Rotor blade resonance

down under

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I am interested in building a four blade teetering rotor and would like to find out more about the resonant frequency of rotor blades.

It is this post from C. Beaty that has me thinking about it.

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If you take a stick of 1/8” welding rod, grasp it between thumb and forefinger ¼ of its length from one end and give it a thump, it will vibrate about as shown in the sketch. This is the in-plane free resonance that causes most of the 2/rev problems with seesaw rotors. There’s a periodic excitation from the airstream in forward flight; broadside, the rotor gets a stronger hit than endwise.

The cure, as most people know, is to make the rotor as stiff in-plane as possible and hang it on a soft mast. This way, the natural in-plane resonance is higher in frequency than the aerodynamic excitation.

A mass attached to the center will inevitably lower the in-plane resonant frequency into the range where it can be excited by the aerodynamic input.

Whether the mass attached to the center is round, square or a rod skewed at a 60º angle is irrelevant.

A rigid rotor pylon is just as bad. The magic rubber bushing on an RAF-2000 does nothing for stability but is a good solution to the 2/rev problem.



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I have tried the test as described and the resonance occurred. Next I held the welding rod in the centre and struck it in the same spot. There was a lower frequency and I could feel the vibration between finger and thumb.
I then tried holding it in the centre, but twirling it between two objects so that both ends struck at the same time. If one end struck slightly before the other there would be resonance but when both ends struck at the same time there was no resonance.

From my experience two per rev shake is worse on high coning rotors, but with fine adjustments to teeter bolt height a point can be found where there is no shake in straight and level flight. Exact teeter height does not seem critical on rotors with a low cone angle.

At the moment I have two thoughts on the issue of resonance in teetering rotors.

1. Resonance may be an issue on rotors that are flexible in plane and operating with high blade loading, but not a problem with rotors that are stiff in plane and operating at low blade loading.

2. Because the was no resonance when both ends of the welding rod were struck at the same time, and what I have found when eliminating two per rev shake, there is no problem with resonance in a teetering rotor.
 
When a welding rod is held between thumb and forefinger ¼ of its length from one end, it will resonate in what would be the xylophone mode if a musical instrument. The grip is at a nodal point where there is no translational motion.

Clamped at the center in a vise, the rod will resonate in the tuning fork mode. But held between thumb and forefinger at the center, there will be no resonance because of the damping (friction) provided by the holder’s fingers.

With a weight clamped to the center, the frequency will be lower, -somewhere between the xylophone mode and the tuning fork mode- and the nodal points will be nearer to the center
 
Wood has not the advantage of damping these resonances?
 
Here’s what an xylophone looks like, Jean Claude. The resonators are wood bars supported at their nodal points.

Wood, of course, has good damping but for higher frequencies. Not so good at the 1/rev frequency of a rotor.

The damping provided by wood depends upon its ratio of internal friction to stiffness; birch, ash and hickory have much lower damping than balsa or white pine.

We perceive a rotor resonance at a 1/rev rate as a 2/rev shake because of the frequency doubling effect of rotation.

If a seesaw rotor is resonant at its rotational speed, 5-6 Hz, the pilot feels a 10-12 Hz shake.
 

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I am interested in building a four blade teetering rotor and would like to find out more about the resonant frequency of rotor blades.

I am no authority on blade resonance, but the only way to accurately measure the resonance of the blade is having a sound generator whereof you can adjust the frequency of the sound waves. Nice and slowly start turning down the potentiometer and the point where the given material has it's self resonance point make a note of the hertz the display shows on the sound generator. Tesla was BIG on resonance and it's advantages. It is certainly something that cannot be over looked. Good luck with your project. BTW even number of blades will always amplify unevenness rather than odd number of blades, due to the gyroscopic precession will transverse forces from the advancing blade to the front on a ccw head. And the largest amount of lift appears on the advancing blade. 90 degrees later it manifests itself. So your revolution is 90 degrees apart and it's going to be rhythmical. Odd number blades tend to break up the rocking :)
Cheers
 
Some information I picked up off the net.
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Mechanical resonance is the tendency of a mechanical system to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration than it does at other frequencies. It may cause violent swaying motions and even catastrophic failure in improperly constructed structures including bridges, buildings, and airplanes. Engineers when designing objects must ensure that the mechanical resonant frequencies of the component parts do not match driving vibrational frequencies of the motors or other oscillating parts a phenomenon known as resonance disaster.
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http://www.tidewater.net/~xylojim/xylocons.html
Xylophone Tuning
First you take a chunk of wood (straight, clear, dense grain is ideal, but I've gotten neat sounds out of pretty gnarly looking stuff) and cut it to a length that suits. Too long or too short won't resonate very well, so experiment. Now, find the nodes by either measuring 22.5% of the length in from the ends or sprinkling some salt along the top and tapping it lightly- the salt will collect at the nodes. Support the wood under the nodes with something soft, like felt, foam, or balled up socks. Tune it by cutting it shorter to heighten the tone, or gouging under the middle to lower the tone. You can also raise the pitch slightly by thinning the ends, and lower the pitch by making a simple saw slice or gouge in the middle.

Xylophone Mallets
As for mallets: hard mallets tend to bring out the high end and soft mallets the low. Super-balls, rubber-band balls, etc. work well for soft mallets, and there's lot's of options for harder mallets.
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Looking at the xylophone tuning it seems that a rotor that is stiffest in the centre both in plane and in cone and tapering to the tips will produce a higher resonant frequency.

A rotor with the conventional hubbar setup is weakest at the hubbar or at the blade roots near the end of the blade tangs. This would produce a low resonant frequency.
 
I‘ve measured the inplane resonant frequency of a rotor by suspending it from the roof by cords attached at nodal points and driving it by a saber saw clamped to the center. The speed of the saber saw was controlled by a variable voltage transformer (Variac). Frequency was determined by a magnetic pickup that drove an electronic counter while sensing saber saw plunger motion.

The particular rotor was resonant at ~6 Hz or 360 cycles/second. Non-rotating resonant frequency is lower than when turning as a result of centrifugal stiffening.

Static resonance can also be calculated by turning the rotor edgewise, supporting it at center and measuring droop at the tips. Most of the droop is caused by the steel attachment straps.

A SkyWheels style hub bar that straddles the rotorhead is ideal since it provides a high order of inplane stiffness.

One of the things we tried was an aluminum plate sawn in the shape of a SkyWheels hub and bolted to the blades. It worked but the better approach was the use of either a limber mast or a slider.

Arthur Young, the designer of the Bell-47, went through exactly the same thing 60 years earlier. His temporary fix was external bracing on the rotors of the B-47 precursors. The developmental model worked fine in a hover and at speeds below 20 mph but encountered violent 2/rev shake in forward flight. The ultimate solution was to soften the engine-transmission rubber mount bushings and internally stiffen the rotor.

There is simply no way a seesaw rotor can be stiffened to the point that its resonant frequency will be above the operating RPM with a mass equal to the weight of another blade set clamped to the center. This could be easily explored with the saber saw technique.
 

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It would seem in a four blade rotor, the way around the resonance problem is to have the teeter bushes act as sliders. This would isolate the rotor resonance from the rotor head.
 
That’s about the only way that I can see of solving the crisscrossed teetering rotor problem without dedicated drag hinges.

DU series bushings work well both for oscillating and sliding motion.
 
Thanks for the input C. Beaty and choppergabor. The DU bushings doubling as sliders look far simpler than drag hinges.
 
A possible problem that I could see using the teeter bushes as sliders in a criss-cross 4 blade rotor would be the possibility of both rigid hubbars finding themselves offset the same way, creating a diverging massive out of balance with destructive consequences.
 
The hubbar system I am thinking of at the moment is cheek plates similar to the Magni setup. The slider would need to be spring loaded to keep the rotor central on the hub. Depending on the amount of movement due to resonance, a thick neoprene type washer either side may be sufficient to isolate the blade resonance from the hub.

This may cover the problem you are thinking about Tim. If not let me know as the more info or thoughts on problems now may save a lot of trial and error testing further down the track.
 
Peter have you explored the possibility of the counter rotating blades rather as they would greatly reduce your vibration and balancing problems? I am not sure if I have seen a Gyro equipped with one. So forgive me I am just running some thoughts by you to pick your (or anyone else's) brain :)
Cheers
 
Peter--I tend to agree with you on the coning angle. Ive flown many blade setup over the years and it has been my experience that low cone angle blades are far easier to adjust and eliminate stick shake--I had horrendous stick shake on my current blades-with a high cone angle hubbbar--to the point that they would go from full fwd to full aft if the stick was released. I fixed the issue by stiffining the hub bar --but I reall think that with a low cone angle I would not have had the problem. The reason I say this is simple--The last four sets of blades I had were identicle the first three sets used a McCutchen Hubbar( no cone) they flew perfectly --the current set uses an aluminum bar for a hubbar -it flexes alot and has a high cone angle -I fixed the stiffness but not the cone angle --as soon as I get the time Im going to make a low cone angle hubbar and see if helps even more. My stick shake now is pretty small it only move 1/4" in either direction----------Stick Shake fascinates me and Ive learned a lot from CB

Heres a link to my cure http://www.rotaryforum.com/forum/showthread.php?t=19613&highlight=hubbar
 
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It is true that coning angle causes 2/rev shake in anything but a vertical descent; the blade mass above and below the teeter bolt is forced to travel in a 2/rev circle, but Mother Nature pretty much takes things out of our hands. About the only possibility for flattening coning angle is to speed up the rotor.

It is difficult to visualize masses above and below the teeter bolt being forced into a 2/rev circle. A simple welding rod model with concentrated masses makes it easier.
 

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Gabor I have seen pictures of coaxial helicopters but have not given it much thought for a gyro. I think it would become complicated as there would need to be a lot of clearance between the rotors. Because of the rotor head height it would then need feathering blades for control rather than a simple tilting rotor head.

With the two per rev shake on high coning aluminium blades I have found that the shake from a slightly low teeter point is a very strong kick from the rear left. This is strong enough that if there is not sufficient play in the controls it will break the control stick. For a low teeter point there must be play in the controls.

If the teeter point is high there is what seems a weak two per shake to start but then becomes a one per rev fore-aft stick bounce that increases if the stick is not held.
For a high teeter height the stick shake is less noticeable if there is no play in the controls.

In between the high and low positions there is a sweet spot where no shake occurs. It is a very fine line and any change in coning angle, due to control inputs, turbulance or air density will cause the shake for high or low teeter to occur.
This is what I have found with aluminium rotors but from what I have heard , fibreglass rotors may have a different shake for the same problem.

It is the shake for the low teeter height in high coning aluminium blades that I think would cause the most problems for a crossed four blade rotor.
 
The main problem is deciding when a vibration level has reached the point of being excessive. Extreme low frequency, and most medium frequency vibrations are caused by the rotor or dynamic controls. Various malfunctions in stationary compartments can affect the absorption of damping of the existing vibrations and increase the overall level felt by the pilot. A number of vibrations are present which are considered a normal characteristic of the machine. The N per revolution (N/rev) vibration is the most prominent of these, with N+1/rev or N-1/rev the next most prominent. There is always a small amount of high frequency present. Flight experience is necessary to learn the normal vibration levels. Even experienced pilots sometimes make the mistake of concentrating on feeling one specific vibration and conclude that the vibration level is higher than normal when actually it is not, it seems so because the pilot is concentrating on it. Low frequency vibrations, 1/rev and 2/rev are caused by the rotor itself. l/rev vibrations are of two basic types, vertical or lateral. A 1/rev is caused simply by one blade developing more lift at a given point than the other blade develops at the same point. A lateral vibration is caused by a spanwise unbalance of the rotor due to a difference of weight between the blades, difference in Span Moment Arms, the alignment of the CG of the blades with respect to the spanwise axis which affects chordwise balance, or unbalance of the hub or stabilizer bar. Rigidly controlled manufacturing processes and techniques, eliminate all but minor differences between blades, resulting in blades which are virtually identical. The minor differences which remain will affect flight but are compensated for by adjustments of trim tabs, pitch settings and Dynamic Balance weights . Smoothing of l/rev verticals is essentially a trial and error process although most rotor heads behave reasonably predicatably. Dynamic Balance Equipment manufacturers use a sample head which is in a known good condition and “map” out the various adjustments required and magnitude of change and in what direction the changes occur. Once in a while it will be found to be impossible to get two blades flying satisfactorily together and it will be necessary to remove and replace one blade – this is more than likely a span moment arm problem and can easily be fixed by passing the blade over a digital static blade balancer. Laterals. Should a rotor, or rotor component, be out of balance, a 1/rev vibration called a lateral will be present. Laterals existing due to an unbalance in the rotor are of two types; spanwise and chordwise. Spanwise unbalance is caused by one blade or hub being heavier than the other (i.e. an unbalance along the rotor span) or the Span moment arm of one blade being different from the other blade's. A chordwise unbalance means there is more weight toward the trailing edge of one blade than the other. N per Rev vibration is a function of the number of blades within the rotor system. For example a 4 bladed system would have an inherent 4 per rev freq, a 5 bladed system, a 5 per rev and so on. Associated with these, are the harmonics of the N per – the N-1 & N+1 rev vibes.
 
[ It is difficult to visualize masses above and below the teeter bolt being forced into a 2/rev circle. ]
C. Beaty can you explain the two rev circle more.
 
Except in a vertical descent where cyclic flapping is zero, mass above and the teeter bolt is forced to make 2 complete revolutions for each 1 revolution of the rotor.

It’s easy to visualize with the aid of a scale model made from welding rod.
 

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I made a model rotor and hub from tube, exaggerated the cone angle to 45 degrees and bolted the hub to a shed post so the rotor tips would scribe a circle on the concrete floor.
The blow back angle was exaggerated to about 20 degrees.
When I turned the rotor I saw that the tips followed a path that had two waves per rev. When in the broadside position the tips were 0.75" off the floor. When the rotor was in the for-aft position the tips were on the floor.
It also looks like the centre of lift would be moving from the hub axis to the tip path axis and back twice per rev.

I could also see the mass above and below making two revolutions.

What I did see that may be causing the stick shake is that the rotor tip at the rear section of the rotor disc must travel at a much higher velocity than the tip at the front of the disc.

The higher the coning angle and the steeper the blow back angle, the greater the difference is in tip velocity between for and aft blade tips.
 
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