Basic structural dynamics in multicopters

[Kisssys]

Hi Max,

I tie a string to each gear and let it hang a couple of feet below the gear. Two lines seems to keep it form getting into the sling load oscillation that you get with longer lines. I leave them long enough that I can lower the bottle to the ground and then fly forward or back a bit and land.

I think it would provide less dampening than have the weight attached directly to the frame.

[afernan]

Thanks to all u guys for the return. OK, we could talk veeery long about structural vibration!. This is one of most important and complex issues in aircrafts. But let´s try to be practical and sinthetic to be useful for our copters.

@Max: you commented one of the key points: what is the excitation frequency?. The formal answer is: infinite values (main frequency + all the resonances = 1st, 2nd, 3rd... or like in music: main, octave, 5th, third, etc.). More powerfull are the lowest ones.

It´s true that for a "perfect" & equilibrated motor+props excitation should be 2xrpm (for two blades). But "perfect" doesn´t exist, and we have always some (even small) unbalance that it´s a very powerfull exciter, happening at 1xrpm. In fact the 2xrpm corresponds to the first resonance (at 1 octave, double freq). But 2xrpm is at higher freq and should not be a problem. We need to consider as refference frequency 1xrpm as our source of problems.

In our copters, the solution for coupling problems should be easy, as explained in the paper. A few numbers on a paper can save a lot of headbreaks. Most dificult thing is to have material properties for the CF tubes, basically the Young Modulus. But this is done one time for all. I could do for you if Jussi or Paul send me long tubes (about 1m) same as sell in the shop, for doing the test, if they don´t feel strong to do it.

@bluuu: for square arms applyies the same. You only need to use the correct "I" inertia and "E" (for alu E=70e12MPa)

The effect of adding mass to central body is to decrease the frequency of all elements attached to it (in particular the camera). At the same time we increase rpm (we added mass) so this double effect increase the freq gap between motors and central part that is very good, so we feel less vibrations in camera (not really damping). In my designs I attach the camera directly to the battery bracket and I got almost no vibration at all.

[afernan]

...more reflexions:

there is a common thought that "stiffer" arms means better performance. This is absolutely not true in general.

Example. If you have heavy copter with 12" props, so high rpm you can have high excitation frequency, let say 50-60Hz.
If you put big CF tubes (22mm diameter) then you will go with your arm freq also high, and could be close of that of the motor, so you can get coupling problems.

It´s true also that the higher the frequency, the less energy of resonance, but it´s still there and will generate a lot of vibrations for you FC and your camera. Our FC board is so good that is almost unsensible to this vibration (inside a certain levels of course), but if we want "the best" we need to eliminate this.

Aluminum frames are much softer than CF (low freq for arms). Combined with small motors/props (high rpm) are a perfect combination to avoid this problem. I´ve been using alu many times in my proyects with big success. But we all like CF!. Anyway you can allways get same stiffness inCF than that of alu, by simply reducing the CF tubes size.



more to come...

[Kisssys]

Angel

Sorry ahead of time for all the questions but there are few things I've had questions about after building dozen's of frames. Take your time in responding and ignore any questions that aren't really pertinent.

Is their not a rotational element to deal with on each boom? The cheaper pultruded booms twist very easily.

If the boom is not round it would seem the resonant frequency would vary reference the disturbance direction. Would a rectangular or square boom be better or worse than a round boom or would it in fact create several resonant frequency's?

Do you want a boom material with a high Q to narrow the window of resonance or would a low Q be better in that it would resonate at a lower amplitude? Maybe this is not something that is even select able by choice of materials or shape.

We assume the boom to be attached to a solid frame but in fact the plates can flex, can the attach point be tuned to change or dampen the natural boom resonance? You mentioned that it's not always best to have the most rigid material, could this also be applied to the main frame plates.

Does adding weight to the middle of the boom significantly change it's resonance ( esc for instance)?

Having a outer ring attaching each boom makes a big difference on some craft's vibration levels. I'm sure it gets quite complicated to analyze depending on the structure of the ring but it would seem to greatly increase the frequency of resonance and would also dampen the rotational characteristics of the boom.

The plate boom construction method is of course the easiest path, if you were to build the absolute most advanced airframe for a multirotor using the most advanced materials, what would be the basic design method, monocoque?

Cheers
Steve

[epyonxero]

Thanks for writing this, it take me back to my college dynamics classes.

[afernan]

@Kisssys:
- Rotational stiffness: you´r right. One mode of vibration of arm will be torsion around the tube axis. Usually this number is higher compared with main bending mode. It will depend on the diameter and thickness of the tube, the cog of the motor wrt axis (the lower the better), and the mass of the motor. Section of the arm must be "closed" (circular, square, etc). Those plastic machined arms are very bad in torsion.
- rectangular section. This section has lower frequency in one transversal direction than the other, but not too different. For instance, an aluminum rectangular tube 12x10x1mm (I used a lot) has 37Hz and 41 respectively )for a 300mm arm, 100g motor): not a dramatic difference
- Q factor is so important like the frequency itself. CF has much higher Q than alu. A cantilever CF tube well clamped can have Q=25-35. Typically alu has Q=15. In the other side we want Q high to get narrow peaks. So it´s a compromise. Each bolted attachement decrease about 3dB the transmission. Anyway most of this factors are design drived so we can´t change. For instance, the motor bracket 3D printed I have in my "monoblock" should have high damping due to the load transmission is done thru a large friction surface.
-Attachments to plates. All affects to the frequency of the arm, in particular the clamping. I´ve tried to simplify the calculations suposing a "infinitely" rigid clamping, which is not the case. Reality will be a bit more flexible, depending of the blocks, CF plates, etc.The simplest way to design is to have motor-arm frequencies as "separated as posible" between them. Other designing way complicates innecesarely the situation.
- adding weight to the boom. Again, try to be simple! and choose very clear solutions. Yes if you add mass in the center of the boom will change the frequency of the arm, but also the "mode" wich is also very important. There are very effitient methods to reduce vibrations along the tube like introducing "bags of sand" or similar inside. We´ve used that solutiion in a real satelite with incredible results.
-outer ring. You said already: it complicates a lot. In fact only reduce(change) the vibration in the plane of the arms. Vertical vibration remain the same. I don´t like that.
- "advanced frame". Yes there is: thick (40mm) sanwich CF skins and Roacell (or any damping foam) as core. Skins can be CF very thin (0.5mm or so) and the whole thing, arms + central plates all in one single piece. Vibration damping is very good. I have one design (on paper) like that. The problem is to manufacture well and cheap, but some day I´ll try one!.

Hope I´ve answer your questions. Please, consider that this is never an absolute truth, and I can be wrong as any mortal!.

Angel

[chschmid]

[afernan]

here it is. Consider it just an idea
Main dimensions are:
700mm motor-to-motor.
Propellers 12".
sandwich thichness = 30 mm
Carbon skins 0.5mm

3D model to play here: https://grabcad.com/library/multicopter ... assy.3dxml

Christoff, if you want the 3D file I can pass for you to play.

Angel

[chschmid]

Thanks Angel, now I see what you mean.

Cheers
Christof

[Kisssys]

Thanks Angel

Your response was great and answered all my questions. Thanks for taking the time in this thread.

If I was going to make that frame I would wet out a couple layers of carbon cloth on 2 flat PVA'd plates and put the Rohacell in the middle and vacuum bag it together. Then CNC the shape out of the sandwich. The Rohacell would cost me as much as the carbon fiber I think.

I like the DJI phantom style of fueselage, if I had a 3D drawing of a nice frame about the size of your quad I would cut the molds and build one.