0941

Item 0941

OTHER: Flight Dynamics - General - Pitch-Flap Coupling; (delta3, δ₃), (k_pβ)

Positive pitch-flap acts as an aerodynamic spring on the flapping motion.

	.		Unlike A/, B/ and C/, this delta3 is in the blade, not the rotorhub. For information click on web link below.
A/ By flap hinge geometry	B/ By control system geometry	C/ By twisted spline geometry	D/ By blade ply bias layup

Re: Twin Main Rotors:

A and D have a pitch-lead coupling (δ3), and this will likely cause a rotor-rotor oscellation.

Pitch - Flap (teeter) Coupling: (Applies to both Method A/ and B/)

Change in blade pitch [θ] equals tangent of delta3 angle times blade flap angle (positive upwards).

Δθ = -Kp * β where Kp = tan(δ3)

Positive for flap up, pitch down

Positive delta3 is actually the reduction of pitch (feathering) when the blade flaps up.

Method 'A/' has an in plane (lead-lag) component (see next section). Method 'B/' does not.

Delta3 can also be applied to Pitch-Cone coupling.

Lead - Flap (teeter) Coupling: (Applies to Method A/ only)

See: DESIGN: SynchroLite ~ Rotor - Disk - Lead-Flap Coupling, for Intermeshing Helicopter This page comes up with 2 different values and one is approximately twice the other. This may explain the problem.

Since there is no lag, the lead may have to be increased by 2 times. Is this a problem?

I read somewhere that when balancing blades, the tips should never lead. If so. Is the above a problem.

Pitch - Flap (teeter) Coupling: (Applies to Method B/ only)

The position of the collective will affect the relationship between the pitch and the flap.

Pitch - Flap (teeter) Coupling: (Applies to Method C/ only)

Description of Operation: The primary mechanism is a slip-fit spline, which has a small twist [δ3]. The blade grip is connected to a torque tube by a universal joint. The universal joint is located below the teetering hinge (undersling). When the blade flaps, it moves the torque-tube axially within the outer spline and this movement causes the torque-tube to rotate. This rotation of the torque-tube results in the blade rotating about its feathering hinge and thereby changing its pitch.

Positive flap (upward) results in a decrease in the pitch and a negative flap results in an increase in the pitch.

Application: For use in offset teetering rotors. See;.Dragonfly ~ Control - Flight - Spider - Layout

On this type of pitch-flap coupling the angle of the spline's twist can probable be considered to be delta3 [δ3]. Look further into this some time.

Change in blade pitch [θ] equals the flap [β] from the precone angle [sin(β_P)], times the virtual undersling [d_u] times the spline's twist [tan(δ3)]

Δθ = sin(β - β_P ) * d_u* tan(δ3) Check to make sure this is correct. If the change in pitch was very large then the rotational change by the universal joint would also have to be included.

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Note: It appears highly likely that the universal joint, by itself, will insert a small amount of delta3, if mounted in the correct radial position. It looks like it will pull 0.438º of pitch for 10º of upward and downward flap. It will pull about 1º of pitch for a flap of 15º. See the link to http://klein-gelenkwellen.de/technik/technis5e.htm on web page Joint.

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To my knowledge, delta3 by twisted spline geometry has never been considered before.

Additional Information:

To calculate values see; FORM: Rotor - Disk - Delta3

More information on Pitch-Flap Coupling [delta3] is available in 'Helicopter Theory' by Wayne Johnson page 238.

Related Information:

DESIGN: SynchroLite ~ Rotor - Disk - Lead-Lag for Intermeshing Helicopter

OTHER: Flight Dynamic - General - Phase Lag

Best Source of Outside Information:

[Source ~ HT p.238], [Source ~ HT p.625]

Additional Information, but unrelated to Intermeshing Helicopters:

Tail Rotors:

Some tail-rotors use Flap Hinge Geometry and some use Control System Geometry.

Most, tail rotors that incorporate delta3 appear to use an angle of +45º. At +45-degrees, pitch change and flapping cancel each other out thereby minimizing a tail rotor's desire to teeter (flap).

Lu says that; "On two blade tail rotors the delta hinge is offset by 60 degrees". 45-degrees will eliminate any pitch change caused by flapping. 60-degrees (negative pitch-coupling) will put in an opposing pitch, which will drive the blade back to the "home position'.

"Delta 3 is used in almost all tail rotors as a quick way to wash out disymetry of lift forces, which would harm tail rotors as speed changed. With 45 degrees of delta 3, the tail rotor flaps a little as the blade sweeps up wind, and this flapping washes out the extra lift the blade was producing." ~ from N.L.

"The sign of the feedback influences the phase of the response, and large negative pitch-flap coupling does have an adverse effect on the flapping stability. It is common to use 45º delta3 on tail rotors to reduce the transient and steady state flapping relative to the shaft. ~ [Source ~ HT p.243]

This page by Bell mentions the NEGATIVE 30º delta3 on its 407 & other tail-rotors. http://www.bellhelicopter.textron.com/en/support/pdf/rb/rb_mar04.pdf ~ Mentioned by Al Hammer.

Main Rotors:

Kaman uses Flap Hinge Geometry. For more information see; DESIGN: SynchroLite ~ Rotor - Disk - Lead-Flap Coupling, for Intermeshing Helicopter

Robinson uses Control System Geometry. For more information see; DESIGN: SynchroLite - Rotor - Hub ~ Robinson

Sketch of Pitch Angle:

The graph is based on the Robinson R-22. ~ delta₃ angle = 18º, Maximum flap = 10º. delta₃pitch change = -β* tan(δ3) = -10* 0.325 = -3.25Ί

The following is a plot of a basic teetering rotor and one with a delta3 of 18º. The 18º was selected because it is the Robinson's angle. Please note that phase-lag is not considered until the end.

Description of above Planes

Some considerations re this graph;

The [control plane] and the [tip path plane w/o delta3] are representative of a basic teetering rotor. I.e. a 1 to 1 ratio between pitch and flap.
The [control plane] plus the remaining three lines are representative of a delta3 rotor.

The [delta3 pitch change] is derived from [tip path plane w/o delta3] times an 18º delta3.
The [no-feathering plane] is the sum of the [control plane] and the [delta3 pitch change].
The [tip path plane w/ delta3] is based on this line reaching 90º azimuth at the flap angle where the [no-feathering plane] pitch changes from positive to negative.

There is an interdependency between the last three lines, and this will change their true location from that which is depicted in the graph. However, I believe that the [no-feathering plane] will remain on the same side of the [control plane], and that the [tip path plane w/ delta3] will remain on the same side of the [tip path plane w/o delta3].

Should this be correct, then two conclusions can be drawn from the graph.
1/ The blade pitch will reach 0º before the blade reaches 90º azimuth. I.e. a phase angle of less than 90º is required.
2/ The blade pitch will reach 90º azimuth before all the flap has been pulled out of it. I.e. additional rotations will be required before the [control plane] and the [tip path plane w/ delta3] are coplanar.

Miscellaneous:

The pitch-flap coupling introduces an aerodynamic spring that increases the effective natural frequency of the flap motion.

Where did this statement come from?

Could it be applying to delta3 on an offset flapping hinge?
Would it be valid for delta3 angles of +45º and greater, such as used on tail rotors?
Would it be valid for negative delta3?
Would a negative delta3 be somewhat analogous to an offset flapping hinge where the flapping hinge is on the opposite side of the mast from its blade?
Can a negative delta3 and the above line's offset flapping hinge be referred to as an aerodynamic spring? Since they do not want to 'spring back'.

Pitch-flap coupling, delta3, plays an important role in reducing steady and transient blade flapping.

Ref. transient blade flapping response to a gust load.

Pitch-flap coupling changes the rotor dynamics by changing the phase lag of the blade flapping to blade pitch,

The phase angle of the Lynx and Bo105 main rotors is about 75º - 80º.

Pitch Change Verses Flap Change:

Delta3 angle of +0º. ~ Pitch angle is not changed.
Delta3 angle of +1º to +44º. ~ Pitch angle change is less than flap angle.
Delta3 angle of +45º. ~ Pitch angle change equals flap angle.
Delta3 angle between +46º and +89º. ~ Pitch angle change is greater than flap angle.

Positive and Negative delta3:

"Note that positive coupling δ3 >0 represents negative feedback, decreasing the blade pitch for a flap increase." ~ [Source ~ HT p.239]. This is the common usage.

Re tandem configuration "..speed stability ...... differential pitch-flap coupling (positive on the front rotor and negative on the rear rotor)." ~ [Source ~ HT p.850] This implies that positive delta3 causes an increase of the flap to decrease the pitch and negative delta3 causes an increase of the flap to increase the pitch. In other words, if the reference flapping or teetering hinge is normal to the span of the blade, then rotating this hinge in the opposite direction to that of the rotor's rotation will result in positive delta3. Conversely, rotating this hinge in the same direction as that of the rotor's rotation will result in negative delta3.

To me, having upward flap increases the pitch sounds scary, since this increase in pitch will want to increase the flap even more.

Method D/: Delta3 by the Bias and Thread Material in the Construction of a Composite Blade.

Video of blade flexure during operation

Initial Thinking:

This method of delta3 is probably advantageous for fully articulated rotors and the so-called hingeless rotors. In addition, it would appear that this method might be attractive for the teetering rotor as well. It may not be applicable to the CVJ w/ HS rotor since the constant velocity joint should eliminate almost all cyclical Corollas. It is not applicable to an 'Absolutely' Rigid Rotor, because these blades have no significant flexure.

The spar and perhaps the outer skin of a composite blade could consist of bias thread. The cloth will probably have elastic (fiberglass) thread in one direction and non-elastic (carbon) thread in the other direction. This will result in any normal-plane bending along the span of the blade to remove some pitch outboard of the bending. All blade elements outboard of the so-called virtual hinge(s) to have their pitch decreased as they flap upward. Conversely, their pitch will increase as the flap downward.

Considering the large flapping movements of very flexible helicopter blades, and perhaps the possibility that the blade may have a 'valley' and a 'hill' at different locations on its span at the same time. The delta3 by ply lay-up just inboard of this 'valley', at the downward bend, will want to reduce the 'valley'. In addition, the delta3 by ply lay-up just inboard of this 'hill', at the upward bend, will want to reduce the 'hill'. All of this is done at the locations of the out-of-plane movements. This may reduce the magnitude of the moment reaching the hub.

This method D/will also create a lead-flap coupling. This will result in some in-plane bending (actually a curling of the blade). This might have an interrelationship with the Coriolis effect. It may counter the cyclical Coriolis during the first halve of the cyclical Coriolis (good?) and add to the cyclical Coriolis during the second half of the cyclical Coriolis (bad?). For more information on this cyclical Coriolis see; OTHER: Flight Dynamics - General - Lead-Flap Coupling, for Intermeshing Rotors (kpβ) & Pitch-Lead Coupling (δ4)

Perhaps this method might be applicable to a simplistic form of slow forward speed Advancing Blade Concept. The high lift on the advancing blades will pull some pitch out of them and the reduced lift on the retreating blades will put more pitch into them.

This method might be very applicable to the SynchroLite and the Dragonfly. This is in reference to the Hub - 2-blade teetering, Hub - 3-blade CVJ w/ hub spring, and Offset Teetering Rotor. This is because a gust near the tip of the blade might be reacted to faster than by the other types of delta3.

Of particular benefit to intermeshing helicopters would be at the azimuth at the rear of the craft where the blade tips close on each other.

PPRuNe, Mart ~ "If you look at the wings of a commercial liner you can actually see the tips reduce AOA when they flex up."

PPRuNe, Mart ~ The Sikorsky S76 blades incorporate this.

Possible disadvantage: Method D may not be beneficial for twin main-rotor helicopters because the pitch-lead component will add to the rotor-rotor oscillation.

Related Web Pages:

Delta3 and Phase Angle (to be reviewed, revised and split into two pages)

OTHER: Flight Dynamics - Rotor Hub

Year 2000 thread on the subject of delta3; B185 Supplement.html

Delta3 and the Gyrocopter:
Initial thought not valid.

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Last Revised: November 23, 2007