Head dampers: choosing the optimal harness for an application?

[jhamel]

I am still mystified by the concept of head dampers. I believe i superficially understand the physics behind them; To allow the feathering shaft to teeter a bit to (1) avoid vibrations that may cause the helicopter to violently shake itself apart and (2) attempt to minimize stalling of the retreating blade.

The stock dampers that come with helicopter kits tend to work well. However, some helicopter kits come with two or even three damper stiffness options on the stock kit. There are also several several after-market companies selling damper "upgrades" for specific applications.

I understand that DFC style heads benefit from hard dampers. I don't own any DFC style heads, so discussing dampers for DFC style heads may be a distraction for this thread.

I assume that the following variables affect the optimal damper selection:

1) Blade size

2) Blade weight

3) Rotor RPM

4) Flight style

5) Head design

I would like to learn how one goes about choosing the optimal head damper harness for a particular application or flight style, and how one troubleshoots head dampening issues.

[RaisedByWolves]

Good topic, I was wondering about this same topic but being new to the newer designs/tech didn't know how to approach it.

Subscribed.

ETA, check thread title.

[extrapilot]

Yea, unfortunately, the physics around this subsystem (main rotor) is horrifying.

It is a little easier if you take what you know from experience. Example, DFC (or heads with no teeter) still work. You don’t get RBS simply because the head doesn’t teeter.

Another thing that should be pretty clear is that if you had free teeter (no dampers, just a pivot), you have no way to impart pitch/roll torques via the rotor purely through cyclic. You could tilt the rotor around, and the machine could not care less. To make the machine pitch/roll, you have to tilt the rotor, and then use collective to pull the machine around by the head- exactly as a horse/wagon operates. And this leads to terrible maneuverability. So, the converse would suggest that rigid dampers would allow for cyclic to impart pitch/roll torques directly on the machine- and increase maneuverability in that context. And- that is true- typically, the more rigid the head, the more maneuverable/responsive the machine (variables exist- headpseed, blade geometry, blade mass, etc, but generally…).

I think you will find that dampers are there to decouple the rotor from the head, to offload large forces that result from flap and lead/lag. Those forces can lead to a system resonance- where you see nodding or shaking at some RPM, etc. Different damper compliance will change the resonant points. Part of that is aero/mechanical. Part of it is control system (i.e. FBL feedback loop).

There is no easy answer to ‘how do I optimize.’ You are best off starting with a known-good config, and then altering the dampers to see what happens in hover, in acro, and in FFF. You may then need to retune the FBL, and retest, etc. Takes some time- and objectivity.

[velo24]

Neat question, let me have a go at it. I want to clarify one thing first, these are not exactly "dampers", they are spring-dampers (mostly spring).

RPM: So what you want to avoid is resonance in the damper. The resonant frequency of a system is:
w = sqrt(k/m)
where k is the spring stiffness and m is the mass. What we really want is a stiffness lower than the critical one, so:
k < mw^2
but we don't have a "mass" because the damper is actually combating flapping torque of the blades. So, I'll replace mass with moment of inertia of one blade in the flapping direction:
I = (mR^2)/3
where m is now the mass of one blade and R is the length of one blade. I'm only considering one blade generating the frequency since this is the worst case scenario. Equivalently, the stiffness is now torsional resistance:
t = (kd^2)/2
where k is the stiffness of the damper (rod in) and d is the distance between dampers on the hub. So this means we want a damper that is:
k < (2mR^2)((RPM/60)^2)/(3d^2)
As a side note, softer dampers adversely effect responsiveness and are bad if you fly aggressively.

now, there are modes of vibration other than the natural one so make sure you stay away from k values like:
k = (2mR^2)((RPM/60/2)^2)/(3d^2)
k = (2mR^2)((RPM/60/3)^2)/(3d^2)
k = (2mR^2)((RPM/60/4)^2)/(3d^2)
etc...

Now that the spring properties of the damper are addressed, on to the damper!

The damper actually absorbs all the energy of vibration but damping is a property of the material and its size. Larger dampers have more damping (and have less stiffness) and materials with high internal friction have high damping. How much you want is determined by two things:
- more damping for more vibrational energy that needs dissipating
- less damping for more aggressive flying styles IF the stiffness is low. This does not matter for stiff dampers.

if a material is squeezed and it slowly returns to shape it has high damping. If you squeeze it repeatedly and it heats up quickly, it has high damping. If the damper is hot after a flight, it has high damping and you also might want something stiffer.

Hope this helps

[extrapilot]

Velo

I think you are looking at this from the perspective of something like a suspension system on a car. That is a poor model for what it is that is happening with these machines.

We are not looking to avoid resonance in the damper. The way we get significant cyclic flap is by inducing resonance in the rotor system. If the dampers did anything like absorb any real fraction that energy, they would melt in seconds. And, it wouldn’t matter if the dampers could absorb a real fraction of it, because the rotor would just invest more power in cyclic flap (it is the vertical component of the blade’s motion that can reduce AOA- if you keep the cyclic pitch, but reduce flap, AOA increases, restoring the flap angle).

The dampers are there to permit teeter and lag in the spindle, which greatly reduce the forces seen at the head. They have a secondary function, which is to partly decouple the components below the head from the rotor. That reduces vibration transmitted to the fuselage, and bending forces on the main shaft.

The trick is just to find a compromise between these two factors.

The coupling between rotor and fuselage remains resonant- you can find an RPM where a soft-dampered or solid dampered head will see fuselage nod.

[velo24]

extrapilot

I do like your insight however I still believe there is an objectively better and a worst choice. I agree that the primary resonance mode is important not attenuate or you'll be cooking rubber. However, there are higher modes of vibration as seen here:

Test footage of a S-56 helicopter blade bending in flight (3 min 8 sec)

The blade is vibrating at 4x the RPM due to the standing waves created by the 4 blades. I could be wrong, but I believe these vibrations are unwanted and, for a 2 blade rotor, a stiffness resonant with 3*RPM will amplify flapping at RPM every 3 revolutions (as oppose each revolution) while damping the 2*RPM resonance of eddies (I'm assuming fixed-fixed dynamics).

[extrapilot]

Hi Velo

Well, it is a tuned system, so there are better and worse selections for a given configuration and flight profile. But if you change variables, then you are out of luck. That is a reason why well-tuned machines often are badly behaved outside their target envelope.

If you look at vibration analysis from an RC heli, you will not see significant contributions in the form you would expect based on a video like the one you attached. There are several reasons. One is the Lock number, which is just a ratio aero to inertial forces on the rotor. Our blades are very stiff, and have very low mass relative to their area- so they are well damped in flap. Likewise, the blades are torsionally stiff, so you don’t tend to see the same sorts local changes in AOA which result.

The behavior you see in the video is not due to standing waves resulting from 4 blades; it is a 5-bladed main rotor. It just happens to be how that blade behaves, and it would change if you moved mass around, or changed the surface area, or altered its mechanical properties.

Anyway- the dampers in our machines have effectively nothing to do with blade flap or standing wave damping. Full scale, you typically see counterweights (bifilar dampers, etc) which are tuned as required. For our machines, dampers are really a misnomer- they simply decouple the spindle from the head to reduce forces there, and to assist with stability.

The later isn’t intuitive I think- but cyclic bias is a function of the delta between the swash and the rotor planes of rotation. It doesn’t matter which changes relative to the other. With soft dampers, the spindle can teeter, which means the blades generate their own corrective cyclic during periods of instability (if the disc changes plane, that causes an aerodynamic bias to fly it back to the swash plane). With a stiff head, that doesn’t happen- since there is no teetering (just blade flex- the flap hinge moves out to the blade). So, you don’t get that automatic correction- and the FBL has to deal with it.