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# Torque in a Synchronous Motor

## Synchronous Motor Torque

The mechanical power developed (P_{m}) by any synchronous motor can be expressed as −

$$\mathrm{P_{m}=\frac{2πN_{S}\tau_{g}}{60}\:Watts\:\:\:\:\:\:...(1)}$$

Also, the mechanical power developed (P_{m}) is,

$$\mathrm{P_{m}=VI_{a}Cos(δ-φ)\:\:\:\:\:\:...(2)}$$

Where,

N

_{S }is the synchronous speed in RPM.τ

_{g}is the gross-torque in N-m.

Therefore, the gross torque of the synchronous motor is given by,

$$\mathrm{\tau_{g}=\frac{60}{2π}\frac{P_{m}}{N_{S}}=9.55\times\frac{P_{m}}{N_{S}}N-m\:\:\:\:\:\:...(3)}$$

And the shaft torque is given by,

$$\mathrm{\tau_{sh}=9.55\times\frac{P_{o}}{N_{S}}N-m\:\:\:\:\:\:...(4)}$$

Where,P_{o} is the mechanical power output at the shaft of the motor.

From Eqns.(3)&(4), it can be noted that the torque is directly proportional to the mechanical power since the speed of the motor is constant i.e. synchronous speed (N_{S}).

## Types of Torque in a Synchronous Motor

In order to select a synchronous motor for a particular application, the following torques are considered −

## Pull-in Torque

As a synchronous motor is started as an induction motor and runs at a speed 2% to 5% below the synchronous speed. Then, the DC excitation voltage is applied and the rotor pulls into step with the rotating magnetic field of the stator which is revolving at synchronous speed. Therefore, the maximum torque at rated voltage and frequency under which a synchronous motor will pull a connected load into synchronism when the DC excitation is applied to the motor, is known as *pull-in torque*.

## Pull-out Torque

There is a limit to the mechanical load that can be applied to a synchronous motor. With the increase in the load, the torque angle (δ) also increases so that a stage is reached when the rotor is pulled out of synchronism and the motor comes to the rest. Therefore, the maximum value of load torque which a synchronous motor can develop at rated voltage and frequency without losing synchronism is called as *pull-out torque or breakdown torque.*

## Locked Rotor Torque

The *locked rotor torque* is the minimum value of the torque developed by a synchronous motor with the rotor locked (i.e. stationary rotor) at any angular rotor position and rated voltage and frequency is applied to the motor. The locked rotor torque is provided by the armature windings of the motor.

## Running Torque

The torque developed by a synchronous motor under running conditions is known as *running torque*. The running torque is determined by the power rating and the speed of the motor.

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