For a linear magnetic circuit:

SubstitutingWe obtain:

Where:

Permanent magnet DC machine Separately excited DC machine Self excited DC machine Shunt wound DC machine Series wound DC machine Compound wound DC machine Cumulative compound Short shunt DC machine Long shunt DC machine

Differential compound Short shunt DC machine Long shunt DC machine

A PM motor does not have a field winding on the stator frame

The armature and the field are fed from two independent sources.

From the figure beside:

The characteristics of the shunt machine are similar to those of the separately excited machine

From figure beside:

The speed of the DC series motor is approximately inversely proportional to the input current.

Therefore, on light loads dangerously high speeds could be reached. In practical applications of the motor, protective devices are used to guard against this contingency.

The torque equation:

Calculate the voltage induced in the armaturewinding of a 4-pole, lap-wound, dc machinehaving 728 active conductors and running at 1800rpm. The flux per pole is 30 mWb.

The armature is lap wound, a=p

What is the voltage induced in the armature of the machine of example 1, if the armature is wave wound?

For a wave-wound armature, a = 2. Thus,

A 100-kW, 230-V, shunt generator has Ra=0.05 and Rf =57.5 . If the generator operates at rated voltage, calculate the induced voltage at full-load. Neglect brush contact drop.

If the generator of example 3 has a total mechanical and core loss of 1.8 kW. Calculate: The generator efficiency at full-load The horsepower output from the prime mover to drive

the generator at this load.

From example 3:The copper losses in the field and armature

winding are:

A separately excited dc generator has a constant loss of Pc(W), and operates at a voltage V and armature current Ia. The armature resistance is Ra. At what value of Ia is the generator efficiency a maximum?

For to be a maximum, d/dIa=0, or

Therefore:

the efficiency is maximized when the armature loss equals the constant loss, Pc.

At what load does the generator of examples (3) and (4) achieve maximum efficiency? What is the value of this maximum efficiency?

From problem 4, the constant losses are:

From example (5):

And

A 10-hp, 230-V shunt motor takes a full-load line current of 40 A. The armature and field resistances are 0.25 and 230 , respectively. The total brush-contact drop is 2 V and the core and friction losses are 380 W. Calculate the efficiency of the motor. Assume that stray-load loss is 1% of output.