What is Pull-in torque and Pull-out Torque in synchronous machines

A synchronous motor is not self starting.  Thus, its speed has to be brought near the rated rpm before it can run on its own.  

There are many methods of starting the synchronous motors such as the use of an external pony motor, amortisseur windings which start the motor as an induction motor and the use of VFDs. 

When the speed of the synchronous motor reaches 97% of the nominal speed, the dc supply to rotor of the synchronous motor is switched on.  This produces a "pull-in" torque which helps the rotor poles to catch the imaginary stator poles and run in synchronism. 

The "pull out" torque of the synchronous motor is the torque which can cause the motor to slip and step out of synchronism.  In some cases, the rotor misses a pole and catches the next stator pole.  In many other cases, the rotor runs like the rotor of an induction motor and never gains synchronism.  This can result in serious damage to the rotor.  Hence, synchronous motors should be provided with a reliable "pull-out" protection