Shimmy Vibration Research Articles

Shimmy vibration analysis of unmanned aircraft coupled with landing gears

Shimmy vibration analysis of unmanned aircraft coupled with landing gears

Towed wheel shimmy suppression through a nonlinear tuned vibration absorber

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.

Research on control methods and technology for reduction of large-scale wind turbine blade vibration

This paper is mainly devoted to the analysis and suppression of large-scale wind turbine blade vibration. Firstly, the mechanism of blade vibration including waved vibration and shimmy vibration is analyzed in detail and the mathematical model of blade vibration is established. Secondly, the influence of tower shadow effect and wind shear on blade flutter is discussed based on the established blade vibration model. In the end, for the suppression of blade vibration, some control schemes based on individual variable-pitch including blade damping control, LQG control, H∞ control and improved LQG control with optimal disturbance observer proposed in this paper are studied. At the same time, the specific processes of controllers design are given and these algorithms are effectively verified by simulations. The results show that the improved LQG control with optimal disturbance observer has the better suppression effect on blade vibration compared with other methods, which can provide a certain theoretical support to choose the control algorithm in reality.

Phase compensation active disturbance rejection control for shimmy vibration with magnetorheological damper of aircraft

The shimmy of nose landing gear is a complex kind of self-excited vibration and it can grave damage to aircraft. The magnetorheological damper (MRD) is used to absorb the vibration energy to inhibit shimmy. In this paper, landing gear and MRD are conceived as a whole, and several specific model-independent control strategies based on error feedback are designed. To improve the performance of active disturbance rejection control (ADRC), phase compensation active disturbance rejection control (PCADRC) is proposed. The simulation results indicate the proposed method has a greater control effect compared with the others. For parameter perturbation and external disturbance, PCADRC also has good robustness and disturbance rejection properties.

Nose Landing Gear Simple Adaptive Shimmy Suppression System

The occurrence of shimmy vibration in aircraft nose landing gear can cause an increase of fatigue stress on the nose landing gear mechanical elements that can eventually lead to high wearing of components as well as to severe damage of the leg, giving raise to safety issues. The use of the Modified Simple Adaptive Controller is investigated for the realization of an adaptive shimmy suppression system. The nonlinear governing equations that model the shimmy vibration behavior of an aircraft nose landing gear are first linearized in order to synthesize the adaptive controller, while nonlinear terms are then taken into account as disturbances. The almost strict passivity of the plant is obtained by using a parallel feedforward compensator. The parallel feedforward compensator is designed as the inverse of a stabilizing controller while the Modified Simple Adaptive Controller is tuned by considering the minimization of some dynamic performance parameters as design requirements. The influence of the advancing speed on the controlled plant response is studied by simulating scenarios of aeronautical interests.

Parametric study of a novel nose landing gear shimmy damper concept

Shimmy dampers are passive solutions for undesired shimmy vibration in aircraft landing gears. Although they mitigate shimmy to variable degrees, they can introduce weight, cost, and reliability penalties especially when added to existing landing gear systems. More effective and compact shimmy dampers with reduced maintenance effort and enhanced stability performance can then greatly contribute to light-weighting, as well as lowering the aviation risk and maintenance costs. Moreover, a robust performance analysis and characterization framework based on high-fidelity computational models is absent from the literature while it is essential to quantify the capabilities of a given damper. In this work, analysis of a novel shimmy damper concept is presented along with an effective methodology for evaluating the performance of shimmy dampers based on nonlinear shimmy amplitude maps and stability boundary plots. The new damper concept is suitable for installation on existing and new landing gears and features a multifunctional torque link member including an assembly of beam and damping units to suppress the undesired vibrations. The influence of torque link damper parameters is then thoroughly explored using the nonlinear Multibody Dynamics model of the nose landing gear employed for both generating the shimmy maps and time histories of the vibrations. The novel concept is shown to be capable of effectively mitigating the rotational shimmy given that the parameters are chosen appropriately based on the systematic approach laid out. The insights from the analysis are then distilled in the form of recommendation for designing next generation shimmy dampers. Moreover, the novel framework introduced for characterizing shimmy dampers offers great benefit to the shimmy suppression research and development practice.

On the effectiveness of shimmy dampers in stabilizing nose landing gears

The challenge of nose landing gear shimmy vibrations is largely addressed through adding passive shimmy suppression devices to the gear, known as shimmy dampers. Despite the wide treatment of the shimmy modeling in the literature using various approaches, little is known about shimmy dampers' performance and their influence on the dynamics. This article presents a multi degree of freedom nose landing gear model including a two-piece strut, with a generic shimmy damper added in between of the strut parts as it is the case in the actual system. Using linear stability analysis and nonlinear time domain simulations, we identify the required equivalent stiffness and damping to be supplied by the shimmy damper in order to ensure stability of the dynamic system. Furthermore, a parametric study of three shimmy dampers is presented in which effect of design parameters on the equivalent stiffness and damping of shimmy dampers are highlighted and compared. Integrating the learnings from both parts of the study, strategies for arriving at an optimized shimmy damper design are offered.

Sensitivity of Lyapunov Exponents in Design Optimization of Nonlinear Dampers

This work presents how the analytical sensitivity of Lyapunov characteristic exponents (LCEs) can be used in the design of nonlinear dampers, which are frequently utilized to stabilize the response of mechanical systems. The kinetic energy dissipated in the form of heat often induces nonlinearities, therefore reducing the reliability of standard stability evaluation methods. Owing to the difficulty of estimating the stability properties of equilibrium solution of the resulting nonlinear time-dependent systems, engineers usually tend to linearize and time-average the governing equations. However, the solutions of nonlinear and time-dependent dynamical systems may exhibit unique properties, which are lost when they are simplified. When a damper is designed based on a simplified model, the cost associated with neglecting nonlinearities can be significantly high in terms of safety margins that are needed as a safeguard with respect to model uncertainties. Therefore, in those cases, a generalized stability measure, with its parametric sensitivity, can replace usual model simplifications in engineering design, especially when a system is dominated by specific, non-negligible nonlinearities and time-dependencies. The estimation of the characteristic exponents and their sensitivity is illustrated. A practical application of the proposed methodology is presented, considering that the problem of helicopter ground resonance (GR) and landing gear shimmy vibration with nonlinear dampers are implemented instead of linear ones. Exploiting the analytical sensitivity of the Lyapunov exponents within a continuation approach, the geometric parameters of the damper are determined. The mass of the damper and the largest characteristic exponent of the system are used as the objective function and the inequality or equality constraint in the design of the viscous dampers.

Control of shimmy vibration in aircraft landing gears based on tensor product model transformation and twisting sliding mode algorithm

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.

A robust active control system for shimmy damping in the presence of free play and uncertainties

Shimmy vibration is the oscillatory motion of the fork–wheel assembly about the steering axis. It represents one of the major problem of aircraft landing gear because it can lead to excessive wear, discomfort as well as safety concerns. Based on the nonlinear model of the mechanics of a single wheel nose landing gear (NLG), electromechanical actuator and tire elasticity, a robust active controller capable of damping shimmy vibration is designed and investigated in this study. A novel Decline Population Swarm Optimization (PDSO) procedure is introduced and used to select the optimal parameters for the controller. The PDSO procedure is based on a decline demographic model and shows high global search capability with reduced computational costs. The open and closed loop system behavior is analyzed under different case studies of aeronautical interest and the effects of torsional free play on the nose landing gear response are also studied. Plant parameters probabilistic uncertainties are then taken into account to assess the active controller robustness using a stochastic approach.

Control of a shimmy vibration in vehicle steering system using a magneto-rheological damper

Vehicle stability largely depends on the vibration of the steering system. A four degrees of freedom dynamic model of an automotive steering system with a magneto-rheological damper is presented in this study. Firstly, an equivalent mathematical model of the steering system is developed. The nonlinear equation of motion obtained from the dynamic model is then linearized around its equilibrium point to make it suitable for the design of an appropriate controller for vibration suppression. In this work, a new type of adaptive sliding mode controller is designed for control of the magneto-rheological damper and hence to control unwanted vibration. It is shown that the proposed control logic is very effective for settling steering motion near the equilibrium position. The shimmy vibrations of the wheels are reduced by a considerable amount and the steering system becomes stable. In addition, a comparative work is undertaken between the proposed controller and an ordinary sliding mode controller to demonstrate the advantage of the proposed methodology.

Nonlinear model based particle swarm optimization of PID shimmy damping control

The present study aims to investigate the shimmy stability behavior of a single wheeled nose landing gear system. The system is supposed to be equipped with an electromechanical actuator capable to control the shimmy vibrations. A Proportional-Integrative-Derivative (PID) controller, tuned by using the Particle Swarm Optimization (PSO) procedure, is here proposed to actively damp the shimmy vibration. Time-history results for some test cases are reported and commented. Stochastic analysis is last presented to assess the robustness of the control system.

Robust and optimal control of shimmy vibration in aircraft nose landing gear

Shimmy vibration of aircraft nose landing gear is damped and controlled using a nonlinear control which is optimal and robust against parametric uncertainties and external disturbances. Shimmy vibration is the lateral and torsional vibrations in the wheel of the aircraft that is self-excited and causes instability in high speed performances which can damage the landing gear of the aircraft, its fuselage and even may result in hurting the passengers. Thus, control and damping of this vibration are extremely important. In this paper a robust optimal controller is designed by integrating sliding mode control (SMC) together with State-Dependent Riccati Equation (SDRE) to prevent the shimmy vibrations in aircraft nose landing gear. The SDRE compensator controls the nonlinear system in an optimal way while the sliding mode controller guarantees its stability against uncertainties and disturbances. The proposed controller can effectively suppress the shimmy vibration of the landing gear with variable taxiing velocity and wheel caster length. To verify the optimal performance and robustness of the proposed controller, vibration response of the system is simulated by MATLAB software and its performance and efficiency are verified using comparative analysis. Considerable improvement can be seen in the performance of the closed loop system since not only the vibrations are effectively damped but also the consumption of energy is minimized.

Study on Shimmy Vibrations of Wheeled Casters

Study on Shimmy Vibrations of Wheeled Casters

The Stochastic Robust Model Predictive Control of Shimmy Vibration in Aircraft Landing Gears

AbstractThis paper considers robust model predictive control (RMPC) methods for a linear parameter varying (LPV) system that has both probabilistic uncertain and time‐varying parameters. The parameters are considered to be measured online. In this regard, the aircraft landing gear system is considered as an LPV system whose parameters variation can affect both stability and performance. By transforming this system into a convex combination of linear time‐invariant vertices form with the tensor‐product (TP) model transformation method, the landing gear system is represented as a polytopic linear parameter‐varying system. A computationally efficient RMPC control signal law is calculated online by carrying out the convex optimization involving linear matrix inequalities (LMIs) in MPC which leads to finding the solutions that can guarantee the closed‐loop robust stability and performance. The proposed controller can effectively suppress the shimmy vibration of the landing gear with variable taxiing velocity and wheel caster length, also with the probabilistic uncertain torsional spring stiffness.

A Study of Wind Generator Set Blades Dynamic Analysis

This paper on wind generator set blades had a simple introduction, and the modal analysis was used on the blades dynamic analysis, the conclusion that blades the different stage in the direction of the force and deformation was drawn, it can be concluded: the first three-order natural frequency at, the blades are expressed as a pure bending vibration. It can be seen from the blade vibration figure: a frequency of blades waving in the direction of the first natural frequency, first natural frequency of the second-order frequency blades shimmy direction, three frequencies for the blades waving direction of the second-order natural frequency, torsional frequency of fourth order for the direction of the shimmy, five order of frequency of blades placed waving direction of the three natural frequencies. According to the theory of vibration, the vibration in the process of energy is concentrated in bands 1 and 2, so the first stage waving vibration (bending vibration) is the main vibration of the wind generator set blades; 4 and 5 vibration modes performance for bending dominated accompanied shimmy and torsional vibration. Visible, the shimmy vibration and torsional vibration in high-end part is still not the main vibration.It provides the theoretical basis so as to improve the quality of the design of wind turbine blades. Blade is one of the wind generator set key components, many aerodynamic problems are faced, the aerodynamic efficiency of the blades is to be considered an important factor in the blade design, and their job security is more important factor. The wind turbine power source is the natural randomness of strong wind, the blades often run in the stall condition, the system has a strong stochastic dynamic process, the transmission of abnormal is irregular power input, the main structural components to withstand higher than normal rotation mechanical fatigue loading several times, forming a unique wind turbine dynamics. Wind generator set blades as a flexible structure, the load acting on has a cross and random variability, which is an inevitable occurrence of vibration, the vibration characteristics of their study is very necessary. Blades the structure and strength of the wind generator set reliability plays an important role. With the emergence of high-power wind generators, finite element numerical analysis of the theories and methods have been applied to the structural design of wind generator set. Modern wind generator set blades shape and internal structure complex calculations,it is necessary to study the exact dynamics model and the analysis of blades structure [. The institutional dynamics is to constitute the institutional elements of the inertia and institutions in the rigid parts caused by the vibration of a subject. The kinetic analysis features include: regular modal complex eigenvalue analysis, frequency and transient response analysis, (noise) acoustic analysis, random response analysis, the response and the impact of spectrum analysis, power sensitivity analysis. Here only the blade to vibrate and modal to be analysed [.

The analysis of shimmy instability of a typical nose landing gear using active torsional magneto-rheological damper

Shimmy is an oscillation in the nose landing gear (NLG) of an aircraft that may occur during taxiing, take-off or landing. Increasing emphasis on reducing the weight of landing gear systems in modern aircraft has, in many cases, induced shimmy problems and active vibration control has gradually been used to suppress vibration. The objective of the current investigation is to introduce an active torsional magneto-rheological (MR) fluid-based damper for shimmy vibration control of a typical NLG. In the present study, the shimmy model is developed based on the formulation of G. X. Li, to study the self-induced dynamic instability at the critical forward taxi velocity. The effect of various parameters on the shimmy behaviour is also studied. The study has been performed to postpone the dynamic instability by introducing MR fluid-based damper as a semi-active device and also a closed-loop feedback control scheme is employed to control the landing gear instability of an aircraft.

Robust Model Predictive Control of Shimmy Vibration in Aircraft Landing Gears

Shimmy vibration is one of the major concerns in the aircraft landing gear design. In this paper, the influence of structural parameters on the shimmy dynamics is analyzed based on a nonlinear dynamical model. A computationally efficient robust model predictive control law is formulated for a linear parameter varying system with guaranteed closed-loop stability. Moreover, an attempt is made to apply the proposed robust model predictive control strategy to suppress the shimmy during the taxiing and landing of an aircraft. Compared with two current robust model predictive controls, the proposed shimmy controller can effectively suppress the shimmy with more efficient computation. To verify the efficiency of the proposed algorithm, the simulation results are presented and discussed. Nomenclature A,B,C = discrete state-space matrices Ac,Bc,Cc = continuous state-space matrices Aj,Bj = discrete state-space matrices ofjth vertex a = half contact length

Shimmy Vibration Analysis of Aircraft Landing Gears

Shimmy vibration is a very important type of motion in the landing gear system during either the takeoff or landing of an aircraft. Energy input for this type of vibration is provided from the kinetic energy of the forward motion of the aircraft. As a result, this energy initiates a self-excited type of vibration in the wheels that may lead to instabilities. An attempt is made to develop a dynamical model for the aircraft nose gear to investigate its transient response for the lateral deviations and shimmy angles. Variations of different design parameters—namely, the energy absorption coefficient of the shimmy damper and the location of the gravity center of the landing gear—are studied. Results are presented graphically to facilitate the investigation of landing gear shimmy vibration.