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 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.

Air Film Thickness Estimation in Web Handling Processes

1999 ◽  
Vol 121 (1) ◽  
pp. 50-55 ◽  
Author(s):  
Hiromu Hashimoto
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Experimental Results ◽  
Finite Width ◽  
Web Handling ◽  
Foil Bearing ◽  
Guide Roller ◽  
The Finite Difference Method ◽  
Air Film ◽  
The Web

In this paper, in order to estimate an air film thickness between moving web and guide roller (web spacing height), an air film thickness formula was derived based on the finite width compressible foil bearing theory. In the derivation of the air film thickness formula, the two-dimensional Reynolds equation and foil equilibrium equation were discretized by the finite difference method and solved iteratively to obtain the pressure and air film thickness distributions for various parameters. Based on the numerical results, the simplified convenience formula for the estimation of air film thickness between web and guide roller was obtained. On the other hand, the air film thickness between web and guide roller was measured by an optical sensor, and the experimental results were compared with the calculated results. Moreover, the variation of air film thickness between two layers in web winding processes was analyzed by making use of the air film thickness formula derived above. From the theoretical and experimental results obtained, the effects of air film thickness on the web transporting systems were clarified.

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.

The Effect of Disk Warpage/Skew on the Deflection and Vibration of a Flexible Disk Spinning Above a Baseplate and in Contact With a Point-Head

1997 ◽  
Vol 119 (1) ◽  
pp. 64-70 ◽  
Author(s):  
R. Y. Wu ◽  
G. G. Adams
Keyword(s):  
Film Thickness ◽  
Rotational Speed ◽  
Numerical Solutions ◽  
Point Contact ◽  
Angle Variation ◽  
Coupled Equations ◽  
Close Proximity ◽  
Small Change ◽  
Flexible Disk ◽  
Air Film

A flexible disk, with small initial warpage/skew, is spinning in close proximity to a stationary baseplate. The partial differential equation for the disk deflection is coupled to the Reynolds equation of the stabilizing air-film. Disk warpage/skew produces a small change in the deflection which rotates with the disk. These deflections are obtained by linearizing the coupled equations about the axisymmetric configuration corresponding to a perfect disk. Numerical solutions are obtained and compared for different values of rotational speed and air-film thickness. The results show that among the three skewed/warped disks modeled, the skewed disk (i.e., the plane of the disk is skewed with respect to its axis of rotation) produces the largest deflection change (axial runout). With the effect of a point-contact head included, the existence of disk warpage/skew causes the head to produce a spatially-fixed harmonically varying force. The total disk motion is determined by superposition of the deflection pattern fixed on the disk and the space-fixed head-induced vibration. The disk pitch angle variation at the head is obtained and the results are compared for various values of the rotational speed and air-film thickness.

scholarly journals Droplet levitation over a moving wall with a steady air film

2019 ◽  
Vol 862 ◽  
pp. 261-282 ◽  
Author(s):  
Erina Sawaguchi ◽  
Ayumi Matsuda ◽  
Kai Hama ◽  
Masafumi Saito ◽  
Yoshiyuki Tagawa
Keyword(s):  
Free Surface ◽  
Film Thickness ◽  
Surface Velocity ◽  
Pressure Balance ◽  
Local Pressure ◽  
Interferometric Method ◽  
Wall Velocity ◽  
Wide Range ◽  
Shape Oscillation ◽  
Air Film

In isothermal non-coalescence behaviours of a droplet against a wall, an air film of micrometre thickness plays a crucial role. We experimentally study this phenomenon by letting a droplet levitate over a moving glass wall. The three-dimensional shape of the air film is measured using an interferometric method. The mean curvature distribution of the deformed free surface and the distributions of the lubrication pressure are derived from the experimental measurements. We vary experimental parameters, namely wall velocity, droplet diameter and viscosity of the droplets, over a wide range; for example, the droplet viscosity is varied over two orders of magnitude. For the same wall velocity, the air film of low-viscosity droplets shows little shape oscillation with constant film thickness (defined as the steady state), while that of highly viscous droplets shows a significant shape oscillation with varying film thickness (defined as the unsteady state). The droplet viscosity also affects the surface velocity of a droplet. Under our experimental conditions, where the air film shape can be assumed to be steady, we present experimental evidence showing that the lift force generated inside the air film balances with the droplet’s weight. We also verify that the lubrication pressure locally balances with the surface tension and hydrostatic pressures. This indicates that lubrication pressure and the shape of the free surface are mutually determined. Based on the local pressure balance, we discuss a process of determining the steady shape of an air film that has two areas of minimum thickness in the vicinity of the downstream rim.

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 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.

High Knudsen Number Molecular Rarefaction Effects in Gas-Lubricated Slider Bearings for Computer Flying Heads

1987 ◽  
Vol 109 (2) ◽  
pp. 276-282 ◽  
Author(s):  
Y. Mitsuya ◽  
T. Ohkubo
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Flow Model ◽  
Slip Flow ◽  
Ambient Air ◽  
Mean Free Path ◽  
Lubricating Film ◽  
Modified Reynolds Equation ◽  
Air Film ◽  
Rarefaction Effects

This paper presents a study into the gas lubrication capability of an ultra-thin 0.025 μm film (converted value for ambient air film). The experimental results obtained using subambient helium as the lubricating film are compared with the calculated results using the modified Reynolds equation considering flow slippage due to the molecular mean free path effects. This comparison confirms that the slip flow model holds true within the range of the present experiments, and that the modified Reynolds equation is applicable for designing the computer flying heads operating at such thin spacing. The reason for the excellent agreement is discussed considering the locality of rarefaction effects on the lubricating surfaces and the anisotropy of these effects between the film thickness and the slider width.

A Numerical Study on Air-Entrainment between a Web and a Convex Guide Roller in a Web Transportation Process

2013 ◽  
Vol 392 ◽  
pp. 110-115 ◽  
Author(s):  
Puttha Jeenkour
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Numerical Study ◽  
Air Entrainment ◽  
Convex Shape ◽  
Transportation Process ◽  
Guide Roller ◽  
Shape Equation ◽  
Newton Raphson ◽  
Air Film

This paper presents a characteristic of air-entrainment between a web and a guide roller with modified convex shape. Air film thickness is derived using the modified Reynolds equation, a roller shape equation, and a web deflection equation. A finite difference method and a Newton-Raphson scheme are employed to achieve numerical results, i.e. air film thickness and air pressure distribution profiles, a minimum air film thickness, and an air film thickness at the middle of roller length under varied convex roller shapes. The results show that both minimum and central air film thicknesses decrease when the roller is designed as convex shape, and a parameter of convex roller shape affects a minimum air film thickness position.

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