Direct Current (D.C) Machines

1. DDKKTT 221133
CCHHAAPPTTEERR 44
Introduction to DC
Machine

2. Contents
– Overview of Direct Current Machines
– Construction
– Principle of Operation
– Types of DC Machine
– Power Flow Diagram
– Speed Control

3. LEARNING OBJECTIVES
• Upon completion of the chapter the student
should be able to:
– State the principle by which machines convert
mechanical energy to electrical energy.
– Discuss the operating differences between different
types of generators
– Understand the principle of DC generator as it
represents a logical behavior of dc motors.

4. Overview of Direct Current
Machines
• Direct-current (DC) machines are divided into dc generators and dc
motors.
• Most DC machines are similar to AC machines: i.e. they have AC
voltages and current within them.
• 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 automobile, aircraft, and
portable electronics, in speed control applications…

5. DC Generator
• A dc generator is a machine that converts
mechanical energy into electrical energy
(dc voltage and current) by using the
principle of magnetic induction.
• In this example, the ends of the wire loop
have been connected to two slip rings
mounted on the shaft, while brushes are
used to carry the current from the loop to
the outside of the circuit.
Principle of magnetic induction in DC machine

6. DC Motor
• DC motors are everywhere! In a house, almost every mechanical
movement that you see around you is caused by an DC (direct
current) motor.
• An dc motor is a machine that converts electrical energy into
mechanical energy by supplying a dc power (voltage and current).
• An advantage of DC motors is that it is easy to control their speed in
a wide diapason.

7. Construction of DC machine
Cutaway view of a dc motor Stator with poles visible.

8. Construction of DC machine
segments
brushes
Rotor of a dc motor.

9. Construction of DC machine
Rotor is the rotating part - armature
Stator is the stationary part - field
Stator: non-moving coil
Rotor: rotating part
Armature coil
BBrruusshheess

10. ARMATURE
• More loops of wire = higher rectified voltage
• In practical, loops are generally placed in slots of an iron core
• The iron acts as a magnetic conductor by providing a low-reluctance path for
magnetic lines of flux to increase the inductance of the loops and provide a
higher induced voltage.
• The commutator is connected to the slotted iron core.
• The entire assembly of iron core, commutator, and windings is called the
armature.
• The windings of armatures are connected in different ways depending on the
requirements of the machine.
Loops of wire are wound around slot in a metal core DC machine armature

11. ARMATURE WINDINGS
• Lap Wound Armatures
– are used in machines designed for low voltage and high current
– armatures are constructed with large wire because of high current
– Eg: - are used is in the starter motor of almost all automobiles
– The windings of a lap wound armature are connected in parallel.
This permits the current capacity of each winding to be added and
provides a higher operating current
– No of current path, A=P

12. ARMATURE WINDINGS (Cont)
• Wave Wound Armatures
– are used in machines designed for high voltage and low current
– their windings connected in series
– When the windings are connected in series, the voltage of each
winding adds, but the current capacity remains the same
– are used is in the small generator in hand-cranked megohmmeters
– No of current path, A=2

13. FIELD WINDINGS
• Most DC machines use wound electromagnets to
provide the magnetic field.
• Two types of field windings are used :
– series field
– shunt field

14. FIELD WINDINGS (Cont)
• Series field windings
– are so named because they are connected in series with the
armature
– are made with relatively few windings turns of very large wire and
have a very low resistance
– usually found in large horsepower machines wound with square or
rectangular wire.
– The use of square wire permits the windings to be laid closer
together, which increases the number of turns that can be wound in
a particular space

15. FIELD WINDINGS (Cont)
– Square and rectangular wire can also be made physically smaller than
round wire and still contain the same surface area
Square wire contains more surface than round wire
Square wire permits more turns than round wire in the same area

16. FIELD WINDINGS (Cont)
• Shunt field windings
– is constructed with relatively many turns of small wire, thus, it
has a much higher resistance than the series field.
– is intended to be connected in parallel with, or shunt, the
armature.
– high resistance is used to limit current flow through the field.

17. FIELD WINDINGS (Cont)
• When a DC machine uses both series and shunt fields, each pole
piece will contain both windings.
• The windings are wound on the pole pieces in such a manner that
when current flows through the winding it will produce alternate
magnetic polarities.

18. MACHINE WINDINGS
OVERVIEW
Winding
armature field
Lap
A=P
Wave
A=2
Separately
Excited
Frogleg
Self excited
series shunt compound

19. Principle operation of Generator
• Whenever a conductor is moved within a
magnetic field in such a way that the conductor
cuts across magnetic lines of flux, voltage is
generated in the conductor.
• The AMOUNT of voltage generated depends on:
i. the strength of the magnetic field,
ii. the angle at which the conductor cuts the magnetic
field,
iii. the speed at which the conductor is moved, and
iv. the length of the conductor within the magnetic field

20. Principle of operation (Cont)

21. Fleming’s Right hand rule
(Generator Rule)
• Use: To determine the direction of the induced emf/current of a
conductor moving in a magnetic field.
• The POLARITY of the voltage depends on the direction of the
magnetic lines of flux and the direction of movement of the
conductor.

22. THE ELEMENTARY
GENERATOR
• The simplest elementary generator that can be
built is an ac generator.
• Basic generating principles are most eeaassiillyy
eexxppllaaiinneedd through the use of the elementary ac
generator.
• For this reason, the ac generator will be
discussed first. The dc generator will be
discussed later.
• An elementary generator ccoonnssiissttss ooff aa wwiirree lloooopp
mmoouunntteedd oonn tthhee sshhaafftt,, ssoo tthhaatt iitt ccaann bbee rroottaatteedd iinn
aa ssttaattiioonnaarryy mmaaggnneettiicc ffiieelldd.
• This will pprroodduuccee aann iinndduucceedd eemmff iinn tthhee lloooopp.
• Sliding contacts ((bbrruusshheess)) ccoonnnneecctt tthhee lloooopp ttoo aann
eexxtteerrnnaall cciirrccuuiitt llooaadd iinn oorrddeerr ttoo ppiicckk uupp oorr uussee tthhee
iinndduucceedd eemmff..
Elementary Generator

23. THE ELEMENTARY GENERATOR (Cont)
• The pole pieces (marked N and S) provide tthhee mmaaggnneettiicc ffiieelldd. The
pole pieces are shaped and positioned as shown to concentrate the
magnetic field as close as possible to the wire loop.
• TThhee lloooopp ooff wwiirree tthhaatt rroottaatteess tthhrroouugghh tthhee ffiieelldd iiss ccaalllleedd tthhee
AARRMMAATTUURREE. TThhee eennddss ooff tthhee aarrmmaattuurree lloooopp aarree ccoonnnneecctteedd ttoo rriinnggss
ccaalllleedd SSLLIIPP RRIINNGGSS. They rotate with the armature.
• The brushes, usually made of carbon, with wires attached to them,
ride against the rings. TThhee ggeenneerraatteedd vvoollttaaggee aappppeeaarrss aaccrroossss tthheessee
bbrruusshheess.. ((TThheessee bbrruusshheess ttrraannssffeerr ppoowweerr ffrroomm tthhee bbaatttteerryy ttoo tthhee
ccoommmmuuttaattoorr aass tthhee mmoottoorr ssppiinnss –– ddiissccuusssseedd llaatteerr iinn ddcc eelleemmeennttaarryy
ggeenneerraattoorr))..

24. THE ELEMENTARY GENERATOR (A)
• An end view of the shaft and wire
loop is shown.
• At this particular instant, the loop of
wire (the black and white conductors
of the loop) is parallel to the
magnetic lines of flux, and no cutting
action is taking place.
• Since the lines of flux are not being
cut by the loop, no emf is induced in
the conductors, and the meter at this
position indicates zero.
• This position is called the NEUTRAL
PLANE.
00 Position (Neutral Plane)

25. THE ELEMENTARY GENERATOR (B)
• TThhee sshhaafftt hhaass bbeeeenn ttuurrnneedd 990000 cclloocckkwwiissee,, tthhee
ccoonndduuccttoorrss ccuutt tthhrroouugghh mmoorree aanndd mmoorree lliinneess ooff
fflluuxx,, aanndd vvoollttaaggee iiss iinndduucceedd iinn tthhee ccoonndduuccttoorr..
• aatt aa ccoonnttiinnuuaallllyy iinnccrreeaassiinngg aannggllee ,, tthhee iinndduucceedd
eemmff iinn tthhee ccoonndduuccttoorrss bbuuiillddss uupp ffrroomm zzeerroo ttoo aa
mmaaxxiimmuumm vvaalluuee oorr ppeeaakk vvaalluuee..
• OObbsseerrvvee tthhaatt ffrroomm 0000 ttoo 990000,, tthhee bbllaacckk ccoonndduuccttoorr
ccuuttss DDOOWWNN tthhrroouugghh tthhee ffiieelldd..
• AAtt tthhee ssaammee ttiimmee tthhee wwhhiittee ccoonndduuccttoorr ccuuttss UUPP
tthhrroouugghh tthhee ffiieelldd..
• TThhee iinndduucceedd eemmffss iinn tthhee ccoonndduuccttoorrss aarree sseerriieess--
aaddddiinngg..
• TThhiiss mmeeaannss tthhee rreessuullttaanntt vvoollttaaggee aaccrroossss tthhee
bbrruusshheess ((tthhee tteerrmmiinnaall vvoollttaaggee)) iiss tthhee ssuumm ooff tthhee
ttwwoo iinndduucceedd vvoollttaaggeess..
• TThhee mmeetteerr aatt ppoossiittiioonn BB rreeaaddss mmaaxxiimmuumm vvaalluuee..
900 Position

26. THE ELEMENTARY GENERATOR (C)
• After another 900 of rotation, the loop
has completed 1800 of rotation and is
again parallel to the lines of flux.
• As the loop was turned, the voltage
decreased until it again reached zero.
• Note that : From 00 to 1800 the
conductors of the armature loop have
been moving in the same direction
through the magnetic field.
• Therefore, the polarity of the induced
voltage has remained the same
1800 Position

27. THE ELEMENTARY GENERATOR (D)
• As the loop continues to turn, the
conductors again cut the lines of magnetic
flux.
• This time, however, the conductor that
previously cut through the flux lines of the
south magnetic field is cutting the lines of
the north magnetic field, and vice-versa.
• Since the conductors are cutting the flux
lines of opposite magnetic polarity, the
polarity of the induced voltage reverses.
• After 270' of rotation, the loop has rotated to
the position shown, and the maximum
terminal voltage will be the same as it was
from A to C except that the polarity is
reversed. 2700 Position

28. THE ELEMENTARY GENERATOR (A)
• After another 900 of rotation, the loop
has completed one rotation of 3600
and returned to its starting position.
• The voltage decreased from its
negative peak back to zero.
• Notice that the voltage produced in
the armature is an alternating polarity.
The voltage produced in all rotating
armatures is alternating voltage.
3600 Position

29. Elementary Generator (Conclusion)
• Observes
– The meter direction
– The conductors of the armature loop
– Direction of the current flow

30. THE ELEMENTARY DC GENERATOR
• Since DC generators must produce DC current
instead of AC current, a device must be used to
change the AC voltage produced in the armature
windings into DC voltage.
• This job is performed by the ccoommmmuuttaattoorr..
• The commutator is constructed from a copper
ring split into segments with insulating material
between the segments (See next page).
• Brushes riding against the commutator segments
carry the power to the outside circuit.
• The commutator in a dc generator replaces the
slip rings of the ac generator. This is the main
difference in their construction.
• The commutator mechanically reverses the
armature loop connections to the external circuit.

31. THE ELEMENTARY DC GENERATOR
(Armature)
• The armature has an axle, and the commutator
is attached to the axle.
• In the diagram to the right, you can see three
different views of the same armature: ffrroonntt,,
ssiiddee aanndd eenndd--oonn..
• In the end-on view, the winding is eliminated to
make the commutator more obvious.
• We can see that the commutator is ssiimmppllyy aa
ppaaiirr ooff ppllaatteess aattttaacchheedd ttoo tthhee aaxxllee.
• TThheessee ppllaatteess pprroovviiddee tthhee ttwwoo ccoonnnneeccttiioonnss ffoorr
tthhee ccooiill ooff tthhee eelleeccttrroommaaggnneett..
Armature with commutator view

32. THE ELEMENTARY DC GENERATOR
(Commutator & Brushes work together)
• The diagram at the right shows hhooww tthhee ccoommmmuuttaattoorr aanndd
bbrruusshheess wwoorrkk ttooggeetthheerr ttoo lleett ccuurrrreenntt ffllooww ttoo tthhee
eelleeccttrroommaaggnneett, and also to flip the direction that the
electrons are flowing at just the right moment.
• TThhee ccoonnttaaccttss ooff tthhee ccoommmmuuttaattoorr aarree aattttaacchheedd ttoo tthhee aaxxllee
ooff tthhee eelleeccttrroommaaggnneett,, ssoo tthheeyy ssppiinn wwiitthh tthhee mmaaggnneett..
• TThhee bbrruusshheess aarree jjuusstt ttwwoo ppiieecceess ooff sspprriinnggyy mmeettaall oorr
ccaarrbboonn tthhaatt mmaakkee ccoonnttaacctt wwiitthh tthhee ccoonnttaaccttss ooff tthhee
ccoommmmuuttaattoorr..
• Through this process the commutator changes the
generated ac voltage to a pulsating dc voltage which also
known as commutation process.
Brushes and commutator

33. THE ELEMENTARY DC
GENERATOR
• The loop is parallel to the magnetic
lines of flux, and no voltage is
induced in the loop
• Note that the brushes make
contact with both of the
commutator segments at this time.
The position is called neutral
plane.
00 Position (DC Neutral Plane)

34. THE ELEMENTARY DC
GENERATOR
• As the loop rotates, the conductors
begin to cut through the magnetic lines
of flux.
• The conductor cutting through the
south magnetic field is connected to
the positive brush, and the conductor
cutting through the north magnetic field
is connected to the negative brush.
• Since the loop is cutting lines of flux, a
voltage is induced into the loop.
• After 900 of rotation, the voltage
reaches its most positive point. 900 Position (DC)

35. THE ELEMENTARY DC
GENERATOR
• As the loop continues to rotate,
the voltage decreases to zero.
• After 1800 of rotation, the
conductors are again parallel to
the lines of flux, and no voltage is
induced in the loop.
• Note that the brushes again
make contact with both segments
of the commutator at the time
when there is no induced voltage
in the conductors 1800 Position (DC)

36. THE ELEMENTARY DC
GENERATOR
• During the next 900 of rotation, the conductors again
cut through the magnetic lines of flux.
• This time, however, the conductor that previously
cut through the south magnetic field is now cutting
the flux lines of the north field, and vice-versa. .
• Since these conductors are cutting the lines of flux
of opposite magnetic polarities, the polarity of
induced voltage is different for each of the
conductors. The commutator, however, maintains
the correct polarity to each brush.
• The conductor cutting through the north magnetic
field will always be connected to the negative brush,
and the conductor cutting through the south field will
always be connected to the positive brush.
• SSiinnccee tthhee ppoollaarriittyy aatt tthhee bbrruusshheess hhaass rreemmaaiinneedd
ccoonnssttaanntt,, tthhee vvoollttaaggee wwiillll iinnccrreeaassee ttoo iittss ppeeaakk vvaalluuee
iinn tthhee ssaammee ddiirreeccttiioonn..
2700 Position (DC)

37. THE ELEMENTARY DC
GENERATOR
• As the loop continues to rotate, the
induced voltage again decreases to zero
when the conductors become parallel to
the magnetic lines of flux.
• Notice that during this 3600 rotation of the
loop the polarity of voltage remained the
same for both halves of the waveform.
This is called rectified DC voltage.
• The voltage is pulsating. It does turn on
and off, but it never reverses polarity.
Since the polarity for each brush remains
constant, the output voltage is DC.
00 Position (DC Neutral Plane)

38. THE ELEMENTARY DC
GENERATOR
• Observes
– The meter direction
– The conductors of the armature loop
– Direction of the current flow

39. Effects of additional turns
• To increase the amount of output voltage, it is
common practice to increase the number of
turns of wire for each loop.
• If a loop contains 20 turns of wire, the induced
voltage will be 20 times greater than that for a
single-loop conductor.
• The reason for this is that each loop is
connected in series with the other loops. Since
the loops form a series path, the voltage
induced in the loops will add.
• In this example, if each loop has an induced
voltage of 2V, the total voltage for this winding
would be 40V
(2V x 20 loops = 40 V).
Effects of additional turns

40. Effects of additional coils
• When more than one loop is used, the average
output voltage is higher and there is less
pulsation of the rectified voltage.
• Since there are four segments in the
commutator, a new segment passes each
brush every 900 instead of every 1800.
• Since there are now four commutator segments
in the commutator and only two brushes, the
voltage cannot fall any lower than at point A.
• Therefore, the ripple is limited to the rise and
fall between points A and B on the graph. By
adding more armature coils, the ripple effect
can be further reduced. Decreasing ripple in
this way increases the effective voltage of
the output.
Effects of additional coils

41. The Practical DC Generator
• The actual construction and operation of a practical
dc generator differs somewhat from our elementary
generators
• Nearly all practical generators use electromagnetic
poles instead of the permanent magnets used in our
elementary generator
• The main advantages of using electromagnetic poles
are:
(1) increased field strength and
(2) possible to control the strength of the
fields. By varying the input voltage, the
field strength is varied. By varying the field
strength, the output voltage of the generator
can be controlled.
Four-pole generator (without armature)

42. DC Motor Operation
• In a dc motor, the stator
poles are supplied by dc
excitation current, which
produces a dc magnetic
field.
• The rotor is supplied by dc
current through the
brushes, commutator and
coils.
• The interaction of the
magnetic field and rotor
current generates a force
that drives the motor

43. DC Motor Operation
• The magnetic field lines enter
into the rotor from the north
pole (N) and exit toward the
south pole (S).
• The poles generate a
magnetic field that is
perpendicular to the current
carrying conductors.
• The interaction between the
field and the current produces
a Lorentz force,
• The force is perpendicular to
both the magnetic field and
conductor
v B
a
Vdc S 30 N
1 2
v
b
Ir_dc
(a) Rotor current flow from segment 1 to 2 (slot a to b)
a
B
S N v 30 v
Vdc
b
1 2
Ir_dc
(b) Rotor current flow from segment 2 to 1 (slot b to a)

44. DC Motor Operation
• The generated force turns the
rotor until the coil reaches the
neutral point between the poles.
• At this point, the magnetic field
becomes practically zero together
with the force.
• However, inertia drives the motor
beyond the neutral zone where the
direction of the magnetic field
reverses.
• To avoid the reversal of the force
direction, the commutator changes
the current direction, which
maintains the counterclockwise
rotation.
v B
a
Vdc S 30 N
1 2
v
b
Ir_dc
(a) Rotor current flow from segment 1 to 2 (slot a to b)
a
B
S N v 30 v
Vdc
b
1 2
Ir_dc
(b) Rotor current flow from segment 2 to 1 (slot b to a)

45. DC Motor Operation
• Before reaching the neutral zone,
the current enters in segment 1
and exits from segment 2,
• Therefore, current enters the coil
end at slot a and exits from slot
b during this stage.
• After passing the neutral zone,
the current enters segment 2
and exits from segment 1,
• This reverses the current
direction through the rotor coil,
when the coil passes the neutral
zone.
• The result of this current reversal
is the maintenance of the
rotation.
v B
a
Vdc S 30 N
1 2
v
b
Ir_dc
(a) Rotor current flow from segment 1 to 2 (slot a to b)
a
B
S N v 30 v
Vdc
b
1 2
Ir_dc
(b) Rotor current flow from segment 2 to 1 (slot b to a)

46. DC Machine Equivalent Circuit

47. DC Machine Equivalent Circuit
• The magnetic field produced by the stator poles induces a
voltage in the rotor (or armature) coils when the generator
is rotated.
• This induced voltage is represented by a voltage source.
• The stator coil has resistance, which is connected in
series.
• The pole flux is produced by the DC excitation/field
current, which is magnetically coupled to the rotor
• The field circuit has resistance and a source
• The voltage drop on the brushes represented by a battery

48. DC Machine Equivalent Circuit
1. Permanent magnet
2. Separately excited
3. Self-excited

49. DC Machine Equivalent Circuit
1. Permanent magnet
• The poles are made of permanent magnets.
• No field winding required.
• Small size.
• Disadvantage is low flux density, so low torque.

50. DC Machine Equivalent Circuit
2. Separately excited
The field flux is derived from a separate power source
independent of the generator itself.
B
Field
winding
Armature
winding

51. DC Machine Equivalent Circuit
3. Self-excited
• Shunt machine
The field flux is derived by
connecting the field directly
across the terminals of the
generator.
B

52. DC Machine Equivalent Circuit
3. Self-excited
Series machine
• field are connected in
series with armature
B

53. DC Machine Equivalent Circuit
3. Self-excited
• Cumulatively compounded
B B
• Differentially compounded
B B

54. DC Machine Equivalent Circuit
3. Self-excited
Compounded dc generator
• both a shunt and a series field are
present

55. DC Machine Equivalent Circuit
3. Self-excited
Compounded dc motor
• both a shunt and a series
field are present

56. Equivalent circuit of a DC
motor
The armature circuit (the entire
rotor structure) is represented by
an ideal voltage source EA and a
resistor RA. A battery Vbrush in the
opposite to a current flow in the
machine direction indicates brush
voltage drop.
The field coils producing the
magnetic flux are represented by
inductor LF and resistor RF. The
resistor Radj represents an
external variable resistor
(sometimes lumped together with
the field coil resistance) used to
control the amount of current in
the field circuit.

57. DC Motor Equivalent Circuit.
 The armature is represented by an ideal voltage source EA and a
resistor RA.
 The brush voltage drop is represented by a small battery Vbrush
opposing the direction of the current flow in the machine.
 The field coils, which produce the magnetic flux, are represented
by inductor LF and RF.
 The separate resistor Radj represents an external variable resistor
used to control the amount of current in the field circuit.
Equivalent Circuit of a DC Motor.

58.  The brush drop voltage is often only a very tiny fraction of the
generated voltage in the motor.
 Therefore, in cases where it is not critical, the brush drop voltage
may be left out or approximately included in the value of RA.
 Also, the internal resistance of the filed coils is sometimes lumped
together with the variable resistor, and the total is called RF , Figure
below.
A Simplified Equivalent Circuit eliminating the Brush Voltage
Drop and Combining Radj with the Field Resistance .

59. Motor types: Separately Excited DC motors.
The Equivalent Circuit of Separately Excited dc Motor.
From the above figure,
F
F
I = V
F R
T A A A V = E + I R
L A I = I
Separately excited DC motor:
a field circuit is supplied from a
separate constant voltage power
source.

60. Motor types: Shunt DC motors.
The Equivalent Circuit of a Shunt dc Motor.
Shunt DC motor:
a field circuit gets its power from the
armature terminals of the motor.
 From the above figure,
F
F
I = V
F R
T A A A V = E + I R
L A F I = I + I

61. Motor types: The permanent-magnet
DC motor
A permanent magnet DC (PMDC) motor is a motor whose poles are
made out of permanent magnets.
Advantages:
1. Since no external field circuit is needed, there are no field circuit copper
losses;
2. Since no field windings are needed, these motors can be considerable
smaller.
Disadvantages:
1. Since permanent magnets produces weaker flux
densities then externally supported shunt fields,
such motors have lower induced torque.
2. There is always a risk of demagnetization from
extensive heating or from armature reaction
effects (via armature mmf).

62. Motor types: The series DC
motor
A series DC motor is a DC motor whose field windings consists of a
relatively few turns connected in series with armature circuit. Therefore:
T A A ( A S ) V = E + I R + R

63. Motor types: Compounded DC
motor
A compounded DC motor is a motor with both a shunt and a series field.
Long-shunt
connection
Short-shunt
connection
Current flowing into a dotted
end of a coil (shunt or series)
produces a positive mmf.
If current flows into the
dotted ends of both coils, the
resulting mmfs add to
produce a larger total mmf –
cumulative compounding.
If current flows into the dotted end of
one coil and out of the dotted end of
another coil, the resulting mmfs
subtract – differential compounding.

64. Motor types: Compounded DC
motor
The Kirchhoff’s voltage law equation for a compounded DC motor is
The currents in a compounded DC motor are
I = V
T
The mmf of a compounded DC motor: Cumulatively compounded
Differentially compounded
The effective shunt field current in a compounded DC motor:
Number of turns
(5.85.1)
(5.85.2)
(5.85.3)
(5.85.4)
(5.85.5)
T A A ( A S ) V = E + I R + R
A L F I = I - I
F
F R
net F SE AR F = F ± F - F
AR
F
I * = I + N -
F F A
N
SE
F
I F
N

65. Torque Equation
A A T = k fI
T = torque of armature (N-m)
kA = geometry constant
f= flux/pole (Wb)
IA = armature current (A)

66. Geometry Constant
k pN A A = =
rad s k pN
' rpm
( )
60
( / ),
p
2
M
M
p = number of field poles
N = number of active conductors on armature
M = number of parallel paths in armature winding (=p for
lap winding, =2 for wave winding)

67. Power Equation
P EI Tw A = =
P=power (W) – not counting losses
E = EMF induced in armature (back EMF)
IA = armature current (A)
T = torque of armature (N-m)
w = speed of rotation (rad/s)
Note that Pin = VLIL which will be higher than P because
of loss in the field and armature windings as well as
rotational (friction) losses.

68. EMF Equation
E k k n A A= fw = 'f p
E = EMF induced in armature (V)
kA = geometry constant
f= flux/pole (Wb)
w = speed of rotation (rad/s)
n = speed of rotation of armature (rpm)
w
2
n = 60

69. Terminal Voltage Equation
T A A V = E + I R
E VT
VT = voltage at motor terminals
E = EMF induced in armature (V)
IA = armature current (A)
RA = armature resistance
+
-
+
-
RA

70. Speed Equation
n = V - I R
T A A
k
f 'A
(applies to shunt connected motor only)
Note that f can also be written as kfIf where kf is
f/If (normally a constant ratio)
Ratio Equation
2
1
n 2
=
1
E
E
n

71. Speed-Torque
Torque
Speed
Differential Compound
Series
Shunt
Cumulative Compound

72. Power flow and losses in DC
machines
Unfortunately, not all electrical power is converted to mechanical power by a motor
and not all mechanical power is converted to electrical power by a generator…
The efficiency of a DC machine is:
or
x100%
P
in
h = out
P P
in loss h = -
P
in
x100%
P

73. The losses in DC machines
There are five categories of losses occurring in DC machines.
1. Electrical or copper losses – the resistive losses in the armature and field
windings of the machine.
Armature loss:
Field loss:
A A A P = I 2R
F F F P = I 2R
Where IA and IF are armature and field currents and RA and RF are armature and
field (winding) resistances usually measured at normal operating temperature.

74. The losses in DC machines
2. Brush (drop) losses – the power lost across the contact potential at the
brushes of the machine.
BD BD A P =V I
Where IA is the armature current and VBD is the brush voltage drop. The voltage drop
across the set of brushes is approximately constant over a large range of armature
currents and it is usually assumed to be about 2 V.
Other losses are exactly the same as in AC machines…

75. The losses in DC machines
3. Core losses – hysteresis losses and eddy current losses. They vary as B2
(square of flux density) and as n1.5 (speed of rotation of the magnetic field).
4. Mechanical losses – losses associated with mechanical effects: friction
(friction of the bearings) and windage (friction between the moving parts of the
machine and the air inside the casing). These losses vary as the cube of rotation
speed n3.
5. Stray (Miscellaneous) losses – losses that cannot be classified in any of the
previous categories. They are usually due to inaccuracies in modeling. For many
machines, stray losses are assumed as 1% of full load.

76. The power-flow diagram
On of the most convenient technique to account for power losses in a
machine is the power-flow diagram.
For a DC
motor:
Electrical power is input to the machine, and the electrical and brush losses must be
subtracted. The remaining power is ideally converted from electrical to mechanical
form at the point labeled as Pconv.

77. The power-flow diagram
The electrical power that is converted is
conv A A P = E I
And the resulting mechanical power is
conv ind m P =t w
After the power is converted to mechanical form, the stray losses, mechanical
losses, and core losses are subtracted, and the remaining mechanical power is
output to the load.

78. Example 1
A 6 pole, 3.0 hp 120V DC lap-wound shunt motor has 960 conductors
in the armature. It takes 25.0 A from the supply at full load.
Armature resistance is 0.75W, flux/pole=10.0 mWb, field winding
current is 1.20A. Find the speed and torque.
÷ ÷ø P 3hp æ
746W ö
= 2.24 I I I A A A A L F = - = 25 -1.2 = 23.8
E V I R V ( A)( ) V T A A = - =120 - 23.8 0.75W =102
( 6 )( 960
)
( )( ) 153
K pN A
= = =
2
pM 2 p
6
V
102
( )( ) rad s
3 = = =
x
E K
A
E
K
A
66.9 /
153 10 10
=
f -
w
fw
60 = ÷ø
ö çè
n 638rpm
2
= æ
p
w
( ) kW
hp
ç çè
=
T = P = kW = 33.5 ×
N m
2.24
rad s
66.9 /
w

79. Example 2
A 10hp, 115V Dc series motor takes 40A at its full load speed of
1800rpm. What is the torque at 30A?
n ( ) 188rad / s
w = 2p = 2 p 1800
=
60
60
÷ ÷ø P 10hp æ
746W ö
= 7.46 ( ) kW
hp
ç çè
=
P T
= = = ×
N m
w
T P 7.46
kW
rad s
=
39.6
188 /
w
A A A F F A T = K fI = K K I I
F A I = I
2
A F A T = K K I
N m
K K T
= = 39.6
× =
2 2 ( ) 0.025
40
A
I
A
A F
T K K I ( )( A) N m new A F Anew = 2 = 0.025 30 2 = 22.2 ×

80. Example 3 (a)
A 220V DC shunt motor draws 10A at 1800rpm. The armature
resistance is 0.2W and field winding resistance is 440W.
(a) What is the torque?
V A
I V
220 =
T
0.5
F R
F
W
440
= =
I I I A A A A L F = - =10 - 0.5 = 9.5
E V I R V ( A)( ) V T A A = - = 220 - 9.5 0.2W = 218
P EI ( V )( A) kW A = = 218 9.5 = 2.07
( ) n 188rad / s
w = 2p = 2 p 1800
=
60
60
T = P = kW =11.0 ×
N m
2.07
rad s
188 /
w

81. Example 3 (b)
A 220V DC shunt motor draws 10A at 1800rpm. The armature
resistance is 0.2W and field winding resistance is 440W.
(b) What will be the speed and line current at a torque of 20 N-m (if
field current is constant)?
1.16
K E V
= = 218 =
188 /
=
rad s
E K
A
A
w
f
fw
N m A
T K f
I
I T
= = 20 × =
K
A
A
A A
17.3
1.16
=
f
I I I A A A L A F = + =17.3 + 0.5 =17.8
E V I R V ( )( ) V T A A = - = 220 - 17.3 0.2W = 217
V rad s
E
A
= = =
K
217
1.79 103
f
w
60
n x rpm
2
187 /
1.16
= =
p
w
(shunt is constant speed)