowers,
Centrifugal
pumps,
Compressors,
Pumps,
Conveyors,
Refrigerators
Fans, turn
Tables, Hair
driers,
Motion
picture
projectors,
Blowers,
A single-phase induction motor draws a current of
0.5 A at 230 V and 0.6 lagging p.f. If it runs at a speed
of 100 radian per second and develops an output
torque of 0.3 Nm, find its output power and
efficiency.
The main winding of a 230V, 0.5 HP single-phase
induction motor (split-phase) draw a current of 6 A
which lags behind the voltage vector by 45°, whereas
the starting winding draw a current of 4A which lags
being the voltage by 15°. Determine
(i) Current drawn by the motor at start and its pf.
(ii) Current draw by the motor during running and its
pf.
(iii) Phase angle between the current drawn by the
main winding and starting winding.
(iv) Power drawn by the motor during starting and
running.
The parameters of the main and starting winding of
a 240 V, 50 Hz split-phase induction motor are given
as:
• Main winding: Rm = 6Ω; Xm = 8Ω
• Starting winding: RS = 8 Ω; XS = 6Ω
Determine:
(i) Current in the main winding
(ii) Current in the starting winding
(iii) Phase angle between Im and IS
(iv) Line current and pf of the motor
(v) Power drawn by the motor.
The main winding of a 110V, 60 Hz, 0.25 hp, single
phase capacitor start motor carries a current of 6-
ampere which lags behind the applied voltage by
42°. The starting winding carries a current of 4A
which leads the voltage vector by 40°. Calculate
(i) the total starting current and the power factor.
(ii) the phase angle between the main winding
current and starting winding current.
The winding impedances of the main winding and
starting winding of a 230 V, 50 Hz, 250 W capacitor
start motor are (5 + j4) ohm and (10 + j4) ohm
respectively. What value of capacitor is required to
be connected in series with the starting winding to
obtain maximum torque at the start.
Testing of Single Phase Induction Motor
Blocked Rotor Test:
• The rotor is blocked. We have to apply reduced
voltage to the main winding so that, rated current
flows through the main winding.
• Auxiliary winding is kept open during the test.
• The applied voltage is very low and the slip at
standstill is unity.
• Rotor impedance is much smaller than the
magnetisation reactance. The excitation branch is
neglected.
Total Impedance referred to stator, 𝑍𝑏 =
𝑉𝑏
𝐼𝑏
Total Resistance referred to stator, 𝑅𝑏 =
𝑊𝑏
𝐼𝑏
2
Total Reactance referred to stator, 𝑋𝑏 = 𝑍𝑏
2
− 𝑅𝑏
2
𝑅𝑏 = 𝑅1 + 𝑅2
′
𝑋𝑏 = 𝑋1 + 𝑋2
′
𝑅1 is already measured,
𝑅2
′
= 𝑅𝑏 - 𝑅1
𝑋1 = 𝑋2
′
=
𝑋𝑏
2
No load Test
The slip is very small.
• Term
𝑅2
′
2𝑠
is very large and treated as o.c as compared to
parallel branch
𝑋𝑚
2
•
𝑅2
′
2(2−𝑠)
reduced to
𝑅2
′
4
which is very much small than
𝑋𝑚
2
.
The term
𝑋𝑚
2
is considered as o.c
Impedance under no load condition, 𝑍0 =
𝑉0
𝐼0
Resistance under no load condition, 𝑅0 =
𝑊0
𝐼0
2
Reactance under no load condition, 𝑋0 = 𝑍0
2
− 𝑅0
2
𝑋0 = 𝑋1 +
𝑋𝑚
2
+
𝑋2
′
2
From blocked rotor test, 𝑋1 = 𝑋2
′
=
𝑋𝑏
2
𝑋0 =
𝑋𝑏
2
+
𝑋𝑚
2
+
𝑋𝑏
4
𝑋𝑚 = 2𝑋0 −
3
2
𝑋𝑏
Mechanical losses:
𝑃𝑚 = 𝑤0 − 𝐼0
2
𝑅1 +
𝑅2
′
4
The following are the parameters of a 230V, 50 Hz,
4-pole, single phase induction motor R1= 2.2Ω; X1=
3.0Ω; R’2 = 3.8Ω; X’2 = 2.1Ω; Xm = 86Ω.Calculate the
input current and power when the motor is
operating at full-load speed of 1410 rpm.
If the mechanical losses (iron and friction loss)
are 60 W, determine gross power developed, useful
power at the shaft, shaft torque and efficiency.
Hysteresis Motors
• A hysteresis motor is a single-phase cylindrical (non-
salient pole type) synchronous induction motor.
• The difference between this motor and reluctance
motor is in (i) the shape of the rotor and (ii) the
• nature of the torque produced.
Stepper motor
Stepper motor is a BLDC motor, whose rotor rotates
through a fixed angular step in response to each input
current pulse received by its controller.
Step angle:
Step angle is defined as, the angle through which the
stepper motor shaft rotates for each command pulse.
It is denoted as 𝛽.
𝛽 =
𝑁𝑠~𝑁𝑟
𝑁𝑠.𝑁𝑟
× 360°
Where,
𝑁𝑠 − Number of stator poles or stator teeth
𝑁𝑟 - Number of rotor poles or rotor teeth
𝛽 =
360°
𝑚𝑁𝑟
m- number of stator phases
Resolution:
it is defined as the number of steps needed to
complete one revolution of the rotor shaft
Resolution =
𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒔𝒕𝒆𝒑𝒔
𝑹𝒆𝒗𝒐𝒍𝒖𝒕𝒊𝒐𝒏
=
𝟑𝟔𝟎°
𝜷
Classification of Stepper motor:
1. Variable reluctance stepper motor
2. Permanent magnet stepper motor
3. Hybrid stepper motor
Variable reluctance(VR) stepper motor:
The stator windings are wound on the stator poles.
The rotor carries no windings. Rotor poles are of a
ferromagnetic material.
The rotor is salient pole type.
The reluctance of the magnetic circuit formed by the rotor
and stator teeth varies angular position of the rotor.
Permanent Magnet Stepper Motor:
Rotor is permanent magnet and is cylindrical type
The direction of rotation of motor depends on the polarity of the stator current
Hybrid stepper motor
The rotor is permanent magnet. It is a salient pole
type rotor.
VR Stepper motor
Construction:
• The VR stepper motor consists of stator and rotor
• There is no permanent in stator or rotor
• The rotor carries no windings
• The stator is made of soft iron stampings
• The stator windings re wound on stator poles.
Operation
1. 1-phase-ON or Full step operation
2. 2-phase-ON mode
3. Alternate 1-phase on and 2-phase-on mode
4. Micro stepping operation
1-phase-ON or Full step operation
Phase A Phase B Phase C 𝜽
+ 0 0 0°
0 + 0 30°
0 0 + 60°
+ 0 0 90°
2-phase-ON mode
2-Phase-ON mode
Phase A Phase B Phase C 𝜽
+ + 0 15°
0 + + 45°
+ 0 + 75°
+ + 0 105°
Half step operation:
It is also called half-stepping operation. Alternate 1-
phase on and 2-phase on modes. (A,AB,B,BC,C etc.,).
Phase A Phase B Phase C 𝜽
+ 0 0 0
+ + 0 15°
0 + 0 30°
0 + + 45°
0 0 + 60°
+ 0 + 75°
+ 0 0 90°
Permanent Magnet Stepper Motor
1-ph ON mode
Phase A Phase B 𝜽
+ 0 0°
0 + 90°
- 0 180°
0 - 270°
+ 0 0°
The motor direction depends on polarity of phase
currents.
Clock wise direction 𝑰𝑨
+
, 𝑰𝑩
+
, 𝑰𝑨
−
, 𝑰𝑩
−
, 𝑰𝑨
+
Counter clock wise
direction
𝑰𝑨
+
, 𝑰𝑩
−
, 𝑰𝑨
−
, 𝑰𝑩
+
, 𝑰𝑨
+
2-phase-ON mode
Phase A Phase B 𝜽
+ + 45°
- + 135°
- - 225°
+ - 315°
+ + 45°
Alternate 1-ph ON and 2-ph ON mode
Phase A Phase B 𝜽
+ 0 0°
+ + 45°
0 + 90°
- + 135°
- 0 180°
- - 225°
0 - 270°
+ - 315°
+ 0 0°
Hybrid Stepper Motor
Construction:
• The stator construction of a hysteresis motor is
either split-phase type or shaded-pole type which
produces a revolving field in the stator when single
phase AC supply is given to it.
• The rotor of hysteresis motor is specially designed
and is made of Hysteresis-type laminations of the
shape.
• These are usually made of hardened high-
retentivity steel rather than commercial low-
retentivity dynamo steel.
• During operations, the cross arms of the rotor are
permanently magnetised due to high retentivity of
the steel used for its construction.
Principle and Working
• When single-phase supply is given to the stator (split-phase
type or shaded pole type), a revolving magnetic field is set-up
by it.
• Eddy currents are induced in the rotor. These eddy currents
set up the rotor magnetic field which causes rotor to rotate.
• A high starting torque is produced as a result of the high rotor
resistance (proportional to the hysteresis loss).
• As the motor approaches synchronous speed, the frequency
of current reversal in the cross bars decreases and the rotor
becomes permanently magnetised in one direction through
cross-arms as a result of high retentivity of the steel used for
the construction of rotor.
• With the two permanently set field poles, the rotor will
develop a speed of 3000 rpm at 50 Hz. Thus, the motor runs
as a hysteresis motor on hysteresis torque because the rotor
is permanently magnetised
Reluctance Motor
“Whenever a piece of ferro-magnetic material is
located in a magnetic field, a force is exerted upon the
material, tending to bring it into the position of the
densest portion of the field. The force tends to align
the specimen of material so that the reluctance of the
magnetic path passing through the material will be at
a minimum”.
Construction
• Reluctance motor is a split-phase induction motor with
properly designed salient (shaped) poles.
• It consists of a stator carrying both the main and auxiliary (or
starting) windings for developing a synchronously rotating
magnetic field.
• The usual method of constructing a rotor for a reluctance
motor is to assemble it from standard squirrel-cage parts,
except that some of the teeth are removed.
• By removing some of the teeth of a normal squirrel-cage
rotor, salient poles are produced, which offer low reluctance
to the stator flux and thereby strongly magnetized.
• The number of salient poles created on the stator must be
equal to the number of poles on stator Rotor punching for a
4-pole reluctance type synchronous motor is shown in
figure.5.14
Operation
When the motor is switched on to a single phase ac supply, the motor
starts as an induction motor, accelerates and attains speed very close to
synchronous speed.
Since the mechanical load is comparatively small, the slip is negligible, in
which case the revolving field permanently magnetizes the projecting
rotor poles.
The rotor poles then "lock in step" with the revolving field poles of
opposite polarity and continue to rotate at synchronous speed, the
speed of the revolving field.
The motor adjusts its torque angle for a change in load in a similar way
to that described for a 3-phase synchronous motor
SERVOMOTORS
• The motors that are used in automatic control systems
re called as servomotors.
• Electrical (voltage) signal →Angular displacement of
shaft
Servo mechanism
• When object of system is to control the position of an
object, then the system is called servomechanism.
Principle of servomotors
• Servos operate on the principle of negative feedback,
where the control input is compared to the actual
position of the mechanical system as measured by
some sort of transducer at the output.
Types of Servomotors
Features
• Linear relationship between speed and electrical control signal.
• Steady state stability.
• Wide range of speed control
• Linearity of mechanical characteristics throughout the entire speed range.
• Low mechanical and electrical inertia.
• Fast response
Field controlled DC servomotor
It is open loop system. The error signal produced by the controller, is not enough to
drive the DC motor. Hence, it is amplified by an amplifier, called as servoamplifier. This
signal is applied to the field winding.
With the help of constant current source, the armature current is maintained
constant.
The motor has large
𝐿𝑓
𝑅𝑓
ratio.
where, 𝐿𝑓 – Field inductance, 𝑅𝑓- Field resistance
Time constant is high. This means the motor cannot give rapid respond to the quick
changing control signals.
Armature controlled DC Servomotor
It is the closed loop system. Hence, the controlled voltage obtained from
the servo amplifier after the amplification. The error signal is applied to
the armature. The motor shaft output is controlled by armature input
voltage and constant current is applied to the field.
Here, motor has small
𝐿𝑓
𝑅𝑓
. Hence, time constant is small and therefore,
the motor give rapid response to the quick changing control signals.
Characteristics of DC servomotor
(i) Torque–speed characteristics
(ii) Performance characteristics of a typical DC servomotor
Advantages of DC servomotor
• Higher output than from a 50Hz of same size
• Linearity of characteristics are achieved easily
• Easier speed control from zero speed to full speed in both directions.
• High torque to inertia ratio that gives them quick response to control
signals.
• DC servomotors have
• Light weight
• Low inertia
• Low inductance armature
• DC motors are capable of delivering over three times of their rated torque
for a short time.
Uses of DC servomotor
• 1. Servo stabilizer
• 2. Position control system
• 3. Robotics
• 4. Process controllers
• 5. Large power applications
AC Servomotor
Stator:
• Carries two windings
• Windings are uniformly distributed, displaced by
90◦ in space, from each other.
Description
• One winding-main winding or fixed winding or
reference winding.
• Other winding-control winding
• Control voltage is obtained from the servo amplifier
after processing the input error signals.
• The control voltage is 90◦ out of phase with respect
to the voltage applied to the reference winding,
necessary to obtain rotating magnetic field.
Rotor:Two types
• 1.Squirrel cage rotor 2.Drag cup type rotor
Squirrel cage rotor
• Have aluminium bars which are short at the ends.
• Overall construction looks like cage.
• Have small diameter and large length in order to reduce inertia.
• Aluminium conductors keeps weight small.
• Its resistance is high and hence, keeps torque-speed characteristics is
kept as linear as possible.
• Air gap is very small. Therefore, magnetising current can be reduced
easily.
• Drag cup type rotor
• To reduce inertia, drag cup type rotors used.
• There are two air gaps.
• Drag cup made up of nonmagnetic material like copper, aluminium or
an alloy.
• Slotted rotor laminations are replaced by a set of stationary ring
shaped laminations.
• These are wound so that the operating speed of motor is very low.
• Used in very low power applications.
Characteristics of AC servomotors
Torque-speed characteristics
Effect of increased resistance
Effect of (X/R) on characteristics
Performance characteristics of a typical AC servomotor
Advantages of AC servomotor
• Lower cost
• Higher efficiency
• Less maintenance since no commutators and brushes
Disadvantages of AC servomotor
• 1. Characteristics is not quite linear
• 2. More difficult to control
Uses of AC servomotor
• Low power applications
• Robotics
• Instrument servos
• Self-balancing recorders
• Process controllers
UNIVERSAL MOTOR
For some applications, it is desirable to employ a
motor that operates on either DC or AC. It is possible
to build, by a compromise design, small series motors
up to about
1
2
𝐾𝑊 rating to operate satisfactorily on
DC or AC at 115 or 230V. Such motors are called the
universal motors.
Construction
SINGLE PHASE INDUCTION MOTORS AND SPECIAL MACHINES

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SINGLE PHASE INDUCTION MOTORS AND SPECIAL MACHINES

  • 1. UNIT V SINGLE PHASE INDUCTION MOTORS AND SPECIAL MACHINES Constructional details – Double revolving field theory – Equivalent circuit – Starting methods – Role of induction motor in industries and household appliances – Reluctance motor - Servo motor - Stepper motor - Universal motor - Switched reluctance motor - Linear induction motor – Linear Synchronous motor.
  • 2. Single-Phase Motors These motors, have output less than one horse-power or one kilowatt, hence are called fractional horse- power or fractional kilowatt motors. AC single-phase, fractional kilowatt motors perform variety of services in the homes, offices, business concerns, factories etc. Almost in all the domestic appliances such as refrigerators, fans, washing machines, hair driers, mixer grinders etc., only 1-phase induction motors are employed.
  • 3. Classification of Single-phase Motors 1. Single-phase induction motors (i) split-phase type (ii) capacitor type (iii) Shaded-pole type 2. AC series motors or universal motors 3. Repulsion motors (i) Repulsion-start induction-run motors (ii) Repulsion-induction motors 4. Synchronous motors (i) Reluctance motors (ii) Hysteresis motors.
  • 4. Single-phase Induction Motors A single-phase induction motor is very similar to a 3- phase squirrel cage induction motor in construction. • Similar to 3-phase induction motor it consists of two main parts namely stator and rotor. 1. Stator: It is the stationary part of the motor. It has three main parts, namely. (i) Outer frame (ii) Stator core and (iii) Stator winding. (i) Outer frame: It is the outer body of the motor. Its function is to support the stator core and to protect the inner parts of the machine. • Usually, it is made of cost iron. • To place the motor on the foundation, feet are provided in the outer frame as shown
  • 5. (ii) Stator core: • The stator core is to carry the alternating magnetic field which produces hysteresis and eddy current losses. • To minimise these losses high grade silicon steel stampings are used to build core. • The stampings are assembled under hydraulic pressure and are keyed to the outer frame. • The stampings are insulated from each other by a thin varnish layer. • The thickness of the stamping usually varies from 0.3 to 0.5 mm. • Slots are punched on the inner periphery of the stampings to accommodate stator winding.
  • 6. (iii) Stator winding: • The stator core carries a single phase winding which is usually supplied from a single phase AC supply system. • The terminals of the winding are connected in the terminal box of the machine. • The stator of the motor is wound for definite number of poles, as per the need of speed.
  • 7. 2. Rotor: It is the rotating part of the motor. • A squirrel cage rotor is used in single phase induction motors.
  • 8. • It consists of a laminated cylindrical core of some high quality magnetic material. • Semi-closed circular slots are punched at the outer periphery. • Aluminium bar conductors are placed in these slots and short circuited at each end by aluminium rings, called short circuiting rings • Thus, the rotor winding is permanently short circuited.
  • 9. The rotor slots are usually not parallel to the shaft but are skewed. Skewing of rotor has the following advantages: (a) It reduces humming thus ensuring quiet running of a motor (b) It results in a smoother torque curves for different positions of the rotor (c) It reduces the magnetic locking of the stator and rotor (d) It increases the rotor resistance due to the increased length of the rotor bar conductors.
  • 10. Nature of Field Produced in Single Phase Induction Motors The field produced in a single-phase induction motor can be explained by double revolving field theory which is given below: •This theory is based on the “Ferraris Principle” that pulsating field produced in single phase motor can be resolved into two components of half the magnitude and rotating in opposite direction at the same synchronous speed. •Thus the alternating flux which passes across the air gap of single phase induction motor at standstill consists of combination of two fields of same strength which are revolving with same speed •one in clockwise direction and the other in anticlockwise direction. The strength of each one of these fields will be equal to one half of the maximum field strength of the actual alternating field •Let 𝜑𝑚be the pulsating field which has two components each of magnitude 𝜑𝑚 2 . • Both are rotating at the same angular speed 𝜔𝑠rad/sec but in opposite direction •The resultant of the two fields is 𝜑𝑚cos𝜃. This shows that resultant field varies according to cosine of the angle𝜃.
  • 11.
  • 12. Mathematically: • where two magnetic fluxes each of magnitude 𝜑𝑚 2 are revolving in opposite direction. • At any instant t, the two fluxes have been rotated through angle𝜃(𝜃 = 𝜔t). • To determine the resultant value at this instant, resolve the flux vectors along x-axis and y-axis • Total value of flux along x-axis = 𝜑𝑚 2 cos 𝜔t + 𝜑𝑚 2 cos 𝜔t =𝜑𝑚cos 𝜔t • Total value of flux along y-axis = 𝜑𝑚 2 sin 𝜔t − 𝜑𝑚 2 sin 𝜔t =0 • Resultant flux, 𝜑 = 𝜑𝑚cos 𝜔t2 + 0 = 𝜑𝑚cos 𝜔t • Thus an alternating field can be represented by the two fields each of half the magnitude rotating at same angular (synchronous) speed of 𝝎𝒔 radians/sec but in opposite direction.
  • 13. Torque Produced by Single-phase Induction Motor
  • 14. • The two revolving fields will produce torques in opposite directions. Let the two revolving fields be field No. 1 and field No. 2 revolving in clockwise and anticlockwise direction. • The clockwise field produces torque in clockwise direction, whereas, the anticlockwise field produces torque in anticlockwise direction. • The clockwise torque is plotted as positive and anticlockwise as negative. • At stand still, slip for both fields is one. At synchronous speed, for clockwise direction, the field-1 will give condition of zero slip but it will give slip = 2 for field No. 2. • At synchronous speed in a counter clockwise direction, will give condition of zero slip for field -2 but slip = 2 for field No. 1. • The resultant torque developed in the rotor is shown by the curve passing through zero position as shown in Fig.
  • 15. • The resultant torque it is observed that the starting torque (torque at slip = 1) is zero. And except at starting there is always some magnitude of resultant torque, • At position 1-1’, the torque developed by field-1 is dominating, therefore, motor will pick-up the speed in clockwise direction. • At position 2-2’, the torque developed by field-2 is dominating, therefore, motor will pick-up the speed in anti-clockwise direction). • This shows that if this type of motor is once started (rotated) in either direction it will develop torque in that direction and rotor will pick-up the required speed.
  • 16. • The above analysis shows that single phase induction motor with single winding develops no starting torque • but if the rotor is rotated in any direction by some auxiliary means in will develop torque in the same direction and will start rotating in that direction. • So the problem is to find out the auxiliary means to give the starting torque to the motor.
  • 17. Equivalent Circuit of Single-phase Induction Motor • The equivalent circuit of a single-phase induction motor may be drawn on the basis of two revolving field theory. • Accordingly, each of the field is producing emf in the rotor by induction. • A single-phase induction motor may be imagined to have common stator but two rotors revolving in opposite directions. • Where, each rotor has resistance and reactance half the actual rotor values: R1 be the resistance of stator winding X1 be the leakage reactance of stator winding Xm be the total magnetising reactance Rm be the total magnetising resistance R2’ be the resistance of rotor referred to stator X2’ be the reactance of rotor referred to stator • While developing the equivalent circuit, it is considered that the stator is having only one winding. • The equivalent circuit can be developed under stand-still (at start) and running (operating) conditions.
  • 18. At Standstill Conditions • At standstill, the motor is considered simply as a transformer with its secondary short-circuited. • The only difference is that in this case, two fields are considered revolving in opposite direction. • Therefore, for each field rotor resistance and reactance is considered to be half the value, i.e., 𝑅2 ′ /2and 𝑋2 ′ /2. Moreover, each rotor is associated with half the total magnetising reactance and resistance i.e., Xm/2 and Rm/2 respectively. • The equivalent circuit of a single-phase induction motor at standstill is shown in Fig. 11.5(a), • Its simplified circuit is shown in Fig. 11.5(b) where core loss component Rm has been neglected.
  • 19.
  • 20.
  • 21. At Running Condition, • At running condition, if the rotor is rotating in the direction of the forward revolving field with the • slip S, the rotor current produced by the forward field will have a frequency Sf. • At the same time the rotor current produced by the backward field will have a frequency (2-S)f. Accordingly, the equivalent circuit of single-phase induction motor at running condition is drawn • it is simplified in Fig. 11.6(b) where core loss component Rm has been neglected
  • 22.
  • 23.
  • 24.
  • 25. Input power 𝑃𝑖𝑛 = 𝑉𝐼1 cos 𝜑 Airgap power due to forward field 𝑃𝑎𝑔 = 𝐼1 2𝑅2 ′ 2𝑠
  • 26. Methods to make Single-phase Induction Motor Self-starting • A single-phase induction motor inherently is not self-starting. • To make it self-starting, some method is required to be evolved to produce a revolving magnetic field in the stator core. • This may be obtained by converting a single-phase supply into two-phase supply which can be achieved by using an additional winding (this additional winding may be or may not be disconnected once the motor starts and picks- up the speed) or by creating another field (by induction) using a short circuiting band or ring. • Accordingly, depending upon the method used to make a 1-phase induction • motor self-starting, single-phase induction motors can be classified as: 1. Split-phase motors: These motors are started by employing two-phase motor action through the use of an auxiliary winding called starting winding. 2. Capacitor motors: These motors are started by employing two-phase motor action through the use of an auxiliary winding with capacitor. 3. Shaded-pole motors: These motors are started by the interaction of the field produced by a shading band or short circuiting ring placed around a portion of the pole structure.
  • 27. Split Phase Motors: • The outer frame and stator core of a split-phase motor is similar to the outer frame and stator core of a 3-phase induction motor. • It is provided with an auxiliary stator winding called starting winding in addition to main winding. These windings are placed in the stator slots. • Both the windings are put in parallel. The purpose is to get two different currents sufficiently displaced from each other so that a revolving field is produced. • The main winding which is highly inductive is connected across the line in the usual manner. The auxiliary or starting winding has a greater resistances and lesser reactance as compared to main winding. • The current in the starting winding Is lags the supply voltage by lesser angle 𝜑𝑠 ′ • whereas the current in the main winding Imbeing highly inductive lags the supply voltage by greater angle 𝜑𝑚. • The two currents have a phase difference of 𝜃°electrical. Thus, a revolving field is set-up in the stator and a starting torque is developed in the rotor.
  • 29. Consequently rotor starts rotating and picks up the speed. A centrifugal switch which is normally closed is incorporated in series with the starting winding. When the motor attains a speed about 75% of synchronous speed, the centrifugal switch is opened automatically with the help of centrifugal force and puts the starting winding out of circuit. It is important that the centrifugal switch should open otherwise the auxiliary winding being made of thin wire will be over heated and may damage. Performance and Characteristics the starting torque is about twice the full load torque. The current at start is about 6 to 8 times. The speed falls with increase in load by only about 5% to 7% otherwise it is a constant speed motor. Speed is governed by the relation NS = 120𝑓 𝑃 𝑅𝑃𝑀 Actual speed is less than synchronous speed NS. For the same weight its rating is about 60% to that of the poly phase induction motor. It has lower p.f. and lesser efficiency. P.f. is about 0.6 and efficiency is also about 60%.
  • 30. The direction of rotation of a 1-phase (split phase) induction motor can be reversed by reversing (interchanging) the connections of either starting winding or running winding.
  • 31. Capacitor Motors • It is also a split phase motor. In this motor, a capacitor is connected in series with the starting winding. This is an improved form of the above said split phase motor. • In these motors, the angular displacement between IS and Im can be made nearly 90º and high starting torques can be obtained • since starting torque is directly proportional to sine of angle 𝜃. The capacitor in the starting winding may be connected permanently or temporarily. Accordingly, capacitor motors may be 1. Capacitor start motors. 2. Capacitor run motors. 2. Capacitor start and capacitor run motors.
  • 32. Capacitor start motors • In the capacitor start induction motor capacitor C is of large value such that the motor will give high starting torque since torque T𝛼sin 𝜃. • and in this case, the phase angle between Im and ISis made near to 90. • Capacitor employed is of short time duty rating. • Capacitor is of electrolytic type. Electrolytic capacitor C is connected in series with the starting winding along with centrifugal switch S. • When the motor attains the speed of about 75% of synchronous speed starting winding is cutoff. • The construction of the motor and winding is similar to usual split phase motor. • It is used where high starting torque is required such as refrigerators.
  • 33.
  • 34. Performance and characteristics: Speed is almost constant with in 5% slip. This type of motor develops high starting torque about 4 to 5 times the full load torque. It draw low starting current. The direction of rotation can be changed by interchanging the connection of either starting or running winding.
  • 35.
  • 36. Capacitor run motors (fan motors): • A paper capacitor is permanently connected in the starting winding. In this case, electrolytic capacitor cannot be used since this type of capacitor is designed only for short time rating and hence cannot be permanently connected in the winding. • Both main as well as starting winding is of equal rating. Performance and characteristics. • Starting torque is lower about 50 to 100% of full load torque. • Power factor is improved may be about unity. Efficiency is improved to about 75%.
  • 37.
  • 38. Capacitor start and capacitor run motors • In this case, two capacitors are used one for starting purpose and other for running purpose. • For starting purpose an electrolytic type capacitor (Cs) is used which is disconnected from the supply when the motor attains 75% of synchronous speed with the help of centrifugal switch S. • Whereas, a paper capacitor CR is used for running purpose which remains in the circuit of starting winding during running conditions. • This type of motor gives best running and starting operation. • Starting capacitor CS which is of higher value than the value of running capacitor CR.
  • 39. Performance and characteristics: • Such motors operate as two phase motors giving best performance and noiseless operation. • Starting torque is high, starting current is low and give better efficiency and higher p.f. • The only disadvantage is high cost.
  • 40. Shaded Pole Motor Construction • Shaded pole motor is constructed with salient poles in stator. • Each pole has its own exciting winding • A 1/3rd portion of each pole core is surrounded by a copper strip forming a closed loop called the shading band • Rotor is usually squirrel cage type.
  • 41.
  • 42. • When a single phase supply is given to the stator (exciting) winding, it produces alternating flux. • When the flux is increasing in the pole, a portion of the flux attempts to pass through the shaded portion of the pole. • This flux induces an emf and hence current in the shading band or copper ring. • As per Lenz’s law the direction of this current is such that it opposes the cause which produces it i.e., increase of flux in shaded portion. Hence in the beginning, the greater portion of flux passes through unshaded side of each pole and resultant lies on unshaded side of the pole.
  • 43. • When the flux reaches its maximum value, its rate of change is zero, thereby the emf and hence current in the shading coil becomes zero. • Flux is uniformly distributed over the pole face and the resultant field lies at the centre of the pole. • After this the main flux tends to decrease, the emf and hence the current induced in the shading coil now tends to increase the flux on the shaded portion of the pole and resultant lies on the shaded portion of the pole • Hence, a revolving field is set up which rotates from unshaded portion of the pole to the shaded portion of the pole as marked by the arrow head • Thus, by electromagnetic induction, a starting torque develops in the rotor and the rotor starts rotating. • After that its rotor picks up the speed.
  • 44.
  • 45.
  • 46. Split Phase Capacitor Start Capacitor run Capacitor start and run Shaded pole Characteristi cs Low and medium starting torque High Starting torque Medium torque High starting torque Low starting torqu Starting torque 100% to 250% of rated value 250% to 400% of rated value 100% to 200% of rated value 200% to 300% of rated value 40% to 60% of rated value Braking torque Upto 300% Upto 350% Upto 250% Upto 250% Upto 10% Power factor 0.5 to 0.65 0.5 to 0.65 0.75 to 0.9 0.75 to 0.9 0.25 to 0.4 Efficiency 55% to 65% 55% to 65% 60% to 70% 60% to 70% 25% to 40% Rating 0.5 to 1 HP 0.125 to 1 HP 0.125 to 1 HP 0.125 to 1 HP Upto 40W Applications Fans, blowers, Centrifugal pumps, washing machines Compressors, Pumps, Conveyors, Refrigerators, AC and Washing Machines Fans, blowers, Centrifugal pumps, Compressors, Pumps, Conveyors, Refrigerators Fans, turn Tables, Hair driers, Motion picture projectors, Blowers,
  • 47. A single-phase induction motor draws a current of 0.5 A at 230 V and 0.6 lagging p.f. If it runs at a speed of 100 radian per second and develops an output torque of 0.3 Nm, find its output power and efficiency.
  • 48. The main winding of a 230V, 0.5 HP single-phase induction motor (split-phase) draw a current of 6 A which lags behind the voltage vector by 45°, whereas the starting winding draw a current of 4A which lags being the voltage by 15°. Determine (i) Current drawn by the motor at start and its pf. (ii) Current draw by the motor during running and its pf. (iii) Phase angle between the current drawn by the main winding and starting winding. (iv) Power drawn by the motor during starting and running.
  • 49.
  • 50.
  • 51. The parameters of the main and starting winding of a 240 V, 50 Hz split-phase induction motor are given as: • Main winding: Rm = 6Ω; Xm = 8Ω • Starting winding: RS = 8 Ω; XS = 6Ω Determine: (i) Current in the main winding (ii) Current in the starting winding (iii) Phase angle between Im and IS (iv) Line current and pf of the motor (v) Power drawn by the motor.
  • 52. The main winding of a 110V, 60 Hz, 0.25 hp, single phase capacitor start motor carries a current of 6- ampere which lags behind the applied voltage by 42°. The starting winding carries a current of 4A which leads the voltage vector by 40°. Calculate (i) the total starting current and the power factor. (ii) the phase angle between the main winding current and starting winding current.
  • 53.
  • 54. The winding impedances of the main winding and starting winding of a 230 V, 50 Hz, 250 W capacitor start motor are (5 + j4) ohm and (10 + j4) ohm respectively. What value of capacitor is required to be connected in series with the starting winding to obtain maximum torque at the start.
  • 55.
  • 56. Testing of Single Phase Induction Motor Blocked Rotor Test: • The rotor is blocked. We have to apply reduced voltage to the main winding so that, rated current flows through the main winding. • Auxiliary winding is kept open during the test. • The applied voltage is very low and the slip at standstill is unity. • Rotor impedance is much smaller than the magnetisation reactance. The excitation branch is neglected.
  • 57. Total Impedance referred to stator, 𝑍𝑏 = 𝑉𝑏 𝐼𝑏 Total Resistance referred to stator, 𝑅𝑏 = 𝑊𝑏 𝐼𝑏 2 Total Reactance referred to stator, 𝑋𝑏 = 𝑍𝑏 2 − 𝑅𝑏 2 𝑅𝑏 = 𝑅1 + 𝑅2 ′ 𝑋𝑏 = 𝑋1 + 𝑋2 ′ 𝑅1 is already measured, 𝑅2 ′ = 𝑅𝑏 - 𝑅1 𝑋1 = 𝑋2 ′ = 𝑋𝑏 2
  • 58.
  • 59. No load Test The slip is very small. • Term 𝑅2 ′ 2𝑠 is very large and treated as o.c as compared to parallel branch 𝑋𝑚 2 • 𝑅2 ′ 2(2−𝑠) reduced to 𝑅2 ′ 4 which is very much small than 𝑋𝑚 2 . The term 𝑋𝑚 2 is considered as o.c Impedance under no load condition, 𝑍0 = 𝑉0 𝐼0 Resistance under no load condition, 𝑅0 = 𝑊0 𝐼0 2 Reactance under no load condition, 𝑋0 = 𝑍0 2 − 𝑅0 2
  • 60.
  • 61. 𝑋0 = 𝑋1 + 𝑋𝑚 2 + 𝑋2 ′ 2 From blocked rotor test, 𝑋1 = 𝑋2 ′ = 𝑋𝑏 2 𝑋0 = 𝑋𝑏 2 + 𝑋𝑚 2 + 𝑋𝑏 4 𝑋𝑚 = 2𝑋0 − 3 2 𝑋𝑏 Mechanical losses: 𝑃𝑚 = 𝑤0 − 𝐼0 2 𝑅1 + 𝑅2 ′ 4
  • 62. The following are the parameters of a 230V, 50 Hz, 4-pole, single phase induction motor R1= 2.2Ω; X1= 3.0Ω; R’2 = 3.8Ω; X’2 = 2.1Ω; Xm = 86Ω.Calculate the input current and power when the motor is operating at full-load speed of 1410 rpm. If the mechanical losses (iron and friction loss) are 60 W, determine gross power developed, useful power at the shaft, shaft torque and efficiency.
  • 63.
  • 64.
  • 65.
  • 66.
  • 67.
  • 68. Hysteresis Motors • A hysteresis motor is a single-phase cylindrical (non- salient pole type) synchronous induction motor. • The difference between this motor and reluctance motor is in (i) the shape of the rotor and (ii) the • nature of the torque produced.
  • 69. Stepper motor Stepper motor is a BLDC motor, whose rotor rotates through a fixed angular step in response to each input current pulse received by its controller. Step angle: Step angle is defined as, the angle through which the stepper motor shaft rotates for each command pulse. It is denoted as 𝛽. 𝛽 = 𝑁𝑠~𝑁𝑟 𝑁𝑠.𝑁𝑟 × 360° Where, 𝑁𝑠 − Number of stator poles or stator teeth 𝑁𝑟 - Number of rotor poles or rotor teeth
  • 70. 𝛽 = 360° 𝑚𝑁𝑟 m- number of stator phases Resolution: it is defined as the number of steps needed to complete one revolution of the rotor shaft Resolution = 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒔𝒕𝒆𝒑𝒔 𝑹𝒆𝒗𝒐𝒍𝒖𝒕𝒊𝒐𝒏 = 𝟑𝟔𝟎° 𝜷
  • 71. Classification of Stepper motor: 1. Variable reluctance stepper motor 2. Permanent magnet stepper motor 3. Hybrid stepper motor Variable reluctance(VR) stepper motor: The stator windings are wound on the stator poles. The rotor carries no windings. Rotor poles are of a ferromagnetic material. The rotor is salient pole type. The reluctance of the magnetic circuit formed by the rotor and stator teeth varies angular position of the rotor.
  • 72. Permanent Magnet Stepper Motor: Rotor is permanent magnet and is cylindrical type The direction of rotation of motor depends on the polarity of the stator current
  • 73. Hybrid stepper motor The rotor is permanent magnet. It is a salient pole type rotor.
  • 74. VR Stepper motor Construction: • The VR stepper motor consists of stator and rotor • There is no permanent in stator or rotor • The rotor carries no windings • The stator is made of soft iron stampings • The stator windings re wound on stator poles.
  • 75. Operation 1. 1-phase-ON or Full step operation 2. 2-phase-ON mode 3. Alternate 1-phase on and 2-phase-on mode 4. Micro stepping operation 1-phase-ON or Full step operation
  • 76.
  • 77. Phase A Phase B Phase C 𝜽 + 0 0 0° 0 + 0 30° 0 0 + 60° + 0 0 90°
  • 79. 2-Phase-ON mode Phase A Phase B Phase C 𝜽 + + 0 15° 0 + + 45° + 0 + 75° + + 0 105°
  • 80. Half step operation: It is also called half-stepping operation. Alternate 1- phase on and 2-phase on modes. (A,AB,B,BC,C etc.,). Phase A Phase B Phase C 𝜽 + 0 0 0 + + 0 15° 0 + 0 30° 0 + + 45° 0 0 + 60° + 0 + 75° + 0 0 90°
  • 81. Permanent Magnet Stepper Motor 1-ph ON mode
  • 82. Phase A Phase B 𝜽 + 0 0° 0 + 90° - 0 180° 0 - 270° + 0 0°
  • 83. The motor direction depends on polarity of phase currents. Clock wise direction 𝑰𝑨 + , 𝑰𝑩 + , 𝑰𝑨 − , 𝑰𝑩 − , 𝑰𝑨 + Counter clock wise direction 𝑰𝑨 + , 𝑰𝑩 − , 𝑰𝑨 − , 𝑰𝑩 + , 𝑰𝑨 +
  • 84. 2-phase-ON mode Phase A Phase B 𝜽 + + 45° - + 135° - - 225° + - 315° + + 45°
  • 85. Alternate 1-ph ON and 2-ph ON mode Phase A Phase B 𝜽 + 0 0° + + 45° 0 + 90° - + 135° - 0 180° - - 225° 0 - 270° + - 315° + 0 0°
  • 87. Construction: • The stator construction of a hysteresis motor is either split-phase type or shaded-pole type which produces a revolving field in the stator when single phase AC supply is given to it. • The rotor of hysteresis motor is specially designed and is made of Hysteresis-type laminations of the shape. • These are usually made of hardened high- retentivity steel rather than commercial low- retentivity dynamo steel. • During operations, the cross arms of the rotor are permanently magnetised due to high retentivity of the steel used for its construction.
  • 88. Principle and Working • When single-phase supply is given to the stator (split-phase type or shaded pole type), a revolving magnetic field is set-up by it. • Eddy currents are induced in the rotor. These eddy currents set up the rotor magnetic field which causes rotor to rotate. • A high starting torque is produced as a result of the high rotor resistance (proportional to the hysteresis loss). • As the motor approaches synchronous speed, the frequency of current reversal in the cross bars decreases and the rotor becomes permanently magnetised in one direction through cross-arms as a result of high retentivity of the steel used for the construction of rotor. • With the two permanently set field poles, the rotor will develop a speed of 3000 rpm at 50 Hz. Thus, the motor runs as a hysteresis motor on hysteresis torque because the rotor is permanently magnetised
  • 89. Reluctance Motor “Whenever a piece of ferro-magnetic material is located in a magnetic field, a force is exerted upon the material, tending to bring it into the position of the densest portion of the field. The force tends to align the specimen of material so that the reluctance of the magnetic path passing through the material will be at a minimum”.
  • 90. Construction • Reluctance motor is a split-phase induction motor with properly designed salient (shaped) poles. • It consists of a stator carrying both the main and auxiliary (or starting) windings for developing a synchronously rotating magnetic field. • The usual method of constructing a rotor for a reluctance motor is to assemble it from standard squirrel-cage parts, except that some of the teeth are removed. • By removing some of the teeth of a normal squirrel-cage rotor, salient poles are produced, which offer low reluctance to the stator flux and thereby strongly magnetized. • The number of salient poles created on the stator must be equal to the number of poles on stator Rotor punching for a 4-pole reluctance type synchronous motor is shown in figure.5.14
  • 91. Operation When the motor is switched on to a single phase ac supply, the motor starts as an induction motor, accelerates and attains speed very close to synchronous speed. Since the mechanical load is comparatively small, the slip is negligible, in which case the revolving field permanently magnetizes the projecting rotor poles. The rotor poles then "lock in step" with the revolving field poles of opposite polarity and continue to rotate at synchronous speed, the speed of the revolving field. The motor adjusts its torque angle for a change in load in a similar way to that described for a 3-phase synchronous motor
  • 92. SERVOMOTORS • The motors that are used in automatic control systems re called as servomotors. • Electrical (voltage) signal →Angular displacement of shaft Servo mechanism • When object of system is to control the position of an object, then the system is called servomechanism. Principle of servomotors • Servos operate on the principle of negative feedback, where the control input is compared to the actual position of the mechanical system as measured by some sort of transducer at the output.
  • 93. Types of Servomotors Features • Linear relationship between speed and electrical control signal. • Steady state stability. • Wide range of speed control • Linearity of mechanical characteristics throughout the entire speed range. • Low mechanical and electrical inertia. • Fast response
  • 94. Field controlled DC servomotor It is open loop system. The error signal produced by the controller, is not enough to drive the DC motor. Hence, it is amplified by an amplifier, called as servoamplifier. This signal is applied to the field winding. With the help of constant current source, the armature current is maintained constant. The motor has large 𝐿𝑓 𝑅𝑓 ratio. where, 𝐿𝑓 – Field inductance, 𝑅𝑓- Field resistance Time constant is high. This means the motor cannot give rapid respond to the quick changing control signals.
  • 95. Armature controlled DC Servomotor It is the closed loop system. Hence, the controlled voltage obtained from the servo amplifier after the amplification. The error signal is applied to the armature. The motor shaft output is controlled by armature input voltage and constant current is applied to the field. Here, motor has small 𝐿𝑓 𝑅𝑓 . Hence, time constant is small and therefore, the motor give rapid response to the quick changing control signals.
  • 96. Characteristics of DC servomotor (i) Torque–speed characteristics (ii) Performance characteristics of a typical DC servomotor
  • 97. Advantages of DC servomotor • Higher output than from a 50Hz of same size • Linearity of characteristics are achieved easily • Easier speed control from zero speed to full speed in both directions. • High torque to inertia ratio that gives them quick response to control signals. • DC servomotors have • Light weight • Low inertia • Low inductance armature • DC motors are capable of delivering over three times of their rated torque for a short time. Uses of DC servomotor • 1. Servo stabilizer • 2. Position control system • 3. Robotics • 4. Process controllers • 5. Large power applications
  • 99. Stator: • Carries two windings • Windings are uniformly distributed, displaced by 90◦ in space, from each other. Description • One winding-main winding or fixed winding or reference winding. • Other winding-control winding • Control voltage is obtained from the servo amplifier after processing the input error signals. • The control voltage is 90◦ out of phase with respect to the voltage applied to the reference winding, necessary to obtain rotating magnetic field.
  • 100. Rotor:Two types • 1.Squirrel cage rotor 2.Drag cup type rotor Squirrel cage rotor • Have aluminium bars which are short at the ends. • Overall construction looks like cage. • Have small diameter and large length in order to reduce inertia. • Aluminium conductors keeps weight small. • Its resistance is high and hence, keeps torque-speed characteristics is kept as linear as possible. • Air gap is very small. Therefore, magnetising current can be reduced easily.
  • 101. • Drag cup type rotor • To reduce inertia, drag cup type rotors used. • There are two air gaps. • Drag cup made up of nonmagnetic material like copper, aluminium or an alloy. • Slotted rotor laminations are replaced by a set of stationary ring shaped laminations. • These are wound so that the operating speed of motor is very low. • Used in very low power applications.
  • 102. Characteristics of AC servomotors Torque-speed characteristics Effect of increased resistance
  • 103. Effect of (X/R) on characteristics Performance characteristics of a typical AC servomotor
  • 104. Advantages of AC servomotor • Lower cost • Higher efficiency • Less maintenance since no commutators and brushes Disadvantages of AC servomotor • 1. Characteristics is not quite linear • 2. More difficult to control Uses of AC servomotor • Low power applications • Robotics • Instrument servos • Self-balancing recorders • Process controllers
  • 105. UNIVERSAL MOTOR For some applications, it is desirable to employ a motor that operates on either DC or AC. It is possible to build, by a compromise design, small series motors up to about 1 2 𝐾𝑊 rating to operate satisfactorily on DC or AC at 115 or 230V. Such motors are called the universal motors.