Determining natural frequency

[g0dam0ng1n53ct5]

Having never done vibration analysis, I'm wondering if anyone has experience in determining the natural frequency of a solid using an accelerometer. Aside from knowing that we can produce a voltage signal through the accelerometer, and that we in some way need to condition this through a fourier transform, I am completely stumped.

Can anyone provide a simple explanation, and hopefully any more complex knowledge of how to go about solving this problem?

Thanks,

Justin

Just as a post note, I'm really completely unfamiliar with vibrations analysis, and am hoping to learn enough through this process to really understand the problem and its solution...

Any help is appreciated!

Message Edited by g0dam0ng1n53ct5 on 12-17-2009 09:01 AM

[CoastalMaineBird]

I've worked with TRANSFER FUNCTIONS, where you have a special hammer (with transducer embedded in the head) as one channel, and an accelerometer on the other side of the structure as another channel.

You either start recording manually, or use the hammer signal as a trigger (and record pre-trigger data).

You record both channels, do an FFT on them, and apply some math to get the transfer function, which is a way of expressing "If you apply X amount of force at frequency F at point A, then you will get Y amount of vibration at frequency F at point B."

I suppose that the peak response is the natural frequency.

Does that help?

I would have to dig up the math - it's real easy to do in the frequency domain: you just divide Sxx * Sxx by Sxy* Sxy or something like that (where Sxx and Sxy are spectra), but I don't remember it off the top of my head.

Message Edited by CoastalMaineBird on 12-17-2009 09:09 AM

[aeastet]

You will have harmonics of the natural frequency too. So you will need to know what order of the natural frequecny that you need to measure. Unless other wise stated we use the highest g level natural frequency.

[g0dam0ng1n53ct5]

Could you break down and explain the purpose of the transfer function and how it works, as in what it does to the signals and how they will need manipulated?

Starting with my +/- 5V signal from the accelerometer, what is the output as a result of the FFT, how must I pass that through the transfer function, and what will be its final output? If it's correct to assume you mean tho pass the accelerometer signal through its Y portion, and the stimulus signal from the hammer through the X portion, then what will be the output, and how can it be interpreted?

[CoastalMaineBird]

OK, I dug up the old code (I'm talking 1994 here).

The TRANSFER function is a statement of the relationship between the independent measurement (Y) and the driving force (X).

You hit point A with force X, and at point B, you see a movement Y.

The transfer function is dependent on structure geometry, materials, mounting, supports, maybe termperature, etc. 

That is frequency-dependent, so doing it in the frequency domain provides a lot of info at one time. 

Here are comments from my 1994 code:

       F(x)     F*(x)           |F(x)|^2

Sxx = ------ * -------     =   ----------   (no phase information)

        N         N               N^2

       F(y)     F*(x)

Sxy = ------ * -------

        N         N

                      Cross power spectrum          Sxy

Transfer function = ------------------------   =   -----

                         Power spectrum             Sxx

             | Sxy | ^2

Coherence = -------------

             Sxx  *  Syy

where:

  F(x) is the complex Fourier transform of the time domain signal x, and

  F*(x) is the complex conjugate of the Fourier transform of x, and

  N is the number of points in x.

Note that SXX is the magnitude squared.  It is faster to compute the square of the magnitude than it is to compute the magnitude. Although the complex-to-polar VI would look simpler on the diagram, it would take longer since it computes the magnitude proper, (an extra square-root operation), and it computes the angle (extra arc-tangent operations).

Since N^2 is a term in both Sxy and Sxx, and since we are dividing one by the other, we do not need to explicitly divide by N^2; it is cancelled automatically.

 ---

Here is the code to process a single channel:

 

I'm not sure of the comment "this is much faster..." anymore, as I've tested it recently and found it not the case.  But it was true in 1994. 

And here is the code to handle the actual Xfer function:

Note that I had an implicit rule that the first channel in the array was always the reference channel, i.e. the hammer (stimulus).  Any other channel(s) were response channels - you can get transfer functions between one stimulus point and any number of response points with one recording.

The middle section there is averaging: you may or may not want to do that.  It's averaging from several hammer blows.

What you get out is a complex spectrum (in the TRANSFER FUNCTION array).

At each frequency, there's a complex number (R+jI) that describes how well the vibration travels from point A to point B. 

If this function shows a clear peak at say, 583 Hz, then the structure in question is best at transferring vibration at that frequency.

If the MAGNITUDE of that peak is close to 1.0, then it's very resonant.  If the magnitude is much lower, it's very damped.

(If it's greater than 1.0... RUN!  It's about to come off it's mountings !)

You also get a COHERENCE spectrum, I'm not as well versed on the uses of that. 

[g0dam0ng1n53ct5]

In many ways, this is going right over my head. But, I think the only way to figure it out is to try it, so I'm going to get a hammer and build up a vi that hopefully does what you've demonstrated, and see what we can get out of it.

Any more advice will definitely help, and I'll surely be back along the way with more questions.

[CoastalMaineBird]

OK.  I don't remember where they got the hammer; I didn't handle the acquisition of that.

But the hammer has a transducer (accelerometer) built into the head, and the head was a moderately soft plastic something (not solid metal). 

Here is one such device, but THIS IS NOT A RECOMMENDATION.

Impact Hammer 

Note that you need a power supply / conditioning box for this; that was true of the ones I saw as well.

I know you said you wanted a simple answer, but this is as close as i can get.

I'm not a mechanical engineer, but I worked with them in the past.  This procedure was in place long before I came along; I simply added the math code to my data-acquisition program. 

Message Edited by CoastalMaineBird on 12-18-2009 08:33 AM

[g0dam0ng1n53ct5]

It might be helpful to see what's going on in the other cases of some of your structures. Can you attach the vi for me to figure out, rather than starting from scratch?

[johnsold]

Many years ago some geologists I worked with had what we called their "electric hammer." It was a standard sledge hammer to which someone had attached a set of electrical contacts.  One of the contacts was fixed to the handle near the head.  The other contact was on a strip of metal with a small mass at the free end.  When the hammer head hit something the contacts closed, triggering the data acquisition.  They were doing simple seismic studies and pounded on rocks as excitation.

Of course when they missed with the hammer head, the handle would smash into the rocks and the contacts would need to be repaired.

Lynn 

[CoastalMaineBird]

Here are the other cases (unseen in the first pics).  There's no magic there.

If integration is NOT selected, the signal is NOT integrated.

If windowing is NOT wanted, you don't window it.

If ZERO PEAK is wanted (as opposed to pk-pk), you change the divisor.

 

 If it's NOT the first channel, you leave the FIRST CHANNEL memory unchanged.

If you do FLUSH the averager, then this data REPLACES the average buffers, rather than being appended to them.

that's it.