Hooke's joint
Guest
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To: Arm ot the window;
The last few posts may have provided you with an answer; but if not, here goes.
The 2 blades form a shallow 'V' of about 3-degrees each off the horizontal.
The teetering hinge is 2" above the bottom of the 'V' and this 2" is called the undersling.
Let's say that the tip of each blade is 4" above the bottom of the 'V'.
Lets also say that the GofG is half way out each blade.
At half way out each blade, the CofGs will be 2" above the bottom of the 'V'.
The two GofG's and the teetering hinge will be in a line since they are all at the same 2" elevation.
The blade tips are another 2" higher at 4" elevation.
As the rotor teeters; one GofG will move UP AND IN toward the mast's centerline and the other GofG will move DOWN AND IN towards the mast's centerline.
Meanwhile, unlike the CofG's, one of the tips will move UP AND IN toward the mast's centerline and the other tip will move DOWN AND OUT away from the mast's centerline.
If this is hard to visualize, then just sketch it out, making sure that the CofG-teetering_hinge-GofG line is at right angles to the line representing the centerline of the mast. This way you will see that the CofG's can only swing inward.
The mass of both blades is moving inward toward the mast an equal amount, therefor(e) because of the conservation of angular momentum (Coriolis or Hookes Joint Effect ~ your pick) there is no lead-lag between the two blades.
To: 212man;
Just a bit of useless trivia.
The universal joint was originally known as a Cardan or Hooke's coupling.
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Project: UniCopter.com
The last few posts may have provided you with an answer; but if not, here goes.
The 2 blades form a shallow 'V' of about 3-degrees each off the horizontal.
The teetering hinge is 2" above the bottom of the 'V' and this 2" is called the undersling.
Let's say that the tip of each blade is 4" above the bottom of the 'V'.
Lets also say that the GofG is half way out each blade.
At half way out each blade, the CofGs will be 2" above the bottom of the 'V'.
The two GofG's and the teetering hinge will be in a line since they are all at the same 2" elevation.
The blade tips are another 2" higher at 4" elevation.
As the rotor teeters; one GofG will move UP AND IN toward the mast's centerline and the other GofG will move DOWN AND IN towards the mast's centerline.
Meanwhile, unlike the CofG's, one of the tips will move UP AND IN toward the mast's centerline and the other tip will move DOWN AND OUT away from the mast's centerline.
If this is hard to visualize, then just sketch it out, making sure that the CofG-teetering_hinge-GofG line is at right angles to the line representing the centerline of the mast. This way you will see that the CofG's can only swing inward.
The mass of both blades is moving inward toward the mast an equal amount, therefor(e) because of the conservation of angular momentum (Coriolis or Hookes Joint Effect ~ your pick) there is no lead-lag between the two blades.
To: 212man;
Just a bit of useless trivia.
The universal joint was originally known as a Cardan or Hooke's coupling.
------------------
Project: UniCopter.com
Guest
Posts: n/a
the c of g of the blades on a teetering system move in toward the centre of the disc and outboard to the tip as the blades flap up and down. this causes the blades to accelerate and decelerate. this is called coriolis effect.
this occurs most noticeably in the flare for an increase in speed and in a bunt or pushover for a decrease in speed.
underslinging the head reduces the stresses on the head due to hunting for the centre of pressure by the blades again as they accelerate and decelerate nomally in forward flight. underslinging is one of those great little inventions we would all like to have come up with, like flapping hinges and delta 3 hinges.
hookes joint effect describes a theoretical axis of rotation that occurs mainly on rigid and fully articulated heads. as the hub is fixed firmly to the mast and the blades are free to flap and drag individually they are at different phases of acceleration and deceleration at exactly the same time. they are also flapping at different rates at the same time as they are in different positions around the disc, unlike the teetering head where everything is directly opposing. when one blade flaps up the other blade flaps down, when one blade speeds up the other does exactly the opposite.
the result of these differing phases on the blades means that at different positions on the disc that the blade tips are not equidistant from the mast axis, the mathematical result is a new theoretical centre of rotation somewhere in space not too far from the mechanical centre.
this point may in fact move about due to unequal damper condition and other factors.
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your too high,your too low, your too fast your too slow
this occurs most noticeably in the flare for an increase in speed and in a bunt or pushover for a decrease in speed.
underslinging the head reduces the stresses on the head due to hunting for the centre of pressure by the blades again as they accelerate and decelerate nomally in forward flight. underslinging is one of those great little inventions we would all like to have come up with, like flapping hinges and delta 3 hinges.
hookes joint effect describes a theoretical axis of rotation that occurs mainly on rigid and fully articulated heads. as the hub is fixed firmly to the mast and the blades are free to flap and drag individually they are at different phases of acceleration and deceleration at exactly the same time. they are also flapping at different rates at the same time as they are in different positions around the disc, unlike the teetering head where everything is directly opposing. when one blade flaps up the other blade flaps down, when one blade speeds up the other does exactly the opposite.
the result of these differing phases on the blades means that at different positions on the disc that the blade tips are not equidistant from the mast axis, the mathematical result is a new theoretical centre of rotation somewhere in space not too far from the mechanical centre.
this point may in fact move about due to unequal damper condition and other factors.
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your too high,your too low, your too fast your too slow
Guest
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Thanks again for your thoughtful replies.
Imabell, I'd have thought that airflow changes would contribute to flare effect much more than C of G movement, especially if what Dave Jackson says about the C of G movements of a 2-bladed underslung teetering head design is correct.
For a bunt, for instance, the C of Gs presumably move in when the disc is tilted forwards, but the rotor slows down.
(or should that be Cs of G?!)
[This message has been edited by Arm out the window (edited 26 June 2001).]
[This message has been edited by Arm out the window (edited 26 June 2001).]
Imabell, I'd have thought that airflow changes would contribute to flare effect much more than C of G movement, especially if what Dave Jackson says about the C of G movements of a 2-bladed underslung teetering head design is correct.
For a bunt, for instance, the C of Gs presumably move in when the disc is tilted forwards, but the rotor slows down.
(or should that be Cs of G?!)
[This message has been edited by Arm out the window (edited 26 June 2001).]
[This message has been edited by Arm out the window (edited 26 June 2001).]
Guest
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To: Arm out the window;
What Imabell is saying is correct. My posts are about the teetering of a 2-blade rotor. He is talking about a separate but related subject, the changes in the coning angle.
All rotors will cone [except for the (theoretical) UniCopter
]. The pre-cone in a teetering hub, of approximately 3-degrees, is the manufacture's estimate of what the average coning angle will be.
As Imabell says;
During a flare; 1/ the load on the rotor disk is increased, 2/ all the blades and/or flapping/coning hinges bend upward, 3/ this causes all the blades' CofGs to move inward, 4/ this causes the rotor to accelerate (Coriolis).
During an unloading of the rotor disk; 1/ the centrifugal force will try to take the conning angle of all the blades to zero, 2/ the CofGs will move outward, 3/ this causes the rotor to decelerate (Coriolis).
To: Imabell;
Your explanation of the Hooke's Joint Effect is different from what my understanding is/was, but yours certainly makes sense. Perhaps it has been used over time to describe two different activities, one related to the teetering rotor (Bell 47) and the other related to the rigid and fully articulated rotor's lead-lag & flapping hinges.
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Dave J. UniCopter.com
What Imabell is saying is correct. My posts are about the teetering of a 2-blade rotor. He is talking about a separate but related subject, the changes in the coning angle.
All rotors will cone [except for the (theoretical) UniCopter
]. The pre-cone in a teetering hub, of approximately 3-degrees, is the manufacture's estimate of what the average coning angle will be.As Imabell says;
During a flare; 1/ the load on the rotor disk is increased, 2/ all the blades and/or flapping/coning hinges bend upward, 3/ this causes all the blades' CofGs to move inward, 4/ this causes the rotor to accelerate (Coriolis).
During an unloading of the rotor disk; 1/ the centrifugal force will try to take the conning angle of all the blades to zero, 2/ the CofGs will move outward, 3/ this causes the rotor to decelerate (Coriolis).
To: Imabell;
Your explanation of the Hooke's Joint Effect is different from what my understanding is/was, but yours certainly makes sense. Perhaps it has been used over time to describe two different activities, one related to the teetering rotor (Bell 47) and the other related to the rigid and fully articulated rotor's lead-lag & flapping hinges.
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Dave J. UniCopter.com
Guest
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to arm out the window
there are valid arguments to a lot of what is thought of as gospel in aviation.
remember that it is a theory of flight. the vectors that are drawn to show the foces at work are a mass of variables.
we know why lift is produced on an aicraft wing that is an aerofoil shape care of that great bloke bernouli and his fluid dynamics but most light helicopter blades are symmetrical to reduce centre of pressure problems so isaac newtons law makes just as much sense when applied to symmetrical helicopter rotor blades. equal and opposite and all that.
why for instance do we flare at the bottom of an autorotative descent?
it is primarily to reduce our rate of descent and the secondary effect is reduction of forward airspeed.
how does it do that? most would say that the angle of attack is increased and the thrust vector is tilted backwards slowing us down.
and thats it, is it?
we know that due to coriolis effect that the blades will spool up in the flare, that is why we carry out forward speed autos', to conserve rotor rpm till it's needed at the bottom then convert the forward speed to more rotor rpm.
as we are slowing down due to the flare our rate of descent is also slowing , then obviously our rate of descent airflow is decreasing therefore our angle of attack is also decreasing.
as the speed of the blades is increasing due to our mate coriolis the angle of attack on the blades is being reduced even further. as a rotor blade accelerates it will flap up inducing an airflow from above reducing the angle of attack. and we still have the collective on the floor.
the change in the angle of attack during the flare is minimal and then two actions take place immediately that constantly reduce it till pitch is pulled.
never stop searching
just something else to ponder.
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your too high,your too low, your too fast your too slow
there are valid arguments to a lot of what is thought of as gospel in aviation.
remember that it is a theory of flight. the vectors that are drawn to show the foces at work are a mass of variables.
we know why lift is produced on an aicraft wing that is an aerofoil shape care of that great bloke bernouli and his fluid dynamics but most light helicopter blades are symmetrical to reduce centre of pressure problems so isaac newtons law makes just as much sense when applied to symmetrical helicopter rotor blades. equal and opposite and all that.
why for instance do we flare at the bottom of an autorotative descent?
it is primarily to reduce our rate of descent and the secondary effect is reduction of forward airspeed.
how does it do that? most would say that the angle of attack is increased and the thrust vector is tilted backwards slowing us down.
and thats it, is it?
we know that due to coriolis effect that the blades will spool up in the flare, that is why we carry out forward speed autos', to conserve rotor rpm till it's needed at the bottom then convert the forward speed to more rotor rpm.
as we are slowing down due to the flare our rate of descent is also slowing , then obviously our rate of descent airflow is decreasing therefore our angle of attack is also decreasing.
as the speed of the blades is increasing due to our mate coriolis the angle of attack on the blades is being reduced even further. as a rotor blade accelerates it will flap up inducing an airflow from above reducing the angle of attack. and we still have the collective on the floor.
the change in the angle of attack during the flare is minimal and then two actions take place immediately that constantly reduce it till pitch is pulled.
never stop searching
just something else to ponder.
------------------
your too high,your too low, your too fast your too slow
Guest
Posts: n/a
to dave jackson
i have never actually seen hookes joint effect related to a teetering system it is usually only related to rotor systems that have three or more blades and articulated.
the concept of the teetering head rather than flapping hinges on each blade as juan de la cierva pioneered {and frank now uses) was a leap forward in helicopter flight back in those days.
the gimbal ring is attached to the mast but you can't attatch the blades to the gimbal
because the hunting stresses would fracture the grips in no time.
the underslung yoke with the grips attached at right anles to the gimbal teeter bearings allows the yoke to rock back and forth.
as the blades are rotating at six times a second approx. the hunting factor is minor and a small amount of rocking of the yoke and teetering of the gimbal ends up as a small twisting motion that alleviates all stress problems.
all very interesting
i have never actually seen hookes joint effect related to a teetering system it is usually only related to rotor systems that have three or more blades and articulated.
the concept of the teetering head rather than flapping hinges on each blade as juan de la cierva pioneered {and frank now uses) was a leap forward in helicopter flight back in those days.
the gimbal ring is attached to the mast but you can't attatch the blades to the gimbal
because the hunting stresses would fracture the grips in no time.
the underslung yoke with the grips attached at right anles to the gimbal teeter bearings allows the yoke to rock back and forth.
as the blades are rotating at six times a second approx. the hunting factor is minor and a small amount of rocking of the yoke and teetering of the gimbal ends up as a small twisting motion that alleviates all stress problems.
all very interesting
Guest
Posts: n/a
Imabell, I agree with most of what you say, except the part about the angle of attack changes in the flare being minimal.
I always thought (open to correction though!) that it happens like this:
As you commence and develop the flare, the aircraft's attitude is raised significantly with respect to the relative airflow.
For example, if you fly level at a highish speed and enter autorotation, you can maintain your height by trading off speed. The flight path is essentially straight, but as the attitude goes from level-ish to quite nose up, there must be a reasonably big change in the angle at which the airflow strikes the disc (coming more and more from the bottom, so to speak).
You can maintain rotor rpm as you do this, and as the Nr is essentially staying constant, the coning angle should also stay the same. What then is maintaining your Nr?
I say it is the changing angle of the relative airflow with respect to the disc which allows the total reaction to tilt more and more forward, maintaining autorotative force.
Therefore, I don't think that conservation of angular momentum is playing such a big part here as airflow is.
Could be total rubbish I'm talking, of course!
I always thought (open to correction though!) that it happens like this:
As you commence and develop the flare, the aircraft's attitude is raised significantly with respect to the relative airflow.
For example, if you fly level at a highish speed and enter autorotation, you can maintain your height by trading off speed. The flight path is essentially straight, but as the attitude goes from level-ish to quite nose up, there must be a reasonably big change in the angle at which the airflow strikes the disc (coming more and more from the bottom, so to speak).
You can maintain rotor rpm as you do this, and as the Nr is essentially staying constant, the coning angle should also stay the same. What then is maintaining your Nr?
I say it is the changing angle of the relative airflow with respect to the disc which allows the total reaction to tilt more and more forward, maintaining autorotative force.
Therefore, I don't think that conservation of angular momentum is playing such a big part here as airflow is.
Could be total rubbish I'm talking, of course!
Guest
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Let me wade in here and make a fool of myself.
Hookes Joint Effect is not anything to do with blade conning.
Blade conning is the term applied to the rotor tip path plane as a whole, not the path of an individual blade (which is called flapping). It is the angle between the tip path plane and the axis of rotation.
Conservation of Angular Momentum is not Coriolis Force, although Coriolis Force is related to the theory of Conservation of Angular Momentum. (is that why the blades go the other way in France?)
The ice skater demo is accurate. As the chick moves her arms in, she is moving mass inwards, and, in accordance with the theory of conservation of angular momentum, rotational speed increases. If you flare, the helicopter pulls harder on the main rotor system as the main rotor system attempts to deccelerate the fuselage. This causes the blades to cone (as distinct from flap). Blade coning causes the CofG of each blade (regardless of blade numbers) to move toward the centre of rotation and RRPM increases. This has nothing to do with Hookes Joint Effect.
And so we return to the original question....
As blades lead, lag or flap, the CofG moves either toward or away from the center of rotation at the hub. As each blade pivots at the hub, the greatest distance the CofG can be from the hub is when the blade is exactly at right angles vertically to the rotor mast, and horizontally in plane. Accordingly, as the rotor disk will have a conning angle in powered flight as a "steady state", a flap up of the blade will cause CofG to move in, and a flap down will cause a move out until it goes past the exact right angle position. In lead and lag, it depends upon movement of the blade away from (CofG moves inward) or toward (CofG moves outward)the steady state right angle position in plane. Blades in a multibladed system can move far more independantly than a two bladed system, thus causing overall CofG to be constatntly shifting in flight.
But all of this is semantics. Now for a simple explanation: As blades lead, lag, and flap, the CofG of the blade moves in relation to the center of rotation. As each blade moves differently, the CofG balance across the rotor system is constantly changing, causing moentary out of balance conditions and the resulting rotor vibration through the airframe. This is known as Hookes Joint Effect. To counter this effect, various systems have been employed. Sikorsky have used a Bifilar system of weights, the BK-117 has pendulum weights on each blade, etc. These systems are designed to react to the harmonics caused by Hookes, shift position and thus readjust the overall CofG of the system to reduce/minimise vibrations.
Hope this helps Arm out window.
My Helmet is now on fire.....aaagggghh
Hookes Joint Effect is not anything to do with blade conning.
Blade conning is the term applied to the rotor tip path plane as a whole, not the path of an individual blade (which is called flapping). It is the angle between the tip path plane and the axis of rotation.
Conservation of Angular Momentum is not Coriolis Force, although Coriolis Force is related to the theory of Conservation of Angular Momentum. (is that why the blades go the other way in France?)
The ice skater demo is accurate. As the chick moves her arms in, she is moving mass inwards, and, in accordance with the theory of conservation of angular momentum, rotational speed increases. If you flare, the helicopter pulls harder on the main rotor system as the main rotor system attempts to deccelerate the fuselage. This causes the blades to cone (as distinct from flap). Blade coning causes the CofG of each blade (regardless of blade numbers) to move toward the centre of rotation and RRPM increases. This has nothing to do with Hookes Joint Effect.
And so we return to the original question....
As blades lead, lag or flap, the CofG moves either toward or away from the center of rotation at the hub. As each blade pivots at the hub, the greatest distance the CofG can be from the hub is when the blade is exactly at right angles vertically to the rotor mast, and horizontally in plane. Accordingly, as the rotor disk will have a conning angle in powered flight as a "steady state", a flap up of the blade will cause CofG to move in, and a flap down will cause a move out until it goes past the exact right angle position. In lead and lag, it depends upon movement of the blade away from (CofG moves inward) or toward (CofG moves outward)the steady state right angle position in plane. Blades in a multibladed system can move far more independantly than a two bladed system, thus causing overall CofG to be constatntly shifting in flight.
But all of this is semantics. Now for a simple explanation: As blades lead, lag, and flap, the CofG of the blade moves in relation to the center of rotation. As each blade moves differently, the CofG balance across the rotor system is constantly changing, causing moentary out of balance conditions and the resulting rotor vibration through the airframe. This is known as Hookes Joint Effect. To counter this effect, various systems have been employed. Sikorsky have used a Bifilar system of weights, the BK-117 has pendulum weights on each blade, etc. These systems are designed to react to the harmonics caused by Hookes, shift position and thus readjust the overall CofG of the system to reduce/minimise vibrations.
Hope this helps Arm out window.
My Helmet is now on fire.....aaagggghh
Guest
Posts: n/a
Absolutely, remember this is a dynamic system, the demonstration using rulers convinces the questioning tyro but leaves a seed of confusion for later in his career.
The most important part of helmets explanation is that it is the dynamic movement of the blade CofG that matters.
In an even bladed system the opposing 3 & 9 oclock blades will APPEAR to be in mirrored positions (about the longitudinal axis) BUT will have different, opposing velocities and should be examined independantly as you cannot introduce false symmetry and ignore the dynamics in the explanation. Hookes Joint Effect occurs in any head, but you may not see it. In a 2 bladed teetering head one could detect bending moments, in the Robinson you will see it, and so on.
The most important part of helmets explanation is that it is the dynamic movement of the blade CofG that matters.
In an even bladed system the opposing 3 & 9 oclock blades will APPEAR to be in mirrored positions (about the longitudinal axis) BUT will have different, opposing velocities and should be examined independantly as you cannot introduce false symmetry and ignore the dynamics in the explanation. Hookes Joint Effect occurs in any head, but you may not see it. In a 2 bladed teetering head one could detect bending moments, in the Robinson you will see it, and so on.
Guest
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Yes mate, it does help, thankyou.
There's been some lack of agreement about what is or isn't Hooke's Joint effect, but the discussion has touched on a lot of points that I hadn't considered before, so good on all you learned contributors for your input!
There's been some lack of agreement about what is or isn't Hooke's Joint effect, but the discussion has touched on a lot of points that I hadn't considered before, so good on all you learned contributors for your input!
