Conversion of acceleration to displacement for vibration

[Midlothian]

They are used in determining velocity and displacement in 6 degrees of freedom -

  http://en.wikipedia.org/wiki/Rate_integrating_gyroscope

  http://en.wikipedia.org/wiki/Ring_laser_gyroscope

  http://en.wikipedia.org/wiki/Inertial_Measurement_Unit

Message Edited by Midlothian on 02-22-2007 11:15 AM

Message Edited by Midlothian on 02-22-2007 11:16 AM

[Midlothian]

Applications:

Spacecraft orientation

The oscillation can also be induced and controlled in the vibrating structure gyroscope for the positionning of spacecrafts such as Cassini-Huygens. Theses small Hemispherical Resonator Gyroscopes made of quartz operate in vacuum. They provide accurate 3 axis positioning of the spacecraft and are highly reliable over the years as they don't have any moving parts.

Automotive

Automotive roll sensors can be built around vibrating structure gyroscopes. These can be used to detect rollovers, or to supply input to electronic stability control systems.

 Entertainment

The Nintendo Gameboy Advance game WarioWare: Twisted! uses a piezoelectric gyroscope to detect rotational movement.

 Photography

Many Image stabilization systems on video and still cameras employ vibrating structure gyroscopes.

Hobbies

Vibrating structure gyroscopes are commonly used in radio-controlled helicopters to help control the helicopter's tail rotor or in radio-controlled airplanes to help keep the tail steady during take-off or hand (especially with discus launched gliders) launch.

 

[Ale83]

I'm willing to perform the 'acceleration-->integration-->integration-->displacement' path mentioned at the beginning of this thread, but I immediately had to face the drift problem just after the 1st integration.

The acceleration signal comes from a piezoelectric accelerometer.

The formerly suggested filterings (bandpass and high pass) has not proven to be helpful, so I arbitrarily removed the average value from the first signal ( acceleration ) before integrating it. Things look better (although I don't think my apporach is theoretically correct), but sometimes it seems that the velocity signal drifts anyway:

http://img160.imageshack.us/my.php?image=driftqa0.jpg

What do you think? thanks in advance for your attention 🙂


Message Edited by Ale83 on 01-21-2008 09:37 AM

[RPJ]

Dear Ale83,

I had to put this on hold for a while and right now I cannot test what you are suggesting. Meanwhile I got the noise and vibration package and I am trying to see if I can make any sense out of it.

I believe the best solution is to use a displacement sensor such as a capacitance probe. However, if this is not possible, then the displacement cannot be calculated with very high accuracy comparing to the real one.

In my case I was trying to detect the most significant frequencies using an FFT or something similar. However, if I apply the FFT to the acceleration signal then I get a "noisy" output and it is difficult to determine which frequencies are significant and which not - it's more an art...

Thank you for answering to my question.

[preston_johnson]

The Sound and Vibration Toolset provides a correct, tested, and supportable integration function for vibration:

http://zone.ni.com/devzone/cda/epd/p/id/5502

and the toolset information is located at:

http://sine.ni.com/nips/cds/view/p/lang/en/nid/12152

[RPJ]

Thank you. This is helpful.

Any other examples are more than welcome...

[RPJ]

Dear Preston,

To add more to my previous message:

I would like to monitor the vibrations of a spindle of a machine tool. I record the acceleration during the cut, then I would like to read the saved file (whenever necessary) to determine if I had chatter or forced vibrations and if I did what is the frequency of that vibration. So I would need a way to see the dominant frequencies of the recorded vibrations (accelerations).

Any additional examples (relative to your previous message) or suggestions would be very helpful.

Thank you for your time and support.

Radu

[Chris_K_]

Here is a DevZone article that links all the SVT shipping examples.

Sound and Vibration Measurement Suite Shipping Examples
http://zone.ni.com/devzone/cda/tut/p/id/6107

There is also a full set of examples in the NI Example Finder located Help>>Find Examples, in LabVIEW. Select the search tab search and enter “vibration”.  This will list the full set of basic vibration measurement examples. 

Also if you look in the DSA manual Start>>All Programs>>National Instruments>>Sound and Vibration>>Manuals>>LabVIEW Sound and Vibration Analysis User Manual, chapters 8 and 11 are helpful. 

Have a great day

Chris_K

[Ale83]

I'm feeling SO stupid... but there's something I'm probably missing about acceleration-->double integration-->displacement.
I'm having some experiments starting from a single sinusoid (amplitude 1, frequency 1 Hz, duration 1 second) representing an acceleration signal.
I attach the VI where I was trying to compare the results coming from two different solutions:

1) "manual" integration using two 'Integral x(t).vi': this gives the result I had expected.
2) 'SVL Integration.vi' to get both velocity and acceleration: this gives VERY different results.

Any comment?

Also, am I missing something about the importance of phase in this integration?

On page 7-2 of the SVT_User_Manual i read "The phase of the displacement lags the acceleration by 180°" and figure 7-1 on the same page shows that, at time instant 0, acceleration is 0 but velocity is negative!! In my ignorance I can't find any physical explanation of this. Equivalently, in the time interval 0-1 sec, acceleration is positive and displacement is negative.... ?!

Do I have to correct phase information in the integrated signal to get representative data? Or what else?

Thank in advance, I hope not to get mad because of these things 😉

[J_Thomas]

The difference (an apparent phase error) being seen by integrating the acceleration with the SVL Integration VI and using two Integral x(t) VI’s is expected.  The SVL Integration VI has a digital highpass filter built into it, something the Integral x(t) VI does not have.

If you right click on the "highpass cutoff frequency" input of the SVL Integration VI and go to Create >> Constant you'll see that the cutoff frequency is 1 by default. Since the frequency of your "acceleration" curve is only 1 Hz, quite a bit is being cut off. Try putting something like 0.00001 in the highpass cutoff frequency input and you should see that the results of the SVL Integration VI begin to look more like the expected integration curve.

Generally, the SVL Integration VI is used with transducers that are rated in a certain frequency range. For example, an accelerometer may show poor response below 20 Hz so you would apply a highpass filter to get rid of the data below 20 Hz.

Look at this link for a good description of how a digital FIR (Finite Impulse Response) filter is implemented.