for student dc motor

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Chapter 2
DC Machine Fundamental
by
Zetty Nurazlinda Zakaria
December 5, 2018
Revision of Electromagnetism
When a conductor carries a current, it creates a magnetic field
around it. The direction of the such magnetic field depends on
the direction of the current passing through the conductor.
1)
2)
3)
Right Hand Thumb Rule
Lenz’s Rule
Faraday’s Laws
I.
First Law
II. Second Law
III. Fleming’s Right Hand Rule
IV. Fleming’s Left Hand Rule
First & Second Law
• First Law
– States that flux linking a conductor or coil changes, an e.m.f is induced
in it.
• Second Law
– States that the magnitude of induced e.m.f in a coil is equal to the rate
of change of flux linkages.
initial flux linkage= Nφ1
final flux linkage= Nφ2
e.m.f induced = e
Nφ 2  Nφ1
dφ
N
Hence, e 
t
dt
Assume (φ2- φ1) = φ
The direction of the induced e.m.f is opposite to the cause producing it
(Lenz’s Law).
e (e.m.f)   N
dφ
dt
Right Hand Thumb Rule
Thumb indicates the direction of current
flowing in the conductor.
Curled fingers point in the direction of
the magnetic field or flux around the
conductor.
Fleming’s Right Hand Rule
Motion of the
conductor
Direction of
flux lines
A
B
S
N
C
Direction of induced
voltage
Fleming’s Left Hand Rule
Motion of the
conductor
N
Direction of
flux lines
S
Direction
of current
Introduction
• What is DC Machine?
– Continuously convert electrical input to
mechanical output or vice versa
– Electromechanical
Mechanical Energy
Electrical Energy
Generator
Electrical Energy
Motor
Mechanical Energy
• Types of electric machine:Electric
Machine
DC Machine
Series
Shunt
AC Machine
Compound
Induction
Synchronous
Basic Construction of DC Machine
Main components of DC
machine are ;
Stator
Rotor/armature
Field winding
Armature winding
Commutator/slip ring
Brush
DC Machine : Construction
• Basic components in DC Machine:– Stator: stationary part ~ does not move, the outer frame of the
machines is made of ferromagnetic materials
– Rotor: rotating part ~ free to move, the inner part of the machine is
made of ferromagnetic materials.
– Field winding: wound on the stator poles to produce magnetic field
(flux) in the air gap.
– Armature winding: 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. Use to convert
AC to DC.
– Brush: placed against the commutator surface. Brush is used to
connect the armature winding to external circuit through commutator.
DC Machine
Stator
Rotor
DC Machine
Commutator
DC MACHINE: Motor Operation
DC MACHINE: Motor Operation
 When a current carrying conductor is placed in a magnetic field, it experiences a
mechanical force.
 In practical DC motor, field winding produces a required magnetic field while
armature winding plays a role as a current carrying conductors and hence
armature conductors experience a force.
In the practical DC motor, the permanent magnet is replaced by a field winding,
which produces the required flux called main flux and all the armature conductors,
mounted on the periphery of the armature drum, get subjected to the mechanical
force. Due to this, overall armature experiences a twisting force called torque and
armature of the motor starts rotating.
DC MACHINE: Motor Operation
• Use Fleming’s Left
Hand Rule
F (thumb)
Commutator
F
Brush
I (middle finger)
B (first finger)
90°
F
DC MACHINE: Motor Operation
• The magnitude of the force
experienced by the
conductor in a motor is :-
F
F = BlI Newtons (N)
F
B = flux density due to the flux
produced by the field winding
l = length of the conductor
I = magnitude of the current passing
through conductor
The Voltage Induced in a Rotating Loop
If the rotor of this machine is rotated, a voltage will induced in the
wire loop.
b
c
a
d
Concepts: A moving wire in the presence of a magnetic field has a voltage
induced in it.(for DC generator operation)
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.
DC MACHINE: Back E.M.F
• When DC supply is given to DC motor, its armature starts rotating.
• The armature rotates and cuts the static magnetic flux produced by the
field magnets.
• So, e.m.f is induced in the armature conductors and known as back e.m.f.
Where;
φZNP
E b (emf ) 
60A
E b  V  Ia R a
Φ=Flux per pole
Z=no.of conductors in the
armature
P=no. of poles
A=no. of parallel paths
N=speed of the motor
V=supply voltage
Ia=armature current (A)
Ra=armature resistance (Ω)
DC MACHINE: Developed Torque
• The force acting on the rotor, is expressed as:F  Il  
B
Due to
the Field
Due to
the Armature
F
r
Te
F
Te = F x r
DC MACHINE: Developed Torque
F
F
r T
e
Te = F x
r
• The rotor rotates at a speed of N rpm, so the angular speed of
the rotor is,
2N
rad / sec
60
• P=power developed=workdone/time
ω

F x  2r
F x  2r
2N

 ( F x r) x (
)
60
time for 1 rev
60
N
Torque
(Nm)
Angular speed
(rad/sec)
DC MACHINE: Developed Torque
• Torque equation of a DC motor is given as
follows:-
1
PZ
Ta 
I a x
(N - m)
2
A
• How to derive Ta?
Armature Winding
•
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.
There are 2 common types of armature winding.
i.
Lap Winding
ii.
Wave Winding
i) Lap Winding
• Connection is started from conductor in slot 1, then connections overlap
each other as winding proceeds, till starting point is reached again.
• Due to such connection, till total number of conductors get divided into P
number of parallel paths, where P = number of poles in the machine.
• Large number of parallel paths shows high current capacity of machine
hence winding is preferred for high current rating machines.
ii) Wave Winding
• In this type of connection, winding always travels ahead avoiding
overlapping.
• It travels continuously and called wave winding.
• Both coils starting from slot 1 and slot 2 are progressing in wave fashion.
• Due to this type of connection, the total number of the conductors get
divided into two number of parallel paths always (P=2), irrespective of
number of poles of the machine.
• As number of parallel paths are less, it is preferable for low current, high
voltage capacity machine.
Action of Commutator
• Commutation is a process of converting the ac voltages &
currents in the rotor of a dc machine to dc voltages and
currents at its terminal.
Action of Commutator
• How?
• Assumed commutator is divided into 2 segments separated by insulating
material (like a split ring).
• Brushed P & Q are stationary and pressed on the surface of the spilt ring.
• Spilt ring is mounted on the shaft and rotates as the rotor rotates.
• Consider a single turn machine with conductors 1 & 2.
• These are armature conductors which connected to the two segments of
split ring (commutator).
• External resistance is connected across the brushes P & Q.
Action of Commutator
• Condition 1 (1st half)
– Current is flowing from left to right across the resistance
– Direction of current through conductor 1 is downwards which is under
N pole, and conductor 2 is upwards which under S pole. (refer figure a)
– At this condition, brush P behaves as positive & brush Q behaves ad
negative.
Action of Commutator
• Condition 2 (2nd half)
– Current still flowing from left to right across the resistance.
– Direction of the current through conductor 1 is upwards under S pole,
and conductor 2 is downwards which is under N pole.(refer figure b)
Action
Actionof
ofCommutator
Commutator
• Commutator is mounted on the shaft and rotates with
armature.
• So, when conductors reverse their positions, the spilt ring will
also reverse their positions.
• But brushes (P & Q) is still remain at their position which
brushes tap the current from the commutator segments as
they are contacting with the brushes.
commutator
brush
shaft
commutator
Action
Actionof
ofCommutator
Commutator
• Figure 1 shows the waveforms of current in
the individual conductor.
• Figure 2 shows the waveforms of load
(external resistance) current.
Fig 1
Fig 2
Example 1
A lap connected DC machine has 8 poles and 120 slots with 8 conductors
in each slot. If the flux per pole is 0.04 weber;
1) Find the e.m.f generated when the speed is 600 rpm
2) what should be the speed of rotation, if the induced emf is to be
500 volts
December 5, 2018
Example 1 : Solution
Given data:Poles = 8
No of slots = 120
Conductor per slot = 8
Flux per pole (φ) = 0.04 weber
1) Find e.m.f generated?
φZNP
E b (emf ) 
60A
Total no of conductors (Z)
 Total no of slots x conductors /slot
 120 x 8
 960 conductors
So,
(0.04)(960)(600)(8)
E b (emf ) 
(60)(8)
 384 V
2) Find speed of rotation?
At E b  500V , N  ?
E b (emf ) 
φZNP
60A
Hence,
E b  60A
φZP
(500)(60)( 8)

(0.04)(960 )(8)
 781.25 rpm
N
Power Losses
• Losses in a DC machine can be divided into 3 classes:1) Copper Losses
2) Iron or Core Losses
3) Mechanical Losses
•
These losses appear as heat thus, raises the temperature of
the machine and lower the efficiency of the machine as
well.
1) Copper Losses
• Occur due to the currents in the various windings of the
machine.
i. Armature copper losses = Ia2Ra
ii. Shunt field copper losses = Ish2Rsh
iii. Series field copper losses = Ise2Rse
2) Iron or Core Losses
•
•
Occur in the armature of a DC machine due to the rotation of the armature in the
magnetic field of the poles.
2 types:i.
Hysteresis loss
- When the armature rotates in the magnetic field, it crosses north pole
and south pole. Therefore, inside the armature core, the reversal of
magnetic flux take place, while the armature core passes from one pole to
another pole in each time. The reversal of magnetic flux in the armature
core causes “Hysteresis Loss”.
Wh  Bm fV (W)
1.6
where;
η=Steinmetz hysteresis coeffient
Bm=max flux density (web/m2)
f=freq of magnetic reversals
V=volume of the armature core (m3)
2) Iron or Core Losses cont…
ii.
Eddy Current Loss
- when armature rotates in the magnetic field of the poles, an emf is
induced in it, which circulates eddy current in the armature core. Power
loss is due to the eddy current.
We  Ke Bm f t V (W)
2 2 2
where;
Ke=constant
Bm=max flux density (web/m2)
t=thickness of lamination
V=volume of the armature core (m3)
3) Mechanical Losses
• These losses consist of friction and windage losses.
• The armature rotates in the air inside the machine. Loss due
to the friction of the bearings in the machine - called friction
loss.
• Windage are caused by the friction between the moving parts
of the machine and the air inside the motor casing’s.
Power Losses Stages : DC Generator
Pin
Pout
Iron & Friction Losses
Copper Losses
Power Losses Stages : DC Motor
Pin
Pout
Copper Losses
Iron & Friction Losses
Power input = VI (Watt)
Total losses in motor = Copper losses + iron & mechanical losses
Power developed in armature = EbIa (Watt)
Efficiency of a DC Machine
• The efficiency of a DC machine is a ratio
between output power and input power.
• It is expressed in percentage.
Efficiency, η =
Output
100% (or)
Input
Output
100%
Output  Losses
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