Question on how to calculate moment of intertia of an assembly.

[yacpro13]

Hi everyone,
see the image attached.
As you can see, there are 2 different assemblie.

The assembly on the left consists of just a single machined part.
The assembly on the right concists of two machined parts.
Both assemblies (ie. on the right and on the left) have the same over all dimentions.

Question:
I would like to compare the moment of inertias of each assembly.
The moment of inertia for the assembly on the left is easy to compute.

For the assembly on the right, however, there are other factors which should be taken into account:
-The number bolts used along the assembly to fasten part #2 to part #3?
-The size of these bolts
-The tightening torque of these bolts.

So I can I calculate the moment of inertia of the assembly on the right?

Thanks in advance.

 

[ivymike]

so aside from the obvious "the bolts have mass," why do you expect them to impact MOI? Will the distribution of mass change appreciably due to assembly (deformation?)?

 

[rb1957]

if the connection between the two pieces causes them to bend together, then the two would bend as one and the section properties would be like the single piece.

But you need to check the connections to make sure they're as stiff as the single piece.

 

[yacpro13]

Exactly!
I need to determine howmuch torque is needed on the bolts in order to obtain this behaviour.

If I continue in the same train of thought, we could say that in order to have both pieces bend as one, we need to eliminate separation.
From a FBD, I can get the forces acting on the assembly. I suppose if the bolts are pre-loaded such that the contact force between the parts is greater than the separation force, then we would have no separation, and the parts would bend together, meaning that the moment of inertia would be the same as the single-part equivalent...

 

[rb1957]

as with most things, the devil's in the details ...

if the load is applied directly to the upper piece, then it'll load the lower piece directly (and the fasteners aren't doing anything)
except for shear ... there'll be shear due to bending

if the load is applied directly to the lower piece, then there'll be a tension in the fasteners (to avoid them separating). you could calc this by considering the upper piece ... what distributed load is needed to bend the upper piece the way it does under load. then you have to figure out how these loads get reacted by the "rest of the world" ... maybe the support for the beam is all in the lower part ?

you can consider "fussing" the effective area of the two pieces, maybe consider the fastener holes/bores are lost area ?

 

[chicopee]

It should be the same for both configurations if the bolts are countersunk and there is no metal depletion for threaded connection of parts 2 and 3 as shown in your drawing; but in reality,moment of inertia for bolted parts 2 and 3 as shown in your drawing, with counter bolt heads, moment of inertia will be slightly less.