What is the Peak G level during Random Vibe Testing

[rlara]

Hellow everyone:

I am trying to determine the peak G level achived during a random vibe test at the main natural frequency. Im using miles equation to estimate the peak acceleration.

I ran a low level random vibe test to determine the natural frequencies of the unit and also the Q's. I had to notch the peak acceleration to 100 G, so what I did was to determine the max PSD level I should limit notch as to achive the 100 G peak.

What I want to determine is the peak acceleraction the unit saw at full level. Should I used the orinal Q I got from the low level run and the peak output PSD? or should I use the Q that I saw at the full level run and the peak output PSD?

thanks in advance

rlara

 

[franck]

Hi Rlara,

I am not fully sure I undertand your post. What do you mean by 100 G peak. Do you want to notch to 100 g2/Hz or do you want to notch so that 3 sigma equivalent static acceleration do not exceed 100 g? Basically do you want to notch on PSD or on grms values?

I do not understand why you are using the Miles equations for doing that. During a random test, you perform a low level random and several intermediate runs that you shape to acheive want you want at full levels. With respect to PSD we can even notch automatically (with the shaker control) the PSD max levels. Regarding the grms value (which is linked to the area of your PSD response) you have to shape your random input profile.

Note, just a clarificatio, if you want to use the Miles equation, make sure that the PSD you are using is the input PSD and not the output PSD as seems to suggest your email. Moreover, be aware that the Miles equation is derived for a single degree of freedom and a flat input, which can be far from your test conditions.

Franck

 

[rlara]

Frank:

Thank you for your response.

Yes, I mean 100 G peak (3 sigma) response at the natural frequency. What I would do is notch the input profile with the controler. The way Im using miles equation is as follows:

If we want to notch to 100 G peak (3 sigma)

I would back track from miles equation to determine the maximum PSD output we would use.

Miles equation is:

Grms=SQRT(PI/2 * Fn * PSDin * Q)

Q=SQRT(PSD out/PSD in)

Substituting Q in the original equation and mutiplying by 3 to get peak acceleration you get:

G peak= 3*SQRT(PI/2 * Fn * (PSD out/Q)

From the above equation you can then back track to determine the required PSD out you need in order to achive the maximum G level.

What I do then is to let the controler notch the input profile (PSD in) by adding a maximum limit output (PSD out), the output PSD is what I determine from the equation.

After the full level test is done I want to determine what the max peak acceleration (3 sigma) that was achived at full level at the natural frequency. The way I want to do it is by using miles equation as I presented it before:

G peak= 3*SQRT(PI/2 * Fn * (PSD out/Q)

I would determine the Q at the natural frequency and the output PSD at nothced peak to determine the max peak acceleration.

Do you consider this a valid method?

I understand Miles equation only works for a single degree of fredom assumption and that is also used on a flat input PSD.

For the test the unit is not a single degree of fredom and the input is not flat. It could be considerd flat at the natural frequency.

Now the way I have determined the peak acceleration before is by taking the area under the natural frequency peak. The question is what frequency bandwidth would you use? would you use half the power band width?

Which of this methods do you think is correct? What other methods are out there to determine what was the maximum acceleration?

thanks for your help

RLARA

 

[franck]

Hi Rlara,

What you are doing makes sense to me. However, you are aware of all the limitations associated with your method (does not take into account modal interaction since written for a SDOF) so it is really difficult to quantify if this approach is conservative. It can be but it truly depends on your input spectrum at frequencies below the natural frequency of interest. If for some reasons the input spectrum is higher in the low frequency range, you are maybe underestimating your equivalent static response.

Now, to assess the Q factor, basically you have 3 methods:

+the mode bandwidth (as you are using)
+a FEM model (which will tell you what Q to be used to get your peak PSD)
+a method based on the slope of peak (more acurate method than the bandwidth).

To tell the truth, I never be confronted in a situation where I have to notch the output response during a random testing. Usually in my business space (this is not allowed except for particular equipment). Usually, you just need to make sure that you provide the appropriate PSD inputs at your Hardware interface and the appropriate overall Grms level. Maybe you can notch based on some quasi static forces criteria (valid for a small satellite for instance when random is the driver and not the sine) but this is not really usual on hardware

Franck

 

[rlara]

Frank, thanks for your comments.

The aplication here is also space, and pretty much all the test I have done have notching in them.

Now its not a requirement to notch but they allow notching in order to not over stress the unit at its natural frequency.

Some times I don’t really understand why notching is needed, if the unit should survive a certain input profile then you should test it to that level.

I can see how notching would be needed if testing an acceptance unit, but not a qual unit.

Any ways thanks for your help, I’m still learning the ropes so any input from experienced engineers is always appreciated.

rlara

 

[franck]

Hi Rlara,

I agree with you! I am not sure that I understand the rationale for the notching either. Your input levels should be somehow representative of what the unit is going to experience at system level. Thus, a notching should be based on a reduction of the input level (if the derivation was too conservative) but not on the fact that you may damage the equipment. I am not sure how the client can accept that. Sometimes, we can reduce the input levels based on the fact that at unit level we are performing the test on a stiff interface so the Q factor is really high (when compared to a flexible interface -when the unit is mounted on a panel for instance). However, notching the response because you are affraid to damage the unit is a news to me!

With respect to qualification/acceptance testing, once again if your unit has survived the 6 minutes of qualification at 3 dB higher than acceptance levels, your unit should be safe going to acceptance testing without any notching!

As a rule, notching cannot be performed without the agreement of the client who defined the unit environment.

It will be interesting to know what is your company.

Franck

 

[IRstuff]

Miles' Equation Does NOT Work in Reverse - Accelerations cannot be determined during random vibration testing using Miles' Equation. An upper bound on loads can be calculated using the 3-sigma value, but that's about it. In other words, a part designed to 3-sigma equivalent static loads will survive a random vibration test. However, Miles' Equation cannot be used to predict the failure of a part designed to less than 3-sigma levels.

from

http://femci.gsfc.nasa.gov/random/MilesEqn.html

TTFN

 

[franck]

Yes TTFN, you are fully right!

 

[rlara]

TTFN and Frank:

I remembered seeing that some where, thanks for showing me that.

So that shows that Miles equation cannot be used in reverse,
If so then the method stated above is not valid. Correct?

Now from your experience what would be a valid method to determine the acceleration experienced during the natural frequency of the unit?

Would the area under the curve give me the value I’m looking for?

Now regarding the notching philosophy, the way I am testing the unit is in a fixed configuration which really does not resemble the actual flight configuration but was determined to be sufficient to create a simple test.

Based on this, the unit will have higher responses at a component test level than at a system level. So here I can see how notching would be a good way to not over test the unit to levels it will never see, this being for a acceptance unit or flight unit. But for the qual unit I would consider a better test to test the unit to its limits.

The duration for a qual level test is usually 3 minutes, and its 6 dB above the acceptance test level. Now that’s for the components I am testing, it may be longer for other components.

TTFN have you done any notching for components? if so what method have you used to determine the acceleration.

Thanks for your comments.

rlara

 

[IRstuff]

Sorry, I'm pretty much clueless.

I ran a search just to find some information on the Miles equation and that happened to be the first site I hit.

As to your original question about Q, our testing is usually done with:

> swept since at low level to find resonance
> endurance vibe at resonance driven by acceleration dictated by spec, e.g., MIL-STD-167,-810. Usually done with three or so different levels, to make sure we done break anything or find and interacting resonance.
> random vibe

In which case, if the Q that we see from the swept sine is too high, we fix the hardware and start over.

TTFN