# A Rational Numerical Method for Simulation of Drop-Impact Dynamics of Oleo-Pneumatic Landing Gear
###### Abstract  
Oleo-pneumatic landing gear is a complex mechanical system conceived to efficiently absorb and dissipate an aircraft's kinetic energy at touchdown, thus reducing the impact load and acceleration transmitted to the airframe. Due to its significant influence on ground loads, this system is generally designed in parallel with the main structural components of the aircraft, such as the fuselage and wings. Robust numerical models for simulating landing gear impact dynamics are essential from the preliminary design stage in order to properly assess aircraft configuration and structural arrangements. Finite element (FE) analysis is a viable solution for supporting the design. However, regarding the oleo-pneumatic struts, FE-based simulation may become unpractical, since detailed models are required to obtain reliable results. Moreover, FE models could not be very versatile for accommodating the many design updates that usually occur at the beginning of the landing gear project or during the layout optimization process. In this work, a numerical method for simulating oleo-pneumatic landing gear drop dynamics is presented. To effectively support both the preliminary and advanced design of landing gear units, the proposed simulation approach rationally balances the level of sophistication of the adopted model with the need for accurate results. Although based on a formulation assuming only four state variables for the description of landing gear dynamics, the approach successfully accounts for all the relevant forces that arise during the drop and their influence on landing gear motion. A set of intercommunicating routines was implemented in MATLAB(r) environment to integrate the dynamic impact equations, starting from user-defined initial conditions and general parameters related to the geometric and structural configuration of the landing gear. The tool was then used to simulate a drop test of a reference landing gear, and the obtained results were successfully validated againsts available experimental data. l 26 February 2021 29 April 2021 30 April 2021  
The piston-cylinder assembly is generally referred to as a _shock absorber_, and the dissipative force generated during the landing is mainly due to the flow of viscous oil into an orifice with a cross-section that varies with the piston stroke. In more detail, the oil flows between two coaxial chambers, depending on the direction of motion of a tapered metering pin mounted on the piston (Figure 1b). During the compression stroke, the metering pin enters the inner chamber through an orifice with net section area \(A_{s}\); to compensate for the reduction in the amount of available volume, part of the oil contained in the inner chamber moves into the outer chamber, flowing into the same orifice crossed by the metering pin and into some holes connecting the two chambers. At the same time, the gas contained in a compensation air chamber (placed at the top of the oil chamber) is compressed, thus contributing to the balance of fluid volume in the different compartments of the cylinder. Unlike the communication holes between oil chambers, the portion of the orifice hosting the oil flow has a variable section area, \(A_{tr}\), given by the difference \(A_{S}\)-\(A_{mp}\), where \(A_{mp}\) is the metering pin's net section area, which varies with the pin length. During the extension stroke, the pin comes out the inner oil chamber, the air chamber volume expands,  
Figure 1: Main types of landing gear: (**a**) cantilever strut [2] and (**b**) oleo-pneumatic shock-absorber [3]. and the oil flows from the outer chamber into the inner chamber. The damping force produced by the oleo-pneumatic system can be then modulated by working on the shock absorber's main characteristics, with the ultimate goal of adequately limiting the aircraft's vertical acceleration to the maximum value the aircraft structure can absorb after impacting the ground.