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 simulationThe 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.
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.
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.
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.
Accelerate modeling and simulation through a dedicated landing gear simulation solution
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.
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 quasistatic 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.
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.
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.
