DIY Vibration Measurement Device for Engineers using Flex Sensors

[Smooth]

Hi,

I need something that would measure vibrations along an axis, so instead of buying a bunch of accelerometers I thought I’d quickly make smth myself. I’m majoring in engineering and not physics, so while I have no problems with the construction, I’m kind of stuck with the physics aspect.

I explained my device on image 1. I have a weight that is suspended by two films (flex sensors - Piezo vibration). When a vibration along the x-axis is introduced, the weight will deviate and oscillate a little until coming back to initial position.
The graphic is on image 2. Suppose the weight deviates from original position. I will have the returning forces of tension from the films, and since I know the Young’s modulus of the films I can calculate the tension force due to the films. I wrote the 2nd Newton’s law on image 3.

Now, here’s my question; how do I factor in air resistance/damping of this half-pendulum? Yeah, I can easily get it experimentally by graphing the waveform. But can I write equations though?

I’ll probably increase the surface area of the weight to increase air resistance and play around with its mass to increase the damping, but question remains - how do theoretically predict that damping effect?

Many thanks for any suggestions.

 

[Dale]

Now, here’s my question; how do I factor in air resistance/damping of this half-pendulum? Yeah, I can easily get it experimentally by graphing the waveform. But can I write equations though?

You could write down the damping forces. There is air resistance and probably some other things too. Those will typically involve constants, like the drag coefficient, that you have to measure experimentally. So you are probably better off to just measure the damping directly.

 

[jrmichler]

In theory, you could calculate the aerodynamic drag on the mass using the standard drag equation - Force = 0.5 X rho X V^2. In practice, that does not work because the equation assumes fully developed flow.

I learned this the hard way when I built a tuned mass damper using oil to damp the tuned mass. The damping oil changed the tuned mass frequency by a lot, my recollection is the change was about 40%. This was a puzzler until I calculated that the kinetic energy of the oil flowing past the tuned mass was about equal to the kinetic energy in the tuned mass. The diagram below shows the setup.

Also, there is likely some hysteresis, and possibly nonlinear stress/strain relationship, in the support film. I agree with @Dale, but amend his last sentence slightly: ..you are definitely better off to just measure the damping directly.

 

[Smooth]

Yep, I didn't want to mess with drag as the shape of the object isn't obvious, approximating Reynolds numbers, factoring the speed - pain in the neck.
I might eventually put it into a vacuum chamber just to approximate damping without air resistance.

Thank you @Dale and @jrmichler! Will be getting it experimentally then.