Everything you need to know about DC Machines

1. BITS Pilani
Pilani Campus
INTRODUCTION TO MACHINES
PART 1 DC MACHINES
EEE Department
BITS Pilani, Pilani

2. BITS Pilani, Pilani Campus
ROTATING MACHINES
 Consider a single rectangular conducting loop of length l and width 2r embedded
in a uniform magnetic field having a constant flux density B rotates about the
z-axis with a constant angular velocity
w radians per second
Slip Rings
 The ends of the loop are connected to slip
rings that rotate with the loop
 Slip rings are in contact with fixed carbon
brushes through which an electrical contact
is made
 Area of the loop (A) = 2rl

3. BITS Pilani, Pilani Campus
 At time t, the angle between the plane of the loop and the y-z axis is wt
 Flux ∅ passing through the loop is
∅ = 𝑩. 𝑨
∅ = 𝑩𝑨 𝐜𝐨𝐬 𝒘𝒕 = 𝑩 𝟐𝒓𝒍 𝐜𝐨𝐬 𝒘𝒕
 By Faraday’s law, the EMF induced in the carbon brushes –
𝑒 = 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑓𝑙𝑢𝑥
𝑒 =
𝑑∅
𝑑𝑡
𝑒 = −𝑩𝑨𝒘 𝐬𝐢𝐧 𝒘𝒕
 If the coil has N turns, then the total EMF induced is given by 𝒆 = −𝑵𝑩𝑨𝒘 𝒔𝒊𝒏 𝒘𝒕
Side View
Dot Product
The – sign comes automatically in accordance with the Lenz law
ROTATING MACHINES

4. BITS Pilani, Pilani Campus
ROTATING MACHINES – AC GENERATOR

5. BITS Pilani, Pilani Campus
 Since the machine produces a sinusoidal voltage, it is called Alternator or AC Generator
 Induced voltage depends on –
1) Speed of rotation
2) Flux Density B
3) Number of turns in the coil
4) Area of the coil
 Let us replace slip rings with split-rings
 Brushes repositioned on either side of the
split ring commutator
 Voltage induced across the loop is given by
𝑒 = −𝑩𝑨𝒘 𝐬𝐢𝐧 𝒘𝒕
ROTATING MACHINES
 This is the voltage v12 between the 2 halves of the commutator

6. BITS Pilani, Pilani Campus
Side view of a split ring commutator
v
+
_
 The voltage across the split ring commutator is given by
𝟎 < 𝒘𝒕 < 𝝅
𝝅 < 𝒘𝒕 < 𝟐𝝅
 This voltage is never negative as it does not change
polarity
 This simple machine is called a DC Generator
ROTATING MACHINES

7. BITS Pilani, Pilani Campus
ROTATING MACHINES - DC GENERATOR

8. BITS Pilani, Pilani Campus
DC GENERATOR - CONSTRUCTION
 Stator comprising of stationary parts
 Magnetic Field is generated when the
Field Windings situated on the poles
are fed with a DC current
 More than 1 pair of poles can be used
to have larger B
 Rotor comprising of rotating parts
 Rotor consists of a cylindrical iron core
that has slots for housing the armature
conductors and a commutator along
with associated brushes
Shown here are 8 conductors forming 4
coils and a commutator with 4 segments

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 Conductors 1 and 1’ form coil 1 and so forth
 Brushes are depicted as riding on the inside but they
actually make contact with the outside of the commutator
 Passing DC current through the field windings produces
Uniform Magnetic Fields in the small air gaps between
the poles and the rotor
 When armature windings are connected to the commutator
in an appropriate manner as shown, the individual EMF’s
will not only be rectified but they will be added together
as well
coil-commutator connections
DC GENERATOR
Coils 1 and 2 are in series
and so are coils 3 and 4

10. BITS Pilani, Pilani Campus
DC GENERATOR
EMF induced (e) across a single coil is given as
Voltage across the brushes (v) is given as
When the coils are connected in an appropriate fashion
Small notches in the
waveform result from the
brushes changing from
different segments of the
commutator
In practice many coils are
employed and this
commutator ripple is
quite small

11. BITS Pilani, Pilani Campus
DC GENERATOR – GENERATED VOLTAGE
The generated voltage is given by
where
p -> number of poles
N -> number of armature conductors
a -> number of parallel paths between the brushes
∅ -> flux per pole
n -> Speed of rotation in r.p.m
Ra - Armature Resistance
(Resistance of the armature coils,
brushes etc. that complete the circuit)

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GENERATOR SYMBOL
𝑖 𝑓 -> Field Current
𝑖a -> Armature Current
A Generator can be represented in a circuit as :
Induced No load armature EMF ->
constant
𝒗 𝒈 = 𝑲∅𝒏
Depends on 𝑖 𝑓

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MAGNETIZATION CURVE
OF A DC GENERATOR
Note that some
EMF is induced in
the Generator even
though the field
current is 0. This is
because of the
residual magnetism
of the poles

14. BITS Pilani, Pilani Campus
GENERATOR FIELD EXCITATION
1. SEPARATELY EXCITED GENERATOR
The Field Windings are excited by a separate
source 𝑉 𝑓
2. SHUNT CONNECTED GENERATOR
The Field Windings are excited using the
generator’s own induced voltage. This is
done by connecting the Field in parallel with
the Armature

15. BITS Pilani, Pilani Campus
GENERATOR FIELD EXCITATION
 Shunt connected generator is an example of self excited generator
 In a shunt connected generator, the Field Winding has many turns and relatively high
field resistance so that the Field current is a small fraction of armature current
 Field current can further be controlled by using a Rheostat in series with the field as
shown

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3. SERIES CONNECTED GENERATOR
GENERATOR FIELD EXCITATION
 The Field Winding is placed in series with the
Armature
 Field current is same as Armature Current and
Field Winding has less turns and less Resistance
 This is done to reduce the voltage drop across the
Field Winding even under No Load conditions
 We can place a Diverter Resistance in parallel
with the Field Winding as shown to reduce the
voltage drop across the Field Winding

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GENERATOR FIELD EXCITATION
4. COMPOUND CONNECTED GENERATOR
 Connecting the Field Winding in
shunt as well as in series with the
Armature as shown
 Rheostat and a Diverter Resistance
can be employed as shown

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GENERATOR FIELD EXCITATION
4. COMPOUND CONNECTED GENERATOR
CUMULATIVE COMPOUND DIFFERENTIAL COMPOUND
EMF due to Shunt Field is added to the
EMF that is induced by the Series Field
EMF due to Shunt Field is subtracted to
the EMF that is induced by the Series Field

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GENERATOR BUILDUP
Consider a self excited shunt generator with a control rheostat
 When the Switch is open (𝑖 𝑓 = 0), some EMF still induced
due to Residual Magnetism
 When Switch is closed, this EMF acts on the Field Winding
generating more ∅ hence more induced EMF
Repetitive process of
increasing generated
voltage and field current
is known as generator
buildup
Due to Residual Magnetism

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EXTERNAL CHARACTERISTICS
Consider a separately excited DC Generator.
vL - Load voltage
iL - Load current
The relationship between the load
current and the load voltage is given by
+
-
vL
𝑖 𝐿
𝑣 𝑔
𝑣 𝐿 = −𝑅𝑎𝑖 𝐿 + 𝑣𝑔
Generated EMFArmature
Resistance
The plot between load voltage and the
load current is termed as an external
characteristic. We can plot the graph
using the equation above. Theoretically,
it is a straight line but practically a bit
curved.

21. BITS Pilani, Pilani Campus
EXTERNAL CHARACTERISTICS
The external characteristics of a
separately and shunt connected DC
Generator
𝑉𝑟 𝑎𝑛𝑑 𝐼𝑟 −
𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟′ 𝑠 𝑓𝑢𝑙𝑙 𝑙𝑜𝑎𝑑
𝑟𝑎𝑡𝑒𝑑 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑎𝑛𝑑 𝑐𝑢𝑟𝑟𝑒𝑛𝑡

22. BITS Pilani, Pilani Campus
 For a shunt connected generator load current is almost equal to armature current
 Due to armature resistance, load voltage will reduce as load current increases
 In addition, when the load voltage reduces, the field current decreases thereby
reducing the generated voltage even further
EXTERNAL CHARACTERISTICS
I am unable to understand this.
It is a bit complicated

23. BITS Pilani, Pilani Campus
DC MOTORS