Shock Isolation 3

[blacktalon]

Hey guys...

Im working on a new project at work that basically requires that an Electrical Control Box be isolated from a 50g saw-tooth shock pulse as per mil-std....

I will be adding more info to this topic tomorrow as I post data etc... but I have some questions...


I have set-up and solved the differential equation of motion for the system numerically by maple and set-up plots of the displacement, velocity, and acceleration.

Now, I keep running into conflicting results with other applied theory....

The Eqn of motion I solved is:


x"(t) + 2*z*w*x'(t) + w^2*x(t) = -h(t)

where:

x"(t) = absolute accleration of the module
x'(t) = relative velocity of the module
x(t) = relative displacement of module with respect
to the structure it is embeded in.
(distance between module and structure wall
which represent spring deflection)
z = damping ratio
w = natural frequency of the isolator(s) chosen
h(t)= acceleration of the surrounding structure which
I defined to be a unit step function
(heaviside function) for 3 pulses.

**This is a base excitation problem


Now the base excitation a sawtooth/50g/0.006s duration pulse 3 times.

The manufacturer of the module states the module cannot withstand more than 10g of shock.

Now I have solved the differential equation and the results look correct. (I will post later)

I am probably going to use a rubber bushings (damp ratio = .05, nat freq's 5-30Hz)


Now.... questions

1) Technically isnt the forcing frequency 1/.006 and not 1/(2*.006)? I mean thats where the same ref point on the pulse re-occurs... why do some texts do that?

For the time being I assume my forcing freq = 1/.006 = 167Hz

2) Despite the space contraints, I cant seem to be able to get the shock down below 10g's, even if I alter the nat freq of the isolators or the damp ratio to rediculous values.... but by the theory of transmissibility....

damp ratio = .05
forcing freq = 167Hz
isolator nat freq = 68Hz or lower

should provide me with a shock isolation 0f T=0.2....

50g *0.2 = 10g

but the differential equation solution doesnt do this... and im 99% sure its right....

Even if I change the nat freq input in the diff eqn model closer to 167Hz... the equation simulates resonance.. (as expected)

***And yes I am converting the nat frqu to angular frequency properlly***


I guess my questions is... is it even possible to reduce a 50g shock to below 10g? Cause I cant seem to simulate it...

Ideas? I will be posting better info tomorrow...

 

[blacktalon]

MY DISPLACEMENT PLOT IS THE SAME HOWEVER, WHEN I SIMPLY PUT IN ONE SHOCK PULSE INSTEAD OF 3

 

[blacktalon]

Thanksm for the input spongebob... that gives me more confidence in my results.

 

[spongebob007]

I made a mistake in my original post, our system isolated frequencies are around 5Hz with a displacement of about 4".

 

[rybose]

Some comments:

Damping ratio effects - Look at Figure 9 in the Passive Shock Isolation paper. You can see that the optimal damping ratio for SDOF velocity shock is 0.26. Unfortunately the isolation difference between 0.05 and 0.26 isn't too dramatic.

Relative vs. Absolute Acceleration - During the residual response (after the load is applied) the relative and absolute acceleration curves are the same (base acceleration = 0). During the primary response (when the load is being applied) they should be different.

Damage thresholds are in terms of absolute accleration so in order to make your code as general as possible I'd recommend gettin things ITO abs. acceleration. (Try making your pulse width really big and see what happens to the relative acceleration curve)

My sweet MATLAB GUI - It's actually much easier than it looks. You just need to get the hang of passing the variables through the "handles" structure. I learned how to do it in a couple of days using these great tutorials:

http://blinkdagger.com/category/matlab/gui-matlab

 

[spongebob007]

For a single 50G sawtooth with a 6ms duration, assuming 5% damping, your isolated system frequency should be 15Hz with a displacement of ~.4"

I have attempted to attach a plot of the pulse

 

[spongebob007]

Here is the pseudo-velocity plot (SRS) for the pulse I posted above.

I think everyone here is making too much out of this problem. Assuming a linear spring as a first attempt, here is how I design an isolated system.

1) Generate SRS of shock pulse. Make sure you use the correct damping ratio for the isolated system when generating the response spectrum.

2) Select the frequency that corresponds to the desired attenuation level.

3) Determine the displacement for the isolated frequency.

4) Using the isolated frequency and isolated mass, back out a spring constant.

5) Select an isolator that has the approriate stiffness, static load rating, and desired stroke.

 

[FeX32]

That doesn't seem to solve the problem as the deflection is still high.



Fe

 

[blacktalon]

SPONGEBOB what was your total damping ratio for the system for that set-up with a 4" deflection?

 

[blacktalon]

SPONGEBOB..... sorry I idnt read enough... got it at 0.05.

But 0.4" to attenuate a 50g shock is very unlikely. how did you arrive at that?

I got 35mm displacmenet with those numbers which only isolates to 40g and dies out after that...

 

[spongebob007]

My results were for a single saw pulse. I created a pulse train of 3 saw pulses and for 5% damping my results are f=8.8Hz and the displacement is about 1.3 inches for 10G's.

You might not be familiar with a pseudo velocity plot. The diagonal lines that rise from left to right represent relative displacement. The diagonal lines that fall from left to right represent acceleration. The axes are logarathmic. Start by following the diagonal line for 10G's. The point where the 10G line intersects the red SRS curve, is your ideal operating point for the isolated system.

 

[spongebob007]

I was actually going to run an FEA model of this to confirm my results, but apparently NASTRAN has a bug in the source code and it won't run until further notice. I kid you not. If you use NASTRAN, you are in for a surprise.

 

[blacktalon]

NASTRAN... surprise? how so...

 

[spongebob007]

There is an error in the source code that returns a divide by zero on any machine where the date is past March 31, 2009. The program will crash a few seconds after you submit a job. As far as I know it applies to all flavors of Nastran.

 

[FeX32]

spongebob007,

I took a look at your pseudo velocity plot. Is the horizontal axis the frequency of the forcing function or the tuning frequency?


Fe

 

[spongebob007]

Fe, the frequency axis is the natural frequency of the isolated system.

 

[spongebob007]

Okay, I made an error with the SRS plots I generated. I thought something seemed funny, so I decided to validate my model with FEA. For the work I do, our input acclerations are low frequency and second in duration.

The software I use to generate the SRS has a lower frequency bound of 1/T. For this time history that gives 1/.018=55.5 Hz. You can request it to go to a lower bound, but as I found out, the accuracy of the result below 1/T are questionable. So what I did is augment the original pulse with a "tail" that has an acceleration of 0 out to 2 sec. Now I was able to generate an SRS that went down to 1Hz.

The bad news is, that with 5% damping, it is going to take almost 7 inches to attenuate the shock to 10G's @ 3.8Hz. I ran a SDOF model in NASTRAN to verify the results, and sure enough the results agreed.

Like I said earlier, attenuating COTS equipment to 10-20 G's is going to take on the oredr of 3-4 inches. This has been my experience, and we use isolators with nonlinear stiffness characteristics and damping on the order of 15-20% of critical.

I have attached a zip file with the new SRS and response time history plots.

 

[spongebob007]

If you want a better explanation of pseudo velocity plots, you can find it in the "Shock And Vibration Handbook" by Cyril M. Harris.

Another book I would highly suggest is "Vibration Analysis for Electronic Equipment" by David Steinberg.

 

[blacktalon]

I have read throught that Steinburg book and when it comes to shock anaylsis ... it is very basci and it even says so in the book.

It says... there are 3 ways to analyse shock isolation... it covers the first too with some equations and at the end it says if the isolators are non-linear like rubber etc... you might as well toss them out th window. Then when it speaks of other methods... its sys the math is real complex and not to be covered in the textbook.

 

[jimkinney]

Search on Howard Gaberson, he wrote several papers on pseudo velocity shock. Here's one -

http://www.saviac.org/78th_Symposiu...locity Shock Spectrum - Part 1 (10-23-07).pdf

I think Tom Irvine may have some papers also.

Jim Kinney
Kennedy Space Center, FL

 

[blacktalon]

Rybose... if you read this... I cant seem to get the absolute acceleration to come out right.

With the substition of z=x+y for the accleration... I solve for relative acceleration.

When i try to us this z=x+y relationship to bring out the absolute acceleration of the mass.... its adds up to 60g over the 50g!


See the derivation on the file I attached earlier? Any idea what im missing because your acceleration plot for the parameters I gave you seem more realistic. My displacement and velocity plots are exactly the same as yours though... its just bringing out the absolute acceleration.