Vibration shaker 2

[rocketmotor]

Hello, we have a request from our customer to perform random vibration test on aerospace black box. The PSD is as follows:

From 3 to 20 Hz, PSD = 0.03
From 20 to 2000 Hz, PSD = 0.06

Can any people help to determine the worse case input vibration displacement on the shaker table in order to meet the test requirement. I just want to make sure our shaker can handle the test.

Thanks.

 

[CESSNA1]

ROCKETMOTOR: In general the lowest frequency will have the highest displacement. Assuming the PSD values are in G^2 rms/Hz the approximate amplitude at 3 hz is around .25 g's peak. This corresponds to a peak displacement of about 600 mils or 0.6 inch peak or 1.2 inches peak to peak. At 20 Hz and .06 g^2rms/hz the approximate amplitude is around 0.346 g's. This corresponds to a peak displacement of about 20 mils or .02 inches or .04 inches peak to peak. Most large shakers have a 1 inch peak to peak displacement. Also since the operating band, before shutdown, around the psd is typically +/- 6 db. You may want to look at the displacements on this band.
The actual fixture/test item amplitude also depends on the fixture and test item. Resonances in the fixture and test item could drive the actual displacements higher.

Out of curosity what type of accelerometer are your using for the shaker? A piezoelectric accelerometer has a lower limit of about 5 Hz. The actual lower limit of use of piezoeletric accelerometers is typically 20 Hz. This is well above teh specified 3 hz. Also, is there a transition between the .03 psd and the .06 psd? A shaker cannot make such a sudden jump in psd. This is an unusual vibration profile, from where did it come? Also, the .06 grms/hz seems high for a frequency of 2000 Hz. Typically the PSD is tapered off at 6 db/oct from a lower frequency to 2000 hz. Likewise the same decrease in g^2rms/hz is usually done at the lower frequencies. There may be a problem driving the .06 amplitude at 2000 hz, and the amplitude at 3 Hz exceeds a 1 inch displacement shaker capacity. Is this test for stress screening or is it an in-service test?

This looks like a slightly over 10 g rms profile

I suggest a low level random resonanace search on the fixture and test item.

Regards
Dave

 

[rocketmotor]

Hi CESSNA1,

Thanks for your response, really appreciated.
It is possible to show how those 0.25g and 0.346g and 0.2 inch displacement arrived. It will help me next time.

Also, is the displacement takes into account the 3 sigma factor? How would this affect your calculation?

I start worrying my shaker now as the displacement is so high....

The accelerometer is of piezo type.
The test profile was given by the customer.
I have the same feeling too for that sudden jump of PSD, I probably need to discuss with the customer further.

Best regards,

 

[rocketmotor]

Oops..

CESSNA1, I mean it...

Is it possible to show how those 0.25g and 0.346g and 0.2 inch displacement arrived. It will help me next time.

 

[CESSNA1]

ROCKETMOTOR: To arrive at the displacement is easier to show than to explain but here gos. The PSD has the units of G^2rms/Hz. The PSD value .03 or .06 in this case is the average of all the peaks around the center frequency (usually +/- 1 db).

1. Take the square root of the G^2 rms term to get Grms

sqrt(.03) = about .176 grms

2. Then multiply it by 1.414 (sqrt 2) to get the peak = about .25grms

4 Using the "vibration computer" (available free from ENDEVCO in San Juan Capistrano, Ca. and also from shaker manufacturers) determine the displacement from the frequency and G level. Double the displacemetn to get peak to peak.

I do not know what the 3 sigma factor is unless that is the error band on the profile.

I hope this helps. Please let me know about your progress and results.

Regards
Dave
dphall@sbcglobal.net

 

[rocketmotor]

Hi CESSNA1,

I am not sure if I follow....

I was doing this to find the Displacement

For the range between 3 to 20 Hz
Grms = sqrt (0.03*(20-3))=0.714

Also, as G=(Af^2)/9.8; Where A is displacement,
f is frequency.

At f = 3 (the max displacement),
A = 0.412*9.8/9=0.78"

At 3 sigma,
A becomes 2.33 inch. The worst case displacement (peak to peak) becomes 4.67 inch.

Any comment?

 

[kaiserman]

Roctemotor:

I reviewed your post. Good question! I have addressed this random vibration question hundreds of times throughout my 17+ year mechanical engineering career in dynamics and vibration testing. Can we perform this random vibration profile on our shaker? It's a great question, easily answered, but not easily derived.

Ling Dynamics Systems published a paper deriving the maximum "possible" instantaneous 3-sigma displacement for a random vibration profile. A formula was derived in the paper. The formula was also incorporated into the LDS vibration shaker systems training literature. I have used the formula and verified the formula both theoretically and emperically.

Random Vibration Rules! Keep on shakin'!
As once spoken by my boss year's ago early in my career, "This ain't your mother's sinusoidal shaker!"

Regards,
Tim Kaiser
VW Kaiser Engineering, Inc.

http://www.vwkaiser.com

 

[kaiserman]

Rocketmotor:

Regarding my reply of 22 Feb 08 please note the following:

The reason it has taken me so long to reply is that unfortunately, I loaned my copy of the Ling Electronics Vibration Training Manual document to a colleague and I am in the process of getting it back. When I obtain it I will forward it to those who have requested it.

In the mean time, the random vibration derivation I mentioned in my earlier post is presented in a document by Ling Electronics.

Vibration Training Manual
Ling Electronics
LTV Ling Electronics Division
Ling-Temco-Vought, Inc.
1515 So. Manchester Avenue
Anaheim, California

In the manual, for random vibrations, a displacement formula (equation 22) is derived. It is assumed that the elctrodynamic shaker and power amplifier are properly matched.

Equation (22) on page 2-28 of the training manual was derived as follows:

D = 42.8 * SQRT (G/(f^3)low)

D = double-amplitude displacement in inches (3 sigma)
G = the acceleration density in (g^2)rms/cps
f low = the lower cutoff frequency in cps

Based on this derived equation, I have listed a few possible scenarios as examples.

EXAMPLE 1:
* Suppose that our electrodynamic shaker is limited to 0.5 in. pk-pk displacement.
* Suppose a customer desires a random vibration test with an acceleration density of 0.4 g^2/cps.
* What is the lowest cutoff frequency of the spectrum, i.e. what cutoff frequency must we use for a 24-dB-per-octave filter?
* Solving for f low from the stated equation (22) we get f low = 14.3 Hz.
* If the shaker were capable of say 1.0 in pk-pk displacement then the lower cutoff frequency would be, f low = 9.02 Hz.

EXAMPLE 2:
* Suppose that our electrodynamic shaker is limited to 1.0 in. pk-pk displacement.
* Also suppose that the customer desires a random vibration profile with a lower cutoff frequency of, f low = 5 Hz.
* What acceleration density can not be exceeded?
* Again solving the stated equation (22) but now for the maximum possible acceleration density, G = 0.068 g^2/Hz.

EXAMPLE 3:
* Suppose that our electrodynamic shaker is limited to 1.5 in. pk-pk displacement.
* Suppose that a customer desires to perform a random vibration profile of G = 0.24 g^2/Hz and f low = 5 Hz.
* Can the test be performed on our shaker?
* Solving for the double amplitude D, yields D = 1.875 in.
* THE REQUESTED TEST CAN NOT BE PERFORMED since the required double amplitude would be too great.

I hope this helps.

Regards,
Tim Kaiser
VW Kaiser Engineering, Inc.

http://www.vwkaiser.com

 

[rocketmotor]

Tim,

Thanks for your info.

Is there any limitation for equation (or assumption)? Would this equation be applicable to PSD profile which is not rectangular shape (e.g. trapezoid with, say, 3 DB up and down),

Regards,

 

[opethian]

Tim,
Thanks for your info,
I have a question regarding to PSD analysis could you please take a look at it also. It is in ideas and also vibration forum.