How do I accurately measure moment of inertia of a small motor rotor

[Horder]

I need to measure the moment of Inertia of a 20mm dianeter rotor. I have calculated the inertia at 3500gmm^2 using the following equation to sum the components (cylinders):

Inertia, I = m(r1^2 + r2^2)/2

I've measured it by timing it rolling down a slope:

Inertia, I = mgr^2t^2Sinq/2L - mr^2

but, despite taking over 30 measurements at 4 different slope angles, the measured results vary significantly from close to the calculated value to almost double. The rotor is a strong magnet which may not help.
Can anyone suggest a more accurate way of quickly and cheaply measuring Moment of Inertia?

 

[GregLocock]

Inertia, I = m(r1^2 + r2^2)/2

would appear to be your problem



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[Horder]

I = m(r1^2 + r2^2)/2

Comes from I = mk^2
Where k, radius of gyration = (0.5(r1^2 + r2^2))^0.5
and m is the mass of the component.

Is this not correct?

The calculated value also agrees with the output from the CAD model. I'm having difficulty getting consistent results from the physical measurement.

 

[IRstuff]

Why doesn't your supplier provide this number?

Your measurement does not see to take into account friction/slippage and would seem to be prone to experimental error.

TTFN

 

[GregLocock]

Well, it rather depends on what m r1 and r2 are physically.

Having said that there is probably a feasible geometry that has that equation, just not the one I thought of.



Cheers

Greg Locock

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[wes616]

Does a cross section of this look like 2 concentric cylinders?





Wes C.

 

[wes616]

it seems to me that we have a unit problem

I = (mm)^4

Wes C.

 

[wes616]

sorry... god I wish i had a takeback.. once in a while

Wes C.

 

[dford]

Horder:

There is an old method called the bifilar-suspension method.

Suspend the rotor from two strings length L, seperated by distance 2R. Displace rotor a small angle to wind up the suspension, release and measure the frequency of oscillation, f. The inertia is:

J = WR^2/((2pi*f)^2 * L)

W is weight
f is Hz

L/(2R) > 10

Good Luck,
Doug

 

[howard1954]

When using bi-filar or tri-filar methods one must be sure the strings are taut and don't stretch during the timing. Make sure there are no kinks in the strings.