Vibration measurements with the H48C Hitachi 3axis accelerometer???

SamW

I needed help with using the accelerometer to measure vibration.· The online documentation talks about using it to measure vibration, but I haven’t found any code examples that would help my case.
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First how would I go about measuring X, Y, & Z amplitude in some unit like micro or millimeters?· Does it have to do with Vref and the X, Y, or Z position?

SRLM

An accelerometer gives acceleration, which is the second derivative of position. So, you'll have to integrate twice to get it in some unit like millimeters. For something that small though, I don't think you'll get accurate measurements. Since you'll be integrating by points (trapezoidal rule or Riemann sum in general), then you'll lose all the information that's between them that a function would capture. Assuming that you want to measure the frequency of vibration, you could just compare the time at which a particular acceleration is positive, to the time when it's negative (peak to peak).

SamW

I’m actually trying to analyze the movement of a point that is attached to an electromagnetic coil.· I wanted the amplitude of vibration of the end of the white rod.
The system is an electromagnetic coil used to force a cantilever.· Since I actually would have a rotated coronate system it would be nice to know what is going on in 3-D.
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I have used the DE for forced harmonic vibration with the magnetic flux proportional to the forcing function.· I have calculated a damping factor for the material.· Long story short the equation become fairly messy, not too bad.· I have also looked a beam analysis and used a second order DE.· The simplest method is the use of matrices to find the eigen values and harmonics.·
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In order to determine which model is correct I need a simple measurement.· I need to know the range, peak to peak maybe.· I have used vibration analysis with FFT in the past and have even considered using an oscilloscope to measure the signals produced by the accelerometer.
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What would you suspect the best approach be?

SamW

I meant to say second order Partial DE.· The general DE for vibration is second order as everyone knows.
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SRLM

This might work:
http://www.parallax.com/Store/Sensors/PressureFlexRPM/tabid/177/CategoryID/52/List/0/Level/a/ProductID/89/Default.aspx?SortField=ProductName,ProductName

You might also try mounting a laser on the beam, projecting onto the wall, and reading where the laser is positioned.

Post Edited (SRLM) : 4/14/2009 2:42:32 PM GMT

SamW

Interesting!· Do you know where I can find examples of code and actual vibration measurement applications?

Dave Hein

It seems like an optical measuring system would be the easiest.· The laser idea sounds good, but you will need a way to measure the position on the wall.· Maybe you can just shine a light source on the white rod, and use a photo-detector on the other side.· The output of the photo-detector will depend on the amount of light being blocked by the white rod.

You can calibrate your measurements by deflecting the electromagnet manually, and measure the received signal as a function of the amount of deflection.· The light source and the photo detector would need to be mechanically isolated from the electomagnet so they do not vibrate as well.

Dave

SRLM

Sorry, no code or even any links... What might work is to get a plexiglass bar stock and attach a phototransistor to one end. Mount it so that the laser light waves up and down the length of the bar, and it may produce different light levels at the phototransistor. You could read the different voltage outputs as a distance measurement, and use some trigonometry to figure out the deflection of the beam. This would only work in 1D though.

SamW

Both of those are really awesome suggestions.· What I didn’t mention was that voltage is also proportional to the forcing function, (variable in calculating magnetic flux).· I will have a potentiometer to control the forcing function, ie the amplitude of vibration.· Additionally I will have 5 different frequencies, 50, 60, … 90 Hz provided by 5 different push buttons.· So really what I need is to take the data from my accelerometer, and manipulate that to fit into one of my differential equations.· Or… if there is a pre-made code for determining the vibration of something, with some predetermined unit of length, I will use it instead.· Which will provide a check on my derived model.
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It would be simple enough to do as you have suggested.· Actually the existing model uses a table with lengths listed on it.· The user simply takes a voltage reading across the coil and looks up the amplitude of vibration on the table.· I wanted to create a “digital” data collection device.· Also I wanted to be able to control the frequencies.· I am trying to stimulate the Meissner receptors in the skin. Statistically it has been shown that these receptors are stimulated in the range of 50 to 120Hz.· Our latest statistical analysis suggests a frequency between 60 and 75 Hz.· So I don’t really want to have to go back and calibrate every time I shift frequency ranges.

SamW

SRLM
This might work:
http://www.parallax.com/Store/Sensors/PressureFlexRPM/tabid/177/CategoryID/52/List/0/Level/a/ProductID/89/Default.aspx?SortField=ProductName,ProductName

You might also try mounting a laser on the beam, projecting onto the wall, and reading where the laser is positioned.<!-- Edit -->

Post Edited (SRLM) : 4/14/2009 2:42:32 PM GMT



I just ordered this, its inexpensive enough that if it doesn’t work its no big loss!

Beau Schwabe

SamW,

An optical measuring system would probably be the easiest to measure as suggested.

But consider what actually happens in the approach using an accelerometer. You are no longer using it as an accelerometer, but rather now you are using it as a a way to detect frequency.
Because of this, the piezo vibra tab becomes a valid option. If you have a known mass at the end of some moment arm (pendulum) and you can measure the frequency the pendulum swings, you can calculate through a few formulas the displacement at the end of the moment arm.

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Beau Schwabe

IC Layout Engineer
Parallax, Inc.

SamW

Attached is a portion of my theory. I read what you were saying Beau, and I thought maybe I could use the ‘G-force’ for my· ‘F’ value in equation 3.· What do you think?

Beau Schwabe

SamW,

You could use the "G-force" to determine frequency, assuming you can sample from the Accelerometer within the nyquist of your periodic motion. However the 'value' returned is no longer acceleration due to gravity since in a periodic wave the +/-g will be canceled out. Forgive my vagueness here... at one time I had my head around this, but I'd really need to sit down and think about this further to re-claim that knowledge.

The well known formula ... F = ma .... Force = mass * acceleration ... would not necessarily apply, since in a periodic motion you have additive and subtractive acceleration that would cancel out. Since the net acceleration is zero, that means that the velocity (or net velocity) is constant.

Velocity can be derived by the frequency and usually expressed in terms of meters per second, but you also need to factor in mass to determine the momentum.

Referring to the velocity of a pendulum, you can re-arrange the equation to finally determine displacement by deriving it from the displaced pendulum angle.

Reference:
http://www.sparknotes.com/testprep/books/sat2/physics/chapter8section5.rhtml ... see Velocity



As I said though... measuring the displacement optically would be a much easier approach.

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Beau Schwabe

IC Layout Engineer
Parallax, Inc.

Post Edited (Beau Schwabe (Parallax)) : 4/15/2009 5:19:29 AM GMT

Dave Hein

One thing you need to be concerned about is the vibration response of the measuring device.· An accelerometer oscillates internally, and measures the effect of accelaration on the oscillation.· There will probably be some interaction between the vibration frequency of your electromagnetc and the accelerometer.· A piezo device would be a more direct way of measruing the displacement.· However, this will have it's own harmonic characteristics.

I think the optical method will have the least amount of interaction with the experiment.· You will just need to figure out a way to measure motion optically.· I mentioned putting a a light source and photo-detector on opposite sides of your test device earlier.· Another possibility is to glue a small mirror on top of the device, and measure the deflection of a light source on the wall.

It will be difficult to measure the position of a spot source, such as a laser.· However, you could use a divergent light source, which will create a larger spot on the wall.· The center of the spot will be brighter than the edges, so you could use a photo-detector to determine the position of the spot by its biightness at the photo-detector.

Dave

SamW

Thanks guys for all of your input!!!!