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Ref. 3-2 treats this subject in much more detail than it is
done in present paper.
3.3.2 Conclusions with Regard to Sensible Brake
Control
3.3.2.1 Brake Control during Braking
Fig. 3-3 is an somewhat exaggerated variation of Fig.3-2.
However, the ordinate has been renamed "Wheel
Torque" after, in ideas, having multiplied circumferential
friction coefficient with wheel load and ground-to-axle
distance.
Best possible deceleration of the aircraft by wheel
braking could certainly be achieved if retarding moment
produced by the brake (!'brake torque") was just equal to
the maximum driving moment achievable by the tyre
("wheel torque"). However, this maximum point will
move around very quickly due to wheel load fluctuation
on uneven ground, due to fluctuation of ground to tyre
friction on varying ground roughness. due to variation of
ground-to-axle distance. and due to other effects (e.g.
side load on a braked wheel).
Although brake torque is measurable directly, wheel
torque is not. Hence it is virtually impossible to exploit
100 percent of achievable wheel torque throughout the
braked ground run. Therefore, brake control systems in
general are aiming for a working point below the
maximum wheel torque on the left (stable) branch of the
wheel torque vs. slip ratio curve. However, if by chance
maximum wheel torque falls below brake torque or if
brake torque is increased beyond maximum achievable
wheel torque, this statically unbalanced torque difference
will decelerate the wheel and thereby increase slip ratio.
Provided torque difference is large enough and is acting
for sufficiently long time, slip ratio will be increased to
the unstable part of the wheel torque curve.
In order to avoid this critical situation it is necessary in
the first place to timely recognise an incipient skid and to
reduce brake torque fast enough such that slip ratio is
kept on the stable side.
However, a backup procedure is needed in case that slip
ratio has eventually reached the unstable side of the
wheel torque vs. slip ratio curve. If this happened the
wheel would continue to decelerate to an eventual
standstill as long as brake torque is larger than actual
wheel torque, even if maximum achievable wheel torque
had meanwhile recovered beyond actual brake torque. To
recover from this "deep skid" the safest way is to lift
brake completely until wheel speed has returned to the
stable part of the wheel torque vs. slip ratio curve.
For better understanding of the case presented it is
necessary to explain the principal method applied here to
recognise an incipient skid: Wheel angular deceleration
is the most important parameter used for skid detection.
3-5
During perfectly steady braking wheel angular
deceleration is proportional to aircraft linear
deceleration. Hence, on first view one could assume that
any wheel deceleration beyond this value could be
interpreted as an incipient skid. In theory this assumption
holds only if the brake is operating at the maximum
wheel torque transmittable to ground, because any loss of
transmittable wheel torque will drive the working point
to the right (unstable) side of the curve (Fig.3-3 and 3-4).
If the brake operates on the stable side somewhere below
maximum transmittable wheel torque a reduction of
transmitted wheel torque will be followed by a "useful"
increment of wheel deceleration which brings transmitted
wheel torque back to brake torque. Therefore, anti-skid
action should only be triggered on exceedance of this
"useful" wheel deceleration increment. As stated above,
admittable trigger level is zero if brake torque equals
transmittable wheel torque; trigger level rises
(progressively) with the ratio of transmittable wheel
torque to brake torque.
Assumed that a brake control system in its anti-skid
branch contains a fixed wheel deceleration trigger
criterion, the control system should also provide for the
appropriate torque reserve between brake torque and
maximum transmittable wheel torque. Since maximum
transmittable wheel torque is not measurable directly,
anti-skid systems of the type considered here contain
algorithms which reduce brake pressure output from the
servo valve according to frequency and intensity of
previous anti-skid actions. Brake pressure will be
cautiously re-increased (eventually to the level
corresponding to pilot's command) if no more anti-skid
action was triggered in a sufficiently long time interval.
3.3.2.2 Brake Initiation
Up to the point of brake initiation, the wheel rolls freely
at negligible wheel torque just balancing rolling drag.
Therefore at brake initiation, rise of brake torque cannot
immediately be counteracted by wheel torque. Rather,
momentary difference between wheel torque and brake
torque leads to angular deceleration of the wheel. This
effects an increase of slip ratio and wheel torque. If brake
torque is limited to a value below maximum
transmittable wheel torque, slip ratio will eventually tune
in to stationary balance of brake torque by wheel torque.
Wheel deceleration occurs during brake initiation as well
as during a skid. Hence, if during brake initiation wheel
deceleration exceeds the threshold set for skid detection,
anti-skid control will unnecessarily lift the brake. The
wheel will recuperate to or nearly to freely rolling
conditions. When brake pressure is re-applied by anti-
skid control another undue skid prevention cycle may
occur.
For sake of a vibration-free brake onset it appears useful
to gain insight into the factors influencing wheel angular