The Hooke's joint effect I mentioned above is more in context for forward flight, when the disc is not level, but in the hover an imbalanced rotor mast can come from a sticky damper. However, for those who are interested, here is HJ effect as I understand it:
In the hover, the C of G of a blade will be the same radius from the axis of rotation all the way round the disc. When you move the cyclic to change the disc attitude, the changed radius will make the blade lead or lag about the dragging hinge as it flaps up or down.
In forward flight, the advancing blade speeds up and moves forward on its drag hinge or bearing as it flaps up (if there isn’t a hinge, the blade will just bend). Similarly, the retreating blade moves back slightly as it starts to slow and flap down. Thus, lead and lag arise from the aerodynamic effects that cause flapping.
Image 1
The end result is that both blades (and their Centres of Gravity) lie forward of a line drawn laterally across the rotor hub as they try to reposition themselves, as well as moving towards the retreating side.
So, whenever the driving and driven axes (the shaft axis and axis of rotation) are not in line with each other, the C of G of the whole rotor system is placed forward of the mast in the direction of flight, which will give the mast a tendency to bend - one reason why the Bell 206 has a speed limit above a certain torque setting (mast bending stresses). This imbalance creates Hooke’s Joint Effect, which looks like this from the side:
Image 2
A Hooke's joint (later called a universal joint by Henry Ford) allows a drive shaft to bend whilst it is rotating - in other words, it can allow power transmission to go round corners, within certain limits, by using two rotating joints at 90° to each other. Thus, it can compensate for misalignments and relative movement between the shafts they connect. It would appear that the Hooke's Joint Effect refers to the Bell 47 which had two hinges at 90° to each other in the rotor hub, gimbal fashion, which is strange, because it ought to relate more properly to articulated heads. In other teetering heads, such as the Bell 206, the ring was not used so there was only one hinge (the teetering one) but the expression was retained.
Phil