MODELING AND SIMULATION OF A LANDING GEAR SYSTEM WITH EULER-LAGRANGE VECTOR BOND-GRAPH APPROACH

This work aims to develop and simulate a model of landing gear system during an aircraft touch down. During an aircraft development process, many experimental tests are made to ensure the functionality and safety of the landing gear systems. Instead of using iron bird prototypes to perform the tests, using digital twins as high-fidelity model simulations to predict their physical behavior is safer and less expensive. This work applies the vector bond-graph method to model the landing gear dynamics during touchdown. The aircraft landing gear dynamics are modeled as a multi-body system. The methodology uses modern modeling tools based on a combination of vector bond graph (VBG) representation allied to the Euler-Lagrange variational method for system dynamics modeling. The system studied consists of a planar aircraft model composed of three main modules: a nose landing gear, the airframe, and the aircraft's main landing gear. The landing gear system was first modeled using a vector bond graph representation. Once the effectiveness of this modeling methodology was proved, the resultant vector bond graph was analyzed from the Euler-Lagrange standpoint by determining the system's generalized coordinates and total Lagrangian function. The symbolic algebraic processing was applied to determine the coupled nonlinear differential equations in a symbolic form. In this case, the energy interactions of all the system elements were calculated to generate equations of motion in the form of Euler-Lagrange equations. The analytical equations were implemented in a Matlab/Simulink computational environment to simulate a typical landing condition. A vertical load was applied to the model, simulating a smooth aircraft touchdown. When the aircraft speed reached 40 m/s, and the vertical load reached the aircraft's total weight, braking force was applied to decelerate the aircraft until it stopped. The simulation results showed the effectiveness of the proposed methodology in the aeronautical field. Although the chosen study case comprises a purely mechanical system, the combined vectorized Lagrangian bond graph modeling methodology can be applied to the Multiphysics domain typical of several aeronautical systems of interest.