Speed Control of a DC Shunt Motor by Armature Resistance
โก DC MOTOR SIMULATION โก
๐น CONNECTION DIAGRAM (Schematic Description)
๐ Armature Resistance Control Scheme โ A variable external resistor (Ra_ext) is connected in series with the armature winding.
Supply (240V DC) โ Field winding (parallel) + Armature circuit: [ Ra_int + Ra_ext ] โ Back EMF path.
The diagram illustrates typical 3-point starter configuration and rheostat in armature loop.
Supply (240V DC) โ Field winding (parallel) + Armature circuit: [ Ra_int + Ra_ext ] โ Back EMF path.
The diagram illustrates typical 3-point starter configuration and rheostat in armature loop.
Fig 1.1: Schematic representation of armature resistance speed control method for DC shunt motor.
This simulation illustrates how adding external resistance (Raext) in series with the armature affects motor speed, while field current remains constant. Adjust the load torque slider to explore performance under different loading conditions.
๐ Load Torque: 14.0 Nยทm | ๐ก Torque โ โ Armature current โ โ Speed drops further
| Parameter | Symbol | Value |
|---|---|---|
| Terminal Voltage | $V_t$ | 240 V |
| Internal Armature Resistance | $R_{a_{int}}$ | 0.5 ฮฉ |
| Field Resistance | $R_f$ | 120 ฮฉ |
| Motor Constant | $K$ (Nยทm/A) = $K$ (V/rad/s) | 1.485 |
โ Field current is constant: $I_f = V_t / R_f = 2.0 A$. Only armature current varies with load torque.
๐ Underlying Principles & Governing Equations
The speed of a DC shunt motor is controlled by inserting external resistance $R_{a_{ext}}$ in the armature circuit. The key relationships are:
- Constant Field Current ($I_f$): Because field winding is directly across supply, $I_f = \dfrac{V_t}{R_f}$ remains fixed, thus flux $\phi$ is nearly constant.
- Armature Current from Load: Developed torque $T_d = K \cdot I_a$ must equal load torque $T_L$ at steady state โ $I_a = \dfrac{T_L}{K}$.
- Back EMF & Speed Equation: Applying KVL to armature loop: $V_t = E_b + I_a (R_{a_{int}} + R_{a_{ext}})$. Since back EMF $E_b = K \cdot \omega$ (mechanical rad/s), solving for speed: $$\omega = \dfrac{V_t - I_a (R_{a_{int}} + R_{a_{ext}})}{K}$$ In RPM: $N = \omega \cdot \dfrac{60}{2\pi}$.
- Effect of $R_{a_{ext}}$: As external resistance increases, the voltage drop $I_a R_{a_{ext}}$ rises, reducing back EMF and thereby reducing speed. For a fixed $T_L$, this method provides smooth speed reduction below base speed.
๐ก LAB TIP: Armature resistance control is economical for low-power motors and provides smooth torques but is inefficient at low speed due to power loss in the external resistor.