Losses in a D.C. Machine

The various losses in a d.c. machine whether it is a motor or a generator are classified into three groups as :
1. Copper losses.
2. Iron or core losses.
3. Mechanical losses.
1.1 Copper Losses
The copper losses are the losses taking place due to the current flowing in a winding. There are basically two windings in a d.c. machine namely armature winding and field winding. The copper losses are proportional to the square of the current flowing through these windings. Thus the various copper losses can be given by,
where        Ra = Armature winding resistance.
and            I= Armature current.
where        Rsh = Shunt field winding resistance.
and           Ish  = Shunt field current
where     Rse = Series field winding resistance
and         Ise = Series field current
In a compound d.c. machine, both shunt and series field copper losses are present. In addition to the copper losses, there exists brush contact resistance drop. But this drop is usually included in the armature copper loss.
There are few losses which vary with the load but their relationship with the load current can not be identified in simple manner. Such losses are called stray load losses and are the part of variable losses. These occur in the windings and the core. These include copper stray load loss and iron stray load loss. These stray load losses are difficult to measure or mathematically calculate hence practically taken as 1% of the output for the d.c.machines. Many times these losses are neglected.
1.2 Iron or Core Losses
These losses are also called magnetic losses. These losses include hysteresis loss and eddy current loss.
The hysteresis loss is proportional to the frequency and the maximum flux density in the air gap and is given by,

η = Steinmetz hysteresis coefficient.
where   V = Volume of core in m3.
f = Frequency of magnetic reversals.
This loss is basically due to reversal of magnetization of the armature core.
The eddy current loss exists due to eddy currents. When armature core rotates, it cuts the magnetic flux and e.m.f. gets induced in the core. This induced e.m.f. sets up eddy currents which cause the power loss. This loss is given by,
where     K = Constant
t = Thickness of each lamination.
V = Volume of core.
f = Frequency of magnetic reversals.
The hysteresis loss is minimized by selecting the core material having low hysteresis coefficient. While eddy current loss is minimized by by selecting the laminated construction for the core.
These losses are almost constant for the d.c. machines.
1.3 Mechanical Loss
These losses consist of friction and windage losses. Some power is required to overcome mechanical friction and wind resistance at the shaft. This loss is nothing but the friction and windage loss. The mechanical losses are also constant for a d.c. machine.
The magnetic and mechanical losses together are called stray losses. For the shunt and compound d.c. machines where field current is constant, field copper losses are also constant. Thus stray losses along with constant field copper losses are called constant losses. While the armature current is dependent on the load and thus armature copper losses are called variable losses.
Thus for d.c. machine,
Total losses = Constant losses + Variable losses
The Fig. 1 shows the various types of losses taking place in a d.c. machine.
 Fig. 1  Losses in a d.c. machine

1.4 Power Flow in D.C. Machines
The power flow and energy transformation diagrams at various stages, which takes place in a d.c. machine are represented diagrammatically in Fig. 2(a) and (b).
 Fig. 2
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