Relative displacement error in SRS

[Mark5000]

I am currently using Laview 2014 with the sound and vibration toolkit.  I was attempting to perform a SRS analysis where the input was a half sine shock pulse measured in G, and the result should be the relative displacement SRS.  I used the NI provided example "Shock Response Specturm (simulated)".  When I use the absolute acceleration as the output, the results are correct. At a natural frequency of 81.27 Hz, the SRS is 165G or ~63,756 in/s^2 When I use the relative displacement as the output with units of inches, the results seem to be in error.  At a natural frequency of 81.27 Hz, the results relative displacement is 63,580 in.  One will quickly notice that the main operation that has taken place is a change of units.  It is unreasable to have a relative displacement of this size for the assumed input.  Does anyone know if the toolkit is making an assumption on the input type?  Maybe the input and ouput must match.  For example if you want relative displacement out, then you have to put a displcament waveform in.  Does anyone have any insight?

I have attached a picture of my settings.

[Roohcifer]

Hi Mark,

The Amplitude input is in Volts, and 100 Volts is an unrealistically high signal from an accelerometer, which is why you're seeing the ridiculously high output value.  The intent of the simulated VI is to do just that - simulate the data coming from a sensor.  In this case, we typically see accelerometers putting out in the +/- 5 or 10 Volt range (you'll notice that the default input is 1).  On the block diagram, you'll see the signal generator VI, which takes in your simulated signal settings and produces the impulse signal of your choice in units of Volts.  The V->EU VI then converts the signal from Volts to Gs.  Finally, the SRS VI performs the analysis and calculates the output response in the distance units you specify.

Regards,

[Mark5000]

I did as you suggested.  I set the sensitivity to 5 mv/G and then had a .5V signal.  That gave a 100G, 20 ms half sine pulse.  I then performed an acceleration SRS with good resutls.  I then performed a relative displacement SRS with the exact same poor results.  There are no units on the AMPLITUDE field, but based on your previous post, I assume they are Volts.

[Roohcifer]

Hi Mark,

I'm sorry if I was unclear in my previous reponse.  It doesn't matter what combination of sensitivity and signal amplitude you use if you're still sending in a 100 G pulse.  A 100 G pulse is going to give you the same results regardless of how you have chosen to scale your accelerometer.

Moving forward, I believe I misinterpreted your original question.  The g units on the Shock Response Spectrum are in SI units.  So with the Relative Displacement model and "no change" units, the y-axis "g*s^2" units are (9.8m/s^2)*s^2, or just units of 9.8m.  If you run the example code in the default configuration, only changing the model to Relative Displacement, the shelf approaches 1 as frequency increases. If you then switch the units to "meters", the shelf then approaches ~9.8.  If you switch to "inches", the shelf scales approptiately to 836 inches.

This scaling relationship still holds true with your settings.  In other words, with units set to "no change", the Relative Displacement and Absolute Acceleration models are very similar, with the shelf at 100 g*s^2.  Changing the units to meters yields a shelf at ~980 meters, and changing the units to inches yields a shelf at ~38.6k inches.

If you want to see the code behind this measurement, you can always delve into the subVIs on the block diagram to see the precise math.  Looking several layers down, there is a formula node that differs between the two models.  The only difference appears to be the forward filter coefficients calculated, which explains why virtually the only thing than changes between the two models' outputs is the frequency response at low frequencies.

Regards,

[Mark5000]

David,

Thanks for your reply.  I noticed the relationship that you explained.  This is what puzzles me.  The relationship between acceleration and relative displacement for SRS analysis is:

(Natural frequency)^2*relative displacement=acceleration.  This should be approximatley true for SRS representations.  Note that the natural frequency here is in radians.  This is described in detail at http://www.vibrationdata.com/tutorials2/pvsrs_rules.pdf page 7.  The values being reported by the SV toolkit are not in agreement with this.  I have investigated the subVI's in detail, including the digital recursive filter coefficients, but I could not determine where the discrepancy occured.  I was trying to determine why the outputs of the SRS do not agree with the above relationship.  In the above example, at 81.27 Hz, the SRS is 165G. This is correct.  The relative displacement should be ~.244 inches, or 6.206mm.  The reported values are extremley far from this.

[Roohcifer]

Hi Mark,

My guess is that regardless of the model you use (acceleration or relative displacement), the output is reported in acceleration.  This seems to be echoed in the fact that the two graphs are identical except for the minor changes in the leading coefficients. If this is the case, then the units reported on the frequency response graph for the relative displacement are incorrect and should be units of acceleration.  I'm going to pass this by R&D and see if they have any input.

Regards,

[Mark5000 · Accepted solution]

Did some more investigating and pulled the applicable paper.  There is definatley a mistake within the NI provided sound and vibration toolkit.  I rewrote my own version and it works fine.  I never did here back from R&D.

[Roohcifer · Accepted solution]

Hi Mark,

After speaking with R&D, we believe there to be an error with the VI.  The absolute acceleration and relative displacement models' transfer functions, Eq. 8 and 9 in the Smallwood paper, are both applied to the recursive model, Eq. 9.  This seems to imply that both models, despite their names, both accept acceleration as an input and display the resulting shock response in units of acceleration v. frequency.  R&D has been notified of the discrepancy, and the required changes will be prioritized and hopefully updated soon in a future revision of the S&V Measurement Suite.  

Regards,

[Mark5000]

David,

Thank you for your reply.  I came to the same conclusions.

[Roohcifer]

Mark,

I'm glad you found the same solution, and my apologies about the delayed response.  Enjoy the holidays!

Regards,