Efficient hit detection on a shot plate with piezo disc

[matthieu1973]

TL;DR Summary

How to determine the natural frequency of the shot plate detect the hit with a fitting piezo disks and its mounting to have an efficient detection.

Hello to all, I wish to detect the hit of a airsoft pellet on a shot plate with an ESP32 board.

to do this I have basically two options:

Either, detect the signal as digital (hit / missed) or detect the signal as analog signal with a piezo disks.
The analog signal will have more information within the detection that i might be able to 'decode' at a later stage so this is my preferred option,
Then there is the option to just add a piezo disk to the shot plate and hope for the best, on the other hand I can try to calculate the most efficient setup.

To do this I would need to go and calculate a few things:
1) Energy transfer (pellet ot shot plate),
2) Shot plate (mounting) physics,
3) Piezo disk size, thickness,, mounting.

So for now I have taken in consideration the following.

the shot plate is a round steel disk (R = 20mm, h = 3.0mm) and is will be atteched through a little stem on one side which has a trough hole, through which there will be a little bold. and the rim will have a U cut out and another bolt will go through that. that all ia attached to a 20KG servo arm and the total lenght of arm and disk will be. 55mm (R = 20 + 25mm)

The approach I was planning (but please correct me If i am doing so thought errors here) is calculate the following approximations in the following order.
1) Natural frequency of the disk.
2) Energy of the pellet. (which I can measure quite accuratly)
3) Energy absoption of the pellet by the system.
4) specifics of the piezo disk (brass disk size, Ceramic disk size) to obtain the specific frequency and specific Impedenca (for the analog filter of the signal to the ESP32 (100's V to 3.3V)

But ofcourse the first part has the expected complications.
All the formula's I found to calculate the natural frequency of the disk.. have a pretty important impact of the mounting system, and none of those approach the way i will need to attach them..
https://autofem.com/examples/determining_the_first_natural_.html
https://autofem.com/examples/determining_the_first_natural_.html

the Engineers website gives a few values for B, but all with a fair amount of difference, so taking the wrong assumption here would set me on the wrong track from the beginning.

https://www.engineersedge.com/vibration/thin_flat_plates_uniform_thickness_14986.htm

so if any of you have any suggestion / corrections on the approach, i would appreciate it.

kind greats

Matthieu

 

[jrmichler]

A round plate has multiple natural frequencies. The relative magnitude of each natural frequency depends on where the pellet hits the plate. One mode has the plate bending into a U shape. Fastening at one point on the edge makes the plate asymmetric, so the natural frequency of that mode will be different depending on the direction of the U. You will not find equations for the natural frequency of a round plate with your mounting. The equation for natural frequency with edges free (plate floating in air without support) should give a number that is in the ballpark.

Strongly exciting a natural frequency requires that the duration of impact be less than 1/2 the period of that natural frequency. You can estimate the duration of impact from pellet velocity and length. If the duration of impact is longer than the period of a natural frequency, any excitation of that frequency will be minimal.

Why do you need natural frequencies? What is the purpose of that servo? If you are using the servo to return the plate after a hit, then the pellet is hitting hard enough to move the plate. The servo should be able to output a position error signal after the hit, which you could use for your hit detection. The industrial servos I am familiar with will do that, I'm not familiar with the capabilities of those little hobby servos.

BTW, I had a project at one time where I had to trigger natural frequencies up to 10 kHz on a 50(?) lb plate attached to a 30,000 lb load cell. That meant that the duration of impact had to be less than 50 microseconds. A hammer did not work because the duration of impact was about 1000 microseconds. Blasting caps did not work even though they were fast enough, because they were not powerful enough. It turned out that a .22 Long Rifle standard velocity rifle bullet was exactly the right combination of force and duration.

 

[berkeman]

BTW, I had a project at one time where I had to trigger natural frequencies up to 10 kHz on a 50(?) lb plate attached to a 30,000 lb load cell. That meant that the duration of impact had to be less than 50 microseconds. A hammer did not work because the duration of impact was about 1000 microseconds. Blasting caps did not work even though they were fast enough, because they were not powerful enough. It turned out that a .22 Long Rifle standard velocity rifle bullet was exactly the right combination of force and duration.

That sounds like a hell of a lab that you worked in. I'm guessing that Happy Hour Fridays were pretty crazy...

 

[DaveE]

TL;DR Summary: How to determine the natural frequency of the shot plate detect the hit with a fitting piezo disks and its mounting to have an efficient detection.

The analog signal will have more information within the detection that i might be able to 'decode' at a later stage so this is my preferred option,

What "more information" would you want?

BTW, when I read "piezo disk", I think "microphone" (of any convenient type). It may not even need to be touching the target plate.

 

[jrmichler]

It was a class project for a Dynamic Measurements class. My partner and I asked the professor for a challenging project. The load cell was for another grad student doing research into crashworthiness of composites. His professor was half owner of a copper mine, and the source of the blasting caps.

My partner was from Malaysia, and not used to guns. He was quite interested in the entire project. Another grad student was frustrated that his 9mm was ruled out - bullet too long, so impact duration too long.

We found out after handing in the final report that the professor's hobby was target shooting.

 

[matthieu1973]

@jrmichler
Oke, the approach of a servo giving an potition error is intrequing. I had not considered that, so my fisrt step will be to dive in that and see if I can get the info and ifso see if i can get info on the amount of displacement.

I have found that the servo (not even connected, responds back upon a push against the arm, so it should give some of that info back. Intreguing, very intreguing indeed.

If not, then I will go with the floating plate approximation.

Figuring out the duration of the hit of the pellets seems to have its own problems, it will be short.. but how short depends on so many factors (the amount of the shock abosbtion of the plate, as well as the plate/servo setup arm movement, as well as the absobtion of the airsoft pellet (read distruction thereof)). As a Former gold/silversmith i can understand (in hind sight ofcourse) that you hammer hit would take to long.. did you hit the plate manually or with a free falling mechanical arm, being completely free to bounce back? I feel there would be a time difference between the two (just being curious here). So an free traveling projectile does seem like the way to go. Do you still have the approximation of the duration of your .22 bullet.?

 

[matthieu1973]

What "more information" would you want?

BTW, when I read "piezo disk", I think "microphone" (of any convenient type). It may not even need to be touching the target plate.

Well, for target practise one usually uses a bullseye with a "grade/point" distribution. If I can determine the "quality" of the hit, I might be able to deduct some similar information out of those figures and grade the hit quality (edge to dead center)

Well yeah, similar.. a piezo disk can indeed be used as detection (microphone) or as a production source (speaker) here a detection ofcourse. for microphones they tend to be as free floating as possible i believe, but here i wish to get the vibration caused by the hit directly transfered to the disk, not use the "soundwaves" traveling through the air, so a mount in one way or another is applicable. I have taken in consideration the 4 following "mounts"
1) glue it flat against the back of the plate (type of glue should be taken in consideration here too, a hard glue like cyanoacrylate, a something more silicon based like an E9000 that remains flexible)
2) mount in a standard ring, that come with some of the disk upon supply.
3) attach on one side of middle of the disk.
4) attach on sides of the disk (two / three?)

but as for now i will dive into the servo suggestion jrmichler gave.