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Chapter 13: Problem 5

Why does the rotor of an induction motor turn slower than the revolving field?

Short Answer

Expert verified
The rotor of an induction motor turns slower than the revolving magnetic field due to slip, which is essential for generating an induced EMF, current, and torque in the rotor. The slip is the difference between the synchronous speed and the rotor speed. If the rotor reaches the synchronous speed, the relative motion between the rotor and the stator's field becomes zero, resulting in no induced EMF or torque, making it impossible to drive the load connected to the induction motor.

Step by step solution

01

Understanding the revolving magnetic field

In an induction motor, a 3-phase supply is given to the stator windings which produce a rotating magnetic field around the stator. This revolving field has a synchronous speed, which depends on the number of poles and the supplied frequency, given by the formula: \[ N_s = \frac{120f}{P} \] Where: - \(N_s\) = synchronous speed (in RPM) - \(f\) = frequency (in Hz) - \(P\) = number of poles
02

Interaction between the revolving field and the rotor

The rotor is placed inside the stator, and when the stator's revolving field passes through the rotor bars, an electromotive force (EMF) is induced in the rotor due to the transformer action. The induced current in the rotor will generate its magnetic field, opposing the stator's field as per Lenz's law. The interaction between these two fields leads to the development of torque, which causes the rotor to turn.
03

Slip and rotor speed

Due to the torque developed and load connected to the rotor, the rotor starts rotating. However, the rotor doesn't reach the synchronous speed of the stator due to what is known as 'slip.' Slip (S) is a crucial factor in understanding the induction motor's operation and is defined as the difference between the synchronous speed and the rotor speed, as a percentage of the synchronous speed: \[ S = \frac{N_s - N_r}{N_s} \times 100\% \] Where: - \(N_s\) = synchronous speed (in RPM) - \(N_r\) = rotor speed (in RPM) - \(S\) = slip (in percentage)
04

Rotor current and torque production

The torque developed in the rotor depends on the relative motion between the revolving field and the rotor (i.e., the slip). If the rotor reaches the synchronous speed, the relative motion between the rotor and the stator's field becomes zero, and hence no EMF will be induced in the rotor. Consequently, the current in the rotor would also become zero, leading to no torque. Therefore, the rotor must always have a relative speed with respect to the stator field to produce torque. In summary, the rotor of an induction motor turns slower than the revolving magnetic field because of the slip, which is essential to generate an induced EMF, current, and torque in the rotor. If the rotor reaches the synchronous speed, the relative motion becomes zero, and no torque is developed to drive the load connected to the induction motor.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Synchronous Speed
In the world of induction motors, the term **synchronous speed** refers to the speed at which the stator's magnetic field revolves. An understanding of synchronous speed is crucial because it is the benchmark against which rotor speed is measured. The formula to calculate synchronous speed is given by:
  • \( N_s = \frac{120f}{P} \)
Here, \(N_s\) is the synchronous speed in revolutions per minute (RPM), \(f\) is the frequency of the electrical supply in hertz (Hz), and \(P\) denotes the number of poles in the motor. This speed is vital as it represents the speed at which the magnetic field spins in the stator, setting a standard that the rotor aspires to meet. However, due to certain operational reasons explored in subsequent sections, the rotor never actually achieves this speed in normal operation.
Slip in Induction Motors
The term **slip** is pivotal when studying induction motors, as it explains why the rotor does not reach synchronous speed. In essence, slip is the difference between the synchronous speed (the theoretical speed) and the rotor speed (the actual speed). It is usually expressed as a percentage:
  • \( S = \frac{N_s - N_r}{N_s} \times 100\% \)
Where \(N_s\) is the synchronous speed and \(N_r\) is the rotor speed. Slip isn鈥檛 just a minor inconvenience; it鈥檚 an essential part of the motor鈥檚 function. Without slip, no electromotive force (EMF) would be induced in the rotor, leading to no generated torque, and thus, no operation. Slip ensures the induction process continues, enabling the rotor to keep turning below the synchronous speed and allowing interaction between the magnetic fields.
Torque Production
The principle of **torque production** in induction motors is both intriguing and crucial for their operation. When the revolving magnetic field of the stator interacts with the rotor, thanks to slip, an electromotive force is induced in the rotor. This induces a current, which, according to Lenz's Law, produces its own magnetic field, opposing the stator's field. The interplay of these magnetic fields results in the production of torque. Therefore:
  • Torque is proportional to the slip; the more the slip, the higher the torque generated.
  • If the rotor speed equals the synchronous speed (no slip), the relative motion between the fields disappears, meaning no EMF or current in the rotor, leading to zero torque.
Thus, for the induction motor to function effectively, a relative difference in speed (slip) is necessary to maintain torque production, enabling the motor to drive its mechanical load.

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Most popular questions from this chapter

A doubly-fed induction generator runs at supersychronous speed. Does the rotor deliver or absorb active power from the source to which the rotor is connected?

What happens to the rotor speed and rotor current when the mechanical load on an induction motor increases?

Explain the principle of magnetic levitation

A 3-phase, 6-pole induction motor is connected to a \(60 \mathrm{~Hz}\) supply. The voltage induced in the rotor bars is \(4 \mathrm{~V}\) when the rotor is locked. If the motor turns in the same direction as the flux, calculate the approximate voltage induced and its frequency: a. At \(300 \mathrm{r} / \mathrm{min}\) b. At \(1000 \mathrm{r} / \mathrm{min}\) c. At \(1500 \mathrm{r} / \mathrm{min}\)

Explain how a revolving field is set up in a 3-phase induction motor.
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