Education for Liberty

European University of Bangladesh

Department of Electrical & Electronic Engineering (EEE)

Faculty of Engineering
Full Module Specification
Course Name Electrical Machines-III
Prepared by Md. Sabbir Hasan Sohag
Edited by Md. Asaduzzaman Sarker
Course Code EEE-329
Academic Year 2021
Semester Fall-2021
Module Credit 3 Credit hours.
Module Contents Single Phase Induction Motor, Shaded Pole
Induction Motor, Reluctance Motor,
Hysteresis Motor, Stepper Motor, Permanent
Magnet Synchronous Motor, Universal
Motors, Servo Motors, Amplidyne and
Metadyne Machines.
Grading As outlined in the University policy
Teaching Methodology Class room lecture, Multimedia
Presentation ,Discussion, Group study,
Assignment, Class test, Viva voce etc.
Method of Evaluation Attendance =20
Continuous Assessment =20
Mid-term =30
Final =30
TOTAL =100
 Single Phase Induction Motor

Module 01
Single Phase Induction Motor
Types of Single-Phase Motors
The single-phase motor, which are designed to operate from a single-phase supply, are
manufactured in a large number of types to perform a wide variety of useful services in home,
offices, factories, workshops and in a business establishment etc.
Small motors, particularly in the frictional kW sizes are better known than any other. In fact,
most of the new products of the manufacturers of space vehicles, aircrafts, business machines and
power tools etc. have been possible due to of the advances made in the design of frictional kW
motors. Since the performance requirements of the various applications differ so widely, the motor
manufacturing industry has developed many different types of such motors, each being designed to
meet specific demands.
Single-phase motors may be classified as under, depending on their construction and method
of starting:
1. Induction Motors (split-phase, capacitor and shaded-pole etc.)
2. Repulsion Motors (sometime called inductive-series motor)
3. AC Series Motor, and
4. Un-excited Synchronous Motors

Single-Phase Induction Motor

Constructionally, this motor is, more or less, similar to a poly-phase induction motor, except
that
(i) its stator is provided with a single-phase winding and
(ii) a centrifugal switch is used in some types of motors, in order to cut out a winding,
used only for starting purpose.
It has distributed stator winding and a squirrel-cage rotor. When fed from a single-phase
supply, its stator winding produces a flux (or field) which is only alternating i.e. one which
alternates along one space axis only. It is not a synchronously revolving (or rotating) flux, as in the
case of a two or three-phase stator winding, fed from a 2 or 3-phase supply.
Now, an alternating or pulsating flux acting on a stationary, squirrel-cage rotor cannot
produce rotation (only a revolving flux can). That is why a single-phase motor is not self-starting.
However, if the rotor of such a machine is given an initial start by hand (or small motor) or
otherwise, in either direction, then immediately a torque arises and the motor accelerates to its final
speed (unless the applied torque is too high).
This peculiar behavior of the motor has been explained in two ways:
(i) by two-field or double-field revolving theory, and
(ii) by cross-field theory.

Double-Field Revolving Theory

This theory makes use of the idea that an alternating uni-axial quantity can be represented by
two oppositely-rotating vectors of half magnitude. Accordingly, an alternating sinusoidal flux can be
represented by two revolving fluxes, each equal to half the value of the alternating flux and each
rotating synchronously (Ns=120f/P) in opposite direction.
For example, a flux given by =mcos2ft is equivalent to two fluxes revolving opposite
directions, each with a magnitude of (1/2) m and an angular velocity of 2f. It may be noted that
Euler’s expressions for cos provides interesting justification for the decomposition of a pulsating
flux. His expression is
1 𝑗𝜃
cos 𝜃 = (𝑒 + 𝑒 −𝑗𝜃 )
2

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 Single Phase Induction Motor
The term ej represents a vector rotated clockwise through an angle  whereas e-j represents
rotation in anticlockwise direction. Now, the above given flux can be expressed as
Φ𝑚 𝑗.2𝜋𝑓𝑡
Φ = Φ𝑚 cos 2πft = (𝑒 + 𝑒 −𝑗.2𝜋𝑓𝑡 )
2
The right-hand expression represents two oppositely-rotating vectors of half magnitude.
As shown in Fig. 36.1(a), let the alternating flux have a maximum value of m. Its
component fluxes A and B will each be equal to m/2 revolving anticlockwise and clockwise
directions respectively. Thus, the resultant flux is r  2  m / 2  m

Fig. 36.1

After sometime, when A and B would have rotated through angle + and -, as in Fig.
36.1(b), the resultant flux would be
Φ𝑚
Φ𝑟 = 2 × sin 𝜃 = Φ𝑚 sin 𝜃
2
After a quarter cycle of rotation fluxes A and B will be oppositely-directed as shown in Fig.
36.1(c) so that the resultant flux r  (m / 2)  (m / 2)  0 would be zero.
After half a cycle, fluxes A and B will have a resultant of r  2  (m / 2)  m. After
three quarters of a cycle, again the resultant flux  r  ( m / 2)  ( m / 2)  0, as shown in Fig.
36.1(e) and so on.

If we plot the values of resultant flux against

 between limits =0o to =360o, then a curve
similar to the one shown in Fig. 36.2 is
obtained. That is why an alternating flux can
be locked upon as composed of two revolving
fluxes, each of half the value and revolving
synchronously in opposite
directions.
Fig. 36.2

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 Single Phase Induction Motor

It may be noted that the slip of the rotor is [ s  (N s  N ) / N s  1  (N / N s ) ; or (N / N s )  1  s ]

w.r.t the forward rotating flux (i.e. one which rotates in the same direction as rotor) then its slip w.r.t
to the backward rotating fluxes is (2-s) [ sb  [N s  (N )] / N s  1  (N / N s )  1  (1  s)  (2  s) ].
Each of the two component fluxes, while revolving round the stator, cuts the rotor, induces an
emf and this produces its own torque. Obviously, the two torques (called forward and backward
torques) are oppositely-directed, so that the net or resultant torques is equal to their difference as
shown in Fig. 36.3.

Fig. 36.3
1−𝑠
Now, power developed by a rotor is 𝑃𝑔 = 𝐼2 2 𝑅2
𝑠
𝑃𝑔 1 1−𝑠
If N is the rotor speed in rps then torque is given by 𝑇𝑔 = 2𝜋𝑁 = 2𝜋𝑁 𝐼2 2 𝑅2
𝑠
1 1−𝑠 1 𝐼2 2 𝑅2 𝐼2 2 𝑅2
Now, 𝑁 = 𝑁𝑠 (1 − 𝑠) ∴ 𝑇𝑔 = 2𝜋𝑁 (1−𝑠) 𝐼2 2 𝑅2 = 2𝜋𝑁 =𝑘
𝑠 𝑠 𝑠 𝑠 𝑠

Hence the forward and backward torques are given by,

𝐼2 2 𝑅2 𝐼2 2 𝑅2
𝑇𝑓 = 𝑘 and 𝑇𝑏 = −𝑘
𝑠 2−𝑠
𝐼2 2 𝑅2 𝐼2 2 𝑅2
Or 𝑇𝑓 = synch.watt and 𝑇𝑏 = −𝑘 synch.watt
𝑠 2−𝑠

Total torque, T = Tf +Tb

Fig 36.3 shows both torques and the resultant torque for slips between zero and +2. At
standstill, s=1 and (2-s) = 1. Hence, Tf and Tb are numerically equal but, being oppositely directed,
produced no resultant torque. That explains why there is no starting torque in a single phase motor.
However, if the rotor is started somewhat, say, in the clockwise direction, the clockwise
torque starts increasing and, at the same time, the anticlockwise torque starts decreasing. Hence,
there is a certain amount of net torque in the clockwise direction which accelerates the motor to full
speed.

Double-Field Revolving theory

The resultant torque of the single motor is zero only at a slip of unity of the
synchronous speed in either direction. Once rotated in either direction, therefore, the
single-phase motor will continue to rotate in that direction because the resultant net torque
is produced to the left or the right of the standstill point shown in Fig. 36.3.

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 Single Phase Induction Motor

Cross-Field Theory
Assume that the rotor of Fig. 22.11 is rotating in a clockwise direction, while the single-phase
distributed stator field sets up a flux along the horizontal axis from right to left as shown. s
represents the stator flux and at this instant indicates a north pole on the right side and south pole on
the left side.
Because of the motion of the conductors in the magnetic field, a rotational emf is induced in
them. Application of Fleming’s right-hand rule shows that these induced rotor-conductor voltages
are in the directions indicated outside the rotor conductors.

The magnitude of the rotational voltage

is proportional to the speed of the rotation and
the magnitude of the stator flux. For a given
speed, therefore, this rotor voltage, and hence
rotor current varies sinusoidally at supply
frequency, as does the stator flux.
It should be remembered that the
inductive reactance of a squirrel-cage rotor at
line frequency is comparatively high, and so
the rotor current lags the induced emf and also
the stator flux by 90o.
Fig. 22.11
Examining Fig 22.11 again, it is seen that the rotor sets up a flux which is at right angles to
the stator flux in space, and hence it is called cross-field. Furthermore, it has already been shown that
this rotor flux also lags the stator flux by 90 o in time. The condition necessary to produce a rotating
field are thus present, namely, two fields are equal, and the rotating field has a constant magnitude.
As slip increases, the rate of cutting is less, and the magnitude of the cross field decreases. A
rotating field is still produced, but the magnitude of the resultant varies as it rotates around the stator,
giving an elliptical pattern rather than a circular one. It should be pointed out that only the magnitude
of the cross field varies with slip, while the frequency depends on that of the stator field.

If at the instant shown in Fig. 22.11, the stator field is at a maximum, then the rotational emf
induced in the rotor is also at a maximum with the direction shown near the rotor conductors. At this
same instant, however, since the cross-field current lags the rotational voltage by 90o, the magnitude
of the cross-field flux is zero. If time is now taken 90o later, when s is zero, the rotor current will be
at a maximum in the direction shown in Fig. 22.12.

The resultant field now has a direction

which is 90o clockwise from that which it
previously had. Thus, not only does the cross-
field combine with the stator field to produce a
resultant rotating field, but this same field rotates
in the direction in which the rotor already
moving. This, of course, produces a rotor torque
in the direction of rotation.
Fig. 22.12 Cross field when stator field is
zero.

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 Single Phase Induction Motor
It should be obvious at standstill there can be no cross-field, only the pulsating stator field.
This leads to the conclusion that the single-phase induction motor has no inherent starting torque. If,
however, there is some means of starting the motor, then it will continue to develop torque as a
single-phase induction motor in the direction given to it upon starting.

Cross-Field Theory
The quadrature pulsating rotor field reacts against the pulsating main field to
produce a resultant magnetic field. The resultant magnetic field is a fairly constant rotating
magnetic field that rotates in the same direction as the direction of the rotation of the rotor.
A squirrel- cage induction motor will continue to rotate, producing induction motor torque
in a rotating magnetic field, once a rotational emf has been initiated.

Making Single-Phase Induction Motor Self-Starting

As discussed above, a single-phase induction motor is not self-starting. To overcome this
drawback and make the motor self-starting, it is temporarily converted into two-phase motor during
starting period.
For this purpose, the stator of a single-phase motor is provided with an extra winding, known
as starting (or auxiliary) winding, in addition to the main or running winding. The two windings are
spaced 90o electrically apart and are connected in parallel across the single-phase supply as shown in
Fig. 36.4.

It is so arranged that the phase-

difference between the currents in the two
stator windings is very large (ideal value
being 90o). Hence, the motor behaves like a
two-phase motor. These two currents produce
a revolving flux and hence make the motor
self-starting.
There are many methods by which the
necessary phase-difference between the two Fig. 36.4
currents can be created.

Split-Phase Induction Motors

The single-phase induction motor which is equipped with an auxiliary winding displaced in
magnetic position from, and connected in parallel with a main running winding is called split-phase
induction motor.
In split-phase machine, shows in Fig. 36.5(a), the main winding has low resistance but high
reactance whereas the starting winding has a high resistance, but low reactance. The resistance of the
starting winding may be increased by connecting a high resistance R in series with it or by choosing
a high-resistance fine copper wire for winding purposes.
Hence, as shown in Fig. 36.5(b), the current Is drawn by the starting windings lags behind the
applied voltage V by a small angle whereas current Im taken by the main winding lags behind V by a
very large angle.
Phase angle between Is and Im is made as large as possible because the starting torque of a
split-phase motor is proportional to sin.

A centrifugal switch S is connected in series with the starting winding and is located inside
the motor. Its function is to automatically disconnect the starting winding from the supply when the
motor has reached 70 to 80 percent of its full-load speed.
In the case of split-phase motors that are hermetically sealed in refrigeration units, instead of
internally-mounted centrifugal switch, an electromagnetic type of relay is used. As shown in Fig.

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 Single Phase Induction Motor

36.6, the relay coil is connected in series with main winding and the pair of contacts which are
normally open, is included in the starting winding.

(b)
(a)
Fig. 36.5
During starting period, when Im is large, relay contacts close thereby allowing Is to flow and
the motor starts as usual. After motor speeds up to 75 percent of full-load speed, Im drops to a value
that is low enough to cause the contacts to open.
A typical torque/speed characteristic of such a motor is shown in Fig. 36.7. As seen, the
starting torque is 150 to 200 percent of the full-load torque with a starting current of 6 to 8 times the
full-load current.

Fig. 36.6 Fig. 36.7

These motors often used in preference to the costlier capacitor-start motors. Typical
applications are: fans and blowers, centrifugal pumps and separators, washing machines, small
machine tools, duplicating machines and domestic refrigerators and oil burners etc. Commonly
available size range from 1/20 to 1/3 hp (40 to 250 W) with speeds ranging from 3,400 to 865 rpm.
As shown in from Fig. 36.9, the connections of the starting winding have been reversed.
The speed regulation of standard split-phase motor is nearly the same as of the 3-phase
motors. Their speed varies about 2 to 5% between no load and full-load. For this reason, such
motors are usually regarded as practically constant-speed motors.
Such motors are sometimes referred to as resistance-start split-phase induction motors in
order to distinguish them from capacitor-start induction run and capacitor start-and-run motors.

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 Single Phase Induction Motor

Fig. 36.8 Fig. 36.9

Capacitor-Start Induction-Run Motors

In these motors, the necessary phase difference between Is and Im is produced by connecting a
capacitor in series with the starting winding as shown in Fig. 36.10. The capacitor is generally of the
electrolytic type and is usually mounted on the outside of the motor as a separate unit as shown in
Fig. 36.11.
The capacitor is designed for extremely short-duty service and is guaranteed for not more
than 20 periods of operation per hour, each period not to exceed 3 seconds. When the motor reaches
about 75 percent of full-load speed, the centrifugal switch S opens and cuts out both the starting
winding and the capacitor from the supply, thus leaving only the running winding across the lines.
As shown in Fig. 36.12, current Im drawn by the main winding lags the supply voltage V by a
large angle whereas Is leads V by a certain angle. The two current are out of phase with each other by
about 180o (for a 200 W, 50 Hz motor) as compared to nearly 30o for a split-phase motor.

Fig. 36.10 Fig. 36.11 Fig. 36.12

Their resultant current I is small and is almost in phase with V as shown in Fig. 36.12.
Since the torque developed by a split-phase motor is proportional to the sine of the angle
between Is and Im, it is obvious that the increase in the angle (from 30 o to 80o) alone increases the
starting torque to nearly twice the value developed by a standard split-phase induction motor. Other
improvement in motor design have made it possible to increase the starting torque to a value as high
as 350 to 450 percent.
Typical performance curve of such a motor is shown in Fig. 36.13.

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 Single Phase Induction Motor

Fig. 36.13

Equivalent Circuit of a Single-Phase Induction Motor without Core Loss

A single-phase motor may be looked upon as consisting of two motors, having a common
stator winding, but with their respective rotors revolving in opposite directions. The equivalent
circuit of such a motor based on double-field revolving theory is shown in Fig. 36.14.

Here the single-phase motor has been

imagined to be made up of (i) one stator
winding and (ii) two imaginary rotors. The
stator impedance is Z=R1+jX1. The
impedance of each rotor is (r2+jx2) where
r2 and x2 represent half the actual rotor
values in stator terms (i.e. x2 stands for
half the standstill reactance of the rotor, as
referred to stator).
Since iron loss has been neglected, the
exciting branch is shown consisting of
exciting reactance only. Each rotor has
been assigned half magnetizing reactance
(i.e. xm represents half the actual
reactance). The impedance of ‘forward
running’ rotor is
𝑟
𝑗𝑥𝑚 ( 𝑠2 + 𝑗𝑥2 )
𝑍𝑓 = 𝑟
2 )
𝑠 + 𝑗(𝑥𝑚 + 𝑥2
And it runs with a slip of s.
Fig. 36.14

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 Single Phase Induction Motor

The impedance of ‘backward running’ motor is

𝑟
𝑗𝑥𝑚 (2 −2 𝑠 + 𝑗𝑥2 )
𝑍𝑏 = 𝑟
2
+ 𝑗(𝑥𝑚 + 𝑥2 )
2−𝑠

And it runs with a slip of (2-s). Under standstill condition, Vf = Vb, but under running conditions Vf is
almost 90 to 95% of the applied voltage.
𝐼32 𝑟2
The forward torque in synchronous watts is 𝑇𝑓 = 𝑠
.
𝐼52 𝑟2
Similarly, backward torque 𝑇𝑏 = 2−𝑠

The total torque is

𝐼32 𝑟2 𝐼52 𝑟2 𝐼32 (2 − 𝑠) − 𝐼52 𝑠 2𝐼32 − 𝑠(𝐼32 − 𝐼52 )
𝑇 = 𝑇𝑓 − 𝑇𝑏 = − = 𝑟2 = 𝑟2
𝑠 2−𝑠 𝑠(2 − 𝑠) 𝑠(2 − 𝑠)
Equivalent Circuit of a Single-Phase Induction Motor with Core Loss
The core loss can be represented by an equivalent resistance which may be connected either
in parallel or in series with the magnetizing reactance as shown in Fig 36.15.
Since under running condition Vf is very high (and Vb is correspondingly, low) most of the iron
loss takes place in the ‘forward motor’ consisting of the common stator and forward-running rotor.
Core-loss current Iw=core-loss/Vf. Hence, half value of core-loss equivalent resistance is rc=Vf/Iw. As
shown in Fig 36.15, rc has been connected in parallel with xm in each rotor.

(a) (b)
Fig. 36.15

Example 36.3. A 250 W, 230 V, 50 Hz capacitor-start motor has the following constants for the
main and auxiliary winding: Main winding, Zm=(4.5+j3.7) ohm, Auxiliary winding,
Za=(9.5+j3.5) ohm. Determine the value of the starting capacitor that will place the main and
auxiliary winding currents in quadrature at starting.
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 Single Phase Induction Motor
Solution: Let XC be the reactance of the capacitor connected in the auxiliary winding.
Then Za=9.5+j(3.5-XC )=(9.5-jX) ohm
where, X is the net reactance
Now, Zm=(4.5+j3.7)=5.8239.4o ohm
Obviously, Im lags behind V by 39.4o.
Since time phase angle between Im and Ia has to be 90o,
Ia must lead V by (39.4o- 90o) =-50.6o.
For auxiliary winding,
tana=(3.5-XC )/R
or tan(-50.6o)= (3.5-XC )/9.5=-1.217
Or (3.5-XC )=-9.51.217=-11.56 ohm
XC=11.56+3.5=15.06 ohm
Or 1/(250C)=15.06
or C=1/(25015.06)= 21110-06 F
C=211 F.

Capacitor Start-and-Run Motor

This motor is similar to the capacitor-start motor except that the starting winding and
capacitor are connected in the circuit at all time.
The advantage of leaving the capacitor permanently in circuit are:
(i) improvement of over-load capacity of the motor,
(ii) a higher power factor,
(iii) higher efficiency, and
(iv) quieter running of the motor which is so much desirable for small power drivers in
offices and laboratories.
Some of these motors which start and run with one value of capacitance in the circuit are
called single-value capacitor-run motor. Other which start with high value of capacitance
but run with a low value of capacitance are known as two-value capacitor-run motor.

Single-value Capacitor Run Motor

It has one running winding and one starting winding in series with a capacitor as shown in
Fig. 36.28. Since the capacitor remains in the circuit permanently, this motor is often referred to as
permanent-split capacitor-run motor and behaves practically like an unbalanced two-phase motor.

Fig. 36.28 Fig. 36.29 Fig. 36.30

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 Single Phase Induction Motor

Obviously, there is no need to use centrifugal switch which has necessary in the case of
capacitor-start motors. Since the same capacitor is used for starting and running, it is obvious that
neither optimum starting nor optimum running performance can be obtained because value of
capacitance used must be a compromise between the best value for starting and that for running.
Generally, capacitors of 2 to 20 F capacitance are employed and are more expensive oil or
pyranol-insulated foil-paper capacitors because of continuous-duty rating. The low value of the
capacitor results in small starting torque which is about 50 to 100% of the rated torque as shown in
Fig. 36.29. Consequently, these motors are used where the required starting torque is low such as air-
moving equipment i.e. fans, blowers and voltage regulator and also oil burners where quiet operation
is particularly desirable.
One unique feature of this type of motor is that it can be reversed by an external switch
provided its running and staring winding are identical. One serves as the running winding and the
other as a starting winding for one direction of rotation. For reverse rotation, the one that previously
served as a running winding becomes the starting winding while the former starting winding serves
as a running winding. As seen from Fig. 36.30 when the switch in the forward position, winding B
serves as running winding and A as starting winding. When switch is in ‘reverse’ position, winding A
becomes the running winding and B the starting winding.
Such reversible motors are often used for operating device that must be moved back and forth
very frequently such rheostats, induction regulations, furnace controls, valves and arc-welding
controls.

Two-Value Capacitor-Run Motor

This motor starts with a high capacitor in series with the starting winding so that the starting
torque is high. For running, a lower capacitor is substitute by the centrifugal switch. Both the running
and starting windings remain in circuit.
The two values of capacitance can be obtained as follows:
1. by using two capacitors in parallel at the starting and then switching out one for
low-value run as shown in Fig. 36.31, or
2. by using a step-up auto-transformer in conjunction with one capacitor so that
effective capacitance value is increased for starting purpose.
In Fig. 36.31, B is an electrolytic capacitor of high capacity (short duty) and A is an oil
capacitor of low value (continuous duty). Generally, starting capacitor B is 10 to 15 times the
running capacitor A. At the start, when the centrifugal switch is closed, the two capacitors are put in
parallel, so that their combined capacitance is the sum of their individual capacitances.
After the motor has reached 75% full-load speed, the switch opens and only capacitor A
remains in the starting winding circuit. In this way, both optimum starting and running performance
is achieved in such motors. If properly designed, such motors have operating characteristics very
closely resembling those displayed by two-phase motors. Their performance is characterized by
1. ability to start heavy loads,
2. extremely quiet operation,
3. higher efficiency and power factor, and
4. ability to develop 25% overload capacity
Hence, such motors are ideally suited where load requirements are severe as in the case of
compressors and fire strokers etc.
As motor speeds up, the centrifugal switch shifts the capacitor from one voltage tap to
another so that the voltage transformation ratio changes from higher value at starting to a lower value
for running. The capacitor which is actually of the paper-tinfoil construction is immersed in a high
grade insulation like wax or mineral oil.
The use of an auto-transformer and single oil-type capacitor is illustrated in Fig. 36.32. The
transformer and capacitor are sealed in a rectangular iron box and mounted on top of the motor. The
idea behind using this combination is that a capacitor of value C connected to the secondary of a

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 Single Phase Induction Motor

step-up transformer appears to the primary as though it had a value of K2C where K is voltage
transformation ratio.

Fig. 36.31 Fig. 36.32

For example, if actual value of C=4 F and K=6, then low-voltage primary acts as if it had a
144 F (=624) capacitor connected across its terminals. Obviously, effective value of capacitance
has increased 36 times. In the ‘start’ position of the switch, the connection is made to the mid-tap of
the auto-transformer so that K=2. Hence, effective value of capacitance at start is 4 times the running
value and is sufficient to give a high starting torque.

Problem A 250 W, 230 V, 50 Hz capacitor-start motor has the following constants for the main and
auxiliary winding: Main winding, Zm=(4.5+j3.7) ohm, Auxiliary winding, Za=(9.5+j3.5) ohm.
Calculate (a) the value of the starting capacitor that will place the main and auxiliary winding
currents in quadrature at starting, and (b) the magnitudes and phase angles of the currents in
the main and auxiliary windings when rated voltage is applied to the motor under starting
conditions.
Solution: Let XC be the reactance of the capacitor connected in the auxiliary winding.
Then Za=9.5+j(3.5-XC )=(9.5-jX) ohm
where, X is the net reactance
Now, Zm=(4.5+j3.7)=5.8239.4o ohm
Obviously, Im lags behind V by 39.4o.
Since time phase angle between Im and Ia has to be 90o,
Ia must lead V by (39.4o- 90o) =-50.6o.
For auxiliary winding,
tana=(3.5-XC )/R
or tan(-50.6o)= (3.5-XC )/9.5=-1.217
Or (3.5-XC )=-9.51.217=-11.56 ohm
XC=11.56+3.5=15.06 ohm
Or 1/(250C)=15.06
or C=1/(25015.06)= 21110-06 F
C=211 F.

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 Single Phase Induction Motor

Problem: A 220 V, 1.5 hp, 59 Hz, two poles, capacitor start induction motor has the following main
winding impedances: R1=4 ohm, X1=2.0 ohm, Xm=200 ohm, R2=3 ohm and X2= 4.04 ohm. At
slip of 0.05, calculate (i) stator current, (ii) stator power factor, (iii) input power, (iv) forward
torque, and (v) backward torque.

Possible Questions
1. Write different classifications of single phase induction motors.
2. Classify the single-phase motors depending on their construction and method of starting.
3. What are the differences between single-phase and three-phase induction motor constructionally?
4. State and explain double field revolving theory.
5. Draw the forward, backward, resultant, torques versus slip curve for a single phase induction
motor according to the double-field revolving theory.
6. Write the equations for forward, backward, resultant, torques at standstill conditions.
7. Using double field revolving theory, show that the forward torque and the backward torque
developed by a single phase induction motor is the same in magnitude at unity slip.
8. Using double field revolving theory, show that the starting torque of a single-phase induction
motor is zero. What is the remedy of this problem?
9. Prove that for a single phase induction motor running at a speed of N rpm, slip corresponding to
the backward field (sb) = 2 – s, here ‘s’ is the slip corresponding to the forward field.
10. State and explain cross-field theory.
11. Using the cross-field theory, briefly explain why the single phase induction motor is not self-
starting.
12. Using the cross-field theory, briefly explain why the single phase induction motor will continue
to rotate; producing induction motor torque in a rotating magnetic field, once a rotational emf has
been initiated.
13. Define a split phase induction motor.
14. Why is phase splitting necessary in a single phase induction motor?
15. Why two windings (one main and other auxiliary) in a single-phase induction motor are
necessary, briefly explain.
16. Draw the equivalent circuit of a single-phase induction motor without core loss.
17. Draw the equivalent circuit of a single-phase induction motor with core loss.
18. With necessary circuit and vector diagram, briefly explain the operation of the split-phase (or
resistance-start split phase) induction motor.
19. Draw the circuit diagram and vector diagram for a resistance-start split phase induction motor.
20. Draw the torque vs speed curve for a resistance-start split phase induction motor.
21. With necessary circuit and vector diagram, briefly explain the operation of the capacitor-start
induction run motor.
22. Draw the circuit diagram and vector diagram for a capacitor-start induction run motor.
23. Draw the torque vs speed curve for a capacitor-start induction run motor.
24. What are the differences between resistance-start and capacitor-start single-phase induction
motors?
25. What are the advantages of leaving the capacitor permanently in the auxiliary circuit of a single-
phase induction motor?
26. With necessary circuit diagram, briefly explain the operation of the single-value capacitor-run
induction motor.
27. Explain why in the case of single-value capacitor-run induction motor, neither optimum starting
nor optimum running performance can be obtained.
28. With necessary circuit diagram, briefly explain the operation of the two-value capacitor-run
induction motor.
29. What are the advantages of two-value capacitor-run induction motor?
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 Single Phase Induction Motor

Example 36.3. A 250 W, 230 V, 50 Hz capacitor-start motor has the following constants for the
main and auxiliary winding: Main winding, Zm=(4.5+j3.7) ohm, Auxiliary winding, Za=(9.5+j3.5)
ohm. Determine the value of the starting capacitor that will place the main and auxiliary winding
currents in quadrature at starting.
Problem 1. 400-W, 120-V, 50-Hz capacitor start motor has main winding impedance Zm = 3 + j4 Ω and
auxiliary winding impedance Za = 6 + j8 Ω at starting. Find the value of starting capacitance that will
place the main and auxiliary winding currents in quadrature at starting.

References
[1] B. L. Theraja, A. K. Theraja, “A Textbook of ELECTRICAL TECHNOLOGY in SI Units Volume
II, AC & DC Machines”, S. Chand & Company Ltd., (Multicolour illustrative Edition).
[2] A. F. Puchstein, T. C. Lloyd, A.G. Conrad, “Alternating Current Machines”, © 1942, Asia
Publishing House, Third Edition (Fully revised and corrected Edition 2006-07).
[3] Jack Rosenblatt, M. Harold Friedman, “Direct and Alternating Current Machinery”, Indian
Edition (2nd Edition), CBS Publishers & Distributors.
[4] A. E. Fitzgerald, Charles Kingsley, Jr. Stephen D. Umans, Electric Machinery, 5th Edition in SI
units, ©1992 Metric Edition, McGraw Hill Book Company.
[5] Irving L. Kosow, Electrical Machinery and Transformers, Second Edition, Prentice –Hall India
Pvt. Limited.

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 Shaded-Pole Motor

Module 02
Shaded-Pole Motor
For applications requiring small power ratings, 1/20 hp or less, the shaded-pole induction motor is
probably most widely used today.

Shaded-Pole Motor: A shaded-pole motor may be defined as a single-phase induction motor provided
with an auxiliary short-circuited winding or winding displaced in magnetic position from the main
winding.
In usual form of construction, salient poles are used, and the auxiliary short-circuited winding consists
of a single turn placed around a portion of the main pole. This coil is known as shading coil because it
causes the flux in that portion of the pole surrounded by it to lag behind the flux in the rest of the pole.

Essential Parts of a Shaded-Pole Motor

Fig. 9-1 gives a schematic representation of a
simple shaded-pole motor. There is but a single
winding which is connected to the line, a second
winding permanently short-circuited upon itself,
and a squirrel cage rotor.
This short-circuited winding is displaced from
the main winding by an angle which can never be
as much as 90 electrical degrees.
It has to be shifted from the axis of the main
winding by a definite amount in order to set up a
component field along an axis in space different
from that of the main winding; furthermore, this
shift has to be less that 90o so that a voltage can be
induced in the short-circuited winding by Fig. 9-1 Shaded-Pole Induction Motor
transformer action of the main winding.

Working Principle of a shaded pole motor

When a single phase ac power is applied to the stator
winding, a magnetic field is created. The winding of shaded
pole delays the creation of magnetic field in the portion of
the stator poles. This produces a magnetic field in the
shaded portion that is approximately 90o apart from the
magnetic field produced in the main portion of the pole.
That means two fluxes are obtained which are displaced
both in time and space. The net effect of these two fluxes is
moved across the pole from the unshaded portion to the
shaded portion. Thus a rotating field is obtained which is
always moved from the unshaded portion to the shaded
portion.
The net rotating flux cut the rotor conductor thus an emf is
induced in the rotor and current flows through the
conductor. Thus the force is developed to the conductor of
rotor and rotor start to rotate.

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 Shaded-Pole Motor

How a rotating field is produced in a shaded pole motor?

Fig. 22.24 Shaded-pole Motor Fig. 22.25 Flux in Shaded-pole motor, main-field
current increasing

The shaded-pole motor is actually split-phase type as shown in Fig. 22.24.

When alternating current is applied to the field winding, there is a change of flux in the core. This
change of flux causes an induced voltage in the shading coil, and this induced voltage causes a shading-
coil current in such a direction as to oppose the core flux.
Since an induced current always flows in such a direction as to oppose the change in flux which induces
it, the current in the shading coil delays the buildup of the shading flux. The flux in the shaded part of
the pole this lags the flux in the main (unshaded) part of the pole.

Fig. 22.26 Flux in Shaded-pole motor, main-field current at maximum.

Fig.22.27 Flux in Shaded-pole motor, main-field current decreasing.

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 Shaded-Pole Motor

Fig.22.28 Flux in Shaded-pole motor, main-field current reversing.

At the same time, the main flux and the shaded-pole flux are obviously displaced in space, although by
less than 90o.
To obtain the rotating field, it is necessary only that there be two component fields, displaced both
in time and in space. Since there are both a time and a space displacement between two fields, the
conditions for setting up a rotating field are present, no matter how imperfectly. Torque is thus
developed in the squirrel-cage rotor.
The movement of flux around the stator may be more clearly illustrated in the following explanation and
diagrams. Only one salient pole is shown, while the shading coil is given two turns to simplify the
discussion that follows:
1. If the line current is rising during its first quarter cycle, as shown in Fig. 22.25(b), the current
caused by induced voltage in the shading coil opposes the setting up the flux. This current is shown in
Fig, 22.25(a). The opposing magneto motive force (mmf) of the shaded coil therefore causes most of the
flux to be concentrated in the main, unshaded portion of the pole.
2. When the line current has reached its maximum positive value, as shown in Fig. 22.26(b), the
flux too is at its maximum value, but now there is no change in the flux. Hence there is no current in the
shading coil, and the flux is uniformly distributed across the entire pole, including the shaded portion.
Essentially the field axis has shifted toward the shaded part of the pole.
3. When the line current is decreasing, the current in the shading coil must be in a direction to
maintain the flux, i.e. oppose the decrease, and must therefore now reverse, as shown in Fig. 22.27(a).
The concentrates the flux in the shaded-pole portion while it gets weaker in the main part of the pole.
The filed has thus shifted even further toward the shaded portion.
4. Finally, when the main-field current reverses, the current in the shading coil maintains some
flux in that portion of the pole, although the polarity of the reminder of the pole has already reversed.
This is shown in Fig. 22.28. At some time after this instant, the mmf of the main field and that of the
shading acting on the shaded-pole piece will be exactly equal and opposite, resulting in zero flux
through the shaded pole. The flux cycle will then repeat itself for the next half-cycle of the line current,
starting first in the opposite direction.
Examine of Figs. 22.25 to 22.28 shows that the flux moves across the pole from the unshaded
portion to the shaded portion, giving the effect of a rotating field. The net effect of time and space
displacement is to produce a shifting flux in the air gap which shifts always toward the shading coil.
Therefore, the direction of rotation of a shaded-pole motor is always from the unshaded to the shaded
portion of the pole.
In the simple motor seen in the previous figures, the direction of rotation is fixed by physical
construction. The motor must always rotate in the same direction as the field motion, or from the

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 Shaded-Pole Motor
unshaded to the shaded portion of the poles. In most cases, therefore, the shaded poles motor cannot be
reversed.

Why the shaded pole motor is noisier than the other single phase induction motor?
The field of the shaded-pole motor is not constant in magnitude but shifts from one side of the
pole to the other. Because the shaded-pole motor does not create a truly revolving filed, the torque is not
uniform but varies from instant to instant. Thus this type of motor tends to make the motor noisier than it
would be for a conventional split-phase or capacitor-type single phase induction motor of the same size.

Reversible Motors
Use of Two Motors in Tandem
Since the ordinary shaded-pole motor is inherently unidirectional, because the shading coil, reversibility
poses a problem. Some manufacturers solve this problem by using two motors, one for each direction of
rotation. Both rotors are mounted on the shaft, and one stator or the other is energized, depending upon
the direction of the rotation desired. One such motor is illustrated if Fig. 9-17.

Fig. 9-1 Shaded-Pole Induction Motor

Use of Two Wound Shading Coils per Pole

Fig. 9-18 shows schematically how a shaded-pole motor can be reversed if it is provided with two
shading coils per pole.

Fig. 9-18: A reversible shaded-pole motor with two Fig. 22.29: Reversing Shaded-Pole Motor.
auxiliary windings.

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 Shaded-Pole Motor
One each salient pole of these motors, there are two shaded segments and hence two shading coils. The
shading coils that are one pole pitch apart are connected in series, and a single-pole double-throw
(SPDT) switch short-circuits either set of coils to change the direction of rotation. The circuit is shown
in Fig. 22.29, with the switch in clockwise-rotation position. This places coils 1 and 3 actively in the
circuit, being shorted by reversing switch. Coils 2 and 4 remain in series with each other, but are on
open circuit and so are inactive.
The main field flux is shown increasing vertically downward, and the arrow on the shaded coils show
the current in them. It thus seen that the shading coils must be connected in such a manner as not to have
their induced voltages in opposition, or there may not be any current in them, and hence no flux lag.

Advantages of shaded-pole motors:

(i) Rugged construction
(ii) There are no brushes, no commutator, no capacitor, no moving switch, no governor, and no
slip- rings.
(iii) Cheaper in cost
(iv) Small in size
(v) Requires little maintenance
(vi) Its stalling locked-current is only slightly higher than its normal rated current so that it can
remain stalled for short periods without harm.

Disadvantages of shaded-pole motors:

(i) Very low starting torque
(ii) Low efficiency due to the presence of harmonics in the winding current particularly third
harmonics.
(iii) Low power factor

Applications:
Shaded-pole motors have many applications, among which are fans, blowers, heaters, vending
machines, hair dryer, slide and moving projectors, advertising displays, rotisseries etc..

Characteristics of a Shaded-Pole Motor

The torque versus speed characteristic curve of a shaded pole motor is shown in the following figure.
It is seen from the figure that the
speed of a shaded pole motor can be
control by varying the applied
voltage.

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 Shaded-Pole Motor
Remember:
 The shaded pole motor is only a very small fractional horsepower motor.
 The direction of rotation is from unshaded to the shaded portion of the pole face.
 The field of the shaded-pole motor is not constant in magnitude but shifts (rotates) from one side
of the pole to the other.

Problem : A 6 W, 115 V, 60 Hz, 2 poles shaded-pole induction motor operates at 2900 rpm when the
input power is 21 W. Calculate (i) the full-load efficiency, and (ii) the slip.
Solution:

𝑷𝒐 𝟔
𝜼= × 𝟏𝟎𝟎% = × 𝟏𝟎𝟎% = 𝟐𝟖%
𝑷𝒊 𝟐𝟏

𝟏𝟐𝟎𝒇 𝟏𝟐𝟎 × 𝟔𝟎
𝑵𝒔 = = = 𝟑𝟔𝟎𝟎 𝒓𝒑𝒔
𝑷 𝟐
𝑵𝒔 − 𝑵𝒓 𝟑𝟔𝟎𝟎 − 𝟐𝟗𝟎𝟎
𝒔= = = 𝟎. 𝟏𝟗𝟒 𝒐𝒓 𝟏𝟗. 𝟒%
𝑵𝒔 𝟑𝟔𝟎𝟎

Possible Questions:
1. Define the shaded-pole motor.
2. What are the essential parts of a shaded-pole motor?
3. Define shading-coil of a shaded-pole motor.
4. Briefly describe the working principle of a shaded-pole motor.
5. How a rotating field is produced in a shaded pole motor?
6. Why the shaded pole motor is noisier than the other single phase induction motor?
7. What are the methods to reverse the rotation of a shaded pole motor?
8. Briefly describe any one method to obtain the reverse operation of a shaded-pole motor.
9. List the advantages of a shaded-pole motor.
10. List the disadvantages of shaded-pole motor.
11. List the applications of shaded-pole motor.

References
[1] Cyril G. Veinott, Joseph E. martin, Fractional and Subfractional horsepower Electric Motors,
Fourth Edition, Tata McGraw-Hill International Editions, Electrical and Mechanical Engineering Series.
[2] Jack Rosenblatt, M. Harold Friedman, “Direct and Alternating Current Machinery”, Indian Edition
(2nd Edition), CBS Publishers & Distributors.

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 Reluctance Motor

Module 03
Reluctance Motor
Definition: A reluctance motor is a synchronous motor similar in construction to an induction motor, in which
the member carrying the secondary circuit has the salient poles, without dc excitation. It starts as an induction
motor but operates normally at synchronous speed.

It is a single phase synchronous motor which does not require dc excitation to the rotor. Its operation is based
upon the following principle:
Whenever a piece of ferromagnetic material is located in a magnet field; a force is exerted on the material,
tending to align the materiel so that reluctance of the magnetic path that passes through the material minimum.

Construction
A reluctance motor (also called synchronous reluctance motor) consists of:
(i) A stator carrying a single-phase winding along with an auxiliary winding to produce a synchronous-
revolving magnetic field.

(ii) A squirrel-cage rotor having unsymmetrical magnetic construction. This is achieved by symmetrically
removed some of the teeth from the squirrel-cage rotor to produce salient poles on the rotor as shown in the
following figure. The salient poles created on the rotor must be equal to the poles on the stator.

The air-gap between stator and rotor is not uniform. No dc supply is given to the rotor. The rotor is free to rotate.
The reluctance i.e. resistance of magnetic circuit depends on the air gap. More the air-gap, more is the reluctance
and vice versa. Due to the variable air-gap between stator and rotor, when rotor rotates, reluctance between
stator and rotor also changes. The stator and rotor are designed in such a manner that the variation of the
inductance of the windings is sinusoidal with respect to the rotor position.

Working Principle
The stator consists of a single winding called main winding. But single winding cannot produce rotating
magnetic field. So for production of rotating magnetic field, there must be at least two winding separated by
certain phase angle. Hence stator consists of an additional winding called auxiliary winding. Thus there exists a
phase difference between the currents carried by the two windings and corresponding fluxes. Such two fluxes
react to produce the rotating magnetic field. The technique is called split phase technique of production of
rotating magnetic field. The speed of this field is synchronous speed which is decided by the number of poles
for which stator winding is wound.
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 Reluctance Motor
The rotor carries the short circuited copper or aluminum bars and it acts as a squirrel cage rotor of an induction
motor. If an iron piece is placed in a magnetic field, it aligns itself in a minimum reluctance position and gets
locked magnetically.
Similarly, in the reluctance motor, rotor tries to along itself with the axis of the rotating magnetic field in a
minimum reluctance position. But due to the rotor inertia it is not possible when the rotor at standstill. So rotor
starts rotating near to the synchronous speed as a squirrel cage induction motor.
When the rotor speed is about synchronous, stator magnetic field pulls rotor into synchronism i.e. minimum
reluctance position and keeps it magnetically locked.
Then rotor continues to rotate with a speed equal to synchronous speed. Such a torque exerted on the rotor is
called the reluctance torque. Thus finally the reluctance motor runs as a synchronous motor. The resistance of
the rotor must be very small and the combined inertia of the rotor and load should be small to run the motor as a
synchronous motor.
Mathematical Analysis

Consider an elementary reluctance motor as shown in Fig. 6.2. The variation of the inductance of the winding is
sinusoidal with respect to rotor position. The variation of the inductance with respect to  is of double frequency
and is given by: 𝐿(𝜃) = 𝐿′′ + 𝐿′ cos 2𝜃
The stator winding is excite by ac supply hence: 𝑖 = 𝐼𝑚 sin 𝜔𝑡
1
The energy stored is a function of inductance and given by: 𝑊 = 2 𝐿(𝜃)𝑖 2
The flux linkage is given by: 𝜆(𝜃) = 𝐿(𝜃)𝑖
𝜕𝑊 𝜕𝜆 1 𝜕𝐿(𝜃) 𝜕𝐿(𝜃) 1 𝜕𝐿(𝜃)
Then the torque is given by: 𝑇 = − 𝜕𝜃 + 𝑖 𝜕𝜃 = − 2 𝑖 2 + 𝑖2 = 2 𝑖2
𝜕𝜃 𝜕𝜃 𝜕𝜃
1 𝜕[𝐿′′ +𝐿′ cos 2𝜃]
Substitute the value of i and L(θ): 𝑇 = 2 [𝐼𝑚 sin 𝜔𝑡]2 = −𝐿′ 𝐼𝑚
2
sin2 𝜔𝑡 sin 2𝜃
𝜕𝜃

If rotor is rotating at an angular velocity 𝜔𝑚 then finally the torque equation can be expressed in terms of 𝜔 and
𝜔𝑚 as

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 Reluctance Motor

The above equation gives the torque produced. The average torque of first two terms is zero but the third term
is not zero, so the magnitude of the average torque is
1 2
𝑇 = − 𝐿′ 𝐼𝑚 sin(−2𝛿)
4
The speed corresponding to the frequency   m is nothing but the synchronous speed. The  is a torque
angle. The maximum torque occurs at   45 which is termed as pull-out torque.
Any load demanding torque more than pull-out torque pulls the motor out of synchronism.

How a Reluctance Motor Pulls into Step?

Let the motor starts to accelerate as an induction motor. As it approaches synchronous speed, the salient poles
of the rotor slip by the poles of the rotating magnetic field which are set by the stator currents, but the near the
rotor gets to synchronous speed, the slower the poles slip. As the rotor poles passes and begins to lag behind a
pole of the rotating field, a synchronizing torque is developed, tending to make the rotor to catch up with the
rotating field.

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 Reluctance Motor

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 Hysteresis Motor
Module 04
Hysteresis Motor
Definition: A hysteresis motor is a synchronous motor without salient (or projected) poles and without
dc excitation which starts by virtue of the hysteresis losses induced in its hardened steel secondary
member by the revolving filed of the primary and operates normally at synchronous speed and runs on
hysteresis torque because of the retentivity of the secondary core.
It is a single-phase motor whose operation depends upon the hysteresis effect i.e., magnetization
produced in a ferromagnetic material lags behind the magnetizing force.

Construction:
It consists of:
(i) Stator: A stator designed to produce a synchronously-revolving field from a single-phase supply.
The stator carries main and auxiliary windings (which are called split phase hysteresis motor) so as to
produce rotating magnetic field as shown in Fig. 1 (a). The stator can also be shaded pole type (which is
called shaded pole hysteresis motor) as shown in Fig. 1 (b).

(a) (b)
Fig. 1 Different type of hysteresis motor
(ii) Rotor: The rotor of hysteresis motors are made with magnetic material of high hysteresis losses i.e.,
whose hysteresis loop area is very large as shown in Fig. 2. The rotor does not carry any winding or
teeth.

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 Hysteresis Motor
One type of rotor, invented by H. E. Warren
and used in the Warren Telechron electric
clock, is as shown in Fig. 1(b). It consists of
two or more outer rings and crossbars, all
made of specially selected heat-treated hard
steel. Steel that has a very large hysteresis loop
is chosen. When a rotating filed moves past the
rotor, this hysteresis effect causes a torque to
be developed and the motor starts to run. As
synchronous speed is approached, the
crossbars presents a low reluctance path to the
flux thereby setting up permanent pole in the
rotor and causing the motor to continue to
rotate at synchronous speed. The Telechron
Fig. 2 Hysteresis loop for rotor material. motor has a shaded-pole stator as shown in
Fig.1(b).
Another type of rotor is smooth cylindrical type. Hysteresis rings of special magnetic material like
chrome, cobalt steel or alnico or alloy are carried on supporting arbor made of a nonmagnetic material
such as brass; the assembly is carried out on the shaft. The rotor is also design to obtain high resistivity
to reduce eddy-current loss.
The hysteresis ring is affected by the rotational hysteresis causes by the stator windings and the direction
of the magnetization of each element of the ring is different from that of the magnetic field or magnetic
flux density. That is to say, the thicker the hysteresis ring becomes the larger the rotational hysteresis
increases and to make matters worse, the output of the thicker ring motor becomes less than that of thin
rotor motor.

Working Principle
When stator is energized, it produces rotating magnetic field. The main and auxiliary, both the windings
must be supplied continuously at start as well as in running conditions so as to maintain the rotating
magnetic field. The rotor, initially, starts to rotate due to eddy-current torque and hysteresis torque
developed on the rotor. Once the speed is near about the synchronous, the stator pulls rotor into
synchronism.
In such case, as relative motion between stator field and rotor field vanishes, so the torque due to eddy-
currents vanishes.
When the rotor is rotating in the synchronous speed, the stator revolving filed flux produces poles on the
rotor as shown in Fig. 3. Due to the hysteresis effect, rotor pole axis lags behind the axis of rotating
magnetic field. Due to this, rotor poles get attracted towards the moving stator poles. Thus rotor gets
subjected to torque called hysteresis torque. This torque is constant at all speeds.
When the stator field moved forward, due to high residual magnetism (i.e. retentivity) the rotor pole
strength remains maintained. So higher the retentivity, higher is the hysteresis torque. The hysteresis
torque is independent of the rotor speed.
The high retentivity ensures the continuous magnetic locking between stator and rotor. Due to principle
of magnetic locking, the motor either rotates at synchronous speed or not at all. Only hysteresis torque is
present which keeps rotor running at synchronous speed.

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 Hysteresis Motor

Fig. 3 (a) Stator poles induce poles in the rotor, (b) Torque developed on the rotor due to residual
magnetism of the rotor, (c) Hysteresis loop of the rotor material.

Mathematical Analysis

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 Hysteresis Motor

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 Hysteresis Motor
Torque-Speed Characteristics
The starting and running torque is almost
equal in this type of motor. As stator carries
mainly the two-windings its direction can be
reversed interchanging the terminals of either
main winding or auxiliary winding. The
torque-speed characteristics are as shown in
Fig. 4.
As seen from the characteristics torque at
start is almost same throughout the operation
of the motor. Fig. 4 Torque-speed characteristics of hysteresis motor

Advantages:
The advantages of hysteresis motor are:
1. As rotor has no teeth, no winding, there are no mechanical vibrations.
2. Due to absence of vibrations, the operation is quiet and noiseless.
3. Suitability to accelerate inertia loads.
4. Possibility of multispeed operation by employing gear train.

Disadvantages
The disadvantages of hysteresis motor are:
1. The output is about one-quarter that of an induction motor of the same dimension.
2. Low efficiency
3. Low power factor
4. Low torque
5. Available in very small sizes

Applications
Due to noiseless operation it is used in sound recording instruments, sound producing equipments, high
quality record players, electric clocks, tele-printers, timing devices et.

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 Stepper Motor

Module 05
Stepper Motor
Introduction
The examples of special machines, whose stator coils are energized by electronically
switched currents and whose have special applications, are: various types of stepper motors,
brushless dc motor, and switch reluctance motor etc.

Stepper Motor
A motor whose rotation is produced by switching signals to suitably connected
windings in some predetermined sequence to produce uniform angular steps of rotation is
called stepper motor.
These motor are also called stepping motors or step motors. The name is used because
this motor rotates through a fixed angular step in response to each input current pulse
received by its controller.
In recent years, there has been wide-spread demand of stepping motors because of the
explosive growth of computer industry. Their popularity is due to the fact that they can be
controlled directly by computers, microprocessor and programmable controller.

The unique feature of a stepping motor is that its output shaft rotates in a series of
discrete angular intervals or steps, one step being taken each time a command pulse is
received. The stepping motor therefore allows control of the loads velocity, distance and
direction.
In a stepper motor, when a definite number of pulses are supplied, the shaft turns
through a definite known angle. This fact makes the motor well-suited for open-loop position
control because no feedback need be taken from the output shaft.
A significant advantage of the stepping motor is its compatibility with digital
electronic systems. These systems are becoming increasingly common in a wide variety
application and at the same time are becoming both more powerful and less expensive.
Such motors develop torques ranging from 1 N-m upto 40 N-m. Their power output
ranges from about 1W to a maximum 2500W.

Step Angle (Step Length)

The angle through which the motor rotates for each command pulse is called step
angle . Smaller the step angle, greater the number of steps per revolution and higher the
resolution or accuracy of positioning obtained. The step size can be as small as 0.72 o or as
large as 90o. But the most common step sizes are: 1.8o, 2.5o, 7.5o, and 15o.
The value of step angle can be expressed either in terms of the rotor and stator poles
(teeth) Nr and Ns, respectively or in terms of the number of stator phases, m, and the number
of rotor teeth.
𝑁𝑠 ~𝑁𝑟
𝛽= × 360°
𝑁𝑠 𝑁𝑟
360° 360°
𝛽= =
𝑚𝑁𝑟 𝑁𝑜. 𝑜𝑓 𝑠𝑡𝑎𝑡𝑜𝑟 𝑝ℎ𝑎𝑠𝑒𝑠 (𝑜𝑟 𝑠𝑡𝑎𝑐𝑘𝑠) × 𝑁𝑜. 𝑜𝑓 𝑟𝑜𝑡𝑜𝑟 𝑡𝑒𝑒𝑡ℎ (𝑜𝑟 𝑟𝑜𝑡𝑜𝑟 𝑝𝑜𝑙𝑒𝑠)
Resolution is given by the number of steps needed to complete one revolution of the
rotor shaft. The higher the resolution, the greater the accuracy of positioning of objects by
the motor.
𝑁𝑜. 𝑜𝑓 𝑠𝑡𝑒𝑝𝑠 360°
𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 = =
𝑅𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝛽
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 Stepper Motor

A stepper motor has the extraordinary ability to operate at very high stepping rates
and yet to remain fully in synchronism with the command pulses.
When the pulse rate is high, the shaft rotation seems continuous. Operation at high
speeds is called ‘slewing’.
If f is the stepping frequency (or pulse rate) in pulses per second (pps) and  is the
step angle, then motor shaft speed is given by
𝛽×𝑓
𝑛= 𝑟𝑝𝑠 = 𝑝𝑢𝑙𝑠𝑒 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑟𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
360°
If the stepping rate is increased too quickly, the motor losses synchronism and stops.
Same happens if when the motor is slewing, command pulses are suddenly stopped instead of
being progressively slowed.
Stepping motors are designed to operate for long periods with the rotor held in a fixed
position and with rated current flowing in the stator windings. It means that stalling is no
problem for such motors whereas for most of the other motors, stalling results in the collapse
of back emf and a very high current which can lead to a quick burn out.

Example 11-2 [5] calculate the stepping angle for (a) a 3-stacks, 16 tooth rotor VR stepper
motor, and (b) a 3-phase, 24-pole PM stepper motor.
Solution: We know that
360° 360°
𝛽= =
𝑚𝑁𝑟 𝑁𝑜. 𝑜𝑓 𝑠𝑡𝑎𝑡𝑜𝑟 𝑝ℎ𝑎𝑠𝑒𝑠 (𝑜𝑟 𝑠𝑡𝑎𝑐𝑘𝑠) × 𝑁𝑜. 𝑜𝑓 𝑟𝑜𝑡𝑜𝑟 𝑡𝑒𝑒𝑡ℎ (𝑜𝑟 𝑟𝑜𝑡𝑜𝑟 𝑝𝑜𝑙𝑒𝑠)
360°
(a) 𝛽 = = 7.5°/𝑠𝑡𝑒𝑝
3×16
360°
(b) 𝛽 = = 5°/𝑠𝑡𝑒𝑝
3×24

Example 39.1. A hybrid VR stepping has motor 8 main poles which have been castellated to
have 5 teeth each. If rotor has 50 teeth, calculate the stepping angle.
Solution: 𝑁𝑠 = 8 × 5 = 40; 𝑁𝑟 = 50
50 − 40
∴𝛽= × 360° = 1.8°
50 × 40

Example 39.2. A stepper motor has a step angle of 2.5o. Determine (a) resolution, (b) number
of steps required for the shaft to make 25 revolutions and (c) shaft speed, if the stepping
frequency is 3600 pps.
Solution:
360° 360°
(a) 𝑅𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 = 𝛽
= = 144 𝑠𝑡𝑒𝑝𝑠/𝑟𝑒𝑣𝑜𝑙𝑢𝑡𝑖𝑜𝑛
2.5°
(b) Now, steps/revolution = 144.
Hence, steps required for making 25 revolutions = 14425 = 36000.
𝛽×𝑓 2.5°×3600
(c) 𝑛 = 360° 𝑟𝑝𝑠 = 360° 𝑟𝑝𝑠 = 25 𝑟𝑝𝑠
Problem: What is the required resolution of a stepper motor that is to operate at a pulse
frequency of 6000 pps and travel 180 o in 0.025s?
Solution: Given stepper motor travels 180 o in 0.025 sec. So to complete one revolution,
stepper motor needs 0.0252 = 0.05 sec.
Since 6000 pulses sent to the motor terminal per second, the resolution is the number of
pulses to complete one revolution.
So, resolution = 60000.05 = 300 steps/revolution.

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 Stepper Motor

Applications
Such motors are used for operation control in computer peripherals, textile industry,
IC fabrications and robotics etc.
Applications requiring incremental motion are typewriters, line printers, tape
drivers, floppy disk drivers, numerically-controlled machine tools, process control systems
and X-Y plotters.
Usually, position information can be obtained simply by keeping count of the pulses
sent to the motor thereby eliminating the need for expensive position sensors and feedback
controls.
Stepper motors also perform countless tasks outside the computer industry. It includes
commercial, military and medical applications where these motors perform such function as
mixing, cutting, striking, metering, and blending.

Difference between conventional motor and stepper motor

1. Conventional ac and dc motors have a free turning shaft. But, the stepper motor
shaft rotation is incremental.
2. Conventional motors are used to convert electrical energy to mechanical energy but
they cannot be used for precision positioning of an object or precision control of
speed without using closed-loop feedback. But, stepping motors are ideally suitable
for situation where either precise positioning or precise speed control or both are
required in automation system without any feedback system.
3. In the case of conventional motor, the repeatability (ability to position through the
same pattern of movements a number of times) is very poor. But, in the case of
stepper motor, the repeatability is very good.
4. The moving part in a conventional motor is less robust and reliable as compared
with that in a stepper motor.
5. Stalling is no problem for stepper motors whereas for conventional motors, stalling
results in the collapse of back emf and a very high current which can lead to a quick
burn out.

Stepper Motor Advantages and Disadvantages

Advantages:
1. The rotation angle of the motor is proportional to the input pulse.
2. The motor has full torque at standstill (if the windings are energized).
3. Precise positioning and repeatability of movement since good stepper motors have an
accuracy of 3 – 5% of a step and this error is non-cumulative from one step to the
next.
4. Excellent response to starting/stopping/reversing.
5. Very reliable since there are no contact brushes in the motor. Therefore, the life of
the motor is simply dependent on the life of the bearing.
6. The motors response to digital input pulses provides open-loop control, making the
motor simpler and less costly to control.
7. It is possible to achieve very low speed synchronous rotation with a load that is
directly coupled to the shaft.
8. A wide range of rotational speeds can be realized as the speed is proportional to the
frequency of the input pulses.

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Disadvantages:
1. Resonances can occur if not properly controlled.
2. Not easy to operate at extremely high speeds.

Types of Stepper Motor

There is a large variety of stepper motors which can be divided into the following
three basic categories:
(i) Variable Reluctance (VR) (or Reactive-Rotor) Stepper
Motor
It has wound stator poles but the rotor poles are made of a ferromagnetic material as
shown in Fig. 39.1(a). It has a rectangular rotor.
It can be of the single stack type (Fig. 39.2) or multi stack type (Fig. 39.5) which
gives smaller step angles.
Direction of the motor rotation is independent of the polarity of the stator current. It is
called variable reluctance motor because the reluctance of the magnetic circuit formed by the
rotor and stator teeth varies with the angular position of the rotor.
As a variable speed machine, VR motor is sometime designed as a switched-
reluctance motor.
VR stepper motor produces the reluctance torque which is varied at twice the sine of
the displacement angle of rotor as shown in Fig. 39.1-1(a).

(a) Variable reluctance (b) Permanent magnet

(c) Hybrid stepper motor
stepper motor stepper motor
Fig. 39.1

(ii) Permanent Magnet (PM) (or Active-Rotor) Stepper Motor

It also has wound stator poles but its rotor poles are permanently magnetized. It has a
cylindrical rotor as shown in Fig. 39.1(b). Its direction depends on the polarity of the stator
current.
As a variable speed machine, PM stepper motor is also called variable speed brushless
dc motor.
PM stepper motor produces the excitation torque which is varied as the sine of the
displacement angle of rotor as shown in Fig. 39.1-1(b).

(iii) Hybrid Stepper Motor

It has wound stator poles and permanently-magnetized rotor poles as shown in Fig.
39.1(c). It is best suited when small step angles of 1.8 o, 2.5o etc. are required. It has a
rectangular rotor.
The hybrid motor combines the features of VR stepper motor and PM stepper motor.
Its construction is similar to the single stack VR motor but the rotor is composed of radially
magnetized permanent magnets. A recent type uses a disc rotor which is magnetized axially
to give a small stepping angle and low inertia.
Unlike the VR or PM stepping motors, the step angle (step length) is independent of

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 Stepper Motor

the number of phases or stacks and is purely a function of the number of rotor teeth or pole.
So the step angle for hybrid stepping motor is given by
360° 360°
𝛽= =
𝑁𝑟 𝑁𝑜. 𝑜𝑓 𝑟𝑜𝑡𝑜𝑟 𝑡𝑒𝑒𝑡ℎ (𝑜𝑟 𝑟𝑜𝑡𝑜𝑟 𝑝𝑜𝑙𝑒𝑠)
Hybrid stepper motor produces both excitation torque (varying as the sine of the
displacement angle of rotor) and reluctance torque (varying at twice the sine of the
displacement angle of rotor) as shown in Fig. 39.1-1(c).

(a) Variable reluctance stepper (b) Permanent magnet stepper

(c) Hybrid stepper motor
motor motor
Fig. 39.1-1
Example 11-3[5] A hybrid stepping motor has 50 variable reluctance rotor teeth. Calculate
the stepping angle (stepping length) in degrees.
Solution: We know for hybrid stepper motor that
360° 360°
𝛽= =
𝑁𝑟 𝑁𝑜. 𝑜𝑓 𝑟𝑜𝑡𝑜𝑟 𝑡𝑒𝑒𝑡ℎ (𝑜𝑟 𝑟𝑜𝑡𝑜𝑟 𝑝𝑜𝑙𝑒𝑠)
360° 360°
∴𝛽= = = 1.8°/𝑠𝑡𝑒𝑝
𝑁𝑟 50

Variable Reluctance Stepper Motors

Construction: A variable reluctance motor is constructed from ferromagnetic
material with salient poles as shown in Fig. 39.2.
The stator is made from a stack of steel lamination and has six equally-spaced
projecting poles (or teeth) each wound with an exciting coil.
The rotor which may be solid or laminated has four poles (or teeth) of the same width
as the stator teeth.
As seen, there are three independent stator circuits or phases A, B, and C and each one
can be energized by a direct current pulse from the drive circuit (not shown in figure).
A simple circuit arrangement for applying current to the stator coils in proper
sequence is shown in Fig. 39.2(e). The six stator coils are connected in 2-coil group to form
three separate circuit called phases. Each phase has its own independent switch.

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Diametrically opposite pairs of stator coils are connected in series such that when one
tooth becomes a N-pole, the other one becomes a S-pole. Although shown as mechanical
switches in Fig. 39.2(e), in actual practice, switching of the phase current is done with the
help of solid-state control.

(a) (b) (c)

Truth Table No.1

A B C 
+ 0 0 0o
0 + 0 30o
0 0 + 60o
+ 0 0 90o

(d) (e) (f)

Fig. 39.2
When there is no current in the stator coils, the rotor is completely free to rotate.
Energizing one or more stator coils causes the rotor to step forward (or backward) to a
position that forms a path of least reluctance with the magnetized stator teeth. The step angle
of this three-phase, four rotor teeth motor is = 360o/(43) = 30o.

Working: The motor has following modes of operation:

(a) 1-phase-ON or Full-Step Operation
(b) 2-Phase ON Mode
(c) Half-Step Operation
(d) Micro-stepping

(a) 1-phase-ON or Full-Step Operation

Initially, if switch S1 is closed and S2 and S3 are kept open, the phase A is energized to
make magnetic flux with its axis along the stator poles of phase A. The rotor is, therefore,
attracted into a position of minimum reluctance of rotor teeth 1’ and 3’ lining up with stator
teeth 1 and 4, respectively, as shown in Fig. 29.2(b).
If switch S2 is closed and S1 and S3 are kept open, the phase B is energized to make
magnetic flux with its axis along the stator poles of phase B. The rotor is, therefore, attracted

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into a position of minimum reluctance of rotor teeth 2’ and 4’ lining up with stator teeth 3 and
6, respectively, as shown in Fig. 29.2(c). The rotor rotates through full-step of 30o in the
clockwise (CW) direction.
If switch S3 is closed and S1 and S2 are kept open, the phase C is energized to make
magnetic flux with its axis along the stator poles of phase C. The rotor is, therefore, attracted
into a position of minimum reluctance of rotor teeth 1’ and 3’ lining up with stator teeth 2 and
5, respectively, as shown in Fig. 29.2(d). The rotor rotates through an additional angle of 30o
in the CW direction.
If switch S1 is closed and S2 and S3 are kept open, the phase A is energized to make
magnetic flux with its axis along the stator poles of phase A. The rotor is, therefore, attracted
into a position of minimum reluctance of rotor teeth 2’ and 4’ lining up with stator teeth 4 and
1, respectively. The rotor rotates through a further angle of 30o in the CW direction.
By now the total angle turned is 90o. As each switch is closed and the preceding one
opened, the rotor each time rotates through an angle of 30 o.
By repetitively closing the switches in the sequence 1-2-3-1 and thus energizing stator
phases in sequence ABCA etc., the rotor will rotate CW in 30o steps.
If the switch sequence is made 3-2-1-3 which makes phase sequence CBAC (or ACB),
the rotor will rotate counter-clockwise (CCW).

(b) 2-Phase ON Mode

In this mode of operation, two stator phases are excited simultaneously.
When phases A and B are energized together, the rotor experiences torque from both
phases and come to rest at a point mid-way between the two adjacent full-step positions.
If the stator phases are switched in the sequence AB, BC, CA, AB etc. the motor will
take full steps of 30o each (as in the 1-phase ON mode) but its equilibrium positions will be
interleaved between the full-step positions. The phase switching truth table for this mode is
shown in Fig. 39.3(a).

Truth Table No. 2

A B C 
Truth Table No. 2
+ 0 0 0o
A B C  A
+ + 0 15o
+ + 0 15o
0 + 0 30o
0 + + 45o B
0 + + 45o
+ 0 + 75o
0 0 + 60o
+ + 0 105o C
+ 0 + 75o
A + 0 0 90o
(a) (b)
Fig. 39.3

The 2-phase-ON mode provides greater holding torque and a much better damped
single-stack response than the 1-phase-ON mode of operation.

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 Stepper Motor

(c) Half-Step Operation

Half-step operation or ‘half-stepping’ can be obtained by exciting the three phases in
the sequence A, AB, B, BC, C, CA etc. i.e. alternately in the 1-phase-ON and 2-phase-ON
modes. It is sometime known as ‘wave’ excitation and it causes the rotor to advance in
steps of 15o i.e. half the full-step angle. The truth table for the phase pulsating sequence in
half- stepping is shown in Fig. 39.3(b).
Half-stepping can be illustrated with the help of Fig. 39.4 where only three successive
pulses have been considered. Energizing only phase A causes the rotor position shown in Fig.
39.4(a). Energizing phases, A and B simultaneously moves the rotor to the position shown
in Fig. 39.4(b) where the rotor has moved through half a step only. Energizing only phase B
moves the rotor through another half-step as shown in Fig. 39.4(c). With each pulse, the rotor
moves 30o/2=15o in the CCW direction.

(a) (b) (c)

Fig. 39.4
It will be seen that in half-stepping mode, the step angle is halved thereby doubling
the resolution. Moreover, continuous half-stepping produces a smoother shaft rotation.

(d) Micro-stepping
It is also known as mini-stepping.
It utilizes two phases simultaneously as in 2-phase-ON mode but with the two
currents deliberately made unequal (unlike in half-stepping where the two phase currents
have to be kept equal).
The current in phase A is held constant while that in phase B is increased in very small
increments until maximum current is reached. The current in phase A is then reduced to zero
using the same very small increments. In this way, the resultant step becomes very small and
is called micro-step.
For example, a VR stepper motor with a resolution of 200 steps/rev (= 1.8o) can
with micro-stepping have a resolution of 20,000 steps/rev (= 0.018o).
Stepper motors employing micro-stepping technique are used in printing and
phototypesetting where very fine resolution is called for. As seen, micro-stepping provides
smooth low-speed operation and high resolution.

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 Stepper Motor

Possible Questions:
1. What are differences between a stepper motor and a conventional motor?
Or, compare a stepper motor with a conventional motor.
2. Write some applications of stepper motors? What are the advantages and disadvantages of
stepper motor?
3. Write detailed classifications of stepper motors.
4. What are the different methods of operation of variable reluctance stepper motors?
5. Briefly described with proper diagram, 2-phase ON mode of operation of a stepper motor
having 6 stator and 4 rotor poles.
6. Briefly described with proper diagram, the one phase ON mode of operation of a stepper
motor having 6 stator and 4 rotor poles.
7. Briefly described with proper diagram, the half-step operation of a stepper motor having 6
stator and 4 rotor poles.
8. Briefly described with proper diagram, the micro-stepping operation of a stepper motor
having 6 stator and 4 rotor poles.
9. Briefly describe the different types of stepper motors.

Example 11-2 [5] calculate the stepping angle for (a) a 3-stacks, 16 tooth rotor VR stepper
motor, and (b) a 3-phase, 24-pole PM stepper motor.
Example 39.1. A hybrid VR stepping has motor 8 main poles which have been castellated
to have 5 teeth each. If rotor has 50 teeth, calculate the stepping angle.
Example 39.2. A stepper motor has a step angle of 2.5o. Determine (a) resolution, (b) number
of steps required for the shaft to make 25 revolutions and (c) shaft speed, if the stepping
frequency is 3600 pps.
Example 11-3[5] A hybrid stepping motor has 50 variable reluctance rotor teeth. Calculate
the stepping angle (stepping length) in degrees.
Problem: What is the required resolution of a stepper motor that is to operate at a pulse
frequency of 6000 pps and travel 180 0 in 0.025s.

References
[1] B. L. Theraja, A. K. Theraja, “A Textbook of ELECTRICAL TECHNOLOGY in SI Units
Volume II, AC & DC Machines”, S. Chand & Company Ltd., (Multicolour illustrative
Edition).
[2] A. F. Puchstein, T. C. Lloyd, A.G. Conrad, “Alternating Current Machines”, © 1942,
Asia Publishing House, Third Edition (Fully revised and corrected Edition 2006-07).
[3] Jack Rosenblatt, M. Harold Friedman, “Direct and Alternating Current Machinery”,
Indian Edition (2nd Edition), CBS Publishers & Distributors.
[4] A. E. Fitzgerald, Charles Kingsley, Jr. Stephen D. Umans, Electric Machinery, 5th
Edition in SI units, ©1992 Metric Edition, McGraw Hill Book Company.
[5] Irving L. Kosow, Electrical Machinery and Transformers, Second Edition, Prentice –Hall
India Pvt. Limited.

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Module 06
Permanent Magnet Synchronous Motor (PMSM)

Introduction
Permanent magnet synchronous motors have been developed as an alternative conventional
motors as an energy converting device. The motor does not operate without suitable position
sensor/controller from the nominal supply system. In this chapter description of the different
components of the drive system discussed. A review of permanent magnet materials and
classification of permanent magnet motors is also given. A detailed mathematical model of the
system is also provided.

Permanent Magnet Synchronous Motor

A permanent magnet synchronous motor (PMSM) is a motor that uses permanent magnets to
produce the air gap magnetic field rather than using electromagnets. These motors have
significant advantages, attracting the interest of researchers and industry for use in many
applications due to its decreased loss and higher torque production rate.

Permanent Magnet Materials

The properties of the permanent magnet material affects directly the performance of the motor
and proper knowledge is required for the selection of the materials and for understanding PM
motors.
The earliest manufactured magnet materials were hardened steel. Magnets made from steel were
easily magnetized. However, they could hold very low energy and it was easy to demagnetize.
In recent years, other magnet materials such as Aluminum Nickel and Cobalt alloys (AlNiCo),
Strontium Ferrite or Barium Ferrite (Ferrite), Samarium Cobalt (First generation rare earth
magnet) (SmCo) and Neodymium Iron-Boron (Second generation rare earth magnet) (NdFeB)
have been developed and used for making permanent magnets.

The rare earth magnets are categorized into two classes: Samarium Cobalt (SmCo) magnets and
Neodymium Iron Boride (NdFeB) magnets. SmCo magnets have higher flux density levels but
they are very expensive. NdFeB magnets are the most common rare earth magnets used in
motors these days. A flux density versus magnetizing field for these magnets is illustrated in
figure 2.2.

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 PMSM

1.5

Br
µo M

NdFeB
1.0

B(Tesla)

NdFeB 120o C SmCo

0.5
FERRITE
MH C

MH c
AlNICo

-1000 -500 0

H(kA/ m)

Figure 2.2 Flux Density versus Magnetizing Field of Permanent Magnetic Materials.

2.4 Classification of Permanent Magnet Motors

Permanent magnet motors are classified into different categories. A classification of the PM
motor is given below.

2.4.1 Direction of field flux

PM motors are broadly classified by the direction of the field flux. The first field flux
classification is radial field motor meaning that the flux is along the radius of the motor. The
second is axial field motor meaning that the flux is perpendicular to the radius of the motor.
Radial field flux is most commonly used in motors and axial field flux have become a topic of
interest for study and used in a few applications.

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 PMSM

2.4.2 Flux density distribution

PM motors are classified on the basis of the flux density distribution and the shape of current
excitation. They are PMSM and PM brushless motors (BLDC). The PMSM has a sinusoidal-
shaped back EMF and is designed to develop sinusoidal back EMF waveforms.

They have the following features:

1. Sinusoidal distribution of magnet flux in the air gap
2. Sinusoidal current waveforms
3. Sinusoidal distribution of stator conductors.

BLDC has a trapezoidal-shaped back EMF and is designed to develop trapezoidal back EMF
waveforms. They have the following features:
1. Rectangular distribution of magnet flux in the air gap
2. Rectangular current waveform
3. Concentrated stator windings.

2.4.3 Permanent magnet radial field motors

In PM motors, the magnets can be placed in two different ways on the rotor. Depending on the
placement they are called either as surface permanent magnet motor or interior permanent
magnet motor.

Surface PM synchronous motors (SPMSM) have a surface mounted permanent magnet rotor.
Each of the PM is mounted on the surface of the rotor, making it easy to build, and specially
skewed poles are easily magnetized on this surface mounted type to minimize cogging torque.
This configuration is used for low speed applications because of the limitation that the magnets
will fly apart during high-speed operations. These motors are considered to have small saliency,
thus having practically equal inductances in both axes. The permeability of the permanent
magnet is almost that of the air, thus the magnetic material becoming an extension

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 PMSM

of the air gap. For a surface permanent magnet motor inductance along d- and q-axes are equal,
i.e., Ld  Lq.
The rotor has an iron core that may be solid or may be made of punched laminations for
simplicity in manufacturing. Thin permanent magnets are mounted on the surface of this core
using adhesives. Alternating magnets of the opposite magnetization direction produce radially
directed flux density across the air gap. This flux density then reacts with currents in windings
placed in slots on the inner surface of the stator to produce torque. Figure 2.3 shows the
placement of the magnet.

Figure 2.3 Surface Permanent Magnet Motor.

Interior PM motors have interior mounted permanent magnet rotor as shown in figure 2.4. Each
permanent magnet is mounted inside the rotor. It is not as common as the surface- mounted type
but it is a good candidate for high-speed operation. There is inductance variation for this type of
rotor because the permanent magnet part is equivalent to air in the magnetic circuit calculation.
These motors are considered to have saliency with q axis inductance greater than the d axis
inductance (Ld  Lq ).

Figure 2.4 Interior Permanent Magnet Motor

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 PMSM

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 PMSM

Fig. 2.15 Torque Vs Current Angle

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 Universal Motors

Module 07
Direct Current (DC) Motors Operated on Alternating
Current (AC)
Changing the polarity of the line terminals of any DC-motor reverses both the direction
of the flux and the direction of the current in armature conductors. The torque developed,
therefore, remains in the same direction, and motor continuous to rotate in the direction in
which it was rotating before the terminals were reversed. From this it would seem that any dc
motor would operate satisfactorily on AC.
The field of a shunt motor must have a relatively high resistance so that the field
current is less than 5% of the rate current. At the same time the flux must be sufficient give the
required torque. This combination of low field current and high flux is obtained by designing
the field with many turns of fine wire. If an AC supply of the same nominal effective voltage
as the rated DC voltage is applied to the shunt field, the resulting field current is much lower
than the DC field current. The many turns of wire cause a significant inductive effect. The
result is very low fields current, far lower than that required to produce sufficient starting
current.
The field inductance produces another effect to further preclude the use of a shunt
motor on AC. Since the inductive reactance is significantly high, the field current lags the
voltage by a considerable angle. The armature current also lags the applied voltage, but
because of its fewer turns, the angle of lag will not be as great as in the field circuit. The flux,
therefore, is not in phase with the armature current, and since torque in an AC motor is
proportional to flux, rotor current and the cosine of the angle between the two (TI cos), the
torque is further reduced. For these reasons, namely, the reduction of field current and the
lagging angle of the flux, a shunt motor will not produce sufficient starting or running torque
when connected to an AC voltage supply.

Alternating Current Series Motor

Compared with a shunt motor, the field of a series motor is wound with relatively few
turns of heavy wire. The inductive effect is thus less, and the flux is almost the same as it
would be on DC. The current is, of course, the same in both field and armature, and there is no
time lag between the alternating flux set up by the field coils and the current in the armature
conductors. Thus the two main objections to the operation of a shunt motor on AC are
overcome in the series motor, and it may operate on both AC and DC.

It is found, however, that when a series motor specifically designed for DC operation is
placed across an AC supply of its rated nominal effective voltage, its operation is poorer than
on DC.
The efficiency is low, the power factor is poor, and there is a considerable sparking at
the brushes. The poorer efficiency is caused by the increased hysteresis and eddy current losses
due to the alternating flux, and the poor power factor is caused by the reactances of the field and
the armature.
To overcome these effects, the AC series-motor field is always laminated; wound with
fewer turns than its DC counterpart, and has an increased field-pole area, so that the field is
operated at a comparatively low flux density. This reduces both the iron losses and the reactive
volt drop. At the same time, in order to obtain the required torque with the low flux, the number
of armature conductors is increased.

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 Universal Motors

In addition to the causes of sparking that occur in a DC motor, transformer action on a

coil undergoing commutation further intensifies commutation difficulties. This coil, short-
circuited by the brushes, links part of the constantly changing main-field flux, and hence a
voltage is induced in it. This transformer effect is somewhat minimized by constructing the
coils with fewer turns, often only one turn per coil, so that this induced voltage is lowered. The
larger number of conductors still required on the armature to produce sufficient torque is then
obtained by increasing the number of coils, and hence more commutator segments are
necessary. This, then, is another characteristic of construction of the AC series-motor.

Armature reaction in the AC motor is more severe than in the equivalent DC motor.
This is due to the necessary for having a greater number of armature conductors, and hence an
increased armature mmf. Also, since the AC series motor requires a small number of series
field turns, the ratio of armature mmf to stator mmf is greater, and hence produces additional
commutation problems. At the same time that armature reaction causes a reduced net flux, it
also causes a reactive volt-drop in the armature in addition to that caused by the leakage flux
linking the individual conductors, and thus results in a lower power factor.

In order to reduce the effect of armature reaction, thereby improving commutation and
reducing armature reactance, a compensating winding is employed. This winding is set in stator
slots, and its axis is 90 electrical degrees to the main-field axis. It may be connected in series
with both the armature and the series field as shown in Fig. 22.1, in much the same manner as
for DC motor, and is then said to be conductively coupled.

Fig. 22.1. Series motor with conductively Fig. 22.2. Series motor with inductively
coupled compensating winding. coupled compensating winding.

On the other hand, for a motor used solely on AC, the compensating winding may be
short-circuited on itself. Since the axis of the compensating winding coincides with the brush
axis, the alternating flux of the armature induces an emf in the short-circuited winding, and the
current in this winding opposes the flux causing it, and hence opposes the armature reaction.
This type of connection is thus called inductive coupling and is shown in Fig. 22.2. In both
cases shown, the flux set up in the compensating winding is proportional to the armature
current, as is always required.

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 Universal Motors

The Universal Motor

The name "universal" is derived from the motor's compatibility with both AC and DC
power.
Thus far, we have shown some of the drawbacks of operation of a series motor
designed for DC operation, on alternation current (AC). Despite these drawbacks, however,
small series motors, designated as universal motors, are used equally well on both AC and DC
circuits.
Universal motors are designed for voltages up to 250V, and for a frequency range of
zero up to 60 Hz. Except for operating the field at low flux density and increasing the number of
armature conductors, no other concession is made for AC operation. Occasionally,
conductively connected compensating windings may be used, but this is rarity in the usual
class of work.
The universal motor exhibits the
usual speed-load characteristics of the series
motor i.e. a no-load speed much higher than
the full load speed. The possibility of
dangerously high no-load speeds is not a
serious handicap for the most commonly
used universal motors.
For such applications as vacuum cleaners,
food mixers, hair-driers, electric shavers,
portable drills, sewing machines, office
machinery, and many similar ones, the load
is never completely removed, since some
parts of the devices, such as the gear train
and cooling fans, are always in motion, even
if no actual work is being one. These moving
parts, which also include the armature, may
be considered as rotational losses for the
entire machine, and serve the additional
purpose of maintaining a safe no- load speed.
Where there is danger of a high no-load
speed, a governor may be used to maintain
reasonable speeds. This governor consists of a
centrifugal switch mounted on the shaft of
the motor. The tension of the springs of the
switch is adjusted so that the switch contacts
open at a predetermined speed and thus
place a resistor in series with the armature,
thereby reducing the speed. When the speed
falls because of loading, the switch contacts
close, thereby shorting out the series resistor,
thus again raising the
speed. The connections are shown in Fig.
22.3. The capacitor is placed across the
governor contacts to reduce sparking. Fig. 22.3. Governor for series motor.

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 Universal Motors

Operation Characteristics of Series Motor

Series motors operating on AC perform almost the same as those operating on DC.
Both develop relatively high starting torques of three to four times the rated torque and also
exhibit the variable-speed characteristic. When the series motor operates by AC, the reactance
must be taken into account, and hence phasor equations must be used, the characteristic
equations are the same. The voltage relationship is thus
VT  Eg  I a (Ra  jX a )  I a (RC  jX C )  I a (RS  jX S )
Where the subscript a, C, and S refer to the armature, the compensating winding, and
the series field, respectively. Eg is the rotational emf set up in the armature because of the
cutting of the resultant field by the conductors. This voltage is in phase with the flux, and
hence in phase with the armature current (except for the small angle of hysteresis lag). If the
armature current is used as the reference phasor, the phasor diagram of the previous voltage
equation is that shown in Fig. 22.4.

Fig. 22.4. Phasor diagram of AC series motor.

 Here is the phase angle between the terminal voltage and the line current. It is
readily seen that  becomes larger and power factor poorer as the relative values of the reactance
are increased, and for this reason, fewer field turns and lower flux densities are employed. Also,
since the presence of a compensating winding materially reduces the armature reactance, it is
absolutely necessary for a large AC series motors used for traction operation to have such a
winding. Such large motors serving railways do not use commercial frequencies because of the
necessity for larger fluxes and the resultant higher inductive effects. Thus, in USA, 25 Hz is the
upper limit used, while in European countries, 16.667 Hz is used.
The power developed by the armature is equal to the product of the generated voltage
and the armature current, multiplied by the cosine of the angle between them. Since the angle
between the generated voltage and the armature current is almost zero, the relationship for the
power developed is the same on both DC and AC circuits. Because of the presence of
reactance, however, it is seen that Eg is somewhat smaller on AC, and hence power developed
will also be less. This is to be expected since on AC there are the additional losses due to eddy
currents and hysteresis.
The speed of a motor depends on the internal voltage drops and the flux. As load is
increased internal voltage drops also act to produce the same effect, so that the familiar speed-
load curve of Fig. 22.5 is typical.

Fig. 22.5. Speed-load characteristic of series motor.

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 Universal Motors

This is the general shape of the curve whether the motor is operated on AC or DC. It is
not readily determined whether a universal motor has a higher or lower speed for a given load
when operated on AC. It is quite probable that without external load, more current is required
to provide the additional iron losses on AC, thereby causing a slightly lower speed. As load is
applied IX drops become more significant and tend to lower the speed more than in the DC case.
At the same time, however, armature reaction is more pronounced on an alternating current,
and this tends to reduce the flux, thereby increasing the speed. The exact characteristic thus
depends on the relative strength of armature reaction compared with reactive volt-drop and
must be determined for each individual motor.
Continuous speed control of a universal motor running on AC is easily obtained by use
of a thyristor circuit, while stepped speed control can be accomplished using multiple taps on
the field coil. Household blenders that advertise many speeds frequently combine a field coil
with several taps and a diode that can be inserted in series with the motor (causing the motor to
run on half-wave rectified AC).

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 Servo Motor

Module 08
Servomotor
A servomechanism, or servo is an automatic device which
uses error-sensing feedback to correct the performance of a
mechanism. The term correctly applies only to systems where the
feedback or error-correction signals help control mechanical
position or other parameters.
Typical servos give a rotary (angular) output. Linear types
are common as well, using a screw thread or a linear motor to give
linear motion. Servomechanisms may or may not use a servomotor.
A servomotor is an electromechanical device in which an
electrical input determines the position of the armature of a motor.
Servos are used extensively in robotics and radio-controlled cars,
airplanes, and boats.
Servomotors are also called control motors and have high-
torque capabilities.
Servomotors are used for precise speed and precise position
control at high torques.
Servomotors are not used for continuous energy conversion.
The basic principle of operation of servomotors is the same
as that of other electromagnetic motors. However, their
construction, design and mode of operation are different. Their
power ratings vary from a friction of a watt up to a few 100W. Due
to their low-inertia, they have high speed of response. That is why
they are smaller in diameter but longer in length. They generally
operate at very low speeds or sometimes zero speed. They find wide
applications in radar, tracking and guidance systems, process
controllers, computers and machine tools. Both DC and AC (2-
phase and 3-phase) servomotors are used at present.
Servomotors differ in application capabilities from large industrial motors in the
following respects:
1. They produce high torque at all speeds including zero speed.
2. They are capable of holding a static (i.e. no motion) position.
3. They do not overheat at standstill or lower-speeds.
4. Due to low-inertia, they are able to reverse directions quickly.
5. They are able to accelerate and deaccelerate quickly.
6. They are able to return to a given position time after-time without any drift.
These motors look like the usual electric motors. Their main difference from industrial
motors is that more electric wires come out of them for power as well as for control. The
servomotor wires go to a controller and not to the electrical line through contractors. Usually, a
tachometer (speed indicating device) is mechanically connected to the motor shaft. Sometimes,
blower or fans may also be attached for motor cooling at low speeds.

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 Servo Motor

DC Servomotors
These motors are either separately-excited dc motors or permanent-magnet dc motors. The
schematic diagram of a separately-excited dc motor along with its armature and field MMFs and
torque/speed characteristics is shown in Fig. 39.26. The speed of dc servomotors is normally
controlled by varying the armature voltage. Their armature is deliberately designed to have large
resistance so that torque-speed characteristics are linear and have a large negative slope as shown
in Fig. 39.26(c). The negative slope serves the purpose of providing the viscous damping for the
servo drive system. As shown in Fig. 39.26(b), the armature mmf and excitation mmf are in
quadrature. This fact provides a fast torque response because torque and flux become decoupled.
Accordingly, a step change in the armature voltage or current produces a quick change in the
position or speed of the rotor.

Fig. 39.26

AC Servomotors
Presently, most of the AC servomotors are of the two-phase squirrel-cage induction type
and are used for low power application. However, recently three-phase induction motors have
been modified for high power servo systems which had so far been using high power DC
servomotors.

(a) Two-Phase AC Servomotor

Such motors normally run on frequency of 60 Hz or 400 Hz. The stator has two
distributed winding which are displaced from each other by 90o (electrical).
The main winding (also called the reference or fixed phase) is supplied from a constant
voltage source, Vm0o as shown in Fig. 39.27.
The other winding (also called the control phase) is supplied with a variable voltage of
the same frequency as the reference phase but is phase displaced by 90o (electrical).
The control-phase voltage is controlled by the phase difference between the main and
control windings. Reversing the phase difference from leading to lagging (or vice versa) reverses
the motor direction.
Since the rotor bars have high resistance the torque-speed characteristics for various
armature voltages are almost linear over a wide speed range particularly near the zero speed. The
motor operation can be controlled by varying the voltage of the main phase while keeping that of
the reference phase constant.

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 Servo Motor

Fig. 39.27

(b) Three-Phase AC Servomotor

A great of research has been to modify a three-phase squirrel-cage induction motor for
use in high power servo systems. Normally, such a motor is highly non-linear coupled circuit
device. Recently, this machine has been operated successfully as a linear decoupled machine
(like a DC machine) by using a control method called vector control or field oriented control.
In this method, the currents fed to the machine are controlled in such a way that its torque
and flux become decoupled as in a DC machine. This results in a high speed and a high torque
response.

Control of Servomotors

Fig. 39.28. Basic Control Structure of a Servo Motor

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 Servo Motor

Servo motors are used in closed loop control systems as shown in Fig. 39.28. The servo
motor controller directs operation of the servo motor by sending velocity command signals to the
amplifier, which drives the servo motor.
An integral feedback device (resolver) or devices (encoder and tachometer) are either
incorporated within the servo motor or are remotely mounted, often on the load itself. These
provide the servo motor's position and velocity feedback that the controller compares to its
programmed motion profile and uses to alter its velocity signal.
Servo motors feature a motion profile, which is a set of instructions programmed into the
controller that defines the servo motor operation in terms of time, position, and velocity.
The ability of the servo motor to adjust to differences between the motion profile and
feedback signals depends greatly upon the type of controls and servo motors used.
Three basic types of servo motors are used in modern servo systems: ac servo motors,
based on induction motor designs; dc servo motors, based on dc motor designs; and ac brushless
servo motors, based on synchronous motor designs.

Possible Questions
1. Define servo motor.
2. Where are servomotor used?
3. What are the difference of servomotors from large industrial motors in application
capabilities?
4. Describe briefly the dc servo motor.
5. Describe briefly the ac servo motor.
6. The speed of dc servomotors is normally controlled by varying the armature voltage.
7. The armature of dc servo motor is deliberately designed to have large resistance so that
torque-speed characteristics are linear and have a large negative slope.
8. The main winding of a two phase servomotor is also called the reference or fixed phase.
The other winding is also called the control phase.
9. The main winding of a two phase servo motor is supplied from a constant voltage source.
The other winding is supplied with a variable voltage of the same frequency as the main
phase but is phase displaced by 90o (electrical).
10. The three-phase ac servomotor has been operated successfully as a linear decoupled
machine (like a DC machine) by using a control method called vector control or field
oriented control.

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 Amplidyne and Metadyne Machines

Module 09
Amplidyne and Metadyne Machines

Amplidyne Machines
The first amplidyne was designed during the II-world war by electrical engineer namely “Ernst
Alexanderson”. It is a general electric name that works as a regulated converter. During the II-world war,
these devices were used for controlling guns. After the world war, they were used in large radar antennas
for providing the high starting currents of the load as well as to evade overshooting and negative feedback
is also given through a tacho generator. This article discusses an overview of amplidyne and its working.

What is an Amplidyne?
Definition: The most common frequent version of the Metadyne is known as amplidyne. It includes
a motor & a generator where an AC motor with a constant speed can be connected mechanically to a dc
generator. The amplidyne working principle is to supply large DC currents by placing heavy loads by using
servo or synchro systems. At present, these are outdated technology as they replaced through power
semiconductor devices like IGBTs and MOSFETs because these devices generate the o/p power in the KW
range. By using this device, huge loads could be stimulated and remote-controlled. The o/p power of this
can be up to several kilowatts including power amplification.

Schematic Diagram of the Amplidyne

The schematic diagram of this can be designed by changing a separately excited DC generator to
amplidyne. It is a special kind of DC generator where this generator can be converted into an amplidyne.
The primary step is to short the brushes jointly so that resistance can be removed within the armature circuit.
Due to extremely low resistance within this circuit, a low control-field flux can generate full-load armature
current. The schematic diagram of this is shown below.

Generator Brushes Short Circuited

Now, the less control field needs one-volt control voltage & 1 watt of input power. The second step
is to include an extra set of brushes so that it will turn into the o/p brushes for the amplidyne. These are
located beside the commutator in perpendicular to the actual brushes.

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 Amplidyne and Metadyne Machines

Load Brushes of Amplidyne

The formerly shorted brushes are known as quadrature brushes because they are in quadrature to
the o/p brushes. These brushes are in order through the armature flux. So, they turn off the induced voltage
within the windings at this end. The o/p voltage will be the same in the generator because it generates huge
output in 1000’s of watts with the i/p 100 watts.
The output generated by this device is 10,000-watt with 1-watt input only. This signifies a 10,000
of gain so that the generator gain can be increased greatly. As formerly stated, an amplidyne is mainly used
for providing huge DC currents by placing huge loads through the synchro or servo systems.

Applications
The applications of amplidyne include the following.

 These are widely used in feedback control systems

 It can also be used as a generator to position or speed control in a Ward-Leonard system.
 These are used for fitting of controlling overturning rolling mills, paper machines, mine hoists, cold
rolling mills, and metal cutting
 These were primarily used in electric and naval guns. After that, used to manage progressions in
steelworks
 These are used to activate the control rods in nuclear submarine designs
 Used in Diesel-electric train engine control systems.
Thus, this is all about an overview of an amplidyne, used in high power servo & control systems in
industries to strengthen small power control signals for controlling strong electric motors. But, amplidynes
have a no. of shortcomings like poor commutation. So sometimes, they will disturb the operating condition
of the fitting & a low efficiency of the process. Here is a question for you, what is the amplidyne transfer
function?

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 Amplidyne and Metadyne Machines

Metadyne Machines
The metadyne was known for several years because it is a DC generator. These generators were
described by Gravier in the year 1882, Rosenburg in the year 1904, and Osnus was discussed the no. of
feasible arrangements in the year 1907. The theory of such devices was developed by Pestarini in between
1922-1930 and proposed a name like Metadyne for the general type of machines. These machines are
attained by arranging extra brushes to normal generators. The fist metadyne device was used in the control
system of electric trains by the company of metropolitan Vickers in the Britain country.

What is a Metadyne?
Definition: An electric DC machine that has two pairs of brushes is known as metadyne.
This dc machine is used as a rotating transformer or an amplifier. It is related to a third brush
dynamo although includes extra windings of varistor otherwise regulator. Metadyne characteristics
are equal to an amplidyne except a compensate winding in the latter which completely offsets the
result of the generated flux through the load current. The technical explanation is “a cross-field dc
machine mainly designed to use armature reaction”. The main function of a metadyne is to change
the input of stable voltage into a stable current and uneven voltage output.

Metadyne Working Principle

The constant current device like metadyne is mainly designed to use armature reaction. The
working principle of metadyne is to change the i/p of constant voltage to current and variable o/p voltage.
The schematic diagram of the metadyne is shown below.

Metadyne Construction
The arrangement of the metadyne control system mainly includes three arrangements which are
shown in the figure. In the first arrangement, it signifies a cross-field machine that includes a single cycle.
In a DC machine, the excitation current effect will generate a flux represented with A1, and at right angles

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 Amplidyne and Metadyne Machines

to the exciting flux, it generates a quadrature flux. By connecting the quadrature brushes mutually, the
current can be generated within the armature. The A2 flux generates at right angles in the direction of the
quadrature axis and gives an armature reaction. This armature reaction is directly proportional to the actual
excitation.
This characteristic is basic to the machine and it does not lie in its rotation direction. Once the
armature reaction is incompletely compensated through a compensation winding, and then the
uncompensated part of the armature reaction works in this way. When the o/p current increases, it restrains
the excitation effect, until it achieves a state where there is sufficient excitation to continue the current. If
any current increases, the flux can be eliminated which maintains its operation and the back emf can be
generated through it. Thus, this machine works like a constant-current generator, wherever the current is
relative to the excitation.
In the second diagram, a machine includes no excitation windings, but in its place, a stable voltage
can be given to the quadrature brushes. This generates a flux similar to the one generated through the
armature rotation within the excitation flux. The machine operation is extremely similar to the increasing
o/p current until the flux generated through the applied voltage. The metadyne generator can be partly
compensated with the Metadyne transformer and operates continually like a stable current device until the
compensation increases are maximum.
In the third diagram, a metadyne is connected to 2 separate motors. This connection was frequently
used to control the traction motors within electric trains. Once the metadyne is connected, it will reduce the
effective loading & allows a small machine to be fixed. The Metadyne works like a booster. Even though
the system is horizontal to the currents within the two divides of the load that becomes unbalanced. The
unbalanced load can be modified through the condition of additional series windings, which work as an
extra circuit resistance.

Applications
The applications of metadynes include the following.

 These are used to control large guns & controlling the speed of electric trains.
 It can be used as a rotary transformer/an amplifier.

FAQs
1) What is metadyne?
It is like a dc electric machine used as a rotary transformer.
2) What is the function of metadyne?
It is used to control the speed of electric trains and control the aiming of guns.
3) What is amplidyne?
It is a special purpose dc generator, used to supply dc current and controls heavy loads like missile
launchers
4) How does amplidyne work?
It includes an electric motor that activates a generator on a similar shaft. Different from motor and
generator, it is not to produce a stable voltage however to produce a voltage that is proportional to
an i/p current to strengthen the input.
Thus, this is all about an overview of Metadyne and its working. It is a DC electrical machine that includes
two sets of brushes. These are used as a rotary transformer otherwise an amplifier. Here is a question for
you, what is amplidyne?

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 Amplidyne and Metadyne Machines

Difference between Amplidyne and Metadyne

The main difference between amplidyne and metadyne are listed below.

Amplidyne Metadyne
Amplidyne is a special purpose DC generator. A metadyne is a DC electrical machine
including two pairs of brushes.
It consists of a motor & a generator. It includes sets of brushes.
It provides huge DC currents. It provides most of the excitation to attain high
power gains.
These are used in electric elevators & naval These are used for speed controlling in electric
guns. trains and control the aiming of guns.

The amplidyne characteristics are equivalent to that of a normal separately excited generator,
however, its rise can be controlled through performing on the compensating winding. The winding of an
amplidyne is generally designed to supply magnetizing force that is fairly larger than the demagnetizing
force of the reaction of armature within the amplidyne. So overcompensate of the armature reaction is
required beneath certain operating conditions of amplidyne.

Prepared by Md. Sabbir Hasan Sohag Page 5 of 5

Edited by Md. Asaduzzaman Sarker