Francis E Cook

Bio: Francis E Cook is an academic researcher. The author has contributed to research in topics: Landing gear & Springing. The author has an hindex of 2, co-authored 2 publications receiving 76 citations.

Analysis of Landing-Gear Behavior

Abstract: This report presents a theoretical study of the behavior of the conventional type of oleo-pneumatic landing gear during the process of landing impact. The basic analysis is presented in a general form and treats the motions of the landing gear prior to and subsequent to the beginning of shock-strut deflection. The applicability of the analysis to actual landing gears has been investigated for the particular case of a vertical landing gear in the absence of drag loads by comparing calculated results with experimental drop-test data for impacts with and without tire bottoming. The calculated behavior of the landing gear was found to be in good agreement with the drop-test data.

Effect of interaction on landing-gear behavior and dynamic loads in a flexible airplane structure

Abstract: The effects of interaction between a landing gear and a flexible airplane structure on the behavior of the landing gear and the loads in the structure have been studied by treating the equations of motion of the airplane and the landing gear as a coupled system. The landing gear is considered to have nonlinear characteristics typical of conventional gears, namely, velocity-squared damping, polytropic air-compression springing, and exponential tire force-deflection characteristics. For the case where only two modes of the structure are considered, an equivalent three-mass system is derived for representing the airplane and landing-gear combination, which may be used to simulate the effects of structural flexibility in jig drop tests of landing gears. As examples to illustrate the effects of interaction, numerical calculations, based on the structural properties of two large airplanes having considerably different mass and flexibility characteristics, are presented.

Vibration Control of a Landing Gear System Featuring Electrorheological/Magnetorheological Fluids

Abstract: The feasibility and effectiveness of electrorheological (ER) and magnetorheological (MR) fluid-based landing gear systems on attenuating dynamic load and vibration due to the landing impact are demonstrated. First, the theoretical model for ER/MR shock struts, which are the main components of the landing gear system,is developed based on experimental data. The analysis of a telescopic-type landing gear system using the ER/MR shock struts is theoretically constructed, and its governing equation is derived. A sliding mode controller, designed to be robust against parameter variations and external disturbances, is formulated, and controlled performance of the simulated ER/MR landing gear system is theoretically evaluated during touchdown of the aircraft.

Shimmy of Aircraft Main Landing Gears

Abstract: The landing gear is an important aircraft system, which has to meet many different design requirements. It is a highly loaded structure, which is designed for minimum weight. Shimmy is a dynamic instability of the landing gear, which is caused by the interaction of the dynamic behaviour of the landing gear structure and tyres. The unstable lateral and yaw vibration of the landing gear can reach considerable amplitudes and may even result in severe damage to the aircraft. Shimmy is easily ignored in the design process, which may be caused by a of lack of knowledge on the shimmy phenomenon, absence of suitable analysis tools or the non-availability of e.g. tyre characteristics. Computer simulations are very important to evaluate the shimmy stability of a landing gear. Experience has shown that it will be very difficult to rigorously prove shimmy stability from experiments, e.g. full-scale flight tests or laboratory tests using a drum. Three fields of research are covered in this thesis: • shimmy fundamentals • modelling of the tyre dynamic behaviour • the development and validation of a detailed landing gear model Analytical expressions for the shimmy stability have been derived for a number of relatively simple systems using the Hurwitz criterion. In particular, an analytical solution has been found for a system where the wheel has a mechanical trail and both the yaw and lateral stiffness of the hinge point are taken into account. The stability boundaries can be represented by two shifted parabolas in the mechanical trail versus yaw stiffness plane; this analytical result is very important to understand the interaction between the different variables. The model may be enhanced by including the gyroscopic behaviour of the rotating wheel and structural damping. The shimmy stability can also be analysed in the frequency domain by considering the landing gear structure and tyre as a feedback system and applying the Nyquist criterion. A design study is performed using a twin wheeled landing gear, having three mechanical degrees of freedom (lateral, roll and yaw). The stability of the baseline configuration can be improved considerably by modifying the length of the mechanical trail, lateral stiffness, yaw stiffness and wheel track. It appears that a small positive mechanical trail is better avoided; this is substantiated by the analytical results. Other methods to improve the stability have been investigated: modification of the cant angle, the introduction of a bob mass, tuned mass, shimmy damper or co-rotating wheels. Furthermore the stability of a bogie landing gear has been evaluated both analytically and using a more complex model; the results indicate that this configuration is far less susceptible to shimmy. Different linear tyre models have been developed for application in a shimmy analysis; in particular the models of Von Schlippe, Smiley, Pacejka (straight tangent and parabolic approximation), Kluiters, Rogers, Keldysh and Moreland are discussed. Expressions for the transfer functions with respect to side and turn slip are derived and equivalence conditions can be established between some of the tyre models. A comparison is made using transfer functions, step response and energy considerations. In addition, the impact of the tyre model on system stability is studied for a number of simple mechanical systems. Some guidelines regarding the values of different tyre parameters are given using measurement data and literature. A detailed model will be required to assess shimmy stability in the design stage or when solving actual shimmy problems. The stiffness of a landing gear is dependent on the shock absorber deflection due to changes in torque link geometry and distance between upper and lower bearing. The flexibility of the back-up structure and wing results in a significant reduction of the lateral stiffness of the landing gear at wheel axle level. Modal testing can be performed to assess eigenfrequencies and mode shapes of the landing gear, but measurements show that the results may be highly amplitude dependent due to free-play and friction. Free-play and friction are also important for the shimmy stability and will have to be included in a detailed model. The shimmy damper may have a non-linear characteristic consisting of a preloaded spring and velocity squared damping force. Various component tests will be required to determine parameters or to validate the characteristics of the model. A detailed simulation model was developed using the MECANO multi-body software package. The flexible slider element proved to be very convenient for modelling the landing gear structure. Full-scale tests on the aircraft may be used to perform a limited validation of the simulation model. During taxi runs an external disturbance is required to provoke a dynamic response of the landing gear. This may be achieved by running over a diagonally positioned plank, introducing an unbalance mass or asymmetrical braking. In a landing event the asymmetrical spin-up of the wheels is the main excitation source. Generally, only limited data will be available when a shimmy event occurs, which makes it difficult to perform a detailed assessment. An interesting exception is a shimmy vibration which occurred on a test aircraft, equipped with an instrumented landing gear. The unstable motion is analysed in detail. This event has also been simulated using the MECANO model, aiming to match the landing conditions as closely as possible. A reasonable agreement can be obtained between simulation model and measurement. Future research may aim at an accurate determination of tyre characteristics and correlation between different tyres. The dynamic tyre model can be extended to describe the non-linear tyre behaviour at large side slip angles more accurately. Also some enhancements of the landing gear and airframe model are possible, in particular the dynamic behaviour of the wing and brakes may be included. Friction may be rather important for an accurate simulation of the landing gear behaviour; in this field both additional experimental data and improved modelling techniques may be required.

Magnetorheological landing gear: 1. A?design methodology

Abstract: Aircraft landing gears are subjected to a wide range of excitation conditions, which result in conflicting damping requirements. A novel solution to this problem is to implement semi-active damping using magnetorheological (MR) fluids. This paper presents a design methodology that enables an MR landing gear to be optimized, both in terms of its damping and magnetic circuit performance, whilst adhering to stringent packaging constraints. Such constraints are vital in landing gear, if MR technology is to be considered as feasible in commercial applications. The design approach focuses on the impact or landing phase of an aircraft's flight, where large variations in sink speed, angle of attack and aircraft mass makes an MR device potentially very attractive. In this study, an equivalent MR model of an existing aircraft landing gear is developed. This includes a dynamic model of an MR shock strut, which accounts for the effects of fluid compressibility. This is important in impulsive loading applications such as landing gear, as fluid compression will reduce device controllability. Using the model, numerical impact simulations are performed to illustrate the performance of the optimized MR shock strut, and hence the effectiveness of the proposed design methodology. Part 2 of this contribution focuses on experimental validation.

Magnetorheological landing gear: 2. Validation using experimental data

Abstract: Aircraft landing gears are subjected to a wide range of excitation conditions with conflicting damping requirements. A novel solution to this problem is to implement semi-active damping using magnetorheological (MR) fluids. In part 1 of this contribution, a methodology was developed that enables the geometry of a flow mode MR valve to be optimized within the constraints of an existing passive landing gear. The device was designed to be optimal in terms of its impact performance, which was demonstrated using numerical simulations of the complete landing gear system. To perform the simulations, assumptions were made regarding some of the parameters used in the MR shock strut model. In particular, the MR fluid's yield stress, viscosity, and bulk modulus properties were not known accurately. Therefore, the present contribution aims to validate these parameters experimentally, via the manufacture and testing of an MR shock strut. The gas exponent, which is used to model the shock strut's nonlinear stiffness, is also investigated. In general, it is shown that MR fluid property data at high shear rates are required in order to accurately predict performance prior to device manufacture. Furthermore, the study illustrates how fluid compressibility can have a significant influence on the device time constant, and hence on potential control strategies.

Optimal inerter-based shock-strut configurations for landing gear touch-down performance

Abstract: This paper investigates the possibility of improving aircraft landing-gear touchdown performance by adding an inerter alongside a linear passive shock strut. The inerter is a novel mechanical eleme...