Customer Application | Reinhard Lernbeiss, TU Wien, Institute of Mechanics and Mechatronics
Simulation of the Dynamic Behavior of
Aircraft Landing Gear Systems
Simulation and the resulting prediction of the dynamic behavior of an
aircraft and its landing gear system during ground maneuvers is an
essential part in the design process. A realistic estimation of unwanted
oscillations, such as gear walk and shimmy, for the landing gear and
whole aircraft can be readily obtained with an MBS-model. It is then
possible to adjust the model for changes in the structural design of the
airframe and the landing gear so as to optimize the aircraft stability.
pre-select certain values of residual vertical
INTRODUCTION
speeds upon touch-down. Additionally, the
Vibrations resulting from the elastic behavior
application of the brakes was performed
or from dynamic loads may result in material
by an automatic braking system combined
fatigue and failure. Loads acting on the landwith an anti-skid system.
ing gear at touch-down are of major interest. Addressing these issues during testing is
DYNAMIC PHENOMENA
crucial. Elastic properties of the airframe and
Undesired oscillations can occur in the
the landing gear have an essential influence
longitudinal, lateral and yaw directions.
on their dynamic behavior. Emphasis was
Longitudinal vibrations are normally
placed on developing an “elastic” model of
induced by changes of vertical and
the whole aircraft so as to realistically simulongitudinal loads acting on the
late a complete landing and rollout with its
wheels. They can be generated
braking, and in particular, the influence of
by landing
the landing gear.
“Emphasis was placed on
impact or
To demonstrate
developing an “elastic” model
during
the capabilities of
of the whole aircraft...”
braking
this approach an
and are
existing aircraft
commonly called gear(Airbus A320-200) was selected. To control
walk. The lateral and
the aircraft during flare, touch-down and
yaw oscillations are
roll-out, a control system was introduced,
called shimmy oscillacapable of achieving any desired angle of
tions when generated
the aircraft in relation to the runway at the
by self excitation forces.
exact moment of touch-down. This enabled
However, such vibrations may also be inthe simulation of possible crosswind condiduced by asymmetric conditions occurring
tions as well as different landing techniques
at landings with prevailing crosswind. Even
applied by the pilot. It was possible to
forward
forward
rolloscillation
longitudinal-oscillation
gear walk
lateral-oscillation
yaw-oscillation
shimmy
Fig. 1: Dynamic phenomena
2 | SIMPACK News | September 2010
the asymmetric structure of the landing gear
itself, as occurs on
most
main
landing
gear
systems, may be a source of unstable conditions, see Fig. 1. Rolling motions of the
wheels about their longitudinal axis also
exist.
SIMULATION MODELS
To generate a good approximation of the
mass distribution of an aircraft like the Airbus
A320 and the structural properties, existing
and accessible data were used together
with the statistical mass approximation
method published by Raymer. These data
were the main sources used to establish
a CAD-model of all of the structures. To
comply with the goal of simulating different
loading cases of passengers, cargo and fuel,
a balance calculation similar to those applied
before each flight of the real aircraft was
used. The data obtained for the air-frame
structure was pre-processed to facilitate the
generation of an elastic model in SIMBEAM.
The elastic structure was assembled with
the use of beam elements accounting for
Reinhard Lernbeiss, TU Wien, Institute of Mechanics and Mechatronics | Customer Application
Fig. 2: Airbus A320; structure of aircraft
the main parts of the fuselage and the
whole wings. Other elements, for example
the foremost part of the fuselage in front
of the nose landing gear, as well as the
empennage, are considered rigid, but
have the correct mass-properties and were
attached to the corresponding elastic beam
element. Implementing beam elements
to generate elastic structures reduced the
required time for simulation. Different
beam elements were defined between
certain markers and reflected a change
in structural properties. In addition, those
markers were set at positions to easily
accommodate major mass concentrations
and structural attachments, especially for
the wings and the landing gear, see Fig. 3.
To compensate for possible elements
which have no structural influence, for
example aircraft systems and fairings, the
masses were equally distributed along the
elastic beams between certain positions,
and the mass was adjusted accordingly.
Fig. 3: Arrangement of flexible beams of fuselage and wings
SIMPACK News | September 2010 | 3
Customer Application | Reinhard Lernbeis, TU Wien, Institute of Mechanics and Mechatronics
1st Eigenmode
2nd Eigenmode
lift and drag forces were calculated using the
basic aerodynamic equations acting on the
corresponding surfaces belonging to each
marker. The angle of attack is measured for
each section of the wing considered, taking
flexibility of the wings into account.
With this aerodynamic model, neither static
nor dynamic stability of the aircraft model
is possible. This is accomplished by using
artificial stability generated by a flight
control model which simply generates forces
on the horizontal stabilizer and elevator to
produce flight stability and control.
In the case of a real aircraft, the vertical
speed upon touch-down is minimized. For
the simulation, however, pre-determined
vertical speeds are required for the intended
parameter variations. Therefore, a schedule
for the target vertical speed, dependent
4th Eigenmode
Fig. 4: Eigenmodes
All other elements were added as rigid
mass elements. This facilitated changing the
loading of the aircraft and the amount of
fuel for simulation of different landing mass
and centers of gravity. Some of the resulting
eigenmodes of the elastic aircraft model are
shown in Fig. 4.
LANDING GEAR
A similar procedure was applied to establish
elastic models of the landing gear system.
The elastic structure of the landing gear
model was comprised of a system of beam
elements. The method of using distributed
masses and mass concentrations, where
needed, was also applied. To generate
appropriate forces acting on the wheels and
tires, a modified HSRI-tyre model was used.
An automatic braking system in conjunction
with an anti-skid system was used to achieve
braking action during the rollout phase. The
functions of these systems were basically
reproduced by models programmed
with MATLAB® and Simulink® using cosimulation.
CONTROLLING OF THE LANDING
MANEUVer
To accomplish a realistic landing-flare, it
is imperative to incorporate aerodynamic
forces. However, one of the goals is to
keep total simulation time low. Therefore,
the aerodynamic model was kept as simple
as possible and only those aerodynamic
loads were applied which are essential to
generate a nearly realistic landing maneuver
and which have possible influence on the
elastic structure with respect to the dynamic
behavior of the landing gear. On the wings
4 | SIMPACK News | September 2010
SIMPACK
model
data
aquisition
SIMPACK
output
aerodynamic
wings
flare trajectory
reverse thrust
aerodynamic
hor. stabilizer
autobrake
selection
engine thrust
yaw & roll
pre-selection
brakes &
directional
control
Fig. 5 and 6: Landing simulation
data
aquisition
SIMPACK
intput
output
Reinhard Lernbeiss, TU Wien, Institute of Mechanics and Mechatronics | Customer Application
CONCLUSION
To facilitate the design process, it is advantageous to implement and use simplified
models to simulate a number of operational
aspects to prevent undesired and costly but
necessary improvements during flight tests. It
is of utmost importance to have an easy to
use and changeable model at any stage of
development to predict the behavior of the
landing gear. It is then possible to modify the
design or to make appropriate adjustments
to a shimmy damper or similar device at an
early stage of design. Implementing a flexible
SIMULATION OF LANDING
structure in the simulation model is essential.
AN AIRCRAFT
In addition, it is possible to produce a realistic
It is crucial to have sufficient model detail
landing maneuver using only limited applicato gain insight into the dynamic behavior
tion of aerodynamic calculations and save
of landing gear. Fig. 8
computational time to fa“It is crucial to have
presents a comparative
cilitate the design process
sufficient model detail to
study of the relative
by testing various structural
gain insight into the
displacement
and
configurations early in the
dynamic behavior of
twisting of the wheel
design process. The model
the landing gear.”
axis of the main landing
presented enables the use
gear using different
of real-time simulations
modeling techniques of the elastic properties
used in flight simulators, and is necessary for
of the aircraft structure. It can be seen that
aircraft that use an extensive amount of flexthe results may differ quite significantly.
ible composite components.
the design of the landing gear and for the
flight test later in the development process.
Therefore, it is imperative to conduct sufficient simulations of that test in advance
to save resources and time. In addition,
the simulation of drop tests of the landing
gear with flexible structure models enables
a touch-down with different side slips (yaw
angles) and the motion of the de-rotation
of the aircraft, which is the lowering of the
nose after touch-down of the main landing
gear.
Fig 7: Nose landing gear; Airbus A320
upon height, was introduced. To simulate
crosswind conditions upon landing and
corresponding landing techniques used by
the pilot or the automatic landing system,
certain angles of roll and bank were
selected. These angles were kept constant
during flare until touch-down of the main
wheels by a separate controlling system.
SIMULATION SET-UP
The model of the elastic
aircraft
structure
together with the landing gear system in the
MBS-software SIMPACK
was simulated with the
controlling system of the
aircraft, programmed in
Simulink using a co-simulation. Simulink was used
for aerodynamic forces,
anti-skid, autobrake system and steering on the
runway during roll out.
Thrust control during
flare and reverse thrust
were also provided, see
Fig. 5 and 6.
DROP TEST
SIMULATION
During the design and
development process, a
so-called drop test conducted in a laboratory is
used. Here a single real
landing gear unit, loaded
with the appropriate
mass, falls onto a rotating drum which represents the moving runway
surface. This test is a vital
source of information
and the data generated
are used to optimize both
Fig 8: Relative displacement of the wheel axis; different levels in modeling the aircraft structure
SIMPACK News | September 2010 | 5