Jean Frene

Theoretical Analysis of the Incompressible Laminar Flow in a Macro-Roughness Cell

The present work deals with the analysis of the incompressible laminar shear driven flow in a channel of which one of the walls carries a macro roughness pattern while the opposite one has a parallel velocity. The problem is discussed from the standpoint of lubrication theory and it is shown that the usual simplified models as the Reynolds or the Stokes equations are not applicable. Numerical results are presented for three types of two dimensional macro-roughness and two versions of a three dimensional one. It is shown that a pressure generation effect occurs with increasing the relative importance of convective inertia. Previous analyses found in the literature discussed only the increase of the shear stress due to the presence of the macro roughness but the lift effect due to the pressure generation has never been enlightened up to now. It is further discussed that, extrapolated to a very large number of macro roughness characterizing a textured surface, this new effect could be added to the other lift generating mechanisms of the lubrication theory. It could thus bring a different light on inertia effects stemming from the use of textured surfaces.

Wear mechanism in graphite–copper electrical sliding contact

The electrical conduction tensor of highly anisotropic graphite is not compatible with the mechanical and tribological tensors that leads to low friction and low mechanical wear rate in sliding electrical contact. This incompatibility increases the electrical resistance and increases thus the thermal effect and the electrical contact wear. The aim of this paper is to present the tribological behaviour of couple and to discuss the effect of the antagonistic mechanical/electrical properties of polycrystalline graphite in thin rubbed layers during sliding electrical tests.

Static and Dynamic Characterization of a Bump-Type Foil Bearing Structure

The performance of Gas Foil Bearings (GFBs) relies on a coupling between a thin gas film and an elastic structure with dissipative characteristics. Due to the mechanical complexity of the structure, the evaluation of its stiffness and damping is still largely inaccurate if not arbitrary. The goal of this paper is to improve the understanding of the behavior of the bump type FB structure under static and dynamic loads. The structure was modeled with finite elements by using a commercial code. The code employed the large displacements theory and took into account the friction between the bumps and the support and between the bumps and the deformable top foil. Static simulations enabled the estimation of the static stiffness of each bump of a strip. These simulations evidence a lack of reliable analytical models that can be easily implemented in a FB prediction code. The models found in the literature tend to over-estimate the foil flexibility because most of them do not consider the interactions between bumps that seem to be highly important. The transient simulations allowed the estimation of the dynamic stiffness and the damping of a single bump of the FB structure. The presence of stick-slip in the structure is evidenced and hysteretic plots are obtained. The energy dissipation due to Coulomb friction is quantified in function of materials, excitation amplitude and frequency. Some energetic considerations allow the calculation of the equivalent viscous damping coefficient and the results are related to experimental data found in literature. The influence of the number of bumps is also briefly addressed.Copyright

A New Bump-Type Foil Bearing Structure Analytical Model

A gas bearing of bump foil type comprises an underlying structure made of one or several strips of corrugated sheet metal covered by a top foil surface. The fluid film pressure needs to be coupled with the behavior of the structure for obtaining the whole bearing characteristics. Unlike in classical elasto-aerodynamic models, a foil bearing (FB) structure has a very particular behavior due to friction interfaces, bump interactions, and nonisotropic stiffness. Some authors have studied this complex behavior with the help of three-dimensional finite element simulations. These simulations evidenced a lack of reliable analytical models that can be easily implemented in a FB prediction code. The models found in the literature tend to overestimate the foil flexibility because most of them do not consider the interactions between bumps that are highly important. The present work then develops a model that describes the FB structure as a multidegree of freedom system of interacting bumps. Each bump includes three degrees of freedom linked with elementary springs. The stiffnesses of these springs are analytically expressed so that the model can be adjusted for any dimensions and material properties. Once the stiffness matrix of the whole FB structure is obtained, the entire static system is solved taking friction into account. Despite its relative simplicity, comparisons with finite elements simulations for various static load distributions and friction coefficients show a good correlation. This analytical model has been integrated into a foil bearing prediction code. The load capacity of a first generation foil bearing was then calculated using this structure model as well as other simplified theoretical approaches. Significant differences were observed, revealing the paramount influence of the structure on the static and dynamic characteristics of the foil bearing. Some experimental investigations of the static stiffness of the structure were also realized for complete foil bearings. The structure reaction force was calculated for a shaft displacement with zero rotation speed, using either the multidegree of freedom model or the usual stiffness formulas. The comparisons between theoretical and experimental results also tend to confirm the importance of taking into account the bump interactions in determining the response of the structure.

Nonlinear Numerical Prediction of Gas Foil Bearing Stability and Unbalanced Response

One of the main interests of gas foil bearings lies in their superior rotordynamic characteristics compared with conventional bearings. A numerical investigation on the stability limit and on the unbalanced response of foil bearings is presented in this paper. The main difficulty in modeling the dynamic behavior of such bearings comes from the dry friction that occurs within the foil structure. Indeed, dry friction is highly nonlinear and is strongly influenced by the dynamic amplitude of the pressure field. To deal with these nonlinearities, a structural dynamic model has been developed in a previous work. This model considers the entire corrugated foil and the interactions between the bumps by describing the foil bearing structure as a multiple degrees of freedom system. It allows the determination of the dynamic friction forces at the top and at the bottom of the bumps by simple integration of ordinary differential equations. The dynamic displacements of the entire corrugated sheet are then easily obtained at each time step. The coupling between this structural model and a gas bearing prediction code is presented in this paper and allows performing full nonlinear analyses of a complete foil bearing. The bearing stability is the first investigated problem. The results show that the structural deflection enhances the stability of compliant surface bearings compared with rigid ones. Moreover, when friction is introduced, a new level of stability is reached, revealing the importance of this dissipation mechanism. The second investigated problem is the unbalanced response of foil bearings. The shaft trajectories depict a nonlinear jump in the response of both rigid and foil bearings when the value of the unbalance increases. Again, it is evidenced that the foil bearing can support higher mass unbalance before this undesirable step occurs.

Comparison between three turbulent models — application to thermohydrodynamic performances of tilting-pad journal bearings

The influence of the flow regime on tilting-pad journal bearing performance is presented. Three turbulent models are studied. The results show that for high rotational speeds the effect of non-laminar flow on the predicted performance is not negligible. At high speeds, lower temperatures and greater power losses are obtained. Isotherms determined with laminar and turbulent models help to explain this phenomenon.

Numerical Study of the Pressure Pattern in a Two-Dimensional Hybrid Journal Bearing Recess, Laminar, and Turbulent Flow Results

The present work is a parametric study of the pressure pattern in a two-dimensional recess of a hybrid journal bearing (HJB). It is known that theoretical models of HJB are largely dependent on the recess pressure pattern especially for severe working conditions (high rotation speeds, shallow pockets, etc.). The difficulty is that the recess flow is dominated by the interaction of viscous and inertia forces and cannot be analyzed using a thin film model. The present analysis is based on the numerical resolution of the two-dimensional Navier-Stokes equations where only one recess is modeled (with the film lands and the supply region), the fluid being regarded as incompressible and isothermal. Both the laminar and the turbulent flow regimes are considered. The study is governed by two parameters, one related to the HJB operating conditions and the other related to the recess geometric characteristics. The first parameter is the ratio of the runner versus the supply Reynolds number, Re r /Re s ∈ {0, 1/ 4, 1/ 2, 1, 4, 8}. The supply Reynolds number is fixed at 100 for the laminar regime and at 5000 for the turbulent one. The second parameter is the ratio of the recess depth versus the film thickness. Six values of this ratio are considered, ranging from 4 (shallow recess) to 152 (deep recess). Detailed pressure patterns on the runner wall are presented in a systematic manner giving a clear insight of the flow effects intervening in the recess and of their mutual interaction. Some effects are explained by analyzing the recirculation zones inside the recess. It is also shown that for certain parameters turbulent flows have qualitatively similar effects as laminar ones but they can also have specific trends. In order to sustain this remark, the pressure variation at the recess downstream end is analyzed in the paper Finally, the present results and specially the turbulent ones are intended to contribute to the understanding of viscous and inertia effects interactions in a recess flow and to represent a database in view of HJB theoretical modeling.

Numerical Three-Dimensional Pressure Patterns in a Recess of a Turbulent and Compressible Hybrid Journal Bearing

The present work investigates the flow in the feeding recess of a hybrid journal bearing. Numerical integration of the complete Navier-Stokes equations was performed with an appropriate turbulence model. Of primary concern is the pressure field on the rotating journal surface that is commonly known as the recess pressure pattern. The goal of the work is to determine the influences of fluid compressibility, operating conditions and recess geometry. Reference parameters selected for this study comprise feeding Reynolds number Re a of 2.10 5 , sliding Reynolds number Re c of 5.10 3 and recess depth over film thickness ratio e/H of 2.2. Compressibility was considered first. Three values of the axial exit Mach number were selected for computation, namely 0.2, 0.45, and 0.7. As no significant variation was found, the Mach number was fixed at 0.45 in subsequent studies concerning other parameters: Feeding Reynolds number, Re a 2.10 4 ,2.10 5 ,4.10 5 Recess depth, e/H 0, 2.2, 8 Feedhole axis inclination 90°, 135°, 165° Feedhole location (Figs. 1(a) and 13) centered, downstream offset As each parameter is varied, wire mesh plot of pressure and its sectional profiles are examined and effects of varying various parameters are discussed in reference to flow processes as they may affect the support characteristics of the hybrid journal bearing.

Non-linear behavior of a flexible shaft partly supported by a squeeze film damper

High speed rotors pose stability problems, especially when the speed of rotation increases above a critical speed. In this case, the dynamic behavior of the fluid bearings has an important effect. This study presents several models of the dynamic behavior of bearings, taking into account the flexibility of the shaft. The behavior of the squeeze film damper is also described. This element provides damping but its behavior is totally non-linear. An approach for an active squeeze film damper is presented: a variable clearance squeeze film damper or a variable viscosity squeeze film damper (feed with electrorheological fluid) is used to control a flexible shaft. These technologies could be very promising in the future.

Investigation about Electrorheological Squeeze FilmDamper Applied to Active Control of Rotor Dynamic

Electrorheological (ER) fluids, discovered in 1947 by W. WINSLOW, are concentrated suspensions of solid particles in an oily base liquid. Exposed to a strong electric field, their resistance to flow increases very greatly and this change is progressive, reversible and occurs very rapidly. Nowadays, ER fluids, made of lithium salt and fluorosilicon got rid of their old abrasive characteristics and are able to provide a good interface between electronics and mechanical components. A bibliographical study on ER fluids and ER technology has been carried out. The aim of this study is adapting ER technology to Squeeze Film Damper. In order to provide an active control on a flexible rotating shaft so as to command the whole shaft/bearings device in case of high rotating speed or heavy load trouble. Results of numerical computation of a shaft bearing assembly with a Squeeze Film Damper using negative ER fluid are showed in order to see the possibility of avoiding critical speeds by natural frequency shifting. A technical study of ER Squeeze Film Damper design is also presented, taking into account ER fluid properties and ER technology requirements.