Landing Gear Dynamics Research Articles

Analysis of the shimmy in the landing gear of a general-purpose helicopter for different payloads

Landing gears, which are designed to absorb impact energy in order to provide support to the aircraft during landing, take-off and ground operations, are important components of the structure. Shimmy, which is one of the causes of aircraft failures, is a vibration that occurs as a result of the interaction of tire and landing gear dynamics and can cause an accident. In this study, the shimmy behavior of a helicopter used for civil, military and air ambulance purposes are investigated at different load and taxiing velocities. A landing gear single degree of freedom mathematical model is obtained and a Von Schlippe stressed spring tire model is included. The eigenvalues of the equations of motion are analyzed and stability maps of the system for different operating conditions are obtained. Runge-Kutta method (MATLAB ode45) is used to solve the equations of motion and a viscous damper is proposed. To obtain the damping, versions of the non-Newtonian silicone oil in the damper with different kinematic viscosities were evaluated. Apparent viscosities were obtained using the rheological values of the silicone oil and the analysis was repeated. As a result of the shimmy analysis at the initial velocities and maximum loading values required for the helicopter to taxiing, it was seen that damping was achieved in all conditions by using versions of the silicone oil with higher kinematic viscosities.

Analysis of Catapult-Assisted Takeoff of Carrier-Based Aircraft Based on Finite Element Method and Multibody Dynamics Coupling Method

Catapult-assisted takeoff is the initiation of flight missions for carrier-based aircrafts. Ensuring the safety of aircrafts during catapult-assisted takeoff requires a thorough analysis of their motion characteristics. In this paper, a rigid–flexible coupling model using the Finite Element Method and Multibody Dynamics (FEM-MBD) approach is developed to simulate the aircraft catapult process. This model encompasses the aircraft frame, landing gear, carrier deck, and catapult launch system. Firstly, reasonable assumptions were made for the dynamic modeling of catapult-assisted takeoff. An enhanced plasticity algorithm that includes transverse shear effects was employed to simulate the tensioning and release processes of the holdback system. Additionally, the forces applied by the launch bar and holdback bar, nonlinear aerodynamics loads, shock absorbers, and tires were introduced. Finally, a comparative analysis was conducted to assess the influence of different launch bar angles and holdback bar fracture stain on the aircraft’s attitude and landing gear dynamics during the catapult process. The proposed rigid–flexible coupling dynamics model enables an effective analysis of the dynamic behavior throughout the entire catapult process, including both the holdback bar tensioning and release, takeoff taxing, and extension of the nose landing gear phases. The results show that higher launch bar angle increase the load and extension of the nose landing gear and cause pronounced fluctuations in the aircraft’s pitch attitude. Additionally, the holdback bar fracture strain has a significant impact on the pitch angle during the first second of the aircraft catapult process, with greater holdback bar fracture strain resulting in larger pitch angle variations.

Shimmy Studies on Simplified Linear Nose-wheel Landing Gears Models

Multiplicity of parameters and complexity of various component models have made modelling and analysis of Landing gear dynamics a very complex task. This paper presents a study of shimmy instability on a simplified linear three degree-of-freedom model of a nose-wheel landing gear. The simplified model considers cornering forces due to tire lateral displacement but ignores forces due to tire twist. This study is carried out as a forerunner to stability studies with detailed tire models along with tire skid. The stability of the system is studied by root locus plots in the complex plane for different values of forward velocity. These studies bring out the role of landing gear torsional/flexibility, viscous damping, caster length and tire lateral flexibility and damping on shimmy oscillations.

Design optimisation and experimental verification of a UAV’s landing gear buffer

The landing gear is a critical aircraft system that absorbs the kinetic energy of the vertical load and reduces the aircraft’s impact at touchdown. This paper proposes a hybrid optimisation method for further optimising the buffer performance of a mature UAV’s main landing gear. This method combines a propagation (BP) neural network method with a genetic algorithm (GA). A landing gear dynamics simulation model is established based on the software LMS Virtual.Lab Motion, and validate the model with tests. The optimisation model is established using a BP neural network and solved using a genetic algorithm. The maximum vertical load, the efficiency coefficient of buffer, and the efficiency coefficient of buffer system are used as the optimisation targets. The air chamber initial gas pressure, initial volume of buffer, and diameter of main oil hole are selected as the optimisation parameters, and the values after optimisation are 148 MPa, 165.2 mL, and 3.17 mm, respectively. The results show that the efficiency coefficient of buffer is increased by 3.7% and the efficiency coefficient of buffer system is increased by 1.13% and the maximum vertical load decreased by 0.6%, which indicated that the hybrid optimisation method is effective for landing gear buffering performance.

Impact of Design and Operational Parameters on Helicopter Vertical Bounce

Vertical bounce is a rotorcraft aeroelastic instability triggered by the feedback interaction between two significantly damped vibration modes: the rotor collective flap mode and the biodynamic vertical oscillation of the pilot’s left arm holding the collective lever in the cockpit. The instability can endanger the safety of flight and in some cases led to catastrophic events. This work develops simple yet complete models that allow us to better understand the dependency of the phenomenon on parameters like the flight condition, the characteristics of the aircraft, and the properties of the pilot’s biodynamic feedthrough. The stability analyses presented demonstrate that the landing gear dynamics may amplify the vertical oscillations driven by the pilot’s biodynamic response when considering on-ground conditions, reducing the stability margins of the pilot–vehicle system. The detailed sensitivity analysis allows inferring indications to develop future rotorcraft that could be less prone to this adverse rotorcraft–pilot coupling phenomenon.

Research on Landing Stability of Four-Legged Adaptive Landing Gear for Multirotor UAVs

Rotorcraft Unmanned Aerial Vehicles (UAVs) often need to take off and land under complex working conditions. The rugged terrains may cause the UAV to tilt during takeoff and landing and even cause rollover and other accidents in severe cases. In this paper, a new four-legged landing gear of multirotor UAVs with a passive cushioning structure is designed, aiming at the landing stability requirement of rotorcraft UAVs in complex terrains. The mathematical model of the landing gear dynamics is established in MATLAB/Simulink, and the drop test simulation is carried out under different landing terrain conditions. By comparing the simulation results of the drop test multibody dynamic model in Simcenter3D dynamics software, the adaptive landing and cushioning capacity of the landing gear and the accuracy of the mathematical model are verified. Combined with the landing stability criterion and control strategy of adaptive landing gear adjustment, the landing stability of adaptive landing gear under different slope angles of landing surface and horizontal velocities is studied. The landing stability boundary under different combinations of these two parameters is found.

Sensitivity Analysis for the Shimmy Dynamics of an Airplane Main Landing Gear

Sensitivity Analysis for the Shimmy Dynamics of an Airplane Main Landing Gear

A Rational Numerical Method for Simulation of Drop-Impact Dynamics of Oleo-Pneumatic Landing Gear

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® 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 against available experimental data.

Nonlinear energy sink to enhance the landing gear shimmy performance

The shimmy phenomenon is a significant concern in aircraft landing gear dynamics. The prediction of the shimmy instability is an essential issue in landing gear design to develop a passive or active suppression method. This work investigates the application of the nonlinear energy sink (NES) concept to mitigate the effects of shimmy in landing gears. The NES concept has been used in recent research on mechanical vibrations. It comprises a passive target energy transfer method that refers to a one-way energy transfer from a primary to a nonlinear subsystem. The landing gear model is based on torsional displacement coupled with the tyre classical elastic string analogy model. The NES device connects to the wheel shaft, and it comprises a mass, a linear damper, and a pure cubic spring. The numerical integration in time was used to assess the shimmy onset speed and the post-shimmy limit cycle oscillations. A parametric analysis of the landing gear nonlinear dynamics without the NES is presented. The design space of possible NES parameters is given, obeying design constraints, and inspected to assess adequate NES designs. The best NES samples are included in the landing gear dynamics to study their influence. Results have shown that the NES can adequately expand the operational speed range for no shimmy and lead to lower LCO amplitudes in the post-shimmy for a reasonable range of speeds. The NES concept’s successful employment for the landing gear dynamics suggests an enormous potential form of passive shimmy control.

Stress analysis of Landing gear of light Unmanned Aerial Vehicle

The landing gear system of an aircraft absorbs energy from the impact of landing. Numerical simulation has become great tool for the assessment of the landing gear dynamics as well as for aircraft structure and landing gear interaction. This paper basically describes the normal structural behavior of a simple landing gear structure model system and accurately simulates the energy absorbed by the gear system without adding substantial complexity with the model. It carries the structure aircraft weight at all required ground operations including landing, take off, taxiing and towing. The stress results obtained from the finite element analysis is used to calculate the factor of safety. This work also focuses on landing gear of small unmanned aerial vehicles, where the landing gears used are of leaf spring type. It has been seen that the stresses are very high during greater impact speeds, which resulted in less factor of safety.

Effects of Spring and Damper Elements in Aircraft Landing Gear Dynamics

In this study a typical Aircraft Landing Gear with shock absorber was modeled a Mass-Spring-Damper System. Basic components of the system were explained. The equations of the model was presented. Aircraft Landing Gear was also modeled in Matlab/Simulink for a given set of aircraft parameters. A case study for an Aircraft Landing Gear was solved and results were presented. Results included the variation of spring (k1 and k2) and damping coefficient (b) in a given interval to show their effects on the impact force and displacement of landing gear as main outputs to consider. Effect of damping coefficient (b) on impact force was found to be highest (3.76%), spring coefficient (k1) effect is moderate (2.29%), and spring coefficient (k2) is lower (0.97%), for a change of ±10% of coefficients.

Design and Folding/Unfolding Dynamics of an Over-Constrained Airplane's Landing Gear With Four Side Stays

This paper introduces the design of a specific landing gear retraction system presenting a mechanism with four redundant side stays and examines its dynamic behavior during the folding and unfolding processes. First, a concept design of a four-side-stay landing gear retraction system is presented. To get the particular motion during folding and unfolding, the main kinematics parameters are given. Then, the influence of the side stay's kinematic redundancy on the mechanism parameters is examined. Because the mechanism is overconstrained, the allowable parameters belong to a specific region of the space called feasible region. Finally, a dynamic analysis of the over-constrained system is executed by using the Newton–Euler approach and compliant equations. Numerical simulations indicate that this kind of landing gear retraction system equitably share the loads between different side stays, and therefore, the total load at one side stay is greatly reduced.

Investigation into the Interaction of Nose Landing Gear and Fuselage Dynamics

Pilots may experience vibrations in the cockpit during ground maneuvers because of energy being transferred from the nose landing gear to the fuselage. This indicates that the fuselage dynamics could also have an effect on the dynamics of the gear. To study this interaction, a mathematical model of a nose landing gear coupled to a fuselage model with yaw and pitch degrees of freedom is developed. Results obtained by bifurcation analysis show the nature of the interaction between the two systems; in particular, the two-degree-of-freedom fuselage does affect the onset and subsequent severity of nose landing gear shimmy.

Multibody rigid models and 3D FE models in numerical analysis of transport aircraft main landing gear

Abstract Dynamic analyses of a transport aircraft landing gear are conducted to determine the effort of such a complex system and provide capabilities to predict their behaviour under hazardous conditions. This kind of investigation with the use of numerical methods implementation is much easier and less expensive than stand tests. Various 3D models of the landing gear part are defined for the multistage static FE analysis. A complete system of the main landing gear was mapped as a deformable 3D numerical model for dynamic analysis with the use of LS-Dyna code. In this 3D deformable FE model, developed in a drop test simulation, the following matters were taken into consideration: contact problems between collaborating elements, the phenomena of energy absorption by a gas-liquid damper placed in the landing gear and the response of the landing gear during the touchdown of a flexible wheel with the ground. The results of numerical analyses for the selected drop tests and the results from the experiments carried out on a real landing gear were used for verification of FE models and a methodology of the landing gear dynamics analysis. The results obtained from the various simulations of the touchdown have proved the effectiveness of the 3D numerical model and how many problems can be solved in the course of only one numerical run, e.g. geometric and material nonlinearities, a question of contact between the mating components, investigation of the landing gear kinematics, investigation of the energy dissipation problem in the whole system and the stresses influence on the structure behaviour, which can appear in some elements due to overload.

Dynamic Characteristics of Aircraft Landing Gear

Aircraft landing gear can absorb the energy generated and consumed in aircraft landing, taxiing process, thus weakening the vibration of the aircraft, flight safety plays a vital role. This paper established a landing gear dynamics modeling, its mechanical analysis, and through trial and simulation of the dynamic characteristics of the landing gear were studied, with some practical significance.

扁簧式起落架柔性变形的实时状态空间描述

According to the requirements of Unmanned Aerial Vehicle (UAV) ground dynamic analysis, a leaf spring landing gear dynamics model was proposed to accurately reflect the dynamic characteristics of leaf spring deformations. On the basis of modal analysis, the leaf spring landing data were obtained by using the finite element method through modifying stiffness matrix and the model was simplified by modal reduction. After dissolving decoupling vibration differential equations by modal coordinate transformation, a state space model was constructed to describe the dynamics of the leaf spring landing gear. Finally, statics, dynamics simulation tests as well as the leaf spring drop experiments were designed to validate the flexible model. These results demonstrate that the results from state-space model and from finite element software static analysis have only 0.07% error under static conditions. The deviation of drop simulation with this model from real drop experiment results is about 5% when its real-time simulation step is 1 ms, which satisfies the flight simulation requirements.

Recent developments at the numerical simulation of landing gear dynamics

Aircraft landing gears support the aircraft during ground operations, including take-off, landing impact, taxiing, gate handling and maintenance. Mostly for reasons of minimum mass and ground clearance, landing gears are slender structures which exhibit a considerable dynamic response to ground load excitations. As the landing gear is one of the few systems on the aircraft without redundancies, the knowledge of landing gear dynamics is crucial for aircraft design and aircraft safety. Simulation of landing gear dynamics is a cornerstone of aircraft loads analysis, as well for vertical loads resulting from touch-down as for longitudinal and lateral loads resulting from braking, steering and towing. Another important field of interest is landing gear vibrations like gear walk and shimmy. Those phenomena can be brake induced or result from tire spin-up at touch-down or simply from a coupling of dynamics of the running tire and structural mechanics of the landing gear leg. All those effects strongly depend on a number of parameters such as aircraft speed, landing gear vertical deflection, tire pressure and wear of the parts. Many of those parameters can only be estimated and might change during the operation of the aircraft. Numerical investigation is thus a challenging task. Analysis methods exist both in the frequency domain and in the time domain. As stability analysis is straight forward in frequency domain methods, this approach is still often used. However, in many cases nonlinearities are dominant which lead to limit-cycle characteristics of the vibrations. Here, multibody modelling or a mixture of multibody and finite element modelling including time domain simulation is used. In the article, a general outline is given of how vibration problems in landing gears can be treated by numerical analysis methods. The article will start with a classification of typical problems, give a short overview of classical papers, and explain typical approaches. In addition, alternative approaches for stability analysis and for the detection of limit-cycle oscillations as well as state-of-the-art modelling approaches will be presented.

State Feedback Fuzzy Adaptive Control for Active Shimmy Damping

In the context of aircraft, shimmy is an oscillatory phenomenon of the landing gear mainly due to the tire and the landing gear structural dynamics. This phenomenon which can result in severe damage to the landing gear must be damped. This paper presents a new nose landing gear model including an actuator model and a simple tire/road interface description approximating the Pacejka model to allow the active damping of the shimmy phenomenon. Two state feedback control solutions, based on indirect and direct fuzzy adaptive theories, are also presented and compared with a more classic Proportional Integral Derivative (PID) solution. Results corresponding to different test scenarios and robustness analysis show that the proposed controllers are able to efficiently damp the shimmy phenomenon, unlike the PID controller.

Non-linear analysis of a typical nose landing gear model with torsional free play

One of the problems faced by the aircraft community is the landing gear dynamics, especially the shimmy. Non-linear behaviour of landing gear makes the evaluation of the shimmy phenomenon more complex and its prediction more difficult. Notably the non-linearities in landing gear torsional free play tend to destabilize the landing gear, whereas the frictional non-linearity dissipates energy and thus increases the landing gear stability. This article presents the study of the shimmy instability of a typical nose landing gear model developed based on the Li formulations with torsional free play. Finally, the study has been performed to postpone the dynamic instability by introducing magneto rheological fluid-based damper.

Lateral Stability of Aircraft Nose-Wheel Landing Gear with Closed-Loop Shimmy Damper

Shimmy of aircraft nose-wheel landing gear is a coupled lateral and torsional dynamic instability that may occur during take off, taxi, and landing. The potential for shimmy is often discovered when the aircraft undergoes taxi (runway) tests. At this stage the options available to the designer are limited, often to introducing a damper in the steering degree of freedom. This paper presents modeling and analysis of shimmy of a 3 degrees-of-freedom linear nose-wheel landing gear model with a closed-loop shimmy damper mechanism attached to its hydraulic steering. A typical control law is considered for representing the closed-loop hydraulic control in the steering rack and pinion system. The stability of the system is studied using root locus plots. The results for critical velocity obtained for different values of gain in the closed-loop shimmy damper show that it can be simulated by an equivalent open-loop shimmy damper with appropriate value of damping. This suggests that an equivalent open-loop shimmy damper model can be used in place of the closed-loop shimmy damper to simplify the modeling of integrated airframe— landing gear dynamics.