How do I calculate sheave sizes?

[mcjeremy]

I have an exhaust fan that operates at 859 rpm with a 1725 rpm motor. The fan sheave has a diameter of 9.75" and the motor sheave has a diameter of 4.625", distance between shafts is 20.75" but can be adjusted ~+/- 2". I am switching the motor out to a 3450 rpm motor to attempt to have the fan achieve around 1200 rpm. What are the formulas, or where can I find them, for determining appropriate fan/motor sheave sizes?

 

[scarecrow55]

The speed is proportional to pulley dias. So the motor pulley will be 2.875 times smaller than the fan pulley. As for the loads, you'll have to check the belt and setup can take it if the power has changed somewhat

 

[Philrock]

Note that when you are doing calculations, you must use pulley PITCH diameters. Pulley manufacturers list pitch diameters in their catalogs. Note also that some pulleys can be used with more than one size of belt, and the pitch diameter of the pulley will depend on which belt it is used with.

 

[electricpete]

Two other considerations
1 - The smaller pulley will have less contact. You need a certain minimum contact around the smaller sheave which will limit how small it can be (based on larger sheave size and center distance).
2 - The smaller the pulleys, the more radial force they will put on the shafts and associated bearings for a given torque. Therefore NEMA gives minimum sheave sizes for motors based on frame size and horsepower.

I don't have the formula's or links handy and I'm a little pressed for time.

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[sacem1]

Have you taken into account that altering the fan speed will vary the CFM moved by the fan, the static pressure varies also and the brake horsepower will also vary, so given the good advice about the proper pulleys to use here goes the other formula you will need:

1.- CFM (cubic feet per minute) varies with fan speed:

Q2 is to RPM2
as Q1 is to RPM1 being Q1 initial volume displaced
Q2 final volume displaced
RPM1 initial FAN speed
RPM2 final FAN speed

2.- Static pressure varies as the square of the fan speed

(SP2/SP1) = (RPM2/RPM1)^2
= (RPM2/RPM1)x(RPM2/RPM1)

3.- Brake horsepower varies as the cube of the fan speed

(HP2/HP1) = (RPM2/RPM1)^3
= (RPM2/RPM1)x(RPM2/RPM1)x(RPM2/RPM1)

so asuming that your fan has now a 1 HP motor and that you are changing final FAN speeds from 859 rpm to 1200 RPM you will find the following results:

1.- your CFM will increse to:
(1200/859) = 1.397 times or an increase of 39.7%

2.- your static pressure will increase to:
(1200/859)^2= 1.95 times or an increase of 95%

3.- your HP demand from the fan will increase to:
(1200/859)^3= 2.726 times

or you will have to install a motor that is 2.7 + times the power of the original motor, the motor speed is not relevant for this matter (it can be 1700 or 3450 rpm) just the power NEED from the fan to work at the new speed of 1200 rpm.

Take this into consideration, thats the reason diferent fan sizes are built, so that getting more air moved is achieved with less HP with a bigger fan than with a higher fan speed.

Cheers

SACEM1