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Society, St Louis, Mo., May 1983.
10. Staple, A. E., ‘An Evaluation of Active Control of Structural Response as a Means of Reducing
Helicopter Vibration’, Fifteenth European Rotorcraft Forum, Amsterdam, September 1989.
9
Aeroelastic and aeromechanical
behaviour
9.1 Introduction
In previous chapters, the effect on the motion of the blade of coupling between its
degrees of freedom has been ignored. For performance and stability and control
aspects, this neglect is, in general, entirely justified, but possible blade and rotor
system instabilities due to coupling must be considered.
There are also important instabilities involving coupling of rotor blade and airframe
motion, and these must also be taken into account.
Rotor blade instabilities to be considered are:
(i) main rotor pitch–lag instability;
(ii) main rotor pitch–flap flutter;
(iii) main rotor stall flutter;
(iv) main rotor blade weaving;
(v) tail rotor pitch–flap (‘umbrella mode’) instability;
(vi) main and tail rotor flap–lag instability;
(vii) tail rotor pitch–flap–lag instability.
A review of the aeroelastic problems of helicopter and V/STOL aircraft has been
given by Loewy1.
The coupled rotor blade and airframe instabilities to be considered are:
(i) ground resonance;
(ii) air resonance.
320 Bramwell’s Helicopter Dynamics
9.2 Main rotor pitch–lag instability
Although referred to as pitch–lag instability, the degrees of freedom participating in
the motion are flap and lag, with the instability arising from the presence of a
kinematic coupling between pitch and lag, or a torsional moment which twists the
blade when it is deflected in the flapping and lagging senses.
The effect of these couplings is to induce aerodynamic lift loads in response to
blade lag deflections which cause the blade to flap and the resulting Coriolis loads
induce more lag motion.
One aspect which can cause a degradation in pitch–lag stability in certain flight
conditions is the change in kinematic pitch–lag coupling as a function of steady
coning angle, steady lag deflection and impressed blade pitch due to changes in the
orientation of the pitch control system track rods. This problem will be exacerbated
by the use of short track rods.
With semi-rigid and bearingless rotors the steady flap and lag deflections tend to
be much smaller than those for articulated rotors, hence this type of instability is less
likely to occur for these types of rotor system.
Pitch–lag instability is generally experienced as a limit cycle oscillation of the
rotor blades phased in a manner which transmits a stirring motion to the airframe,
due to the oscillatory shear forces generated by the blades in the plane of rotation.
On some helicopters, this type of instability occurs only under conditions of
large amplitude forced oscillation of the blades in the lag plane (due to the Coriolis
forces generated by large amplitude cyclic flapping), so that the effectiveness of
any lag plane damper which may be present is reduced. The frequency of the
oscillation of the blades relative to the rotating hub is that of the fundamental lag
plane mode.
The first cause of coupling referred to in the first paragraph of this section may be
regarded as the α2 effect (see section 1.2), and the relationship between the blade
pitch and lagging angle is, for small angles,
Δθ = – α2ξ
The second cause of coupling can be understood with reference to Fig. 9.1. Forces
dFy and dFz are capable of exerting torques about the blade span axes when the blade
Z
Y dFz
dFy
Fig. 9.1 Blade bending deformation
Aeroelastic and aeromechanical behaviour 321
is deformed in bending. To calculate these torques, consider the moments exerted by
these force components, with reference to the projections of the deformed blade onto
the XY and XZ axes, Figs 9.2 and 9.3. The torque exerted by the sum of the elementary
forces dFy and dFz about a point P at a distance r from the axis of rotation is
L r Z Z r r Zr
F
r
r
r
r
y ( ) = – ( – ) – ( – ) d
d
d
d
d
1
1 1
1
∫[ ] 1
+ ( – ) – ( – ) d
d
d
d
d
1
1 1
1
1
r
r
z Y Y r r Yr
F
r
∫[ ] r (9.1)
Differentiating eqn 9.1 with respect to r and cancelling terms results in
d
d
= – d
d
( – ) d + d
d
( – ) d
2
2 1
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