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Lecture 3: Special-Purpose Motors
Instructor:
Dr. Gleb V. Tcheslavski
Contact:
gt.lamar@gmail.com
Office Hours:
TBD; Room 2030
Class web site:
http://www.ee.lamar.edu/
gleb/tps/Index.htm
Image from http://www.jeromedemers.com/
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Introduction
Approximately 90% of all motors manufactured today are single-phase.
Most of them are built as fractional-horsepower or subfractional horsepower
motors (1 hp = 746 W). Standard ratings for fractional-horsepower motors
range from 1/20 to 1 hp. Motors rated for less than 1/20 hp are
subfractional-horsepower motors; they are rated in millihorsepower (mhp)
in the range from 1 to 35 mhp.
The single-phase motors manufactured in standard integral horsepower
sizes are in the 1.5, 2, 3, 5, 7.5-10 hp range. Special integral horsepower
sizes can range from several hundreds up to a few thousands hps.
Unlike integral horsepower motors, small single-phase motors are
manufactured in many different types of designs with different
characteristics. This is especially true for subfractional-horsepower motors.
Three basic types of single-phase AC motors are single-phase induction
motors, universal motors, and single-phase synchronous motors.
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Single-phase induction motors
Single-phase induction motors generally have a
distributed stator winding and a squirrel-cage
rotor. The AC voltage is applied to the stator
winding, which creates a non-rotating (stationary
in space and pulsating in time) magnetic field
(sometimes called a breathing field).
Currents are induces in the squirrel-cage rotor
windings by transformer action. These currents
produce an mmf opposing the stator mmf. Since
the axis of the rotor-mmf wave coincides with that
of the stator field, the torque angle is zero and no
staring torque develops.
As standstill, therefore, the motor behaves like a single-phase transformer
with a short-circuited secondary side.
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Single-phase induction motors
A single-phase induction motor is not self-starting. However, if the rotor of a
single-phase induction motor is started by external means, it will continue to
run and will develop torque.
This phenomenon can be explained by the
double-revolving field (or cross-field) theory.
A pulsating mmf (or flux) field can be replaced by
two rotating fields half the magnitude and rotating
with the same speed but in opposite directions.
Assuming a sinusoidally distributed stator
winding, mmf at the angular position  is
(3.4.1)
where N is the effective number of turns of the
stator winding; i is the instantaneous value of the
current in the stator winding.
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Single-phase induction motors
Since
(3.5.1)
the mmf is a function of space and time:
(3.5.2)
(3.5.3)
(3.5.4)
In other words, the stator mmf is the superposition of a positive- and
negative-rotating mmfs in the direction of . Ff is the rotating mmf in the
direction of  – forward-rotating field; Fb is the mmf rotating in the opposite
direction – backward-rotating field. We assume that the direction of Ff is
the same as the direction of rotor’s rotation.
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Single-phase induction motors
The forward-rotating and backward-rotating mmfs both produce the
induction motor action – torques on the rotor, although in the opposite
directions.
At standstill, the torques caused by the fields are equal in magnitude and
the resulting starting torque is zero. However, at any other speed, the
torques are not equal and the resulting torque causes the motor to rotate.
Assuming that the motor is made to rotate at a speed nm rpm forward and
that the synchronous speed is ns rpm. The slip to the forward-rotating field:
(3.6.1)
Since the direction of rotation is opposite to that of the backward-rotating
field, the slip with respect to the backward field is:
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Single-phase induction motors
(3.7.1)
or
(3.7.2)
The torque-speed
characteristics of a singlephase induction motor:
At standstill, the resultant
torque is zero
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Single-phase induction motors
Equivalent circuit
At standstill, a single-phase induction motor behaves like a transformer with
a short-circuited secondary side.
The equivalent circuit at standstill:
R1 and X1 are the resistance and
reactance of the stator winding;
Xm is the magnetizing reactance;
R2 and X2 are standstill values of
rotor resistance and reactance
referred to the stator winding by
the appropriate turn ratio.
The core losses are not shown but
are included in the rotational
losses.
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Single-phase induction motors
Using the double-revolving field theory, the equivalent circuit can be
modified to include the effects of two counter-rotating fields of constant
magnitude. Since at standstill the magnitudes of the forward and backward
fields are equal to half the magnitude of the original field, the equivalent
circuit of the rotor can be split into
equal sections.
The corresponding modified
equivalent circuit at standstill:
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Single-phase induction motors
After the motor is accelerated to its rated speed by an auxiliary winding
(that is turned off after reaching the appropriate speed) and is running in the
direction of the forward-rotating field at a slip s, its equivalent circuit should
be modified.
The rotor resistance in the forward
equivalent circuit is 0.5R’2/s.
Since the rotor is rotating at a speed
that is s less than the forwardrotating field, the difference in
speed between the rotor and the
backward-rotating field is 2-s.
Therefore, the rotor resistance in
the equivalent backward circuit is
0.5R’2/(2-s).
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Single-phase induction motors
To simplify the calculations, the impedances corresponding to the forward
and backward fields are defined as
(3.11.1)
(3.11.2)
The impedances representing the reactions of the forward- and backwardrotating fields with respect to the single-phase stator winding are 0.5Zf and
0.5Zb respectively.
After the motor is started, the forward air-gap flux wave increases and the
backward wave decreases, since during normal operation, the slip is very
small.
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Single-phase induction motors
Therefore, the rotor resistance in the forward field, 0.5R’2/s, is much greater
than its standstill value, while the resistance in the backward field,
0.5R’2/(2-s), is smaller.
As a result, the forward-field impedance Zf is greater than its standstill
value, while the backward-field impedance Zb is smaller. Therefore, during
normal operation of motor, Zf >> Zb.
Since each of these impedances carries the same current, the magnitude of
the voltage Ef >> Eb. Therefore, the magnitude of the forward field f that
produces Ef is much greater than the backward field b that produces Eb.
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Single-phase induction motors
Performance analysis
Based on the equivalent circuit in slide 10, the input current is
(3.13.1)
Therefore, the air-gap powers developed by the forward and backward
fields are
(3.13.2)
and
(3.13.3)
Therefore, the total air-gap power is
(3.13.4)
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Single-phase induction motors
Hence, the developed torques due to the forward and backward fields are
(3.14.1)
and
(3.14.2)
The total developed torque is
(3.14.1)
Since the rotor currents are produced by the two-component air-gap fields,
the total rotor copper loss is the sum of the rotor copper losses caused by
each field.
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Single-phase induction motors
These rotor copper losses of the forward and backward fields are
(3.15.1)
and
(3.15.2)
Therefore, the total copper loss is
(3.15.3)
The mechanical power developed in the motor can be found as
(3.15.4)
Developed torque
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Single-phase induction motors
(3.15.4) for the developed power can be rewritten as
(3.16.1)
Therefore, the output power is
(3.16.2)
Friction and windage losses
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Single-phase induction motors
Ex. 3.1: A 1/4 hp, single-phase, 120V, 60Hz, two-pole induction motor has
the following resistances and reactances referred to the stator:
The core losses are 30 W, the friction, windage, and stray losses are 15 W.
The motor is operating at the rated voltage and frequency with its starting
circuits open. For a slip of 5%, determine:
a) The shaft speed in rpm;
b) The forward and backward impedances of the motor;
c) The input current;
d) The power factor;
e) The input, total air-gap, developed, and output powers;
f) The developed torque;
g) The output torque;
h) The motor’s efficiency.
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Single-phase induction motors
Solution: a) The synchronous speed is
Therefore, the rotor’s mechanical speed is
b) The forward impedance of the motor is
The backward impedance of the motor is
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Single-phase induction motors
c) The stator input current of the motor is
d) The stator power factor of the motor is
e) The input power of the motor is
The air-gap power due to the forward field is
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Single-phase induction motors
The air-gap power due to the backward field is
The total air-gap power of the motor is
The developed mechanical power of the motor is
The output (shaft) power of the motor is
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Single-phase induction motors
f) The developed torque is
g) The output torque is
h) The efficiency of the motor is
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Single-phase induction motors:
Starting
22
Starting of single-phase induction motors
As we already discussed, a single-phase induction motor cannot start by its
main winding alone and requires an auxiliary (starting) winding or some
other means. The auxiliary winding may be disconnected automatically by a
centrifugal switch at approximately 75% of synchronous speed. Once the
motor is started, it continues to run in the same direction.
A single phase motor is designed so that the current in its auxiliary winding
leads that of the main winding by 90. Therefore, the motor behaves as a
two-phase motor. The field of its auxiliary winding builds up first. The
direction of rotation may be reversed by reversing the connections of the
main or the auxiliary winding. Reversing the directions of both the main and
auxiliary windings will not change the direction of rotation.
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Single-phase induction motors:
Starting
Considering the following phasor diagram of
a motor at starting:
The phase angle  between the two currents
Im and Ia is approximately 30-45.
Therefore, the starting torque is
(3.23.1)
Main winding
current
Auxiliary winding
current
A constant
Therefore, the starting torque is a function of the magnitudes of the currents
in the main and auxiliary windings and the phase difference between these
two currents.
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Single-phase induction motors:
Classification and types
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Classification of single-phase induction motors
Single-phase induction motors are classified based on the methods used to
start them. Each starting method differs in cost and in the amount of
starting torque it produces.
1. Split-phase motors
A split-phase motor is a singlephase induction motor with two
stator windings: a main (stator)
winding, m, and an auxiliary
(starting) winding, a, as shown.
The axes of these two windings are
displaced 90 electrical degrees in
space and less than 90 in time. The auxiliary winding has a higher
resistance-to-reactance ratio than the main winding, so its current leads the
current in the main winding (see phasor diagram in slide 23).
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Classification and types
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The most common way to obtain this higher R/X ratio is to use smaller wire
for the auxiliary winding. This is acceptable since the auxiliary winding is
only energized during the starting. The auxiliary winding is disconnected by
a centrifugal switch or relay when the speed of the motor is approximately
75% of the synchronous speed.
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The rotational direction of the motor can be reversed by switching the
connections of the auxiliary winding while keeping the same connections of
the main winding when the motor is NOT running.
A typical torque-speed
characteristic of a split-phase
motor.
A higher starting torque can be
achieved by inserting a series
resistance in the auxiliary winding
or by inserting a series inductive
reactance in the main winding. In
both cases, the R/X ratio is
increased.
Split-phase motors that are rated up to ½ hp are relatively cheep compared
to other motors and are used with loads that are easy to start: fans,
blowers, saws, pumps, etc.
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Single-phase induction motors:
Classification and types
When the motor is at standstill, the impedances of the main and the
auxiliary windings are
(3.27.1)
Therefore, the magnitude of the auxiliary (starting) winding current is
(3.27.2)
where
(3.27.3)
Number of turns of the main and the auxiliary windings
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Single-phase induction motors:
Classification and types
and
(3.28.1)
For the design purposes, it is easier to assume a
number of turns for the auxiliary winding Na to
determine the value of Ra for maximum starting
torque and the current of the auxiliary winding. If
the optimum values of starting torque and current
are not achieved, the process can be repeated
until the proper design is found.
An alternative to the centrifugal switch
Images from http://www.kipautomatika.ru/
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Classification and types
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2. Capacitor-start motors
A capacitor-start motor is also a
split-phase motor. A capacitor is
connected in series with the
auxiliary winding. By selecting the
proper capacitor size, the current in
the auxiliary winding can be made
to lead the voltage V1 and,
therefore to cause about a 90 time
displacement between the phasors
of currents Im and Ia as shown.
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Capacitor starting produces a much
higher starting torque than the
resistance split-phase starting.
The auxiliary winding is
disconnected by a centrifugal
switch when the motor speed
reaches approximately 75% of the
synchronous speed. Unlike the
regular split-phase motor, the
capacitor-start motor is reversible.
To reverse the direction of the motor, it is temporarily disconnected and its
speed is allowed to drop to a slip of 20%. At the same time, its centrifugal
switch is closed over a reversely connected (with respect to the main
winding) auxiliary winding. These two simultaneous actions reverse the
rotational direction of the motor.
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Single-phase induction motors:
Classification and types
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Single-phase induction motors:
Classification and types
The cost of the capacitor makes capacitor-start motors more expensive
than split-phase motors. They are used in the applications requiring high
starting torque, such as compressors, pumps, air conditioners, conveyors,
larger washing machines, etc.
For design purposes, the value of the capacitive reactance that is
connected in series with the auxiliary winding and provides the maximum
starting torque can be found as
(3.32.1)
Therefore, the value of the capacitor can be determined as
(3.32.2)
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Single-phase induction motors:
Classification and types
Another, supposedly better, design for the motor can be found by
maximizing the starting torque per ampere of starting current rather than by
maximizing the starting torque alone. In this case, the value of capacitive
reactance can be found as
(3.33.1)
Then, the capacitor’s value is determined as
(3.33.2)
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3. Capacitor-run motors
The capacitor-run motor is also
called the permanent-split capacitor
motor, or simply a capacitor motor,
since it operates with its auxiliary
winding permanently connected in
series with a capacitor.
This motor is simpler than the
capacitor-start motor since it a
centrifugal switch is not needed.
Torque, efficiency, and power factor are also better since the motor runs as
a two-phase motor producing a constant torque, unlike other single-phase
motors that produce a pulsating torque.
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Single-phase induction motors:
Classification and types
In this motor, the value of the capacitor is based on its running rather than
its starting characteristic.
Since at starting, the current in the
capacitive branch is very low, the
capacitor motor has a very low
starting torque.
The reversible operation is more
easily achieved than in other
motors. Its speed can be controlled
by varying its stator voltage.
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Single-phase induction motors:
Classification and types
Capacitor-run motors are used for fans, air conditioners, and refrigerators.
Since at starting, slip s = 1 and Rf = Rb, the starting torque of a capacitorrun motor is determined as
(3.36.1)
where a is the turns ratio of the auxiliary and main windings, m and a are
the impedance angles of the main and auxiliary windings.
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Classification and types
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4. Capacitor-start Capacitor-run motors
The capacitor-start capacitor-run
motor is also called the two-value
capacitor motor.
In this motor, the high starting
torque of the capacitor-start motor
is combined with the good running
performance of the capacitor-run
motor.
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Classification and types
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The letter is achieved by using
two capacitors as shown.
Both the auxiliary winding
(starting) capacitor and the
running capacitor are usually the
electrolytic type and are
connected in parallel at starting.
Since the running capacitor Crun must be in the circuit all the time, this
motor is more expensive but provides the best performance.
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Classification and types
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5. Shaded-pole motors
The shaded-pole induction motor is
widely used in applications requiring
1/20 hp or less. The motor has a salientpole construction, with one-coil-per-pole
main winding and a squirrel-cage rotor.
Image from
www.electricmot
ors.machinedesi
gn.com
One portion of each pole has a shading band or
coil. The shading band is a short-circuited
copper strap (or a single-turn copper ring)
wound around the smaller segment of the pole.
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Classification and types
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The purpose of the shading band is to retard, in time, the portion of the flux
passing through it in relation to the flux coming out of the rest of the pole
face. In other words, the current induced in the shading band causes the
flux in the shaded portion of the pole to lag the flux in the unshaded portion.
Therefore, the flux in the unshaded portion reaches its maximum before the
flux in the shaded portion. The result is like a rotating field moving from the
unshaded to the shaded portion of the pole, and causing the motor to
produce a slow starting torque.
The shaded-pole motor is rugged,
cheap, small in size, and needs
minimum maintenance. It has very
low starting torque, efficiency, and
power factor. This motor is used in
turntables, film projectors, small fans,
vending machines, etc.
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Classification and types
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Ex. 3.2: Assume that a single-phase, 120V, 60Hz, two-pole induction motor
has the following standstill impedances when tested at rated frequency:
Main winding: Zm = 1.6 + j4.2 
Auxiliary winding: Za = 3.2 + j6.5 
Determine the following:
a) The value of external resistance that needs to be connected in series
with the auxiliary winding to produce the maximum starting torque, if
the motor operates as a resistance split-phase motor.
b) The value of the capacitor connected in series with the auxiliary
winding to produce the maximum starting torque, if the motor operates
as a capacitor-start motor.
c) The value of the capacitor connected in series with the auxiliary
winding to produce the maximum starting torque per ampere of the
starting current, if the motor operates as a capacitor-start motor.
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Solution: a) The value of the external resistance needed to be connected in
series with the auxiliary winding can be found from (3.27.3):
Here
Therefore, the value of the external resistance is
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Classification and types
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b) The value of the capacitive reactance needed to be connected in series
with the auxiliary winding can be found from (3.32.1):
Therefore, the value of the capacitance is
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Classification and types
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c) For the maximum starting torque per ampere of the starting current, the
value of the capacitive reactance can be found from (3.33.1):
Therefore, the value of the capacitance is
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Universal motors
A universal motor is a single-phase series motor that can operate on either
AC or DC with the similar characteristics, as long as both the stator and the
rotor cores are laminated. It is essentially a series DC motor with
laminated stator and rotor cores. Without lamination, the core losses would
be tremendous when the motor is connected to the AC source.
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Universal motors
The name Universal Motor indicates that such a motor can run from either
an AC – at any frequency up to design frequency – or a DC (zero
frequency) power source.
The main field and armature field are in phase, since the same current
flows through the field and armature windings. For instance, a shunt DC
motor cannot operate on an AC source since the shunt field is highly
inductive and the armature is highly resistive. The high inductance of the
field winding causes the field current to lag the armature current by such a
large angle that a very low net torque is produced. The armature and main
fields of a shunt motor would be not in phase.
When the universal motor is supplied by an AC power source, both the
main field and the armature field will reverse at the same time. However,
the torque will always be in the same direction as the rotation of the shaft.
Similarly to all series motors, the no-load speed of the universal motor is
usually high, often 1,500-20,000 rpm, and is limited by windage and friction.
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Universal motors
Universal motors are typically used in fractional horsepower ratings (1/20
hp or less) in many commercial appliances (requiring a high starting torque
and speeds higher than the maximum synchronous speed of 3600 rpm),
such as electric shavers, portable tools, sewing machines, mixers, vacuum
cleaners, drills, etc. The motor in such applications is always loaded with
little danger of motor runaway.
The best way to control the speed and torque of the universal motor is to
vary its input voltage by using a solid-state device (an SCR or a TRIAC).
Large (up to 500 hp) single-phase series AC motors are still extensively
used in electric locomotives.
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Universal motors
Under DC excitation, the developed torque and induced voltage of a
universal motor are
(3.48.1)
(3.48.2)
Where Ka is an armature constant:
(3.48.3)
Z is the total number of conductors in the armature winding;
p is the number of poles;
a is the number of parallel paths in the armature winding;
is the direct-axis air-gap flux per pole.
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Universal motors
Assuming magnetic linearity (no saturation), the developed torque and the
induced voltage (under DC excitation) are
(3.49.1)
(3.49.2)
Under AC excitation, the average developed torque and the rms value of
the induced voltage of a universal motor are
(3.49.3)
(3.49.3)
is the rms value of the direct-axis air-gap flux per pole;
Ia is the rms value of the motor current.
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Universal motors
Assuming magnetic linearity (no saturation), the average developed torque
and the rms value of the induced voltage (under AC excitation) are
(3.50.1)
(3.50.2)
Since the developed mechanical power is
(3.50.3)
the developed torque is
(3.50.4)
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Universal motors
The terminal voltage (under AC excitation) is
(3.51.1)
Since the armature and series impedances are
(3.51.2)
(3.51.3)
The terminal voltage (under AC excitation) can be rewritten as
(3.51.4)
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Universal motors
Then, the induced voltage is
(3.52.1)
Assuming that the armature current under the DC excitation and the rms
value of the armature current under AC excitation are the same, it can be
shown that
(3.52.2)
If saturation exists while the motor is under AC excitation, then the flux
under the AC excitation is slightly less than the flux under DC excitation.
The ratio of the induced voltages becomes
(3.52.3)
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Universal motors
When the terminal voltage,
armature current, and torque are
constant, the speed of a universal
motor is lower under AC excitation
than under DC excitation.
Images from www.o-digital.com and www.asia.ru
Under AC excitation, the
universal motor produces a
lower speed, a poorer PF,
and a pulsating torque.
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Universal motors
Ex. 3.3: A a single-phase, 120V, 60Hz universal motor is operating at 1800
rpm and its armature current is 0.5 A when it is supplied by a 120 V DC
source. Its resistance and reactance are 22  and 100 . Assuming that
the motor is supplied by an AC source, determine the following:
a) Speed of a motor connected to an AC source;
b) Power factor of a motor connected to an AC source;
c) Developed torque of a motor connected to an AC source.
Solution: a) When the motor is supplied by a DC source, the reactance is
zero (since frequency is zero), then:
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Universal motors
When the motor is supplied by an AC source, the reactance is non-zero:
Therefore:
Assuming the same flux for the same current under the DC and AC
operation, by (3.52.2):
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Universal motors
Therefore, the speed of the motor when it is connected to an AC source is
b) The power factor of the motor can be found as
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Universal motors
c) The developed (mechanical) power of the motor is
Therefore, the developed torque of the motor is
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Single-phase synchronous motors
Single-phase synchronous motors are used in applications that require
precise speed. They include the reluctance motor, the hysteresis motor, and
the stepper motor. Reluctance and hysteresis motors are used in electric
clocks, timers, and turntables. Stepper motors are used in electrical
typewriters, printers, disc drives, etc.
1. Reluctance motors
A reluctance motor (aka a single-phase salient-pole synchronous-induction
motor) is a salient-pole synchronous machine with no field excitation. The
operation of this motor depends on reluctance torque that tends to align the
rotor under the nearest pole of the stator and defines the direction of
rotation. The torque applied to the rotor is proportional to sin(2), where  is
the angle between the rotor and stator magnetic fields. Therefore, the
reluctance torque of the motor becomes maximum when the angle between
the rotor and stator magnetic fields is 45.
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Single-phase synchronous motors
In general, any induction motor can be
modified into a self-starting reluctance
synchronous motor. This can be achieved
by modifying the rotor so that it would have
salient poles as shown.
We notice that the saliency is achieved by
removing some rotor teeth to make a fourpole structure.
This rotor can be used for a four-pole
reluctance motor. The reluctance of the airgap flux path will be much greater where
rotor teeth are absent. Therefore, the
reluctance motor can start as an induction
motor as long as the squirrel-cage bars and rings are left in place.
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Single-phase synchronous motors
This motor, coming up to speed as an induction motor, will be pulled into
synchronism by the pulsating AC single-phase field due to a reluctance
torque produced by the salient poles with lower-reluctance air gaps.
In summary, the torque develops because of the tendency of the rotor to
align itself with the rotating field so that a reluctance motor starts as an
induction motor, but continues to operate as a synchronous motor.
Stator contains two windings: a main and auxiliary windings. When the
motor starts in its induction mode, it has both windings energized. At a
speed of approximately 75% of the synchronous speed, a centrifugal switch
disconnects the auxiliary winding so that the motor accelerates to almost
the synchronous speed. At that time, as a result of the reluctance torque,
the rotor snaps in synchronism and continues to rotate as the synchronous
speed. If the load of a reluctance motor increases significantly, the motor
may slip out of synchronism. However, it will continue to run with some slip
like an induction motor.
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Single-phase synchronous motors
A torque-speed characteristic
of a typical single-phase
reluctance motor.
The value of the staring torque
depends on the position of the
rotor with respect to the field
winding.
Due to no DC excitation in the
rotor of a reluctance motor, it
develops less torque than an
excited synchronous motor of
the same size. Since the volume of a machine is approximately
proportional to the torque, the reluctance motor is approximately three
times larger than a synchronous motor with the same torque and speed.
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Single-phase synchronous motors
2. Hysteresis motors
These motors use the
phenomenon of hysteresis to
develop a mechanical torque.
The rotor of a hysteresis motor is
a smooth cylinder made out of a
specific magnetic material, such
as hard steel, chrome, or cobalt,
and has no teeth, laminations, or
windings.
Image from www.electrical-knowhow.com
The stator windings are distributed to produce a sinusoidally-distributed
flux. The stator windings can be either single or three phase.
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Single-phase synchronous motors
In single-phase motors, the stator
windings are usually permanentsplit-capacitor type as shown.
If the stator windings are energized,
a revolving magnetic field is
developed that rotates at the
synchronous speed. This rotating field
magnetizes the metal of the rotor and
induces eddy currents. Because of
hysteresis, the magnetization of the rotor
lags with respect to the inducing revolving
field.
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Single-phase synchronous motors
The lag angle  exists because the metal of the rotor has a large
hysteresis loss. The angle, by which the rotor magnetic field lags the
stator magnetic field, depends on the hysteresis loss of the rotor. At the
synchronous speed, the stator flux stops to sweep across the rotor,
causing the eddy currents to disappear and the rotor behaves like a
permanent magnet. At that time, the developed torque in the motor is
proportional to the angle  between the stator and rotor magnetic fields
that is determined by the
hysteresis of the motor.
Consequently, a constant
torque (indicated as the
hysteresis torque) exists from
zero up to the synchronous
speed.
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Single-phase synchronous motors
A hysteresis motor, whose rotor is round and not laminated, has an
induction torque that is added to the hysteresis torque until the
synchronous speed is reached. Hysteresis motors are self-starting and are
manufactured up to about 200 W for use in precise-speed applications
including clock, record players, CD players, servomechanisms…
Images from openbookproject.net and www.o-digital.com
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Single-phase synchronous motors
3. Stepper motors
These motors are also referred to as stepping or step motors. A stepper
motor is a type of an AC motor that is built to tolerate a specific number of
degrees in response to an impulse-shaped digital input. Step sizes typically
vary from 1, 2, 2.5, 5, 7.5, 15, or more for each electrical pulse.
Stepper motors are often used in digital control systems, where the motor
receives open-loop commands in the form of a train of pulses and the
controller directs pulses sequentially to the motor windings to turn a shaft or
move an object a specific distance.
Step motors are well-suited for accurate speed control or precise position
control without any feedback. In such usage, the axis of the motor’s
magnetic field steps around the air gap at a speed that is based on the
frequency of pulses. The rotor tries to align itself with the axis of the
magnetic field. Therefore, the rotor steps in synchronism with the motion of
the magnetic field.
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Single-phase synchronous motors
Step motors have a relatively simple construction and can be controlled to
step in equal increments in either direction. They are used in digital
electronic systems since they do not need position sensors or a feedback
system to produce the output response following the input command.
A simple form of
control
implementation in
a stepper motor.
A train of f pulses per second is supplied to a digital driver circuit; the
controller’s input is divided so that the output is sent in sequence to one
phase winding at a time.
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Single-phase synchronous motors
When 2p is the number of phases and k is the number of teeth, the rotor
angular motion per pulse is a steps of /kp radians. Assuming that the
rotor moves n steps per second, the angular speed is precisely n/kp
radians per second.
Step motors are classified according to the type of motor used. If a
permanent magnet motor is used, it is called a permanent-magnet stepper
motor (PMSM).
If a variable-reluctance motor is used, it is called a variable-reluctance
stepper motor (VRSM).
PMSMs have a higher inertia and thus a slower acceleration than VRSMs.
For instance, the maximum step rate for PMSMs is 300 pulses per
second, while it can reach 1200 pulses per second for VRSMs.
On the other hand, PMSM develops more torque per ampere stator
current than the VRSM. Also, a hybrid stepper motor (HSM) exists that
has a rotor with an axial permanent magnet in the middle and
ferromagnetic teeth at the outer sections. The hybrid step motor combines
the characteristics of the VRSMs and PMSMs.
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Single-phase synchronous motors
A variable-reluctance stepper motor can be the single-stack type or the
multiple-stack type. The latter (shown below) is used to provide smaller
step sizes. Its rotor is segmented along its axis into magnetically isolated
sections called stacks, which
are excited by a separate
winding called a phase.
Although VRSMs with up to
seven stacks and phases
are used, three-phase
arrangements are more
often used.
Image from commons.wikimedia.org
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Single-phase synchronous motors
Assume a rotor
with 8 poles and
three separated
8-pole stators
arranged along
the rotor.
If phase-a poles of a stator are energized by a set of series-connected
coils with current ia, the rotor poles align with the stator poles of phase a.
We notice that the phase-b stator is the same as the phase-a stator except
that its poles are displaced by 15 in the clockwise direction. Similarly, the
phase-c stator is displaced from the phase-b stator by 15 in the clockwise
direction.
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Single-phase synchronous motors
When the current ia in phase a is interrupted and phase b is energized, the
motor develops a torque that rotates its rotor by 15 in the counterclockwise direction. Similarly, when the current ib in phase b is interrupted
and phase c is energized, the motor develops a torque that rotates its rotor
by 15 in the counter-clockwise direction.
Finally, when the current ic in phase c is interrupted and phase a is
energized, the motor develops a torque that rotates its rotor by 15 in the
counter-clockwise direction, completing a one-step (i.e., 45 in this case)
rotation in the counter-clockwise direction. Reversing the current-pulse
sequence to acb will reverse the direction of rotation.
For an n-stack motor, the rotor or stator (but not both) on each stack is
displaced by 1/n times the pole-pitch angle.
PMSMs require two phases and current polarity is important.
Hybrid motors differ from a multi-stack VRSM in that the stator pole
structure is continuous along the length of the rotor.
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Single-phase synchronous motors
An alternative
view: 15° per
step VRSM
(single stack).
The stator has
eight poles that
are spaced 45°
apart.
Energizing coils
1-2-3-4, rotor
will rotate by 45
clockwise.
Image from homemaderobo.blogspot.com
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Single-phase synchronous motors
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Sub-synchronous motors
A sub-synchronous motor has a rotor with an overall cylindrical outline
and with teeth as a many-pole salient-pole rotor. For instance, a motor may
have 16 teeth or poles, and in combination with a 16-pole stator will
normally rotate at a synchronous speed of 450 rpm when operated at 60 Hz.
The motor starts as a hysteresis motor. At synchronous speed, the rotor
poles induced in a hysteresis rotor stay at fixed spots on the rotor surface as
the rotor rotates into synchronism with the rotating magnetic field of the
stator. The hysteresis torque is in effect when the rotor rotates at less than
synchronous speed.
Sub-synchronous motors (being self-starters) start and accelerate with
hysteresis torque just as the hysteresis synchronous motor does.
These motors have a higher starting torque but less torque at synchronous
speed than the reluctance motor. If such a motor running, for instance, at
450 rpm is temporarily overloaded, it may drop out of synchronism. As the
speed drops towards the maximum torque point, the motor will again lock
into synchronism at a sub-synchronous speed of 225 rpm (thus the name).
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Permanent-magnet DC motors
A permanent-magnet motor is a motor with
poles made up of permanent magnets.
Even though most permanent-magnet
machines are used as DC machines, they are
occasionally built as synchronous machines
with the rotating field winding replaced by a
permanent magnet.
The permanent-magnet AC motor operation
resembles that of the permanent-magnet
stepper motor. Just as the stepper motor, the
excitation frequency determines the motor
Image from www.ewh.ieee.org
speed, and the angular position between the
rotor magnetic axis and a particular phase when it is energized affects the
developed torque.
Often, permanent-magnet (AC) motors are called brushless motors.
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Permanent-magnet DC motors
Permanent-magnet DC (PMDC) motors are widely used in automobiles to
operate AC, heater blowers, windshield wipers and washers, power seats,
windows, and mirrors, etc.
They may be found in electric shavers, electric toothbrushes, carving knives,
vacuum cleaners, power tools, miniature motors in toys, lawn mowers, and
other battery-operated equipment.
PMDC motors are also used in control systems, such as DC servomotors
and tape drives. In such applications, these motors are often used as
fractional-horsepower motors, although they may be built for over 200 hp.
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Permanent-magnet DC motors
Since field windings are absent in PMDC motors, their stators are smooth
resembling a cylindrical shell where permanent magnets are mounted.
The magnetic
field is produced
by the permanent
magnet. The rotor
has a wound
armature; the DC
power supply is
connected to the
armature through
a brush/
commutator
assembly.
Image from mitrocketscience.blogspot.com
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Permanent-magnet DC motors
Basically, three types of magnets are used in PMDC motors: alnico
magnets, ceramic (or ferrite) magnets, and rare-earth magnets (samariumcobalt magnets, for instance).
From Wikipedia: “Alnico is an acronym referring to a family of iron alloys
that, in addition to iron, are composed primarily of aluminum (Al), nickel (Ni),
and cobalt (Co), hence al-ni-co. They also include copper, and sometimes
titanium. Alnico alloys are ferromagnetic, with a high coercivity (resistance
to loss of magnetism) and are used to make permanent magnets. Before
the development of rare earth magnets in the 1970s, they were the
strongest type of magnet.
The composition of alnico alloys is typically 8–12% Al, 15–26% Ni, 5–24%
Co, up to 6% Cu, up to 1% Ti, and the balance is Fe. The development of
alnico began in 1931, when T. Mishima in Japan discovered that an alloy of
iron, nickel, and aluminum had a coercivity of 400 oersted (Oe; 32 kA/m),
double that of the best magnet steels of the time.”
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Permanent-magnet DC motors
Ceramic magnets are usually found in low-horsepower slow-speed motors.
They are most economical in fractional horsepower motors and are also
less expensive than alnico in motors up to 10 hp. They are made out of iron
oxides and produce magnetic field of 400 to 2000 oersteds (hard ferrites).
Alnico magnets
Ceramic magnets
Rare-earth magnet
Images from sinomagnet.en.made-in-china.com, www.stevespanglerscience.com and apexdistribution.stores.yahoo.net
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The rare-earth magnets are very expensive. However, they are the most
cost effective in very small motors.
From Wikipedia: “Developed in the 1970s and 80s, rare-earth magnets are
the strongest type of permanent magnets made, producing significantly
stronger magnetic fields than other types such as ferrite or alnico magnets.
The magnetic field typically produced by rare-earth magnets can be in
excess of 1.4 T, whereas ferrite or ceramic magnets typically exhibit fields of
0.5 to 1 T. There are two types: neodymium magnets and samarium-cobalt
magnets. Rare earth magnets are extremely brittle and also vulnerable to
corrosion, so they are usually plated or coated to protect them from
breaking and chipping.”
In general, alnico magnets are used in very large motors up to 200 hp. It is
also possible to use special combinations of magnets and ferromagnetic
materials to achieve high performance (i.e., high torque, high efficiency, and
low volume) at a low cost.
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Permanent-magnet DC motors
A cutaway view of a PMDC motor.
A PMDC motor is basically a shunt
DC motor with its field circuits
replaced by permanent magnets.
Since the flux of permanent magnets
cannot be changed, its speed can
only be controlled by varying its
armature voltage and the armature
circuit resistance.
The equivalent circuit of a PMDC
motor consists of an armature
connected in series with the armaturecircuit resistance Ra.
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Permanent-magnet DC motors
Therefore, the internal generated voltage is found as
(3.82.1)
where Ka is the armature constant;
d is the net flux per pole.
Since the flux is constant in PMDC motors:
(3.82.2)
where K is the torque constant of the motor that is determined by the
armature geometry and the permanent magnet’s properties:
(3.82.3)
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Permanent-magnet DC motors
The developed torque of the motor is found as
(3.83.1)
Typical currenttorque and speedtorque
characteristics of
a PMDC motor.
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Permanent-magnet DC motors
Varying terminal voltage Vt of the motor changes the no-load speed of the
motor but the slope of the curves remains constant.
However, varying the armature-circuit resistance Ra modifies the speedtorque characteristic, although does not affect the no-load speed of the
motor 0.
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Permanent-magnet DC motors
Ex. 3.4: Assume that the armature resistance of a PMDC motor is 1.2 .
When operated from a 60 V DC source, motor no-load speed is 1950 rpm
and the armature no-load current is 1.5 A. Determine the following:
a) The torque constant;
b) The no-load rotational losses;
c) The output in horsepower if the motor is operating at 1500 rpm from a
50 V source.
Solution: a) The internal generated voltage of the motor is:
At the speed of 1950 rpm, the torque constant is
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Permanent-magnet DC motors
b) Since all input power is supplied at no load, the input power goes to
rotational losses of the motor.
c) At 1500 rpm:
then, the internal generated voltage is
Therefore, the input power is:
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Permanent-magnet DC motors
The armature current can be expressed as
the input power is:
Since rotational losses are approximately constant (speeds are similar), the
output power of the motor is
or in horsepower:
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Linear motors
“A linear motor is an electric motor that has its stator and rotor "unrolled"
so that instead of producing a torque (rotation) it produces a linear force
along its length. The most common mode of operation is as a Lorentz-type
actuator, in which the applied force is linearly proportional to the current
and the magnetic field.” – from Wikipedia.
(3.88.1)
Various types of linear motor design can be subdivided into two major
categories: low-acceleration and high-acceleration linear motors.
Low-acceleration linear motors are suitable for maglev trains and other
ground-based transportation applications. High-acceleration linear motors
are normally rather short, and are designed to accelerate an object to a
very high speed (for example, see the coilgun).
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Linear motors
High-acceleration motors are usually used for studies of hypervelocity
collisions, as weapons, or as mass drivers for spacecraft propulsion. They
are usually of the AC linear induction motor (LIM) design with an active
three-phase winding on one side of the air-gap and a passive conductor
plate on the other side. However, the direct current homopolar linear motor
railgun is another high acceleration linear motor design.
The low-acceleration, high speed and high power motors are usually of the
linear synchronous motor (LSM) design, with an active winding on one
side of the air-gap and an array of alternate-pole magnets on the other
side. These magnets can be permanent magnets or energized magnets.
The Shanghai Transrapid motor is an LSM.
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Linear motors: history
The history of linear electric motors begun at least in 1840s, with the work
of Charles Wheatstone but his model was too inefficient to be practical. A
feasible linear induction motor was described in 1905 by Alfred Zehden for
driving trains or lifts. The German engineer Hermann Kemper built a
working model in 1935. In the late 1940s, Dr. Eric Laithwaite developed
the first full-size working model. In a single sided version, the magnetic
repulsion forces the conductor away from the stator, levitating it, and
carrying it along in the direction of the moving magnetic field. He called
the later versions of it magnetic river.
A regular electric speaker can be
viewed as a linear motor!
Image from www.animations.physics.unsw.edu.au
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Linear motors: history and use
Because of these properties, linear motors are often used in maglev
propulsion, as in the Japanese Linimo magnetic levitation train line near
Nagoya. However, linear motors have been used independently of
magnetic levitation, as in Transit systems worldwide and a number of
modern Japanese subways, including Tokyo's Toei Oedo Line.
Similar technology is also used in some roller coasters with modifications
but, at present, is still impractical on street running trams, although this, in
theory, could be done by burying it in a slotted conduit.
Linimo www.skyscrapercity.com
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Linear motors: history
Outside of public transportation, vertical linear motors have been proposed
as lifting mechanisms in deep mines, and the use of linear motors is
growing in motion control applications. They are also often used on sliding
doors, such as those of low floor trams such as the Citadis and the
Eurotram.
Dual axis linear motors also exist. These specialized devices have been
used to provide direct X-Y motion for precision laser cutting of cloth and
sheet metal, automated drafting, and cable forming. Most linear motors in
use are LIM (linear induction motor), or LSM (linear synchronous motor).
Linear DC motors do exist but are not used due to higher cost and linear
SMs suffer from poor thrust. So, for long run in traction LIM is mostly
preferred and for short run LSM is mostly preferred.
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Linear Induction motors
In linear induction motors, the force is produced by a moving linear
magnetic field acting on conductors in the field. Any conductor, such as a
loop, a coil or simply a piece of plate metal, that is placed in this field will
have eddy currents induced in it; therefore, creating an opposing magnetic
field, in accordance with Lenz's law. The two opposing fields will repel each
other, thus creating motion as the magnetic field sweeps through the metal.
Images from www.electrical4u.com
and sharepoint.umich.edu
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Linear Synchronous motors
Synchronous linear motors are
straightened versions of permanent
magnet rotor motors
The rate of movement of the magnetic
field is controlled, usually electronically, to
track the motion of the rotor. For cost
reasons synchronous linear motors rarely
use commutators, so the rotor often
contains permanent magnets, or soft iron.
Examples include coilguns and the
motors used on some maglev systems,
as well as many other linear
motors.
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Linear Synchronous
motors
U-channel linear synchronous motor
The two coils at the center are
mechanically connected, and are
energized in "quadrature" (with a
phase difference of 90° (π/2 radians)).
If the bottom coil (as shown) leads in
phase, then the motor will move
downward (in the drawing), and vice
versa. (Not to scale)
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Homopolar (Railgun)
A homopolar motor is a direct current electric motor with two magnetic
poles, the conductors of which always cut unidirectional lines of magnetic
flux by rotating a conductor around a fixed axis that is parallel to the
magnetic field. The resulting Electromotive Force is continuous in one
direction; the homopolar motor needs no commutator but still requires slip
rings. The name homopolar indicates that the electrical polarity of the
conductor and the magnetic field poles do not change (i.e., that it does not
require commutation).
A linear version of a homopolar motor is a
railgun. In this design, a large current is
passed through a metal sabot across
sliding contacts that are fed from two rails.
The magnetic field this generates causes
the metal to be projected along the rails.
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Piezoelectric motors
A piezoelectric motor is a type of electric motor based
upon the change in shape of a piezoelectric material when
an electric field is applied. Piezoelectric motors make use of
the converse piezoelectric effect whereby the material
produces acoustic or ultrasonic vibrations in order to
produce a linear or rotary motion. In one mechanism, the
elongation in a single plane is used to make a series of
stretches and position holds, similar to the way a caterpillar
moves.
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Short-stator vs. Long-stator motors
Another classification of linear motors is based on the length of a stator
(called an active part) compared to the rotor (or reactive part).
Considering the transportation (propulsion)
applications, in short-stator linear systems, the
stator and the frequency converter are
installed on board the vehicle and the reactive
part is fitted along the track. Thus, the weight
of the vehicle increases with the design
speed. In addition, a power transmission
system for feeding traction energy to the
vehicle is necessary. For the long-stator linear system, a multiphase
traveling-field winding is installed along the track. This winding is fed section
by section by stationary power converters. Thus the vehicle is the passive
part of the motor. This is a major advantage of the long-stator linear motor,
permitting speeds of up to more than 500 km/h (from http://mohagami.wordpress.com).
ELEN 4301/5301 Trends in Modern Power Systems
Summer 2013
Lamar University
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