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# Measuring moment of inertia3

## Measuring moment of inertia

(OP)
I would like to measure the moment of inertia of an axial fan.  Can anyone tell me a method for doing this?

### RE: Measuring moment of inertia

Hello
You can do that by mesuring the electrical absorbed power from the fan motor which is equal P = I x V
where I : current (A)
V: Voltage (V)

Theoritacly most of this power converted to mechanical power which is P = 1/2 x I" x w^2
Where I" : moment of inertia ( requested )
w : rotational speed ( rad \ s)

equate both equarions you can find I"

Good luck

### RE: Measuring moment of inertia

If you have access to the fan blade outside of the assembly, there is an experimental way of determining the moment of Inertia.  It is often used to measure the inertia of motor rotor assemblies.  In fact the procedure is described nicely in the NEMA standard for motors.  The NEMA standard is MG-7 if you want to look it up yourself, but I'll try to describe it here.

Suspend the fan with the center shaft oriented vertically using two parallel wires.  You may have to make an attachment fixture, but if you keep it's geometry simple, it's added inertia can be calc. and subtracted out in the end.  The wires should be attached equally spaced from the centerline of the fan.  The ratio of length of the wire(L) to the distance between the wires (D) should be about 10.

Once setup, rotote the fan a small amount from equilibrium and release.  After release, measure the frequency of oscillation.  The moment of inertia can then be calc. using the following:

I = c*m*D^2/(L*f^2)

I = moment of Inertia about the rotation axis
m = fan weight
D = distance between wires
L = Length of wire
f = measured frequency in HZ
c = conversion factor depending on units used

If Inertia is in kg-m^2, with 'm' in kg and "L" & "D" in meters, the c = 6.2e-2

If Inertia is in lb-ft^2, with 'm' in lb and "L" & "D" in feet, the c = 2.04e-1

If Inertia is in lb-in-sec^2, with 'm' in lb and "L" & "D" in inches, the c = 7.61e-2

If desired, don't forget to subtract out the inertia effect of any attachemnt fixture.  The procedure works well for motor rotors.  I think if you keep the amount of rotation low so it doesn't spin to fast such that the drag forces of the fan blades is not to high, it should give a good value.

Good Luck.

### RE: Measuring moment of inertia

I don't think you can use the current (I) method suggested because most of the electrical energy is used move air. The best way will probably be to calculate it mathematicaly. The solution using the wires also sounds good.
If you can run this fan in a vacuum and measure the current draw to get up to running rpm, then you can use the mathematical relationship between
the change delta I (amps) and delta rad/sec to obtain I (moment of inertia)

Hope this helps.

You might try contacting the fan manufacturer who might already have this  information.

Don

### RE: Measuring moment of inertia

I am sorry bescause i did not mention in my first reply that mesuring should be done in aprrox. vacume conditions.

good luck,

### RE: Measuring moment of inertia

This sounds like fun.

If the fan can be repositioned to the center of the axle, try this...

Orient two-horizontal edges (creating a channel) to support the ends of the shaft with the fan suspended into the channel (from the side, it kind-of looks like a table saw).

Attach and wrap string around the axle then attach a known mass to the string (preferably hung by parallel strings spanning the fan blades).

When you let the mass (weight) hang freely, the weight will rotationally and translationally accelerate the system.

Torque = I * alpha (the rotational acceleration)

Force = mass * a (linear acceleration), include the hanging weight's translation

a and alpha are related.

and solve for I

Alternately...

The mass falling a given distance and now moving horizontally with a velocity, was caused by the work of the mass being lowered.

weight * distance fallen (potential energy)= the SUM (of the rotational and translational kinetic energies)

If all else fails try attaching a tin-foil shroud over the fan blades, looking at it axially it kind-of looks like a minature bicycle wheel covered with tin-foil, then use the electrical current method previously proposed.

As a last resort...

If you can catch the next Space Shuttle, you might give the fan (freely held in your hands) an axial spin (and release it), then, have an observer measure the rotational velocity of the fan and the rotational velocity of your body.  Then you simply back-calculate the moment of inertia of the fan, through a simple relationship, incorporating your body's moment of inertia, but that my friends will have to be another topic of discussion.

Well gotta go,
pi

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