Effect of Contact on Modal Frequency? 2

[jvian]

Hello,

I perform random vibration analysis for a small company utilizing cast aluminum housings which are typically piloted into to a gearbox of some sort and mounted via a bolted mounting flange. A recent housing has the main body outside of the gearbox and is mounted via a bolted flange. There are various masses/components attached to the body which creates an overhung mass cantilever beam type system. Whenever I perform an analysis I constrain a volume 1.5 times the mounting bolt diameter and apply base excitation. When I do this the results are always the housing mounting flange in between the bolt locations either lifts off of the fixture plane, or penetrates into the fixture plane. This has always been conservative when compared to fixing the entire mounting face, and we have been able to make modifications to the housings to facilitate passing the vibe test with success. This is however not what will actually happen in application as the housing cannot penetrate the fixture plane (though theoretically it can lift off slightly). My question now is is there an effect on the natural frequencies as a result of this contact between the housing and fixture and can anyone provide some insight as to ways of handling this effect? I keep thinking of a guitar string which does nothing when something obstructs its motion, yes it is free in one direction but not in the other and therefore the mode does not exist (at least as I understand anyway). I know that this is more along the lines of a wave rather than a modal analysis but hopefully gets my thoughts across. Is it possible for a mode to exist if half of its motion is prevented?

Again any help would be appreciated and thanks in advance,

- J -

 

[GregLocock]

Yes it will affect the frequencies, substantially. Incidentally don't cross post between forums, it aggravates the other users and is frowned on by the management.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[jvian]

I posted in both forums in hopes to capture potentially different audiences under the assumption that not everyone in the FEA forum would be following the vibrations/acoustics forum. Otherwise I would not but thanks for your replies.

 

[amanuensis]

I didn't understand whether the contact was continuous or not.

If the contact is continuous, then you can apply the continuity conditions between the two structures and express the coupling force as
F=(V2-V1)/(Y1+Y2) where V1 and V2 are respectively the velocities of structures 1 and 2 before coupling and Y1 and Y2 are the mobilities.

If the contact is non-continuous, then it can be supposed that shocks appears between the structures. Generaly, these shocks lead to harmonic distorsions or broad band noises.

 

[spongebob007]

If you feel that the contact is important, the only way you can account for it is by performing a nonlinear transient FEA with contact. When you have contact in a model the stiffness matrix is not constant and this makes the model nonlinear. Eigenvalue solvers used in FEA programs need to have a constant stiffness matrix.

 

[izax1]

If you suspect that the contact face is separating (or is it only reducing the face pressure?) you need to apply more bolts or inreasing the bolt pretension. If the face is separating you have a non-linear system, and the natural frequency is not defined.
(The natural frequency is always a linear sinusoidal movement.) To be precise, any bolted connection is non-linear, but in most well designed bolted connections the non-linearity is small enough to assume linearity.
If you need to do a FE analysis of the opening bolted connection, it is done by non-linear dynamic analysis. This will of course not give you the natural frequency of the system but reponse values will tell you if your design is OK or not. That is if the analysis is "correct" which is not the case.
I would go for a bolted connection that is guaranteed not to open. If it opens you will get hammering and subsequent fatigue failure.

 

[GregLocock]

Yes, in theory you can't do a modal analysis of a non linear system. Non linear systems have resonances, which have a 'worst' frequency, defined damping and amplitude and phase, and hence recognisable mode shapes. Since in practice every interesting system is non linear we can throw the little aphorism in the first sentence away.

You either linearise the non linear system, or analyse it non linearly.

Typically in real modal testing we linearise the system by testing at only only one force amplitude, using sine sweep. We also hot-glue all the rattly bits together. In the case of contact that means we see some sort f average stiffness from the joint, and a fair bit of damping, but we don't mess up the analsysis because the frequencies created by the contact are ignored.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

http://eng-tips.com/market.cfm?

 

[spongebob007]

You need to realize the a mathematicl model is simply an approximation of reality. Real world systems, even ones that seem simple are highly complex and highly nonlinear. Assuming you could come up with a differential equation to model your system there may not even be a closed form solution. You could turn to numerical methods but your model may quickly become so large as it would be impractical or even impossible to run. This is the challenge engineers face-how to predict reality with reasonable accuracy in a reasonable amount of time. This is why we make simplifying assumptions and approximations. Many real life systems can be modeled with a reasonable level of accuracy with relatively simple linear models. So it sounds like you are doing a modal analysis of something mounted to something else using a bolted flange. By pinning your model only at the attachment points you are making a conservative model. In reality the joint will have stiffness that will raise the natural frequency of your structure. One thing I often do in FEA when I can't model a system exactly with a linear model is I try to bound the solution. As you correctly identified, your modeling technique is conservative in that the predicted natural frequency is lower than the real natural frequency. You can consider what your FEA gives you as the lower bound of the natural frequency of your structure. Next change the constraints on your mounting flange so that the entire flange surface is rigidly fixed. The natural frequency you predict now is the upper bound of your structure. You now know that your real system natural frequency will be somewhere between your lower and upper bounds. This may be good enough for what you are trying to do.