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

1995 ◽  
Vol 117 (1) ◽  
pp. 103-111 ◽  
Author(s):  
H. Hashimoto
Keyword(s):  
Theoretical Analysis ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Computation Time ◽  
Hybrid Performance ◽  
Foil Bearings ◽  
Wide Range ◽  
Wrap Angle ◽  
Element Technique

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.

Effects of Foil Bending Rigidity on Spacing Height Characteristics of Hydrostatic Porous Foil Bearings for Web Handling Processes

1997 ◽  
Vol 119 (3) ◽  
pp. 422-427 ◽  
Author(s):  
H. Hashimoto
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Computation Time ◽  
Finite Width ◽  
Bending Rigidity ◽  
Weighted Residual Method ◽  
Web Handling ◽  
Foil Bearings ◽  
Wide Range ◽  
Foil Bending

In this paper, the effects of foil bending rigidity on the spacing height characteristics of hydrostatic foil bearings with a hollow porous shaft for web handling processes are analyzed by the finite width bearing theory. In the analysis, in order to save computation time and to improve the convergence of solutions, the two-dimensional modified Reynolds equation considering the added flow through porous shaft is reduced to an ordinary differential equation based on the weighted residual method. The reduced Reynolds equation and elastic equation for the foil are discretized by the finite difference method and solved numerically by the iterative technique. The numerical solutions for the pressure and film thickness distributions between foil and shaft are obtained for a wide range of bearing width-to-diameter ratio under various combinations of foil bending rigidity and foil wrap angle, and the spacing height characteristics of the foil bearings are examined theoretically.

Theoretical and Experimental Investigations Into Spacing Characteristics Between Roller and Three Types of Webs With Different Permeabilities

2004 ◽  
Author(s):  
H. Hashimoto ◽  
M. Okajima
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Experimental Investigations ◽  
First Order ◽  
Wide Range ◽  
Entrained Air ◽  
Air Diffusion ◽  
Air Film ◽  
The Web

A new theoretical model for estimating the entrained air film thickness between a web and roller is presented for both impermeable and permeable webs. A simple closed-form formula for estimating the air film thickness, which considers the effects of air leakage from the web edges and air diffusion due to the permeability of web, was obtained based on a large number of simultaneous numerical solutions of the compressible Reynolds equation and the web equilibrium equation. The variation of air film thickness with roller velocity is measured for three typical webs: PET (polyethylene terephthalate), coated paper, and newsprint. The effects of web permeability, web width and web tension on the air film thickness are examined theoretically and experimentally for a wide range of roller velocity. Reasonable agreement is seen both quantatively and qualitatively between the predicted and measured results. The validity of the formula for the first order estimation of web-roller interface problems is verified experimentally.

Theoretical and Experimental Investigations Into Spacing Characteristics Between Roller and Three Types of Webs With Different Permeabilities

2005 ◽  
Vol 128 (2) ◽  
pp. 267-274 ◽  
Author(s):  
H. Hashimoto ◽  
M. Okajima
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Experimental Investigations ◽  
Curve Fit ◽  
Wide Range ◽  
Entrained Air ◽  
Air Diffusion ◽  
Air Film ◽  
The Web

A new theoretical model for estimating the entrained air film thickness between a web and roller is presented for both impermeable and permeable webs. A simple curve fit formula for estimating the air film thickness, which considers the effects of air leakage from the web edges and air diffusion due to the permeability of web, was obtained based on a large number of simultaneous numerical solutions of the compressible Reynolds equation and the web equilibrium equation. The variation of air film thickness with roller velocity is measured for three typical webs: polyethylene terephthalate, coated paper, and newsprint. The effects of web permeability, web width, and web tension on the air film thickness are examined theoretically and experimentally for a wide range of roller velocity. Reasonable agreement is seen both quantitatively and qualitatively between the predicted and measured results. The validity of the formula for the first-order estimation of web-roller interface problems is verified experimentally.

Theoretical Studies of a Continuously Adjustable Hydrodynamic Fluid Film Bearing

2001 ◽  
Vol 124 (1) ◽  
pp. 203-211 ◽  
Author(s):  
J. K. Martin ◽  
D. W. Parkins
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Solution Procedure ◽  
Fluid Film ◽  
Theoretical Studies ◽  
Analysis Model ◽  
Operating Characteristics ◽  
Hydrodynamic Bearing ◽  
Wide Range ◽  
Fluid Film Thickness

Principles of a continuously adjustable hydrodynamic bearing are described together with an analysis model for studying its theoretical performance. The model included an expanded form of the governing Reynolds equation which took account of non-uniform variations in the fluid film thickness. A solution procedure was devised whereby for a given set of adjustment conditions, simultaneously converged fields of fluid film thickness, temperature, viscosity and pressure would result, together with oil film forces. A wide range of operating characteristics were studied with results predicting advantages and benefits over conventional hydrodynamic bearings.

Film Thickness and Asperity Load Formulas for Line-Contact Elastohydrodynamic Lubrication With Provision for Surface Roughness

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
M. Masjedi ◽  
M. M. Khonsari
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Reynolds Equation ◽  
Surface Deformation ◽  
Elastohydrodynamic Lubrication ◽  
Load Ratio ◽  
Material Surface ◽  
Line Contact ◽  
Wide Range ◽  
Minimum Film Thickness

Three formulas are derived for predicting the central and the minimum film thickness as well as the asperity load ratio in line-contact EHL with provision for surface roughness. These expressions are based on the simultaneous solution to the modified Reynolds equation and surface deformation with consideration of elastic, plastic and elasto-plastic deformation of the surface asperities. The formulas cover a wide range of input and they are of the form f(W, U, G, σ¯, V), where the parameters represented are dimensionless load, speed, material, surface roughness and hardness, respectively.

Stiffness Effects on the Infinitely Wide Foil Bearing

1967 ◽  
Vol 89 (1) ◽  
pp. 92-97 ◽  
Author(s):  
A. Eshel ◽  
H. G. Elrod
Keyword(s):  
Film Thickness ◽  
Numerical Solutions ◽  
Foil Bearing ◽  
Wrap Angle

Numerical solutions are presented for the film thickness of the infinitely wide, self-acting foil bearing for various values of tape stiffness. The solutions indicate that with increasing stiffness there are: (a) a slow reduction in the nearly uniform clearance prevailing under most of the wrap angle; (b) an increase in the peak of the undulations occurring in the region where the tape leaves the spindle; and (c) virtually no change in the trough of these undulations.

Influence of Laser Micro-Mesh Texturing on the Tribological Performance in an EHL Point Contact

2007 ◽  
Vol 353-358 ◽  
pp. 796-800
Author(s):  
Xiao Wang ◽  
Jian Li ◽  
Wei Chen ◽  
Lan Cai ◽  
Jian Ying Zhu
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Pressure Distribution ◽  
Reynolds Equation ◽  
Point Contact ◽  
Tribological Performance ◽  
Design And Optimization ◽  
Thickness Profile ◽  
Wide Range ◽  
Key Factor

Fabricating surfaces with controlled micro-geometry may be an effective approach to improved tribological performance. In this paper, the effect of laser surface micro-mesh texturing on the tribological performance is investigated theoretically with numerical solution of EHL point contact. In the theoretical model, the Reynolds equation is used as the governing equation. Well controlled micro-mesh texturing is described in film thickness equation. By Full Multi-Grid (FMG) method, the solutions of film thickness profile and pressure distribution map are present over a wide range of texturing parameters. The influence of width, depth and orientation of mesh texturing on the friction coefficient is analyzed. Result shows that, the film thickness profile and pressure distribution are sensitive to the parameters of micro-mesh texturing. The curve result of friction coefficient under two load conditions indicated that the parameters of mesh are key factor for texturing design. Solutions demonstrate the ability of numerical simulation on the design and optimization of surface mesh texturing.

A Reynolds-Eyring Equation for Elastohydrodynamic Lubrication in Line Contacts

1987 ◽  
Vol 109 (4) ◽  
pp. 648-654 ◽  
Author(s):  
T. F. Conry ◽  
S. Wang ◽  
C. Cusano
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Numerical Solutions ◽  
Elastohydrodynamic Lubrication ◽  
Newtonian Flow ◽  
Line Contacts ◽  
Different Temperatures ◽  
Eyring Model ◽  
Eyring Theory ◽  
New Equation

A new Reynolds equation, based on the Eyring theory of non-Newtonian flow, is derived for flow in one dimension. It is shown that this new equation reduces to the traditional Reynolds equation as the Eyring model approaches the Newtonian model in the limit. Numerical solutions are presented for a selected oil at two different temperatures. The central film thickness decreases with increasing dimensionless viscosity parameter and slide/roll ratios. A transition zone is noted through which the ratio of minimum to central film thickness passes as the pressure distribution goes from near Hertzian to a distribution that appreciably deviates from Hertzian.

On the Stribeck Curves for Lubricated Counterformal Contacts of Rough Surfaces

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Dong Zhu ◽  
Jiaxu Wang ◽  
Q. Jane Wang
Keyword(s):  
Film Thickness ◽  
Numerical Solutions ◽  
Rough Surfaces ◽  
Elastohydrodynamic Lubrication ◽  
Real Data ◽  
Operating Conditions ◽  
Stribeck Curve ◽  
Flash Temperature ◽  
Wide Range ◽  
Stribeck Curves

The “Stribeck curve” is a well-known concept, describing the frictional behavior of a lubricated interface during the transition from boundary and mixed lubrication up to full-film hydrodynamic/elastohydrodynamic lubrication. It can be found in nearly every tribology textbook/handbook and many articles and technical papers. However, the majority of the published Stribeck curves are only conceptual without real data from either experiments or numerical solutions. The limited number of published ones with real data is often incomplete, covering only a portion of the entire transition. This is because generating a complete Stribeck curve requires experimental or numerical results in an extremely wide range of operating conditions, which has been a great challenge. Also, numerically calculating a Stribeck curve requires a unified model with robust algorithms that is capable of handling the entire spectrum of lubrication status. In the present study, numerical solutions in counterformal contacts of rough surfaces are obtained by using the unified deterministic mixed elastohydrodynamic lubrication (EHL) model recently developed. Stribeck curves are plotted in a wide range of speed and lubricant film thickness based on the simulation results with various types of contact geometry using machined rough surfaces of different orientations. Surface flash temperature is also analyzed during the friction calculation considering the mutual dependence between friction and interfacial temperature. Obtained results show that in lubricated concentrated contacts, friction continuously decreases as speed and film thickness increase even in the full-film regime until extremely high speeds are reached. This is mainly due to the reduction of lubricant limiting shear stress caused by flash temperature rise. The results also reveal that contact ellipticity and roughness orientation have limited influence on frictional behaviors, especially in the full-film and boundary lubrication regimes.

scholarly journals Optimising the AR Engraved Structure on Light-Guide Facets for a Wide Range of Wavelengths

Optics ◽  
2020 ◽  
Vol 2 (1) ◽  
pp. 25-42
Author(s):  
Ioseph Gurwich ◽  
Yakov Greenberg ◽  
Kobi Harush ◽  
Yarden Tzabari
Keyword(s):  
Theoretical Analysis ◽  
Light Guide ◽  
Spectral Band ◽  
Angular Range ◽  
The Past ◽  
Input And Output ◽  
Wide Range ◽  
The Given ◽  
Theoretical Results ◽  
Shape And Size

The present study is aimed at designing anti-reflective (AR) engraving on the input–output surfaces of a rectangular light-guide. We estimate AR efficiency, by the transmittance level in the angular range, determined by the light-guide. Using nano-engraving, we achieve a uniform high transmission over a wide range of wavelengths. In the past, we used smoothed conical pins or indentations on the faces of light-guide crystal as the engraved structure. Here, we widen the class of pins under consideration, following the physical model developed in the previous paper. We analyze the smoothed pyramidal pins with different base shapes. The possible effect of randomization of the pins parameters is also examined. The results obtained demonstrate optimized engraved structure with parameters depending on the required spectral range and facet format. The predicted level of transmittance is close to 99%, and its flatness (estimated by the standard deviation) in the required wavelengths range is 0.2%. The theoretical analysis and numerical calculations indicate that the obtained results demonstrate the best transmission (reflection) we can expect for a facet with the given shape and size for the required spectral band. The approach is equally useful for any other form and of the facet. We also discuss a simple way of comparing experimental and theoretical results for a light-guide with the designed input and output features. In this study, as well as in our previous work, we restrict ourselves to rectangular facets. We also consider the limitations on maximal transmission produced by the size and shape of the light-guide facets. The theoretical analysis is performed for an infinite structure and serves as an upper bound on the transmittance for smaller-size apertures.

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