Estimation of mounted resonant frequencies on isolators

[jeyaselvan]

Is is required to estimate the mounted resonant frequencies (the first translational and rotational modes) while doing a isolation design apart from the transmissibility requirements? This, I believe, could possibly eliminate any coincidence with the excitation frequencies. I am analysing a system which is isolated on six isolators. How do I estimate the rigid body mounted resonant frequencies?

 

[GregLocock]

Well, in the good old days we'd figure out the most likely low frequency modes and do a hand calc.

Probably these days you'll stick it into some computer model.






Cheers

Greg Locock

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

 

[VibeAC]

The amount of analysis to some extent depends on what you are isolating and where the forces are coming from.

For mechanical equipment in buildings, efficient vertical force isolation is typically the most critical. A good rule of thumb is the isolator natural frequency should be 10 times less than the lowest forcing frequency. For a single-degree-of freedom approximation, you can calculate the vertical natural frequency of the isolated system by summing all of the spring stiffness together (springs in parallel) and knowing the mass of the system use the formula fn=(1/2*pi)*(stiffness/mass)^0.5.

This is the most simple case and you may need to go further (e.g. all 6 DOF's).

Andrew Gorton, MSc
Noise & Vibration Consultant

http://www.PapadimosGroup.com

 

[Tmoose]

Some of the isolator catalogs included advice that the best location was with the isolators up around the CG, as a method to help avoid creating unwanted non-translational modes.

 

[electricpete]

Just thinking out loud a little bit.

The isolators I presume are designed to be resilient in the vertical direction but stiff in the horizontal direction, and not particularly stiff for angular twisting at the isolator.

In that case, assuming we are interested in the lower modes, we could rule out the modes that involve horizontal motion (right?). That removes 2 translational modes and 1 rotational modes, and leaves us with only one translational mode (vertical) and two rotational = rocking modes. I am interested if others agree these 3 modes would usually be the lowest (assuming the thing on top of the isolators acts rigid = does not deform).

I can certainly think of situations when the rocking modes woudl be the lowest... if the mass is concentrated toward the center. What about if the mass is uniformly distributed thorughout its volume (like a rectangular blcok of steel)... is it always the case that the vertical mode will have lower frequency than the rocking modes or not?

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[GregLocock]

Rocking modes are lowest if the mass is largely /outboard/ of the isolators. The setup your suggesting is roughly that of a car on its suspension and tires, which are roughly 250 N/mm each in longitudinal and lateral, and the suspension itself which is maybe 40 N/mm vertically.

If you put the isolators at the corner for a uniform box then the pitch mode will be at some function of (L/2)^2*k/(m/4*1/12*L^2) (assuming a 'shallow' box)
whereas the bounce mode will be at k/m/4

So in practice the pitch mode is higher than the bounce mode. As you move the isolators inboard then you can reverse this - in theory if you move all the isolators under the cg then the pitch mode will be at 0.

The height of the isolators relative to the CG doesn't really affect the frequencies much for a relatively low slung box, it does strongly affect how easy it is to excite the pitch and roll modes with accelerations at the CG.

The height of the box is important. You'll notice that RWD cars typically have their engine mounts rather low compared with the CG of the engine . This is deliberate, as it reduces the roll mode frequency, which is the easiest to excite.





Cheers

Greg Locock

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

 

[electricpete]

I can certainly think of situations when the rocking modes woudl be the lowest... if the mass is concentrated toward the center.

Rocking modes are lowest if the mass is largely /outboard/ of the isolators

You're right of course. That's what I meant. but somehow got lost between brain and fingers and keyboard (probably at the front end of that sequence... a duhh moment).

Your other comments make good sense. Thanks.

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[VibeAC]

Steel spring isolators from Mason Industries have roughly the same stiffness in both the vertical and transverse directions.

Andrew Gorton, MSc
Noise & Vibration Consultant

http://www.PapadimosGroup.com