Separation of Core Losses

Separation of Core Losses

The no load losses of d.c. machines are classified as shown in the Fig. 5.10.1.

The two components of iron losses are eddy current losses and hysteresis losses. While other no load losses are friction and windage losses.

If N is the speed of the d.c. machine then,

Hysteresis loss Ph ∞ B_max^1.6 N i.e. Ph = A_N

Eddy current loss p_h ∝ B_max² N²  i.e. P_e = BN²

And B_max is the maximum flux density in the core.

 Total iron losses = AN+ BN^{2 .................}(5.10.1)

Where A and B are constants and flux density is constant.

The friction losses also depend on the speed as,

Brush friction loss ∝ N

Bearing friction loss & N^1.5

Windage loss ∞ N²

Out of these losses, the bearing losses are negligible and can be neglected.

.. Friction and windage loss = CN + DN²..................(5.10.2)

Where C and D are constants.

Let P_i = Total iron losses

P_fw = Total friction and windage losses

P_NL = Total no load losses = P_i + P_fw

P_NL = AN + BN² + CN + DN²

P_NL = (A + C) N + (B + D)N² … (5.10.3)

Thus to separate these losses means to find the constants A,B,C and D.

The equation (5.10.5) is the equation of a straight line in which constants K1 and K2 can be obtained experiementally.

By conducting the Swinburne's test, the stray losses PNL at various speeds can be obtained, at the rated P_NL / N excitation current. The graph of against N can be obtained, which is a straight line passing through the points which are obtained experimentally.

At N = 0, P_NL / N= K₁, i.e. the intercept of the straight line on Y-axis which is axis. Which is P_NL / NHence K₁ can be obtained.

While the slope of the line gives the value of the constant K₂. The slope can be calculated by identifying any two points on the line. This is shown in the Fig. 5.10.2.

The test is repeated for other excitation field current I '_f and hence other set of constants K'₁ and K'₂ is obtained.

By using the values of constants obtained graphically, the no load losses can be separated.

Ex. 5.10.1 The total iron loss in a d.c. machine is 7 kW at the rated speed and excitation. With the same excitation and speed reduced by 30 %, the total iron losses were found to be 4 kW. Calculate the hysteresis and eddy current losses at i) Full speed ii) Half of full speed.

Sol. :

Review Question

1. How to seperate the no load losses of a d.c. machine ?