Frequency response analysis specification 4

[elogesh]

Hi,

This is regarding one of the specification, we came across for frequency response analysis.

In one of our group analysis involved in the design and manufacture of filter systems would like to perform virtual simulation before proceeding for actual testing.

The test specification is
In the 10 to 25 Hz range, the amplitude displacement
is ± 1.2 mm and remains constant.
b. In the 25 to 200 Hz range, the acceleration amplitude is 30 m/s2 and remains constant.
c. The frequency variation speed is 1 octave per minute
d. Test conducted for 8 hrs.

Meanwhile we requested for the standards and will be getting in a day or two....

Based on the prior mails and replies from Greg locock, we could able to calculate the no. of octaves and other details.

But I have couple of clarifications about the specifications,
1) What is the intention of specifying part of the excitiation load as displacement (between 10 to 25 hz) and remaining part as constant accleration(25 to 200Hz).

2) In virtual simulation, can I convert the displacement in to accleration and apply it as a excitation load for the frequency range between 10 to 25 hz?

Acceleration = (2*pi*frequency)^2 * displacement

Thanks in advance for your responses.


Regards,
elogesh

 

[electricpete]

The limit you describe is similar to the Rathbone chart shown here:

http://books.google.com/books?id=WI...UTB&sig=JIAKnafmtsu6NfUBW1GPplvNLNY#PPA247,M1

go to page 247 to see the figure... page 246 for the discussion.

For many rotating equipment specs such as NEMA MG-1, the limit is often given as a displacement, a velocity, and acceleration. Assuming the vibration is sinusoidal, the displacement limit is the lowest of the three in a low frequency range below some cutoff. The acceleration limit is the lowest of the three in a high frequency range above some cutoff. The velocity is the lowest of the three in between. This type of limit is as shown in figure 2 on page 247.

What is the intention? I think primarily these curves are based on experience. You could also make some guesses at the Engineering basis for these curves. For example limiting displacement limits the strain (and therefore stress). There is also an interesting fact that a simply supported beam vibrating at resonance has a maximum stress which is a function of vibration velocity and material properties, but amazingly, NOT not a function of the beam length, cross section, or whether it is the first, second, third etc mode! (which points toward the usefulness of limiting velocity) I think dimensional analysis can show some other interesting relationships between velocity and stress for a range of situations.

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[electricpete]

"NOT not a function of the beam length, cross section, or whether it is the first, second, third etc mode! "
More specifically, for a simply supported rectangular beam vibrating at resonance, the max stress is indepdent of length, width, height. 1 ips pk/0 corresponds to 260 psi. This does not take stress concentrators into account.

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[GregLocock]

I'd always wondered why stress guys think in velocity terms.

One other reason is that many times the energy into a system is more nearly a function of velocity than acc or dis.

Anyway back to elogesh's problem, yes it is just a crude form of spectrum shaping. It may represent real world results, or it may represent the limitations of a test rig somewhere that gave reasonable results. For instance electical shaker tables often have acceleration limited regions (max current) and displacement limits (max articulation of the coil).





Cheers

Greg Locock

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

 

[spongebob007]

What you are doing is essentially ramping from .5G to 3G over the range of 10Hz to 25Hz and then holding at 3G from 25Hz to 250Hz. The other way to look at it is that you are at a constant amplitude of 1.2mm from 10-25Hz, then you ramp down from 1.2mm to .019mm from 25Hz to 200Hz.

Vibration test spectra are usually defined in this manner. It could have something to do with the limits of shaker tables. If you were to be at 1.2mm over the entire range then at 200Hz you would be seeing almost 200G!

In terms of analysis, here is what I would do. First, determine the modal response of your structure. Is the lowest natural frequency >400Hz. If yes, simply apply a 3G body load to your model, determine stresses.


If the natural frequency is less than 400Hz, is the 2nd mode seperated from the fundamental by at least one octave? If yes, then your model can be treated as a 1DOF system. Say the first mode is 300Hz, and the 2nd is 700 for example. Your frequency ratio would be 200/300 or ~.67. Find a transmissibility curve for a 1DOF system. Get the transmissibility ratio for R=.67. Multipy that number by 3G and apply it to your model.

If the first two modes are separated by less than an octave then you can't treat your model as a 1DOF system because dynamic coupling between the modes can lead to amplifications that are orders of magnitide higher than those for a 1DOF system.

Even if your frequencies are separated by at least an octave but you have multiple frequencies in the 10 to say 300Hz band I would be cautious about using a quasi-static analysis.

If resonance of multiple frequencies is a possibility then you should do a full response spectrum analysis. It really doesn't matter whether you convert your test spectrum to displacement or acceleration since most FEA programs will accept either one.

 

[elogesh]

Hi,

Thanks to electripete, Greg and spongebob007.

Regards,
E.Logesh

 

[jeyaselvan]

As you first question is concerned,I remember being informed in a training for electrodynamics shakers, that the change over from displacemnt to acceleration needs to amooth from the shaker's control point of view. This is ensured here by having the 1.2mm disp at 25 Hz being equivalent to the 30m/s^2 at 25Hz. This ensures better control of the shaker,typically in case os sine sweeps.

 

[IRstuff]

There's no choice about that, specifying 2 out the 3, displacement, frequency, acceleration, uniquely defines the curve.

acc = disp*(2*pi*f)²

so 1.2mm displacement at 25 Hz IS 30 m/s², you can't make it anything else.

TTFN

FAQ731-376

 

[elogesh]

Hi,

Thanks IRstuff.

Here is the update about the project.

My colleague has carried out the virtual simulation, Modal analysis followed by frequency response analysis.

The first modal frequency was found to be 87 Hz, which is close to the experimental values. The second natural frequency is 118Hz. Two modal frequencies (87 Hz, 118Hz) are within the 200 Hz range.Third natural frequency is greater than 400 Hz.

In experimental response analysis the component has passed the testing. Experimental displacment response was measured and the virtually simulated frequency displacement response values reasonably correlates with the experimental values.

The number of sweeps between the 10 to 200 Hz range calculated using the formula
2^n = 200/10
Number of sweeps between 10 to 200 Hz, n = 4.3 cycles
Considering 1 octave per minute with total duration of 8 hr, it is found that the total no.of cyles is 112 sweep of 10 to 200 Hz.

In our virtual frequency response analysis, we have extracted modes upto 500 Hz, more than twice the frequency range of interest(200Hz) and also checked for more than 70% effective modal mass contibution. From the analysis,it was found that the stress is maximum,nearly 10 MPa at the 1st natural frequency. Considering only the peak stress of 10 MPa at 87 Hz with 112 cycles, we concluded it is safe by comparing with limiting strength values.

During the review of the report, we had few queries,

1) Virtual Frequency response simulation was carried out at narrow constant band width 2 Hz. In real time, testing involves octave band width. Will there be difference in response, by carrying out the virtual simulation at constant narrow band width instead of constant percentage octave band width.

2) Regarding fatigue calculations, we only know that there are 112 cycles of 10 to 200Hz sweep. But we don't know, independtly how many cycles for each sweep frequency. We just calculated using the maximum stress value at 1st natural frequency for 112 cycles, but not accounted the other frequencies for the calculation.
How to account it?

Spongebob07: The metodology indicated for converting into 1-DOF system and arriving out the response based on transmissibility ratio and static analysis is very useful. We look forward for applying it, whenever the situation arises for converting into 1-DOF system.

Thanks in advance for your responses.

Regards,
Loganathan.E

 

[Tmoose]

re: displacement vs velocity vs acceleration.

Balmac's literature used to make an analogy something like this -

If I'm going to crash into a telephone pole the figure of merit is mph, not so much whether if I'm accelating or drove 6 miles to have the accident.