B274

OTHER: Mechanics - Joint

Additional information on mechanical will be found interwoven with specific information in the 'Rotor' and 'Power Train' sections of the various craft noted at the bottom of this page.

The Universal joint, the Hooke's joint and the Cardan joint are three names for the same devise. The word 'Gimbal' also refers to this devise. However, it appears that some people may be applying the word 'Gimbal' to the Constant Velocity Joint.

Topics:

		Topic:		Location:
		Cyclical Coriolis Effect & Hooke's Joint Effect		this page
		Hooke's Joint Effect		this page
		Universal Joint Effect		this page
		Constant Velocity Joint		1339

Q. What is the difference between constant velocity joints and universal joints?

A. The difference between a constant velocity joint and a Universal joint is in the theory of operation. A single constant velocity joint transmits the same speed from input to output regardless of the misalignment. A single universal joint with a constant input speed will have changing output speed due to angular velocity changes inherent to a universal joint. When a second joint is put in phase with the first joint, the velocity change is countered from joint to joint so the input speed at the first joint will be the same as the output speed after the second joint. Constant velocity joints are usually much larger than the equivalent universal joint and are generally used in the automotive industry, not in industrial applications.

Hooke's Joint Effect in Respect to the Semi Rigid (teetering) Rotor:

Conditions: Azimuth 0 is aft. Rotation is CCW. Disk is tipped down at front.

The following results are as viewed from the perspective of the mast's plane.

Azimuth:	Teetering:	Feathering:
0º	Highest	Neutral pitch
90º	Max. downward velocity	Minimum pitch
180º	Lowest	Neutral pitch
270º	Max. upward velocity	Maximum pitch

Analogy with Hooke's (Universal) Joint:

Using the Hooke's joint with the shafts vertical.

The upper shaft represents the blades.
The X-yoke represents the rotor's yoke.
The lower shaft represents the mast.

The hinge between 1 & 2 is the feathering hinge and the hinge between 2 & 3 is the teetering hinge.

The axis of the upper shaft represents the no-feathering-plane axis.
The axis of the yoke represents the tip-path-plane axis.
The axis of the lower shaft represents the shaft (mast) axis.

The feathering hinge axis is always in the plane of the tip path.

The teetering hinge axis is always in the plane of the shaft (mast).

Analogy with Knuckle Joint:

This represents the 'mast - teetering hinge - yoke' portion of the rotor. [same as universal except that item 1 is excluded] It is useful when considering the rotation of the rotor mass in relationship to the rotation of the shaft (mast).

Answer:

It appears that the association between 'Hooke's Joint Effect' and the teetering hinge comes from the Bell 47 rotor hub which had two hinges, located at 90 to each other. In the Bell 206 the ring was not used so that there now was only one hinge, the teetering hinge, but the expression was retained.

Coriolis Effect:

This is applicable to a change in the coning angle. It is also applicable to teetering, when viewed from the hub's plane.

Hooke's Joint Effect in Respect to Rigid and Fully Articulated Heads:

Hooke's 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. ~ from Imabell on PPRuNe

This a different explanation of the Hooke's Joint Effect form the one above.

Universal Joint Kinematics:

	β	Deflection angle of joint (probably same as teeter)
	ω	Angular velocity
	α	Twist angle (probably same as azimuth)
	Δ α_max	Max. difference in twist angle.
	subscript ₁	Drive shaft
	subscript ₂	Driven shaft

Algorithms and Notes for Driven Shaft:
α₂ = arc tan (tan(α₁) / cos(β))

Δ α_max2= arc tan((1-cos(β)) / (2 * root(cos(β))))

The above 2 algorithms are from: http://klein-gelenkwellen.de/technik/technis5e.htm

The maximum difference in twist angle occurs 4 times per revolution, at 45/135/225/315 degrees. This difference alternates between positive and negative on each of the above four occurrences. This might mean that the total amount of lead-lag in the yoke will be two times the value obtained from the second algorithm above.

For doing calculations see: FORM: Rotor - Disk - Delta3

For additional information see; [RW p.154]

Cyclical Coriolis Effect & Hooke's Joint Effect:

Could be referred to by both names, this could depend upon the point of view. Assume that the tip path plane's axis is at an angle to the mast's axis. Assume also that each blade has a large black dot painted on it, at the CG. It is a given that since the two axis are not in line, if mast's axis has a constant rotational velocity then the disk's axis must be undergoing rotational acceleration and deceleration, twice per rotation.

If the 'point of view' is along the mast's axis, then the two black dots would appear to be moving in an elliptical path and they would be experiencing acceleration and deceleration. This could be referred to as cyclical Coriolis Effect (or to be more technically correct - Coriolis Acceleration/Deceleration Effect or Cyclical Coriolis).

- alternatively -

If the 'point of view' is along the disk's axis, then the two black dots would be moving in an circular path but the disk would be experiencing acceleration and deceleration. This could be referred to as Knuckle Joint Effect (or the possibly technically incorrect - Hooke's Joint Effect). The reason for using the term knuckle joint is that it has a single pivot, as does the teetering hinge, whereas the universal (formally known as Cardan or Hooke's coupling) joint has two pivots.

It appears that the analogy with a Hooke's joint is used since the feathering hinge is included in the operational consideration. [Source ~ RW p.306]

My personal preference is to refer to it as a Knuckle Joint Effect.

For additional information see: OTHER: Flight Dynamics - General - Lead-Flap Coupling for Intermeshing Rotors

For additional information see: OTHER: Flight Dynamics - General - Lead-Lag

Additional Outside Information:

For Coriolis [See ~ RW, cp. 57]

For Hooke's Joint [See ~ RW, p. 154] & [See ~ MH, p. 2239]

There is a booklet called 'Mechanical Design and Description - Rotary Wing Aircraft Handbooks And History - Vol. 8'; dated 1954. It consists of 273 pages of information on the mechanical design and mechanical description of early helicopters.

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Last Revised: February 29, 2008