ARMATURE CORE DESIGN
The armature of a dc machine consists of core and winding.
The armature core is cylindrical in shape with slots on the outer periphery of
the armature.
The core is formed with circular laminations of thickness 0.5 mm.
The winding is placed on the slots in the armature core.
The design of armature core involves the design of main dimensions D & L,
number of slots, slot dimensions and depth of core.
Number of armature slots
The factors to be considered for selection of number of armature slots are
Slot width (or pitch)
Cooling of armature conductors
Flux pulsations
Commutation
Cost
A large number of slots results in smaller slot pitch and so the width of tooth
is also small. This may lead to difficulty in construction.
But large number of slots will lead to less number of conductors per slot and
so the cooling of armature conductors is better.
If the air-gap reluctance per pair of pole is constant then the flux pulsations
and oscillations can be avoided.
It can be proved that the air-gap reluctance is constant if the slots per pole is
an integer plus 1/2.
For sparkless commutation the flux pulsations and oscillations under the
interpole must be avoided. This can be achieved with large number of slots per
pole.
In fact, the number of slots in the region between the tips of two adjacent
poles should be at least 3.
The slots per pole should be greater than or equal to 9, for better commutation.
When large number of slots are used the cost of lamination and the cost of
insulation will be high.
Guiding factors for number of armature slots
The slot pitch should lie between 25 to 35 mm. For small machines it can be
20 mm or even less than 20 mm.
The slot loading should not exceed 1500 ampere conductors.
Slot loading = Number of conductors in the slot x Current per conductor.
To reduce flux pulsation losses the slots per pole should be an integer plus 1/2
for lap winding and slots per pole arc should be an integer plus 1/2 for wave
winding.
To avoid sparking the number of slots per pole should have a minimum value
of 9. The slots per pole varies from 9 to 1 6. In case of small machines it can be 8.
The number of slots selected should be suitable for the type of winding. In
case of simplex lap winding the number of slots should be a multiple of pole pair.
In case of wave winding the number of slots should not be a multiple of pole pair
to avoid dummy coils.
Slot dimensions
The dimensions of the slot are slot width and depth.
Usually the slot area is estimated from the knowledge of conductor area and
slot space factor.
The slot space factor lies in the range of 0.25 to 0.4 and the value depends on
the thickness of insulation.
Slot area= Conductor area/Slot space factor
After deciding the slot area, the depth of slot is assumed based on the diameter
of the armature.
The following factors can be considered before finalising the slot dimensions.
Flux density in tooth
Flux pulsations
Eddy current loss in conductors
Reactance voltage
Fabrication difficulties
The table below can be used as a guideline for choosing the slot depth. Once
the depth is finalised, the width can be estimated from the slot area and depth.
Diameter of
Armature(m)
Slot Depth
(mm)
0.15
22
0.20
27
0.25
32
0.30
37
0.40
42
0.50
45
The dimensions of the slot and the number of slots will decide the dimensions
of the tooth. The dimensions of the tooth should be chosen such that the flux
density in any part of tooth does not exceed 2.1 Wb/m2.
The slot opening should be as small as possible in order to reduce flux
pulsation losses.
With increase in depth of the slot the eddy current loss in conductor increases,
specific permeance of slot increases, reactance voltage increases and it becomes
difficult to fabricate the lamination with narrow width at the roots of teeth.
Depth of armature core
The depth of armature cannot be independently designed, because it depends
on the diameter of armature (D), inner diameter of armature (Di) and the depth of
slot (ds). The figure shows the cross-section of armature.
From figure,
D = Di + 2dc + 2ds
Depth of core, d = 1/2(D-Di-2ds)
After estimating D, Di and ds the available depth of core dc can be calculated.
With this value of dc, the flux density in the core can be estimated and if it
does not exceed 1.5 Wb/m2, then the available depth of core is sufficient.
Otherwise we have to increase the diameter of the armature D to give
sufficient depth for core. The usual value of flux density in the core is 1.0 to 1.5
Wb/m2
Finally, the depth of the core is given by,
dc= ½(
/L
iBc)
where,
= Flux per pole
Li = Net iron length of the armature
B = Flux density in the core
ARMATURE WINDING DESIGN
In general the armature winding consists of a number of coils connected in
series and number of such series circuits are connected in parallel.
The coils are diamond shaped and are made in special forming machines. The
coils may be single turn or multi turn coil, and a turn consists of two conductors.
The coils are placed in the slots on the armature periphery. In full pitched
winding the two coil sides of a coil are placed one pole pitch apart.
The dc machine armature windings are double layer windings, which mean
that each slot has two coil sides.
The design of armature winding involves the selection of type of winding,
estimation of number of armature coils, turns per coil, conductors per slot, total
number of armature conductors and dimensions of the conductor.
Types of armature winding
DC machines employ two general types of double layer windings. They are
Simplex lap winding
Simplex wave winding
These two types of windings primarily differ from each other in the following
two factors.
The number of circuits between the positive and negative brushes,
i.e., number of parallel paths.
The manner in which the coil ends are connected to the
commutator segments.
In simplex lap winding the number of parallel paths is equal to number of
poles, whereas in simplex wave winding the number of parallel paths is two.
In simplex lap winding the finish of a coil is connected to start of next coil. In
simplex wave winding the finish of a coil is connected to start of a coil which is
lying one pitch away from the finish.
The simplex lap or wave windings are suitable for most of the dc machines
used for various applications. But occasionally the number of parallel paths has to
be increased to a value more than that provided by simplex windings. In such
cases the multiplex windings are employed.
When the number of parallel paths in a multiplex winding is twice that of
simplex winding it is called duplex winding. When the number of parallel paths in
a multiplex winding is thrice that of simplex winding it is called triplex winding
and so on.
In general the lap winding and wave winding refers to simplex windings.
Definition of various terms used in armature winding
Conductor: The active length of copper or aluminium wire in the slot is
called conductor.
Turn: Two conductors connected for additive emf is called a turn. The two
conductors of a turn are placed approximately a pole pitch apart.
Coil: A coil consists of a number of turns and it is the principal element of
armature winding. The coil with single turn is called single turn coil and the
coil with several turns is called multi turn coil.
Coil side: The active portions of the conductors in a coil are called coil sides.
A coil will have two sides and they are upper coil side and lower coil side.
Usually the top coil side is represented by solid line and bottom coil side by
dotted line. The top coil side is placed in the upper portion of a slot and the
bottom coil side is placed at the lower portion of another slot. The distance
between the two coil sides is kept approximately as one pole pitch.
Overhang: The end portion of the coil connecting the two coil sides is called
overhang.
Coil span: The distance between the two coil sides of a coil is called coil
span. It is expressed in terms of number or slots or in electrical degrees.
Full pitch coil: When the coil span is equal to pole pitch, the coils are called
full pitched coils.
Short pitched or chorded coil: When the coil span is less than the pole pitch,
the coils are called short pitched or short chorded coils.
Single layer winding: When the coil sides are arranged in a single layer in a
slot, the winding is called single layer winding.
Double layer winding : When the coil sides are arranged in two layers in a
slot, the winding is called double layer winding.
Back Pitch (Yb): The distance between top and bottom coil sides of a coil
measured around the back of the armature (away from the commutator) is
called the back pitch. The back pitch is measured in terms of coil sides. Since
Yb is difference between odd and even number, it is always an odd number.
The back pitch of a coil determines the size of the coil and is nearly equal to
coil sides per pole or pole pitch.
Front Pitch (Yf): The distance between two coil sides connected to the same
commutator segment is called the front pitch (Yf). The front pitch determines
the type of the winding only and it does not affect the size of the coils.
Winding Pitch (Y): The distance between the starts of two consecutive coils
measured in terms of coil sides is called winding pitch (Y). The winding pitch
is always an even integer.
Y = Yb - Yf for lap winding
Y = Yb + Yf for wave winding
Commutator Pitch (Yc): The distance between the two commutator segments
to which the two ends (start and finish) of a coil are connected is called the
commutator pitch (Yc) and it is measured in terms of commutator segment.
Number of armature coils: The number of turns per coil and the number of
coils are so chosen that the voltage between adjacent commutator segments is
limited to a value where there is no possibility of a flashover. Normally, the
maximum voltage between adjacent segments at load should not exceed 30V.
SIMPLEX LAP WINDING
In simplex lap winding the finish of a coil is connected to start of next coil.
This winding scheme results in a number of parallel paths which is equal to
number of poles.
The simplex lap winding is a closed winding. In a closed winding if we trace
the winding starting from one point, we will reach the same point after traveling
through all the turns.
But the electrical circuit closes through external load in case of generator and
through external supply in case of motor. The simplex winding has one closed
electrical circuit. (i.e., all the parallel paths electrically closes through external
load or supply).
The two types of simplex lap winding used are
progressive lap winding and
Retrogressive lap winding.
In the progressive lap winding the joining to the commutator progress around
the commutator in the same direction as the coils progress around the armature, as
shown in figure.
In the retrogressive lap winding the joining to the commutator segment
progresses around the commutator in the opposite direction to the progress of
coils around the armature, as shown in figure.
The various winding pitches for simplex lap winding are listed in table below.
In lap winding the back and front pitch are always odd integers. The winding
pitch is always two and commutator pitch is always one.
Usually the simplex lap winding is wound with two coil sides per slot. But
simplex lap winding is possible with 4, 6, etc, (i.e., even number) coil sides per
slot.
When the coil sides per slot is more than two, the back pitch (yb) should be
chosen such that all the coils having their top coil sides in one slot should have all
their corresponding bottom coil sides together in another slot, which is one pole
pitch away.
If the back pitch is not properly chosen then the coil sides in the upper layer of
one slot will be connected to bottom coil sides of two different slots. For this
arrangement split coils have to be used, which is not desirable from practical point
of view.
The split coils will have more than two coil sides. When all the top coil sides
of a coil are lying in one slot and their corresponding bottom coil sides are
accommodated in two different slots then the coil is called split coil.
Steps for designing of lap winding for a dc machine
Step 1: Find the range of slots from the range of slot pitch. Armature slot
pitch, Ysa = 25 to 35 mm. Slots, itD/y where D is diameter of armature
Step 2: In the above range of slots, list the values of slots which are multiples
of pole pairs.
Step 3: In order to reduce flux pulsations, the slots per pole should be an
integer ± 1/2. The integer should be in the range of 8 to 16. List all the
multiples of integer ± 1/2 from the list obtained in step 2.
Step 4: Choose the suitable slot from the list obtained in step 3.
Step 5: Estimate the total number of armature conductors, Z using the
equation of induced ernf. Find the conductors per slot and choose it to the
nearest even number.
Step 6: Find the minimum number of coils.
Step 7:
Assume, u = 2, 4, 6, 8 etc., where u = coil sides per slot.
Step 8: For each value of u, calculate the number of coils. Choose the number
of coils such that, it is greater than minimum number of coils. Also the value
of u should be a divisor of conductors per slot.
Step 9: Once the number of coils and slots are finalized, Estimate the new
value of total number of conductors and number of turns per coil.
Total armature conductors, Z = Slots x Conductor per slot.
Number of turns per coil = Z/2C.
If a suitable value of C is not obtained to satisfy the above condition, then
make another choice of slots from the list obtained in step 3.
Guide lines for drawing simplex lap winding diagram
The following guidelines will be useful for drawing simplex lap winding with two
coil sides per slot.
Determine the number of coil sides and represent the coil sides by parallel
straight lines as shown in figure. The top coil sides are shown by solid (or
continuous) lines and bottom coil sides are shown by broken (or
discontinuous) lines. In the winding diagram, the top and bottom coil sides are
shown alternatively because each slot has one top coil side and one bottom
coil side.
Number the coil sides such that the top coil sides are represented by odd
numbers and bottom coil sides by even numbers as shown in figure.
Determine the coil sides per pole, which gives the number of coil sides lying
under a pole at any instant of time. The enclosure of coil sides by a pole is
represented by a shaded rectangle as shown in figure below. Different types of
shadings are provided for north and south poles. The north and south poles are
placed alternatively.
The direction of current through conductors under the north pole will be
opposite to the direction of current through conductors under the south pole.
Mark the direction of current through conductors under north pole as upwards
and that of south pole as downwards as shown in the above figure.
Calculate the back pitch and front pitch. The back connection is decided by
back pitch and the front connection is decided by front pitch. Connecting the
top coil side to bottom coil side of the same coil is called back connection.
Connecting the bottom coil side of a coil to the start of next coil is called front
connection.
Bottom coil side of a coil = Top coil side of same coil + Back pitch
Top coil side of next coil = Bottom coil side of previous coil – Front pitch
Determine all the back and front connections. Represent the connections by a
winding table. For progressive lap winding, the winding table can be prepared
as shown below.
Let, Back pitch, Yb = 7
Front pitch, Yf = 5
After preparing the winding table, draw all the front connections and back
connections. One back connection and one front connection are shown in figure
3.10. All the back connections are shown in figure 3.11 and all the front
connections are shown in figure 3.12.
The meeting points of coil ends formed by the front connections are
terminated on the commutator segments. In simplex lap winding with two coil
sides per slot, the number of commutator segments is equal to number of coils.
The commutator segment connection is represented by placing one segment at the
meeting point of one top coil side and one bottom coil side of each front
connection as shown in fig 3.12.
The number of brushes will be equal to number of poles. Half the number of
brushes are positive and the remaining half are negative. Brush locations can be
shown in the diagram by observing the currents entering and leaving the
commutator segments. The current enters or leaves the commutator segment
through the conductors connected to them. Two conductors are connected to each
commutator segment.
If current enter the segment through one conductor and leaves via another
conductor then the brush cannot be located at that segment. If current enters the
commutator segment from both the conductors then a positive brush can be placed
at that location for a generator. If current leaves the commutator segment through
both the conductors then a negative brush can be placed at that location for a
generator. The locations of brushes are shown in fig 3.12.
Note: The direction of current through armature conductors for a motoring operation
is opposite to that of generator, provided the direction of field (or flux) and speed
remaining same as that of generator operation.
PROBLEMS