The torque-speed characteristic curve is one of the most important performance indicators of a three-phase induction motor. It shows how the motor’s developed torque varies with rotor speed, from standstill to synchronous speed, and helps engineers understand starting performance, running behavior, and overload capacity.
Torque Equation:
The torque \( T \) developed by a three-phase induction motor is given by:
\( T = \frac{3}{2\pi N_s} \cdot \frac{s E_2^2 R_2}{R_2^2 + (s X_2)^2} \)
- \( E_2 \) = standstill rotor emf per phase
- \( R_2 \) = rotor resistance per phase
- \( X_2 \) = rotor reactance per phase at standstill
The typical torque-speed curve has three regions:
Starting Region (N = 0 to ~20–30% of Ns)
At standstill (\( s = 1 \)), starting torque is moderate (1.5–2.5 times full-load torque). Rotor frequency \( f_2 = s \cdot f = f \), so reactance is high, limiting torque.
Motoring Region (Stable Operating Region)
Torque increases with speed and reaches maximum (pull-out torque) at slip \( s_m \). \( s_m \approx \frac{R_2}{X_2} \). Motor operates near synchronous speed with slip 2–5%.
Generating Region (N > Ns)
Slip becomes negative and motor acts as a generator.
Key Points:
- Starting Torque: Torque at \( N = 0 \)
- Maximum Torque: 2–3 times full-load torque
- Full-load Torque: Occurs at slip 2–5%
Effect of Rotor Resistance
- Low \( R_2 \): High efficiency, low starting torque
- High \( R_2 \): High starting torque, peak shifts to lower speed
- Maximum torque value remains constant, only its position changes
Typical Numerical Values
| Parameter | Approximate Value |
|---|---|
| Synchronous Speed | 1500 rpm |
| Full-load Speed | 1440–1480 rpm |
| Starting Torque | 1.5–2.5 × \( T_{fl} \) |
| Maximum Torque | 2.0–3.0 × \( T_{fl} \) |
| Full-load Slip | 2–4% |
Table of Contents
Key Regions of the Curve
| Region | Speed Range | Torque Behavior | Practical Importance |
|---|---|---|---|
| Starting (Locked Rotor) | 0 speed | High torque (≈1.5 × full-load torque) | Determines ability to start heavy loads |
| Acceleration | 0 → near full speed | Torque rises, peaks at breakdown torque | Ensures smooth acceleration |
| Breakdown Torque | At critical slip | Maximum torque (≈2.5 × full-load torque) | Safety margin against overload |
| Full-Load | Slightly below synchronous speed | Rated torque | Normal operating point |
| Synchronous Speed | Ns = 120f/P | Torque = 0 | Motor cannot reach synchronous speed |
Important Characteristics
- Slip (s): \( s = \frac{N_s – N}{N_s} \)
- Starting Torque: Determines if the motor can start under load.
- Breakdown Torque: Maximum torque before instability.
- Stable Operation: Occurs between full-load torque and breakdown torque.
- Unstable Region: Beyond breakdown torque, motor stalls.
Factors Affecting the Curve
- Rotor Resistance: Higher resistance increases starting torque but reduces efficiency.
- Supply Voltage: Torque ∝ Voltage²; reduced voltage lowers torque.
- Frequency & Poles: Synchronous speed depends on supply frequency and number of poles.
- Load Type: Pumps, fans, and conveyors require different torque-speed profiles.