Thermo-elastohydrodynamic analysis of the inhomogeneous foil bearing with misalignment

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Hao Li ◽  
Haipeng Geng ◽  
Hao Lin
Keyword(s):  
Reynolds Equation ◽  
Energy Equation ◽  
Dynamic Performance ◽  
Gas Temperature ◽  
Content Type ◽  
Rotor Systems ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Deformation Equation ◽  
Small Perturbation Method

Purpose The misalignment is generally inevitable in the process of machining and assembly of rotor systems with gas foil bearings, but the exploration on this phenomenon is relatively less. Therefore, the purpose of this paper is to carry out the thermo-elastohydrodynamic analysis of the foil bearing with misalignment, especially the inhomogeneous foil bearing. Design/methodology/approach The rotor is allowed to misalign in two non-rotating directions. Then the static and dynamic performance of the inhomogeneous foil bearing is studied. The thermal-elastohydrodynamic analysis is realized by combining the Reynolds equation, foil deformation equation and energy equation. The small perturbation method is used to calculate the dynamic coefficients, then the critical whirl ratio is obtained. Findings The gas pressure, film thickness and temperature distribution distort when the misalignment appears. The rotor misalignment can improve the loading capacity but rise the gas temperature at the same time. Furthermore, the rotor misalignment can affect the critical whirl ratio which demonstrates that it is necessary to analyze the misalignment before the rotordynamic design. Originality/value The value of this paper is the exploration of the thermo-elastohydrodynamic performance of the inhomogeneous foil bearing with misalignment, the analysis procedure and the corresponding results are valuable for the design of turbo system with gas foil bearings.

The performance of Generation II journal gas foil bearing with misalignment

2020 ◽  
Vol 72 (7) ◽  
pp. 857-863
Author(s):  
Hao Li ◽  
Peng Hai Geng ◽  
Hao Lin
Keyword(s):  
Peer Review ◽  
Dynamic Performance ◽  
Hydrodynamic Pressure ◽  
Normal Operation ◽  
Content Type ◽  
Foil Bearing ◽  
Bearing Load ◽  
Small Perturbation Method ◽  
Stiffness And Damping ◽  
Experimental Researches

Purpose The normal operation of a rotor system is generally vulnerable to misalignment between gas foil bearing (GFB) and rotor. However, most theoretical and experimental researches about the characteristics of GFBs have ignored this phenomenon. Therefore, the main purpose of this paper is to evaluate the static and dynamic performance of GFBs considering misalignment. Design/methodology/approach The shaft is allowed to misalign in two directions. Then the variations of bearing load, friction force, restoring moment, stiffness and damping coefficients are thoroughly explored. The hydrodynamic pressure on the gas film is modeled with compressible Reynolds equation, and the deformation of the flexible bearing is calculated with finite element method. Small perturbation method is used to obtain the displacement and moment dynamic coefficients. Findings The film thickness and pressure distribution distort when misalignments appear. The inclination of GFBs can enhance the restoring moment to withstand the imposed misalignment. Furthermore, the simulation phenomenon demonstrates the misalignment around load direction should be avoided as much as possible, while a small value misalignment around another direction is allowed. Originality/value The value of this paper is the exploration of the influence of misalignments on the static and dynamic performance of the Generation II journal GFB. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-10-2019-0418/

On the Coupling of Foil Bearing Supported Rotors: Part 1 — Analysis

2007 ◽  
Author(s):  
Hooshang Heshmat ◽  
James F. Walton ◽  
Crystal A. Heshmat
Keyword(s):  
Dynamic Characteristics ◽  
High Speed ◽  
Ball Bearing ◽  
Dynamic Performance ◽  
Rotor Systems ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Flexible Rotors ◽  
Coupling Dynamic ◽  
Bearing System

The expanded application of high-speed rotor systems operating on compliant foil bearings will be greatly enhanced with the ability to adequately couple multiple shaft systems with differing bearing systems and dynamic performance. In this paper the results of an analytical tradeoff study assessing coupling dynamic characteristics and their impact on coupled rotor-bearing system dynamics are presented. This analysis effort was completed in an effort to establish the form of characteristics needed to couple foil bearing supported rotors to ball bearing supported rotors, other foil bearing supported rotors as well as coupling rigid and flexible rotors both supported on foil bearings. The conclusions from this study indicate that with appropriate coupling design, a wide array of foil bearing supported rotor systems may be successfully coupled.

A Study of Thermohydrodynamic Features of Multi Wound Foil Bearing Using Lobatto Point Quadrature

2008 ◽  
Author(s):  
Kai Feng ◽  
Shigehiko Kaneko
Keyword(s):  
High Speed ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Three Dimensional ◽  
Iteration Process ◽  
Element Model ◽  
Air Bearings ◽  
Foil Bearing ◽  
Deformation Equation ◽  
Wide Range

The applications of foil air bearings, which are recognized to be the best choice for oil free applications, have been extended for use in a wide range of turbo-miachineries with high speed and high temperature. Lubricant temperature becomes an important factor in the performance of foil air bearings, especially at high rotational speeds and high loads or at high ambient temperature. However, most of the published foil air bearing models were based on the isothermal assumption. This study presents a thermohydrodynamic analysis (THD) of Multi Wound Foil Bearing (MWFB), in which the Reynolds’ equation is solved with the gas viscosity as a function of temperature that is obtained from the energy equation. Lobatto point quadrature, which was proposed by Elrod and Brewe and introduced into compressible calculation by Moraru and Keith, is utilized to accelerate the iteration process with a sparse mesh across film thickness. A finite element model of the foil is used to describe the foil elasticity. An iterative procedure is performed between the Reynolds’ equation, the foil elastic deformation equation and the energy equation, until the convergence is achieved. A three-dimensional temperature prediction of air film is presented and a comparison of THD to isothermal results is made to emphasize the importance of thermal effects. Finally, published experimental data are used to validate this numerical solution.

Effects of wedge curvature on performances of foil thrust bearing and the profile design in compressor system

2020 ◽  
pp. 135065012097552
Author(s):  
Hao Li ◽  
Haipeng Geng ◽  
Lei Qi ◽  
Lu Gan
Keyword(s):  
Reynolds Equation ◽  
Thrust Bearing ◽  
Dynamic Performance ◽  
Testing System ◽  
Thrust Bearings ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Set Up ◽  
Foil Thrust Bearing ◽  
Excellent Stability

Foil thrust bearings have attracted considerable attention in small-sized turbo machines with its excellent stability, high compliance, temperature durability. Geometric structure play an important role on the performance of foil thrust bearings. However, the current research on the structure mainly focuses on the underlying foil type, such as bump foil, protuberant bump. In fact, the foil profile, especially in the convergent region has significant influence. In this paper, foil thrust bearings were classified into convex, slope and concave types according to the profile curvature. A numerical model of six pads foil thrust bearing was established by combining the shell model and Reynolds equation. The static and dynamic performance of thrust bearings with different curvature was calculated. The results showed that the convex convergent possessed higher capacity and was not sensitive to displacement disturbance. A stiffness testing system for thrust foil bearing was set up, and the results verified that the foil with convex wedge had higher stiffness. The experiment also indicated that all the thrust foil bearings had typical damping hysteresis. The axial force of a 10 kW on-board compressor was calculated. Based on the conclusion of this paper, the design scheme of curvature value β = 0.6 and gas thickness h2=15 µm was given in consideration of bearing capacity and machining robustness.

On the Coupling of Foil Bearing Supported Rotors: Part 2 — Experiment

2007 ◽  
Author(s):  
Michael J. Tomaszewski ◽  
James F. Walton ◽  
Hooshang Heshmat
Keyword(s):  
High Speed ◽  
Dynamic Performance ◽  
Experimental Program ◽  
Motor Drive ◽  
Combined System ◽  
Rotor Systems ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Rotor Bearing ◽  
Full Speed

The expanded application of high-speed rotor systems operating on compliant foil bearings will be greatly enhanced with the ability to adequately couple multiple shaft systems with differing bearing systems and dynamic performance. In this paper the results of a successful experimental program are presented. Test results are presented for three different foil bearing coupled rotor systems. First, a coupled 32 kW, 60,000 rpm induction motor drive supported on compliant foil bearings was coupled to an identical 32 kW 60,000 rpm generator rotor and operated to full speed. Next, a high-speed 30,000 rpm capable ball bearing mounted precision spindle was driven to full speed when coupled to a 32 kW foil bearing supported drive motor. Third, the 32 kW, 60,000 rpm foil bearing based motor drive was coupled to a foil bearing supported rotor having a bending critical speed at approximately 29,000 rpm. This combined system was operated successfully to 60,000 rpm. Results of this experimental test program confirm the rotor-bearing system dynamic analysis and demonstrate the feasibility of coupling foil bearing supported rotors to a wide array of other rotor-bearing systems.

Static and Dynamic Analysis of Multileaf Foil Journal Bearings Considering Misalignment Effects

1997 ◽  
Author(s):  
D. Sudheer Kumar Reddy ◽  
S. Swarnamani ◽  
B. S. Prabhu
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Performance Characteristics ◽  
Frictional Torque ◽  
Static And Dynamic Analysis ◽  
Foil Bearing ◽  
Deformation Equation ◽  
Load Carrying ◽  
Static Performance ◽  
Stiffness And Damping

Abstract In the present work the analysis of gas lubricated multileaf journal bearing has been presented. The two dimensional compressible Reynolds equation was solved to establish the pressure field in the clearance space of the bearing. Elastic deformation equation is coupled with the Reynolds equation to get the foil deflections and change in film thickness. The effect of bearing misalignment on foil bearing performance characteristics has been presented. The problem has been formulated using incremental finite element method. The effect of bearing misalignment on static performance characteristics like load carrying capacity, frictional torque, minimum film thickness and on dynamic characteristics in terms of stiffness and damping coefficients have been presented.

Thermohydrodynamic Analysis of Bump Type Gas Foil Bearings: A Model Anchored to Test Data

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Luis San Andrés ◽  
Tae Ho Kim
Keyword(s):  
Test Data ◽  
Thermal Energy ◽  
Gas Flow ◽  
Energy Transport ◽  
Static Load ◽  
Isothermal Condition ◽  
Gas Temperature ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Forced Cooling

The paper introduces a thermohydrodynamic (THD) model for prediction of gas foil bearing (GFB) performance. The model includes thermal energy transport in the gas film region and with cooling gas streams, inner or outer, as in typical rotor-GFBs systems. The analysis also accounts for material property changes and the bearing components’ expansion due to temperature increases and shaft centrifugal growth due to rotational speed. Gas inlet feed characteristics are thoroughly discussed in bearings whose top foil must detach, i.e., not allowing for subambient pressure. Thermal growths determine the actual bearing clearance needed for accurate prediction of GFB forced performance, static and dynamic. Model predictions are benchmarked against published measurements of (metal) temperatures in a GFB operating without a forced cooling gas flow. The tested foil bearing is proprietary; hence, its geometry and material properties are largely unknown. Predictions are obtained for an assumed bearing configuration, with bump-foil geometry and materials taken from prior art and best known practices. The predicted film peak temperature occurs just downstream of the maximum gas pressure. The film temperature is higher at the bearing middle plane than at the foil edges, as the test results also show. The journal speed, rather than the applied static load, influences more the increase in film temperature and with a larger thermal gradient toward the bearing sides. In addition, as in the tests conducted at a constant rotor speed and even for the lowest static load, the gas film temperature increases rapidly due to the absence of a forced cooling air that could carry away the recirculation gas flow and thermal energy drawn by the spinning rotor; predictions are in good agreement with the test data. A comparison of predicted static load parameters to those obtained from an isothermal condition shows the THD model producing a smaller journal eccentricity (larger minimum film thickness) and larger drag torque. An increase in gas temperature is tantamount to an increase in gas viscosity, hence, the noted effect in the foil bearing forced performance.

Rotor-dynamic performance of porous hydrostatic thrust bearing operating under magnetic field

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Vivek Kumar ◽  
Vatsalkumar Ashokkumar Shah ◽  
Simran Jeet Singh ◽  
Kuldeep Narwat ◽  
Satish C. Sharma
Keyword(s):  
Magnetic Field ◽  
Finite Element ◽  
Steady State ◽  
Magnetic Fluid ◽  
Reynolds Equation ◽  
Thrust Bearing ◽  
Dynamic Performance ◽  
Performance Indices ◽  
Content Type ◽  
Rotor Dynamic

Purpose The porous bearings are commonly used in slider thrust bearings owing to their self-lubricating properties and cost effectiveness as compared to conventional hydrodynamic bearings. The purpose of this paper is to numerically investigate usefulness of porous layer in hydrostatic thrust bearing operating with magnetic fluid. The effect of magnetic field and permeability has been analysed on steady-state (film pressure, film reaction and lubricant flow rate) and rotor-dynamic (stiffness and damping) parameters of bearing. Design/methodology/approach Finite element approach is used to obtain numerical solution of flow governing equations (Magneto-hydrodynamics Reynolds equation, Darcy law and capillary equation) for computing abovementioned performance indices. Finite element method formulation converts elliptical Reynolds equation into set of algebraic equation that are solved using Gauss–Seidel method. Findings It has been reported that porosity has limited but adverse effects on performance parameters of bearing. The adverse effects of porosity can be minimized by using a circular pocket for achieving better steady-state response and an annular/elliptical pocket, for having better rotor-dynamic response. The use of magnetic fluid is found to be substantially enhancing the fluid film reaction (53%) and damping parameters (55%). Practical implications The present work recommends use of circular pocket for achieving better steady-state performance indices. However, annular and elliptical pockets should be preferred, when design criteria for the bearing are better rotor-dynamic performance. Originality/value This study deals with influence of magnetic fluid, porosity and pocket shape on rotor-dynamic performance of externally pressurized thrust bearing. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2020-0289/

A Comparison of the Steady-State and Dynamic Performance of First- and Second-Generation Foil Bearings

2010 ◽  
Author(s):  
M. J. Conlon ◽  
A. Dadouche ◽  
W. M. Dmochowski ◽  
R. Payette ◽  
J.-P. Be´dard
Keyword(s):  
Steady State ◽  
Experimental Evaluation ◽  
First Generation ◽  
Second Generation ◽  
Load Capacity ◽  
Dynamic Stiffness ◽  
Dynamic Performance ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Stiffness And Damping

Oil-free foil bearing technology has advanced intermittently over the years, driven by research efforts to improve both steady-state and dynamic performance characteristics, namely: load capacity, stiffness, and damping. Bearing designs are thus classified according to “generation”, with first-generation bearings being the most primitive. This paper presents an experimental evaluation of a first- and a second-generation foil bearing, and aims to provide the high-fidelity data necessary for proper validation of theoretical predictive models of foil bearing performance. The aforementioned test bearings were fabricated in-house, and are both 70mm in diameter with an aspect ratio of 1; bearing manufacturing details are provided. The work makes use of a facility dedicated to measuring both the steady-state and dynamic properties of foil bearings under a variety of controlled operating conditions. The bearing under test is placed at the midspan of a horizontal, simply-supported, stepped shaft which rotates at up to 60krpm. Static and dynamic loads of up to 3500N and 450N (respectively) can be applied by means of a pneumatic cylinder and two electrodynamic shakers. The bearings’ structural (static) stiffnesses are highly nonlinear, and this affects the accuracy of the dynamic coefficient determination. Both dynamic stiffness and damping are found to vary nonlinearly with excitation frequency, and are over-predicted by a structural experimental evaluation — the film plays an important role in bearing dynamics. The second-generation bearing is found to have a higher load capacity, dynamic stiffness, and damping than the first-generation bearing.

The Effect of External Pressurization on Self-Acting Foil Bearings

1965 ◽  
Vol 87 (3) ◽  
pp. 631-638 ◽  
Author(s):  
M. Wildmann ◽  
A. Wright
Keyword(s):  
Pressure Distribution ◽  
Equilibrium Equation ◽  
Reynolds Equation ◽  
Foil Bearings ◽  
Foil Bearing

The effects of introducing a small amount of lubricant under pressure into a self-acting foil bearing film are investigated. Foil shape and pressure distribution under the foil are obtained by combining the equilibrium equation with the Reynolds’ equation and solving the resulting equation. The results show that the effect of even small external pressurization in a self-acting foil bearing is very important.

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