# A Rational Numerical Method for Simulation of Drop-Impact Dynamics of Oleo-Pneumatic Landing Gear
###### Abstract
A reliable simulation tool for landing gear impact dynamics can therefore provide tremendous support for the design of new airplanes, as it facilitates the integrated definition of coherent layouts for both the landing unit and the airframe. In full awareness of this consideration, several approaches have been proposed to efficiently model the dynamic behavior of oleo-pneumatic landing gear, each with its own level of complexity, pros and cons. The first attempt at shock absorber analysis was made by [PERSON] [4], who focused on evaluating the system's overall damping efficiency rather than proposing effective models for simulating the impact dynamics. [PERSON] and [PERSON] [5] presented an integral model for the entire shock absorber, which was considered as a dynamic system with a single degree of freedom. The model was successfully validated by experiments but did not accurately account for the influence of many parameters involved in the drop dynamics. [PERSON] [6] investigated the relationship between the dissipated energy and the air chamber's physical characteristics and described effective thermodynamic models to predict the behavior of the gas during the compression and extension stroke of the piston. Relying on these studies, [PERSON] [7] built a sophisticated model allowing for precise simulation of hydraulic dissipative forces; unfortunately, its validity was limited to telescopic landing gears only. Working on a six degree-of-freedom system, [PERSON] and [PERSON] [8; 9] were able to fairly represent shock absorber dynamics during taxiing. Their approach adopted linear differential equations of motion, which were very useful in predicting the vibration levels induced by the ground asperities on the fuselage structure and passengers. On the other hand, the equations could not realistically capture the energy dissipation mechanism at touchdown due to their linear formulation. To overcome this limitation, [PERSON] and [PERSON] [10] used a series of two mass-spring-damper models to simulate the impact dynamics of the shock absorber and wheel assembly. The model was validated against the numerical results of finite element analysis carried out in ABAQUS [11] and proved to be reliable in predicting the time history of vertical displacement, acceleration, and reaction force. Unfortunately, no equations were considered for obtaining the wheel axle's vibrations along the horizontal direction consequent to the aircraft flight speed at the moment of impact, and the friction between the tire and the ground. This made it impossible to estimate spin-up and spring-back loads, which are among the most severe loads in landing gear design [12]. Recent studies offer comprehensive simulation strategies for landing gear impact dynamics, relying upon ever more advanced finite element solvers; some relevant examples can be found in a good review article by [PERSON] and [PERSON] [13]. An interesting finite element analysis accounting for the nonlinear problems in landing dynamics was proposed by [PERSON] [14], while [PERSON] et al. used multibody dynamics software (Simpack) combined with the FE solver NASTRAN to investigate the load instability produced by the interaction of the brake mechanism with the landing gear's wheels [15]. [PERSON] introduced a multi-body system-based landing gear model for numerical simulation of simple static and dynamic load conditions and successfully correlated the simulation results with the outcomes of a more accurate finite element simulation [16]. The Lernbeiss model was then revised and improved by [PERSON], based on drop-impact analysis and experiments conducted on a smart UAV landing system [17]. LMS(r) analysis software for multi-body dynamics was used by [PERSON] and [PERSON] to build a coupled rigid-flexible simulation model of light aircraft main landing gear, showing very good capability in terms of drop-test load estimation [18].