2/15/2013
EEE 118: Energy Conversion
Dr. Mongkol Konghirun
Department of Electrical Engineering
King Mongkut’s University of Technology Thonburi
Chapter 8
DC Machinery Fundamentals
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8.1 A Simple Rotating Loop
between Curved Pole Faces
A Simple Rotating Loop
Between Curved Pole Faces
The simplest possible rotating dc machine with a single rotating
loop is shown
- Rotating part : rotor
- Stationary part : stator
- To minimize the reluctance of the
flux path, the air gap width should
be shortest possible and uniform.
- The magnetic flux is perpendicular
to the rotor surface everywhere
under pole faces.
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A Simple Rotating Loop
Between Curved Pole Faces
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A Simple Rotating Loop
Between Curved Pole Faces
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The Voltage Induced in a
Rotating Loop
If the rotor of this machine is rotated, a voltage will be induced in
the wire loop.
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The Voltage Induced in a
Rotating Loop
To determine the total induced voltage on the loop, examine each
segment of the loop separately and sum all the resulting voltages.
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The Voltage Induced in a
Rotating Loop
To determine the total induced voltage on the loop, examine each
segment of the loop separately and sum all the resulting voltages.
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The Voltage Induced in a
Rotating Loop
The total induced voltage on the loop eind is given by
When the loop rotates through 180o , segment ab is under
the north pole face instead of the source pole face.
At this time, the direction of the voltage on the segment
reverses, but its magnitude remains constant.
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The Voltage Induced in a
Rotating Loop
The waveform of total induced voltage on the loop eind is shown
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The Voltage Induced in a
Rotating Loop
Alternative way to express the voltage induced in a rotating loop.
The tangential velocity v of the edges of the loop can be expressed as
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The Voltage Induced in a
Rotating Loop
Substituting this velocity expression into equation (8-5) gives
The area of the rotor under each pole (ignoring the small gaps
between poles), Ap = πrl (= a half of area of rotor surface).
Therefore,
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The Voltage Induced in a
Rotating Loop
Since the flux density B is constant everywhere in the air gap
under the pole faces, the total flux under each pole is
Therefore, the final form of the voltage equation is
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The Voltage Induced in a
Rotating Loop
Thus, the induced voltage in any real
machine will depend on the same three
factors :
1. The flux in the machine.
2. The speed of rotation
3. A constant representing the
construction of the machine.
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Getting DC Voltage out of the
Rotating Loop
The induced voltage etot in Figure 8-3 is alternatively a constant
positive and negative values.
How can this machine be made to produce a dc voltage instead of
the ac voltage it now has ?
See following Figure 8-5(a) for a solution. Two key elements are
commutator and brushes.
Commutator : two semicircular conducting segments are added to
the end of the rotating loop. So, both commutator and wire loop
rotate together.
Brushes : two fixed contacts are set up at an angle such that at the
instant when the voltage in the loop is zero (wire loop is on the
vertical position), the contacts short-circuit the two conducting
segments. There is no current flowing to the wire loop at this time.
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Getting DC Voltage out of the
Rotating Loop
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The Induced Torque in the
Rotating Loop
Suppose a battery is now connected to the machine as shown in
Figure 8-6.
How much torque will be produced in the loop ?
How much current is allowed to flow into the loop ?
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The Induced Torque in the
Rotating Loop
Consider the force on each segment of the loop separately
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The Induced Torque in the
Rotating Loop
While the loop is under the pole faces, the torque is
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The Induced Torque in the
Rotating Loop
While the loop is under the pole faces, the torque is
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The Induced Torque in the
Rotating Loop
While the loop is under the pole faces, the torque is
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The Induced Torque in the
Rotating Loop
While the loop is under the pole faces, the torque is
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The Induced Torque in the
Rotating Loop
The resulting total induced torque on the loop is given by
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The Induced Torque in the
Rotating Loop
Thus, the torque produced in any real
machine will depend on the same three
factors :
1. The flux in the machine.
2. The current in the machine
3. A constant representing the
construction of the machine.
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8.2 Commutation in a Simple
Four-Loop DC Machine
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A Simple Four-Loop, Two-Pole
dc Machine
- Four loops are buried in the slots
carved in the laminated steel of its
rotor.
- The pole faces are curved to provide
a uniform air-gap width to give a
uniform flux density everywhere
under the faces.
- The “unprimed” end of each loop is
the outermost wire in each slot (eg,
1, 2, 3, and 4).
- The “primed” end of each loop is the
innermost wire in the slot directly
opposite (eg, 1’, 2’, 3’, and 4’).
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A Simple Four-Loop, Two-Pole
dc Machine
Connections of wire loop ends
Loop 1 :
1 => commutator segment a
1’ => commutator segment b
Loop 2 :
2 => commutator segment b
2’ => commutator segment c
Loop 3 :
3 => commutator segment c
3’ => commutator segment d
Loop 4 :
4 => commutator segment d
4’ => commutator segment a
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A Simple Four-Loop, Two-Pole
dc Machine
At the instant shown in Figure 8-7(a),
the voltage in each of the 1, 2, 3’ and 4’ ends
of the loop under north pole face is given by
the voltage in each of the 1’, 2’, 3 and 4
ends of the loop under south pole face is
given by
The overall result is shown in Figure 87(b).
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A Simple Four-Loop, Two-Pole
dc Machine
In this Figure 8-7(b), each coil represents one side (or conductor) of
a loop. If the induced voltage on any one side of a loop is called
e = vBl, then the total voltages at the brushes is
There are two parallel paths for current through the machine.
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A Simple Four-Loop, Two-Pole
dc Machine
What happens to the terminal voltages E as the rotor continues to rotate ?
Figure 8-8 shows the machine at time ωt=45o.
Segments ab and cd
are shorted circuit
but no problem due
to zero voltages
across them.
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A Simple Four-Loop, Two-Pole
dc Machine
What happens to the terminal voltages E as the rotor continues to rotate ?
Figure 8-9 shows the machine at time ωt=90o.
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A Simple Four-Loop, Two-Pole
dc Machine
Compare Figure 8-7 to Figure 8-9 (ωt= 0o, 45o and 90o). Notice that the
voltage on wire loops 1 and 3 have reversed between the two pictures, but
since their connections have also reversed, the total voltage is still being
built up in the same direction as before.
Commutation : the process
of switching the loop
connections on the rotor of a
dc machine just as the voltage
in the loop switches polarity, in
order to maintain an
essentially constant dc output
voltage.
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8.3 Commutation and Armature
Construction in Real DC Machines
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The Rotor Coils
Most of rotor windings themselves consist of diamond-shaped preformed
coils which are inserted into the armature slots as a unit.
Each coil consists of a number of turns (loops) of wire, each turn taped
and insulated from the other turns and from the rotor slot.
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The Rotor Coils
The number of conductors (i.e., each side of a turn) on a machine’s
armature is given by
Normally, a coil spans 180 electrical degrees. Then, the voltages in the
conductors on either side of the coil will be exactly the same in
magnitude and opposite in direction at all time.
Such a coil is called a full-pitch coil.
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The Rotor Coils
The relationship between the electrical angle and mechanical angle is
given by
Sometimes a coil is built that spans less than 180 electrical degrees.
Such a coil is called a fractional-pitch coil.
A rotor winding would with fractional pitch coils is called a chorded
winding. A amount of chording is described by a pitch factor p
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The Rotor Coils
Most rotor windings are two-layer windings, meaning that sides from
two different coils are inserted into each slot. The winding installation is
very elaborate procedure.
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Connections to the
Commutator Segments
Once the windings are installed in the rotor slots, they must be
connected to the commutator segments.
There are a number of ways for connections with different winding
arrangements, resulting different advantages and disadvantages.
The distance (in number of segments) between commutator segments
to which the two ends of a coil are connected is called the
commutator pitch yc.
For wave construction,
Yc=-1
Yc=1
Progressive
winding
Retrogressive
winding
Progressive winding VS
retrogressive winding
=> different rotational
direction
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Connections to the
Commutator Segments
Rotor (armature) windings are further classified according to the plex
of their windings.
- A simplex rotor winding is single, complete closed winding wound
on a rotor
- A duplex rotor winding is a rotor with two complete and
independent sets of rotor windings. Each of the windings will be
associated with every other commutator segment: One winding will
be connected to segments 1,3,5, etc., and the other winding will be
connected to segments 2,4,6, etc.
- A triplex rotor winding will have three complete and independent
sets of windings, each winding connected to every third
commutator segment.
- A multiplex windings: more than one set of windings.
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The Lap Winding
Armature windings are also classified according to the sequence of
their connections to the commutator segments.
Two basic sequences: lap windings and wave windings.
The simplest winding construction used in modern dc machines is the
simplex series or lap winding.
A simplex lap winding is a rotor winding consisting of coils containing
one or more turns of wire with the two ends of each coil coming out at
adjacent commutator segment (Figure 8-13).
Figure 8-14 shows a simple two-pole machine with lap windings.
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The Lap Winding
C=8, P = 2
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The Lap Winding
Interesting feature of simplex lap windings: there are as many parallel
current paths through the machine as there are poles on the machine.
A number of coils in each parallel current paths = C/P
where C = number of coils = commutator segments
P = parallel current paths = number of poles = number of
brushes
Figure 8-15 shows a simple four-pole motor having four parallel current
paths, each having an equal voltage.
More parallel current paths (multi-pole machine) => low-voltage, high
current machine.
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The Lap Winding
C=16, P = 4
Simple four-pole motor
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The Lap Winding
Serious problem with multi-pole lap-wound machine.
Figure 8-16 shows six-pole machine as an example. In the long usage,
there has been slight wear on the bearings of machine, and the lower
wires are closer to their pole faces than the upper wires are.
As a result, there is a larger voltage in the current paths involving wires
under the lower pole faces than in the paths involving wires under the
upper pole faces.
Since all the paths are in parallel => this cause the large circulating
current flowing out some brushes as shown in Figure 8-17. Potentially
serious heating problems.
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The Lap Winding
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The Lap Winding
The circulating currents in four or more poles can be reduced somewhat
by equalizers or equalizing windings.
Equalizers are bars located on the rotor of a lap-wound dc machine that
short together points at the same voltage level in the different parallel
paths.
Using equalizers, the circulating current would flow inside the small
sections of windings shorted together and to prevent this circulating
current from flowing through the brushes.
These circulating currents even partially correct the flux imbalance due to
non-uniform air-gap.
Figure 8-18 shows an equalizer for four-pole machine in Figure 8-15.
Figure 8-19 shows an equalizer for a large lap-wound dc machine.
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The Lap Winding
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The Lap Winding
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The Lap Winding
In case of duplex lap winding, therefore, the commutator pitch yc = ± 2
(depending on whether the winding is progressive or retrogressive).
Since each set of windings has as many current paths as the machine
has poles, there are twice as many current paths as the machine has
poles in a duplex lap winding.
In general, for an m-plex lap winding, the commutation pitch yc is
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The Wave Winding
The series or wave winding is an alternative way to connect the rotor
coils to the commutation segments.
Figure 8-20 shows a simple four-pole machine with a simplex wave
winding.
There are two coils in series between the adjacent
commutator segments, having a side under each pole
face.
All output voltages are the sum of the effects of every
pole, and there can be no voltage imbalance.
Progressive winding : second coil is connected to the
segment ahead of the first coil.
Retrogressive winding : second coil is connected to
segment behind the first coil.
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The Wave Winding
For P pole machines, then there are P/2 coils in series between
adjacent commutator segments.
In a simplex wave winding,
- There are only two current paths (ie., two brushes needed).
- There are C/2 or one-half of the windings in each current path.
- The brushes will be located a full pole pitch apart from each other.
What is the commutator pitch yc for a wave winding ?
Figure 8-20 shows a progressive non-coil winding, and
the end of coil occurs five segments down from its
starting point.
In a retrogressive wave winding, the end of the coil
occurs four segments down from its starting point.
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The Wave Winding
In general, the commutator pitch in any simplex wave winding is
where C is number of coils on the rotor and P is number of poles. The
sign in the equation (8-27) indicates
Plus sign => progressive winding
Minus sign => retrogressive winding
Figure 8-21 shows a simplex wave winding.
Wave windings are well suited to building higher-voltage dc machines,
since the number of coils in series between commutator segments
permits a high voltage to be built up more easily than with lap
windings.
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The Wave Winding
Simplex wave winding for four-pole machine
For a multiplex wave winding => multiple independent sets of wave windings.
=> number of current paths, a (m=plex of winding)
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The Frog-Leg Winding
The frog-leg winding or self-equalizing winding consists of a
lap winding and a wave winding combined.
Equalizers in lap winding are connected at point of equal
voltage on the winding.
Wave windings reach between points of equal voltage
under successive pole faces of the same polarity, which
are same locations that equalizers tie together.
⇒ Wave windings can function as equalizers for the lap
winding.
The number of current paths is as
(P= number of poles, mlap = plex of lap winding)
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8.4 Problems with Commutation
in Real Machines
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Problems with Commutation in
Real Machines
Two major effects occur in the
real dc machine to disturb the
commutation process.
1. Armature reaction
2. L.di/dt voltages
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Armature Reaction
(Neutral-Plane Shift)
There are two serious problems caused by armature reaction in real
dc machines.
1. neutral-plane shift.
- Flux is distributed uniformly under
the pole faces as shown in Figure 823(b).
- As rotor rotates with ω, the rotor
windings have voltage built up as
shown in Figure 8-23(a).
- The magnetic neutral plane is exactly
vertical.
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Armature Reaction
(Neutral-Plane Shift)
There are two serious problems caused by armature reaction in real
dc machines.
- Now this generator is loaded.
- The flow of load current produces a
1. neutral-plane shift.
magnetic field from the rotor
windings as shown in Figure 8-23(c).
- As a combination of rotor magnetic
field and magnetic field from poles,
the magnetic flux in the air-gap of
the machine is skewed. See Figure 823(d)
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Armature Reaction
(Neutral-Plane Shift)
There are two serious problems caused by armature reaction in real
dc machines.
1. neutral-plane shift.
- The neutral plane is now shifted in the
direction of rotation as shown in Figure 823(e).
- For motor, the current in its rotor would
be reversed. The rotor magnetic field is in
the opposite. The neutral plane is shifted
the other way, opposite with the direction
of rotation.
- Amount of shift depends on the amount of
load current.
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Armature Reaction
(Neutral-Plane Shift)
So, what is the big deal about neutral-plane shift ?
If the brushes are set to short out conductors in the vertical plane, then
the voltage between commutator segments is indeed zero.
When the machine is loaded, the neutral plane shifts and the brushes
short out commutator segments with a finite voltage across them.
The result is a current flow circulating between shorted commutator
segments and large sparks at the brushes when the current path is
interrupted as the brush leaves a commutator segment.
The end result is arcing and sparking (even flashover near
segments) at the brushes :
⇒ reducing brush life
⇒ pitting of the commutator segments
⇒ greatly increased maintenance costs
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Armature Reaction
(Flux Weakening)
There are two serious problems caused by armature reaction in real
dc machines.
2. Flux weakening.
- In most machines, the operating flux density
near saturation point (@pole mmf).
- At the locations on the pole surfaces where
the rotor magnetomotive force adds to the
pole magnetomotive force => smaller
increase in flux (smaller ∆φi)
- At the locations on the pole surfaces where
the rotor magnetomotive force subtracts
from the pole magnetomotive force =>
larger decrease in flux (larger ∆φd)
- The net result: total average flux under
entire pole face is decreased.
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Armature Reaction
(Flux Weakening)
Effects of flux weakening
Generator : lower induced voltage
Motor : - lower produced torque
- runaway condition
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L.di/dt Voltages
Sometimes this problem related to L.di/dt is called inductive kick.
When a commutator segment is shorted out, the current flow through
that commutator segment must reverse. Assuming that the total
current in the brush is 400 A.
Assuming that the machine is turning at 800 rpm, there are 50
commutator segments, each commutator segment moves under a
brush and clear it again in t= 0.0015 sec = 60/(800*50) sec
Therefore, the rate of change in current with respect to time in the
shorted loop must average
Even tiny inductance (L) in the loop, a very significant inductive
voltage kick v = L.di/dt induced in the shorted commutator segment.
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L.di/dt Voltages
This high
inductive
voltage causes
sparking at
the brushes.
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Solutions to the Problems with
Commutation
Three approaches partially or completely
correct the problems of armature reaction
and L.di/dt voltages :
1. Brush shifting
2. Commutating poles and interpoles
3. Compensating windings
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Brush Shifting
Today, the brush shifting approach was already obsolete.
The idea of the brush shifting is to adjust the brushes every time the
load on the machine changed. As the neutral plane moves with
every change in load, and the shift direction reverses when the
machine goes from motor to generator.
Another slightly different approach was to fix the brushes in a
compromise position causing no sparks at a specific load. As for
different loads from this specific load, the sparks occur.
However, the brush shifting actually aggravates the flux-weakening
effect of the armature reaction because of two effects:
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Brush Shifting
However, the brush shifting actually aggravates the flux-weakening
effect of the armature reaction because of two effects:
1. Rotor magnetomotive force now has a vector component that
opposes the magnetomotive force from the poles (see Figure 827).
2. The change in armature current distribution causes the flux to
bunch up even more at the saturated parts of the pole faces.
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Brush Shifting
Rotor magnetomotive
force now has a vector
component that opposes
the magnetomotive force
from the poles (see Figure
8-27).
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Commutating Poles or
Interpoles
Basic idea is that if the voltage in the wires undergoing commutation can
be made zero, then there will be no sparking at the brushes.
To accomplish this, small poles called commutating poles or interpoles
are placed midway between the main poles.
These interpoles are located directly over the conductors being
commutated.
By providing a flux from the interpoles, the voltage in the coils undergoing
commutation can be exactly canceled. If the cancellation is exact, then
there will be no sparking at the brushes.
Interpoles do not affect both machine operation and armature reaction.
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Commutating Poles or
Interpoles
How it work ?
This is done by simply connecting the interpole windings in series with the
windings on the rotor (armature winding). See Figure 8-28.
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Commutating Poles or
Interpoles
As the load increases, and the rotor current increases, both neutral-plane
shift and L.di/dt effects increase the voltage in the conductor undergoing
commutation.
The interpole flux increases too, producing a large voltage in the
conductors that opposes the voltage due to the neutral-plane shift.
Interpoles work for both motor and generator operation.
The interpoles must induce a voltage in the conductors undergoing
commutation that is opposite to the voltage caused by neutral-plane shift
and L.di/dt effects.
The use of interpole is very common due to its fairly low cost. Almost
found in dc machines of 1 hp or higher.
Interpoles do nothing for the flux distribution under the pole faces.
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Commutating Poles or
Interpoles
Opposite polarity
of voltages
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Compensating Windings
To completely cancel armature reaction, the compensating windings in slots
carved in the faces of the poles parallel to the rotor conductors, to cancel
the distorting the effect of armature reaction.
These compensating windings are connected in series with the rotor
windings, so that the load changes in the rotor, the current in the
compensating winding changes too.
See Figure 8-30(a) for the pole flux by itself.
In Figure 8-30(b), the rotor flux and the compensating winding flux are
shown.
Figure 8-30(c) represents the sum of these three fluxes, which is just equal
to the original pole flux by itself.
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Compensating Windings
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Compensating Windings
Figure 8-31 shows the development of the effect of compensating windings
on a dc machine.
The magnetomotive force due to compensating windings is equal and
opposite to the magnetomotive force due to the rotor at every point under
the pole faces.
The resulting net magnetomotive force is just the magnetomotive force due
to the poles, so the flux in the machine is unchanged regardless of the load
on the machine.
The main disadvantage of compensating windings is that they are
expensive. Any motor that used them must also have interpoles.
Compensating windings do not cancel L.di/dt effect while interpoles do.
Compensating windings do correct the neutral-plane shifting only.
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Compensating Windings
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8.5 The Internal Generated
Voltage and Induced Torque
Equations of Real DC Machines
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The Internal Generated
Voltage of Real DC Machines
The induced voltage in any given machine depends on three factors:
The voltage in any single conductor under the pole faces is
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The Internal Generated
Voltage of Real DC Machines
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The Internal Generated
Voltage of Real DC Machines
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The Internal Generated
Voltage of Real DC Machines
It is common to express the speed of a machine in revolutions per
minute (rpm, unit of n) instead of radians per second (unit of ω).
So, the voltage equation with speed in rpm is
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The Internal Generated
Torque of Real DC Machines
The induced torque in any given machine depends on three factors:
The torque in any single conductor under the pole faces is
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The Internal Generated
Torque of Real DC Machines
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The Internal Generated Voltage
and Torque of Real DC Machines
Both internal generated voltage and the induced torque equations just
given are only approximations.
Reasons:
- Not all conductors in the machine are under the pole faces at any
given time.
- The surfaces of each pole do not cover an entire 1/P of the rotor
surface.
To achieve greater accuracy, the number of conductors under the pole
faces could be used instead of the total number of conductor on the
rotor.
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Example Problem
Example 8-4 on page 517
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8.6 The Construction of DC
Machines
Simplified Sketch of a dc Machine
The physical structure of the machine consists of two parts: stator and
rotor.
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Pole and Frame Construction
The main poles of newer machines are
made entirely of laminated material.
The laminated main poles reduce the
eddy current losses in the much higher ac
content in the power supplied to dc
motor driven by solid-state drive
packages.
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Pole and Frame Construction
Pole faces: chamfered or eccentric type.
The outer tips of a pole face have higher air-gap than the rotor
surface at the center of the pole face. This increases reluctance at
the tips and thus reduces the flux-bunching effects of armature
reaction.
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Rotor and Armature Construction
Core is composed of many laminations stamped from the steel plate,
with notches along its outer surface to hold the armature windings.
Commutator is built onto the shaft of
the rotor at one end of the core.
Armature coils are laid into the slots
on the core, as described in Section
8.4, and their ends are connected to
the commutator segments.
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Commutator and Brushes
Commutator is typically made of copper bars insulated by a mica-type
material. The copper bars are made sufficiently thick to permit normal
wear over the lifetime of the motor.
Mica insulation between
segments is harder than the
commutator material itself.
Brushes made of carbon,
graphite, metal graphite or a
mixture of carbon and
graphite. (high
conductivity reducing
electrical losses & low
coefficient of friction,
reducing excessive wear)
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Commutator and Brushes
Brushes are too soft => replaced too often
Brushes are too hard => commutator surface will wear excessively over
the life of the machine.
Brush pressure is too great => Both brushes and commutator bars wear
excessively.
Brush pressure is too low => brushes tend to jump slightly and a great
deal of sparking occurs at the brushcommutator segment interface.
Another factor which affects the wear on the brushes and segments :
amount of current flowing in the machine.
If the current is too small, thin oxide layer (which lubricates the motion
the brushes over segments) will break down, increasing frictions
between brushes and commutator (rapid wear).
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Winding Insulation
To prevent the winding insulation from breaking down, it is necessary to
limit the temperature of the windings. This can be partially done by
⇒ Cooling air circulation
⇒ Limit power that can be supplied continuously by machine.
Increase in temperature => gradual degradation of the insulation.
Rule of thump: motor life expectancy is halved for each 10% rise in
winding temperature.
National Electrical Manufacturers Association (NEMA) in USA has
defined a series of insulation system classes in NEMA standard MG11993, Motors and Generators.
International Electrotechnical Commision (IEC) or various national
standards in other counties has also defined the insulation classes.
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Winding Insulation
National Electrical Manufacturers Association (NEMA) in USA has
defined a series of insulation system classes in NEMA standard MG11993, Motors and Generators.
There are four standard NEMA insulation classes for integral-horsepower
dc motors. Each class represents the highest permissible winding
temperature.
Class
Class
Class
Class
A .. is limited to 70oC
B .. is limited to 100oC
F .. is limited to 130oC
H .. is limited to 155oC
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8.7 Power Flow and Losses in DC
Machines
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Efficiency in DC Machines
The efficiency of a dc machine is defined by the equation
The difference between input power and the output power of a
machine is the losses that occur inside it. Therefore,
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The Losses in DC Machines
The losses that occur in dc machines
can be divided into five categories:
1.Electrical or copper losses (I2R losses)
2.Brush losses
3.Core losses
4.Mechanical losses
5.Stray load losses
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Electrical or Copper Losses
Copper losses are losses that occur in the armature and field windings of
the machine.
Resistance used in these calculations is usually winding resistance at
normal operating temperature.
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Brush Losses
Brush loss is the power lost across the contact potential at the brushes
of the machine.
Voltage drop across a set of brushes is approximately constant over a
large range of armature currents.
The brush voltage drop is usually assumed to be about 2 V.
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Core Losses
Core losses are the hysteresis losses and eddy current
losses occurring in the metal of the machine.
These losses are described in Chapter 1.
These losses vary as the square of the flux density
(B2) and, for the rotor, as the 1.5th power of the speed
of rotation (n1.5).
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Mechanical Losses
Mechanical losses in a dc machine are losses
associated with mechanical effects. There are two
basic types:
1. Friction losses : losses caused by the friction of the
bearings in the machine.
2. Windage losses : losses caused by the friction
between moving parts of the machine and air
inside the motor’s casing.
These losses vary as the cube of the speed of rotation
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(n3).
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Stray Losses (or Miscellaneous
Losses)
Stray losses are losses that cannot be placed in one of
the previous categories.
Some losses always escape inclusion in one of the
above categories.
All such losses are lumped into stray losses.
For most machine, stray losses are taken by
convention to be 1 percent of full load.
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The Power-Flow Diagram
One of the most convention techniques for accounting for power losses
in a machine is the power-flow diagram.
The mechanical power that is converted is given by
The resulting electric power produced is given by
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The Power-Flow Diagram
generator
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The Power-Flow Diagram
motor
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EEE 118: Energy Conversion
Dr. Mongkol Konghirun
Department of Electrical Engineering
King Mongkut’s University of Technology Thonburi
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