1257

Item 1257

DESIGN: Dragonfly ~ Rotor - Disk - Lead-Lag on Offset Teetering Rotor

Drawing:

The Rod ends are horizontally 2.5" off the centerline of the yoke.

The distance between the centers of the two tie-bars is 1.3241" when the flap is +15º. This should be of no importance.

The center of the center of the two tie-bars is 0.1691" off the center of the mast when the flap is +15º. This may be of importance

Note:

It has been shown in OTHER: Rotor Concept - Offset Teetering Rotor that the tie-rod will result in the masses of all three blades being in the same plane as the virtual teetering hinge, when the disk tips, under mean thrust. This page is to show that the twin tie-rod arrangement on a 3-blade rotor will satisfy the lead-lag required for the Coriolis effect that is created by the tipping of the disk. (Hopefully).

Note: ~ The ability to eliminate the lead-lag hinges and one of the two tie-rods might be worth looked into. In the future, the actual lead-lag may be so small that an in-plane flex of the hub and blades may accommodate it. Alternatively, consider handling the lead/lag separately.

Potential Problems:

When the coning angle is under or over the 'mean' coning angle and the rotor tilts, the lead-lag will not be 'pure' as above.
In addition, the profile drag in forward flight will affect the 'pure' lead-lag.

Could the use of fiberglass thread in the tie-bars give enough elasticity to handle the 'exceptional' in-plane motion between the blades? Or, just use carbon thread and eliminate the 'exceptional' in-plane motion.

More on Lead/Lag:

Overview:

The primary source of lead lag is the flapping of the blade. This flapping cause the mass of the blade to move in and out on the control plane during its travel around the mast. As the mass moves in, the blades angular velocity will increase. Therefore, if the blades on a rotor are at different flap angles, they will want to rotate around the mast at different angular velocities. The lead/lag hinge accommodates the varying angular velocities. This action may be referred to, and calculated as, Hooke's joint. It may also be referred to, and calculated as, cyclical Coriolis. For a 2-blade teetering rotor with undersling, this lead/lag between the two blades does not occur at mean thrust, since the undersling causes the mass of both blades to move inward at the same rate during teetering.
A secondary cause is variation in profile and induced drag as the blade rotates about the mast. There is symmetry of lift about the mast but the moment arm from the flapping hinge to the center of a blade's lift will vary depending on the velocity and the angle of attack at the various blade elements. The blade's center of drag will not be exactly the same as its center of lift at all azimuths, since the blade's drag coefficient does not vary linearly with its lift coefficient. Therefore, while there is symmetry of lift there will not be symmetry of drag.

Relevant to this Page's Tri-teetering Rotor:

The virtual undersling due to the 3-rod tie-bar should balance the requirement for lead/lag, under mean thrust loads.
The interlocking of the three yokes by the two tie-bar assemblies should control the 'reduced' lead/lag motions when the rotor is subjected to thrusts that are higher or lower than the mean thrust.
The drag induced lead/lag is much smaller and it may be handled by;

Chordwise flexure in the blade.
In-plane flexure in the hub's arms, particularly if the hub is made of fiberglass.
Provision in the single vertical attachment pin between the blade and its grip.
Linear elasticity in the drag linkage.

Description of Operation:

Consists of two independent 3-bar tie-rod assemblies. One is connected to the leading arm of all three yokes and the other is connected to the trailing arm of all three yokes. If one blade leads by say 5º then the other two blades must lag by a sum of 5º. In other words, the sum of the lead/lag of all three blades is always 0º. In other, other, words, if one blade leads then one or both of the other blades must lag.

The three rods that come from the yoke housings come together at a central joint. This joint could have a stiff spring (e-glass pultruded thread) and damper on all three of the rods. The springs would maintain a centralization of the joint, if the temporary load were not excessive. The damper will, of course, dampen any motion between any one or more of these rod- joint connections.

The theory is that this spring/damper will play a negligible role in the cyclical Corollas, but will play a roll in the advancing blade lead and retreating blade lag.

The current drawing shows the two lead/lag rods per blade, which are both operating in tension.. These two 3-rod assemblies are independent of each other. The rods, as currently envisioned, are incapable of handling compression.

Ground Resonance:

On the Dragonfly's 3-blade rotors, the lead/lag tie-bars may or may not eliminate any chance of ground resonance. They do not maintain the center of the rotor's mass on the centerline of the mast.

The resultant centrifugal force in the rotor will be 23.83 / 72 = 33% of the centrifugal force of one blade; assuming that one of the blades was subjected to a 15º lead or lag. I think.

See: OTHER: Flight Dynamics - General ~ Ground Resonance

Lateral Vibration:

The Offset Teetering Hinge may reduce the cyclical Coriolis but what cyclical Coriolis there is will cause a lead/lag, which in turn will move the 3-blade rotor's center of mass off of the centerline of the mast. See; OTHER: Flight Dynamics - General - Lead-Flap Coupling, for Intermeshing Rotors (kpβ) & Pitch-Lead Coupling (δ4)

Start Up:

An in-plane flex in the mast head-to-yoke bearing would imply that all blades would lag when the rotor was initially speed up. This should not happen because the desire for ALL the blades to lag will put a three lag rods in tension and they will 'collectively' cancel each others desire to lag.

Lead/Lag Dampers:

A circular friction pad located between the lead and the lag 'Y's at the mast's centerline. This dampening is in addition to that of the bushings in the yoke's drag bearing. Note that the thrust washers on each side of the this bushing could have variable tension applied so as to set the appropriate amount of damping.

All six attachment locations at the yokes are in the same plane. The 'Y' centers of both tie-bar units will be pressing together and this is where the friction pad will go.

In addition, the lead/lag bushings will offer some damping.

Related Pages:

DESIGN: Dragonfly ~ Rotor - Disk - Flap on Offset Teetering Rotor

OTHER: Flight Dynamics - General - Lead/Lag

DESIGN: Dragonfly ~ Rotor - Hub - Tie-rod - Layout

DESIGN: SynchroLite ~ Rotor - Disk - Blade Lag Angle

OTHER: Flight Dynamics - General - Pitch-Lag Coupling, for Intermeshing Rotors

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Last Revised: June 22, 2007