Basic structural dynamics in multicopters

[afernan]

Attached is a short technical note showing some basic aspects to consider in the design of a multicopter respect the structural dynamics behaviour (natural frequencies of the frame). This will make you to get best performances and flight time.

Hope this help you

Angel

[LordPikaChu]

Great read! One question, though: how much of a difference between motor frequency and arm natural frequency should we aim for?

Thanks for posting this!

[kinderkram]

Good writeup, Angel.

Will upload it to the documentation dl section.

[afernan]

@LordPikaChu:
to be safe, a factor of 2 is suitable. Anyway this will depend of how narrow is the resonance peak of the arm or leg. If it´s very narrow you could have really close frequencies without disturbance each other, normally not the case.

Forget to comment that you can decouple by one side or by the other side. That is, imagine you have 30Hz for motor and 30Hz for arms. You can:
- change motor/propeller combination to get higher rpm (increase frequency excitation) OR (never both)
- increase arm size (tube diameter) to get higher arm stiffness.

Obviously, if you do both you could get again same problem but at higher frequency!

[srinath]

Angel

This writeup is so useful and practical. I have never paid attention to structural analysis at school. All my Aerospace knowledge is in cfd and controls. I am definitely saving this for future reference.

[chschmid]

Wow Angel

Your document is amazing. Still trying to make my narrow mind understanding what you calculate t get the propeller excitation.

Cheers
Christof

[Max]

Nice writeup, Angel!

I'm a little confused about what the motor rotation frequency represents, or rather what influence it has. To my layman's understanding, and assuming a well-balanced motor/prop combo, doesn't most (?) of the vibration happen due to a prop blade passing over the arm (or other obstruction)? Which would be 2x the RPM, assuming it's even relevant. I've definitely seen what you describe in terms of some RPM ranges setting up horrible resonant frequency vibrations elsewhere on the MR, often in the props themselves, as well as the arms and LG like you say. Seems to happen most at RPMs below normal hover/50%, but that's based on very limited observation.

Can any of this help determine the right material/application to use for dampening something like a camera, or perhaps even the FC itself? Or isolating the arms/LG from the body. Seems like a lot of that stuff is guesswork/trial & error at this point in our hobby, with many attempts just making things worse. Is it "just" a matter of analyzing the most common/disruptive frequencies, say during a flight? And we even have this data in the AQ ACC logs, but need a way to compute frequency averages? (Is lack of sleep catching up with me? )

Cheers,
-Max

[bluuu]

angel, good work, lot of new knowlege (for me)

What about square arms ? other formula ?

[Kisssys]

Good Stuff Angel, desperately needed.

I have several machines that flirt with resonance depending on the weight they are flown. I generally fly them heavy and don't see the problem because the rpm is more like 3000 rpm which gets you up near 50 hz and seems to be far enough away from my boom resonance.

I have started to test my machines by putting a liter bottle of water with a small hole in it so it will leak the water out over a couple of minutes. Amount of water should correspond to the weight range you would expect to fly the craft at.

I go lift the bottle full of water and go into a hover and fly until the water leaks out and land. I usually have to look at the logs to see it but you will usually see a considerable difference in vibration. I had always assumed that vibration would be higher the heavier I was but it's not always the case if you have a machine that has the problems that Angel describes. If you don't see a major difference in vibration levels from heavy to light corresponding to high to low rpm then I would assume you don't have resonance problems.

[Max]

That's a nice test Steve, good way to run through a bunch of sustained RPM ranges. And better than using explosive LiPos as ballast.

Would the extra weight attached to the frame in itself have any dampening characteristics? Depending on how it was attached? (btw do you just lift the bottle on a string and let it dangle?)

Thanks,
-Max