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Making an induction motor go crazy fast.
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Yansi:
Well I think that is not as easy question to answer.

The torque characteristic may depend not only on the maximum flux, but also the type of rotor winding (wirewound + slip ring, squirrel cage, doubled squirrel cage)...

Circlotron:
The rotor bars have a slight amount of inductance and the rotor aluminium end rings have a certain low value of resistance. The frequency of the current induced into the rotor is the difference between the "rotation" rpm of the stator magnetism and the actual rpm of the rotor. This difference in rpm is the "slip" speed. At some particular slip speed (rotor current slip frequency) the rotor inductive reactance equals the rotor resistance and the rotor current lags rotor voltage by 45 deg(?) and everything is happy. If you load the motor too much the rotor induced slip current frequency gets too high and consequently so does the rotor reactance, compared to the rotor resistance. This means the rotor power factor gets very low and so the torque decreases as the motor is loaded more and more. Something like that.

With a slip ring motor you can add additional external resistance to the rotor so the motor can give full torque at any rpm, right down to zero. To continually run the motor like this would be very wasteful though.
Yansi:
I do not think that is the answer to the question.

I understand the question as what limits the maximum achievable value of breakdown torque, in an induction motor.  And the answer to that has to be very complex, as it depends on the exact geometry and its specific construction details of an individual motors. There are at least so many types and shapes of the rotor, that it is impossible to answer that all.

Maximum flux density in the machine is definitely one of the limiting factors.  F = B*I*len still counts.

Miyuki:
Even slip ring motor have always same Tmax
Just curve change its shape

mzzj:
https://www.landbelectric.com/download-document/85-torque-characteristics-of-nema-abcd-e-motors.html

In many cases its desirable to limit the maximum starting torque(less mechanical strain) and peak currents.
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