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A typical photograph (ψ = 290°, 54 m/s, level flight) is shown in Fig. 7.28. It was
assumed that the contributions of the first three modes were sufficient to account for
the measured blade deflection. The calculated mode shapes and their associated
frequencies are shown in Fig. 7.29.
The flapping deflection of any part of the blade would then be expressible in the
form
Z(x, ψ) = R[S1(x)φ1(ψ) + S2(x)φ2(ψ) + S3(x)φ3(ψ)]
With S1, S2 and S3 known, the generalised co-ordinates φ1, φ2, φ3 in terms of
azimuth could be determined from analysis of the photographs. The results, expressed
in terms of the displacement of the blade tip, are shown in Fig. 7.30.
It should be emphasised that the displacements are measured relative to the hub
axis. The amount of first-mode displacement which occurs, is of course, directly
dependent on the amount of cyclic pitch applied and will be such as to trim the
longitudinal and lateral moments about the hub, including the hub moments due to
blade deflection in the second and third modes.
It can be seen that the contributions of the second and third modes to the blade
deflection are quite small and would be still smaller if the first mode deflection were
measured relative to the no-feathering axis. This justifies the assumption of the rigid
blade which is used in much of helicopter analysis. Calculations show that, for the
flight case considered, neglect of the second and third modes results in only about a
7 per cent error in the hub moment.
Structural dynamics of elastic blades 277
Fig. 7.28 Typical photograph of blade in flight (hingeless Westland ‘Scout’, 53.5 m/s, ψ = 290°)
7.5 Basic features of the hingeless rotor
Many helicopters now employ hingeless rotor systems. The design of such systems
has become possible due to two main factors: the increased understanding of the
aeroelastic and dynamic hebaviour of rotor systems and the application of composite
material to critical components in the aeronautical field.
The initial development was the replacement of the conventional flapping and
lagging hinges by flexible structural elements. Such a system is normally referred to
as the semi-rigid rotor. Subsequent developments led to the totally bearingless rotor
where, in addition to the elimination of the flapping and lagging hinges, blade feathering
is accommodated by the torsional flexibility of the hub elements.
The main advantages claimed for hingeless rotors are:
278 Bramwell’s Helicopter Dynamics
1.0
0.8
0.6
0.4
0.2
0
–0.2
–0.4
–0.6
–0.8
0.2 0.4 0.6 0.8 1
S3
S1 λ1 = 1.087
r/R
S2 λ2 = 2.587 λ = 4.553
Blade deflection
Fig. 7.29 Blade-flapping mode shapes
100
50
0
–50
–100
–120
0° 90° 180° 270° ψ 360°
3rd mode
2nd mode
1st mode
Flap-mode components
(Tip deflection in mm relative to built-in coning angle)
Fig. 7.30 Modal content of blade flapwise deflection
Structural dynamics of elastic blades 279
(i) the elimination of hinges leads to a great simplification of hub design, with
consequent reduction of manufacture and maintenance costs, and also reduced
aerodynamic drag;
(ii) much greater hub moments, leading to improved control power which is virtually
independent of the level of rotor thrust, and increased angular rate damping.
Both these features contribute to an improvement in handling qualities.
In this section we shall consider only the flapping mode shapes and frequencies of
the hingeless blade and the hub moments exerted when the blade is deflected. The
problems of the various forms of intermodal coupling and the particular problem of
air resonance are considered in Chapter 9. A comprehensive review of the benefits
and problems associated with hingeless rotors has been given by Hohenemser17.
The mode shape analysis of the hingeless blade can be dealt with by the methods
described earlier in this chapter, noting that the root boundary conditions are z = 0
and dz/dx = 0, or perhaps some fixed value (‘built-in’ coning).
Typical lower mode shapes and frequencies are given in Fig. 7.31.
The first flapping frequency ratio of hingeless rotors usually lies within the range
1.08 to 1.17 and, as can be seen from Fig. 7.31, the curvature of the blade is confined
mainly to the root region, most of the outer part of the blade being almost straight.
It is this local curvature, however, when combined with a typical distribution of
bending stiffness in this region, which produces the large hub moments characteristic
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