ELASTIC
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From HELICOPTER ENGINEERING - Chapter 10 ~ R. A. Young ~ (1949)
Blade Balance.
Rotor blades having symmetrical airfoil sections are usually designed so that the aerodynamic center, the blade center of twist, and the blade center of gravity coincide (or at least are located on the zero lift chordline of the blade). Theodorsen, in his studies of flutter characteristics of rotor blades, indicates that so long as the center of gravity of the blade is located ahead of the quarter-chord point, flutter difficulties can be avoided. Blade flutter is caused by the coupled flapping and torsional forces.The primary reason for balancing rotor blades is to reduce the tendency for blade flutter. As a blade flaps, the forces acting on the blade tend to balance one another in magnitude as the blade rotates. If the center of pressure and the center of gravity do not coincide, then large fluctuating torsional moments result. This cyclic variation of twist of the blade is such that the maximum up-twist occurs near the azimuth position ψ = 90°, and the maximum down-twist occurs near an azimuth position of ψ = 270°.
The forces acting on a blade element can be seen in Figure 136 as presented in the studies (reference 54) of the coupling of twisting and flapping blade motions by Beaven and Lock. The twist in any blade element due to aerodynamic forces has been given (reference 54, p. 962) as
dθ = KT dr, (284)
where
1/K is the torsional stiffness as determined by static tests on a similar blade.The twist then becomes
θ
= (1/12) A(x4 - 4x) + ((1/3)Aμ sin ψ -(1/6)Βa)(x3 - 3x) + ((1/2)A,μ2 sin2 ψ - (1/2)C)(X2 - 2x) + θroot (285)where
(U = rΩ+μRΏsinΨ)
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Figure 136. Forces Acting on a Rotor Blade that Cause Aerodynamic Twist
It is to be noted that when the chord wise center of gravity is forward of
E (Figure 136), the outer blade sections twist downward; when the center of gravity is aft of E, the outer blade sections twist upward. Likewise, when the center of pressure is forward of E, the blade will twist upward; when the center of pressure is aft of E, the blade will twist downward.In general, the chord wise mass distribution is the chief factor that determines the flutter stability of a rotor blade, although the span wise mass distribution affects the blade stresses and flapping characteristics. A blade which is mass-balanced about the quarter-chord line will not flutter. The stabilizing influences are internal damping in bending and torsion, and, to some extent, aerodynamic damping in torsion. If there is little or no internal or aerodynamic torsional damping, then flutter is practically inevitable when the chordwise center of gravity is located aft of the aerodynamic center of the blade section.
In vertical flight or at slow forward speeds, only the relative location of the center of gravity and the center of pressure is important; the elastic axis has no bearing on the behavior so long as flapping is at a minimum. This is not true, however, at high speeds where the flapping is greater.