**9.2. Losses **

Losses in a D.C. machine can be classified as follows :

1. Electrical losses (copper loss) :

- i. Armature = I
_{a}^{2}R_{a} - ii. Series field = I
_{se}^{2}R_{se} - iii. Shunt field = VI
_{sh} - iv. Com mutating field = I
_{e}^{2}R_{c}.

2.Rotational losses (stray·power loss) :

(i) Core loss:

- Hysteresis
- Eddy currents.

(ii) Mechanical (or friction) loss :

- Bearings
- Brushes
- Windage.

- The core losses and friction losses are supplied from the mechanical power developed by the machine. They are put into a single group called mechanical losses or more generally, stray-power losses. When a generator or motor runs at a fixed speed and generates a given voltage, the stray-power loss is constant regardless of the electrical output or input of the machine for speed and flux density are the only factors that influence the stray-power loss.
- The electrical losses are supplied from the electrical power generated by or delivered to the machine, as the case may be. Of these, the shunt field loss is somewhat, though not entirely independent of the load, while the remaining electrical losses are nearly proportional to the square of the load current. Fig. 95 shows the combined power-flow diagram for motor or generator action which is self-explanatory.
Fig. 95. Combined power-flow diagram for motor or generator action.

9.2.1. Copper (or electrical) losses. When an electric current of I ampere flows in a

resistance of R ohms, heat energy is lost at the rate of I^{2}R joules/see, and the power loss is I^{2}R watts. Generators and motors have one or more field circuits and an armature circuit in which such losses occur. All resistance losses of kind are classed as copper loss.1) Armature copper loss = I

_{a}^{2}Ra. This is about 30% to 40% of total full-load losses.2) Field copper loss. This loss equals I

_{sh}^{2}R_{sh}for the shunt field winding and I_{se}^{2}R_{se}for the series field winding. This loss constitutes about 30% of the total full-load losses.3) Brush contact loss. This loss is due to the resistance of brush contacts. The voltage drop at the brush is almost independent of I

_{a}. For carbon brushes the voltage drop is around 1 volt per brush. The power loss due to brush contact resistance is 2e_{b}I_{a}where e_{b}is the voltage drop at one brush.4) Loss in commutating pole winding. This loss equals Ia

^{2}x resistance of com mutating pole winding.5) Loss in compensating winding. This loss equals Ia

^{2}x resistance of compensating winding.**9.2.2. Iron losses.**Iron losses are a function of both flux and speed.Hysteresis loss. The hysteresis loss Ph is a measure of the electric energy required to overcome the retentivity of the iron in the magnetic flux path. using watts as unit,

P

_{h}= K_{h}B^{x}fVwhere V = volume of iron in dynamo subject to change of flux … (15)

K

_{h}= constant for the grade of iron employedB = flux density raised to the Steinmetz exponent. With modern values of dynamo x is no longer 1.6 but closer to 2.0. This is not to imply that for a given volume, V,of iron the loss has increased, because K

_{h}has been reduced considerablyf = frequency (Hz) of reversal of flux.

Eddy current losses. These losses occur not only in the dynamo iron but in all conductive materials with the flux path of the rotating or varying magnetic field of the dynamo. The eddy current loss P

_{c}, in watts isP

_{s}= K_{c}t^{2}B^{2}f^{2}V … (16)where K, = an eddy current constant for the grade of iron employed

t = thickness of the laminations of the pole core and armature

B = flux density

f = frequency (Hz) of reversal of flux

V = volume of iron subject to change of flux.

For a D.C. dynamo the frequency, f, reversal of flux varies with speed. Thus the hysteresis loss varies directly with speed whereas the eddy current loss varies as the square of speed. Both hysteresis loss and eddy current loss vary approximately as the square of the flux density. For this reason core losses are considered a function of both flux and speed.

**9.2.3. Mechanical (or friction) losses.**When a machine is running, there are various

frictional forces to be overcome, each of which requires a continuous expenditure of energy and results in heating the rubbed parts. There is friction loss in the machine bearings. at the surface of the commutator due to the rubbing of the brushes. and in the armature core due to its fanning action. These losses depend upon the speed but are independent of the load on the machine. They are difficult to estimate by direct calculation but may be found by measurement.

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