Aug. 20, 2013 — One of the lesser known
concerns about commercial aircraft is their
stability on the ground during taxiing, takeoff,
and landing. During these processes, planes
must maintain stability under various operating
conditions. However, in some situations, the
aircraft landing gear displays unwanted
oscillations, which are referred to as shimmy
oscillations.
In a paper published last month in the SIAM
Journal on Applied Dynamical Systems, authors
Chris Howcroft, Bernd Krauskopf, Mark
Lowenberg, and Simon Neild study the
dynamics of aircraft landing gear using
nonlinear models. The dynamics of landing
gear shimmy and the wheel-ground interaction
are fundamentally nonlinear.
"Shimmy oscillations of aircraft landing gear
have long been a problem, and their
prediction and prevention remains an ongoing
challenge in landing gear design," explains
author Chris Howcroft. "The issue is that a
landing gear may display the desired behavior
during ground take-off/landing manoeuvres
over several hundred or so flights, but then
suddenly oscillate given just the right -- or
rather, the wrong -- conditions."
Fortunately, mathematical models provide
cost-effective ways to study the dynamics of
the main landing gear (MLG) and determine the
types of oscillations that may occur under
different conditions. "The work we conducted
clarifies under which conditions shimmy
oscillations can be encountered in the MLG of
a representative midsize passenger aircraft. We
identified different types of shimmy
oscillations and showed where they occur,"
says Howcroft.
"Having the right mathematical model is really
the key," he adds. "Actual testing is extremely
expensive; however, nonlinear analysis
methods are very well suited to identifying
these hard-to-find dynamics. They may also be
employed to determine the shimmy
characteristics before the aircraft has actually
been built."
The model can provide insights not only into
aircraft operation, but also design features,
and can aid in adjusting both for optimum
stability.
Aircraft landing gear supports the weight of
the aircraft during landing and ground
operations. In addition to their wheels, landing
gear also have shock absorbing equipment or
"shock struts" as well as brakes, retraction
mechanisms, controls, and structural entities
that attach the gear to the aircraft.
The model in the paper takes into account tire-
contact dynamics and the orientation of the
side-stay, the part of the aircraft that supports
the shock strut. It characterizes the motion of
the system in terms of dynamics of the MLG,
which are expressed as three degrees of
freedom: rotation about the main strut, and
in-plane and out-of-plane motion with respect
to the plane of main strut and side-stay. After
determining the dynamics for the simplest
geometric case, where the side-stay is
perpendicular to the direction of travel, the
authors use the model to study different side-
stay orientations.
"For the specific case of MLG, we developed a
nonlinear and fully parameterised model that
allowed us to map out how its dynamics
depends on operational parameters, such as
aircraft velocity and loading, and design
parameters describing the geometry of the
landing gear," explains Howcroft. "In contrast
to the more traditional approach of performing
large numbers of simulations, this was
achieved by employing advanced tools from
dynamical systems that track solutions and
stability changes in parameters directly."
Moreover, other parameters could be
incorporated into the model further down the
road, such as runway conditions or tire
pressure, or physical effects such as the
dynamics of the shock absorber.
"Future directions of this research will focus
on the incorporation and assessment of
additional nonlinear effects," says Howcroft.
"For example, mechanical joints loosen over
the lifespan of an aircraft landing gear, and
this may have a dramatic effect on dynamic
performance, service life and maintenance
requirements of the landing gear."
"Nonlinear modeling and analysis are now
being introduced as tools into industrial
practice, via the recent development of a
MATLAB toolbox," says author Simon Neild.
"This is exciting to see, and has allowed our
group to tackle not only the problem of
landing gear shimmy, but of aircraft ground
manoeuvres and airliner loss-of-control in
flight."
Author Bernd Krauskopf adds.
"This project is
part of a larger research effort in collaboration
with Airbus into aircraft ground dynamics via
the bifurcation analysis of nonlinear models.
Related work concerns shimmy in nose landing
gears and its interplay with the dynamics of
the fuselage."
Future work would integrate many different
aspects into a unifying model.
"Ultimately our
current research is moving towards the
integration of landing gear and airframe into
an overall model that allows us to create a full
dynamic picture of aircraft ground dynamics,"
says author Mark Lowenbergm.
Story Source:
The above story is based on materials provided
by Society for Industrial and Applied
Mathematics. And ( sciencedaily magazine )
Note: Materials may be edited for content and
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Journal Reference:
1. Chris Howcroft, Bernd Krauskopf, Mark H.
Lowenberg, Simon A. Neild. Influence of
Variable Side-Stay Geometry on the Shimmy
Dynamics of an Aircraft Dual-Wheel Main
Landing Gear . SIAM Journal on Applied
Dynamical Systems , 2013; 12 (3): 1181 DOI:
10.1137/120887643
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