A 10 -hp six-pole 60 -Hz three-phase induction motor runs at...

Name: Problem 4, Chapter 17: Electrical Engineering: Principles and Applications
Uploaded: 2021-11-20T03:07:01-08:00
Duration: 1 min 49 s
Channel: Narayan Hari
Description: A 10 -hp six-pole 60 -Hz three-phase induction motor runs at 1160 rpm under full-load conditions. Determine the slip and the frequency of the rotor currents at full load. Also estimate the speed if the load torque drops in half.

A 10 -hp six-pole 60 -Hz three-phase induction motor runs at 1160 rpm under full-load conditions. Determine the slip and the frequency of the rotor currents at full load. Also estimate the speed if the load torque drops in half.

Key Concepts

Load Torque and Speed Response

The load torque is the external torque demand imposed on the motor, and any changes in this load affect the motor’s operating point on its torque-speed curve. In induction motors, a reduction in load torque (such as a halving of the original torque) tends to allow the rotor to accelerate toward the synchronous speed, thus reducing the slip. However, due to the characteristics of the motor’s torque-speed curve and the dependence of developed torque on slip, even a modest decrease in load torque can result in a relatively small increase in operating speed, given that the motor is already close to synchronous speed.

Rotor Frequency

Rotor frequency refers to the frequency of the currents induced in the rotor windings, and it is directly proportional to the slip of the induction motor. It is calculated by multiplying the slip by the supply frequency (f_r = s × f). This frequency is lower than the stator frequency, and it determines the dynamic behavior of the rotor currents, including their effect on torque production and energy losses in the motor.

Synchronous Speed

Synchronous speed is the theoretical speed of the rotating magnetic field in an AC motor, determined solely by the supply frequency and the number of poles in the motor. It is calculated using the formula Ns = 120f/P, where f is the frequency and P is the number of poles. This concept establishes the maximum speed that the motor’s magnetic field can achieve under ideal conditions and serves as the reference speed for determining slip.

Slip

Slip is the difference between the synchronous speed and the actual rotor speed, expressed as a fraction or percentage of the synchronous speed. It is a critical parameter in induction motors because it is necessary for torque production. Slip is defined by the formula s = (Ns - N) / Ns, where Ns is the synchronous speed and N is the rotor speed under load. The slip indicates how far the rotor lags behind the magnetic field, which is essential for energy conversion from the electrical to the mechanical domain.

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