This paper proposes a simple and novel principle for suppressing frictional vibration using viscous damping effect generated by “lateral slip” given to a typical sliding system. This principle was applied to the measurement of friction coefficient and an anti-vibration tribometer (AVT) was developed. The AVT suppressed frictional vibration caused by the negative dependence of the friction coefficient on the relative velocity, and it enabled one to measure friction coefficient accurately in the force balance between the friction force and spring force. If using the mean value of oscillating spring force to calculate friction coefficient under frictional vibration, it was found that considerable errors (e.g., approximately 30%) appears.

Dynamic coefficients are very important for the stability of a hydrodynamic journal bearing and therefore for its design. In order to determine the stiffness, damping and added mass coefficients of the hydrodynamic bearing, the finite perturbation method around its stabilization position was employed. Based on the Reynolds equation with Gumbel cavitation algorithm, the maximum magnitude of the perturbation was judged by comparing results from finite perturbation (numerical way) to those from infinitesimal perturbation (additional analytical equations need to be derived based on order analysis), as well as theoretical analysis. Using the determined perturbation amplitude, the full three-dimensional Navier-Stokes equations in CFD-ACE+ were used to evaluate coefficients from an actual lubricant and compare to those obtained with Reynolds equation. Finally, a homogeneous gaseous cavitation algorithm is coupled with the Navier-Stokes equation to establish the pressure distribution in the bearing. When gas concentration was varied, the pressure distribution as well as the dynamic coefficients changed significantly.

Water lubricated rubber bearings are used from many years in ship building and other industry because of their advantages such as: long serviceable life, low coefficient of friction, long life of shaft sleeve, good vibration damping, good abrasion resistance, low maintenance required, grit particles and other abrasives are expelled through the grooves [1,2,3,4].

The numerical analysis for the equivalent stiffness and damping of a single EHL contact between the rolling element and raceways under wider load and speed ranges is presented. The unsteady EHL model and free vibration model are applied to describe the motion characteristics of the rolling element. The inlet length and dimensionless natural frequency are determined according to the corresponding working load and speed. The DC-FFT method is implemented in order to increase the computational efficiency associated with elastic deformations and the semi-system approach is applied to ensure solution convergence under severe conditions which makes the analysis of stiffness and damping in the larger ranges of load and speed possible. The numerical results demonstrate that the stiffness increases with the increasing load and decreases with speed. However, the changes of the damping are complex, which are different in various load and speed ranges, especially under heavier load and higher speed. It is also indicated that the stiffness and damping increases with the increase in ambient viscosity and the decrease in pressure-viscosity coefficient.

The motion of a wave bearing sleeve exposed at a differential pressure at the axial ends and supported by an elastic element is considered in this paper. The influence of the stiffness and damping properties of the elastic element and of the wave amplitude on the sleeve motion is analyzed. It was found that the wave amplitude ratio and the damping of the elastic element support have an important influence on the dynamic behavior of the wave bearing. The stiffness of the elastic support does not significantly affect the bearing behavior.

The nonlinear normal vibration of a block of rough surface in visco-elastic interaction with a rough plane is considered. The nonlinear normal free vibration response corresponds to the application of a constant compressive external load, thereby establishing an equivalent contact stiffness for the system. Closed-form equations relating contact damping ratio and contact natural frequency to the surface parameters are given.

The stability, reliability, efficient performance of high speed turbo machinery is very important, and accordingly has increased the demand for advanced bearings. In order to meet the advanced bearing needs, Heshmat proposed a hybrid foil-magnetic bearing [1]. The hybrid bearing combining the two bearings takes advantage of the strengths of each while compensating for each other’s weaknesses. This paper presents dynamic characteristics of the combined smart bearing (CSB) of different structure from Heshmat’s bearing. The CSB and test rig were designed, fabricated and carried out the test. Numerical predictions of Air foil bearing (AFB) and CSB were compared the dynamic force performance, and analysis of bearings are performed by finite element method (FEM). Experiments were conducted to determine the structural static and dynamic characteristics of AFB. The dynamic characteristics of AFB and CSB compared depending on the rotating speed change. The experimental results were obtained the dynamic characteristics of the CSB 50% higher than value of the stiffness effect. In addition to, the CSB 100% higher than value of the damping effect.

In aircraft engine the blade resonant vibration amplitude is reduced by increasing the structural damping by using, for example, tip shrouds. These devices dissipate the energy generated at the contact surfaces between the relative motion and the friction force. Contact parameters as friction coefficient and contact stiffness are required to characterize the dynamics of the shrouded blade systems. Moreover if at the contact surfaces severe wear occurs a loss of interference takes place, the shroud is not longer able to dissipate energy and a catastrophic blade failure could take place. A test rig for contact parameters measurement and micro wear characterization of flat-on-flat contact surfaces has been developed. One of the specimens is attached to the rig frame, basically an inertial mass and four springs, excited by an electromagnetic shaker. The second specimen is allowed to approach the first specimen and to rotate in such a way the geometric contact between the two surfaces occurs on three points. In this way a real “flat-to-flat” contact has been obtained. The tangential contact force and the relative displacements between specimens are measured and the friction coefficient and contact stiffness, are determined. The expected results are the contact parameters and the wear behaviour of real flat-on-flat contact surfaces. The aim of this work is to describe the design principle of the test rig and show the first measurements.

Most of elasto-aerodynamic approaches under dynamic conditions proposed in the technical literature include only the static pressure induced deformation of foils. This paper presents a theoretical investigation on the effects of both static and dynamic deformations of the foils on the dynamic performance characteristics and stability of a self-acting air foil journal bearing operating under small harmonic vibrations. To take into account the dynamic deformations of foils, the perturbation method is used for determining the gas-film stiffness and damping coefficients for given values of excitation frequency, compressibility number, and compliance factor of the bump foil. The nonlinear stationary Reynolds’ equation is solved by means of the Galerkin’s finite element formulation while the finite differences method are used to solve the first order complex dynamic equations resulting from the perturbation of the transient compressible Reynolds’ equation. It was found that the dynamic properties and stability of the compliant finite length journal bearing are significantly affected by the compliance of foils especially when the dynamic deformation of foils is considered in addition to the static one by applying the principle of superposition.

A bump-type foil bearing consists of a compliant corrugated sheet metal supporting structure that is covered by a thin top foil surface. Bumps serve as stiffener and damping elements to increase the stability of the system while top foil creates necessary wedge surface for aerodynamic film formation. Foil bearings are hard to analyze as flexible foil surface deforms and changes shape while aerodynamic film pressure forms. Fully coupled finite element approach is presented. To increase the accuracy, the geometry is discretized with quadratic hexagonal elements. The gas film is modeled by compressible Reynolds equation. The effect of velocity on load capacity will be investigated to reveal the performance of the code.

When dealing with mechanical systems including contact interfaces, two different mechanics at two different time and length scales have to be accounted for: the contact mechanics and the structural mechanics. The mechanics of the contact and the mechanics of structure are coupled by friction (forces and moments), local body deformations and wear (geometrical coupling). In the past, dynamic and tribological problems were treated separately and the analysis was focused either on the mechanism scales or on the contact scales, as a function of the problem. The analysis of the dynamic response of the mechanical system accounted for the contact interfaces thought global coefficients (global contact stiffness, damping, energy loss factor, etc.); vice versa, the analysis of the local behaviour at the contact interface accounted for the system dynamics imposing global boundary conditions on the contact model (pressure distribution, relative velocities, etc.). During last decades mechanical system design led to a power increase and to a drastic optimization, increasing as well the number of contact interfaces between deformable bodies. Thus, the need for coupling dynamic and tribological analyses arises for solving and understanding either wear phenomena or dynamic response of a mechanical system. On this sense, experimental tools showed their limits on the estimation and prediction of friction and wear phenomena. This paper proposes a first step toward a more general approach aimed to couple the dynamic analysis of the mechanism with the local tribological analysis at the contact, by the coupling of two different numerical models dealing with the two different scales. Two applications are then mentioned: the analysis of “false Brinelling” wear and the understanding of brake squeal instability.

This paper presents numerical analysis of the dynamic characteristics of an air bearing system of a magnetic head under ultra-thin spacing. First, the static pressure distribution is numerically calculated by using up-wind scheme for a very large bearing number and a harmonic algorithm to calculate the flux factor for the abrupt change of film thickness. Then, the dynamic characteristics are analyzed in frequency domain by a perturbation method and finite difference method. The varying tendencies of the stiffness and damping coefficient in the translation, pitch and rolling directions with the frequency and the minimum film height are obtained.

The purpose of this paper is to study the dynamic behavior of a journal bearing sleeve center by using a transient approach. Unlike other papers presenting the motion of the shaft inside the bearing sleeve, in this paper the rotor is considered rigid having only a small unbalance and the motion of the sleeve center is analyzed. The sleeve is supported by elastic elements. In addition, the axial ends of the bearing are exposed at two different pressures. To the authors’ knowledge, this paper is the first study of such a bearing configuration. Moreover, the influence of the stiffness and damping properties of the elastic element on the sleeve dynamic behavior (trajectories, motion frequencies, etc.) is also analyzed. Relative and absolute trajectories of the sleeve center and FFT analysis of the motion are presented.

The purpose of this paper is to present the experimental evaluation of the stiffness and damping coefficients of a pair of elastic rings used to support a fluid film bearing into a turbojet engine body. The experimental rig, the method of analysis and the experimental data are presented.

The differences in load and unload paths in an elastic-plastic contact of a rough surface and a flat leads to hysteretic energy loss. The nonlinear normal vibration response of the block is examined when subject to an external compressive load. The vibration response corresponds to the application of a constant compressive external It is shown that vibration decay rate is constant as opposed to the exponential decay rate for the linear vibrating systems. Closed form equations relating contact damping and contact natural frequency to the surface parameters are given.

Ingestion and entrainment of air into the Squeeze Film Dampers (SFDs) with open end result in a bubbly mixture that affects their damping capacity. The industrial applications demand dampers with low pressure supply and operating high speed, it means, it exists a necessity of propose a model to predict the air ingestion in this kind of bearing. Diaz and San Andre´s reported results of an extend research to quantify the effect bubbly mixture in the performance of the SFDs. They also advanced an analytic model for short infinity bearings (L/D = 0) which estimate the air ingestion as function of non-dimensional number named by them feed squeeze flow number. Me´ndez et al. advanced the understanding of the effect air entrainment. They propose a new dimensionless map to estimate the air volume fraction in finite length bearings. Although, their results are immediate applicability, they do not have been validated. The present work looks for confirm the results presented by Me´ndez et al. To achieve this, it is solved a compressible Reynold equation with a different numerical method. The results indicate that is necessary another dimensionless number to estimate the entrapment air and the dimensionless map proposed by Me´ndez et al. is valid only to bearings with an eccentricity-clearing ratio of 0.5248.

Demonstrated gas foil bearing (GFB) operation at high temperature is of interest for gas turbine applications. The effects of (high) shaft temperature on the structural stiffness and damping parameters of a foil bearing must be assessed experimentally. Presently, a hollow shaft warmed by an electric heater holds a floating 2nd generation FB that is loaded dynamically by an electromagnetic shaker. In tests with the shaft temperature up to 184°C, the measurements of dynamic load and ensuing FB deflection render the bearing structural parameters, stiffness and damping, as a function of excitation frequency and amplitude of motion. The identified FB stiffness and viscous damping coefficients increase with shaft temperature due to a reduction in the FB clearance. The bearing material structural loss factor, best representing mechanical energy dissipation, decreases slightly with shaft temperature while increasing with excitation frequency.

Small perturbation and modal-analysis methods were employed to systematically study a damped slider’s dynamic characteristics. We found that a design with grooves distributed on a trailing pad effectively improved the slider’s damping at higher frequencies, and the damping ratio was dependent on the number of grooves, their depth, location, width, length, distribution, orientation, and types. A higher damping ratio could be obtained by optimizing these parameters. The femto slider with distributed damping grooves on a trailing pad had a higher damping ratio in the third mode, and hence, its responses to disk parallel and wavy motion were greatly reduced. This new design for the damped slider was an effective solution reducing the slider’s modulation.

This work is intended to evaluate a cavitation model based on the complete Rayleigh Plesset (RP) equation for use in squeeze film damper (SFD) calculations. The RP equation governs the variation of the radius of the cavitation bubbles at rest, surrounded by an infinite incompressible fluid and subject to an external pressure. This equation is obtained from the momentum equation and it takes into account the ensemble of the phenomena related to the dynamics of the bubbles (surface tension, damping, inertia). All the terms in the RP equation will be taken into account in the present work. Numerical results will be compared with experimental data obtained by Adiletta and Pietra [1]. The results then underline the influence of the effects contained in the RP equation on the pressure field.

Elastic-plastic interaction of a block of rough surface with a smooth plane is considered in this paper. The nonlinear normal vibration response of the block is examined when subject to an external compressive load. Free vibration response of the block is studied. The vibration response corresponds to the application of a constant compressive external load and the study yields closed-form equations for the contact damping rate and contact natural frequency. It is shown that vibration decay rate is constant as opposed to the exponential decay rate for the linear vibrating systems. Closed form equations relating contact damping rate and contact natural frequency to the surface parameters are given.