Question

Draw the torque slip characteristics of three phase induction motor.

Answer 1

The torque-slip characteristics of a three-phase induction motor illustrate the relationship between the torque produced by the motor and the slip, which is the difference between synchronous speed and actual rotor speed expressed as a fraction of synchronous speed.

### Understanding Key Concepts

1. **Synchronous Speed (\(N_s\))**: This is the speed of the magnetic field produced by the stator, calculated using the formula:
   \[
   N_s = \frac{120 \times f}{P}
   \]
   where \(f\) is the frequency of the AC supply in Hertz and \(P\) is the number of poles.

2. **Slip (\(s\))**: Slip is defined as:
   \[
   s = \frac{N_s - N_r}{N_s}
   \]
   where \(N_r\) is the rotor speed. It is expressed as a percentage or a fraction.

3. **Torque (\(T\))**: The torque generated by the motor increases with slip until it reaches a maximum point (breakdown torque) and then decreases with further increase in slip.

### Torque-Slip Curve Features

1. **Zero Slip**: At synchronous speed (zero slip), the motor produces no torque. This is because the rotor does not experience any relative motion with respect to the rotating magnetic field.

2. **Increasing Torque**: As the slip increases from zero, the torque increases. This is due to the induced current in the rotor being higher as the relative motion between the stator’s magnetic field and rotor increases.

3. **Maximum Torque (Breakdown Torque)**: There is a point where the torque reaches its maximum (also called breakdown torque or pull-out torque). Beyond this point, any further increase in slip results in a decrease in torque. This maximum point is critical for motor operation as it indicates the maximum load the motor can handle without stalling.

4. **Torque Drop-off**: After reaching the maximum torque, as slip increases further (indicating that the rotor speed is significantly lower than synchronous speed), the torque starts to decline. This happens because the rotor currents reduce, leading to lower torque production.

5. **Negative Slip**: The curve often continues into negative slip, which represents regenerative braking or operation as a generator. In this region, the motor can supply power back to the electrical system.

### Graphical Representation

- **X-Axis**: Slip (\(s\)) ranging from \(-1\) (full reverse speed) to \(0\) (synchronous speed) and extending into positive values (indicating high slip).
- **Y-Axis**: Torque (\(T\)) typically expressed in Nm or as a multiple of rated torque.

The curve typically looks like a concave shape, rising to a peak (maximum torque) and then falling off towards the right.

### Conclusion

The torque-slip characteristics of a three-phase induction motor are crucial for understanding its performance under various loading conditions. They help in determining the suitable motor for specific applications and understanding how the motor will react under different operational scenarios.

Answer 2

The torque-slip characteristics of a three-phase induction motor are essential for understanding how the torque produced by the motor varies with the slip. Slip is the difference between the synchronous speed of the rotating magnetic field and the actual speed of the rotor.

Here’s a detailed explanation of the torque-slip characteristics and how to draw them:

### Key Terms:
- **Slip (s):** \( s = \frac{N_s - N_r}{N_s} \)
  - \( N_s \): Synchronous speed of the motor (in RPM).
  - \( N_r \): Rotor speed (in RPM).

- **Torque (T):** The torque developed by the motor.

### Typical Torque-Slip Characteristics Curve

1. **X-Axis (Slip):**
   - The x-axis represents the slip, ranging from 0 to 1 (where 1 corresponds to full slip, meaning the rotor is stationary).

2. **Y-Axis (Torque):**
   - The y-axis represents the torque produced by the motor.

### Drawing the Curve

1. **Starting Point:**
   - At **s = 0** (no slip, rotor speed is equal to synchronous speed), the torque is very low. This is because there is no relative motion between the rotating magnetic field and the rotor, resulting in minimal induced current and torque.

2. **Increasing Slip:**
   - As slip increases, the torque starts to increase. The rotor's relative speed to the rotating magnetic field increases, which induces more current in the rotor windings and therefore generates more torque.

3. **Torque Peak:**
   - The curve reaches a peak point. This peak is the **maximum torque** (also called breakdown torque). At this point, the motor delivers the highest torque.

4. **Beyond Peak:**
   - After reaching the peak, if the slip continues to increase, the torque starts to decrease. This happens because the impedance of the rotor winding increases with higher slip, reducing the current and hence the torque.

5. **Saturation and Stall:**
   - Beyond a certain slip, the torque falls off sharply. This region indicates that the motor is approaching a stall condition where it cannot produce sufficient torque to maintain speed.

### Characteristics Curve:

1. **Curve Shape:**
   - The torque-slip curve is typically a curve that starts from the origin (0,0), rises to a peak, and then falls off as slip increases.

2. **Torque vs. Slip:**
   - The curve is nonlinear. Initially, it rises slowly, then steeply as it approaches the peak, and finally falls off more gradually.

### Graphical Representation:

Here’s a simplified representation of the torque-slip characteristics:

```
Torque
|      
|         *
|       *   \   (Maximum Torque)
|      *     \
|     *       \
|    *         \
|   *           \
|  *             \
| *               \
|*___________________ Slip
```

### Notes:

- **Starting Torque:** At slip close to 1 (when the motor starts), the torque is usually quite low but increases quickly as the motor gains speed.
- **Running Torque:** The torque that the motor can sustain under normal operating conditions, where the slip is moderate.
- **Breakdown Torque:** The highest torque the motor can provide before it starts to slip excessively or stall.

Understanding this curve helps in selecting the right motor for specific applications and ensures that the motor operates efficiently within its designed torque and speed ranges.