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Old 12th Mar 2004, 05:32   #1 (permalink)
 
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Rotor Dynamics ~ Lead-Lag

There was a thread about a year ago where the subject of led-lag was discussed. I believe it was Lu who mentioned an interesting phenomena, in a 2-blade or 4-blade rotor, where the advancing blade is leading while the retreating blade is lagging. I.e. the opposing blades are not at 180-degrees to each other.


During an-mail discussion about vibration in a teetering rotors, the subject of coning angle, undersling height and high levels of thrust came about. It is obvious to many that the rotor's CG will not be aligned with the teetering hinge, nor with the centerline of the mast when; 1/ the disk is tipped forward, 2/ the rotor thrust is very high or very low, and, 3/ the opposing blades are at 0 and 180-degrees azimuth.

Under the same conditions, he ALSO felt that the rotor's CG will not be aligned with the teetering hinge, nor with the centerline of the mast, when the blades are at 90 and 270-degrees azimuth. It looks like what he is saying gives cause for the apparent lead of the advancing blade when looking at the mast plane, as Lu mentioned.

What he is saying is that; Under the above conditions the blades are subjected to a higher than normal coning angle. This means the blades will be 'higher' than normal. The blade at 90 azimuth is pitched down, therefore the large upward coning will have a forward component (movement toward the front of the craft), when view in the mast plane. The blade at 270 azimuth is pitched up, therefore the large upward coning will have a rearward component (movement toward the front of the craft), when view in the mast plane.

In other words, when looking at the two blades at 90 and 270 azimuths, from the perspective of the mast plane, these two blades will appear to not be at 180-degrees to each other. They will appear to be pointing slightly forward, just as Lu mentioned.

Any thoughts?

Error in initial post corrected in red. The word 'tip path' has been replaced by the word 'mast'.

Last edited by Dave_Jackson; 14th Mar 2004 at 08:44.
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Old 12th Mar 2004, 08:53   #2 (permalink)

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Thumbs up My mind is clouding over.

To: Jave Dackson

I'm really confused by what you said that I said but I'll try to respond.


Lead/lag or conservation of angular momentum. First letís address a fully articulated rotor system. Assume the helicopter is in a hover and there is no correction for tail rotor translation. In other words the disc is parallel to the horizon. In this case the driving and driven axes are coincident with each other. This reference to two axes will be cleared up in just a minute. In this condition there is no leading and lagging. When the pilot moves the cyclic forward the disc will tilt forward and in doing so the driven axis will tilt forward in relation to the driving axis (rotor shaft).

With this tilting of the driven axis you will get leading of the advancing blade and lagging of the retreating blade and assuming a four-blade rotor system the blades over the nose and tail will be aligned with the longitudinal axis of the helicopter. If this is the case then why doesnít the rotor system go out of balance if the blades are not evenly disposed. I donít know the answer to that question but this is what a prominent aerodynamasist wrote in his book.

Quote: If you could stand in space and look down on the rotor system with your eye aligned with the rotor mast (driving axis) the blades would look as if they were not aligned like a cross. In fact the blade over the right side (Sikorsky) would be forward of the lateral axis of the helicopter and the retreating blade would also be forward of the lateral axis.

Now move your position in space with your eye aligned with the rotating axis (driven axis) of the rotor system and the blades would appear to be 90-degrees apart. I donít know if this explains why the rotor system is not imbalanced but I donít have the brainpower to explain this phenomenon any other way. So lead and lag is allowed on this type of rotor system and on other rotor systems that are soft in plane. On rigid rotors there is also a misalignment of the two axes but there is no lead/lag hinge. The blades flex inplane.

Now we go to a semi rigid head. Bell did not want to have their blades lead and lag as this would involve beefing up their blades and rotorheads. To counter lead and lag they dropped the rotorhead in relation to the teetering hinge. This was referred to as underslinging the rotorhead.

In the case of moving the cyclic forward with the attendant tilting of the disc the rotorhead would shift rearwards on the teeter hinge and although there was a misalignment of the two axes the driven axis would intersect the driving axis. By doing this the Bell engineers eliminated the tendency to lead and lag and any lead and lag that was there would be reacted by the drag link that attached the rear of the rotor blade to the rotorhead.

Now we get to the Robinson head. This design is also underslung so as to eliminate lead and lag. However this rotorhead also has cone hinges so when the blades cone or flap about this hinge there is a misalignment of the respective drive and driven axes resulting in leading and lagging. This movement of the blade is reacted by the cone hinges with the resultant force being transmitted to the teeter bolt and down through the rotor shaft to the final reaction by the fuselage. Although Robinson purists wold reject this writer opinion it has been proven by checking the cone hinges on some R-22s and you will see that the hinges are worn elliptically.

Here is another little known fact and I may get the terminology screwed up but here goes. Since it is very difficult to get the CP and the spanwise CG in perfect alignment with the pitch change axis designers will move the pitch change axis forward on each blade by as much as ľĒ in relation to the centerlines of the rotorhead. Because it is difficult to get these points in alignment the blade will bend inplane in order that the tip of the blade brings these points into alignment. This places a strain on the blade so by moving the pitch change axis ľĒ forward this movement of the tip is eliminated.

With that being said I will patiently await correction by those of you that went to engineering school as mathematics was not taught in the fine arts department when I went to school.



Lu Zuckerman is offline  
Old 12th Mar 2004, 22:44   #3 (permalink)
 
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I though the difference between the driving and driven axes is known as Hookes Joint Effect. And that the differential lead and lag was due to the movement of the CofG of the blade system. Or maybe they're linked. Or maybe I'm getting very confused ? Nope, no maybe, I'm very confused.
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Old 14th Mar 2004, 10:26   #4 (permalink)
 
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Lu,
Quote:
"I'm really confused by what you said ....."
That makes two of us.
Sorry. I typed in the wrong plane in the original posting. It has now been corrected. Your 'prominent aerodynamist' said it properly.
________________________

Quote:
With this tilting of the driven axis you will get leading of the advancing blade and lagging of the retreating blade and assuming a four-blade rotor system the blades over the nose and tail will be aligned with the longitudinal axis of the helicopter. If this is the case then why doesnít the rotor system go out of balance if the blades are not evenly disposed. I donít know the answer to that question .....
When viewed, as mentioned by you, with your eye aligned with the mast axis, the four blades will appear to not be evenly disposed. But, the rotor's CG will remain ahead of the mast's centerline throughout the complete rotation of the rotor.

When viewed with your eye aligned with the tip path axis, the four blades will appear to be evenly disposed and they are evenly disposed. The rotor's CG will remain ahead of the mast's centerline throughout the complete rotation of the rotor.


The position of the original post in this thread is; that vibration, resulting solely from coning, may be very small, irrespective of whether the disk is tilted or note. This is because conning does not cause the rotor's CG to move about during the rotation of the rotor. This may well be factual for all types of rotor heads.
________________

Vibration due to flapping will be another story and as mentioned by Robbo Jock, rotational vibration (acceleration/deceleration) will exist because of the Hookes joint effect.
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