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Harmonic Blade Motion and Vibration

In the last section (Rotordisc and Forward Flight) we found that in forward flight, lift distribution is not symmetrical across the rotordisc. This asymetry must be compensated for by applying corrective cyclic control. We will now look at this situation in more detail and show that the blades are contineously subjected to an oscillating force due to aerodynamical lift which changes with angular phase. This oscillating force, in combination with the properties of the blades itself, leads to blade vibrations. Every helicopter suffers form this phenomenon.

In the image below, the lift function, as an element of phase angle, is derived for a helicopter in forward flight. The key formula is the Lift function  Flift = CL (1/2)  ρ V2 S, and, as can be seen, we must look at the product of the airspeed squared and the lift coefficient for each phase angle. The first 2 graphs denote V and V2 (in blue and red), while the third shows the CL for each phase angle (yellow). The CL depends upon the angle of attack, which is defined by cyclic input. Note that this is the cyclic input which must be applied by the pilot to compensate for the effects of asymmetrical lift during forward flight. The result is shown in the final graph (green), where it is seen that each blade will encounter an Flift that varies within each revolution with something that looks like a distorted sinus function. Because of this ('distorted' sinus function), several higher order harmonics (especially the third and the fifth ) exist.

There are several effects of this oscillating Flift. The first is that the blades continuously wave in and out of the (tilted) cone (blade flapping). Secondly, the Flift function drives several blade vibration modes which depend upon a number of factors, such as the damping of the blade, stiffness due to centrifugal forces, shape, etc.

As a result, the thrust that is generated to the mast is not constant, but is modulated by the flapping action and blade vibrations. This can be felt in the helicopter as vibrations. The type and precise design of the rotor head have a major influence on the extent of the vibrations that are transmitted to the shaft.

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