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# Moment of inertia

Genius

Hi guys, I hope you can help me on this one.
I need to create balance (red) in assembly with respect to the axes of rotation (Z) as a function of position, dimension, weight..., so that the moment of inertia rotating axis Z (Z is the centerline of the hole-blue part) and moment of inertia of the assembly match, in other words I want dynamic loading to be as low as possible for Z axes. Yellow and blue part are fixed, only the red part has DOF in plane XY.

11 REPLIES 11

# Re: Moment of inertia

Phenom

As I understand, you have to balance your rotating assembly by applying the red cylinder, and when you say that you want "the moment of inertia of the assembly match" you actually mean that you want the assy center of mass to lie on the rotation axis, don't you ?
If this is the case, it just takes finding the center of mass, calculating its torque with respect to the rotation axis and placing the red cylinder so that its torque w.r.t. the rotation axis cancels out the previous one, so that the whole thing is balaced on XY (the blue and red centers of mass should also have the same Z coords, so that their centrifugal forces don't create a wobbling torque).
I suppose by "dynamic loading" you actually mean the total moment of inertia, so you should place the red cylinder in order to minimize it.
If your question is about how to automate the whole calculation, the measure body feature is associative, it creates the actual center of mass, so you should manage to compute everything.

I'm not sure I have understood your question though, you may want to explain your point a bit further and post an example part.

# Re: Moment of inertia

Genius

Maurizio, you perfectly understood what I wanted. I don't know if you tried that in Catia, but she can iterate position or some other variable (mass, geometry of the body) for the target inertia. I was hoping that something like that exists in NX also, that system itself can find where is that position for the balance body, so you can have assembly moment of inertia on Z axes.

# Re: Moment of inertia

Siemens Phenom

Do you have the Optimization tool?  If not, this can be done inside the Modeling spreadsheet using the Goal Seek tools.

John R. Baker, P.E. (ret)
EX-Product 'Evangelist'
Irvine, CA

# Re: Moment of inertia

Genius

Yes, I do have optimization tool. Can you give me brief insight how to use it in my case.

# Re: Moment of inertia

Siemens Phenom

OK...

Attached is an assembly similar to your image with an optimization already set up.  Note that difference between the assembly's centroid and the center-line of the axis of rotation is defined by the Measurement expression 'Difference' and the location of the Red 'Counterweight' is controlled by the expression 'Offset_Distance'.  The optimization Study that I've already defined, named 'Offset', will update the value of the expression 'Offset_Distance' until the value of the measured distance, 'Difference', approaches zero (to within 0.0001mm in current Study).  All you have to do to run the Optimization and find the ideal 'Offset_Distance' is to open the...

Analysis -> Optimization and Sensitivity -> Optimization...

...dialog, select the 'Offset' Study and hit the 'Run Optimization' icon near the bottom of the dialog.  When it's completed, check the values of the expression.  Note that you do an Undo, change whatever settings that you wish, and rerun the Study.

Note that I used NX 8.5 (as indicated in your post) for the model and the tests.

John R. Baker, P.E. (ret)
EX-Product 'Evangelist'
Irvine, CA

# Re: Moment of inertia

Phenom

as I understand, the OP wanted "dynamic loading to be as low as possible for Z axes" though, that is minimum moment of inertia.

This is not quite clear though as, being the unbalancing torque fixed, the balancing torque (i.e. distance of the red cylinder from the axis * its mass) is also fixed and the added moment of inertia would be just such fixed value times the distance again (mass * squared distance).  In the end, among all the possible combinations of distance and mass of the red cylinder that do balance the assembly, the one with minimum moment of inertia would just be the one with minimum distance, that is the one closest to the rot. axis, so I can't see this as an actual optimization problem.

As I understand, once a miminum acceptable clearance is set between the red and blue parts all the rest could be found by an algebraic closed form (although pretty tough to calculate).

I'm not sure I have understood though, Aleksa may want to explain this a little bit.

# Re: Moment of inertia

Genius

Thank you, Mr. John, that is exactly what I was looking for. Just out of curiosity, can you tell us something about Goal Seek tools.

@Maurizio

Your right, it's not that difficult to calculate moment of inertia, but for simple shapes, if you have an assembly and not so simple shapes in it, there is no other way, then do it this way. In conclusion, distance between the centerline of red cylinder and assembly axis of rotation is a function of how unbalanced assembly was before we added red cylinder.

# Re: Moment of inertia

Siemens Phenom

The Goal Seek capability is part of the Spreadsheet function.  It's been part of UG/NX since the spreadsheet option was first introduced into the software, in 1996 with the release of Unigraphics V11.0, and while it's still supported, the newer Optimization tools are now the recommended way to do this sort of thing.

John R. Baker, P.E. (ret)
EX-Product 'Evangelist'
Irvine, CA

# Re: Moment of inertia

Phenom

actually, even if you have more complex shapes it is NX which calculate body properties, so no matter the shape you can easily find the distance (as in attached modified example), as the "function" you refer to is actually just a multiplication and a division, which can be solved without resorting to optimization.

This doesn't address the minimum total moment of inertia requirement you raised earlier though, for which an algebraic solution could be found (if this is considered to be interesting) if the counterweight is a simple cylinder (at it is often the case when one has to balance a crankshaft, for example).

Having said this, I understand that using the Optimizer is perhaps even simpler than that