Direct-current (DC) machines have a stationary stator and a rotating rotor. DC machines can operate as motors or generators. In a DC machine, the magnetic field produced by the stationary field winding is perpendicular to the magnetic field produced by the rotating armature winding, allowing torque to be produced. Separately excited DC machines have independent field and armature windings, allowing control of speed and torque. The dynamic behavior and torque production of DC machines can be modeled using circuit equations that relate the flux linkages and currents in the field and armature windings.

1. Direct-Current Machine

2. Electric Machine
 Electric machines can be used as motors and
generators
 Electric motor and generators are rotating energy-
transfer electromechanical motion devices
 Electric motors convert electrical energy to
mechanical energy
 Generators convert mechanical energy to electrical
energy

3. Electric Machine
 Electric machines can be divided into 2 types:
 AC machines
 DC machines
 Several types DC machines
 Separately excited
 Shunt connected
 Series connected
 Compound connected
 Permanent magnet

4. Electric Machine
 All Electric machines have:
 Stationary members (stator)
 rotating members (rotor)
 Air gap which is separating stator and rotor
 The rotor and stator are coupled magnetically

5.  Schematic representation of a DC
Machine
DC Machines
StatorStator
RotorRotor
+
VVff
-
If
If
If
NN
ΦΦff
22
SS

6. Electric Machine
 The armature winding is placed in the rotor
slot and connected to rotating commutator
which rectifies the induced voltage
 The brushes which are connected to the
armature winding, ride on commutator

7. DC Machines
 Elementary two-pole DC Machine

8. Electric Machine
 The armature winding consists of identical coils carried in
slots that are uniformly distributed around the periphery of the
rotor
 Conventional DC machines are excited by direct current, in
particular if a voltage-fed converter is used a dc voltage uf is
supplied to the stationary field winding
 Hence the excitation magnetic field is produced by the field
coils
 Due to the commutator, armature and field windings produce
stationary magnetomotive forces that are displaced by 90
electrical degrees

9.  The field winding is placed on the stator
and supplied from a DC Source.
DC Machines
RotorRotor
NN
ΦΦff
22SS
x
x
x
x x
x
x
x
ArmatureArmature
WindingWinding

10. Magnetic Flux in DC machines
Φf/2
rotor
stator
If
SS
NN
Vf
+
-
.. .. ..
x
x
x x x
x
Armature
Winding
If
Φa

11.  The current is induced in the RotorRotor
WindingWinding (i.e. the Armature WindingArmature Winding)
since it is placed in the field (Flux
Lines) of the Field Winding.
DC Machines
ΦΦff

12.  mmf produced by the armature and mmf
produced by the field winding are
orthogonal.
Orthogonality of Magnetic Fields in
DC Machines
B
IL F( )o
ILBL 90sin=×= BIF
Magnetic field due to
field winding
Magnetic field due to
armature winding
90o

13.  The force acting on the rotor, is
expressed as
DC Machines
 
Fieldthe
toDue
Armaturethe
toDue
BLIf ×=
ll
ff
ff
TTee
TTee = xff ll

14.  The Field winding is placed on the stator
and the current (voltage) is induced in
the rotor winding which is referred also
as the armature winding.
 In DC Machines, the mmfmmf produced by
the field winding and the mmfmmf produced
by the armature winding are at right-
angle with respect to each other.
 The torque is produced from the
interaction of these two fields.
DC Machines

17. Transducer with stator and rotor windings

18. Equivalent circuit for separately excited DC motors
SEPARATELY EXCITED DC MOTORS

19. Electric Machine
 Conventional separately excited DC electric machine
 Stator and rotor windings excited by dc current
 The rotor has the commutator
 Dc voltage to the armature windings is supplied through the
brushes which establish electric contact with the commutator
 The brushes are fixed with respect to the stator and they are placed
in the specified angular displacement
 To maximize the electromagnetic torque, the stator and rotor
magnetic axes are displaced by 90 electrical degrees using a
commutator
rrssre iiLT θsin−=

20. Electric Machine
 Electric machine can be either a motor or a generator
depending on whether it drives a load or it is driven by a prime
mover
 The direction of the armature current is reversed when an
electric machine changes from motor to generator operation
 However line voltage polarity, direction of rotation and field
current are the same
a
aa
a
r
Eu
i
−
=
 (MOTOR) If is greater than , the armature
current is positive
 (GENERATOR) If is greater than , the armature
current is negative
aEau
ai
aE au

21. Electric Machine
 Conventional separately excited DC electric machine
 Using kirchhoff’s second law and assuming the
differential equation of a motor
0== frar rr
dt
di
LiriLu a
aaarfafa +=− ω
dt
di
Liru
f
ffff +=
 In motor application, the output is the angular velocity

22. Equivalent circuit for separately excited DC generators
SEPARATELY EXCITED DC
GENERATORS

23. Electric Machine
 Conventional separately excited DC electric machine
 Using kirchhoff’s second law and assuming the
differential equation of a generator
0== frar rr
dt
di
LiriLu a
aaarfafa −−=− ω
dt
di
Liru
f
ffff +=
 The steady state operating condition for a generator are
 In generator application, the output is the voltage induced
aarfafa iriLu −=− ω fff iru =

24. DC Machines
sin
equationtorqueThe,
cos
2
1
2
1 22
rafafe
r
c
e
rafafaaffc
LiiT
Therefore
W
T
LiiiLiLW
θ
θ
θ
−=
∂
∂
=
++=
constant
)90(
max =
ℜ
=== °
m
af
srMaf
NN
LLL
Energy stored in inductor is stored in the magnetic field within the coil
2
.
2
1
ILWm =
The mutual inductance between the armature and field windings
( )°
ℜ 90m
 The armature and field magnetic axes are displaced by 90 electrical degrees and the magnetizing reluctance
is constant

25. DC Machines
 The torque equation
aaem iEP =
( )
)3(2
−−−−−−=
−
= e
faf
a
faf
a
faf
aaa
r T
iL
r
iL
u
iL
iru
ω
remec TP ω=
)1(−−−−−−−=
r
aa
e
iE
T
ω
)2(−−−−−= rfafa iLE ω
afafe iiLT =
 Electromagnetic power
 Given that
emmec PP =
 Therefore
 Electromotive force formula is given as
 Substituting (2) into (1), yields
aarfafa iriLu −=− ω afafe iiLT =using and
Steady state relationship between the angular velocity end electromagnetic torque

26.  The DC Machine Dynamic Equations for
the circuit represented bellow is
DC Machines
dt
d
irV
f
fff
λ
+=

27. DC Machines
 The flux linkage equations are:
cos
''
'
rfaaf
aaaafafaa
aaafffff
-LLL
iLiL
iLiL
θ
λ
λ
==
+=
+=
Where Lff = field self-inductance
Laa= armature self-inductance
Laf = mutual inductance between the field
and rotating armature coils

28. DC Machines - Shunt ConnectedShunt Connected
 The Shunt ConfigurationShunt Configuration for a DCDC
MachineMachine is as shown below,

29. DC Machines - Shunt ConnectedShunt Connected
 The Dynamic Equations (assuming rrf extf ext ==
00 ) are follows,
fafra
a
faaaaa
f
fffff
iLe
dt
di
LireV
dt
di
LirV
ω=
++=+=
Where Lff = field self-inductance
Lfa = mutual inductance between the field
and rotating armature coils
ea = induced voltage in the armature coils
(also called countercounter or back emfback emf )

30. DC Machines - Shunt ConnectedShunt Connected
 The torque equation for a ShuntShunt
Connected DC-MachineConnected DC-Machine is
sin
,
cos
2
1
2
1 22
rafafe
r
c
e
rafafaaafffc
LiiT
Therefore
W
T
LiiiLiLW
θ
θ
θ
−=
∂
∂
=
++=

31. DC Machines - Shunt ConnectedShunt Connected
 For DC MachinesDC Machines,
2
π
θ −=r
mmf fieldmmf field
mmf armaturemmf armature
++
--
2
π
θ −=r
faafe iiLT =