An Investigation of Self-Acting Foil Bearings

1965 ◽  
Vol 87 (4) ◽  
pp. 837-846 ◽  
Author(s):  
J. T. S. Ma
Keyword(s):  
Film Thickness ◽  
Experimental Results ◽  
Capacitive Sensors ◽  
Exit Region ◽  
Empirical Expressions ◽  
Foil Bearings ◽  
Minimum Film Thickness ◽  
Theoretical Predictions ◽  
Predicted Values ◽  
Thickness Measurements

Experimental results on the interior and the exit region film-thickness measurements of self-acting foil bearings are presented and discussed. These measurements were made with capacitive sensors and conductive foils. The measured and predicted values agree very well within the range of nondimensional parameters, h0/R, from 10−4 to 10−3 and, T/μU, from 105 to 106. The agreement deviates for values beyond these ranges. Empirical expressions for predicting the constant and minimum film thickness applicable beyond these ranges are also presented. They are valid within the range of h0/R from 5(10)−5 to 10−2 and T/μU from 104 to 105. Growing sinusoidal film thickness in the exit region was also observed, measured, and checked with theoretical predictions.

Some Limitations in Applying Classical EHD Film Thickness Formulas to a High-Speed Bearing

1981 ◽  
Vol 103 (2) ◽  
pp. 295-301 ◽  
Author(s):  
J. J. Coy ◽  
E. V. Zaretsky
Keyword(s):  
Film Thickness ◽  
High Speed ◽  
Heating Effects ◽  
Theoretical Predictions ◽  
Traction Fluid ◽  
Shear Heating ◽  
Thickness Measurements ◽  
Inner Race ◽  
Maximum Stresses ◽  
Good Agreement

Elastohydrodynamic film thickness was measured for a 20-mm ball bearing using the capacitance technique. The bearing was thrust loaded to 90, 448, and 778 N (20, 100, and 175 lb). The corresponding maximum stresses on the inner race were 1.28, 2.09, and 2.45 GPa (185,000, 303,000, and 356,000 psi). Test speeds ranged from 400 to 14,000 rpm. Film thickness measurements were taken with four different lubricants: (a) synthetic paraffinic, (b) synthetic paraffinic with additives, (c) neopentylpolyol (tetra) ester meeting MIL-L-23699A specifications, and (d) synthetic cycloaliphatic hydrocarbon traction fluid. The test bearing was mist lubricated. Test temperatures were 300, 338, and 393 K. The measured results were compared to theoretical predictions using the formulae of Grubin, Archard and Cowking, Dowson and Higginson, and Hamrock and Dowson. There was good agreement with theory at low dimensionless speed, but the film was much smaller than theory predicts at higher speeds. This was due to kinematic starvation and inlet shear heating effects. Comparisons with Chiu’s theory on starvation and Cheng’s theory on inlet shear heating were made.

An Interpolation Procedure for the Minimum Film Thickness in Point Contacts

1990 ◽  
Vol 204 (3) ◽  
pp. 199-206 ◽  
Author(s):  
C J Hooke
Keyword(s):  
Film Thickness ◽  
Contact Geometry ◽  
High Accuracy ◽  
Operating Conditions ◽  
Experimental Results ◽  
Point Contacts ◽  
Design Charts ◽  
Minimum Film Thickness ◽  
Interpolation Procedure

Most engineering point contacts operate in, or close to, the elastic piezoviscous regime. A general interpolation procedure is presented by which the minimum film thickness in any such contact may be estimated. This procedure matches all existing numerical and experimental results with high accuracy. Design charts are provided and these enable the minimum film thickness to be read directly and also allow the effect of changes in contact geometry and operating conditions to be assessed.

scholarly journals Elastohydrodynamic Film Thickness Model for Heavily Loaded Contacts

1974 ◽  
Vol 96 (3) ◽  
pp. 472-479 ◽  
Author(s):  
S. H. Loewenthal ◽  
R. J. Parker ◽  
E. V. Zaretsky
Keyword(s):  
Film Thickness ◽  
Measured Data ◽  
Type Ii ◽  
X Ray ◽  
Polyphenyl Ether ◽  
Load Dependence ◽  
Test Conditions ◽  
Wide Range ◽  
Minimum Film Thickness ◽  
Thickness Measurements

An empirical elastohydrodynamic (EHD) film thickness formula for predicting the minimum film thickness occurring within heavily loaded contacts (maximum Hertz stresses above 1.04 × 109 N/m2 (150,000 psi)) was developed. The formula was based upon X-ray film thickness measurements made with synthetic paraffinic, fluorocarbon, Type II ester and polyphenyl ether fluids covering a wide range of test conditions. Comparisons were made between predictions from an isothermal EHD theory and the test data. The deduced relationship was found to adequately reflect the high-load dependence exhibited by the measured data. The effects of contact geometry, material and lubricant properties on the form of the empirical model are also discussed.

Report Paper 2: Approximate Short Bearing Analysis and Experimental Results Obtained Using Plastic Bearing Liners

1969 ◽  
Vol 184 (12) ◽  
pp. 190-196 ◽  
Author(s):  
J. P. O'Donoghue ◽  
P. R. Koch ◽  
C. J. Hooke
Keyword(s):  
Approximate Solution ◽  
Film Thickness ◽  
Journal Bearings ◽  
Experimental Results ◽  
Approximate Theory ◽  
Hydrodynamic Problem ◽  
Dynamic Conditions ◽  
Oil Film ◽  
Theoretical Predictions ◽  
Bearing Analysis

This paper outlines a new approximate theory for liquid lubricated plain journal bearings with elastic liners. This is a modified form of Ocvirk's theory and includes the effect of circumferential flow. The results of a series of tests on short plastic bearings are presented to compare with the theoretical predictions of the new theory. The authors conclude that for short bearings the theory gives reasonably good predictions of performance, but the elasticity assumptions cause major errors for length/diameter ratios greater than 0·5 due to the decrease in oil film thickness that occurs near the ends of the bearing. The approximate solution adopted for the hydrodynamic problem may be of use for considering dynamic conditions taking the Reynolds conditions for cavitation.

Elastohydrodynamic Film Thickness in Concentrated Contacts: Part 2: Correlation of Experimental Results with Elastohydrodynamic Theory

1986 ◽  
Vol 200 (3) ◽  
pp. 219-226 ◽  
Author(s):  
R J Chittenden ◽  
D Dowson ◽  
C M Taylor
Keyword(s):  
Film Thickness ◽  
Experimental Studies ◽  
Elastohydrodynamic Lubrication ◽  
Operating Conditions ◽  
Experimental Results ◽  
Experimental Techniques ◽  
Dimensionless Parameters ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Computational Procedures

The existence of a coherent film of lubricant between highly loaded machine elements has been recognized for many years. Over this period of time measurements of film thickness have gone hand in hand with theoretical analyses in the field now known as elastohydrodynamic lubrication. The experimental techniques of capacitance, electrical resistance and X-ray measurement have been supplemented by the use of optical interferometry while the analytical expressions obtained with the use of elegant simplifications have been superseded by those developed from extensive and comprehensive computational procedures. These developments in experimental techniques have yielded a substantial number of measurements of both minimum and central film thickness. Likewise, the advent of the digital computer has allowed the derivation of a large number of solutions to the problem of elastohydrodynamic lubrication of concentrated contacts. All these results, covering a wide range of geometrical conditions, are to be found in the literature, yet little attempt appears to have been made to assemble a representative set of experimental data to permit a detailed evaluation of the theoretical formulae for elliptical contacts. The second part of this paper therefore considers the correlation between a number of experimental studies covering a wide range of operating conditions and geometries, and the predictions of recent elastohydrodynamic theory. Some of the important aspects of each set of experimental results are then considered and examples are provided which illustrate the following points: 1. Good estimates of lubricant film thickness may be obtained from the theoretical expressions recently derived, even when the dimensionless parameters involved are outside the ranges considered in the derivation of the formulae. 2. The discrepancies which exist between theoretical predictions and some of the measured film thicknesses are nevertheless quite large, even when the dimensionless parameters are within their usual limits. On the whole there is good agreement between experiment and theory, while the general trend of the results indicates that theoretical predictions may underestimate the minimum film thickness by about 10 per cent and the central film thickness by about 25 per cent. This measure of agreement is quite remarkable when the extreme difficulty of interpreting the magnitudes of effective and very thin mean film thicknesses between machined components in various forms of experimental equipment is considered.

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

2019 ◽  
Vol 71 (5) ◽  
pp. 677-685 ◽  
Author(s):  
Hongyang Hu ◽  
Ming Feng
Keyword(s):  
Film Thickness ◽  
Bending Moment ◽  
Deformation Energy ◽  
Journal Bearings ◽  
Content Type ◽  
Foil Bearings ◽  
Attitude Angle ◽  
Minimum Film Thickness ◽  
Static Performance ◽  
Fully Coupled

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.

Elastohydrodynamie Lubrication of Big-End Bearings Part 2: Ratification

1991 ◽  
Vol 205 (2) ◽  
pp. 107-119 ◽  
Author(s):  
M B Aitken ◽  
H McCallion
Keyword(s):  
Film Thickness ◽  
Close Correlation ◽  
Connecting Rod ◽  
Test Rig ◽  
Collapse Mechanisms ◽  
Minimum Film Thickness ◽  
Inertial Loading ◽  
Film Collapse ◽  
Thickness Measurements

The elastohydrodynamic analysis developed in Part 1 of this work is ratified against previous Ruston and Hornsby big-end studies. Sufficiently close correlation with published in situ film-thickness measurements allows big-end bearing performance to be determined with some confidence; significant new insight was obtained. Elasticity body forces from connecting-rod motion were found to be an integral component of the big-end representation; it is a prevalent misconception that these forces can be neglected from theoretical as well as experimental test-rig works. Film collapse mechanisms, likened to vapour cavitation, were observed in the dynamically loaded elastic bearing; these were not detected in equivalent rigid bearing simulations. Cyclic minimum film thickness was observed during inertial loading, irrespective of gas force loading. Two separate minimum-film conditions were identified: one in the connecting-rod's neck and a second, at higher load, in the rod's cap. The second condition is critical from a design standpoint; significantly thinner films are predicted than by rigid bearing theory.

An analysis of the influence of oil supply conditions on the thermohydrodynamic performance of a single-groove journal bearing

2003 ◽  
Vol 217 (2) ◽  
pp. 133-144 ◽  
Author(s):  
L Costa ◽  
A. S. Miranda ◽  
M Fillon ◽  
J. C. P. Claro
Keyword(s):  
Film Thickness ◽  
Journal Bearing ◽  
Hydrodynamic Pressure ◽  
Quantitative Information ◽  
Published Data ◽  
Oil Supply ◽  
Supply Pressure ◽  
Minimum Film Thickness ◽  
Theoretical Predictions ◽  
Loss Maximum

In this work a thermohydrodynamic analysis has been developed in order to investigate the influence of oil supply conditions on the performance of a journal bearing. The supply conditions considered were oil supply temperature, supply pressure, groove length and groove location. To carry out this study, the hydrodynamic pressure distribution inside the bearing has been determined using a mass-conserving cavitation model with realistic supply conditions. The energy equation and the heat conduction equation have been used for the determination of oil film and bush temperature distributions. The agreement observed between theoretical predictions and experimental published data is acceptable. Quantitative information shows that the oil supply conditions affect bearing performance parameters in different ways. Oil flowrate was markedly affected by all supply parameters studied. Power loss, maximum bush temperature and minimum film thickness were mainly dependent on oil supply temperature. The effect of supply pressure on minimum film thickness was dependent on groove location. An axial groove located at 90° to the load line gave rise to more favourable bearing performance characteristics.

Improvements to the Analysis of Gas Foil Bearings: Integration of Top Foil 1D and 2D Structural Models

2007 ◽  
Author(s):  
Luis San Andre´s ◽  
Tae Ho Kim
Keyword(s):  
Film Thickness ◽  
Gas Turbines ◽  
Load Capacity ◽  
Structural Models ◽  
Underlying Structure ◽  
Fe Model ◽  
Foil Bearings ◽  
Damping Coefficients ◽  
Minimum Film Thickness ◽  
Stiffness And Damping

Gas foil bearings (GFBs) find widespread usage in oil-free turbo expanders, APUs and micro gas turbines for distributed power due to their low drag friction and ability to tolerate high level vibrations, including transient rubs and shaft misalignment, static and dynamic. The static load capacity and dynamic forced performance of GFBs depends largely on the material properties of the support elastic structure, i.e. a smooth foil on top of bump strips. Conventional models include only the bumps as an equivalent stiffness uniformly distributed around the bearing circumference. More complex models couple directly the elastic deformations of the top foil to the bump underlying structure as well as to the hydrodynamics of the gas film. This paper details two FE models for the top foil supported on bump strips, one considers a 2D shell anisotropic structure and the other a 1D beam-like structure. The Cholesky decomposition of the stiffness matrix representing the top foil and bump strips is performed off-line prior to computations coupling it to the gas film analysis governed by Reynolds equation. The procedure greatly enhances the computational efficiency of the numerical scheme. Predictions of journal attitude angle and minimum film thickness for increasing static loads and two journal speeds are obtained for a GFB tested decades ago. 2D FE model predictions overestimate the minimum film thickness at the bearing centerline, while underestimating it at the bearing edges. Predictions from the 1D FE model compare best to the limited tests data; reproducing closely the experimental circumferential wavy-like minimum film thickness profile. The 1D top foil model is recommended due to its low computational cost. Predicted stiffness and damping coefficients versus excitation frequency show that the two FE top foil structural models result in slightly lower direct stiffness and damping coefficients than those from the simple elastic foundation model.

scholarly journals A New Structural Bump Foil Model With Application From Start-Up to Full Operating Conditions

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Mihai Arghir ◽  
Omar Benchekroun
Keyword(s):  
Film Thickness ◽  
Numerical Solutions ◽  
Operating Conditions ◽  
Experimental Results ◽  
Static Loads ◽  
Contact Algorithm ◽  
Start Up ◽  
Theoretical Predictions ◽  
Full Speed ◽  
Contact Pressures

Abstract This paper presents a new structural bump foil model that can handle all operating conditions from start-up to full speed. The model is based on a nonlinear contact algorithm with friction and gaps. The top foil is modeled as a curved beam while bump foil uses a coupled truss model. The model considers the gaps between the bump foil and the bearing casing, between the bump foil and the top foil and between the rotor and the top foil. Thus, any numerical interference between the rotor and the top foil is avoided. A mixed lubrication model is used for the thin film pressures. Following this algorithm, contact pressures appear if the film thickness is less than three times the equivalent roughness of the rotor and of the top foil. Fluid pressures are calculated from numerical solutions of Reynolds equation while contact pressures, if present, are calculated with the model of Greenwood and Williamson. The model is validated by comparisons with the experimental results obtained for start-up operating conditions of a first-generation foil bearing of 38.1 mm diameter with static loads of 10–50 N. Theoretical predictions of the start-up torque and takeoff speed compare well with experimental results. It is also shown how manufacturing bump height errors can explain the differences between theoretical and experimental predictions. Further validations are presented for the same bearing operating at high speeds (30, 45, and 55 krpm) and heavy static loads (up to 200 N). The calculated minimum film thickness and attitude angle are compared with experimental data from the literature.

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