An EMF is induced in a conductor whenever there is relative motion between the conductor and a magnetic field. In a DC generator, rotating armature conductors cut through the field flux, inducing a voltage. The magnitude is proportional to the rate of flux linkage change.
e = dλ/dt = N(dΦ/dt)
A current-carrying conductor in a magnetic field experiences a force. In a DC motor, the armature current-carrying conductors in the field flux experience tangential forces, producing developed torque.
F = BIL → Te = 2BiLr (single turn)
The induced EMF opposes the change that caused it. In a motor, the back-EMF Ea opposes the applied voltage Vt. In a generator, the developed torque Td opposes the prime mover torque.
The MMF (ampere-turns) provided by the field winding drives flux through the magnetic circuit of the machine. The reluctance of the iron core and air gap determines the flux per pole Φp.
Φp = kfIf (linear region only)
Power balance governs both modes. In a generator: mechanical input power = electrical output + losses. In a motor: electrical input = mechanical output + losses. The coupling equation is Pd = EaIa = Tdωm.
The commutator and brushes rectify the alternating EMF induced in the rotating armature coils into a unidirectional (DC) terminal voltage. Current reversal in commutating coils must complete within commutation time tc to prevent sparking.
Equivalent circuit equations (by connection type):
Vt = Ea − IaRa − Vbrush
IL = Ia − If (shunt)
Terminal voltage falls with load due to armature resistance drop and armature reaction demagnetization.
Vt = Ea + IaRa + Vbrush
ωm = (Vt − IaRa) / (KaΦp)
Speed is nearly constant with load variations (shunt field ≈ constant flux). Good for constant-speed drives.
Vt = Ea + Ia(Ra + Rse)
Φp ∝ Ia → Td ∝ Ia²
High starting torque. Speed varies widely with load; may overspeed at no-load. Suited for traction drives.
Both shunt & series field windings present
Cumulative: Φtotal = Φsh + Φse
Combines stable speed (shunt) with high starting torque (series). Differential type used for specialized speed control.
Vt = Ea − IaRa
Vt = Ea + IaRa | IL = Ia + If
| Machine Type | Speed-Torque Behaviour | Speed Regulation | Applications |
|---|---|---|---|
| Shunt Motor | Nearly constant speed. Slight drop in speed with increasing load due to IaRa voltage drop reducing back-EMF. | Good (5–15%) | Fans, pumps, machine tools, centrifugal compressors |
| Series Motor | Speed decreases sharply with increasing torque (T ∝ Ia², Φ ∝ Ia). Very high starting torque. Dangerous at no-load (overspeed). | Poor — large variation | Traction, cranes, hoists, electric vehicles |
| Compound Motor (Cum.) | Intermediate — better starting torque than shunt, better speed regulation than series. Stable at all loads. | Moderate | Rolling mills, presses, compressors |
| Separately Excited Generator | Terminal voltage droops with increasing load current due to IaRa drop and armature reaction. Controlled by adjusting If. | VR = (Ea − VFL)/VFL | Laboratory supplies, electroplating, Ward-Leonard |
| Shunt Generator | Voltage droops moderately with load. Self-excited from residual magnetism. Critical field resistance for self-excitation. | Moderate (10–15%) | Battery charging, small power supplies |
| Compound Generator (Cum.) | Series field compensates for load drops. Over-compound: V rises with load. Flat-compound: V ≈ constant. Under-compound: V drops slightly. | Excellent (near zero for flat-compound) | Welding, lighting, long distribution feeders |
Magnetization curve: The no-load characteristic (Ea vs If at constant speed) mirrors the B-H curve. Initially linear (air-gap dominates), then bends to saturation. The air-gap line (tangent through origin) separates the air-gap MMF from total MMF. Scaling to a different speed: Ea2 = (ωm2/ωm1) × Ea1.
Pmech,in (prime mover) → Rotational losses (friction, windage, core) → Pd = EaIa → Armature copper loss Ia²Ra + brush losses → Pout = VtIL
η = Pout / Pin = VtIL / (Tappωm)
Pelec,in = VtIL → Field copper loss If²Rf + armature copper loss Ia²Ra + brush losses → Pd = EaIa = Tdωm → Rotational losses → Pshaft = Tshaftωm
From ωm = (Vt − IaRa) / (KaΦp), three control methods follow:
(a) Field weakening — reduce If → reduce Φp → increase speed (above base speed); (b) Armature voltage control — reduce Vt → reduce speed (below base speed); (c) Armature resistance control — insert external resistance in series with armature; poor efficiency.
Under load, the armature MMF (q-axis) distorts the field flux, shifting the magnetic neutral plane in the direction of rotation (generator) or against rotation (motor). This causes: demagnetization (flux reduction), cross-magnetization (distortion), and sparking (improper commutation). Remedies: (1) advance brushes to new neutral plane (constant load only); (2) interpoles — wound with armature current, cancel armature flux at neutral zone for any load; (3) compensating windings — embedded in pole faces, carry armature current in opposition, fully cancel cross-magnetization.