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0.3
0.2
0.1
0
Longitudinal
Vertical
Harmonic of rotor speed
1 2 3 4 5 6
1 2 3 4 5 6
0.6
0.5
0.4
0.3
0.2
0.1
0
Amplitude
the problem, and the beneficial effect of the rotor head fairing (often referred to as the
‘beanie’).
There can also be vibration problems due to mechanical excitation arising from
the transmission system. The effects of these sources of vibration can be held to
acceptable limits by the correct positioning of shaft whirling speeds, an adequate
standard of static and dynamic balancing of main and tail rotor hubs and transmission
shafts, and the accurate machining of gear teeth profiles.
8.9 Measurement of vibration in flight
As an example of the vibration amplitudes and forces occurring on a helicopter in
Rotor induced vibration 317
*Now the Defence Evaluation and Research Agency (DERA).
0.4
0.3
0.2
0.1
0
0.2
0.1
0
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0
10 20 30 40 50
10 20 30 40 50
10 20 30 40 50
m/s
m/s
Airspeed
m/s
lateral
Amplitude
Longitudinal
Vertical
Fig. 8.34 Vibration amplitude as a function of airspeed
Each type of symbol refers to a separate flight.
flight, we discuss below some results from measurements made at the Royal Aircraft
Establishment.* The measurements of the amplitudes and forces in three perpendicular
directions were made near the hub of a three-bladed single rotor helicopter over the
full range of flight speeds.
The results showed that the amplitude of the first-harmonic vibrations were quite
large, as can be seen from the harmonic spectrum, Fig. 8.33. However, the first
harmonic measurements showed a large amount of scatter, particularly from flight to
flight, and this indicates that the vibration was probably due to a variable amount of
rotor blade imbalance. The next largest component of vibration was that of the third
harmonic, but the amount of scatter in this case was very small, Fig. 8.34, indicating
excitation from aerodynamic and inertia forces of the complete three-bladed rotor, as
discussed in section 8.2.
The results shown in Fig. 8.34 show two features in common with those of other
helicopter vibration measurements. The first is that the level of vibration generally
increases with speed. This is to be attributed, of course, to the increasing asymmetry
of the rotor thrust loading and the corresponding increase of the harmonic content in
mm
318 Bramwell’s Helicopter Dynamics
the blade flapping. The other feature is the pronounced ‘hump’ at about 13 m/s (μ ≈
0.07). It is in this region that the influence of the trailing vortices from the blades is
greatest. As was discussed in Chapter 6, at low speeds the upwash at the front of the
rotor is quite large in relation to the forward speed, and this has the effect of keeping
the trailing vortices close to the rotor. Consequently, there will be large velocity
gradients near the front part of the rotor, giving rise to large higher harmonics in the
flapping motion. It is of interest to note that large lateral blade flapping also occurs
in this range of flight speeds, and this was found to be due to the asymmetry of the
induced-velocity distribution with respect to the lateral axis.
References
1. Thomson, W. T., Theory of vibrations with applications, New Jersey, Prentice-Hall Inc., 1981.
2. Flannelly, W. G., ‘The Dynamic Anti-Resonant Vibration Isolator’, 22nd Annual Forum of the
American Helicopter Society, Washington, May 1976.
3. Gaffey, T. M. and Balke, R. W., ‘Isolation of Rotor Induced Vibration with the Bell Focal
Pylon Nodal Beam System’, Paper 760892, SAENAEM Meeting, November 1976.
4. Done, G. T. S. and Hughes, A. D., ‘Reducing vibration by structural modification’, Vertica, 1,
31–38, 1976.
5. McCormick, C. W., ‘NASTRAN users’ manual’, NASA SP–22, 1969.
6. Paul, W. F. ‘The Main Rotor Bifilar Pendulum Vibration Absorber’, Vertiflite, February 1970.
7. White, R. W. ‘A Fixed Frequency Rotor Head Vibration Absorber Based upon GFRP Springs’,
Fifth European Rotorcraft Forum, Amsterdam, 1979.
8. Amer, K. B. and Neff, J. R., ‘Vertical-Plane Pendulum Absorbers for Minimising Helicopter
Vibratory Loads’, AHS/NASA Specialists Meeting on Rotorcraft Dynamics, Moffett Field,
Calif., February 1974.
9. Wood, E. R., Powers, R. W., Cline, J. H. and Hammond, C. E., ‘On Developing and Flight
Testing a Higher Harmonic Control System’, 39th Annual Forum of the American Helicopter
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