and what is minimum possible RPM ratio for a high power motor
Inductive Motor – Effects of Decreasing RPM on Current, Torque, and Heating
electricalinduction motorpower-engineeringvfd
Related Solutions
Relating a motor's current to a fan output airflow requires you to know details about the motor, the fan, the mechanical system surrounding the fan, and the ambient atmosphere.
The motor current depends on the motor speed, as shown by a speed vs. current curve.
The motor speed depends on the motor's speed-torque curve vs. the fan's speed-torque curve.
The fan's speed-torque curve depends on the inlet air density.
The speed of the air exiting the fan presumably depends on mechanical details such as - the pressure drop in the fan's duct work, the open/closed position of air dampers, and so on.
It should be evident there is no 'simple' relation between fan motor current and fan output airflow!
I will add two useful pieces of information.
The "Fans and Blowers Energy Efficiency Reference Guide" (published under the branding of BC Hydro, Manitoba Hydro, and others) is an excellent introduction to fan and blower design. This is required reading for all electrical engineers dealing with fans and blowers.
Contrary to your statement that fans have constant torque: Some loads have a constant torque, but fans aren't one of them. From a book by Schneider Electric we have the following table:
Here is an example of a motor's torque-speed curve and speed vs. current curve.
Here is an example of a centrifugal fan's load-torque curve.
Here is an example of a centrifugal fan's power vs. airflow curve (note - power = torque × speed.) Note that the relationship is non-linear.
With frequency control, there is not just one torque curve, but an infinite number of curves, one for every operating frequency. The voltage needs to be proportional to frequency. If the voltage is carefully regulated using a mathematical model of the motor with motor operating voltage, current and power factor information, the torque curve can be made to have the same shape at any speed. The required current to produce a given torque at zero speed, will be close to the current required to produce the same torque at rated speed. The motor is never operated at high slip, the operating point is always to the right of the pullout torque point.
When starting, the applied frequency is enough above zero so that enough slip is created to produce the maximum torque that the motor can safely produce.
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Best Answer
Induction motors are available with power ratings ranging from about 1/500 Hp (1.5 W) to 30,000 Hp (22MW). It is difficult to say just where in that range the motor in question may be. It is likely that the question is about a low to medium power motor rather than a motor that is more than a meter in diameter.
If the motor is controlled by a reasonably good variable frequency drive (VFD) it can be operated down to practically zero speed at 100% rated torque.
The motor current will not exceed the rated full-load current. The VFD input current will be proportional to the mechanical power output of the motor, so it will decline as the motor speed declines. The mechanical power output of the motor is proportional to load torque multiplied by speed. There will be some harmonic current content in the VFD input current. That will increase the current somewhat.
The heat lost in the motor will decline a little bit as speed declines, but the ability of the motor to dissipate losses will decline due to the reduction of the speed of the motor's self-cooling fan. That will limit the time that it is safe to operate the motor at rated torque and any given speed. At half speed, most motors will probably be able to operate at rated torque continuously. If the motor is cooled by a separate blower that is selected and furnished as part of the motor by the manufacturer, it is possible to get a motor that operates continuously at or near zero speed.