Converting Between: [PSD] [Sine Sweep] [Sine Tone]

[dstobbe]

OK, I know this has been debated before, but I never really got a solution from the previous threads.

Problem statement:

I have an electrodynamic shaker capable of applying only broadband random vibration 5-2000 Hz (hypothetical).

I would like to apply the MIL-STD-810F endurance vibration for rotary aircraft (specifically the Apache). Spec details (for an external store)

Broadband
10 Hz 0.002 g^2/Hz
100 Hz 0.02 g^2/Hz
300 Hz 0.02 g^2/Hz
500 Hz 0.002 g^2/Hz

Narrow Band (sine tones)
4.86 Hz 0.12 g
19.44 Hz 1.94 g
38.88 Hz 2.5 g
58.32 Hz 2.5 g

I would like to convert the narrow band sine tones to psd curves and super impose them on the broadband signal.

Previous post have suggested using Miles equation Grms=sqrt(pi/2*PSD*Q), to get an equivalent (1-sigma) acceleration (multiple to 3-sigma) get a "random damage" and equate that to the damage that would be incurred by an equivalent sine vibe.

Questions:

What is the "random damage" equation?

Is resonant and transmissibility information on your system really needed before the conversion can be made?

(In response to the previous thread) Where is this technique detailed in Steinbergs Vibration book? (I have the book right next to me)

Has anyone read the COTS Relating Sinusoid to Random Vibration paper? From what I can tell, it is totally wrong!

Thanks

 

[mechengdude]

I can help with some of this but I have some questions.
Are you performing an analysis, a test, or both?
I'm not familiar with a random damage equation, I believe you are referring to Miners equation for cumulative damage, yes? I'll assume you are familar with Miners equation or can find a source.
resonant and transmissibility information is always nice to have but the 3 sigma Miles equation design philosophy should provide enough margin for some error in estimating these values.
look at the examples in steinbergs book pages 226 and 250 for example problems on random vibration. Not sure this helps you on the sine questions but I'm not really sure where you're going with that and why you need it. Maybe someone smarter than me can tell us.

 

[dstobbe]

I am trying to get 1 broadband vibration requirment which will encompase both the broadband and narrowband rotary requirements in 810-F. Instead of running two tests, one random and one sine.

The Miles equation requires knowledge of the transmissibility and resonant frequency (i missed the fn in my equation above).

"
franck (Aerospace) 29 Oct 04 9:36
Hi Tomliu,

I am not sure if it is really the answer since the description of the problem is very limited but here is a try. Basically I guess this is finding the equivalent sine vibration for equal random damage.

A PSD of 0.0243g2/Hz at 289Hz gives you an equivalent static acceleration of 18 grms using a Q of 30 and the Miles equation:

sqrt(Pi/2*289*30*0.0243)=18 grms

Now, the damage produce by this random environment assuming the 3 sigma value (3*grms) occurs for only 4.33% of the time and an exponent of 3 for fatigue damage you get a random damage of:

random damage = 0.0433*(3*18)^3=4692

Now the peak value from a sine input to get the same damage during a sine test is (still assuming a Q of 30 and the same exponent):

(Input_Sine*30)^3=4692 gives Input_Sine= 0.616g

This approach is defined in 'Vibration Analysis for Electronic Equipment' -Dave Steinberg-Wiley Interscience-

Franck
"

from previous thread, however, random damage equation doesn't even compute correctly

I'll check those steinbeck pages

 

[FrankFanWang]

I am the author of the COTS journal article "Relating Sinusoid to Random Vibration for Electronic Equipment Testing". See here

http://www.cotsjournalonline.com/pdfs/2003/04/COTS04_test&screen2.pdf

I would like to know which part does or does not make sense in detail.

Thanks a lot

Frank

 

[FrankFanWang]

dstobbe (Mechanical)

Could you be specific about the "wrong" part of my article?

Thanks

Frank