Question

What is the relationship between slip and torque in an induction motor's torque-speed curve?

Answer 1

In an induction motor's torque-speed curve, the relationship between slip and torque is fundamental to understanding its operation. Let's break down the concepts:

Slip: Slip refers to the difference between the synchronous speed of the rotating magnetic field generated by the motor's stator and the actual speed of the rotor. It's expressed as a percentage:

Slip
(
%
)
=

sync
−

actual

sync
×
100
Slip(%)=
N
sync
    ​

N
sync
    ​

−N
actual
    ​

    ​

×100

Where

sync
N
sync
    ​

 is the synchronous speed (in RPM) determined by the frequency of the power supply and the number of pole pairs in the motor, and

actual
N
actual
    ​

 is the actual rotor speed (in RPM).

Torque: Torque is the rotational force produced by the motor that enables it to perform mechanical work. In an induction motor, the torque generated is directly proportional to the square of the stator current and the slip. It's given by the equation:

T = \frac{{3 \times V^2 \times R_{\text{2}}}{{\omega_{\text{sync}}}} \times \frac{{s}}{{(R_{\text{2}}^2 + (s \times X_{\text{2}})^2)}}

Where:


T is the torque produced

V is the voltage applied to the motor's stator

2
R
2
    ​

 is the rotor resistance

2
X
2
    ​

 is the rotor reactance

sync
ω
sync
    ​

 is the synchronous angular velocity (radians per second)

s is the slip (as a fraction)

Now, considering the torque-speed curve:

Starting Point: At standstill (zero speed), the slip is 1 (100%), and the torque is at its maximum value, known as the "starting torque" or "breakdown torque." This is the point where the motor can develop the maximum torque to overcome the inertia and start the rotation.

Operating Region: As the motor starts to accelerate, the slip decreases, causing the torque to decrease. The torque decreases roughly linearly with slip until a point where the torque curve intersects the load curve (the mechanical load the motor is driving). This point is known as the "pull-out torque" or "maximum torque."

Synchronous Speed: As the motor accelerates further and reaches the synchronous speed, the slip becomes zero, and the torque also becomes zero. At this point, the motor is no longer producing any torque since there is no relative speed between the rotating magnetic field and the rotor.

The torque-speed curve essentially illustrates how the motor's ability to produce torque changes as its speed increases. It's important to match the motor's characteristics with the requirements of the mechanical load to ensure proper operation and efficiency.