Moment of Inertia

[Josh2008]

I'm trying to calculate the total system mass for a friction hoist.

My question is in the conversion of the moment of inertia of a hoist drum and pulleys.

If a catalogue gives me the moment of inertia I, then would I be able to calculate the equivalent mass (or mass required to turn the drum from rest) using the inertia and radius of the drum?

I=1/2 m r^2

m=(2) I/r^2

I would think this is true if the drum was a solid cylinder. But since it has a different shape, how do I calculate this?

Thanks

 

[imcjoek]

Can you rephrase what you are trying to do?

It sounds like you want inertia, and they give you inertia.

Or do you want mass? In that case, call the manufacturer?

 

[Josh2008]

Yes I am looking for an equivalent mass. Is the formula I listed valid? Besides calling the manufacturer is there a way to compute this?

Thanks

 

[imcjoek]

The formula you listed being valid will depend on how accurate you need to be.

You can get closer by breaking the shape up into segments and using the moment of inertia transfer formulas to get your total inertia. Then solve it for mass.
(Look up 'Inertia Transfer Formula', or 'Parallel Axis Theorum')

An alternative would be to draw the drum in a 3d cad program (solidworks, inventor, etc) and then tweak the material density until the inertia matches the catalog value. Then read off the mass.

 

[imcjoek]

I be able to calculate the equivalent mass (or mass required to turn the drum from rest)

Err... or by this are you actually looking for total inertia of your system as seen by X component (say, the drum) taking into account pulley ratios? I don't really grasp what "mass required to turn the drum" is supposed to mean.

Try googling "reflected inertia". Maybe some of this will get you near the right track.

 

[Josh2008]

Thanks, to verify, the mass that is determined is the minimum mass required to change the components velocity? Or to start turning the drum from rest?

 

[FeX32]

That does not makes sense.
Inertia cannot be converted to mass.

An inertial system can be converted into a simpler equivalent inertial system only.
For eg. MMOI about a point O is simply m*r^2, where r is the distance to the mass "m".

But, what are you really trying to do?


Fe

 

[Josh2008]

I'm trying to figure out how much force is required to overcome the inertia of a giant sheave. I have the inertia publicated from the manufacturer. How do I do this?

 

[FeX32]

So b/c it is a sheave, I assume you want a torque value.

T=I*alpha,

T= the torque required
this generates an acceleration "alpha"
given mass moment of inertial "I"

This is dynamic, ie. if it is spinning, that relation holds always.
If you are trying to figure out how much torque (Force*distance) from a stop, you need to know how much friction is present ect.




Fe

 

[FeX32]

...note alpha is angular acceleration


Fe

 

[FeX32]

Oh and that dynamic relation neglects dynamic friction ect. ect.
It is fundamental dynamics.


Fe