Can someone enlighten me please (Vibration absorbers)

[Dave_Jackson]

Comments and a question.

There will be symmetry of lift between the advancing side and the retreating side during forward flight, therefor the induced drag on the advancing side and the retreating sides must be very similar.

However, the profile drag will be very different between the advancing and the retreating sides. The rotor drag force (drag from the forward velocity) and rotating shear force (drag from the rotation) will be summed on the advancing side and in opposition on the retreating side.

This difference in profile drag between the advancing and retreating sides will increase as the forward velocity of the craft increases.

At higher forward velocities, retreating tip stall and advancing tip compression must further increase the rotating shear force. God knows what this does to the basket of assorted/P vibrations.

One thing that I have difficult understanding is why an increase in the rigidity of a rotor will cause an increase in the rotor's in-plane vibration. Perhaps, in a 3-blade rotor it might, but in a 'theoretical' 4-blade rotor with no provision for led/lag the total profile drag of the complete rotor should be quite constant throughout the full rotation.

Could it simply be a case of the vibration increasing with forward velocity, and faster craft tend to have greater rotor rigidity?
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The Bifilar vibration damper is a means of isolating some of the problems of the rotor from the rest of the craft. The slowed rotor concept appears to be a means of reducing the actual cause of the problem.

Dave

[NickLappos]

Dave,
You are looking at it with the right set of glasses, we call the N/Rev disturbences "root shears" to mark their equivilent vertical and in-plane vibratory shear force acting on the head. These have strong content that varies with the number of blades, so that going from 2 to 3 or 3 to 4 blades makes a non-linear improvement on the size of the root shears. The root shear magnitude drops markedly due to the number of blades, and its frequency rises at the same time, making the net effect a reduction in root shear effect that is not quite N squared (so that 4 blades has something like 15% of the vibration of 2 blades.)

The root shears rise due to the rigidity of the blade attachment (since the blade can't flap or hunt to relieve some of this shear mechanically.) Thus, your hope that an awsomely rigid blade would be immune to N/rev vibration is actually backwards. Most of the time, we try to tune the blade to be compliant (softer) in a given frequency where it can help relieve these vibrations or absorb them.

The response of the fuselage is important to vibration supression. The low N/rev frequency of a 2 bladed rotor is a problem all by itself, because as the frequency drops, more things on the aircraft "like" that frequency, and try to resonate at it. This makes the ride quality much worse, of course. Also, as fuselages get bigger, their natural frequencies drop, so they need more vibration treatment.

All rotors produce N/rev, it is not a sign of a poor rotor. Pilots have this mythological belief that if they feel an N/rev, there must be something unhappy in the rotor, or it needs redesigning. Actually, all rotors give off about the same vibration (based on the number of blades, the hinge offset and the rpm) but what you feel is a measure of how well the manufacturer has learned to hide it or absorb it, or how the place where your seat is bolted is responding to it. It is possible for a complex airframe to have variability of 5 to 1 depending on where the seat is attached.

[outhouse]

Many thanks NickLappos, I had a very simplistic explanation when doing a S61 conversion many years ago. I presume that the dampers on the 412 have the same function as they seem to follow the theory. Thanks to all and very interesting.

[Graviman]

"...3-blade rotor it might, but in a 'theoretical' 4-blade rotor..."

Dave, i think you need to find a good aerodynamic efficiency justification for 4 blades per rotor. Removing vortex wake interaction between both rotors will by itself greatly reduce vibration. [Slightly off topic]

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Nick,

"Most of the time, we try to tune the blade to be compliant (softer) in a given frequency where it can help relieve these vibrations or absorb them."

Has any work been done on blade material damping? I also imagine that the gearbox mounting is carefully designed to maximise lateral compliance (good isolation in X and Y), while minimising torsional compliance (good manouvreing). Are hydromounts the norm (hydraulically damped elastomers - usually Lord or Simrit), and have active mounts been considered?

"The response of the fuselage is important to vibration supression."

I've done a lot of work on modal response and input point force spectrum sensitivity. Powertrain mounting systems are normally the best means of isolation, although you can tune structures to some extent. Since i'm understanding that Np ties up with one of the main airframe bending modes, i imagine structural tuning to be limited.

Mart

[Edit: typing while watching Disco do it's dance with the ISS]

[Dave_Jackson]

Nick,

I understand your concern about high rigidity, and the efforts that are applied in attempting to tune components about a selected RRPM. I hope that the following response will clarify my 'brute strength' approach.


Graviman,

Dave, i think you need to find a good aerodynamic efficiency justification for 4 blades per rotor.

For a quick justification, how about Sikorsky's coaxials? The S-69 (XH-59) ABC had three blades per rotor. It did not quite achieve the anticipated maximum forward velocity due to excessive vibration. Note that the X2 coaxial shows four blades per rotor.


For a longwinded justification; I did a crude and error prone comparison of a 3-blade rotor and a 4-blade rotor for the twin main rotor UniCopter, a couple of years ago. It was done to evaluate the lateral dissymitry of lift, but I suspect that its conclusions can be applied to drag.

The addition of a 4th blade provides a reduction in the drag of the individual blade, as mentioned by Nick. In addition, it appears that the moment about the craft's X-axis, from the advancing side of an 4-blade 'theoretical' absolutely rigid rotor is a constant, irrespective of what azimuth(s) the (one or two) advancing blades(s) are at.

What I surmise from this is that the individual blades will be subjected to varying in-plane shear as they rotate through the 360º. However, if the rotor is 'absolutely' rigid, the total rotor will not experience any cyclical moment about the Z-axis or cyclical forces along the X and Y-axii.

This makes me think that the closer the rotor can come to 'absolute' rigidity the less the vibration (from this source) should be. In other words; the very high frequencies will be well above what could be detrimental to the structure, components and occupants of the craft.


Dave

[Graviman]

hmmm....

Been thinking about this a while, Dave.

It depends very much on the lift distribution of the rotor. A single rotor could be argued to maintain constant lift throughout the azimuth, so there is "theoretically" no source of vibration regardless of blade number. This was why i had to use the "N bladed rotor is being slammed backward N times per revolution" explanation to explain cyclic drag variation. I'm hoping Nick will expand on the root shear = ~1/(N^2) relationship.

The main vibration source to my mind is during roll or pitch. Since i favour feathered retreating (i know we are at a difference of opinion on that one ), then this cyclic input could also be seen as the hover condition for ABC intermeshing. Since i gather S-69 ABC had at least reduced retreating lift, if not fully feathered, then perhaps i should conclude that your calculations about 4-blade over 3-blade rotors is right.

However....

If blade pitch/lift is linearly varied from max at 90' azimuth to min (ie feathered) at 270' azimuth then, considering each individual rotor during full azimuth rotation:

3-bladed rotor has total lift varying from 1 1/3 to 1 2/3 blade equivalents, and moment about x-axis of constant 2/3 blade equivalent at 90'. So max blade equivalent variation 20%

4-bladed rotor has constant lift of 2 blade equivalents, and moment about x-axis varying from 0.707 to 1 blade equivalent at 90'. So max variation 29%

From that perspective there is an arguement for 3 blade, but i'm expecting Nick to jump in and tell me i'm talking nonsense...

Mart

[NickLappos]

Graviman,
The issue is still that you tend to see the blade as some static source of lift (as in the phrase "maintain constant lift throughout the azimuth") when in fact that blade is whipping about, getting its butt kicked by the relative wind (which changes its azimuth relative to the chord line at about 5 to 10 times per second) and also by the rotor controls, which are constantly changing its feathering in the hopes that the net lift averages out to 1/N of the aircraft's need.

At the hover, there is no N/rev because all the blades are experiencing almost no azimuthal variations, and the flapping across the revolution is approximately the same. As you build forward speed, the blade begins to see this varying velocity vector, varying as to speed and angle from the chord line.

At Vmax, the blade advancing abeam at precisely 90 degrees sees the "wind" as Vrotation plus Vairspeed. When that passes over the nose, it sees the "wind" as the vector sum of Vrotation and Vairspeed (which are 90 degrees apart). Each blade chord segment going out from the root sees the lateral angle of the "wind" differently. At the hub, the "wind" is along the blade, and no lift is produced. At 1/3 span, the "wind" is about 45 degrees to the chord line, at the tip it is about 20 degrees. Do the math for the confusion of the lift distribution, and the net wild spanwise swings of the center of net lift as that blade travels around. Then remember that this variability occurs at 5 to 10 times per second. In effect, the blade is bucked and kicked by its chore, which rings every natural frequency it has. Look up that classic blade movie to see the wild ride the blade takes.

Again, only a stolid ME with a feeling for static solutions could see this as a nice, solvable problem of statics!

If there were one blade, the pounding of the root shear is eye watering, with two blades it is less than half the variability, by 7 or 8 blades, the root shears approximate a steady flow of lift.

I have no idea how you showed the proof that you did, where 3 is the optimal number of blades, but I'd suggest two things :

1) Get a good book on helo engineering (Prouty, and Stepnewski + Keys are two that come to mind)

2) If you have a mortgage, don't quit your day job to run off designing a helo!!

[Graviman]

Hehehe - wipes egg from face....

Nick,

"Again, only a stolid ME with a feeling for static solutions could see this as a nice, solvable problem of statics!"

Not at all - i was just trying to find a way to do some rough sums for the post. I was assuming a blade made from "unobtanium" (spanwise at least), which adjusted pitch and twist in an attempt to maintain lift distribution required through azimuth (ignoring reverse velocity region). The calcs were just to show how, with the equivalent of extreme roll input , total lift and rolling moment will still vary. Prouty had a neat way of integrating a "rigid" blade lift around azimuth to predict rotor performance, but i thought that too much for one post!

From your (as usual, extremely knowledgable) posts i understand that the main cause of the hub vibration input is blade eigenmodes, excited by azimuth rotation air velocity vector variation. This was why i was curious about whether blade material damping had been considered, to get even closer to the source. If blade material technology improves (which is DJs stance), then a theoretically spanwise rigid blade can be approached.

I was really trying to highlight that even with the "perfect" blade design, there would still be sources of vibration (including of course drag variation around azimuth). This was the reason for my question regarding gearbox elastomeric isolation mounting.

It may very well be that feathered retreating is far less practical than ABC. It may be that 4-blade coaxial is the best solution (Sikorsky seem to think so). I'm just trying understand the contraints of the problem.

It may equally be that i should just stick to precision hammer adjustment...

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Dave,

"One thing that I have difficult understanding is why an increase in the rigidity of a rotor will cause an increase in the rotor's in-plane vibration."

My understanding of this dynamic system is that stiffer blades of similar mass will have higher frequency eigenmodes. This is more likely to lead to the blade resonance which result in hub input forces. Bifilars effectively attempt to "rigidify" the root mechanical impedance, but a much better solution might be to damp the blade flexural modes directly...

Mart