Electrical Engineering ⇒ Topic : Torque-slip Characteristics

TORQUE-SLIP AND TORQUE-SPEED CURVES:-

The expression for torque is as follows

From the above expression it evident that :

Torque is zero when slip 's' = 0 (i.e., speed is synchronous).

When slip `,s' is very low the value of the term sX₂ is very small and is negligible in comparison with R₂, therefore torque T is approximately proportional to slip 's' if rotor resistance R₂ is constant. This means that at speeds near to synchronous speed the torque-speed and torque-slip curves are approximately straight lines

 When the slip 's' increases (i.e., as, the speed decreases with increase in load) torque increases and reaches its maximum value when    The maximum torque is also known as 'pull-out' or 'break-down' torque.

        Torque-speed curves                                                                   Torque-slip curves

When the slip is further increased the torque decreases. The result is that motor slows down and eventually stops. The motor operates for the value of slip between zero and that corresponding to maximum torque.

With higher slip, R₂ becomes negligible as compared to sX₂ and torque varies as follows :

This means that speed-torque or slip-torque curves are rectangular hyperbola with the speed or slip beyond, -that corresponding to maximum torque. Fig. show that the torque-speed and torque-slip curves for different values of rotor resistance. It is observed that although maximum torque is independent of rotor resistance R₂, yet the exact location of T_max is dependent on it. -Greater the R₉, greater is the value of slip at which maximum torque occurs.

TORQUESLIP CHARACTERISTICS

Figure (a) reduces to Figure (b) by using Thevenin's theorem

Figure (a) Equivalent circuit of a three-phase induction motor without core loss

                                      .............. (1)

                                      ............... (2)

                                figure (b)  Thevenin's equivalent circuit

X₁ + X_Φ, is much greater than r₁ for most of the induction motors. So r₁ can be neglected. Thus,

Eqs. (1) and (2) become

where X₁ = x₁ + X_Φ, is the stator self reactance per phase.

From Figure (b), the rotor current is given by

                                       .............. (3)

Using Eq. (3), the torque is given by

        ............. (4)

Figure (c) shows the variation of torque with slip or speed of an induction motor.

          Figure (c) Torque-slip characteristic curve of an induction motor.

The following are the three different modes of operation of an induction motor:

• Motoring mode (0≤ s ≤1): In this mode of operation, rotor rotates in the same direction of rotating magnetic field. The speed of the rotor is less than the synchronous speed.
• Generating mode (s < 0): In this mode of operation, the stator terminals of an induction motor are connected to constant frequency voltage source. The rotor is being rotated above the synchronous speed with the help of a prime mover. It may be noted that the stator should not be disconnected from the supply.
• Braking mode (s > 1): In this mode, slip is greater than 1. The rotor is being driven by the prime mover in the direction opposite to the rotating magnetic field.
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