DC Motors

Chapter Four
Chapter Four
DC Machines
By Yimam A.(MSc.)
May 31, 2022
By Yimam A.(MSc.) Chapter Four May 31, 2022 1 / 99

Chapter Four
Outline
1 Introduction
2 Working principles of DC Motor
3 Equivalent circuit of a DC motor
4 Emf and torque equations of DC motor
5 Types of DC Motor
6 Characteristics of DC Motors
7 Power Flow and Losses in DC Motors
8 Speed Control Methods of DC Motors

Chapter Four
Learning Objectives
At the end of this chapter the students should be able to:
Understand the working principle of DC motor
Understand the equivalent circuit of a dc motor.
Understand how to derive the torque speed characteristics of separately excited, shunt,
series, and compounded dc motors.
Perform nonlinear analysis of dc motors using the magnetization curve, taking into
account armature reaction effects.
Understand how to control the speed of different types of dc motors.
Understand the special characteristics of series dc motors, and the applications that
they are especially suited for.

Chapter Four
Introduction
Introduction
The dc machine can operate both as a generator and as a motor.
When it operates as a generator, the input to the machine is mechanical power, and
the output is electrical power
When the dc machine operates as a motor, the input to the machine is electrical
power, and the output is mechanical power.
If the armature is connected to a dc supply, the motor will develop mechanical torque
and power
The dc machine is used more as a motor than as a generator.
DC motors can provide a wide range of accurate speed and torque control.

Chapter Four
Introduction
Cont...
In both modes of operation (generator and motor) the armature winding rotates in
the magnetic field and carries current.
DC machines have DC outputs just because they have a mechanism converting AC
voltages to DC voltages at their terminals.
This mechanism is called a commutator; therefore, DC machines are also called
commutating machines.
DC generators are not as common as they used to be, because direct current, when
required, is mainly produced by electronic rectifiers.
While dc motors are widely used, such as automobile, aircraft, and portable
electronics, in speed control applications

Chapter Four
Working principles of DC Motor
Working principle of a DC motor is based on simple electromagnetism.
“When a current-carrying conductor is placed in an external magnetic field, it will
experience a mechanical force” i.e. Lorentz force.
Due to this force torque is produced which rotates the rotor of motor and hence a
motor runs.
The direction of this force is given by Fleming’s left hand rule and it’s magnitude is
given by
F = BIL
Where, B = magnetic flux density,
I = current passing through the conductor
L = length of the conductor within the magnetic field.

Chapter Four
Cont...

Chapter Four
Fleming’s left hand rule
If we stretch the first finger, middle
finger and thumb of our left hand to
be perpendicular to each other,
Direction of magnetic field is
represented by the first finger,
Direction of the current is represented
by second finger
The thumb represents the direction of
the force experienced by the current
carrying conductor.
Figure 2: Fleming’s left hand rule

Chapter Four
Cont...
In a particular motor to reverse its direction of rotation either direction of main field
produced by the field winding is reversed ((a),(c)) or direction of the current passing
through the armature is reversed((b),(d)).
Figure 3: Direction of force experienced by conductor

Chapter Four
Back emf
According to fundamental laws of nature, no energy conversion is possible until there
is something to oppose the conversion. In case of generators this opposition is
provided by magnetic drag, but in case of dc motors there is back emf.
When the armature of the motor is rotating, the conductors are also cutting the
magnetic flux lines and hence according to the Faraday’s law of electromagnetic
induction, an emf induces in the armature conductors. The direction of this induced
emf is such that it opposes the armature current (Ia).
This induced emf(back emf) in the armature always acts in the opposite direction of
the supply voltage.(Lenz’s law)
Back emf is generated by the generating action (moving conductors cutting the
magnetic flux)
This emf always opposes the supply voltage, it is called back emf (Eb)

Chapter Four
Significance of Back Emf
Magnitude of back emf is directly proportional to speed of the motor. Consider the
load on a dc motor is suddenly reduced. In this case, required torque will be small as
compared to the current torque.
Speed of the motor will start increasing due to the excess torque.
Hence, being proportional to the speed, magnitude of the back emf will also increase.
With increasing back emf armature current will start decreasing.
Torque being proportional to the armature current, it will also decrease until it
becomes sufficient for the load. Thus, speed of the motor will regulate.
If a dc motor is suddenly loaded, the load will cause decrease in the speed. Due to
decrease in speed, back emf will also decrease allowing more armature current.
Increased armature current will increase the torque to satisfy the load requirement.
Presence of the back emf makes a dc motor self regulating.

Chapter Four
Equivalent circuit of a DC motor
Two circuits are involved in DC motors
Armature Circuit
Field Circuit
Armature circuit represents Thevenin equivalent of the entire rotor.
It contains an ideal voltage source EA and a resistor RA.
Brush voltage drop is represented by a small battery
The field coils, which produce the magnetic flux
Inductor LF and resistor RF .
Radj for field current control

Chapter Four
Cont...
Figure 4: The equivalent circuit of a dc motor
Figure 5: A simplified equivalent circuit of a dc
motor with RF combining the resistances of
the field coils and the variable control resistor.

Chapter Four
Emf and torque equations of DC motor
EMF equation of DC machines
Let, ϕ = flux per pole in weber
Z =Total number of armature conductors
= Number of slots × Number of Conductors/slot
P = Number of poles in the machine
A = Number of parallel paths
N = armature speed in rpm
Eg = EMF induced in any parallel path in the armature

Chapter Four
Cont...
Now
Average emf generated per conductor is given by dϕ
dt
Flux cut by 1 conductor in 1 revolution is dϕ = P × ϕ
Number of revolutions per second (speed in rps) N/60
Flux cut by 1 conductor in 60 sec = PϕN
60
Therefore, time for one revolution = dt = 60/N (seconds)
The emf generated in one conductor of the generator is
Eg =
dϕ
dt
=
PϕN
60A

Chapter Four
Cont...
The conductors are connected in series per parallel path, and the emf across the
generator terminals is equal to the generated emf across any parallel path.
Eg =
PϕZN
60A
For simplex lap winding, number of parallel paths is equal to the number of poles (i.e.
A=P),
Eg =
PϕZN
60A
=
KϕN
60
, Where K =
PZ
A
For simplex wave winding, number of parallel paths is equal to 2 (i.e P=2),
Eg =
PϕZN
120

Chapter Four
Voltage equation of a DC motor
Figure 6: Equivalent circuit
Eb =
PϕZN
60A
V = Eb + IaRa + brush drop
Neglecting the brush drop
V = Eb + IaRa
Ia =
V − Eb
Ra

Chapter Four
Power equation of a DC motor
V = Eb + IaRa
Multiplying the above equation by Ia
V Ia = EbIa + I2
aRa
V Ia = net electrical power input to the armature
I2
aRa = power loss due to the resistance of the armature called armature copper loss
EbIa = gross mechanical power developed by the armature(Pm)

Chapter Four
Torque equation of a DC motor
When armature conductors of a DC motor carry current in the presence of stator
field flux, a mechanical torque is developed between the armature and the stator.
workdone in one revolution is
W = F × distance travelled in one revolution
= F × 2πR joules
power developed =
word done
time
=
F × 2πR
time for 1 rev
=
F × 2πR
(60/N)
= (F × R)

2πN
60

P = T × ω watts
Where T=Torque in Nm ω =Angular speed in rad/sec

Chapter Four
Cont...
Power in armature = Armature torque × ω
Eb × Ia = Ta ×
2πN
60
But Eb =
PϕZN
60A
PϕZN
60A
× Ia = Ta ×
2πN
60
Ta =
1
2π
ϕIa ×
PZ
A
= 0.159ϕIa ×
PZ
A
Nm

Chapter Four
Cont...
ω =
2πN
60
rad/sec
Ta = Tf + Tsh

Chapter Four
Types of torque
Load torque(shaft torque)(Tsh): the torque which is available at the motor shaft for
doing useful work is known as shaft torque.
Lost torque(Tf ):The total or gross torque (Ta) developed in the armature of a motor
is not available at the shaft because a part of it is lost in overcoming the iron and
frictional losses in the motor.
Armature torque (Ta):The sum of the torques due to all armature conductors is
known as gross or armature torque.

Chapter Four
Types of DC Motor
Types of DC Motors

Chapter Four
Types of DC Motor
1. DC Shunt Motor
The armature and field winding are connected in parallel
The parallel combination of the two windings is connected across a common dc power
supply.
The resistance of shunt field winding (Rsh) is always higher than that of armature
winding(Ra).
This is because the number of turns for the field winding is more than that of
armature winding.
The cross-sectional area of the wire used for field winding is smaller than that of the
wire used for armature winding.

Chapter Four
Types of DC Motor
Cont...
Figure 7: dc shunt motor
IL = Ia + Ish
Ish =
Vsh
Rsh
V = Eb + IaRa

Chapter Four
Types of DC Motor
2. DC Series Motor
The the armature and field windings are connected in series with each other
The current passing through the series winding is same as the armature current
The resistance of the series field winding (Rs) is much smaller as compared to that of
the armature resistance (Ra).
Also therefore the field winding will posses a low resistance than the armature
winding.

Chapter Four
Types of DC Motor
Cont...
Figure 8: dc series motor
IL = Ia = Ise
V = Eb + IaRa + IaRse
V = Eb + Ia (Ra + Rse)

Chapter Four
Types of DC Motor
3. DC Compound Motor

Chapter Four
Types of DC Motor
I. Long Shunt Compound Motor
In this the series winding is connected
in series with the armature winding
and the shunt winding is connected in
parallel with the armature connection.
IL = Ia + Ise Ia = Ise
Ish =
Vsh
Rsh
V = Eb + IaRa + IaRse
V = Eb + Ia (Ra + Rse)
Figure 9: Long shunt compound motor

Chapter Four
Types of DC Motor
II. Short Shunt Compound Motor
The series winding is connected in
series to the parallel combination of
armature and the shunt winding.
This helps to get good starting torque
and constant speed characteristics
IL = Ise IL = Ia + Ish
Ish =
Vsh
Rsh
V = Eb + ILRse + IaRa
Figure 10: Short shunt compound motor

Chapter Four
Types of DC Motor
Cont...
1 Cumulative Compound Dc Motors:
If the two field windings i.e. series and shunt are wounded in such a way that the
fluxes produced by them add or assist each other
2 Differential Compound Dc Motors:
If the two field winding i.e. series and shunt are wounded in such a way that the
fluxes produced by them always try to oppose and try to cancel each other.

Chapter Four
Types of DC Motor
Torque and speed of a DC motor
For any motor, the torque and speed are very important factors.
T ∝ ϕIa
This is because 0.159PZ
A is a constant for a given motor
Now ϕ is the flux produced by the field winding and is proportional to the current
passing through the field winding, ϕ ∝ Ifield
Current through the field winding is different for vrious types of motors.
For dc shunt motors, Ish is constant as long as supply voltage is constant,ϕ is also
constant
T ∝ ϕIa
For dc series motors Ise is same as Ia .Hence ϕ is proportional to the armature
current Ia
T ∝ Iaϕ ∝ I2
a

Chapter Four
Types of DC Motor
Cont...
As Eb = PϕZN
60A , the speed equation is
Eb ∝ ϕN N ∝
Eb
ϕ
V = Eb + IaRa neglecting brush drop.
Eb = V − IaRa N ∝
V − IaRa
ϕ
For shunt motor flux ϕ is constant
N ∝ V − IaRa
For series motors, flux ϕ is proportional to Ia
N ∝
V − IaRa − IaRse
Ia

Chapter Four
Types of DC Motor
Speed regulation
The speed regulation is defined as the change in speed from no load to full load,
expressed as a fraction or percentage of full load speed.
% Speed regulation =
Nnl − Nfl
Nfl
× 100%
Where Nnl is no load speed
Nfl is full load speed

Chapter Four
Characteristics of DC Motors
Characteristics of DC Motors
The performance of a DC motor under various conditions can be judged by the
following characteristics
1 Torque vs armature current
2 Speed vs armature current
3 Speed vs torque.
These characteristics are determined by keeping the following two relations in mind.
T ∝ ϕIa and N ∝ Eb
ϕ
These characteristics play a very important role in selecting a type of motor for a
particular application.

Chapter Four
Characteristics of DC motors
Characteristics of DC series motors
i)Torque - Armature Current (Ta − Ia)
This characteristic is also known as electrical characteristics.
In case of series motor the series field winding is carrying the entire armature current.
So flux produced is proportional to the armature current
ϕ ∝ Ia Hence Ta ∝ ϕIa ∝ I2
a
Thus torque in case of series motor is proportional to the square of the armature
current.
This relation is parabolic in nature as shown in the Figure 11

Chapter Four
Cont...
As load increases, armature current increases and torque produced increases
proportional to the square of the armature current upto a certain limit.
As the entire Ia passes through the series field, there is a property of an
electromagnet called saturation may occur.
After saturation the characteristics take the place of straight line as flux becomes
constant.
The difference between Ta and Tsh is loss torque Tf .
At start as Ta ∝ I2
a , these types of motors can produce high torque for small amount
of armature current hence the series motors are suitable for the applications which
demand high starting torque.

Chapter Four
Cont...
Figure 11: Torque - armature current characteristics

Chapter Four
ii)Speed -Armature Current (N-Ia)
From the speed equation,in case of series motor
N ∝
Eb
ϕ
∝
Ia
asϕ ∝ Ia
Now the values of Ra and Rse are so small that the effect of change in Ia on speed
overrides the effect of change in V − IaRa − IaRse on the speed.
Hence in the speed equation, Eb ≈ V and can be assumed constant.
So speed equation reduced to, N ∝ 1/Ia
When armature current is very small the speed becomes dangerously high.

Chapter Four
Cont...
That is why a series motor should never be started without some mechanical load.
Figure 12: speed - armature current characteristics

Chapter Four
Cont...
But, at heavy loads, armature current Ia is large. And hence, speed is low which
results in decreased back emf Eb.
Due to decreased Eb, more armature current is allowed.
N ∝
Eb
ϕ
N ∝
Ia
As ϕ ∝ Ia in case of series motors

Chapter Four
iii)Speed - Torque (N − Ta)
This characteristic is also called as mechanical characteristic.
Thus as torque increases when load increases, the speed decreases.
On no load, torque is very less and hence speed increases to dangerously high value.
Thus the nature of the speed-torque characteristics is similar to the nature of the
speed-armature current characteristics.
T ∝ I2
a N ∝
1
Ia
N ∝
1
√
T

Chapter Four
Cont...
Figure 13: speed - torque characteristics

Chapter Four
Characteristics of DC Shunt Motors
i) Torque-Armature Current (Ta − Ia)
In case of DC shunt motors, we can assume the field flux ϕ to be constant. Though at
heavy loads, ϕ decreases in a small amount due to increased armature reaction.
As we are neglecting the change in the flux ϕ, we can say that torque is proportional
to armature current.
Hence, the Ta − Ia characteristic for a dc shunt motor will be a straight line through
the origin.
Since heavy starting load needs heavy starting current, shunt motor should never be
started on a heavy load.

Chapter Four
Cont...
Figure 14: Torque - armature current characteristics

Chapter Four
ii) Speed -Armature Current (N − Ia)
As flux ϕ is assumed to be constant, we can say N ∝ Eb. But, as back emf is also
almost constant, the speed should remain constant. But practically, ϕ as well as Eb
decreases with increase in load.
Back emf Eb decreases slightly more than ϕ, therefore, the speed decreases slightly.
Generally, the speed decreases only by 5 to 15% of full load speed.
Therefore, a shunt motor can be assumed as a constant speed motor.
N ∝
V − IaRa
ϕ
N ∝ V − IaRa as ϕ is constant

Chapter Four
Cont...
Figure 15: speed - armature current characteristics

Chapter Four
iii) Speed - Torque characteristics (N − Ta)
These characteristics can be derived from the above two characteristics.
This graph is similar to speed-armature current characteristics as torque is
proportional to the armature current.
This curve shows that the speed almost remains constant through torque changes
from no load to full load conditions.

Chapter Four
Cont...
Figure 16: speed - torque characteristics

Chapter Four
Characteristics of DC compound motor
Characteristics of D.C. Compound Motor
Compound motor characteristics basically depends on the fact whether the motor is
cumulatively compound or differential compound.
All the characteristics of the compound motor are the combination of the shunt and
series characteristics.
Cumulative compound motor is capable of developing large amount of torque at low
speeds just like series motor. However it is not having a disadvantages of series motor
even at light or no load. The shunt field winding produces the definite flux and series
flux helps the shunt field flux to increase the total flux level.
So cumulative compound motor can run at reasonable speed and will not run with
dangerously high speed like series motor, on light or no load condition.

Chapter Four
Cont...
In differential compound motor, as two fluxes oppose each other, the resultant flux
decreases as load increases, thus the machine runs at a higher speed with increase in
the load.
This property is dangerous as on full load, the motor may try to run with dangerously
high speed. So differential compound motor is generally not used in practice.
The exact shape of these characteristics depends on the relative contribution of series
and shunt field windings.
If the shunt field winding is more dominant then the characteristics take the shape of
the shunt motor characteristics.
While if the series field winding is more dominant then the characteristics take the
shape of the series characteristics.

Chapter Four
Cont...
Figure 17: Compound motor characteristics

Chapter Four
Power Flow and Losses in DC Motors
Losses in a DC machine

Chapter Four
1.Copper Losses
The copper losses are the losses taking place due to the current flowing in a winding.
There are basically two windings in a d.c. machine namely armature winding and
field winding.
The copper losses are proportional to the square of the current flowing through these
windings.
are around 30% of the total full-load losses.
Thus the various copper losses can be given by,
Armature copper loss = I2
aRa
Where Ra armature resistance
Ia armature current

Chapter Four
Cont...
Shunt field copper loss = I2
shRsh
Where Rsh shunt field winding resistance
Ish Shunt field current
Series field copper loss = I2
seRse
Where Rse series field winding resistance
Ise Series field current
In a compound d.c. machine, both shunt and series field copper losses are present.

Chapter Four
Cont...
Brush Loss also occurs at point of contact between copper commutator and the
carbon brush.This loss is also very small as compared with all other losses in machine.
There are few losses which vary with the load but their relationship with the load
current can not be identified in simple manner.
Such losses are called stray load losses and are the part of variable losses. These occur
in the windings and the core.
These include copper stray load loss and iron stray load loss.
These stray load losses are difficult to measure or mathematically calculate hence
practically taken as 1% of the output for the d.c.machines.

Chapter Four
Cont...
Stray load losses include
Increase in iron losses at load
Increases in copper losses due to eddy currents in armature conductors
Additional losses caused by short circuit currents in the coils under commutation and
occur in
a) Armature teeth,
b) Armature core and
c) Armature winding

Chapter Four
2. Iron or Core Losses
These losses are also called magnetic losses.
These losses include hysteresis loss and eddy current loss.
The hysteresis loss is proportional to the frequency and the maximum flux density in
the air gap.
Hysteresis loss = ηB1.6
m fV
Where η = Steinmetz hysteresis coefficient. V = Volume of core in m3.
f = Frequency of magnetic reversals. Bm = Max. flux density in armature
This loss is basically due to reversal of magnetization of the armature core.
The loss depends upon the volume and grade of the iron, frequency of magnetic
reversals and value of flux density.

Chapter Four
Cont...
The eddy current loss exists due to eddy currents. When armature core rotates, it
cuts the magnetic flux and e.m.f. gets induced in the core.
This induced e.m.f. sets up eddy currents which cause the power loss.
Eddy current loss = kB2
mf2
t2
V
Where K is constant Bm = maximum flux density in armature
f = Frequency of magnetic reversals.
t = thickness of each lamination. V = Volume of core.
The hysteresis loss is minimized by selecting the core material having low hysteresis
coefficient.
While eddy current loss is minimized by selecting the laminated construction for the
core.
These losses are almost constant for the dc machines.

Chapter Four
3. Mechanical Losses
Some power is required to overcome mechanical friction and wind resistance at the
shaft.
The mechanical losses are constant for a dc machine and consists of the friction
windage loss .
The magnetic and mechanical losses together are called stray losses.
For the shunt and compound dc machines where field current is constant, field copper
losses are also constant. Thus stray losses along with constant field copper losses are
called constant losses.
While the armature current is dependent on the load and thus armature copper losses
are called variable losses.

Chapter Four
Cont...

Chapter Four
Power flow in DC motors
Figure 18: power flow block diagram of dc motor

Chapter Four
Cont...
Figure 19: Power flow diagram of a DC motor

Chapter Four
Efficiency of a DC Machine
For a dc machine, its overall efficiency is given by,
η =
Pout
Pin
× 100
=
Pout
Pout + losses
× 100
=
Pout
Pin + Pcu + Pf
× 100
Where Pcu is variable losses Pf is constant losses
Pin is input power Pout is output power

Chapter Four
Condition for maximum efficiency
In case of a dc generator the output is given by
Pout = V I, Pcu = variable losses = I2
aRa = I2
Ra, Ia = I neglecting shunt field current
η =
V I
V I + I2Ra + Pf
× 100 =
1
1 +
h
IRa
V +
Pf
V I
i × 100
The efficiency is maximum when the denominator is minimum
d
dI

1 +

IRa
V
+
Pf
V I

= 0 ⇔
Ra
V
−
Pf
V I2
= 0
I2
Ra − Pf = 0, I2
Ra = Pf = Pcu
For the maximum efficiency,the condition is variable losses= constant losses

Chapter Four
Current at Maximum Efficiency
For shunt machines
The Ish is constant and the loss V Ish is treated to be the part of constant losses.
The variable losses are I2
aRa.
At maximum efficiency,
I2
Ra = Pf = Stray + shunt field losses
Ia =
s
Pi
Ra
=
s
constant losses
armature resistance
This is the armature current at maximum efficiency.
Neglecting Ish, Ia = IL is the line current of the machine.

Chapter Four
Cont...
For series machines :
The current through series field is same as armature current which is same as line
current.
Hence the constant losses are only mechanical losses while the variable losses are the
copper losses in armature as well as series field winding due to the armature
current.
At maximum efficiency,
I2
a (Ra + Rse) = Pi = Mechanical losses
Ia =
s
Pi
Ra + Rse

Chapter Four
Speed Control Methods of DC Motors
DC motors are used for various applications in domestic,commercial and industrial
area.
But for different application we need to operate the dc motor at different speed to get
the best outcomes.
Speed control means intentional change of the drive speed to a value required for
performing the specific work process.
N ∝
Eb
ϕ
∝
V − IaRa
ϕ
The factors affecting the speed of a dc motor are
1 The speed is inversely proportional to flux (ϕ).
2 Speed is directly proportional to armature voltage (Va).
3 Speed is directly proportional to applied voltage (V ).

Chapter Four
Speed Control of Shunt Motor
1. Flux Control Method
The speed of a dc motor is inversely proportional to the flux per pole.
Thus by decreasing the flux, speed can be increased and vice versa.
To control the flux, a rheostat is added in series with the field winding.
Adding more resistance in series with the field winding will increase the speed as it
decreases the flux.
In shunt motors, as field current is relatively very small, I2
sh loss is small and, hence,
this method is quite efficient.
Though speed can be increased above the rated value by reducing flux with this
method, it puts a limit to maximum speed as weakening of flux beyond the limit will
adversely affect the commutation.

Chapter Four
Cont...
Figure 20: Flux Control Method

Chapter Four
Advantages of Flux Control
It provides relatively smooth and easy control.
Speed control above rated speed is possible.
As the field winding resistance is high, the field current is small. Hence power loss in
the external resistance is very small, which makes the method more economical and
efficient.
As the field current is small, the size of rheostat required is small.

Chapter Four
Disadvantages of Flux Control
As flux can be increased only upto its rated value,the speed control below normal
rated speed is not possible
As flux reduces, speed increases. But high speed affects the commutation making
motor operation unstable.
So there is limit to the maximum speed above normal possible by this method.

Chapter Four
2. Armature Voltage Control Method (Rheostatic Control)
The speed is directly proportional to the voltage applied across the armature.
As the supply voltage is normally constant, the voltage across the armature can be
controlled by adding a variable resistance in series with the armature.
The field winding is excited by the normal voltage hence Ish is rated and constant in
this method.
Initially the rheostat position is minimum and rated voltage gets applied across the
armature. So speed is also rated.

Chapter Four
Cont...
Figure 21: Rheostatic Control Method
Figure 22: N vs voltage across

Chapter Four
Cont...
For a given load, armature current is fixed. So when extra resistance is added in the
armature circuit, Ia remains same and there is voltage drop across the resistance
added (IaR).
Hence voltage across the armature decreases, decreasing the speed below normal
value. By varying this extra resistance, various speeds below rated value can be
obtained.
So for a constant load torque, the speed is directly proportional to the voltage across
the armature.

Chapter Four
2.1 Potential Divider Control
The main disadvantages of the above method is, the speed up to zero is not possible
as it requires a large rheostat in series with the armature which is practically
impossible.
If speed control from zero to the rated speed is required, by rheostatic method then
voltage across the armature can be varied by connecting rheostat in a potential
divider arrangement as shown in Figure 23.
When the variable rheostat position is at ’start’ point shown, voltage across the
armature is zero and hence speed is zero.
As rheostat is moved towards ’maximum’ point, the voltage across the armature
increases, increasing the speed.

Chapter Four
Cont...
Figure 23: Potential Divider Control
Figure 24: N vs V

Chapter Four
Cont...
At maximum point the voltage is maximum i.e. rated hence maximum possible speed
is rated speed.
When the voltage across the armature starts increasing, as long as motor does not
overcome inertial and frictional torque, the speed of the motor remains zero.
The motor requires some voltage to start hence the graph of voltage and the speed
does not pass through the origin as shown in Figure 24.
Advantages of Rheostat Control
Easy and smooth speed control below normal is possible.
In potential divider arrangement, rheostat can be used as a starter.

Chapter Four
Cont...
Disadvantages of Rheostat Control
As the entire armature current passes through the external resistance, there are
tremendous power losses.
As armature current is more than field current, rheostat required is of large size and
capacity.
Speed above rated is not possible by this method.
Due to large power losses, the method is expensive, wasteful and less efficient.
The method needs expensive heat dissipation arrangements.

Chapter Four
3. Applied Voltage Control
Multiple voltage control
In this technique the shunt field of the motor is permanently connected to a fixed
voltage supply, while the armature is supplied with various voltages by means of
suitable switch gear arrangements.
Figure 25 shows a control of motor by two different working voltages which can be
applied to it with the help of switch gear.
In large factories, various values of armature voltages and corresponding arrangement
can be used to obtain the speed control.

Chapter Four
Cont...
Figure 25: Multiple voltage control

Chapter Four
Cont...
Advantages of Applied Voltage Control
Gives wide range of speed control.
Speed control in both directions can be achieved very easily.
Uniform acceleration can be obtained.
Disadvantages of Applied Voltage Control
Arrangement is expensive as provision of various auxiliary equipments is necessary.
Overall efficiency is low.

Chapter Four
Speed Control of DC Series Motor
The flux produced by the winding depends on the mmf i.e. magnetomotive force
which is the product of current and the number of turns of the winding through
which current is passing.
So flux can be changed either by changing the current by adding a resistance or by
changing the number of turns of the winding
1. Flux Control
The various methods of flux control in a dc series motor are:
i) Field Divertor Method
ii) Armature Divertor Method
iii) Tapped Field Method
iv) Series-Parallel Connection of Field

Chapter Four
i) Field Divertor
In this method the series field winding is shunted by a variable resistance (Rx) known
as field divertor.
Due to the parallel path of Rx , by adjusting the value of Rx, any amount of current
can be diverted through the divertor.
Hence current through the field winding can be adjusted as per the requirement. Due
to this, the flux gets controlled and hence the speed of the motor gets controlled.
By this method the speed of the motor can be controlled above rated value.

Chapter Four
Cont...
Figure 26: Field Divertor method

Chapter Four
ii) Armature Divertor
This method is used for the motor which require constant load torque.
An armature of the motor is shunted with an external variable resistance (Rx) is
called armature divertor as shown in Figure 27.
Any amount of armature current can be diverted through the divertor. Due to this ,
armature current reduces.
But as T ∝ ϕIa and load torque is constant, the flux is to be increased.
So current through field winding increases, so flux increases and speed of the motor
reduces.
The method is used to control the speed below the normal value.

Chapter Four
Cont..
Figure 27: Armature Divertor

Chapter Four
iii) Tapped Field Control
Flux change is achieved by changing the number of turns of the field winding. The
field winding is provided with the taps as shown in Fig 28.
The selector switch ’S’ is provided to select the number of turns (taps) as per the
requirement. When the switch ’S’ is in position 1 the entire filed winding is in the
circuit and motor runs with normal speed.
As switch is moved from position 1 to 2 and onwards, the number of turns of the field
winding in the circuit decreases.
Due to this mmf require to produce the flux, decreases. Due to this flux produced
decreases, increasing the speed of the motor above rated value.
The method is often used in electric traction.

Chapter Four
Cont...
Figure 28: Tapped Field Control

Chapter Four
iv) Series - Parallel Connection of Field
In this method, the field coil is divided into various parts. These parts can then be
connected in series or parallel as per the requirement.
For the same torque, if the field coil is arranged in series or parallel, mmf produced
by the coils changes, hence the flux produced also changes. Hence speed can be
controlled.
Some fixed speeds only can be obtained by parallel grouping, the mmf produced
decreases, hence higher speed can be obtained by parallel grouping.
The method is generally used in case of fan motors.

Chapter Four
Cont...
Figure 29: Series connection of field Figure 30: Parallel connection of field

Chapter Four
2. Rheostatic Control
In this method, a variable resistance (Rx) is inserted in series with the motor circuit.
As this resistance is inserted, the voltage drop across this resistance ( IaRx) occurs.
This reduces the voltage across the armature.
As speed is directly proportional to the voltage across the armature, the speed
reduces.
As entire current passes through Rx, there is large power loss (figure 31) .
The speed vs armature current characteristics with changes in Rx are shown in
Figure 32.

Chapter Four
Cont...
Figure 31: Rheostatic Control Figure 32: speed vs armature current

Chapter Four
3. Applied Voltage Control
In this method, a series motor is excited by the voltage obtained by a series generator
as shown in Figure 33.
The generator is driven by a suitable prime mover.
The voltage obtained from the generator is controlled by a field divertor resistance
connected across series field winding of the generator.
As Eg ∝ ϕ, the flux change is achieved, gives the variable voltage at the output
terminals.
Due to the change in the supply voltage, the various speeds of the dc series motor can
be obtained.

Chapter Four
Cont...
Figure 33: Applied Voltage Control

Chapter Four
General steps to solve problems on speed control
1 Identify the method of speed control i.e. in which of the motor, the external
resistance is to be inserted.
2 Use the torque equation, T ∝ ϕIa to determine the new armature current according
to the condition of the torque given. Load condition indicates the condition of the
torque.
3 Use the speed equation N ∝ Eb
ϕ to find the unknown back emf or field current.
4 From the term calculated above and using voltage current relationship of the motor,
the value of extra resistance to be added, can be determined.
Note!
The above steps may vary little bit according to the nature of the problem but are
always the base of any speed control problem.

Chapter Four
Applications of DC Motors
DC Shunt motor has fairly constant speed and medium starting torque.
Blowers and fans
Centrifugal and reciprocating pumps
Lathe machines
Machine tools
Milling machines
Drilling machines
DC series motors has high starting torque, no load condition is dangerous, variable speed
Electric trains
Cranes, hoists
Elevators
Trolley cars and trolley buses
Conveyors
Locomotives

Chapter Four
Cont...
Cumulative compound motor has high starting torque, no load condition is allowed
Rolling mills
Punches
Shears
Conveyors
Heavy planners
elevators
Differential Compund motors : speed increases as load increases.
They are not suitable for any practical applications
Employed for experimental and research work

Chapter Four
Questions
Thank You!

DC Motors

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