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CHAPTER 2
DC Machines Fundamentals
Introduction
•
•
•
A DC Machines can be used as either a DC generator or a DC motor.
DC generators
- To convert mechanical energy to electrical energy.
- Limited use due to solid state rectifier.
DC motors
- To convert electrical energy to mechanical energy
- Widely used
- Main feature: speed control is simple and cheap
Construction
• DC Machine = Stator + Rotor (armature)
- Stator: stationary part ~ does not move, the outer frame of the machines is made
of ferromagnetic materials.
- Rotor (Armature): rotating part ~ free to move, the inner part of the machine is
made of ferromagnetic materials.
- Field winding: is wound on the stator poles to produce magnetic field (flux) in the
air gap.
- Armature winding: is composed of coils placed in the armature slots.
- Commutator: is composed of copper bars, insulated from each other. The
armature winding is connected to the commutator.
- Brush: placed against the commutator surface. Brush is used to connect the armature
winding to external circuit through commutator.
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•
•
The conductor placed in the slots of the stator or rotor are interconnected to form
windings.
The winding in which voltage is induced is called the armature winding.
The winding through which a current is passed to produce the primary source of
flux in the machine is called the field winding.
In the DC machine, the field winding is placed on the stator and the armature winding on
the rotor.
DC motor stator
DC motor rotor
Cutaway view of a dc motor
Details of the commutator of a dc motor
Armature Windings
A turn consists of two conductors connected to one end by an end connector.
A coil is formed by connecting several turns in series.
A winding is formed by connecting several coils in series.
Cut and unroll of DC machine
Pole pitch is the distance between the centers of two adjacent poles
Two basic sequences of armature winding connections:
a) Lap windings
b) Wave windings
Lap Winding
Consider coil shown by the dark lines with one end connected to the commutator bar no
2. The coil is placed in slots 2 and 7 such that the coils sides are placed in similar
positions under adjacent poles. This is called lap winding because as the winding
progresses the coils laps back on itself.
We can conclude, in a lap winding, the number of parallel paths, “a” is always equal to
the number of poles, “P” and also to the number of brushes.
Wave Winding
The coil arrangement and the end connections are illustrated by the dark lines shown in
figure above for two coils. One end of the coil starts at commutator bar 2 and the coil
sides are placed in slots 7 and 12. The other end of coil is connected to commutator bar
13. The second coil starts at this commutator bar and is placed in slots 18 and 2 and ends
on commutator bar 3. This winding is called a wave winding because the coils are laid
down a wave pattern.
In wave windings, the number of parallel paths, ”a” is always two and there may be two
or more brush positions.
DC machines operates as a generator
A simple rotating loop between curved poles faces
Perspective view
Magnetic for DC machine is supplied by the magnetic north and south poles shown on
the stator (field winding)
A simple rotating loop between curved poles face
View of field lines
Top view
Front view
The Voltage Induced in a Rotating Loop
If the rotor of this machine is rotated, a voltage will induced in the wire loop.
Concepts: A moving wire in the presence of a magnetic field has a voltage
induced in it.
The loop of wire shown in rectangular, with sides ab and cd perpendicular to the plane of
the page and with sides bc and da parallel to the plane of the page.
The induced voltage for one conductor is
eind  vBl
where
B = magnetic flux density (T)
v = velocity of the conductor (ms-1)
l = length of conductor (m)
The induced voltage depends on three factor:
1. The flux, Ф in the machine
2. The speed ω of the rotor
3. A constant depending on the construction of the machine
The internal generated voltage
The voltage out of the armature is;
ZvBl
a
EA 
where
Z = the total number of conductors
a = the number of current paths
We know , v =rω, r = radius of the rotor
ZrBl
a
EA 
The total flux per pole in the machine is;
  BA p 
B(2rl ) 2rlB

P
P
The internal generated voltage is
ZrBl
a
 ZP  2rlB 



 2a  P 
E A
EA 
ZP

2a
EA  K
where
K
ZP
2a

2n
60
or
E A  K '
K' 
ZP
60a
DC machines operates as a motor
The induced torque in the rotating loop
A battery is now connected to the machine. When the switch is closed and a current is
allowed into conductor loop. The torque will be induced on the conductor loop.
The force for one conductor is
F  i(lxB)
F  ilB
where
i = magnitude of current in the segment
l = length of the segment, with direction of I defined to be in the direction of current
B = magnetic flux density vector
The torque on that segment is
  (force applied)(p erpendicul ar distance)
 Fr sin 
The induced torque depends on three factors:
1. The flux Ф in the machine
2. The armature (or rotor) current IA in the machine
3. A constant depending on the construction of the machine
The induced torque
The torque in any single conductor under the pole faces is
 cond  rI cond lB
Ia
a
I cond 
The torque in a single conductor on the motor is
 cond 
rI a lB
a
Since there are Z conductors, the total induced torque in rotor is
 ind 
ZrlBI a
a
The total flux per pole in the machine is
B(2rl ) 2rlB

P
P
  BA p 
The total induced torque is
ZPI a
2a
The total induced torque is
 ind 
 ind  KI a
where
K
ZP
2a
Power flow and losses in DC machines
DC generators take in mechanical power and produce electric power while DC motors
take in electric power and produce mechanical power
Efficiency;

Pout
x100%
Pin

Pout  Ploss
x100%
Pin
The losses that occur in DC machine can be divided into 5
categories:
1.
2.
3.
4.
5.
Copper losses (I2R)
Brush losses
Core losses
Mechanical losses
Stray load losses
Ia = armature current
If = field current
Ra = armature resistance
Rf = field resistance
*VBD = brush voltage drop
- Usually assumed to be 2V
Power Losses
Core losses – hysteresis losses and eddy current losses
Mechanical losses – the losses that associated with mechanical effects. Two basic types
of mechanical losses: friction & windage. Friction losses caused by the friction of the
bearings in the machine. Windage are caused by the friction between the moving parts of
the machine and the air inside the motor casing’s
Stray losses (Miscellaneous losses) – cannot placed in one of the previous categories.
The Power Flow Diagram
For generator
For motor
Equivalent circuit of DC generator
Vf = field voltage
If = field current
Rfw = rheostat resistance
Rf = Rfc + Rfw = field circuit resistance
Ra = armature resistance
Ea = KФω
where Ф = flux generated by field current, If
VT = terminal voltage
Ia = armature current
Equivalent circuit of DC motor
Vf = field voltage
If = field current
Rfw = rheostat resistance
Rf = Rfc + Rfw = field circuit resistance
Ra = armature resistance
Back EMF, Eb = KФω
where Ф = flux generated by field current, If
VT = terminal voltage
Ia = armature current
Example :
A 4 pole DC machine has an armature of radius 12.5cm and effective length of 25cm.
The poles cover 75% of the armature periphery. The armature winding consists of 33
coils, each coil having seven turns. The coils are accommodated in 33 slots. The average
flux density under each pole is 0.75T.
1) If the armature is lap wound, determine:
a. the armature constant K
b. the induced armature voltage when the armature rotates at 1000 rpm.
c. the current in the coil and the electromagnetic torque developed when the
armature current is 400A.
d. The power developed by the armature.
2) If the armature is wave wound, repeat parts a. to d. above. The current rating of the
coils remains the same as in the lap wound armature.
Solution :
1. Lap wound DC machine
a)
K
ZP
2a
Z  2x33x7  462
K
ZP 462 x 4

 73.53
2a 2 x 4
Always equal number of poles
( 2 x 33 coils x 7 turns)
b)
2rl 2 x 0.125 x 0.25 x 0.75

P
4
-3
2
 36.8 x 10 m
Ap 
  BA p  36.8 x 10-3 x0.75  0.0276Wb
E  K  73.53 x 0.0276 x
2 x 1000
60
 212.5V
c)
I coil 
I a 400

 100 A
a
4
  kI a  73.53 x 0.0276 x 400  811.8Nm
d)
Pdev  Ea I a  212.5 x 400  85kW
or
Pdev    811.8 x
2x1000
 85kW
60
2. Wave wound DC machine
a)
ZP 462 x 4
K

 147.06
2a 2 x 2
b)
2 x 1000
E  K  147.06 x 0.0276 x
60
 425V
c)
I a  aI coil  2 x 100  200 A
  kI a  147.06 x 0.0276 x 200  811.8Nm
d)
Pdev  Ea I a  425 x 200  85kW
Magnetizing curve of a DC machine
The internal generated voltage, Ea of a DC motor or generator is
Ea  K
The internal generated voltage, Ea is proportional to the flux in the machine and the
speed of rotation of the machine.
Magnetization curve of a ferromagnetic material (Ф vs F)
Magnetomotive Force, F = NfIf
Most motors and generator are designed to operate near the saturation point on the
magnetization curve. This implies that a fairly large increase in field current is often
necessary to get a small increase in Ea when operation is near full load.
Classification of a DC machine
Separately Excited DC Machine
Shunt DC Machine
Series DC Machine
Compounded DC Machine