Understanding Rotor Frequency in Induction Motors: Slip Calculation

A 4-pole 3-phase induction motor operates from a supply of 50 Hz. What is the frequency of the rotor when the slip is 3?

To find the frequency of the rotor in an induction motor, we need to follow several steps involving calculations related to synchronous speed, actual speed, and rotor frequency. Let's break down the process to understand how to determine the rotor frequency based on the given slip.

Calculating Rotor Frequency

The first step involves determining the synchronous speed (Ns) of the motor. This is given by:

(N_s frac{120 times f}{P})

Where:

Ns - Synchronous speed in RPM f - Supply frequency in Hz P - Number of poles

For a 4-pole motor operating at 50 Hz:

(N_s frac{120 times 50}{4} 1500 text{ RPM})

Calculating Actual Rotor Speed

Next, we calculate the actual speed (N) of the rotor using the slip (s). The slip is defined as:

(s frac{N_s - N}{N_s})

Rearranging the formula, we can express the rotor speed as:

(N N_s times (1 - s))

Given a slip of 3 or 0.03:

(N 1500 times (1 - 0.03) 1500 times 0.97 1455 text{ RPM})

Calculating Rotor Frequency (fr)

The rotor frequency is calculated using the formula:

(f_r s times f)

Substituting the given values:

(f_r 0.03 times 50 1.5 text{ Hz})

Hence, the frequency of the rotor when the slip is 3 is 1.5 Hz.

Additional Insights into Slip in Induction Motors

The slip of an induction motor is proportional to its load. Typically, the figure quoted is for full load. If the field is rotating at 1500 RPM with a 3% slip (0.03), the rotor is turning at 1455 RPM (1500 - 1500 x 0.03).

From an engineering perspective, the rotor frequency is the product of the slip and the stator frequency. For a 50 Hz supply:

(f_r 0.03 times 50 1.5 text{ Hz})

This indicates that the rotor currents are at a frequency of 1.5 Hz.

From an outside observer's perspective, the rotor currents are relative to the rotor, while for a stationary observer, the rotational speed of the rotor corresponds to (1-s) x stator frequency. The rotor current frequency is the product of the rotor's rotational frequency and its current frequency relative to itself, which is the same as the stator frequency from an outside observer's perspective.