The Art of the Helicopter John Watkinson - Karatunov.net

Rotors in practice 133
In a real helicopter, the rotor is not rigidly attached to the hull because of the presence
of flapping hinges or flexures. As the rotor disc tilts, the hull will lag behind so that the
tip path axis and the shaft axis do not coincide. This non-coincidence causes moments
and it is these that govern the tilt of the hull. As the hull tilts, it causes a further tilt
of the swashplate. This causes a further tilt of the rotor and so on. This is an example
of positive feedback. Consequently in practice a steady application of cyclic control
causes the rotor disc to tilt at constant speed. The ratio between the two is the response
rate. The stiffer the connection between the rotor and the mast, the more the rotor is
able to tilt the hull and swashplate, and so the greater is the positive feedback and the
greater the response rate for a given cyclic application.
In general the stiffer the rotor head, the more rapid the response rate will be. Before
the mechanism was understood, some experimental helicopters had response rates
beyond the ability of the pilot and were uncontrollable. The use of hinged rotor heads
in early helicopters had the advantage of reducing the response rate to what the pilot
could manage.
The case of a machine that is initially hovering in equilibrium will be considered.
In the zero-offset head, the application of a cyclic input causes the tip path plane to
tilt with respect to the mast. As a result the thrust vector no longer passes through
the CM, and a roll couple is created as shown in Figure 4.13(a). This will be proportional
to the height of the rotor above the CM, and is a further reason for tall masts
on teetering machines. The tip path plane initially tilts without the mast following
it. Since the cyclic pitch control operates with respect to the mast axis, tip path tilt
opposes the cyclic pitch control, so the further the disc tilts with respect to the mast,
the less cyclic pitch change the blades get. Excessive following rate is thus prevented.
As the teetering head cannot exert a couple on the mast, it can only pitch or roll the
hull if the rotor thrust is tilted. If the rotor thrust is reduced for any reason, the cyclic
control becomes less effective. This may happen in a pushover manoeuvre. The rotor
disc will follow the cyclic control, but the hull doesn’t follow the disc. Such a situation
may result in mast or droop stop pounding and all pilots who want to live will
avoid it.
In the case of an articulated rotor head with offset flapping bearings, the tip path
plane tilts as before, and moves the thrust vector with respect to the CM as before, but
in addition the blade tensions no longer align and this results in a roll couple being
applied to the rotor head as shown in Figure 4.13(b). The further apart the flapping
bearings are, the more powerful this effect will be, speeding up the following rate.
Consider a fully articulated head with torsion springs fitted to the flapping and
dragging axes. If the springs are stiff, there will be little deflection of the bearings.
Deflection will be transferred to the blades and they will flex. If the springs are weak,
there will be little to prevent deflection of the bearings, and bending loads on the
blades are minimized. Clearly the flexural rotor head (c) can behave more or less like
an articulated head depending on the stiffness of the flexures. The stiffness of the flexures
may be different in the flapping and dragging directions. Sections 4.16 and 4.17 will
explore the effects of dragging stiffness.
In the flexural rotor head, a single structural element often acts both as a bearing
and as a spring. It will bend, but not without an applied moment, and so flapping and
dragging are allowed by a combination of rotor head and blade flexing. The distribution
of bending is clearly a function of the relative stiffness. All other things being equal, in
an articulated head the flapping hinge offset determines the magnitude of the couple
applied to the mast when the tip path axis deviates from the mast axis, whereas in
a hingeless head this couple is determined by the stiffness of the system. In order to
simplify analysis of the dynamics of a helicopter having a hingeless head, it is possible