How to calculate the maximum RPM of a motor?

[Physics is awesome]

Hello all,

Just wondering if there is a mathematical formula that calculates the maximum rpm. If I have a fan that puts out 3 pounds of rotational force at stall speed(completely still) at the end point of a 1.5 ft blade what would be the maximum rpm of this fan with the blade attached. What would be the maximum rpm of the fan motor with no blade/load. Is there a formula for this? Also if there is an answer to this would the same formula apply to gas motors as well as a human peddling a bike?

 

[davenn]

Hello all,

Just wondering if there is a mathematical formula that calculates the maximum rpm. If I have a fan that puts out 3 pounds of rotational force at stall speed(completely still) at the end point of a 1.5 ft blade what would be the maximum rpm of this fan with the blade attached. What would be the maximum rpm of the fan motor with no blade/load. Is there a formula for this? Also if there is an answer to this would the same formula apply to gas motors as well as a human peddling a bike?

much of it would depend on the power, size, and a few other factors of the motor in question

 

[CWatters]

Just wondering if there is a mathematical formula that calculates the maximum rpm. If I have a fan that puts out 3 pounds of rotational force at stall speed(completely still) at the end point of a 1.5 ft blade what would be the maximum rpm of this fan with the blade attached. What would be the maximum rpm of the fan motor with no blade/load. Is there a formula for this?

Sorry it can't be done with just the information you mention.

Some motors cannot be operated without a load as they would spin too fast and damage themselves. In such cases you apply a variable load and plot a graph of rpm vs Torque (rotational force). Then extrapolate to give an estimate of the rpm with no load.

Ideally what you need is data on the torque vs rpm for both the motor and the fan from each manufacturer. Then if you plot both lines on the same graph where they cross will be the operating point of the motor and fan combination.

 

[Dr.D]

What type of motor is this? An induction motor, or something else?

 

[David Lewis]

If it's a DC motor, you can assume torque is inversely proportional to motor speed. The torque absorbed by the fan blades goes up approximately as the square of motor speed.

 

[CWatters]

What type of motor is this? An induction motor, or something else?

Good point. Some types of motor depend on the mains frequency.

 

[Dr.D]

Good point. Some types of motor depend on the mains frequency.

The two common types of AC motors are synchronous machines and induction machines. For a synchronous machine, the rotor speed is absolutely locked to the power line frequency. On a 60 Hz system (USA), a synchronous machine will run at 3600 rpm, 1800 rpm, 1200, rpm, 900 rpm, etc, depending on the number of poles.

For an induction machine, again on a 60 Hz system, the rotor speed is a little bit less than a line frequency submultiple, such as 3520-3585 rpm, 1725-1785 rpm, 1125-1185 rpm, etc, depending on the loading. For an induction machine, the slip is required in order to develop the torque required to support the load. An induction machine at no-load will run close to synchronous speed, with only enough slip to support the internal losses (bearing friction, windage, etc.)