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An Overview of Landing Gear Dynamics
Abstract
One of the problems facing the aircraft community is landing gear dynamics, especially shimmy and brake-induced vibration. Although neither shimmy nor brake-induced vibrations are usually catastrophic, they can lead to accidents due to excessive wear and shortened life of gear parts and contribute to pilot and passenger discomfort. Recently, NASA has initiated an effort to increase the safety of air travel by reducing the number of accidents by a factor of five in ten years. This safety initiative has spurred an increased interest in improving landing gear design to minimize shimmy and brake-induced vibration that are still largely misunderstood phenomena. In order to increase the understanding of these problems, a literature survey was performed. The major focus of the paper is to summarize work documented from the last ten years to highlight the latest efforts in solving these vibration problems. Older publications are included to understand the longevity of the problem and the findi...
... Material response to dynamic loading distinctly differs from that of static loading [8,9,10]. In order to improve safety and reliability, advanced materials that offer suitable dynamic loading response are selected during landing gear design [11]. Safelife fatigue of aerospace components is used to predict the life. ...
... From strength data compiled for different processing routes, the Weibull scale, shape and location parameters indicating respectively spread, characteristics and minimum strength can be estimated and ranked. Weibull analysis and the applicability of the interpretations are discussed [11], the above relation suggests that the Weibull analysis is an effective quantitative tool for engineering applications. This survey suggests that ductile materials, possess Weibull modulus of 10 to 200 especially in metal alloys. ...
Functional and constraints optimized materials selection procedures using normalized property maps is a notable advancement in the area of materials development. Advances in manufacturing include techniques such as Dynamic Materials Modeling (DMM), that enables prediction of suitable processing conditions applied during bulk forming operations to obtain designed microstructures. Design of components for safety-critical applications is best done by combining these advancements in materials and manufacturing with reliability analysis. The present work examines the influence of processing history on the strength of 4340 steel which is used in the aircraft landing gear, estimated using Weibull Reliability Analysis (WRA). From strength data compiled for different processing routes, the Weibull scale, shape and location parameters indicating respectively spread, characteristics and minimum strength are estimated and ranked. These rankings guide designers to recommend appropriate processing routes for reliable performance. Weibull analysis of strength data of 4340 steel derived from various processing routes, including that of as-cast and wrought conditions, indicate that better ranking is obtained in wrought condition than the as-cast condition. The high Weibull modulus is indicative of better reliability of the wrought material. It is concluded that processing history significantly influences the reliability of safety-critical components.
... Substantial friction develops in the oleopneumatic shock absorber in slip and stick modes (Kru¨ger et al., 1997). Since friction dissipates energy it has a stabilizing effect and alleviates the subcritical limit-cycles of the nonlinear system (Padmanabhan and Dowell, 2015;Arreaza et al., 2016) as observed in physical tests as well (Pritchard, 2001). Coulomb friction is typically modeled as a constant torque, while an effective damping coefficient representing Coulomb friction (Padmanabhan and Dowell, 2015) and hysteresis characteristic for Coulomb friction (Somieski, 2001) have also been proposed. ...
... The calculation of the net Coulomb friction force is presented here following Fled's analysis (Fled, 1990) who computed the equivalent viscous damping contributed by friction in shock absorber bearings and pressure seals. Bearing friction force depends on the normal force acting on it, which is in turn a function of the gear dynamics (Pritchard, 2001). The friction torque resisting the piston's rotational motion is ...
Landing gear shimmy remains a challenge in aircraft design despite abundant advances in aircraft engineering in the past few decades. Accurate shimmy prediction is closely tied to availability of dynamic models with all relevant types of motions and key nonlinear elements, a matter which has been accomplished in the present study through including rotational, lateral, longitudinal, and axial degrees of freedom and tire, shock absorber, and Coulomb friction nonlinearities. Using multi-body dynamic simulations, stability of the nose landing gear is studied as a function of key system parameters. Influences of nonlinearities are investigated in isolation, with a more in-depth look at the Coulomb friction effect, which is modeled as a function of the shock absorber stroke rate and rotational shimmy speed. It is found that Coulomb friction is a key factor in determining the onset and type of shimmy. The effect of friction parameters is then studied using nonlinear sensitivity analyses, and witnessed trends are utilized to draw design recommendations.
... In [15] lateral response of the landing gear investigated with the effect of ground unevenness using mathematical model. Summary of the literature survey on solving landing gear vibration problems are presented in [16]. In this paper, mathematical model is developed to analyze the shimmy oscillation of nose wheel landing gear with consideration of total 5 DOF such as torsional angle , lateral bending angle , axial displacement of strut , axial displacement of tire and slip angle . ...
This paper presents mathematical modeling and analysis of shimmy oscillations for a light weight airplane single wheel nose landing gear. Shimmy is a self-excited oscillation which occurs usually on the nose wheel landing gear assembly during ground maneuvers which is governed by the dynamic characteristics of the landing gear and tires. Shimmy oscillation may lead to reduce the fatigue life of the landing gear and fuselage structure. So, the study of dynamic response and stability boundaries of landing gear plays crucial role while designing of airplanes. In earlier studies of vehicle shimmy only 3 degrees of freedom (DOF) considered such as torsional mode, lateral bending mode and tire lateral deformation. In this work along with above mentioned DOF, two more additional DOF introduced such as axial vibration of strut and tire in order to include the effect of vertical dynamics on shimmy model. Gyroscopic coupling effect also included in the model to study its influence on shimmy. Analysis carried out to determine critical velocity region for occurrence of shimmy and to investigate the effectiveness of ground unevenness on the landing gear system for two different runway conditions such as flat runway and random roughness runway. The results are more helpful to study significant interaction between the different parameters of landing gear and to represent stability boundaries.
... Namely, they must be light, since during the flight landing gear is just a dead weight; they must be long enough to allow a sufficient rotation of the aircraft during take-off; they should be able to absorb the energy of landing impact, which requires shock absorbers with a considerable stroke in order to limit the load occurring during landing [8]. All these requirements result in relatively slender landing gears, which are therefore prone to undergo undesired vibrations, if not properly designed [16,45,57]. ...
The implementation of the nonlinear tuned vibration absorber (NLTVA) for the suppression of shimmy vibration in towed wheels is addressed in this study. We adopt a modified straight tangent tyre model of a single-degree-of-freedom towed wheel system with an attached NLTVA. Stability analysis illustrated that the NLTVA can significantly improve the stability of the equilibrium of the wheel. Bifurcation analysis highlighted the existence of large bistable regions, which undermines the system’s safety. However, numerical continuation analysis, coupled with a dynamical integrity investigation, revealed that the addition of an intentional softening nonlinearity in the absorber restoring force characteristic enables the complete suppression of the bistable regions, also reducing the amplitude of shimmy oscillations in the unstable region. Quasiperiodic motions were also identified; however, their practical relevance seems marginal.
... Brake-induced vibrationof landing gear is a complex multi-disciplinary coupling problem [1]. When the aircraft brakes, the huge kinetic energy generated by the wheel deceleration is transformed into heat energy, which causes different vibration of landing gear [2], such as chatter, squeal and gear walk. ...
The low-frequency landing gear walk of aircraft during braking processis studied. Firstly, by virtual of LMS Virtual.Lab motion software, the multi-body dynamic model of the landing gear is established, the motion pair and internal and external loads are applied, and the torsion spring is set at the connection between the landing gear and the fuselage to simulate the flexibility of the landing gear. Then, the variation of friction coefficient of brake discis considered in the model of braking pressure and torque. When the braking control system works, if the braking pressure is less than the limit value, the gear walk is less affected by the friction characteristics of the brake disc. If the braking pressure reaches the limit value, the law of gear walk is the same as that of the pilot's manual control of the braking pressure. At this time, the gear walk is only affected by the positive and negative slope of the friction coefficient of the brake disc. If the friction coefficient curve of the brake disc presents a negative slope, it may cause gear walk, and the greater the absolute value of the slope, the more obvious the gear walk is. Improving the friction characteristics of brake discs can provide a new strategy forgear walk control.
... The majority of the literature sources take up one or two aspects of the mechanical design, such as structural integrity [12], the strength of materials [13], gear behavior in a thermal environment [14], vibration and dynamics [15,16] and shimmy phenomenon [17] including the nonlinear analysis of the structure and deflections in multibody dynamics [18] as well as uncertainty analysis [19]. Such activities are suited for below the preliminary-level of the design. ...
We analyze the functionality of the landing system of a regional aircraft in the extension and cruise flight modes and validate safety requirements through the fault tree analysis. The main landing gear system is captured in the electromechanical–fluidic domain and system behavior is abstracted in an elementary hydraulic circuit. The functional representation is then constructed into a fault tree which allows analysis of the failure propagation originating at different branch terminals, for instance, at the main landing gear actuator which extends the gear and holds it retracted during the cruise, door actuator, door uplocks, and hydraulic power supply. Each component is assigned a failure probability. Each failure mode is abstracted as a top-level event having a probability of failure and through Boolean combinations of component failures in the lower branches. Two reliability aspects considered are the availability to fully lower the landing gear and the integrity of inadvertent gear or door extension while cruising. Architectural changes through undercarriage system reconfiguration and component redundancy have been exploited to improve system failure rates. The analysis determines the overall system failure rate against the flight cycles. The process is agile to accommodate design changes with the evolution of architecture during the systems engineering lifecycle.
... The landing gear is highly likely to vibrate during the aircraft take-off, landing, and taxiing [29,30], so the downlock mechanism must possess a certain function of perturbation resistance. The stop block, as the important component of the downlock mechanism, is mainly used to prevent the excessive motion of lock links. ...
A dual-sidestay landing gear is prone to locking failure in the deployed state due to the restriction of movement between two sidestays. However, the principle of its locking movement still remains unclear. The present study is aimed at investigating the synchronous locking performance of the dual-sidestay landing gear based on the singularity and bifurcation theory. From the perspective of the kinematic mechanism, the reason for high sensitivity to structural dimensions in the locking process is explained, and the locked position is investigated by employing the numerical continuation method in the case of a single-sidestay landing gear. Afterwards, the reason for the locking failure of the dual-sidestay landing gear is analyzed, and a kinematic optimization method for the synchronous locking is proposed. The results reveal that the lock links must reach the lower overcenter singular point to fully lock the landing gear, and the singular point is sensitively affected by structural parameters. Owing to the different positions of singular points, the movements of fore and aft sidestays seriously restrict each other, causing locking failure of the dual-sidestay landing gear. The singular points of two sidestays can be optimized to be approximately identical, making their movements more coordinated.
... Such kinds of monitoring systems can be also used for the assessment of system vibrations, which may include self-induced and brake-induced oscillations. The aircraft industry and researchers have dedicated many efforts in developing techniques and methods devoted to the measurement of operational loads and have elaborated proper processes for flyable hardware architectures overcoming many obstacles [4][5][6]. Within the following paper, a short bibliography summary of a number of the prevailing solutions for landing gear loads monitoring, for various purposes, is reported. ...
In aeronautics, hard landing is a critical condition as the aircraft approaches the runway with a vertical velocity that exceeds 2 m/s. Beyond that level, the energy that should be then absorbed by the whole structure could cause severe damage to the landing gear and the whole structural system. This document reports on the set-up, execution and results of a preparatory test campaign performed on a small landing gear (LG) demonstrator instrumented with a fibre-optic sensor system. In detail, a leaf spring landing gear was released from a drop tower to detect information about the strain state and the related acceleration history of some specific components during the impact. The objective of the present research is the development of a method for assessing whether hard landing is experienced, and to what extent. Deformation measurements through an integrated Fibre-Bragg grating (FBG) network allowed retrieving impact velocity by a devoted, original algorithm. The proposed preliminary methodology is the base for assessing a more complex procedure to correlate structural response to the energy entering the structure during the touchdown event.
... Typically, the airframe flexibility effects reduce the maximum force at the LG, but the resulting structural dynamic response is more severe when compared to a rigid equivalent model [12,1]. Airframe flexibility effects in landing dynamic simulations are typically captured by a modal representation of the airframe using the Craig and Bampton method [13,14,15] and this linear model is acceptable for a typical transport-category aircraft [16]. Since this structural model is a linear one, a linear transfer function can be identified to replace the flexibility effects and capture the behaviour at selected interface nodes with only a slight reduction in accuracy and a reduction in computation time [17]. ...
... The importance of including airframe flexibility was investigated in 1956 by Cook and Milwitzky, who found that, when compared to a completely rigid airframe, the interactions with the flexible structure and dynamic magnification effects could either reduce or increase the loads on the landing gear [1]. Reviews of landing dynamics conducted by Krüger et al. [2] and by Pritchard [3] indicate the importance of including aircraft flexibility effects in the modeling of ground dynamics for simulation. The work by Pritchard focuses on the importance of airframe flexibility in predicting and managing LG instabilities, such as shimmy. ...
The landing impact that occurs during aircraft touchdown results in the development of significant loads and accelerations within the airframe. Accurate knowledge of the landing loads is not only necessary for predicting the resulting stresses for design of the airframe, but also for designing strategies to mitigate the vibratory loads and improve the ride quality. Perceived passenger comfort is dependent both on the magnitude of the acceleration experienced by the passengers and on the frequency content of the vibrations. Using a flexible airframe model to better capture the loading regime and frequency response at landing impact, this study optimizes various single-port (two-terminal) passive mechanical networks that consist of an arrangement of springs, dampers, and inerters to minimize passenger discomfort and peak forces applied to the aircraft. The performance is compared to a baseline oleo-pneumatic shock absorber. First, the candidate layouts are optimized, then the observations from this exercise are used to synthesize a mechanical network with a desired frequency response. All considered mechanical networks demonstrated the ability to control the frequency content of the input loading, thus resulting in a reduction in accelerations and an improvement in all comfort parameters used in this study over the oleo-pneumatic baseline.
... The dynamic modeling and analysis of a landing gear with an oleo-pneumatic shock absorber has received relatively large attention in the literature [4][5][6]. The analysis model with sprung and unsprung mass vertical degrees of freedom is established in Milwitzky [7]. ...
The aim of this paper is to obtain the strut friction–touchdown performance relation for designing the parameters involving the strut friction of the landing gear in a light aircraft. The numerical model of the landing gear is validated by drop test of single half-axle landing gear, which is used to obtain the energy absorption properties of strut friction in the landing process. Parametric studies are conducted using the response surface method. Based on the design of the experiment results and response surface functions, the sensitivity analysis of the design variables is implemented. Furthermore, a multi-objective optimization is carried out for good touchdown performance. The results show that the proportion of energy absorption of friction load accounts for more than 35% of the total landing impact energy. The response surface model characterizes well for the landing response, with a minimum fitting accuracy of 99.52%. The most sensitive variables for the four landing responses are the lower bearing width and the wheel moment of inertia. Moreover, the max overloading of sprung mass in LC-1 decreases by 4.84% after design optimization, which illustrates that the method of analysis and optimization on the strut friction of landing gear is efficient for improving the aircraft touchdown performance.
... In this study, the authors represented airframe flexibility using an equivalent spring-mass-damper system to capture the first two flexible modes. This approach has generally been abandoned with the advent of dynamic substructuring methods, such as the Craig and Bampton Method [3], where modal representations of the airframe have been the dominant approach seen in literature [4,5]. ...
Airframe flexibility effects have typically been captured by modal reduction of the airframe. Although efficient, this model may still be prohibitively expensive for preliminary design studies. This paper employs time- and frequency-domain system identification techniques to form a multi-objective optimization problem to identify equivalent transfer functions representing airframe flexibility effects. Pareto-optimal sets are first identified for an equivalent transfer function of a force element between the landing gear attachment point and the centre of gravity of a 150-passenger regional jet, and a second transfer function from the input landing gear force to the cockpit acceleration. The reduced models demonstrate the ability to generally capture flexibility effects with reduced computation times. The combination of time-domain and frequency-domain information ensures the positive time-history matches while the model remains physically realizable as it is rooted to frequency response obtained from the finite element model. It is hypothesized that this physical link allowed the model to be robust to the landing initial conditions.
... At a robust design for antiskid control, the gear walk phenomenon must be considered, since the estimation of braking force depends on the angular velocity of the wheel and the velocity of the wheel hub. Pritchard (2001) remarks the relevance of the study of the dynamics of landing gear, mainly due the effects of vibration and shimmy induced by braking, highlighting its criticality on aircraft safety. Krüger et. ...
In many aircraft applications, especially on an antiskid control design, it is important to understand and consider the gear walk phenomenon, which is characterized by the deflection on the landing gear structure due the high braking force acting at the tire contact with the ground. This phenomenon is observed on drop tests, and its prediction on landing gear design depends on an adequate evaluation of the equivalent stiffness and damping of the structure, which is difficult, since they depend on the mechanism configuration. In this paper, it is presented a grey-box identification methodology for estimating these parameters of the landing gear, based on simulated data of a drop test. As the drop tests are mandatory obligatory for certificating modern aircraft according to e.g. Federal Aviation Regulations (FARs) by the Federal Aviation Administration (FAA), we hope to introduce a method based on measurements that are available at the design phase. The method will be useful to decrease men/hour costs and increase reliability by enabling better and more accurate anti-skid design.
... Aircraft industry and research have dedicated many efforts in developing both suitable load measurement techniques and methods, and proper processes for flyable hardware architectures overcoming many showstoppers. [5][6][7] In the following, the authors report a bibliography scenario overviewing some of the existing solutions for landing gear loads monitoring, for different objectives. ...
With the prospective of developing an integrated monitoring system aimed at assessing whether a landing gear has experienced hard impact during the approach, a dedicated method is developed aimed at determining vertical speed by means of strain measurement via FBG strain sensors. Representative impacts on simple structural elements have been reproduced in laboratory, as aluminum slender beams of different lengths were dropped from given heights onto a steel plate base. Contact velocities have been estimated by deformations detection.
... Mark Arnold et.al. [1] analyzed the uplock mechanism frame, linkages and hook. Each machined from billets of steeling having a number of different grades dependent upon the required yield stress and ultimate stress allowables. ...
In aviation, the undercarriage or landing gear is the structure (usually wheels) that supports an aircraft on the ground and allows it to taxi. The landing gear being one of the components of the aircraft experiencing very high loads, very high strength materials are made use of in its construction, in order to keep its size and weight to a minimum. This paper deals with the study and design of the uplocks lever, which is an important part of the landing gear in aircraft in an existing aircrafts and record the various design parameters and determining the optimal design. Model of the uplock lever is generated in CATIA V5 and calculation of loads acting at various points is done in NASTRAN and minimum required dimensions of different components in the assembly and their design with drafting tools is done.
... The difficulties vary between a nose gear and a main gear and a tail gear. Although Richard Courant first introduced the Finite Element Analysis theory in 1943, the study of the UAV landing gear using FEA is not heavily done and published [6][7][8][9][10][11][12]. In order to do FEA, it is necessary to complete many steps in order to procure accurate results, including appropriate assumptions. ...
... The resulting simulations revealed that the vibrations were due to the elastic properties which were maximum in the free ends of the landing gear model. And also the stresses generated were particularly higher in the adjoining section with the fixed fuselage [6][7][8][9][10][11]. During the landing phase of such a plane, at first, the main gears generally will touchdowns on two points and will then after several seconds, the tire of the nose gear touchdowns the ground. ...
During the landing of aircraft, the landing gear system absorbs energy through the impact of landing. Impact landing produces stress as well as deformation. The current study focuses on the numerical simulation of the landing gear system with the help of ANSYS software. Deformation is an important criterion to consider when testing a model under certain loading conditions which occurs along its span length. The majority of the deflections occur at free ends of the forks of the landing gear. The bottom plate being fixed has zero deflections in all directions. The deflections occur along the y-axis. As the impact loads were increased, the deformation increased gradually. Modal analysis has been performed to obtain the natural frequency of the model made of Aluminum Alloy Al 6061-T6. The maximum frequency was found to be 974 Hz causing a deflection of 403.59 mm. These Natural frequencies have help in calibrating the operating frequency to avoid resonance.
... The importance of including airframe flexibility was investigated in 1956 by Cook and Milwitzky, who found that the interactions with the flexible structure and dynamic magnification effects could either reduce or increase the loads when compared to a completely rigid airframe [1]. Reviews of landing dynamics conducted by Krüger et al. [2] and by Pritchard [3] indicate the importance of including aircraft flexibility effects in the modeling of ground dynamics for simulation. The work by Pritchard focuses on the importance of airframe flexibility in predicting and managing LG instabilities, such as shimmy; the work by Krüger covers the requirements for the simulation of various cases, including the shimmy problem, and the dynamics at touchdown and ground-roll. ...
... The vertical force, Fz can be correlated with the grass compression and can be used for coefficient calculations (braking friction μB, and rolling resistance kRR, coefficients, side force FY, coefficient). This approach is alternative to commonly used laboratory drop tests of landing gear [9][10][11][12][13]. ...
... Vibration absorbers are common in many structures which undergo large motions or are subject to vibrations which are detrimental to the overall performance or health of the structure. Considering aerospace applications, for decades they have been used to ensure lead-lag stability of helicopter rotor blades [15] as well as alleviate landing loads and suppress shimmy in aircraft landing gear [16]. Typically these absorbers are restricted to a combination of springs, dampers and lumped masses [17], however, in 2002 Smith [18] introduced a mechanical element known as an inerter that is now being used extensively in the field of mechanical networks * . ...
This paper presents a novel method for gust loads alleviation in a truss-braced wing in which an inerter-based device located in the truss-structure is used to reduce peak-loads during a discrete “1-cosine” gust. Three candidate layouts are considered, and the device parameters are optimized to target the response of the first three structural modes. It is demonstrated that either a single damper or a combination of inerter-based devices can be used to achieve a reduction of approximately 4% for spanwise locations inboard of the strut attachment point and that this reduction is consistent across the full range of gust gradients. Furthermore, it is noted that the inerter-based device has a significantly smaller damping coefficient than the case where just a damper is used and that the device parameter values are viable within the scope of an aerospace application.
... Landing gear is one of the critical systems of an airplane and its design as well as reliability play a significant role in the safety of operation, airfield performance and comfort for passengers. First, it is crucial to know the loads on landing gear for airfield maneuvers in order to design and parametrize this system properly [1][2][3][4]. Second, the knowledge of reaction forces and moments on a landing gear wheel enables to calculate structural loads that causes possible fatigues and cracks during the life. ...
The aim of this study was to design, develop and apply practically a wheel dynamometer for aircraft landing gear testing. The dynamometer system was designed to measure two force components acting along the longitudinal and vertical axes of the wheel as well as and three moments acting around the longitudinal, transversal and vertical axes. It consists of a sensor unit that is embedded in the wheel hub, a modified rim with a tyre as well as a data acquisition and transfer system that enables the measured signals to transfer wirelessly to a portable computer or another device (smartphone, tablet). The sensor unit was developed based on strain gage measurement technology. The prototype system was calibrated in a stationary test stand, then installed on a PZL 104 Wilga 35A for airfield tests. Primary test measurements were performed with the aircraft taxiing at “walking man” speed and proved system’s performance. Certification for ground and flight tests of airplanes has been considered for the presented dynamometer system.
... In this investigation, the aircraft structural flexibility was reduced to an equivalent spring-mass-damper system and, as such, cannot capture higher-frequency modes. Reviews of landing dynamics conducted by Krüger et al. [2] and by Pritchard [3] indicate the importance of including aircraft flexibility effects in the modelling of ground dynamics for simulation. The work by Pritchard focuses on the importance of airframe flexibility in predicting and managing gear instabilities, such as shimmy; and the work by Krüger covers the requirements for the simulation of various cases, including the shimmy problem, and the dynamics at touchdown and ground-roll. ...
Advancements in simulation and analysis tools and the use of composite materials have allowed for optimized and lightweight aircraft structures; however, that comes at a cost of increased airframe flexibility. The importance of including airframe flexibility effects in landing loads analysis was recognized in the 1950s where these effects resulted in either an increase or decrease in loads transferred to the airframe. Since that time, there have been significant developments in substructure coupling methods for dynamic analysis allowing for accurate and computationally-efficient analysis of coupled substructure loads. Despite this, common practice is to obtain landing loads by representing the airframe as a rigid structure, then apply this loading to a dynamic finite element simulation. This simplification of the airframe is also manifested in the standard landing gear drop-test technique where a landing gear is attached to a rigid structure that represents the aircraft. In this study, the structural dynamics for a generic 150 passenger regional jet in three landing conditions were compared when using a flexible and fully-rigid airframe model. In general, the peak forces were decreased but the peak moments were increased at the attachment point of the main landing gear for a fully-flexible airframe model when compared to the rigid equivalent. The inclusion of flexibility effects also resulted in the introduction of higher-frequency vibrations and a change in the open-loop response of the aircraft.
... Recently, the mechanism of the conventional landing gear has been studied through load analyses [16][17][18][19] made by CAD software. The different ways that a failure can occur, 20,21 and the reliability of the landing gear system 22,23 have also been recently analysed. And these researches provided an interesting basis of knowledge for the design of reliable landing gear. ...
It is the first mission for a landing gear retraction system to extend the structure during the phases of take-off and landing of the flight. Besides, the structure should be available to improve the reliability, strength and stability of the system while reducing the influence of the landing gear on the total drag. However, a large number of airplane accidents are due to the malfunctions or failures of the landing gear retraction system. In this paper, a novel design of retraction system is proposed. Instead of having only one side-stay to execute the desired motion, this new design proposed an over-constrained mechanism with four side-stays, which augments the structural strength and stability of the landing gear system with six over constraints. With such configuration, a second actuating motor to retract the landing gear can be inserted regardless of the first actuator to augment the reliability on the execution of the mechanism. Analyses on the properties of the landing gear retraction system with four side-stays show that the landing gear strut has a vertical motion, which decreases the working and storage spaces used for the system. Finally, this paper examines the statics and the stiffness coefficients of the retraction system with respect to its structure parameters. This provides the optimum structure for the landing gear system in terms of strength and reliability.
... The used analysis tool provides a powerful and unified system for tackling the engineering problem. The selected tool effectively handled various parts of the work including static structural analysis, parametric study, optimization study and impact analysis (Pritchard 2001). ...
... Dynamic simulations in the systems development process should ensure that the dynamic loads on the LG components are within the design limits necessary to comply with high performance and safety requirements for operation on rough runways. A complete overview of recent developments in the area of LG dynamics is provided in [7], including a survey of the most critically needed enhancements to LG simulations; among those listed is the requirement for a comprehensive (nonisothermal) friction model for LG bearings. A relevant example of the dynamic modeling of LG is shown in [8], where the impact of repetitive and excessive bearing loads on the LG fatigue life is investigated, demonstrating the application of the general theory of multibody systems [9]. ...
A transient numerical model for studying the thermo-tribomechanical behavior of an aircraft landing gear is presented. The study reveals the major heat sources and heat sinks that impact the characteristic thermal behavior of the landing gear shock absorber. The severe in-service performance degradation and reported structural damage can be explained as a consequence of the heat generated by the high drag loads induced by rough runways on the bearings, and by the high sliding velocities of the piston. A conclusive model may lead to improved landing gear performance once the transient process of heat generation in a phase-changing grease- lubricated lower bearing is fundamentally understood. A novel tribotopological lubrication theory is derived in order to take into account all distinct physical phases of the non-Newtonian Bingham lubricant. The governing equations are solved using a hybrid numerical solver that is optimized for numerical efficiency and fast convergence. The proposed framework is validated against existing theories and results, and it demonstrates accurate predictions of the thermal performance of the landing gear. Strategies to passively optimize the lower bearing lubrication mechanism are further suggested in order to achieve optimal thermal performance of future aircraft landing gear.
... A number of modeling techniques proposed by Denti and Fanteria (2010) and Tadeusz et al. (2006) have been utilized to accurately capture the effects of wheel ground contact and the corresponding response. A literature survey conducted by Pritchard (2001) summarizes the work that has been done in the past with regards to analytical, experimental, and some computational modeling of landing gear dynamics. ...
Aircraft landing gear assemblies comprise of various subsystems working in unison to enable functionalities such as taxiing, take-off and landing. As development cycles and prototyping iterations begin to shorten, it is important to develop and improve practical methodologies to meet certain design metrics. This paper presents an efficient methodology that applies high-fidelity multi-disciplinary design optimization techniques to commercial landing gear assemblies, for weight, cost, and structural performance by considering both structural and dynamic behaviours. First, a simplified landing gear assembly model was created to complement with an accurate slave link subassembly, generated based of drawings supplied from the industrial partner, Safran Landing Systems. Second, a Multi-Body Dynamic (MBD) analysis was performed using realistic input motion signals to replicate the dynamic behaviour of the physical system. The third stage involved performing topology optimization with results from the MBD analysis; this can be achieved through the utilization of the Equivalent Static Load Method (ESLM). Lastly, topology results were generated and design interpretation was performed to generate two designs of different approaches. The first design involved trying to closely match the topology results and resulted in a design with an overall weight savings of 67%, peak stress increase of 74%, and no apparent cost savings due to complex features. The second design focused on manufacturability and achieved overall weight saving of 36%, peak stress increase of 6%, and an estimated 60% in cost savings.
... The used analysis tool provides a powerful and unified system for tackling the engineering problem. The selected tool effectively handled various parts of the work including static structural analysis, parametric study, optimization study and impact analysis (Pritchard 2001). ...
As of today, most aircraft are endowed with Anti-lock Braking Systems that are active during landings and rejected take-off manoeuvres, ensuring the maximum exploitation of road-friction capability. Due to strict certification issues, the braking controller must function using only signals that are local to the landing gear, which is the aircraft sub-system hosting the braking actuators. In the most common scenarios, the only available signals are the wheel speed and the braking pressure. This limited set of information prevents the use of advanced braking control architectures which are now mainstream in the automotive sector, i.e., those based on the regulation of the wheel slip, so that typical aircraft Anti-lock Braking Systems are usually based on the regulation of the wheel deceleration. This paper investigates how a reliable wheel slip estimation can be achieved using wheel speed and braking pressure signals, analysing different wheel slip observers options. In particular, a model-based approach that uses a sliding-mode observer is proposed, together with a black-box approach based on Nonlinear Auto-Regressive models with eXogenous input, with a neural network implementation. Both approaches are tested and compared on experimental data, proving that the obtained estimation performance are adequate for use in closed-loop braking systems.
Consideration of standard landing cases from technical guideline document is the traditional design practice followed to ascertain aircraft landing loads. A rationale approach on landing load generation and its impact on flexible airframe dynamic response is explored, considering multi-variate landing conditions for the first time on land-base high performance aircraft. Methodology on nonlinear landing dynamic response simulation is developed by amalgamating inputs such as nonlinear nose and main landing gear dynamic models, aircraft rigid body dynamics, low speed aerodynamic and thrust forces. True representation of landing gear nonlinear oleo-pneumatic strut and tire characteristics, variable geometric strut structural stiffness and nonlinear spin-up friction resulted in satisfactory correlation of vertical and longitudinal dynamic response simulation with experimental drop test results. The adequacy of lateral dynamic model is established from the compatibility condition of landing gear and tire dynamics. A down selection methodology is worked out considering total probability and first order sensitive multi-variate landing parameters such as pitch, roll and vertical descent speed, taking into account the plausible statistical variation. Transient dynamic response simulation is then performed for the critical landing cases, on a flexible airframe finite element model by inputting landing load time history as base excitation motion. The dynamic amplification of acceleration response on flexible fuselage nose location from the simulation, is verified with flight data accelerometer frequency response. The application of flexible dynamic responses in ensuring the structural integrity of airframe is elaborated. The proposed methodology on landing load generation is pragmatic, in comparison with the traditional design practice and provides insight during early design phase thereby achieving landing gear subsystem development in-unison with airframe structural clearance aspects.
A new combined electric anti-skid braking system of a high-speed unmanned aerial vehicle is designed to improve the stability and to reduce the system sensor noise. An electric anti-skid braking mechanism model considering the sensor noise effect is built in MATLAB/Simulink. The stability of a slip ratio braking system and a deceleration braking system is analyzed using the Routh criterion and Lyapunov stability method. Then the UAV ground taxiing dynamic model is built in LMS Virtual. Lab Motion. The braking performance and dynamic responses are studied under the control of the designed braking system using a co-simulation method. Conclusions show that the designed braking control system can solve the sensor noise problem effectively and the stability and robustness are both ensured under this control law.
In this paper, a nonlinear dynamic landing gear model considering the influence of the coupling of the shock absorber stroke variation and the landing gear longitudinal motion with an anti-skid PID braking control system that captures gear walk is established. This gear walk model is verified by comparing with the response from a virtual prototype model. Then a parameter sensitivity analysis is carried out to find out the parameters with greater effects on gear walk and braking performance. The short time Fourier transform is employed to study the transient gear walk amplitude-frequency response, whose results are used to define the optimization constraints. A feedforward controller is proposed as part of the braking control law. Single-objective optimizations are then carried out to improve the gear walk performance while maintaining the braking efficiency. It is shown that the feedforward control, together with the PID feedback controller, can provide 25.68% reduction of the maximum gear walk angle while satisfying other constraints. The stability and robustness of the optimized braking law is verified under different working conditions. Multi-objective optimization is then used to highlight the trade-off between the gear walk vibration and the braking efficiency.
The stability of tailsitters is severely impacted by ground friction/reaction forces when the landing gear contacts the ground. This paper analyzes the stability of tailsitters during taking off from and landing on the ground. A distributed propulsion tailsitter with four electrically driven propellers is studied and modeled. The pitch loop of this tailsitter can be stabilized by both aerodynamic effectors immersed in the propeller slipstream and differential thrust of the propellers installed on upper and lower wing sides. The stability criteria and stability margin of tailsitters in the landing-gear/contact-ground flight stage are defined. The open-loop stability of tailsitters on high-friction and low-friction grounds is analyzed. The closed-loop stability of tailsitters with thrust-vectoring control and trailing-edge elevators control are discussed separately. On high-friction ground or uneven terrain, the tailsitter pivots about the ground contact point instead of the center of gravity. It is shown that the ground friction/reaction forces induced by the trailing-edge elevators generate a reversed pitching moment, which makes the pitch loop of the tailsitter unstable. A Proportional–Derivative controller with thrust vectoring as an effector is given and proved to guarantee the pitch loop stability. The influences of the thrust increase rate are also discussed. The experimental results of a tailsitter unmanned air vehicle verify the conclusions of this paper.
Landing gear is the undercarriage of an aircraft and is typically designed to support the vehicle only at post-flight. A strut is a structural component designed to resist longitudinal compression. Struts provide outwards-facing support in their lengthwise direction, which can be used to keep two other components separate, performing the opposite function of a tie. The need for lightweight, high performance flying machine has today shifted the emphasis from the use of conventional advanced metallic materials to that of composites. At critical situations for both civil and military aircraft, they are needed to be landed on rough landing surfaces which may cause structural damage to the landing strut. For that specified reason, the landing strut made to be very strong, the main parameter that here to be considered is a strength to weight ratio, the strength of the strut should be very high at the same time the weight should be reduced. For that here we have introduced the strut which is made of composite material which satisfies our requirements. The composite material that we have selected here for our fabrication of strut is glass fiber and carbon fabric of alternate layers and also the structural analysis of landing strut is carried out in ANSYS for various impacting conditions with respect to aircraft weight.
Landing gear shimmy is an important issue in modern civil aircraft development and airworthiness certification. For the complex nose landing gear of a civil aircraft, the three-dimensional(3D) simplified dynamic model is developed and shimmy characteristic parameters of the rigid-flexible coupling structures are obtained under different simulated shimmy flight test scenarios-typical taxing speed, weight/center of gravity and runway plank excitation. The landing gear stability in normal configuration is validated. The influence of the shimmy damping, tire relaxation length and cornering stiffness on the stability is analyzed respectively. Interpretation and induction of applicable Chinese Civil Aviation Regulations for shimmy, besides landing gear shimmy airworthiness certification practice are illustrated. A reasonable airworthiness verification and certification “Building Block Model”, which includes airworthiness requirements capture, simulation, virtual test and test (equipment qualification test, landing gear system laboratory test and shimmy flight test), is proposed. The civil aircraft shimmy case study demonstrates the feasibility of virtual verification technology to assist the shimmy compliance finding.
To study the dynamic characteristics of aircraft landing gear and carry out successive optimizations, a mathematical model of flexible landing gear is established by the Hamiltonian principle. The dynamic model includes a tire force estimation derived from the impact model. Dynamic analysis with the flexible model is then conducted. Stress distribution is obtained from the dynamic analysis, which can be used for fatigue analysis, optimization design, etc. To achieve better dynamic characteristics in terms of vibration reduction, a multi-objective optimization problem is formulated and solved via a simple cell mapping algorithm. Optimal simulations indicate the quality of optimal structural designs. Compared with the baseline structure, candidate optimal designs can improve dynamic performance of fuselage vibration suppression, shock absorber efficiency, and stress settling time. The proposed multi-objective optimal parameter design provides a fast tuning procedure that saves considerable time compared to finite element method-based optimization. In addition, the optimal parameter set provides useful interface information for detailed landing gear structural modeling that serves other analysis purposes.
Shimmy vibration is a common phenomenon in landing gear systems during either the take-off or landing of aircrafts. The shimmy vibration is undesirable since it can damage the landing gear and discomforts the pilots and passengers. In this work, tensor product model transformation (TPMT) and twisting sliding mode algorithm (TSMA) are utilized to design a robust controller for suppression of the shimmy vibration. The design has two steps. First, the TPMT is applied to determine the first part of the controller to suppress the vibration of the undisturbed system. After that, the TSMA is adopted to obtain another part of the controller to eliminate the remaining vibration caused by disturbances. By integrating these two parts, the proposed controller is obtained. Simulation studies are provided to demonstrate the effectiveness of the controller.
This paper describes the details of an experimental investigation focusing on the structural integrity and evaluates the structural characteristics like strain and deformation of the full-scale composite wing of aerial vehicle. The structural testing of composite wing is greatly influenced by the size of the structure, nature of loads, and boundary conditions at the supports. It is conventional to assume span-wise aerodynamic load distribution for aerial structure of typical aspect ratio, i.e., between 10 and 15. Apart from the span-wise load distribution on the wing, the other important parameters like chord-wise distribution of load, angle of attack at which the primary composite structure to be tested, the landing gear loads at the wing, and engine interfaces need to be simulated during the test. Generally, wing structures are tested for the worst case in terms of combined lift and drag which simulates the worst bending and twisting loads of the flight envelope. Care should be taken for distributing the lumped loads at desired locations; else it could lead to local stress concentration and local failure of the structure. In most of the structural tests, shear and bending will be captured, but twisting needs special attention in distributing the loads at spar/rib locations without altering the center of pressure of the aerodynamic load distribution. Adequacy of the test rigs and proper simulation of all attachments are addressed. The design and implementation of the structural integrity test along with experimental results are presented.
Landing skids of Helicopter are directly attached to the helicopter structure. These skids should be able to withstand buckling of struts, stresses &strains. So in the current study, we will consider a Composite material, High strength steel alloy, Aluminum alloy, for the structure and perform structural analysis and drop tests to study which material can perform satisfactorily under normal lending conditions. Helicopter skids are modeled based on the design of an Ultra Light Helicopter.
The maximum horizontal impact load experienced by an aircraft's landing gear wheel during landing is an important parameter in the landing gear's safety design and performance analysis. Using a noncontact photoelectric testing method, this paper experimentally obtained the temporally varying data of the instantaneous rotational speed for an aircraft wheel at the instant of its contact with the test platform. Moreover, the kinetic relationship between the transient rotational speed of the aircraft's wheel and the horizontal impact force was established. According to the temporally varying data measured from the transient rotational speed of the aircraft's wheel, the maximum horizontal impact load at the instant the aircraft contacted the platform was calculated. To verify the accuracy of this method in which changes in rotational speed of the aircraft's wheel determine the horizontal impact load, verification equipment without lateral constrains was designed and used for testing. The experimental results showed that the horizontal impact load determined based on the transient rotational speed of the aircraft's wheel are consistent with the results obtained using direct measurements obtained from custom-made equipment free of lateral constrains. This paper provides a new experimental method for measuring the horizontal impact load on the aircraft's wheel.
Takeoff and landing overruns account for most of the accidents that occur on or in the immediate vicinity of the runway, and it would cause accidental aircraft damage and loss of life. The current Engineered Material Arresting System (EMAS) materials are weak in water resistance and durability, expensive in acquiring and installing, and have negative environmental impacts. So it is significantly required to find a new alternative material with good mechanical properties, higher arresting coefficient and excellent environmental performance. In this article, the arresting properties of metal honeycomb material are studied. A Tire-Honeycomb material Interaction Mechanical Model (THIMM) is proposed. Combing with the dynamic model of aircraft, the theoretical model is coded by MATLAB to finish arresting simulation on aircraft B737-900ER and B727-100. In addition, finite element model of the tire-honeycomb material interaction was built to verify the correctness of the theoretical model. The results obtained by finite element simulation are in a good agreement with the theoretical results. In comparison with the results for traditional materials, the calculated results show that the honeycomb material can stop the overrunning aircraft more efficiently in the condition that the forces induced by the stopping process are safe for the passengers and aircraft.
In order to optimize one UAV current braking system, a new aircraft anti-skid braking system based on pressure servo control using high-speed on/off valves driven by PWM signals is proposed in this paper. The operation principle of PWM on/off valves is analyzed in details to prove the feasibility of pressure servo control. The brake controller contains pressure and slip ratio two closed loops to achieve accurate control and provide high stability. Experimental results show that the new system indeed improve the braking performance and efficiency.
The equations of motion are derived for a single wheel steerable pneumatic tire system. Included in this system are a built-in wheel wobble and wheel-tire irregularities which produce oscillation of the normal load. Special emphasis is placed on the dynamic characterization of the tire cornering force and aligning torque. The results show that the built-in wheel wobble causes a steady shimmy which is large when the wheel rotation frequency is close to the natural shimmy frequency. The results also show that a normal load oscillation which has a frequency approximately twice the natural shimmy frequency causes a decrease in shimmy stability.
This paper shows how vibratory modes of a brake/landing gear system can interact strongly when there is nonlinear negative damping being generated at the brake’s friction interface. The approach first considers the normal modes of the linearized system. The nonlinear frictional interface force is then added to the modal equations of motion. The energy added to each of the modes, per cycle of the lowest frequency mode, is then determined. From these functions an amplitude path map and limit cycle amplitudes are determined. Multiple limit cycles are found to exist for certain combinations of damping. Amplitude modulation of the higher-frequency mode at multiples of the lower frequency mode is explained. Time solutions of the motion are obtained and compared to computer simulation results. Results compare closely.
The method yields a global view of the stability and modal interactions caused by nonlinear negative damping at the brake’s friction interface.
The feasibility of computing non-linear transient finite element simulations of aircraft landing gear brake whirl and squeal is demonstrated and discussed. Methodology to conduct the high frequency brake transient analysis is developed using an explicit integration finite element approach. Results indicate the approach has the capability to simulate brake dynamic behavior in dynamometer and aircraft landing gear installations — thus enabling evaluation of modifications to braking systems that lead to more stable and robust designs. A simple multi-disk brake model is developed and described. Modeling techniques for including the dynamometer road wheel and runway in the simulations are given. Issues such as piston housing hydraulic fluid stiffness and damping effects, and parametric friction modeling are discussed.
A mathematical model is developed of the hydraulic damper with an account for the parameters of its mounting. A technique for determining the effective values of the mounting, damping, and stiffness coefficients is presented. Specific calculations are presented.
The objective of this paper is to address finite element modeling for dynamics and its applications to aircraft landing and braking systems. The components of the system in the example model include the entire landing gear, wheels, brakes, and tires. The use of finite element modeling techniques in dynamics as a design tool for landing and braking systems is discussed. Vibration mode shapes from the finite element analysis, including both whirl and squeal, are shown. Correlation between the finite element models and the experimental modal analyses of various system components are presented. Correlation between the performance of the complete landing and braking system model and the actual system during aircraft operation is also presented.
The pros and cons of landing gear simulators and a proposed approach that will utilize in a program to more accurately predict actual airplane landing gear vibrational characteristics are presented. Dynamometer testing is used, together with the landing gear simulators, to examine the vibrational characteristics of the brake as part of landing gear.
This paper shows how vibratory modes of a braked/landing gear system can interact strongly when there is nonlinear negative damping being generated at the brake's friction interface. The approach first considers the normal modes of the linearized system. The nonlinear frictional interface force is then added to the modal equations of motion. The energy added to each of the modes, per cycle of the lowest frequency mode, is then determined. From these functions an amplitude path map and limit cycle amplitudes are determined. Multiple limit cycles are found to exist for certain combinations of damping. Amplitude modulation of the higher-frequency mode at multiples of the lower frequency mode is explained. Time solutions of the motion are obtained and compared to computer simulation results. Results compare closely. The method yields a global view of the stability and modal interactions caused by nonlinear negative damping at the brake's friction interface.
An experimental and analytical program for prediction of airplane landing gear shimmy stability is outlined. The method makes use of laboratory shimmy tests on a flywheel which simulates the rumway and a landing gear mounting structure which simulates the fuselage. DIfferences between the laboratory tests and airplane tests are detailed. Because of the latter differences, the prediction of airplane results is carried out by an experimentally verified analysis rather than a direct application of the laboratory test results. The analytical model is outlined including the tire mechanics. Samples of correlation between analytical results and experimental results (laboratory and airplane) are given.
The landing gear is an inevitable system for the aircraft. It absorbs the energy of the landing impact and carries the aircraft weight at all ground operations, including take off, taxiing, and towing. Numerical simulation has become an invaluable tool for the assessment of landing gear dynamics as well as of aircraft/landing gear interaction. This paper gives an overview of the landing gear requirements and illustrates landing gear operational conditions, i.e., the shimmy problem, the dynamics at touch down and at ground roll. Furthermore, three software packages used in the simulation of aircraft ground dynamics are presented. A look at flight simulators and landing gear test facilities follows. Finally, the possible application of controlled landing gears is discussed.
Results are presented from analyses of primary squeal-mode vibration in aircraft brake systems. System stability is investigated by determining the eigenvalues of linearized perturbation equations at each steady-state operating point of the nonlinear system. Time-history responses are obtained by integrating the complete set of nonlinear dynamic equations. Results are given from analyses conducted using two versions of the nonlinear squeal model, a single-wheel model representing a typical dynamometer configuration, and a fore-aft wheel pair model representing one side of a main landing-gear truck. In general, the model predicts system instability at low braking pressures and stability at high braking pressures. The effects on stability of variations in brake pressure, friction coefficient, and torsional stiffness are shown. The nonlinear squeal model indicates that system instability can occur with a constant friction coefficient and that system stability decreases with increasing brake-friction coefficient. It is shown that proper selection of brake heat stack mechanical properties and design geometry can produce a stable system. Results indicate that a fore-aft brake pair will be more unstable than a single brake, which is in agreement with dynamometer and airplane test data.
In this work, a new approach for analysis of random vibration in light aircraft landing gear for a given duty cycle is developed and studied, The aircraft is modeled as a linear, single-degree-of-freedom oscillator with random properties, including nonstationary damping and random nonstationary load, Note that this type of problem is difficult to analyze efficiently using most conventional techniques. Two approaches to analyze the random vibration of the system are examined: a new variant of the random matrix approach, a statistical random vibration analysis method developed previously by the authors; and a hybrid Monte Carlo technique containing a spectral representation approach and a variant of Latin hypercube sampling, Random response results are shown for two light aircraft landing on three different terrain types using each method, and comparisons are offered. These results show that Monte Carlo analysis cannot compute accurate solutions for this problem, It is anticipated that the proposed random matrix technique could be used in conjunction with current fatigue analysis methods so that accurate landing gear fatigue information may be computed.
A model is presented for the analysis of primary squeal-mode vibration in aircraft braking systems. The destabilizing mechanism in the model utilizes nonlinear mechanical and material surface properties of the brake heat stack to couple lateral translation and yaw of the rotors and stators. Geometric and stiffness properties of the brake and landing-gear structure couple piston-housing torsional rotation and axle fore-aft bending with lateral translation and yaw of the heat stack. The model does not use brake negative damping and it predicts that system instability can occur with a constant brake-friction coefficient as has been observed on both dynamometer and flight tests. System stability can be altered by changes in the brake-friction coefficient, pressure, stiffness, geometry, and various brake-design parameters. Enhanced versions of the model are presented that include a more detailed structural representation of the piston-housing torque tube and the hydraulic now equations for each piston. The model is extended to a fore-aft wheel pair on a two-axle, main-landing gear truck. Stability is investigated by determining eigenvalues of the linearized perturbation equations about each steady-state operating point of the nonlinear system. The nonlinear dynamic equations are integrated numerically to obtain time-history responses. Results from stability analyses and parametric studies using this model are presented in a companion paper.
This paper presents a mathematical model to analyse the stability of motion of the two-wheeled 'Fokker F.28-like' landing gear including tyers. The model is validated by means of ground vibration tests and aircraft taxy tests. The model is equally applicable to similar landing gears. The influnce of the introduction of a specially designed tortional damper on the dynamical behaviour of the landing gear-tyre combination is invistigated. Results of the stability calculations are supported by test results.
Landing gear dynamics for an aircraft has been analyzed with a heave-pitch model having telescopic main gear and articulated nose gear using oleopneumatic shock absorber. System equations have been presented incorporating the effects of linkage dynamics, frictional forces, and nonlinearities in the tyre, air spring, and oleo damping forces. Sensitivity of the system response to variations in some shock strut parameters has been investigated for the landing touchdown impact phase to bring about improvement in the performance.
Some theories on tire mechanics and wheel shimmy are discussed and their results comparedin an effort to clarify uncertainties as to the validity of the theories. Of particularinterest is the comparison of the stretched string and the point contact theories of the mechanicsof tires. Contrary to conclusions of some previous investigations, it is found thateither of these fundamental, linear theories will predict the shimmy characteristics ofwheeled systems if the parameters involved are properly chosen. Nonelastic effects and tireslippage can be and should be included in either theory if further improvement is desired. Asimple but important correlation between certain of the parameters of these two basic tiremechanics theories is also demonstrated. The theories are compared with each other andwith experimental data. © 1971 American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
The ability to accurately predict the dynamic response of an aircraft while it is operating in the taxi mode depends, in part on the correct modeling of the dynamic characteristics of the landing gear system. Traditionally, landing gear have been designed to absorb landing impact ('shock absorber') and their characteristics during periodic, oscillatory response ('spring') have been considered as secondary. With the increased emphasis on the rough or damaged field taxi operation, there is a requirement to determine the best methods for modeling the gear system. This report documents a brief review of the state of the art of gear modeling. A study was then conducted to evaluate important model parameters, using a simple cantilevered gear computer simulation. Also included is the development of a technique for the experimental determination of important gear system parameters. (Author)
A literature survey, including 314 references, is presented for the fields of automobile and airplane wheel shimmy. The coverage is believed to be relatively complete insofar as the available, published world-wide literature is concerned. In addition to the bibliographic listings, a short review and appraisal of the contents of each reference is given. The report contains indices according to subject, author and nationality of the contributions; the periodical coverage of the survey is also given in detail. A general survey of the problems of automobile and airplane wheel shimmy is included, which highlights the principal trends and contributions to the subject over the years. Finally, on the basis of the survey indications, recommendations are advanced for further research and development in the field. (Author)
Taxiing induced vibrations in large aircraft due to runway and taxiway unevenness have been recognized as a significant factor in causing airframe metal fatigue damage and dynamic stressing, as well as discomfort for the crew and passengers. Vibration of the landing gear also causes seal wear with subsequent leakage of air and hydraulic fluid. The report presents an analytical method of determining the random vibration response of a flexible aircraft caused by runway unevenness transmitted through the main landing gear struts. The aircraft used in the computation of vibration response is the Boeing KC-135A (Stratotanker) in the fully loaded configuration (324,000 lb) (146,963 kg).
An improved approximation of the theory of the dynamic frequency response of side force and aligning torque acting upon the rolling wheel when the latter is moved laterally and swivelled about the vertical axis, is presented. The method is particularly suitable for application in vibration problems of steering and suspension systems of automobiles and aircraft where relatively high speed and high frequency phenomena play a role. The theoretical results show satisfactory agreement with experimental data. Calculations indicate that the inertia of the tire decreases the tendency to shimmy at higher frequencies and speeds of travel. For castered wheels however, tire inertia may have an adverse effect due to its unfavorable influence upon the side force response to swivel motions.
Shimmy oscillations are still a problem in design and operation of aircraft landing gears, and accurate and appropriate analysis is required to master the task. Based on a nonlinear model of the mechanics of the landing gear and tire elasticity according to elastic string theory, some well known linear and nonlinear mathematical methods are applied to the shimmy analysis of a simple model of a nose gear: Computing eigenvalues, solving analytically the stability boundaries with a parameter space method, getting limit cycles by analytical formulae from describing functions, and last but not least numerical simulation of time histories. It seems that linear or quasi linear methods and analytical solutions are well suited to obtain extensive insight, respecting limitations of these methods. Numerical simulation on the other hand is a valuable tool for pointing out specific effects of a nonlinear system in large amplitude regions.
Thesis (M.A.E.)--University of Virginia, 1957. Bibliography: leaves 164-166.
This document presents an approach for modeling and simulating landing gear systems. Specifically, a nonlinear model of an A-6 Intruder Main Gear is developed, simulated, and validated against static and dynamic test data. This model includes nonlinear effects such as a polytropic gas model, velocity squared damping, a geometry governed model for the discharge coefficients, stick-slip friction effects and a nonlinear tire spring and damping model. An Adams-Moulton predictor corrector was used to integrate the equations of motion until a discontinuity caused by a stick-slip friction model was reached, at which point, a Runga-Kutta routine integrated past the discontinuity and returned the problem solution back to the predictor corrector. Run times of this software are around 2 mins. per 1 sec. of simulation under dynamic circumstances. To validate the model, engineers at the Aircraft Landing Dynamics facilities at NASA Langley Research Center installed one A-6 main gear on a drop carriage and used a hydraulic shaker table to provide simulated runway inputs to the gear. Model parameters were tuned to produce excellent agreement for many cases.
An overview of previous studies involving aircraft nose gear shimmy behavior is given together with some test results identifying the influence of different factors inducing shimmy. A NASA Langley test program conducted at the Landing Loads Track (LLT) facility to evaluate shimmy characteristics of an actual Space Shuttle nose gear is described together with some of the test results. Based on results from these various evaluations, recommendations are made concerning nose gear design features, such as corotating wheels, to minimize the occurence of shimmy.
The Suspension of the Automobile Steering Mechanism: Shimmy and Tramp
- G Broulhiet
Broulhiet, G., "The Suspension of the Automobile Steering Mechanism: Shimmy and Tramp", Bull
Soc. Ing. Civ. Fr. 78, pp. 540-554, July 1925.
Shimmy, Pseudo-Shimmy and Tramp of an Automobile
- Sensaud
- D Lavaud
Sensaud de Lavaud, D. "Shimmy, Pseudo-Shimmy and Tramp of an Automobile", C.R. Acad. Sci., Paris, Fr. 185, pp. 254-257, July 1927.
Aircraft Landing Gear Brake Squeal and Strut Chatter Investigation
- F A Biehl
Biehl, F.A., "Aircraft Landing Gear Brake Squeal and Strut Chatter Investigation", The Shock and
Vibration Bulletin, Naval Research Laboratory, Washington, D.C., January 1969.
Experimental Investigation of Brake Characteristics Conductive to Strut Chatter Report #: AD-780505 GAW/MC/74-2, Thesis for Master's Degree, Air Force Institute of TechnologySelf Excited Multi-Mode Vibrations of Aircraft Brakes With Nonlinear Negative Damping
- J D Brewer
- R J Black
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Numerical Analysis of the Stabilities on Main Landing Gear Walking
- L Zhagn
Zhagn, L. "Numerical Analysis of the Stabilities on Main Landing Gear Walking", Proceedings of the
Third Asian-Pacific Conference on Computational Mechanics, Seoul, Korea, September 16-18, 1996.
A Review of Aircraft Landing Gear Dynamics AGARD-R-800Dynamic Response of Landing Gears on Rough Repaired Runway
- W E T W Krabacher
Krabacher, W.E., "A Review of Aircraft Landing Gear Dynamics", AGARD-R-800, March, 1996. 15 45. Lee, T.W., "Dynamic Response of Landing Gears on Rough Repaired Runway", Proceedings of The Aerospace Technology Conference and Exposition, Long Beach, CA, September 23-26, 1991.
Dynamic Simulation of Landing Gears
- P Thomas
- M Geradin
- B Guyot
Thomas, P.; Geradin, M.; and Guyot, B., "Dynamic Simulation of Landing Gears", International Forum
on Aeroelasticity and Structural Dynamics, Strasbourg, France, pp.1077-1096, May 1993.
The Prediction of Landing Gear Behavior Using Dynamic Simulation
- D Cowling
- A Shepherd
Cowling, D. and Shepherd, A., "The Prediction of Landing Gear Behavior Using Dynamic Simulation",
Proceedings of the International Forum on Aeroelasticity and Structural Dynamics, Manchester
Business School, U.K.,June 26-28, 1995.
Analysis of Dynamical Behaviour of an Aircraft at Touchdown
- S S Kothari
- M R Ananthasayanam
- K Rajaiah
Kothari, S.S.; Ananthasayanam, M.R.; and Rajaiah, K., "Analysis of Dynamical Behaviour of an
Aircraft at Touchdown", Proceedings of the 31 st Aircraft Symposium, Hikoki Shinpojiumu Koenshu,
Japan, Vol. 31, pp. 82-85, 1993.
Dynamic Bahavior Analysis For Landing Gear With Different Types of Dual-Chamber Shock Struts
- H Nie
- X Qiao
Nie, H. and Qiao, X., "Dynamic Bahavior Analysis For Landing Gear With Different Types of Dual-Chamber Shock Struts", Chinese Journal of Aeronautics, Vol. 4, May 1991.
Flight Simulation: Comparison of Articulated Gear Leg Models
- A M Cameron
- C R Hogg
- C J Harris
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Models", Proceedings of The 27 th Summer Computer Simulation Conference, Ottowa, ON, Canada, July
24-26, 1995.
Pseudo-Shimmy and Tramp of an Automobile
- Sensaud
- D Lavaud
- Shimmy
Sensaud de Lavaud, D. “Shimmy, Pseudo-Shimmy and Tramp of an Automobile”, C.R. Acad. Sci., Paris, Fr. 185, pp. 254-257, July 1927
Aircraft Vibrations Due To Brake Chatter and Squeal
- J L Edman
Edman, J.L., "Aircraft Vibrations Due To Brake Chatter and Squeal", WADC Technical Report 55-326,
Wright Air Development Center, Air Research and Development Command, USAF, Wright Patterson
Air Force Base, OH, October 1955.
Landing Gear Vibration
- W J Moreland
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