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I am a mechanical engineer and fairly new to real life usage of electric motors. I have a 2.2 kW 3 phase AC motor. At 1450 rpm, it can generate 14.49 Nm torque (I understand this is called nominal torque). Given that power = torque x rotational velocity, I thought I could generate any torque I desire given that I stay below 2.2 kW (multiplied with corresponding rotational velocity). I recently started learning about torque-speed curves and I realized that I can not make the motor generate any torque I want. Is this true?

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The 14.5 Nm torque is correctly called nominal. The 2.2 kW is even more nominal.

There are several limits to torque. Broadly speaking, torque is proportional to current. If you load the motor with an excess load, it may well develop more torque than nominal, and draw more current than rated to do it. It will then tend to overheat, so limiting the time you can operate at that level.

With enough current, you'll meet the next limitation, which is saturation of the iron in the stator and rotor. Once you hit that, then the output torque is truly limited.

The output power of 2.2 kW is a rated power, that tells what what you'll get at rated speed and rated maximum torque, it's informative rather than anything else. At lower speeds, you'll get lower power, power = torque * speed. The rated power isn't some magical motor parameter that allows you to develop torque = power/speed.

At lower speeds, you may not be even able to reach the rated torque. You'll have less cooling at lower speed, so the current needed to overheat the motor will be less. As this is an AC induction machine, if you're at lower speed due to increased slip, the rotor frequency will have increased, and rotor inductance will limit your torque-generating current. If using a VFD, then you should be able to generate rated torque down to low speeds, subject to the cooling limitation.

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The only way to have good speed control with an induction motor is by using a variable frequency drive (VFD). With basic VFD, the torque vs. speed curve is similar to the the low slip portion of and induction motor operating from utility power. See my answer to Condition for max torque.

The best VFD control techniques essentially provide a vertical, or nearly vertical torque vs. speed curve that can be adjusted for any speed from zero to maximum. The continuous safe operating torque can be the motor's rated torque with a separately powered motor cooling fan. The short-time operating torque is limited by the motor design and the VFD current capability. The motor design generally limits the short-time torque to a value close to the peak torque for utility power operation.

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