Vibration Mounts: Nat. freq. Vs Displacement

[remlap]

This question is from an electrical engineer, so I apologise is I'm missing some fundamental knowledge...

1. Given a graph of "force vs displacement" for a particular anti-vibration mount, is it possible to determine its natural frequency?

2. If two mounts have similar "force vs displacement" curves (with the exception of a slightly broader hysteresis), is it safe to say that the mechanical characteristics of the two mounts are the same? (i.e. If a component passed a vibration test with one mount, is it necessary to re-test with the second mount?)

Thanks!
Ray

 

[GregLocock]

Ack. I thought you guys solved these things by turning them into LCR circuits, and then solving them in your heads?

However:

1) If you are treating the machine on the mount as a single degree of freedom system then you need the mass of the machine as well. The stiffness of the mount is the gradient of the force displacement curve. Then f=1/2/pi*sqrt(k/m)

The confusion in my mind comes because the mount itself does have a resonance, analogous to spring surge. It may be possible to predict this accuarately, and don't think it is easy. I doubt this is what you mean anyway.

2) In general the isolator with the broader hysteris will be better, at or near resonance, but it really depends on the operating speed (frequency) of your system comapred with the resonant frequency. If the resonance is a long way below the frequency of interest then the more lightly damped isolator may be a better choice.




Cheers

Greg Locock

 

[electricpete]

Sounds like good comments from Greg. It is not EE's who turn everything into LRC circuits. It is ME's who stole our math. Just kidding.

I wanted to ask Greg... I assume hysteresis is roughly comparable to damping. In that case, the effect of increased damping is to decrease response at all frequencies, but those near resonance are decreased more (making the curve shape look fatter, even though response at all frequencies are lower). So why is it that broader hysteresis would ever be undesirable for isolation purposes?

 

[Spirit]

Just to add smthg to Greg's answer:
in case you don't have a Single Degree Of Freedom system, it is not so straightforward to calculate the fundamental frequency of the equipment on the mountings; the handbooks of the manufacturer should anyway help you find the frequency for a given mounting fashion and equipment mass/CoG/inertia properties.
As for the second question, yes, it is correct to assume the same dynamic behaviour for two similar force/displacement diagrams, preferring the on with the higher hysteresis for the reasons described by elecricpete. Just consider also the maximum force and/or displacement allowed for the mounting as design criterion, and the design of the mounting itself for durability. For motorcycles we found two kinds of mountings with the same characteristics, but designed slightly differently, that under test exhibited VERY different operative life durations.

Cheers

Spirit
'Ability is 10% inspiration and 90% perspiration.'

 

[machineryguy]

Gentlemen,
Allow me to give my 2 bits worth. I am still tickled that I found this forum and feel it is great.

Remlap,
My views on your questions are as follows:
1) You probably shouldn't care what the natural frequency of the mount is. I am assuming you are using the anti-vibration mounts as mounts for something else, probably much bigger and heavier. It is important to keep in mind that you are after the overall SYSTEM response, and not that of one individual component (probably). The characteristics of your dampers will contribute (hopefully a significant amount, as that is what you are using them for) to the overall system dynamics.
2) My view is to say no, you might get in trouble assuming similar mechanical characteristics (and resulting system response) on two different mounts with near identical F vs D plots. The reason is that the stiffness is only one values that you need and damping is the other. To me it doesn't seem impossible to have two material/geometry configurations that match one and not the other. However, providing your mounts are "similar", your assumption seems like a good place to start to me. If your tests are long and expensive, then maybe you can run the test with say Mount A, and record the response. If your part "passes", then just jig it up with the second mount, and compare overall response. If it is similar, then maybe you can not test the second mount out to 6 weeks, 10 million cycles, etc and have some confidence in it?
Side note: (You may need to be aware that materials can give different F v K plots depending on how they were generated: statically or dynamically)

Electric Pete,
Your logic is good, but as I think was mentioned above, you are not necessarily better off to just pic the one with the higher energy loss. (sorry if I sound like a lawyer). You can view hysteresis as energy loss. Again, the overall system response is what you are after, which will be sensitive to the mount characteristics. The damping of the mount shifts the natural frequencies around. So, allthough the higher damped one may absorb more energy, that benefit may be lost if you are moving the system closer to resonance.

Hope I helped, and didnt mislead or say something inaccurate. Good luck.

 

[GregLocock]

Why more damping might not be better.

If your goal is to minimise the force transferred into the foundation, and the excitation frequency is >sqrt(2)* the resonant frequency, then it is better to have no damping. This is why low Duro rubber bushes are better for high frequncy NVH in cars - you get beetr isolation in exchange for poor control at resonance.




Cheers

Greg Locock

 

[electricpete]

Thanks Greg and Machineryguy. Those are both good points to answer my question.

 

[objengrs]

Three further comments:
1) Given two mounts that appear to have the same stiffness and damping, the ability to sustain constant cycling is related to size (and therefore heat buildup per unit volume). For the EE's, this is loosely analogous to needing a 200K resistor, and decided whether to choose a 1/4 Watt versus 1 Watt resistor.
2) When elastomeric mounts fail, the tension side of the cycle is usually the problem. A good rule of thumb is that they won't take a continued stretch beyond 10% of their free height. (i.e. the thickness of the stretching portion of the mount)
3) Laboratory life testing of mounts typically won't work faster than 0.5 to 1 Hz, due to heat buildup in the elastomer. You can help somewhat by trying to cool it with external blowers, but most elastomers don't conduct heat well.