An integrated approach to the dynamic
simulation of landing gear systems
�LMS International | info@lms.be | www.lmsintl.com
Introduction
Dynamic simulation of the landing gear and the
airframe is used to support the engineering
development process early in new aircraft programs
and make better use of testing downstream.
Simulation is used to verify that certification
requirements set forth in regulations like FAR/
JAR 25.491 can be met. Aircraft companies have
used increasingly more complete analyses after
starting a few years ago with simulation of a runway
(random) profile, a discrete (tuned bump or 1.7g
static) and a combined load condition based on
a formula. The runway profile and tuned bump
analyses involved dynamic analyses of the aircraft
over the respective ground profiles. More advanced
user groups have automated their simulation
processes, running thousands of simulations for
many aircraft designs, landing gear configurations
and ground profile conditions to verify that the
aircraft can tolerate the loads in all scenarios.
The focus of simulation is to predict loads on the
landing gear system and airframe for all aspects
of the flight envelope. This includes landing, taxi,
ground maneuvers, and take-off. Other events like
the drop tests previously done with early prototypes
are now done with simulation prior to any prototype
being available. The LMS Virtual.Lab Motion
software for multi-body simulation is used to
predict the forces on all components of the aircraft
and the landing gear system. The simulations are
both accurate and versatile and can closely match
what was once only possible with physical testing
of aircraft.
Load prediction for accurate simulation
The simulation model is created from solid model
geometry for mass and inertia properties along with the
connection location and kinematic constraints that make
up various joint. Several force elements are also used
to complete the simulation model. A tire force element
is included that computes the lateral, longitudinal,
and vertical forces when in contact with the ground
profile. A correct representation of the friction forces
in the joints, and primarily in the strut sliding action, is
critical for getting accurate simulation result. These are
sometimes represented as an idealized coulomb function,
or alternately as part of the oleo strut hydraulic equations
so the pressure dependent behavior can be captured.
The force relationships are usually nonlinear functions
of position and velocity between connected bodies. The
geometry, mass, stiffness, and damping information is
used to construct the nonlinear equations of motion.
LMS Virtual.Lab Motion is applied to optimize landing gear designs from the
early development stage onwards.
LMS Virtual.Lab Motion includes extensive capabilities to model landing
gear systems
Rigid and flexible multibody formulation
The LMS Virtual.Lab Motion Solver is based on a
Cartesian formulation for the translational degrees of
freedom along with Euler parameter (quaternions) to
represent the rotational degrees of freedom. The bodies
are connected together by force and joint elements. The
relative degrees of freedom between two bodies can be
constrained by a set of joints or constraint equations. The
Newton-Euler equations of motion plus the joint constraint
equations form a set of differential-algebraic equations of
motion (DAE) in the following form.
�LMS International | info@lms.be | www.lmsintl.com
Where M is the mass matrix, q are the generalized
coordinates, Qa are the generalized forces applied to
the rigid bodies in the model, l the so called Lagrange
multipliers, Fq is the Jacobian of the constraint forces and
g the second derivative the constraint equations.
The flexible body implementation used in Virtual.Lab
Motion couples equations based on linear FE or test
modes with the Cartesian equations in the same model.
This results in the best performance and most versatile
set of equations. The augmented set of independent
differential-algebraic equations is very efficient and
produces more accurate results than a comparable rigid
body simulation.
A Craig-Bampton set of linearly independent modes
is used and is based on a combination of static and
vibration modes that can well represent local and general
deformation of the part. Landing gear systems, airframes,
and smaller parts in the system each have their own
set of modes. The results can be used to animate the
flexible deformation through time, and to calculate stress.
Relatively course FE meshes can be used to get fast
simulation results as part of the multibody model, and
then the computed response mode displacements can be
used with more detailed meshes to calculate local stress.
In addition to the added refinement that comes from
including the flexible body behavior, control and hydraulic
states are also included. The details associated with oil
flow and pressure response further improve the simulation
fidelity.
Flexible body stress results at one instant in time
Flexible modes are automatically generated from FE analysis
Optimizing the hydraulic
oleo strut system
The hydraulic forces can be modeled in a simpler way
using nonlinear stiffness and damping functions. But
the combination of 1-D system simulation in Imagine.
Lab AMESim and 3-D multi-body simulation in LMS
Virtual.Lab Motion provides the most accurate and
detailed representation of these forces. The only extra
requirement is that the oleo orifice and piston dimensions
are known. The hydraulic model equations are coupled
to the nonlinear DAE’s and solved using the numerical
integration algorithm in Virtual.Lab Motion. The results
include the pressure, and pressure derivatives, and oil
flow in the strut. In the cases where hydraulic system are
also used for the retract and other actuators, the power
requirements and dynamic response is predicted.
LMS Virtual.Lab Motion interfaces with LMS Imagine.Lab AMESim to
optimize the design of hydraulic control systems/
�LMS International | info@lms.be | www.lmsintl.com
Accelerate modeling and simulation
through a dedicated landing gear
simulation solution
The Landing Gear Interface in LMS Virtual.Lab Motion supports inputs
provided by LMS or user created gear models driven by design tables.
LMS Virtual.Lab Motion offers a dedicated solution for
aircraft landing gear modeling and dynamic simulation,
including a user interface which is fully customized
to the specific landing gear simulation process. The
solution offers capabilities to import models from most
industry standard CAD programs like ProE, Unigraphics,
SolidWorks, Autodesk, etc… When working within the
CATIA V5 environment, the solution offers full associativity
with all CAD data.
LMS Virtual.Lab Motion allows the
user to select from pre-defined and
fully parameterized landing gear
templates or gives the user the ability
to create their own landing gear
configuration template. This allows
users to fill in the model parameters,
have LMS Virtual.Lab automatically
assemble the complete landing gear,
apply the ground load cases, run the
simulation and perform standardized
post processing of the results.
The modeling and post processing
effort is minimized thanks to the
automation of standard tasks and
a streamlined process from model
definition through solving to post
processing.
Virtual.Lab landing gear solution simulates the absorption
of the kinetic energy in the landing gear – typically
an oleo/pneumatic design - as the aircraft lands and
taxis. A drop test simulation is performed to account
for the landing conditions. The wheels are spun up to
simulate the effect of the tires spinning up as the aircraft
touches the runway. Spring-back effects of the landing
gear can here also be simulated. During this process,
energy must be absorbed by the landing gear without
generating reaction forces exceeding the dynamics loads
envelope. The simulation allows adjusting the damping
characteristics to ensure that the dynamic loading stays
within the dynamic loads envelope.
The seamless integration with LMS Virtual.Lab Structures
gives the user direct access to all dynamic loads for
optimizing the design of individual parts such as the lugs
that are used to connect the side and drag brace to the
outer cylinder. This area of the landing gear is critical for
fatigue due to the interaction with other highly loaded
components during braking and turning while taxiing.
The predicted stresses directly serve as input to LMS
Virtual.Lab Durability which highlights the critical
spots and accurately predicts the fatigue life of each
component.
Users can also optimize the design with LMS Virtual.Lab
Optimization, which offers an integrated set of powerful
capabilities for single and multi-attribute optimization.
Through Design of Experiments and Response Surface
Modeling techniques, engineers gain a rapid insight in all
the possible design options that meet their requirements.
Landing
gear
design
Load
analysis
Kinematic
analysis
Structural
analysis
Fatigue
analysis
Ground
loads
analysis
Landing gear
assembly level
Aircraft level
Overview of the landing gear simulation process covered by LMS Virtual.Lab Motion
�LMS International | info@lms.be | www.lmsintl.com
Optimizing designs before
prototype testing
Models can be used to predict all the loads, reaction
forces, position, velocity, and accelerations of the landing
gear. In general, the multibody dynamic solution from
Virtual.Lab Motion provides both more accurate results for
transient dynamic events, and ways to pose more versatile
problems than the older CAE methods sometimes
used in the past. These older methods often did quasi-
static solution of FE models based on assumed peak
accelerations. With LMS Virtual.Lab Motion, a single fully
parameterized model can be used to do a ground loads
analysis (quasi-static/dynamic) and a parameterization for
different load cases.
Simulation provides the required insight to eliminate
weak designs before making prototypes, and ensures that
aircraft engineers can make the most of the limited test
time once a prototype is available. It is also possible to
study normal, abnormal and failure load cases where it
might be too dangerous or costly to do physical tests. It
has also proven to be useful to aircraft companies who
want to evaluate the landing gear loads on rough runways
found in the developing world. Simulation based on LMS
Virtual.Lab Motion can also predict specific landing gear
phenomena like wheel shimmy. The lateral excitation of
certain landing gear configurations can lead to dangerous
lateral deflections and this behavior can be predicted
using Virtual.Lab Motion and the available advanced tire
models.
Landing gear simulation drop test results
The Virtual.Lab Motion solver and modeling interface are
ideally suited to landing gear and aircraft loads calculation
applications and has delivered proven results in multiple
aircraft programs to predict total system dynamic
performance and loads.
LMS INTERNATIONAL
Researchpark Z1, Interleuvenlaan 68
B-3001 Leuven [Belgium]
T +32 16 384 200 | F +32 16 384 350
info@lmsintl.com | www.lmsintl.com
Worldwide For the address of your local representative, please
visit www.lmsintl.com/lmsworldwide
LMS is an engineering innovation
partner for companies in the automotive,
aerospace and other advanced
manufacturing industries. LMS enables its
customers to get better products faster
to market, and to turn superior process
efficiency to their strategic competitive
advantage. LMS offers a unique
combination of virtual simulation software,
testing systems and engineering services.
LMS is focused on the mission
critical performance attributes in key
manufacturing industries, including
structural integrity, system dynamics,
handling, safety, reliability, comfort and
sound quality. Through our technology,
people and over 25 years of experience,
LMS has become the partner of
choice for most of the leading discrete
manufacturing companies worldwide.
LMS is certified to ISO9001:2000 quality
standards and operates through a network
of more than 30 subsidiaries in key
locations around the world.
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