How to calculate natural freq. with a spring/mass w/constant preload? 8

[stillfeelme]

Hello,

I hope I am asking this in the right location. I have a fairly simple question that I have not been able to determine. I want to know how to calculate the natural frequency of a spring mass system that undergoes a constant preload in the spring. This would be for a simple compression spring. I am trying to compare FEA results to hand calculations. I have looked in a couple different textbooks and online and I can't find anything that has this. I did a search here and I couldn't find anything as well.

 

[desertfox]

have a look at this site:-

http://www.roymech.co.uk/Useful_Tables/Vibrations/Vibrations_Index.html#Tables

 

[stillfeelme]

desertfox,

Thanks I searched that link and I couldn't find anything with a constant preload. It does have all the scenarios for single degree of freedom with damping etc.

 

[israelkk]

To my best knowledge the natural frequency of mass spring system depends only on the mass and the spring rate and has nothing to do with the preload which doesn't change the spring rate.

 

[desertfox]

Hi Again

The formula under "free natural vibrations" is what your looking for :-
Natural frequency" n = ? n ( 2 ? )= Sqrt (k /m )/ ( 2 ? ).....(units = cycles/s)

forget the preload its just spring stiffness and mass


desertfox

 

[Tmoose]

In some situations preload can change stiffness/spring rate.
Angular contact ball bearings come to mind.

http://img.photobucket.com/albums/0803/jstanley/pre02.jpg

http://www.docstoc.com/docs/74528752/PRELOADING-BEARINGS-Barden-Precision-Ball-Bearings

 

[stillfeelme]

Desertfox,

I am aware of that equation you listed as I have been using it under non preloaded conditions to match pretty close to what the FEA model says. What I experience is when I add the preload the natural frequency goes up even though I didn't necessarily change the stiffness of the spring. So I am trying to figure out what is the correlation under preload to the natural frequency so that I can do a hand calculation to predict or match analysis.

 

[desertfox]

hi stillfeelme

One possibility is that spring stiffness or rates for the first and last 15% of compression are not a straight lines,so the stiffness particularly towards the maximum compression could quite easily be an increase its stiffness which might account for the descrepancy.
Another source of error might be that the calculation your doing uses the theoretical spring stiffness as opposed the the actual spring stiffness unless you measured the spring stiffness first.

desertfox

 

[IRstuff]

Natural frequency supposedy varies with the inverse square root of mass

TTFN

FAQ731-376
Chinese prisoner wins Nobel Peace Prize

 

[GregLocock]

is your fea model linear?

Cheers

Greg Locock


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

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[zekeman]

"I have looked in a couple different textbooks and online and I can't find anything that has this. I did a search here and I couldn't find anything as well. "

And you are not likely, since preload never enters the differential equation.

It doesn't matter where the mass is located in the single degree system. What matters if you quasistatically move the mass dx, then you get an opposing force dF and

the spring constant, k, is dF/dx remains independent of the preload and hence,

wn=sqrt(k/M)

T

 

[FeX32]

In a linear system (one with linear stiffness), I agree with zekeman (and a few others above). No matter what, the square root of the systems eigenvalues only depend on the mass matrix and hence will not change with load, gravity (in any direction) or anything else for that matter.
However, in a nonlinear system (which I think Greg is hinting at) a preloaded spring will exhibit different "fundamental frequencies" dependent on a few factors. A system with a nonlinear spring in some engineers eyes doesn't even have a fundamental frequency, just a frequency that, given certain load, deflection and mass conditions, it "mostly" vibrates at.
Many real life systems are inherently nonlinear. Thus, your answer in short to wether preload can effect a fundamental frequency is yes.


Fe

 

[Tmoose]

"What I experience is when I add the preload the natural frequency goes up even though I didn't necessarily change the stiffness of the spring."

How are you preloading the real life spring(s)? And what kind of spring(s) are they ?

 

[stillfeelme]

Hello,

All thanks for the feedback what I am doing is forcing the compression by deflection in one direction. So I displace the spring and the displacement is fixed, then calculate the natural frequency. The only thing I can think of is maybe the deflection is causing it to behave non linear

 

[desertfox]

Hi stillfeelme

How far are you compressing the spring, can you give us spring dimensions

 

[desertfox]

Hi again

Take a look at page 58 of this ref it shows a typical load deflection curve for a compression spring :-

http://www.scribd.com/doc/29044778/Spring-Design-Handbook

notice the change in stiffness at each end of the curve

desertfox

 

[drawoh]

stillfeelme,

What do you mean by a constant preload?

If the thing is vibrating along the axis of the preload spring, the preload is not constant, and this is (part of) your spring element in your vibration equations.

If the spring acts normal to the vibration, it is part of a friction damper, and the preload would be constant.

JHG

 

[IRstuff]

Well, one possible analogy would be a car suspension, which has relatively low "sprung" mass, but is essentially "preloaded" by the weight of the vehicle. And, static compression of the suspension springs do change the natural frequency of the suspension.

TTFN

FAQ731-376
Chinese prisoner wins Nobel Peace Prize

 

[btrueblood]

"I want to know how to calculate the natural frequency of a spring mass system that undergoes a constant preload in the spring. "

"So I displace the spring and the displacement is fixed, then calculate the natural frequency. "

Those appear to be mutually cancelling statements.

The first statement implies you have a spring (theoretically modelled as mass-less), with an attached mass, and want to know the fundamental frequency. Posts have been given that give the correct answer, which is that the frequency is independent of any preload.

The second statment implies that you are fixing the spring ends, to achieve a preload, thus anything attached to the spring ends cannot vibrate.

Based on the second statement - are you trying to calculate the modes of vibration of the spring itself? These can, and do vary depending on preloading, see a good spring design book.

The only other possibility I can see is that you are calculating/modelling transverse oscillations, not axial oscillations, of the spring/mass system? Here again, the tranverse charactersitics of the spring can vary depending on its preloaded length.

If neither of the above assumptions by me are correct, then can you kindly explain what the heck you are talking about? Perhaps a picture would help us understand your question.

 

[ivymike]

sounds like he's calculating the surge frequency.