DC Machines
Dr Gamal M. A. Sowilam
DC Machine Fundamentals
 Electrical Energy Applications such as light bulbs and heaters.
 Mechanical Energy Applications, such as fans and rolling mills,
 Converters that are used to continuously translate electrical input to
mechanical output or vice versa are called electric machines.
 The process of translation is known as electromechanical energy
conversion.
 If the conversion is from mechanical to electrical, the machine
is said to act as a generator.
 If the conversion is from electrical to mechanical, the machine
is said to act as a motor.
Electromechanical energy conversion.
In these machines, conversion of energy from electrical to mechanical form or
vice versa results from the following two electromagnetic phenomena:
1. When a conductor moves in a magnetic field, voltage is induced in the
conductor.
2. When a current-carrying conductor is placed in a magnetic field, the
conductor experiences a mechanical force.
Any DC machine can act either as a generator or as a
motor.
Electrical and mechanical, are different in nature. In the
electrical system the primary quantities involved are voltage
and current, while the analogous quantities in the
mechanical system are torque and speed.
Coupling field between electrical and mechanical systems.
DC Machine Fundamentals
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DC Machine is most often used for a motor.
The major advantages of dc machines are the easy
speed and torque regulation.
Applications: machine tools, conveyors, fans, pumps,
hoists, cranes, paper mills, rolling mills, etc (large),
traction motors (medium), and control devices
(small)
The electronically controlled ac drives are gradually
replacing the dc motor drives in factories.
Nevertheless, a large number of dc motors are still
used by industry and several thousand are sold
annually.
Motional Voltage, e
if a conductor of length l moves at a
linear speed v in a magnetic field B, the
induced voltage in the conductor is
where B, l, and v are mutually perpendicular. The polarity of the
induced voltage can be determined from the so-called right-hand
screw rule.
Electromagnetic Force, f
For
the
current-carrying
conductor shown in Figure, the
force (known as Lorentz force)
produced on the conductor is
The direction of the force can be determined
by using the right-hand screw rule
If a screw is turned in the same
way, the direction in which the
screw will move represents the
direction of the force f.
Basic Structure of Electric Machines
Cylindrical machine (uniform air gap).
Salient pole machine (non-uniform air gap).
Structure of electric machines.
Stator: This part of the machine does not move and normally is
the outer frame of the machine.
Rotor: This part of the machine is free to move and normally is
the inner part of the machine.
If the stator or rotor (or both) is subjected to a time-varying magnetic
flux, the iron core is laminated to reduce eddy current losses. The thin
laminations of the iron core with provisions for slots
 The conductors 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.
 Permanent magnets are used in some machines to provide the
major source of flux in the machine.
DC Machine
 Variable speed, large and small power range.
 Field winding produces flux symmetrically distributed about pole axis
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= direct axis.
Armature winding in rotor  Alternating voltage is induced.
Mechanical commutator and brush assembly rectify the voltage.
Commutator-brush combination makes armature current distribution
fixed in space.
mmf of armature winding along quadratic axis  maximum torque
EVOLUTION OF DC MACHINES
Consider a turn a-b placed on diametrically opposite slots of the rotor. The
two terminals a and b of the turn are connected to two slip rings. Two
stationary brushes pressing against the slip rings provide access to the
revolving turn a-b. There are two voltages are in series and aid each other. The
voltage induced in the turn, eab (same as the voltage e12 across the brushes), is
alternating in nature, and its waveform is the same as that of the flux density
distribution wave in space.
Induced voltage in a dc machine. (a) Two-pole de machine. (b) Induced voltage in a turn.
Let us now replace the two slip rings by two commutator segments (which are
copper segments separated by insulating materials) as shown in Figure.
Segment C, is connected to terminal a of the turn and segment C, to terminal b
of the turn.
For counterclockwise motion of the rotor the terminal under the N pole is
positive with respect to the terminal under the S pole.
Voltage rectification by commutators
and brushes. (a) DC machine with
commutator segments. (b) Single-turn
machine. (c) Multi-turn machine.
Current reversal in a turn by commutators and brushes. (a) End a touches brush
B1 ; current flows from a to b. (b) The turn is shorted; turn is in inter-polar region.
(c) End a touches brush B2 ; current flows from b to a.
Note that turn a-b is short-circuited by the brushes when its sides pass
midway between the field poles (i.e., the q-axis). In the case of a dc motor,
current will be fed into the armature through the brushes. The current in the
turn will reverse when the turn passes the inter-polar region and the
commutator segments touch the other brushes.
DC Machines Construction
• Stator: Stationary part of the
machine. The stator carries a field
winding that is used to produce the
required magnetic field by dc
excitation. Often know as the field.
• Rotor: The rotor is the rotating part
of the machine. The rotor carries a
distributed winding, and is the
winding where the emf is induced.
Also known as the armature.
• The field windings produce an air gap flux distribution that is symmetrical
about the pole axis (also called the field axis, direct axis, or d-axis ).
• The voltage induced in the turns of the armature winding is alternating. A
commutator-brush combination is used as a mechanical rectifier to make the
armature terminal voltage unidirectional and also to make the mmf wave due
to the armature current fixed in space.
 The brushes are so placed that when the sides of an armature turn (or coil)
pass through the middle of the region between field poles, the current
through it changes direction. This makes all the conductors under one pole
carry current in one direction.
 As a consequence, the mmf due to the armature current is along the axis
midway between the two adjacent poles, called the quadrature (or q) axis.
 For improved performance, interpoles (in between two main field poles) and
compensating windings (on the face of the main field poles) are required.
DC motor stator with poles
Rotor of a dc motor.
Details of the commutator of a dc motor.
Armature Windings
 Large machines have more than two poles
most of the conductors are in region of high flux density
• electrical degrees θed
• mechanical degrees θmd
• p number of poles
ed
p
  md
2
• pole pitch = distance between centers of two adjacent poles =180oed
• coil pitch = distance between two sides of a coil
• full-pitch
coil pitch = pole pitch
• short-pitch: coil pitch < pole pitch (mainly in ac-machines)
Armature Windings - Lap winding
 one coil between two adjacent
commutator bars
 1/p of the total coils are connected
in series
 suitable for high-current low voltage
number of parallel paths = number of poles
= number of brushes
Armature Windings - Wave winding
 p/2 coil connected in series between
two adjacent commutator bars.
 The brushes are located under the
field poles at their centers.
 suitable for high voltage low current.
• number of parallel paths = 2
• number of brushes positions = 2 or more
• number of brushes is increased in large
machines to minimize the current density
In brushes.
Armature Windings - Voltage
As the armature rotates in the magnetic field produced by the stator poles,
voltage is induced in the armature winding.
The induced voltage in a turn a-b
The average value of the induced voltage in the turn is
p
et  2 B() lm r 
m

B() 



A 2 rl p
The voltages induced in all the turns connected in series for one parallel path
across the positive and negative brushes will contribute to the average terminal
voltage Ea.
N
Np
Ea  et 
 m  K a  m
a
a
N = total number of turns in the armature
winding
a = number of parallel paths
Ka 
Np
a
Ka 
Zp
2 a
Z the total number of conductors =2N
Ea independent of operation mode
• in generator: generated voltage
• in motor back emf
Armature Windings - Torque
 The force on a conductor
Ia
f c  B()lic  B()l
a
 The torque on a conductor
Tc  f c r
 The average torque on a conductor
Ia
pI a
Tc  B( ) l r 
a
2 a
 The total torque developed
T  2 NTc 
N p
I a  K a I a
a
• Machine constant
Np
Ka 
a
 Power balance
T  K a I a
E a  K a  m
E a I a  K a  m I a  T m
Example 1
A four pole dc machine has an armature of radius 15 cm and an
effective length of 30 cm. The poles cover 75% of the armature
periphery. The armature winding consists of 35 coils, each coil
having seven turns. The coils are accommodated in 35 slots. The
average flux density under each pole is 0.85T.
If the armature is lap-wound,
(a) Determine the armature constant Ka.
(b) Determine the induced armature voltage when the armature rotates
at 1000 rpm.
(c) The current in the coil and electromagnetic torque developed when
the armature current is 400 A.
(d) The power developed by the armature.
Example 2
If the dc machine armature in example 1 is wave-wound, repeat parts (a)-(d).
Example 3
 A lap-wound armature is used in a six-pole dc machine. There are 72 coils on
the armature, each containing 12 turns. The flux per pole in the machine is
0.039 Wb and the machine spins at 400 rpm.
Determine the induced voltage Ea.
Example 4
 A 12 pole dc generator a wave wound armature containing 144 coils of 10
turns each. Flux per pole is 0.05 Wb and it is running at a speed 200 rpm.
a) Ea = ?
b) If a 1k ohm resistor is connected to the terminals of generator, T = ?
Magnetization
 A dc machine has two circuits: a field circuit and an armature circuit.
 The mmf produced by these two circuits are: the field mmf is along the direct
axis and the armature mf is along the quadrature axis.
 The flux passes through the pole, air gap, rotor teeth, rotor core, rotor teeth, air
gap, and opposite pole and returns through the yoke of the stator of the
machine.
Review d-q axis
 At low values of flux, the magnetic material may be considered to have
infinite permeability.
 The magnetic flux in each pole is then
 If Fp is increased, flux will increase and saturation will occur in various
parts of the magnetic circuit, particularly in the rotor teeth.
 It is more convenient if the magnetization curve is expressed in terms of
armature induce voltage Ea at a particular speed (Fig. a).
 The magnetization curve obtained experimentally by rotating the dc
machine at 1000 rpm and measuring the open-circuit armature terminal
voltage as the current in the field winding is changed (Fig b). Represents the
saturation level in the magnetic system of the dc machine for various values
of the excitation mmf.
Classification of DC Machines
 The field circuit and armature circuit can be interconnected in
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various ways to provide a wide variety of performance
characteristics-an out standing advantage of dc machines.
The field poles can be excited by two field windings, a shunt filed
winding and a series field winding.
The shunt winding has a large number of turns and takes only a small
current (< 5% rated armature current).
The series winding has fewer turns but carries a large current.
If both windings are used, the series winding is wound on top of the
shunt winding.
 The various connections of the field circuit and armature circuit are shown
in the figures.
 In the separately excited dc machine, the field winding is excited from a
separate source.
 In the self-excited dc machine, the field winding may be connected in series
with the armature, resulting a series dc machine. It may connected across
the armature, resulting in a shunt machine.
 Both shunt and series windings may be used , resulting in a compound
machine.
 If the shunt winding is connected across the armature, it is known as shortshunt machine.
 In an alternative connection, the shunt winding is connected across the
series connection of armature and series winding, and the machine is known
as long-shunt machine.
DC Motors
 The dc machine can operate as a generator and as a motor.
 When the dc machine operates as a motor, the input to the
machine is electrical power and the output is mechanical power.
 In fact, the dc machine is used more as a motor.
 DC motors can provide a wide range of accurate speed and torque
control.
DC motor
• Separately Excited and Shunt Motors
Field and armature windings are either connected
separate or in parallel.
• Series Motors
Field and armature windings are connected in series.
• Compound Motors
Has both shunt and series field so it combines features
of series and shunt motors.
Comparisons of DC Motors
Shunt Motors: “Constant speed” motor (speed regulation is very
good). Adjustable speed, medium starting torque.
Applications: centrifugal pump, machine tools, blowers fans,
reciprocating pumps, etc.
Series Motors: Variable speed motor which changes speed drastically
from one load condition to another. It has a high starting torque.
Applications: hoists, electric trains, conveyors, elevators, electric cars.
Compound motors: Variable speed motors. It has a high starting
torque and the no-load speed is controllable unlike in series motors.
Applications: Rolling mills, sudden temporary loads, heavy machine
tools, punches, etc
Shunt Motor
 The armature circuit and the shunt field circuit are connected across a
dc source of fixed voltage Vt
Separately Excited DC Motor
Example 5
A variable speed drive system uses a dc motor which is supplied from a
variable-voltage source. The drive speed is varied from 0 to 1500 rpm (base
speed) by varying the terminal voltage from 0 to 500 V with the field current
maintained constant.
(a) Determine the motor armature current if the torque is held
constant at 300N up to the base speed.
(b) Determine the torque available at a speed of 3000 rpm if the
armature current is held constant at the value obtained in part (a).
Neglect all losses.
Series Motor
Example 6
A 220 V, 7 hp series motor is mechanically coupled to a fan and draws
25 amps and runs at 300 rpm when connected to a 220 V supply with
no external resistance connected to the armature circuit ( Rae= 0).
The torque required by the fan is proportional to the square of the
speed. Ra= 0.6 ohm and Rsr= 0.4 ohm. Neglect armature reaction and
rotational loss.
(a) Determine the power delivered to the fan and the torque
developed by the machine.
(b) The speed is to be reduced to 200 rpm by inserting a
resistance Rae in the armature circuit. Determine the value of this
resistance and the power delivered to the fan.
Power Flow and Efficiency of dc motor
How to obtain the following characteristics
Speed Control
 Numerous applications require control of speed, as in
rolling mills, cranes, hoists, elevators, machine tools,
and locomotive drives.
 DC motors are extensively used in many of these
applications.
 Control of dc motors speed below and above the base
(rated) speed can easily be achieved.
 The methods of control are simpler and less expensive
than ac motors.
Solid-State Control
 In recent years, solid state converters have been used
to control the speed of dc motors.
The converter used are controlled rectifiers or choppers:
Controlled Rectifiers
 If the supply is ac, controlled rectifiers can be used to
convert a fixed ac supply voltage into variable-voltage
dc supply.
Choppers
 A solid state chopper converts a fixed-voltage dc supply
into a variable-voltage dc supply.
Closed-loop Operation
 Open loop operation: If load torque changes, the speed
will change too.
 May not be satisfactory in many applications where a
constant speed is required
 Close loop operation: the speed can be maintained
constant by adjusting the motor terminal voltage as the
load torque changes.
DC GENERATORS
1. Separately excited dc generator
Armature Reaction (AR)
If the current flows in the armature
circuit it produces its own mmf
(hence flux) acting along the qaxis. The flux produced by the
armature mmf opposes flux in the
pole under one half of the pole and
aids under the other half of the
pole,
Compensating Winding
 The zero flux density region shifts from the q-axis and this causes poor
commutation leading to sparking.
 Much of the rotor mmf can be neutralized by using a compensating
winding, which is fitted in slots cut on the main pole faces.
 The compensating winding is connected in series with the armature
winding so that its mmf is proportional to the armature mmf.
EXAMPLE
A 12 kW, 100 V, 1000 rpm dc shunt generator has armature resistance Ra
= 0.1 , shunt field winding resistance Rfw= 80 , and Nf= 1200 turns per
pole. The rated field current is 1 ampere. The magnetization
characteristic at 1000 rpm is shown in Figure. The machine is operated as
a. separately excited dc generator at 1000 rpm with rated field current
(a) Neglect the armature reaction
effect. Determine the terminal voltage
at full load.
(b) Consider that armature reaction
at full load is equivalent to 0.06 field
amperes.
(i) Determine the full-load terminal
voltage.
(ii) Determine the field current
required to make the terminal
voltage Vt = 100 V at full-load
condition.
Solution
(a)
(b)
(i) From Figure, at this field current =0.94A
(ii)
From Figure, the effective field current required is
SHUNT (SELF-EXCITED) GENERATOR
Voltage buildup in a self-excited dc generator.
1. Residual magnetism must be present in the
magnetic system.
2. Field winding mmf should aid the residual
magnetism.
3. Field circuit resistance should be less than the
critical field circuit resistance.
Effect of field resistance.
EXAMPLE
The dc machine in above Example is operated as a
self-excited (shunt) generator at no load.
(a)
Determine the maximum value of the
generated voltage.
(b) Determine the value of the field circuit control
resistance (Rfc) required to generate rated
terminal voltage.
(c) Determine the value of the critical field
circuit resistance.
Solution
(a) The maximum voltage will be generated at the lowest value of the field
circuit resistance, Rfc = 0. Draw a field resistance line (Figure) for Rf =
Rfw= 80 . The maximum generated voltage is
(b)
Draw a field resistance line that intersects the magnetization curve at 100 V
(Figure). For this case,
(c) Draw the critical field resistance line passing through the linear
portion of the magnetization curve (Figure. For If = 0.5, Ea is 85 V.
COMPOUND DC MACHINES
Short Shunt
Equivalent circuits of compound
de machines of Short shunt. (b)
Long shunt.
Long Shunt
Equivalent circuits of compound
dc machines of Long shunt.
For either connection, assuming magnetic linearity, the generated voltage is
When these two fluxes aid each other the machine is called a cumulative
compound machine, and when they oppose each other the machine is called
a differential compound machine.
SERIES GENERATOR
Power Flow and Efficiency of dc generator