But if you are referring to standard AC Squirrel Cage Induction Motors, you cannot vary the speed only by varying the voltage. Voltage will only cause a loss of torque, and torque varies by the square of the voltage reduction. So if the voltage is reduced to 80%, torque is reduced to 64%; 50% voltage nets 25% torque etc. etc. Now, an AC motor will slow down if the torque is insufficient to maintain the load rotation, but when that happens, the slip increases, causing the motor to pull more current and it over loads.
By the way, if you ONLY vary the frequency, you also cannot do that without causing problems. That is why it is called VV VF; you must vary them TOGETHER. And to maintain the proper amount of torque, you must maintain the same V/F ratio as what the motor was originally designed for.
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The reason I said you did not provide enough information is that you forced me to guess that you were referring to an AC Squirrel Cage Induction Motor, as opposed to an AC Wound Rotor Induction Motor, or an AC Synchronous Motor, or an a Brushless DC Servo Motor etc. etc. etc.
Others have answered the rest. If you don't yet grasp the concept, you need more help than you can attain here.
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The motor turn by given formula. it means the frequency of AC current is the key thing. you can not control RPM by VV. Voltage is just a factor to be sure the motor torque is stable.
As the frequency is varied, the voltage is too varied to keep the V/f constant.
This value V/f is proportional to the magnetic flux, and must be kept constant to avoid the oversaturation, as well as the under (which will obviously reduce the motor power)
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