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possible without major redesign, it may still be the case that the levels of vibration
experienced in flight at crew stations or passenger locations are unacceptable.
In this case, it will be necessary to have recourse to additional methods of vibration
reduction which can be incorporated with minimum disturbance to the existing design.
The absorbers described in this section are all based on the principle of the simple
sprung mass vibration absorber described and analysed in vibration text-books1. This
shows that by attaching an extra small mass by means of a spring or elastic mount to
a body undergoing forced vibration, the amplitude of vibration can be reduced to zero
(if the system is undamped, as in the ideal case), or nearly zero for small damping,
if the natural frequency of the sprung mass by itself is made to coincide with that of
the forcing frequency.
The available absorbers may be conveniently divided into two categories:
(i) those designed to reduce overall levels of vibration throughout the fuselage;
(ii) those designed to produce a reduction in vibration in a local area of the
fuselage.
Fig. 8.17 Fuselage finite element model
Rotor induced vibration 305
Passive methods which fall into the first category are:
(a) The rotor head mounted vibration absorber, of which two distinct types have
been successfully employed:
(i) The centrifugal pendulum (bifilar) absorber6 as developed by Sikorsky
(Fig. 8.18.)
In the bifilar type, the required spring stiffness is provided by centrifugal force
and hence the natural frequency of the device varies with rotor speed, as does
the forcing frequency. Thus the bifilar absorber exhibits a degree of selftuning
with respect to changes in rotor speed.
Since the natural frequency also depends on the square root of the ratio of
mounting radius to pendulum length, the small value of the latter which the
bifilar geometry confers allows a practical design which can be mounted close
in to the centre of the hub.
Figure 8.19 illustrates the basic geometry of the bifilar absorber, and also
the model from which the following equation of motion can be derived:
b γ˙˙ + (a + c) Ω2γ = 0
Fig. 8.18 Bifilar absorber fitted to Lynx rotor head
306 Bramwell’s Helicopter Dynamics
Oscillating mass, m
a b c
Ω
d
D
X
ψ
c m
a
Fig. 8.19 Geometry and model of the bifilar
where γ is the angular motion of the pendulum arm
a is the offset of the fixed pendulum point from the rotor centre of
rotation
b is the effective length of the pendulum
c is the offset of the centre of gravity of the oscillating mass from its
pivot point
d is the diameter of the pin connecting the fixed arm and the oscillating
mass
D is the diameter of the holes in the fixed arm and the oscillating mass
Thus b = D – d
It should be noted that in the model, the arm of length c always remains
parallel to the arm of length a.
For the case of small amplitudes of oscillation of the moving mass, we may
write γ˙˙ = ω2 γ
n , where ωn is the natural frequency of oscillation of the moving
mass, giving
w a c
D d
n
Ω


2
= +
–
Assuming some typical values of absorber geometry
a = 75 cm c = 6 cm D = 10 cm
then, for an absorber tuned to 3Ω forcing frequency, the pin diameter, d, is
equal to 1 cm. The equivalent pendulum length, (D – d), is equal to 9 cm, thus
confirming its very small value.
However, due to the large oscillatory amplitude necessary to provide adequate
force from a device of acceptable mass, the absorber exhibits a tuning nonlinearity
with respect to amplitude and hence flight condition. Other features
of this type of absorber include the fact that a single bifilar can only reduce the
γ
Y
Ω
b
CL of
rotation
Rotor induced vibration 307
Fig. 8.20 Flexispring absorber
magnitude of either the (b – 1)Ω or the (b + 1)Ω components in the rotating
system, the relatively low ratio of mass producing the cancelling force to the
total installed mass, and the significant maintenance requirements necessary
to maintain minimum damping of the moving mass.
Applications include the S-61 series, the Black Hawk and the S-76 Sikorsky
helicopters. The S-76 uses two bifilars tuned to 3Ω and 5Ω forcing frequencies.
(ii) The fixed frequency ‘flexispring’ absorber7 as developed by Westland (Fig. 8.20).
This type of absorber utilises glass fibre reinforced plastic for the spring
　
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本文鏈接地址：Bramwell’s Helicopter Dynamics(152)