EMF Equation of DC Machine
According to Faradays Laws of induction, Average emf generated per
conductor is given by
Eg = dΦ/dt
(Volts) ... eq. 1
Flux cut by one conductor in one revolution =
dΦ = PΦ
(Weber)
Number of revolutions per second (speed in RPS) =
N/60
Therefore, time for one revolution =
dt = 60/N
(Seconds)
From eq. 1, emf generated per conductor Eg = dΦ/dt
Eg = PΦN/60
(Volts) …..(eq. 2)
Above equation-2 gives the emf generated in one conductor of the
generator.
The conductors are connected in series per parallel path, and the emf
across the generator terminals is equal to the generated emf across any
parallel path.
Multiply equation 2 by Z/A
we got,
Eg = PΦNZ / 60A
(Volts)
P = number of field poles
Ø = flux produced per pole in Wb (weber)
Z = total no. of armature conductors
A = no. of parallel paths in armature
N = rotational speed of armature in revolutions per min. (rpm)
Torque Equation of DC Machine
Torque is given by the product of the force and the radius at which this
force acts.
T
=
F × r (N-m)
Work done by this force in once revolution = Force × distance
w
=
F × 2πr
where 2πr = circumference of the armature
Net power developed in the armature = work done / time
P
=
(force × circumference × no. of revolutions) / time
P
=
(F × 2πr × N) / 60 --------------------- eq 1
But we know T
= F x r and ω = 2πN/60
Putting these in the above equation 1, Net power developed in the
armature is
P
=
T×ω
(Joules per second)
The power developed in the armature can be given as:
Pa = Ta × ω
Pa = Ta × 2πN/60
The mechanical power developed in the armature is converted from
the electrical power,
mechanical power
=
electrical power
Ta × 2πN/60
=
Eb.Ia
We know, Eb = PΦNZ / 60A
Therefore,
Ta × 2πN/60
=
(PΦNZ / 60A) × Ia
Rearranging the above equation,
Ta
=
(PZ / 2πA) × Φ.Ia (N-m)
The term (PZ / 2πA) is practically constant for a DC machine. Thus,
armature torque is directly proportional to the product of the flux and
the armature currenti.e.
Ta ∝ Φ.Ia
Armature Winding
A type of winding that is housed in the slots of core and is responsible
for the production of flux. The produced flux opposes the developed
main field flux known as an armature reaction.
Before going through this section, we should understand some basic
terms related to armature winding.
Pitch of Armature Winding
Back Pitch (Yb)
Front Pitch (Yf)
Resultant Pitch (Y)
Commutator Pitch
Types of Armature Winding
Generally there are two types of Armature winding in the DC machines.
They are classified as follow,
 Lap winding
 Wave winding
The difference between these two is merely due to the end
connections and commutator connections of the conductor.
Lap Winding
In lap winding, the ending of one coil has connected the beginning end
of the succeeding coil through commutator which is under the same
pole.
Equalizer Ring
In lap winding all the conductors in any parallel path lie under one pair
of poles. The currents flowing in various paths may also differ due to
difference in their resistances. Hence there is always slight difference in
the generated voltage in the various parallel paths, and as a result,
large circulating currents flow in the armature winding. These
circulating currents not only tend to heat the armature above the
temperature cause an undue amount of sparking at the brushes and
commutator.
To overcome the effects resulting from the circulating currents, it is
customary to employ equalizer rings in all lap wound armatures. These
are low resistance copper wires that connect together points in the
armature winding.
Wave Winding
In wave winding, the last coil is attached to the beginning end of the
succeeding coil through a commutator which is under the beside pole.
Dummy Coils
In the case of wave winding, some slots are not filled completely. This
causes some mechanical imbalance in the rotor. The life of the machine
decreases due to this imbalance. So, in order to overcome this problem,
the empty slots are filled by some dummy coils.
The dummy coils provide mechanical support to the rotor. These are
also called dead coils. No energy conversion takes place inside the
dummy coils and these are not connected to the commutator.