DC Motor/Generator Theory
One machine, two functions
A current-carrying conductor in a magnetic field experiences a force F = BIl (times sin θ for angle). This is motor action: force produces torque, and the commutator reverses the coil current every half turn to keep torque in one direction. Conversely, relative motion between conductor and field induces an emf (generator action): E = Blv. A DC machine can do either; which it is depends on the direction of energy flow, not on construction.
Generator emf
For a DC generator, E = ΦZNP/(60A), with Φ flux per pole, Z armature conductors, N speed in rpm, P poles and A the number of parallel paths (2 for lap, 2p for wave). Emf is therefore proportional to flux and speed.
Motor behaviour
Back emf E_b = V − I_aR_a opposes the supply. At starting E_b is zero, so armature current is limited only by resistance - hence starters or current limiting. When load increases, speed falls, back emf falls and armature current rises until torque matches the load.
Traps
- A shunt motor that loses its field can overspeed; a series motor must never be run unloaded.
- Armature reaction distorts the field; interpoles and compensating windings correct it.
- The commutator is a mechanical rectifier in a generator and an inverter in a motor.
- Back emf is not the supply voltage; it is supply minus the resistive drop.
Worked example
A 110 V shunt motor with R_a = 0.5 Ω draws 20 A: E_b = 110 − (20 x 0.5) = 100 V. If the load raises current to 30 A, E_b = 110 − 15 = 95 V, so speed falls.