Single phasing of squirrel cage induction motor

The motor will continue to run at significantly reduced Hp. It will get hot and be damaged if it is not de-energized.

No load or light load it may run for a while without hurting anything at all---

BUT--with a normal load it won't run, long, if the motor has normal overload protection---

A normal thermal overload relay(Not single phase protection) will will drop the motor out on the high amps of the other legs, typically--Then when you try to restart the motor it won't have a reason to turn.

The amount of load is directly proportional to the time required for winding insulation damage.

The amount of load is directly inversly proportional to the time required for winding insulation damage at single phasing if no protection.

Sorry for the mistake.

The available torque will be less, 1/3^-2 of the original value, so will be less the available power. If the load remains below this value the motor will keep running. If the load exceeds that value the motor will stop and - if you have it - the overload protection will trip.

1/3^-2= 9

You sure that is what you meant?

If the motor still runs (light loading), it will be mechanically very loud and as has already been pointed out, it will overheat.

With one phase, there are any rotation fields and induction motor cannot run.

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All of the others are correct. Another thing to note is that if the motor is not running and it is single phased, when you try to start the motor it will not turn and will give off a very loud humming sound. Once you have heard it once it is very distinctive and a dead giveaway that a motor is single phased. The most common reason that I have seen personally is one of the contacts in a starter is no longer making contact or a cut wire in the power leads to a motor.

If the motor is correctly installed, then (a) protection device(s) will operate, thereby disconnecting and protecting it from damage.