Sine on Random - single profile is possible?

[vibrationnewbie]

Apologies in advance: This exact question has been asked in the last couple years, but I didn't quite follow the answer!

Years ago I saw a random vibration profile for an aircraft, the profile had sinusoidal "spikes" representing the rotating propellers. This was for a turboprop, and the spikes were located at the propeller blade passage frequency and the first few harmonics. I believe this is called a "sine on random" vibration profile?

Now I'm trying to create a single vibration profile for an upcoming test that will cover the random profile for a helicopter, and will also incorporate the purely sinusoidal excitation of the main rotor. The hope is to have a single vibration test; avoid two separate tests.

Here's a greatly simplified equivalent of the helicopter profile:
1. Random Profile: PSD level of 0.001 g^2/Hz from 10Hz to 50Hz, negligible level at all other frequencies.
2. Sinusoidal vibration: 15Hz with peak acceleration of 1.0g. (If it helps, call it 15Hz +/- 1Hz.)

What level can I select for a sinusoidal spike, centered at 15Hz, to be added to the random profile that will make a new sine-on-random profile that matches #1 and #2 combined?

In other words: Is there a formula that can take the 15Hz with 1g peak and "transform" it into some magnitude of g^2/Hz so that it can become part of the random PSD?

(I understand that random vibration is TOTALLY different than sinusoidal vibration...but that turboprop random vib spec really did have spikes at 67.5Hz and 135Hz and so on.)

Thanks so much!

 

[IRstuff]

I think you're confused about something. You never turn a single frequency into a PSD, since it's a SINGLE frequency.

You just add #1 and #2 together. Your vibe guy can do that trivially on his controller.

TTFN

FAQ731-376

 

[vibrationnewbie]

Thanks IRstuff!

I understand a single frequency doesn't have an equivalent PSD. But rotating or reciprocating parts of assorted vehicles (aircraft, automobiles, etc) DO add sinusoidal spikes, typically a few Hz wide, to the overall random vib PSD. That's why I added the comment "If it helps call it 15Hz +/- 1Hz".

If the testing guy can easily add the random and the sinusoid on his controller, that would be good.

But I still would like to know how to create an accurate sine-on-random profile graph by combining the two separate profiles. I am assuming the math wouldn't be intractable.

 

[IRstuff]

The simple conceptual approach is to look at the frequency representation. You have a constant frequency signal and a random frequency signal at a lower amplitude

TTFN

FAQ731-376

 

[vibrationnewbie]

Yes, thanks, the simple conceptual approach is readily understood. In fact, it's more or less present in my original post.

Note that I'm looking for actual numbers with units of measure like g^2/Hz...the kind of stuff you can make a graph with. ;-)

If you're not sure how to solve the original question with a formula or technique that results in a number, don't feel bad...neither do I!

cheers!

 

[IRstuff]

I repeat, you don't.

The solution is as shown in MIL-STD-810F, Figure 514.5C-10. The graph shows frequency on the x-axis, spectral density on the left y-axis, and peak sine acceleration on the right y-axis.

TTFN

FAQ731-376

 

[vibrationnewbie]

Thanks so much for the reply, I sincerely appreciate your taking the time and effort!

Actually I prefer Figure 514.6D-3 in MIL-STD-810G, p. 327. But hey, it's the same figure.

Here's the problem, IMHO, with what the authors did (considering emailing them a question about it, since I'm sure I'm the one making the conceptual mistake). Compare the profile you referenced with the previous Figure 514.5C-9. The propeller aircraft vibration exposure is a sine-on-random profile with sinusoidal spikes at the blade passage frequency and the first few harmonics. Note that the y-axis is g^/Hz and they give you the L(0) magnitude value in Table 514.5C-II, in units of g^2/Hz of course.

If you're familiar with Excel it's fairly easy to re-create Figure 514.5C-9 using a log-log plot. (I've done it for several profiles in Method 514, makes it easier to compare with one another if you make sure the scales match.)

Figure 514.5C-10 should be quite similar to Figure 514.5C-9 since they are both sine-on-random profiles. But instead they put the sinusoidal spikes in units of peak sine acceleration g's.

So if you're hoping to sell some great equipment to helicopter people and turboprop people, you'll be very intrested in comparing L(0) from Fig C-9 to A(3) or A(4) in Fig C-10. You know, to find out which one is bigger...and for that you need numbers.

Hence the question of how to take a specific value of peak sine acceleration in units of g and transform it into a specific value of g^2/Hz. Of course you would have to assume the single frequency they show in Fig C-10 would be transformed to match what they're doing in Fig C-9 (a center frequency +/- 5%, per Table 514.5C-II).

Hey, if it works for a turboprop then it should work for a helicopter, right? In fact in Annex D of 810G they imply as much, ref. Category 14, Section 2.3(b&c), p. 326. I doubt if the "pseudo steady state rotor speed" is any more steady than a turboprop RPM.

Regards.

 

[IRstuff]

No, if you read the authors' text, they make it clear that there is never any equivalence, and that the graphs are different because the source and its behavior is different.

The text clearly distinuishes between narrow band random over broadband random vs. sine over broadband random.

I don't know enough about the actual environment to say whether the choice is correct or not, but, clearly, the authors' position is that they are different, and that there is no equivalence.

TTFN

FAQ731-376