Test data and acceleration signal

[suviuuno]

Hi,

We are going to measure accelerations from piece of machinery. Goal really is displacement by double integration.
Before attempting this, I have done some preliminary work with simple cantilever beam. In short, I glued a strain gage to fixed end and mounted single axis accelerometer to the free end. I set up beam into decaying vibratory motion.
I calibrated system such that I know displacement at the end given strain (beam theory holds...checked.) We stay linear the whole time.
First few amplitudes are about 2 gs at 10Hz. I cannot get free end velocity integrated from acceleration signal to match even close. Not to even mention displacement.
I am not filtering acceleration signal because it is well-defined.
Does anyone see what is being done wrong here? Does decaying signal introduce a problem here, maybe?

 

[FeX32]

Did you take into account the sampling freq. ?

Also, integrating accel. twice to get disp. is not really a good idea. It will be difficult to get anything worth while.


Fe

 

[BobM3]

Does the integrated velocity look like a sine wave (assuming your accel was a sine wave)? Or does it look like a nearly linear ramp?

 

[suviuuno]

Thanks for replies.
FeX32 - Yes, sampling frequency checks. What would you recommend as better approach?

BobM3 - Acceleration is decaying sine wave. Yes, velocity is sine wave as well. Also, velocity is at zero at max. acceleration points...as it should be. Amplitude is way off. Integrating this velocity signal produces nearly linear ramp.

This is quite interesting little experiment, because it appears so simple. School teaches double integration to get displacement...real life is not so simple. Thanks.

 

[SomptingGuy]

As FeX32 said, you will probably be disappointed. You will need to at least high-pass filter your signal, otherwise a ramp is all you'll get. There is always some DC that'll get in the way. In my experience, getting a time-domain signal by double-integrating accelerometer data is just not practical. Single frequencies - perhaps. But general position data - no.

Can you use a proximity sensor? I've used these for measuring the displacements of gears on a timing drive before.

- Steve

 

[BobM3]

Remove the offset and any DC value from the acceleration signal before integrating. Also remove it from the velocity signal before integrating that. The ramp is the result of integrating an offset or DC value.

 

[MikeyP]

Do you have an acceleration signal that starts and ends at zero(i.e. you allow it to decay to rest before you stop recording data?)

If your signal is naturally windowed like this then Fourier transform the signal (with no other windowing), high pass filter to remove DC and as many lower specral lines as you dare. Do the integration in the frequency domain (divide by minus omega squared) then inverse Fourier transform back to time domain.
You might also want to filter out some of the very high frequnency crud as this will probably just be noise.

I have done this quite successfully a number of times before. It works best if you design your test with this type of processing in mind. i.e have plenty of pre-trigger on the signal and leave plenty of time for the decay. Then you can apply a 1/2 cosine taper window to the start and end of the signal to make sure you don't get leakage.

M

--
Dr Michael F Platten

 

[TPL]

If displacement is what you want, then use a displacment transducer i.e proximity probe. Use a disgital scope to record and analyse the output

 

[suviuuno]

SomptingGuy - in the real problem use of proximity sensor is not possible. We have sensors but they are not practical for this problem.

MikeyP - Yes, signal is exactly as you describe. Thanks a lot.

 

[GregLocock]

I certainly wouldn't give up on it as an approach, sometimes it works surprisingly well, sometimes not. In your favour with the simple experiment is that you can do a lot to clean up the data before you start.

Are you integrating in the time domain or the frequency domain?

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[electricpete]

I think what BobM3 said is key. Remove dc component ("hi-pass filter") before 1st integration, before 2nd integration, and after 2nd integration.

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[FeX32]

What if you can't afford the phase distortion between the 1st and last signal?


Fe

 

[MikeyP]

Then you do it in the frequency domain like I said.

M


--
Dr Michael F Platten

 

[suviuuno]

Success in one part. Thanks for replies. I get good results integrating in time domain, however, there is some (slight) phase change. In the test case this is not critical.

In the real problem this needs to be fixed, so frequency domain integration may be the key like MikeyP said. I am having problem processing signal in frequency domain as I am quite new to this. I get back.