DC Machine (Generators & Motors)
Constructional details, commutator action, generator EMF and motor torque derivations, self-regulating role of back EMF, 3-point starters, and speed control methods.
8.1 & 8.2 Constructional Details & Governing Equations
Major Constructional Components
- Yoke (Magnetic Frame): Outer cast steel or cast iron housing that provides mechanical protection and carries magnetic flux for the pole cores.
- Pole Core & Pole Shoes: Laminated steel projecting inward to carry field coils. Pole shoes spread magnetic flux uniformly across the air gap and support the coils.
- Armature Core: Slotted cylinder made of laminated silicon steel sheets to carry insulated armature conductors while minimizing eddy current losses.
- Armature Windings:
• Lap Winding: Coils overlap each other. Number of parallel paths \(A = P\). Suitable for high current, low voltage machines.
• Wave Winding: Coils progress forward in a wave. Number of parallel paths \(A = 2\) always. Suitable for high voltage, low current machines. - Commutator: Cylindrical assembly of wedge-shaped copper segments insulated by mica. In generators, acts as a mechanical rectifier converting AC induced EMF into DC terminal voltage. In motors, reverses current in each coil as it crosses magnetic neutral zone to maintain unidirectional torque.
- Carbon Brushes: Spring-loaded carbon/graphite blocks riding on the commutator surface to conduct current between the rotating armature and stationary external terminals.
Governing EMF and Torque Derivations
8.3 & 8.4 DC Motor Types, Back EMF & Performance Curves
The Self-Regulating Role of Back EMF
When a DC motor rotates, its armature conductors cut the field flux, inducing a counter-EMF (Back EMF \(E_b\)) that opposes the applied terminal voltage:
\[E_b = \frac{P \Phi Z N}{60 A} = V - I_a R_a\]
Armature current:
\[I_a = \frac{V - E_b}{R_a}\]
Why \(E_b\) acts as an automatic governor:
1. If mechanical load on the motor increases, the motor momentarily slows down (\(N \downarrow\)).
2. Because \(E_b \propto N\), back EMF decreases (\(E_b \downarrow\)).
3. This allows armature current to rise automatically: \(I_a = \frac{V - E_b}{R_a} \uparrow\).
4. Torque \(T \propto \Phi I_a\) increases to match the new mechanical load demand until equilibrium is restored!
Performance Characteristics Comparison
| Machine Type | Torque vs Current (\(T\) vs \(I_a\)) | Speed vs Current (\(N\) vs \(I_a\)) | Standard Applications |
|---|---|---|---|
| DC Shunt Motor | Linear: \(T \propto I_a\) (since \(\Phi\) is constant). | Almost constant speed with slight drop (5–8%) due to \(I_a R_a\) drop. Known as a "constant-speed motor". | Lathes, centrifugal pumps, fans, machine tools. |
| DC Series Motor | Parabolic before saturation: \(T \propto I_a^2\). Produces huge starting torque! | Hyperbolic: \(N \propto \frac{1}{I_a}\). Speed becomes dangerously high at no-load! Must never be started on no-load. | Electric trains/traction, cranes, elevators, hoists. |
| Cumulative Compound | Higher starting torque than shunt due to aiding series field. | Moderate speed drop under load without runaway danger at light load. | Rolling mills, heavy punching presses, shears. |
8.5 & 8.6 Starting of DC Motors & Speed Control
Why Starters are Essential & 3-Point Starter Operation
At standstill (\(t = 0\)), rotor speed \(N = 0 \implies E_b = 0\). If direct line voltage is applied: \[I_{\text{start}} = \frac{V - 0}{R_a} = \frac{V}{R_a}\] Since armature resistance \(R_a\) is very small (\(< 0.5\,\Omega\)), direct switching draws 15–25 times rated full-load current, blowing fuses, melting insulation, and burning commutator segments.
• Starting Resistor: Arranged in tapped studs to introduce high resistance at start, cut out step-by-step as the motor accelerates and builds \(E_b\).
• No-Volt Coil (NVC): Electromagnet connected in series with the shunt field. Holds the starter handle in the 'ON' position. If power fails or the field circuit breaks, NVC de-energizes and a spring pulls the arm back to 'OFF', preventing dangerous re-energization.
• Overload Release (OLR) Coil: Connected in series with the main supply. If excessive current flows, OLR lifts an iron armature that short-circuits the NVC, immediately tripping the starter handle.
Speed Control Methods
From the basic speed equation: \[N = \frac{V - I_a R_a}{k \Phi}\]
| Method | Operational Mechanism | Speed Range | Drawback / Trade-off |
|---|---|---|---|
| Armature Resistance Control | Add variable resistance \(R_{\text{ext}}\) in series with armature. Increases circuit resistance: \(E_b = V - I_a(R_a + R_{\text{ext}})\) drops. | Below rated base speed only | Poor efficiency (huge \(I_a^2 R_{\text{ext}}\) power waste in controller resistor); poor speed regulation. |
| Field Flux Control | Insert variable rheostat into shunt field circuit. Reduces field current \(I_{sh}\), reducing flux \(\Phi\). Because \(N \propto 1/\Phi\), motor speeds up! | Above rated base speed only | Very high efficiency (field current is small, \(< 2\%\) of rated); limited at upper speeds by mechanical centrifugal limits and commutation sparking. |
Master Worked Example: Speed Control with Added Armature Resistance
Armature resistance \(R_a = 0.4\,\Omega\)
Field resistance \(R_{sh} = 120\,\Omega\)
Initial current \(I_{L1} = 30\text{ A}\), Initial speed \(N_1 = 1400\text{ rpm}\)
Added series resistance \(R_{\text{ext}} = 1.2\,\Omega\)
Load torque is reduced by 20% \(\implies T_2 = 0.8 T_1\)