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]

Hi desertfox,

The first link yes I have seen that link before as it appears to describe the surge frequency of the spring. The calculated surge frequency is 20 times higher than the natural frequency of the spring mass if they behave linearly SQRT(k/m). We are trying to keep this device away from 50Hz and multiples of 50Hz and some other higher order natural frequencies. I have seen evidence of a possible resonance so now I am trying to predict what I have seen in the field with calculations and FEA analysis to decide the next course of action.

The second link is very interesting and is exactly what I was asking for in my original post. My spring is always under some sort of preload and is never in the free condition. So I was trying to see what equation would let me hand calculate the frequency if it was under preload. Now I am not sure that equation applies 100% but it does not match my model. To be honest I don't know if my model is comparable at the moment with the boundary conditions applied. However the hand calculation numbers I am getting are close to 50 Hz so it is making a case.

flash3780,

That looks like something a Fourier series can solve.

 

[drawoh]

stillfeelme,

I am still having problems with your preload.

If a mass and spring are vibrating, the system starts out with the spring deflected some distance. If there is not a lot of damping, the mass moves such that the spring passes through its free state, and winds up deflected opposite from where it started out.

If the spring is always preloaded, the mass and spring are not a vibrating system.

JHG

 

[PNachtwey]

electricpete, I am wondering WHY there is still a question about if the spring is linear or non-linear. stillfeelme should know what he entered for the spring constant in the FEA. stillfeelme should know whether the FEA spring is linear or not. It isn't up to us to guess.

The simulation using ODEs is trivial EVEN if the spring is non-linear. I do simulations of hydraulic systems that are similar to the example flash3780 has shown but hydraulic systems ARE non-linear. The natural frequency changes as a function of position.

electricpete, I don't like being told to read the posts. I can read. I know what questions to ask. I can do the simulations using multiple non-linear ODEs with little effort. The mechanical people are not scoring points, they aren't supplying a transfer function for the system. My experience with mechanical people is that most systems are kludged and not designed. The mechanical people can never tell the control guys the system gain, damping factor, and natural frequency. Why don't we have it in this case?

Here is a trivial example mass on a spring simulation.

http://www.deltamotion.com/peter/Mathcad/Mathcad - T0C1 MassOnASpring-PID.pdf

In this example the spring constant is a constant. The motion of the spring is being controlled. This worksheet was generated for a PLC forum to show the importance of using the derivative gain. It was done over a year ago.

All I see is a lot of guessing or speculating. stillfeelme need to supply information.














Peter Nachtwey
Delta Computer Systems

http://www.deltamotion.com

 

[FeX32]

PNachtwey,

With all due respect. Relax. I am a mechanical engineer and can tell you anything there is to know about control (and much more)....no bashing. Don't generalize!

The answer to this thread was given many many posts ago by about 5 intelligent people. However, some very helpful members have stuck around and tried to help the OP conceptually.

The mechanical people are not scoring points, they aren't supplying a transfer function for the system.

This makes me laugh. Try thinking about an analytical solution to a nonlinear DE by Laplace. Then we can talk.

The rest of your post is nonsensical.

The problem with this tread was only one thing. The OP.
I mean no disrespect by this post.







Fe

 

[alister1370]

Hi,
The answer is in the second order motion equation of a simple spring-mas system.

wn=2*pi*fn
fn=1/tn
a2y^2+a1y+a0=0
r1,r2

 

[stillfeelme]

All,

Thanks for the help. I should have given out more information on the original post. I would never thought it would cause a war of words between people on a forum. Last post again thanks all