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Originally I was going to use accelerometers, but they are to big for the disk I'm trying to measure.

Basically I have a set of planetary gears for which I need to measure the vibrations in the x and y components, mainly. I´ll be performing modal testing with an instrumented hammer and a laser single point vibrometer.

Since my gears are straight teeth spur gears I didn't take into account the "z" coordinate or vibrations of the system for my dynamic model, so if I point the laser perpendicularly to the gear´s plane the vibrations being measured by the laser will be those in z, which I'm not interested in.

I read that if I had two Laser Doppler Vibrometers I could measure the in-plane motions I'm looking for, but since I only have one I was wondering if there´s a way of decomposing the projected component by pointing the laser at certain angle?

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    $\begingroup$ If your structure can vibrate in two independent directions, the bottom line is that you need to make two measurements somehow. Since the real structure has geometrical imperfections etc and there is no way to tell what linear combination of the two (theoretically) identical modes it will vibrate it. If accelerometers are too big, you might consider strain gauges, to measure both directions. and compare the gauge outputs with your LDV data. $\endgroup$ – alephzero Aug 16 '17 at 3:57
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    $\begingroup$ You could try to repeat the measurement to first measure in x direction, then in y direction and then optionally in z direction. If your system behaves linearly (which has to be the case for a modal analysis to make sense anyway) you can then combine this data to extract the modeshapes. Some caution is needed as the accuracy of your results will depend on how well you can replicate your excitation (location and force) and response measurements. $\endgroup$ – user883521 Aug 16 '17 at 10:15
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There's just no way that you are going to turn a single Z measurement into an X or Y measurement. With multiple Z measurements, you could calculate pitch and yaw angles, but for a spur gear, that's not going to get you want you want as the gear is going to translate, not bend or rotate.

Suggestion 1: Glue something to the spur gears that sticks up far enough out of plane that you can get the laser to reflect off of it in the X and Y direction. e.g. glue a small reflective cube to the disk. Point the laser at it in the X direction, perform the impact test, and then move the laser to the Y direction, and repeat.

Suggestion 2: regarding accelerometers... How big of a disk are we talking here? They do make some very small accelerometers. e.g. Endevco Model 22 is a mere 0.14 grams.

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