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.

 

[stillfeelme]

All,

The easiest way to explain it would be a spring that is precompressed to fit within a cavity. I fix the spring by the the amount it is displaced and then I am trying to get the natural frequency of this system. I was looking for a hand calculation that gives me the natural frequency something along the lines of a suspension system but I can't find an example that fits what I am trying to do. Again thanks for the help but I am reaching the point where I don't know if a hand calculation exists for this.

 

[FeX32]

Make sure you are doing the FEA right.
How much different is the unpreloaded fn from the preloaded one?


Fe

 

[FeX32]

Remember there is a tolerance in FEA for model convergence. And make sure the elements are linear.


Fe

 

[stillfeelme]

FeX32,

The displacement is about 25% of the free length.

 

[stillfeelme]

FeX32,

The difference between unloaded and loaded results in a factor close to 4. Loaded giving me a natural frequency ~4 times higher. Elements are linear.

ivymike,

I actually thought it would be close to the surge frequency but they were far apart. I have looked into that equation already as well.

 

[Tmoose]

So the mode would be axial surge of the spring at a fixed length?

Not the "preloaded" end bouncing axially like this?

http://comp.uark.edu/~jjrencis/femur/Learning-Modules/The-Basic-Finite-Element-Equation/sdof3-7.gif

 

[stillfeelme]

Tmoose,

The mode is the preloaded end bouncing like that. I will have to take a look tomorrow.

 

[FeX32]

Alright.

From this:

I fix the spring by the the amount it is displaced and then I am trying to get the natural frequency of this system.

I can gather that you have effectively fixed the spring in a cavity. Thus resulting in a system in which this cavity (or whatever else is in your design) is now involved in the eigenvalue decomposition.
Basically I think you are calculating the fundamental freq. of you design with a spring fixed in a cavity (which means the spring now cony contributes to a small amount of the stiffness). Where as before you had just the spring contributing to the stiffness.

btw, a factor of 4 is a very large difference. It is worth finding out the reasons for this, wether it is an modeling FEA error or the such.




Fe

 

[electricpete]

I think it would help to provide a simple figure.

I'm going to assume a simple case that your "spring" has distributed mass and is captured at a fixed unmovable position on both ends. Then I think your result might be plausible (axial resonant frequency increases as the restrain points are pushed closer together). This would be vaguely analogous to the familiar situation to a rubber band held a certain distance apart. For the rubber band, we intuitively know that if we increase the preload (non-vibrating) strain by making the distance between rubber band support points longer, we will increase the resonant frequency of rubber band. Likewise I think that for the axial beam, increasing the preload (non-vibrating) strain by moving the support points away from their free=non-preloaded position (either longer or shorter) will increase the resonant frequency of the axial-vibrating beam.


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(2B)+(2B)' ?

 

[izax1]

I'm not sure what your "spring" is like. but most mechanical springs are non-linear, which means a preload is changing the spring stiffness and thus the natural frequency. A natural frequency is by definition linear and will give a distinct numerical value dependent on the preload of a "normal" mechanical spring.

btw: Do you trust your FE results for the preloaded spring? Is the preload constant? Does the results give you a value for the natural frequency?

 

[electricpete]

Sorry, I think I was wrong in my comments. There is a math analogy between string in tension vibrating transversely and a beam vibrating axially, however tension in string does not play similar role to tension/compression in beam. My analogy was incorrect. (Ref “Fundamentals of Vibration” by Meitrovic, Table 8.1)

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(2B)+(2B)' ?

 

[izax1]

This has been a looong discussion, so I might have missed the point along the way. But it is fundamental if the problem is about calculating the natural frequency of a SPRING or calculating the natural frequency of a SPRING/MASS SYSTEM. The natural frequency in preloaded string (spring) is very much dependent on preload. Just look at the natual frequency variations in the transverse vibrations of a jet engine turbine. The higher the rpm, the higher the tansverse natural frequency. Each turbine blade is preloaded by the centrifugal forces as the turbine revs up. (You might even hear it when you are onboard the airplane and sitting in the "right" position relative to the engine.) When the engine revs up, the "singing" in the engine is changing with revs. (I am not talking about the aerodynamic sound for increased aerodynamic pressure)

To try to answer the original question: Find the stiffness of the preloaded spring, and use that for the natural frequency calculation. It should not be more complicated than that.

 

[btrueblood]

Unless you know what the preload initial condition actually does in your FEA model, your output is worthless. Suggest you look at the mode shapes between the unloaded and preloaded cases. Further suggest that you post some imagery here, you've led a lot of smart people down the garden path and into a maze. Without a lot more definition of what you are doing and how/why (like a PICTURE), it's going to be hard for a clear message of helpfulness to be conveyed...and that is annoying to people who are going out of their way to help you. And probably annoying to you as well.

 

[stillfeelme]

All,

I was looking for a hand calculation but is not simple to find. In my head I thought maybe someone here may have done a calculation on a spring to calculate a natural frequency if the spring had been compressed. I was just trying to figure out the relationship between preload amount and natural frequency.

 

[electricpete]

Just to clarify:
Are there any masses involved in your problem other than the spring?

What are the boundary conditions?....Both ends fixed at a certain distance (i.e. 75% of the uncompressed distance) ?


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(2B)+(2B)' ?

 

[stillfeelme]

Electricpete,

A mass is connected and the spring is compressed at the amount you said fixed at both ends. If you know of a way to calculate the natural frequency I am interested.

 

[electricpete]

So, in addition to the spring distributed mass, there is a lumped mass attached somewhere? Where is this lumped mass attached.... in the middle of the spring?
Attachment at an end would not seem consistent with the comment that both coil ends are fixed boundary condition.

I’m not trying to be picky. But the problem description is still not understandable.


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(2B)+(2B)' ?

 

[drawoh]

stillfeelme,

Does the mass move? We are only interested in masses that move.

It sounds like you are trying to find the resonant frequency of the compressed spring. In that case, the only mass that does anything is that of the spring itself.

JHG

 

[hydtools]

stillfeelme,
a sketch would help.

Ted

 

[stillfeelme]

Electricpete,

I tried to make the problem simple to see if anyone would respond with a hand calculation relating preload with natural frequency. The design is a mass connected to a spring. The spring is compressed to an amount. All I am trying to figure is what is the natural frequency in this example. In my analysis I fixed the displacement and then calculated what the natural frequency is. So I have one spring a mass and preload disacement