Transcript Chapter 7: DC Machine Fundamentals

BASIC ELECTRICAL TECHNOLOGY
DET 211/3
Chapter 7
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
Construction
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.
Construction
- 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.
Construction
• 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.
Construction
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.
Armature Windings
Cut and unroll of DC machine
Armature Windings
Electrical degree and mechanical degree
Pole pitch is the distance between the centers of
two adjacent poles
Armature Windings
Two basic sequences of armature winding connections:
a) Lap windings
b) Wave windings
Lap Winding
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.
Lap Winding
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.
Wave Winding
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 faces
View of field lines
Top view
A simple rotating loop between curved poles faces
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 Voltage Induced in a Rotating Loop
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
EA 
a
where
Z = the total number of conductors
a = the number of current paths
We know , v =rω, r = radius of the rotor
ZrBl
EA 
a
The internal generated voltage
The flux of the pole is equal to the flux density under
the pole times the pole’s area:
  BA p
The rotor of the DC machine is shaped like a cylinder,
so its area is
A  2rl
If there are P poles on the machine, then the portion
of the area associated with each pole is
A 2rl
Ap  
P
P
The internal generated voltage
The total flux per pole in the machine is
B( 2rl ) 2rlB
  BA p 

P
P
The internal generated voltage is
ZrBl
E A
a
 ZP  2rlB 



 2a  P 
ZP
EA 

2a
The internal generated voltage
EA  K
where
ZP
K
2a
2n

60
or
E A  K ' 
ZP
K 
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.
Concepts: a current carrying wire in the presence of a
magnetic field has a force induced on it
Lorentz Law : use right hand rule.
Index finger – vector l
Middle finger – Magnetic flux density
Thumb - Force
The induced torque in the rotating 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 induced torque in the rotating loop
The torque on that segment is
  (force applied)(p erpendicular 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
If there are “a” current paths in the machine, then the
total armature current Ia is split among the “a” current
paths, so the current in a single conductor is
I cond
Ia

a
The torque in a single conductor on the motor is
rI a lB
cond 
a
The induced torque
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
  BA p 

P
P
The total induced torque is
ind 
ZPI a
2a
The induced torque
The total induced torque is
ind  KI a
where
ZP
K
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
Power flow and losses in DC machines
The losses that occur in DC machine can be divided into 5
categories:
1. Copper losses (I2R) Pa  I a Ra
2. Brush losses PBD  VBD I a
3. Core losses
4. Mechanical losses
5. Stray load losses
2
Pf  I 2f R f
Ia = armature current
VBD = brush voltage drop
If = field current
- Usually assumed to be
2V
Ra = armature resistance
Rf = field resistance
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
Pout = VTIL
For generator
The Power Flow Diagram
Pout   app
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.
Example
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.
Z = 2CNc
ZP
K
2a
Always equal number of poles
Z  2x33x7  462
ZP 462 x 4
K

 73.53
2a 2 x 4
( 2 x 33 coils x 7 turns)
Example
b.
2rl 2 x 0.125 x 0.25 x 0.75
Ap 

P
4
 36.8 x 10 -3 m 2
  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
2x1000
   811.8 x
 85kW
60
2. Wave wound DC machine
a.
ZP 462 x 4
K

 147.06
2a 2 x 2
2 x 1000
b. 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