Performance Of Foil Bearings Research Articles

Thermal analysis and optimization of bionic cooling channels of gas foil thrust bearings

Under high-temperature conditions, heat evacuation of foil bearing has a significant impact on bearing performance, including loading performance and reliability. During bearing operation, viscous dissipative heat in the lubricant gas film is the main source of heat generation. For foil bearings, enhancing the heat evacuation efficiency is essential to extend the bearing service life in high-temperature environments. For heat evacuation, foil-side cooling is a very effective method. For more in-depth analysis of thermal characteristics of the foil bearing, a three-dimensional (3D) thermal-elasto-hydrodynamic (TEHD) coupling model of multi-leaf thrust foil bearing (MLTFB) with cooling channel is established in this paper. In view of the good heat transfer performance and more uniform gas velocity distribution in bionic flow channels, various bionic cooling channels of foil bearings are proposed and the structural parameters are optimized. The effects of cooling channel type, cooling channel width, span ratio, cooling gas supply mode, and rotational speed on the thermal and loading performance of foil bearings are investigated. The studies demonstrate that the spider net round cooling channel exhibits higher heat transfer performance and improved uniformity of temperature. Compared to the cooling gas supply from inner edge, the cooling gas supply from the outer edge proves to be more effective. The maximum temperature of lubricant gas film can be greatly reduced with wider cooling channels and a smaller channel span at the outer edge. The maximum temperature of lubricant gas film and bearing load are reduced as the Reynolds number of cooling gas increases. There exists an optimal Reynolds number that can achieve the highest uniformity of temperature.

The limiting static and dynamic performance of foil bearings

Foil bearings have attracted considerable attention in small-sized turbomachines with its excellent stability, high compliance, and temperature durability. However, as the foil bearing is applied to turbine machinery with higher load and impact, the evaluation of its limiting performance becomes more important. Thus, a simple analytical method is proposed for predicting the limiting performance of the journal and thrust foil bearings. The analytical model is verified by comparing it with the full numerical algorithm. The results indicate that with the increase of rotating speed, the pressure distribution of both journal and thrust foil bearing approach to the analytical model but can never reach due to the boundary conditions. When the rotating speed tends to infinity, the principal stiffness Kxx, Kyy, Kzz converge to a certain value, while the cross stiffness Kxy and Kyx approach to infinity and 0, respectively. The static and dynamic performance are evaluated with foil compliance, rotor eccentricity, and film thickness as independent variables to provide further reference for system design.

Design and Research of New Type High-speed Hydrostatic Spindle Test Rig

Aiming at the air dynamic pressure foil bearing performance test rig, design and research a new high-speed static pressure spindle test rig. Carry out aerodynamic design of the driving turbine and compressor, obtain the three-dimensional impeller shape and carry out the strength calculation, design a new high-speed static pressure spindle test rig; use the finite element method to model the test bed rotor system, and use the transfer matrix method to analyse the shaft system structure critical speed and mode, so that the test rig can effectively avoid the critical speed and run stably. Analyse the unbalanced response and stability of the rotor system, and reasonably arrange the test rig device to achieve the purpose of measuring the performance of the dynamic pressure foil bearing, and ensure that the turbine static pressure spindle test rig can provide for the measurement of the air dynamic pressure foil bearing performance stable high speed.

The Influence of Material Selection and Pre-deformation on the Perfor-mance of Foil Bearing

Material selection is one of the most important steps in the manufacturing process of foil bearing. In this study, an experimental work is carried out to study the effect of operating temperature on the damping coefficients and the elastic modulus of Inconel X-750 and SUS321. Then, the influence of pre-deformation on the damping coefficients and the elastic modulus of Inconel X-750 are discussed. Finally, this paper calculates the rotor trajectory supported by the foil bearing considering the different pre-deformation of the foil. The results show that for the foil bearing supporting the rotor system shown in this paper, the Inconel X-750 with 10% pre-deformation is the best choice.

Evaluation of Lubrication Performance of Foil Bearings with New Texturing

Foil bearings have excellent characteristics such as a high damping performance and acceptable dimensional changes caused by installation errors and thermal expansion. However, the problem of large friction losses also occurs at the top foil under the high rotational speed required to support a shaft without any contact. In this paper, a new type of foil bearing with a surface texture on the top foil is proposed. The effects of the texture were verified by the rotational motion experimental analysis under a high circumferential speed and dry lubrication. For a bearing with dimples on the contact area, the effect of friction reduction could be observed under boundary lubrication. Moreover, it was also confirmed that the dimples adversely affected the air film formation with the sliding speed increase. For a newly designed F-grooved model, the phenomenon of an early transition from boundary lubrication to fluid lubrication can be seen. However, the friction coefficient increases at the boundary lubrication. In this study, it was also the highest friction reduction effect was confirmed at the maximum sliding speed. Furthermore, an additional friction reduction effect and a small temperature rise were obtained by combining the above textures.

The effect of rounding radius in bump foil structure on the static performance of foil journal bearings

Purpose The purpose of this paper is to investigate the effect of the rounding in bump foil on the static performance of air foil journal bearings. Design/methodology/approach During the study, the bending moment of the new foil structure with rounding is proposed, and the bump foil stiffness is obtained from the elastic deformation energy theory. The validity of the presented foil model is verified through comparison with previous models. The static characteristics of foil bearings such as film thickness and attitude angle are obtained using a fully coupled elastic-gas algorithm and are compared to models with various rounding radius and friction coefficients. Findings There is an optimal rounding radius that makes the stiffness of bump foil maximum. As the static load increases, the minimum film thickness is proportional to the rounding radius but the attitude angle is inversely proportional. The effect of rounding with a large friction coefficient becomes negligible. Originality/value The rounding brings fundamental difference in the structural stiffness and static performance of foil bearings. The results are expected to be helpful to bearing designers, researchers and academicians concerned.

Effect of Foil Geometry on the Static Performance of Thrust Foil Bearings

Gas foil bearings can operate in extreme conditions such as high temperature and high rotating speed, compared to traditional bearings. They also provide better damping and stability characteristics and have larger tolerance to debris and rotor misalignment. Gas foil bearings have been successfully applied to micro- and small-sized turbomachinery, such as microgas turbine and cryogenic turbo expander. In the last decades, a lot of theoretical and experimental work has been conducted to investigate the properties of gas foil bearings. However, very little work has been done to study the influence of the foil bearing pad configuration. This study proposes a robust approach to analyze the effect of the foil geometry on the performance of a six-pad thrust foil bearing. In this study, a three-dimensional (3D) computational fluid dynamics (CFD) model for a parallel six-pad thrust foil bearing is created. In order to predict the thermal property, the total energy with viscous dissipation is used. Based on this model, the geometry of the thrust foil bearing is parameterized and analyzed using the design of experiments (DOE) methodology. In this paper, the selected geometry parameters of the foil structure include minimum film thickness, inlet film thickness, the ramp extent on the inner circle, the ramp extent on the outer circle, the arc extent of the pad, and the orientation of the leading edge. The objectives in the sensitivity study are load capacity and maximal temperature. An optimal foil geometry is derived based on the results of the DOE process by using a goal-driven optimization technique to maximize the load capacity and minimize the maximal temperature. The results show that the geometry of the foil structure is a key factor for foil bearing performance. The numerical approach proposed in this study is expected to be useful from the thrust foil bearing design perspective.

On the manufacturing of compliant foil bearings

The fabrication of foil bearings is challenging due to the dependence on sheet metal forming to produce the compliant structure. This paper is an attempt to shed light into the foil bearing manufacturing know-how. Design of experiments techniques are used to quantify the effects of the different manufacturing parameters, as well as defining an optimum manufacturing procedure. The effect of manufacturing noise on the static performance of foil bearings is quantified using a Monte Carlo simulation of a bump foil stiffness model. A non-intrusive optical measurement technique which has been developed to measure the formed bump foils is also presented. An uncertainty quantification was performed for the produced foils, showing large uncertainty in the bump dimensions, which significantly affect both nominal bearing clearance and compliance. Finite element simulations are used to model the bump foil forming process that would present potential problems during fabrication, suggesting sharp bends in the bump foil as the main driver for manufacturing deviations. Based on this outcome an improved design for the compliant bump foil with reduced curvature is proposed, manufactured and measured. The novel design allows to reduce springback error by 69% compared to classical bump foils and thus offers an equivalent yet more robust foil bearing design.

Dynamic performance of foil bearings with a quadratic stiffness model

Hydrodynamic foil bearings found various applications in high speed small turbomachinery due to several advantages compared with traditional oil lubricated bearing and rolling element bearings such as high speed, pollution free, high temperature, long service life, etc. Corrugated bump foils made of thin sheet metal is the most widely adopted foil structure used in many commercial foil bearings. However, due to various factors during manufacturing process of the foil structure and mounting methods of the foil structure on to the bearing sleeve, measured stiffness curves of the foil structure show very strong non-linearity. The non-linearity of the foil structure is often neglected in most simulation studies in the past, and single value of bump stiffness combined with appropriate structural loss factor were used in these simulation studies. Based on measured non-linear structural stiffness of entire foil bearing, a quadratic stiffness model of individual bump foil was derived and utilized in transient rotordynamic simulations in time domain by solving Reynolds equation, rotor equations of motion, and bump deflections together. The simulation results using the quadratic bump stiffness model were compared with those using linear bump stiffness models.

Development of a Computational Tool to Simulate Foil Bearings for Supercritical CO2 Cycles

The foil bearing is an enabling technology for turbomachinery systems, which has the potential to enable cost efficient supercritical CO2 cycles. The direct use of the cycle's working fluid within the bearings results in an oil-free and compact turbomachinery system; however, these bearings will significantly influence the performance of the whole cycle and must be carefully studied. Moreover, using CO2 as the operating fluid for a foil bearing creates new modeling challenges. These include highly turbulent flow within the film, non-negligible inertia forces, high windage losses, and nonideal gas behavior. Since the flow phenomena within foil bearings is complex, involving coupled fluid flow and structural deformation, use of the conventional Reynolds equation to predict the performance of foil bearings might not be adequate. To address these modeling issues, a three-dimensional flow and structure simulation tool has been developed to better predict the performance of foil bearings for the supercritical CO2 cycle. In this study, the gas dynamics code, eilmer, has been extended for multiphysics simulation by implementing a moving grid framework, in order to study the elastohydrodynamic performance of foil bearings. The code was then validated for representative laminar and turbulent flow cases, and good agreement was found between the new code and analytical solutions or experiment results. A separate finite difference code based on the Kirchoff plate equation for the circular thin plate was developed in Python to solve the structural deformation within foil thrust bearings, and verified with the finite element analysis from ansys. The fluid-structure coupling algorithm was then proposed and validated against experimental results of a foil thrust bearing that used air as operating fluid. Finally, the new computational tool set is applied to the modeling of foil thrust bearings with CO2 as the operating fluid.

Experimental Studies on Foil Bearing With a Sliding Coating Made of Synthetic Material

The paper discusses the research on foil bearings with antifriction coating manufactured from synthetic materials. The tests were carried out on a special test stand of our own construction, designed with the use of numerical analysis. In the course of the experimental studies, the test stand was set up in two configurations: with one or two foil bearings. The measurements were done, which focused on temperature distributions with the aid of thermocouples and thermovision camera. The measurements were being performed under varying conditions of bearing operation. The conducted experiments permitted to verify the durability, thermal characteristics, and dynamic performance of foil bearings in different configurations. An original method to measure temperature of a top foil has been worked out.

A fully coupled 3D thermo-elastohydrodynamics model for a bump-type compliant foil journal bearing

Coupled thermo-elastohydrodynamics model has been developed to predict three-dimensional thermal, structural and hydrodynamic performance of foil bearings. Bearing deformation and film pressure has been coupled in FEM considering thermal/centrifugal growths, and thermo-mechanical material properties. Energy equation has been solved for film temperature using FDM, which is also coupled to FEM via successive iterations. Augmented-Lagrangian method and thermal contact models have been applied to solve for mechanical and thermal contacts. The predicted values have been benchmarked against published measurements, which indicated reasonable correlation. A parametric study has been conducted for various shaft speeds and load conditions to visualize bearing performance.

Prediction of Gas Thrust Foil Bearing Performance for Oil-Free Automotive Turbochargers

Green technologies are a mandate in a world concerned with saving resources and protecting the environment. Oil-free turbocharger (TC) systems for passenger and commercial vehicles dispense with the lubricant in the internal combustion engine (ICE), hence eliminating not just oil coking, but also suppressing nonlinear behavior, instability and excessive noise; all factors to poor reliability and premature mechanical failure. The work hereby presented is a stepping stone in a concerted effort toward developing a computational design tool integrating both radial and thrust foil gas bearings for oil-free automotive TCs. The paper presents the physical analysis and numerical model for prediction of the static and dynamic forced performance of gas thrust foil bearings (GTFBs). A laminar flow, thin film flow model governs the generation of hydrodynamic pressure and a finite element plate model determines the elastic deformation of a top foil and its support bump strip layers. For a specified load, the analysis predicts the minimum gas film thickness, deformation and pressure fields, the drag torque and power loss, and the axial stiffness and damping force coefficients, respectively. Open source archival test data on load capacity and drag torque serves to benchmark some of the model predictions. Next, predictions are obtained for a GTFB configuration designed for an oil-free TC operating at increasing gas temperatures, axial loads, and shaft rotational speeds. The largest drag torque occurs at the highest temperature since the gas viscosity is also highest, whereas the largest load determines operation with a minute film thickness that sets a limit for the manufacturing tolerance. While airborne, the drag friction factor for the bearing is small, ranging from 0.009 to 0.015, thus demonstrating the advantage of an air bearing technology over engine oil-lubricated bearings. The synchronous speed axial stiffness increases with operating speed (and load), whereas the axial damping coefficient remains nearly invariant. The operating gas temperature plays an insignificant role on the variation of the force coefficients with frequency, whereas the operating speed and the ensuing applied thrust load determine the largest changes. The model predicts, as an excitation frequency (ω) increases, a GTFB axial stiffness (Kz) that hardens and a damping coefficient (Cz) that quickly vanishes. The most important finding is that CzΩ/Kz ≈ γ = the material loss factor for the bearing. Hence, the success of foil bearing technology relies on the selection of a metal underspring structure that offers the largest mechanical energy dissipation characteristics.

Simulation of Compliant Bump Foil Journal Bearing Using Coupled Reynolds Equation and Finite Element Model Method

Based on a “1st generation” compliant foil journal bearing, the performance of foil bearing was simulated according to the model base on Reynolds equation coupled the finite element method. Model considers the bending of top foil, elastic deformation of bump foil, the friction between top foil and bump foil and the interaction between bumps. After compared analysis results to test data, the result of simulation was more accurate than other models, thus this model establish a basis for further study of the compliant foil bearing.

Application of Materials on Foil Thrust Bearings for Micro Turbines

Foil bearing that has a soft surface is a kind of air bearing. The performances of foil bearings are greatly affected by the materials of bearing surface, which is called foil element. In order to estimate the performance of foil bearings, two kinds of foil thrust bearings that are made of different materials respectively were tested in a micro turbine system, which contains rotation part and static part. Load capacity and stability of these foil thrust bearings were investigated in experiments. The results show that bearing which contains rubber has higher load capacity and bearing which contains copper foil has higher stability. According to the work in this paper, applications with different requirements can adopt suitable foil thrust bearing.

Structural Properties of Foil Bearings: A Closed-Form Solution Validated with Finite Element Analysis

Fluid film thickness in a compliant foil bearing is greatly influenced by the deflection of the bearing structure. Therefore, in order to properly model performance of a foil bearing, it is mandatory that the deflection of the compliant bearing structure due to the generated hydrodynamic pressure is determined accurately. This article proposes an easy-to-use two-dimensional model, which takes into account detailed geometry of the bump foil-top foil assembly and the interaction between bumps and which can predict the bearing deflection and stresses due to an arbitrary pressure load. The proposed model is first validated using a finite element analysis and the results available in the literature and then used to conduct a parametric study investigating the influence of bump foil geometry, the coefficient of friction between the bearing components, and the type of loading on the structural properties of the bearing. The most important parameters are also identified. The proposed analytical model is completely algebraic and can be easily implemented using any programming language, a spreadsheet, or even a calculator. The resulting solution can also be coupled with the appropriate hydrodynamic model to predict static performance of compliant foil bearings.

The Dynamic Performance Analysis of Foil Journal Bearings Considering Coulomb Friction: Rotating Unbalance Response

The dynamic performance of air foil bearings relies on a coupling between a thin air film and the frictional motion of a foil structure. A number of successful analytical techniques to predict their performance have been developed. However, the evaluation of their dynamic characteristics is still not adequate because of the mechanical complexity of the foil structure and the strong nonlinear behavior of the friction force. This work presents a nonlinear transient analysis method to predict the dynamic performance of foil bearings considering Coulomb friction. In this method, the time-dependent Reynolds equation is solved to calculate pressure distribution and a finite element method is used to simulate bump motion. The analysis is treated with a direct implicit integration technique that can handle nonlinear problems and an algorithm to solve for stick-slip motion of bump foil is applied. Using this method, the hysteretic behavior and dissipative characteristics of bump foil resulting from the unbalance excitation is observed. In addition, a number of parametric studies are performed to evaluate the effects of design parameters on the unbalance response. The parameters are friction coefficient, bump half wavelength, amount of mass unbalance, and the number of bump foil strips. The predictions of the unbalance response show that the foil bearing is very effective on the restriction of the vibration at the resonance frequency and there exist optimum values of design parameters such as friction coefficient, bump foil stiffness, and the number of bump foil strips with regard to minimizing the amplitude at the resonance frequency.

Theoretical Analysis of Externally Pressurized Porous Foil Bearings—Part I: In the Case of Smooth Surface Porous Shaft

In this paper, the theoretical analysis for the hybrid performance of externally pressurized foil bearings with a hollow porous shaft is described. In the analysis, in order to save computation time and to improve the convergency of solutions, the two-dimensional modified Reynolds equation considering the added flow through hollow porous shaft is reduced to the ordinary differential equation by expanding the film pressure to the Fourier series with respect to the axial coordinate. The reduced Reynolds equation and the equilibrium equation for the perfectly flexible foil are solved iteratively by the finite element technique. The numerical solutions for the pressure and film thickness distributions between the foil and the shaft are obtained for a wide range of bearing width-to-diameter ratio under the various combinations of dimensionless supply pressure, dimensionless permeability of porous shaft and dimensionless wrap angle of foil, and the hybrid performance of foil bearings are examined theoretically. It is found from the numerical results that the bearing width has the significant effect on the pressure and film thickness distributions between the foil and the shaft.