DC Machines: Generators and Motors

A DC machine converts between mechanical power and DC electrical power through a commutator. The same machine works as a generator or a motor.

EMF and torque

E = P Φ N Z/(60 A) (V)

• P = poles, Φ = flux per pole (Wb), N = speed (rpm), Z = armature conductors, A = parallel paths: A = P for lap winding, A = 2 for wave winding.
• Torque T = P Φ Z I_a/(2π A) = E I_a/ω. So T ∝ Φ I_a and E ∝ Φ N.

Types

Separately excited, and self-excited: shunt, series and compound (cumulative or differential).

• Generator: V = E − I_a R_a. Motor: V = E_b + I_a R_a (E_b = back EMF).
• Armature reaction distorts and weakens the main flux; interpoles and compensating windings counter it and help commutation.

Generator characteristics

• Shunt generator builds up only if there is residual flux, the field resistance is below the critical resistance, and the field is connected the right way.
• Series generators have a rising characteristic; over-compounded generators make up line drop.

Motor characteristics

Speed: N ∝ E_b/Φ = (V − I_a R_a)/Φ.

Speed control

• Field control (shunt motor): weakening Φ raises speed above base speed (constant power).
• Armature voltage / resistance control: reduces speed below base speed (constant torque). Ward–Leonard gives smooth control.

Starting and losses

At standstill E_b = 0, so the starting current V/R_a would be huge: a starter adds series resistance (3-point and 4-point starters).

Losses: copper (I²R), iron, mechanical, brush contact. Maximum efficiency when variable (copper) loss = constant loss.

Worked example

A 4-pole lap-wound generator has 500 conductors and 0.02 Wb per pole at 1200 rpm.

• E = 4 × 0.02 × 1200 × 500/(60 × 4) = 200 V.

Practice