Study of airfoil gust response alleviation using an electro-magnetic dry friction damper. Part 2: Experiment

In Part 1 of this work, a theoretical simulation study of the non-linear gust response of a three degree-of-freedom typical airfoil section with a control surface using an electro-magnetic dry friction damper is presented. For validation of this theoretical model, an electro-magnetic dry friction damper has been designed and an experimental investigation of the gust response has been carried out in a wind tunnel. Results for both periodic and linear frequency sweep gust excitations have been computed and measured. The fair to good quantitative agreement between theory and experiment verifies that the present electro-magnetic dry friction damper can be used to alleviate the gust response, especially for the plunge and pitch responses. It also shows that the present theoretical method can be successfully applied to determine the non-linear gust response when an electro-magnetic dry friction damper is used in the linear aeroelastic system.     

A dynamic Lagrangian frequency-time method for the vibration of dry-friction-damped systems

A new frequency-time domain procedure, the dynamic Lagrangian mixed frequency-time method (DLFT), is proposed to calculate the non-linear steady state response to periodic excitation of structural systems subject to dry friction damping. In this formulation, the dynamic Lagrangians are defined as the non-linear contact forces obtained from the equations of motion in the frequency domain, with the adjunction of a penalization on the difference between the interface displacements calculate by the non-linear solver in the frequency domain and those calculated in the time domain from the non-linear contact forces, thus accounting for Coulomb friction and non-penetration conditions. The dynamic Lagrangians allow one to solve for the non-linear forces between two points in contact without using artifacts such as springs. The new DLFT method is thus particularly well suited to handling finite element models of structures in frictional contact, as it does not require a special model for the contact interface. Dynamic Lagrangians are also better suited to frequency-domain friction problems than the traditional time-domain method of augmented Lagrangians. Furthermore, a reduction of the non-linear system to relative interface displacements is introduced to decrease the computation time. The DLFT method is validated for a beam in contact with a flexible dry friction element connected to ground, for frictional constraints that feature two-dimensional relative motion. Results are also obtained for a large-scale structural system with a large number of one-dimensional dry-friction dampers. The DLFT method is shown to be accurate and fast, and it does not suffer from convergence problems, at least in the examples studied.     

Analysis of Coulomb friction vibration dampers

An analysis of the steady state response of a rotational Coulomb friction vibration damper has been carried out. Such dampers are sometimes used in various industrial applications. Analysis of the steady state phase plane is used to determine various response quantities such as amplitude ratio, phase lag, energy dissipated per cycle, and rms power loss. The analysis shows that the response can be categorized into one of three main types. Expressions are developed to predict effect of the addition of a damper on the power and the disturbance amplitude transmitted to the load. It is shown that simple one parameter relationships exist for predicting the maximum vibration reduction achievable with this type of damper.     

An inverse model of MR damper using optimal neural network and system identification

Magnetorheological (MR) damper is one of the more promising new devices for vibration control of structures. External energy required by the adjustable fluid damper is minuscule while speed of its response is in the order of milliseconds. The MR damper is a semi-active control device and has been characterized by a set of non-linear differential equations which represent a forward model of the MR damper, i.e., the model can generate a force to a given displacement and applied voltage.This paper presents an inverse model of the MR damper, i.e., the model can predict the required voltage so that the MR damper can produce the desired force for the requirement of vibration control of structures. The inverse model has been constructed by using a multi-layer perceptron optimal neural network and system identification, which are Gauss-Newton-based Levenberg-Marquardt training algorithm, optimal brain surgeon strategy and autoregressive with exogenous variables (ARX) model. Based on the data from numerical simulation of the MR damper, the trained optimal neural networks can accurately predict voltage. If the inverse model is used in a control system, the semi-active vibration control can be implemented easily by using the semi-active MR damper.     

Mitigation of edgewise vibrations in wind turbine blades by means of roller dampers

Edgewise vibrations in wind turbine blades are lightly damped, and large amplitude vibrations induced by the turbulence may significantly shorten the fatigue life of the blade. This paper investigates the performance of roller dampers for mitigation of edgewise vibrations in rotating wind turbine blades. Normally, the centrifugal acceleration of the rotating blade can reach to a magnitude of 7–8g, which makes it possible to use this kind of damper with a relatively small mass ratio for suppressing edgewise vibrations effectively. The parameters of the damper to be optimized are the mass ratio, the frequency ratio, the coefficient of rolling friction and the position of the damper in the blade. The optimization of these parameters has been carried out on a reduced 2-DOF nonlinear model of the rotating wind turbine blade equipped with a roller damper in terms of a ball or a cylinder, ignoring the coupling with other degrees of freedom of the wind turbine. The edgewise modal loading on the blade has been calculated from a more sophisticated 13-DOF aeroelastic wind turbine model with due consideration to the indicated couplings, the turbulence and the aerodynamic damping. Various turbulence intensities and mean wind speeds have been considered to evaluate the effectiveness of the roller damper in reducing edgewise vibrations when the working conditions of the wind turbine are changed. Further, the optimized roller damper is incorporated into the 13-DOF wind turbine model to verify the application of the decoupled optimization. The results indicate that the proposed damper can effectively improve the structural response of wind turbine blades.     

Torsional friction damper optimization

A new approach for the analysis of friction dampers is presented in this work. The exact form of the steady-state solution for a friction damper implemented on a primary system is developed and numerical solutions are used to determine the optimum friction in a friction damper applied to a specific primary system. When compared to classical results presented by earlier authors, the new approach provides a more optimal solution. In addition, viscous damping in the primary system may be included with the new analysis approach. The ability to optimize a friction damper when viscous damping is included in the primary system is a significant improvement over earlier methods and shows potential for serving as a guide to realizing a more accurate estimate of the optimal damping for friction dampers.     

Two-dimensional friction oscillator: group-preserving scheme and handy formulae

With vibration isolation of buildings and turbomachinery blades in mind, we study the dynamic behaviour of a single-mass two-degree-of-freedom oscillator with dry friction damper, viscous damper and elastic spring connected in parallel. The mass is mounted on an elastic supporting plate allowing movement in two directions on a plane. We formulate a multi-dimensional friction model, from which the sliding conditions and the sticking conditions of the mass are derived. For calculations we develop a group-preserving scheme, which preserves the projective proper orthochronous Lorentz group PSO_o(2,1) symmetry of the model in the sliding phase so as to satisfy automatically the sliding conditions at each time step without iteration at all. The oscillator is then subjected to simple harmonic excitations, and the responses are displayed. According to the simple harmonic balance method together with a circular orbit assumption on displacements, we derive closed-form formulae for handily estimating the steady state responses, which are then compared with the results calculated by the group-preserving scheme to confirm the applicability of the formulae. We also derive formulae specifically for a two-dimensional friction oscillator with rigid base support, which include an exact formula of the magnification factor and a simple formula for estimating the minimum driving force amplitude (or the maximum friction force bound) to avoid sticking.     

Observed transition from linear to non-linear friction-load behavior using a lateral force microscope

The most commonly observed friction behavior for sliding systems is that described by Amontons laws of friction. In this case, sliding friction is independent of the gross or apparent area of contact between the materials and a linear function of the applied normal load, where the constant of proportionality is called the friction coefficient. However, for dry sliding solids in contact via a single-asperity junction, Amontons (linear) friction-load behavior is not strictly relevant. In experiments measuring sliding friction between a silicon tip and a quartz surface using an atomic force microscope (AFM), a transition from linear to non-linear friction-load behavior has been observed. This is proposed to result from a nanoscale ‘conditioning’ of a multiple-contact tip-surface interface to form a single-asperity contact.     

Whirling motion of a shallow cable with viscous dampers

The paper deals with the non-linear dynamic analysis of cables with a pair of viscous dampers close to one support. Such cables are characterized by a sag-to-chord-length ratio below 0.02, for which natural frequencies for the vertical and the horizontal vibrations are pair-wise close. Under resonance the non-linear coupling of pairs of modes may cause whirling harmonic motions around the chord line. Whirling motion may occur after bifurcation from single-mode response for harmonic loads in either vertical or horizontal direction. The non-linear features are included in the two coupled modes, while all other modes are treated as linear. The motion is discretized by expansion in terms of the damped complex eigenfunctions. The applied base functions fulfil the transition condition at the damper, leading to fast convergence of the expansion. It is demonstrated that the behaviour of the whirling motion is controlled primarily by the damper acting in the direction of the unloaded mode, whereas the magnitude of the damper in the loaded mode is less important. If the dampers in the vertical and horizontal direction are close to the optimal value of the corresponding taut cable case, substantial reduction of the vibration level of the whirling mode as well as the frequency interval of its occurrence is attained.     

The plunging-mode response of an idealized airplane to atmospheric turbulent gusts

For the plunging-mode motion of an idealized airplane with pitch neglected, the response statistics have been formulated subject to atmospheric turbulence prescribed by the so-called Dryden's energy spectrum. The stationary input-response relation yields the following conclusions. (1) Atmospheric turbulent gusts should be modeled by incorporating not only the intensity modulation but also the time-varying energy spectrum. (2) The response exceedance curve can display convexity depending on the combination of gust intensity and spectrum parameter. (3) The integral length scale may be estimated alternately from the accelerometer data at the center of gravity and the gust intensity. As a consequence of conclusion (1), a discrete non-stationary gust model is proposed, consisting of a series of stationary processes, having different gust intensities and spectrum parameters. For such a modified Press' gust model, the response covariances of the plunging velocity and acceleration have been computed. Based on the elementary two-stationary-process gust model, sample calculations indeed produce convexity in the response exceedance curves, thereby substantiating (2). Finally, the implication of (3) is that one now has a means of checking consistency of the integral-length-scale measurements.     

Detailed ball bearing model for magnetic suspension auxiliary service

Catcher bearings (CBs) provide backup protection for rotating machines with active magnetic bearings (AMBs). The CBs are required in the event of an AMB failure or high transient loads. Numerical simulations of a rotor drop on CBs in flywheel energy storage system are conducted with a detailed CB model which includes a Hertzian load–deflection relationship between mechanical contacts, speed-and-preload-dependent bearing stiffness due to centrifugal force, and a Palmgren's drag friction torque. The transient simulation results show the rotor shaft response variations with the design parameters: shaft/bearing friction coefficients, axial preload, support damping of damper liner, and side loads from magnetic bearings. The results reveal that friction coefficients, support damping, and side loads are critical parameters to satisfy CB design objectives and prevent backward (super) whirl.     

Optimal control of structures with semiactive-tuned mass dampers

In this paper, the optimal performance of a magnetorheological (MR) damper which is used in a tuned mass damper in reducing the peak responses of a single-degree-of-freedom structure subjected to a broad class of seismic inputs including the harmonic, pulse, artificially generated and recorded earthquake excitations are studied. The optimal semiactive control strategy minimizes an integral norm of the main structure squared absolute accelerations subject to the constraint that the non-linear equations of motion are satisfied and is determined through a numerical solution to the Euler-Lagrange equations. The optimal performance evaluated for an MR damper is compared to an equivalent passive-tuned mass damper with optimized stiffness and damping coefficients. It is shown numerically that the optimal performance of the MR damper is always better than the equivalent passive-tuned mass damper for all the investigated cases and the MR damper has a great potential in suppressing structural vibrations over a wide range of seismic inputs.     

Effect of an impact damper on a multi-degree of freedom system

Theoretical analysis of the steady state vibrational motion of a multi-degree of freedom system equipped with an impact damper is presented. The analysis is based on the assumption that two generally distributed impacts occur in each cycle. The theory is applied to the special case of a single degree of freedom main system and the effects of various parameters are investigated. The theoretically possible modes of steady state motion with two impacts/cycle and with no impacts are predicted. The non-linear behaviour of the damper is manifested by the existence of as many as three modes of steady state motion for a given exciting frequency. The conditions leading to more or less than two impacts/cycle are predicted although the system response under such conditions is not studied. Experimental results are presented and compared with theoretical predictions.     

Component mode analysis of a simple non-linear,non-conservative system

A component mode analysis is carried out based upon the use of constraint conditions and Lagrange multipliers to treat exemplary physical systems with non-linear damping. Both viscous and dry friction dampers attached to a linear elastic (beam) system are examined. The method is shown to possess conceptual and computational advantages by its ability to reduce the analysis of a multimode system to a small number of degrees of freedom equal to that associated with the non-linear component.     

An analytical particle damping model

Particle damping is a passive vibration control technique where multiple auxiliary masses are placed in a cavity attached to a vibrating structure. The behavior of the particle damper is highly non-linear and energy dissipation, or damping, is derived from a combination of loss mechanisms. These loss mechanisms involve complex physical processes and cannot be analyzed reliably using current models. As a result, previous particle damper designs have been based on trial-and-error experimentation. This paper presents a mathematical model that allows particle damper designs to be evaluated analytically. The model utilizes the particle dynamics method and captures the complex physics involved in particle damping, including frictional contact interactions and energy dissipation due to viscoelasticity of the particle material. Model predictions are shown to compare well with test data.     

Energy dissipation of a friction damper

In this paper the energy dissipated through friction is analysed for a type of friction dampers used to reduce squeal noise from railway wheels. A one degree-of-freedom system is analytically studied. First the existence and stability of a periodic solution are demonstrated and then the energy dissipated per cycle is determined as a function of the system parameters. In this way the influence of the mass, natural frequency and internal damping of the friction damper on the energy dissipation is established. It is shown that increasing the mass and reducing the natural frequency and internal damping of the friction damper maximizes the dissipated energy.     

The detectability of kissing bonds in adhesive joints using ultrasonic techniques

This paper concerns a study of the detectability of dry contact kissing bonds in adhesive joints using three ultrasonic inspection techniques. Conventional normal incidence longitudinal and shear wave inspection were conducted on dry contact kissing bonds using a standard damped ultrasonic transducer and an electro-magnetic acoustic transducer (EMAT) respectively. The detectability of the dry contact kissing bonds was assessed by calculating the reflection coefficient of the imperfect interface at varying loads for a number of surface roughnesses. A high power ultrasonic method was also employed to determine the non-linear behavior of the adhesive interface. The non-linearity of the interface was determined by the ratio of the amplitudes of the first harmonic and fundamental frequencies of the transmitted waveform. It was found that the high power technique showed the greatest sensitivity to these kissing bonds at low contact pressures, however at high loads conventional longitudinal wave testing was more sensitive. It was also noted that a combination of two or more techniques could provide enhanced information about the kissing bond compared to a single technique alone.     

掺硅类金刚石薄膜摩擦过程的分子动力学模拟

掺硅类金刚石(Si-DLC) 薄膜表现出优异的摩擦学性能, 在潮湿空气和高温中显示出极低的摩擦系数和很好的耐磨性, 但是许多实验表明Si-DLC膜的摩擦性能受其硅含量的影响很大. 因此, 本文采用分子动力学模拟的方法分别研究干摩擦和油润滑两种情况下不同硅含量的Si-DLC膜的摩擦过程. 滑移结果表明干摩擦时DLC膜和掺硅DLC膜之间生成了一层转移膜, 而油润滑时则为边界膜. 因此干摩擦时的摩擦力明显大于油润滑时的摩擦力. 少量添加硅确实能降低DLC膜的摩擦力, 但是硅含量大于20%后对DLC膜的摩擦行为几乎无影响. 干摩擦时硅含量对转移膜内键的数量影响很大, 转移膜内CC键和CSi键都先增加后减少, 滑移结束时几乎不含CSi键.     

Transient response of a hydraulic engine mount

Linear and non-linear transient responses of a typical hydraulic engine mount are analytically and experimentally studied in this paper. First, a lumped parameter linear model is used to approximate the typical step response and to suggest parameters that must be experimentally determined. Various configurations as related to inertia track and decoupler are analyzed. Two bench experiments are constructed for the identification of non-linear compliances and resistances. One of the main non-linear characteristics, however, comes from the decoupler mechanism. To accurately predict the time events of the decoupler opening and closing, an equivalent viscous damper model is employed along with a multi-staged switching mechanism. Additionally, non-linear behavior arising due to the vacuum formation in the top chamber is studied by defining a bi-linear asymmetric stiffness curve. New transient experiments are conducted on an elastomer test system, and measured transmitted force and top chamber pressure signals are analyzed. Results of the proposed simulation model match well with measured responses when step up, step down and triangular waveforms are applied. Areas for future research are identified.     

Identification of the dynamic characteristics of a structure with coulomb friction

The effect of coulomb friction on the Kennedy and Pancu vector plot of a single degree-of-freedom system is analyzed by using the method of harmonic balance. It is shown that the resulting diagram no longer conforms to a locus of a circle in the resonant region, which restricts the usual methods of analysis. A technique, based upon the in-phase and quadrature power dissipated when exciting a normal mode, is presented which allows the magnitude of the non-linear friction force and the hysteretic damping constant to be evaluated. The technique is also applied to systems having several degrees-of-freedom and it shows that it is possible to identify the characteristics of a single non-linear coulomb device situated within a structure, but in the case of more than one device, the technique has some restrictions. The theoretical results are compared with experimental data from a structure containing a non-linear coulomb device.