Linear Resonant Actuator Notes

07.12.2023 - Spring & Rubber band extension test

Rubber band test- Adding mass and measuring end-to-end extension

Fit = p1 * x + p2

p1 = 0.2711 +/- 0.03 (2 sigma) mm/gr

p2 = 43.7 +/- 6 (2 sigma) mm

R^2 ~ 0.98

So 1 rubber band has a spring constant of ~ 36.2 N/m (calculation).

With 100 rubber bands; we reach a resonant frequency of the LRA of ~ 27 Hz. 100 ruber bands in parallel have ~ 3.6 kN/m.

In order to get to a resonant frequency of ~65 Hz, we need (65/27)^2 x 100 = 580 rubber bands.

Not practical -> 580 rubber bands would have a combined spring constant of ~ 21 kN/m.

Found SS springs with an adverstised const. of ~0.6 mm/N -> 1.65 kN/m each.

Put 18 of them and freq is ~29 Hz -> dissapointing, I think the 0.6 mm/N value is wrong. So I checked.-

Turns out .- the springs only work after a load of ~8N each; so they must be extended by at least 2 mm in operation (required anyways between we are aiming at +/-2.5 oscillations).

Also, more importantly: the spring constant is 1.2 mm/N or 0.833 kN/m !

So half of what I saw in the amazon listing.

For completeness; here is the plot for the rubber band (now ignoring the first point):

So, removing the first point, the spring constant is 30.5 mm/N, so 32.8 N/m.

100 rubber bands -> gives 3.28 kN/m.

580 rubber bands -> 19 kN/m.

I put 20 springs; that should have been -> 20 * 0.833 16.7 kN/m. So a frequency of ~ (16.7/19)^2 * 65 Hz ~ 50 Hz. But I observed the same freq. of ~29 Hz.

I now think it is because the prings were not pre-loaded. I did try preloading the springs but the connection broke -> I am 3-D printing new ones; but now I am realizing that the mass on the moving parts also plays a big role and needs to be optimized.

08.12.2023 - Spring scalings and the need to re-design.

Preloaded all the springs; now they are pre-extended by ~ 1 cm or so.-> That was not the issue.

Measured resonance frequency with 9 springs attached.- it is 20.8 Hz; consistent with the frequency for the double (18 springs) of ~29 Hz. Note sqrt(2)*20.8 = 29.41.

 Taking 20.8 Hz, and the spring constant of 9 x 833 N/m we can estimate the mass.

Using omega^2 = k/m

2pi f = sqrt( k/m )

We get 440 grams (calculation ). - Directly weighting the moving part I get 350 grams; but part of the spring is also moving, likely contributing to this. Note each spring weighs ~17 grams.

There's about 90 grams extra from the calculation, which would make sense if ~50% of the spring mass is counted toward the moving mass.-> By this logic, there's about ~180 grams extra when the 18 springs are attached.

What mass would be tolerated for our situation?

Target oemga = 65 Hz

20 springs -> k = 20*833 N/m

m = 100 grams! (calculation) 

Note that we expect a 200 gram contribution from the moving springs alone.- This will not work; we need stiffer springs.

08.12.2023

Ok, lets say we can reduce the mass; for example using a small magnet (driving force is not an issue; currently driving coils with 50 mA is enough to go ballistic, and we can go up to ~1 A [limited by wire]). And a more compact design.

We can realistically reach 300 grams after attaching the 5mm NMR tube coupler & tubes etc.

Then, let's say we aim for 80 Hz, to have some wiggle room if needed.

What would be the required spring rate? - A total of 75.8 kN/m (calculation).

If we distribute this in:

4 springs -> 19 kN/m per spring.

6 springs -> 12.6 kN/m per spring.

8 springs -> 9.5 kN/m per spring.

Found something good -> Here

10.12.2023

Bought 12 of these springs: Zugfeder Edelstahl , ø 15 mm, 40 mm lang, d= 2,2 mm.

Each will have ~ 10-11 kN/m. (Getting it from a similar product from the catalog here). or here.