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.

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.

Effect of Load Variation on Elastohydrodynamic Lubrication Film Collapse

2014 ◽  
Vol 592-594 ◽  
pp. 1366-1370
Author(s):  
Tapash Jyoti Kalita ◽  
Punit Kumar
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Elastohydrodynamic Lubrication ◽  
Transient Behavior ◽  
Computer Code ◽  
Practical Situation ◽  
Lubrication Film ◽  
Newton Raphson ◽  
Simulation Results ◽  
Film Collapse

Elastohydrodynamic line contact simulations have been carried out in the present study. A practical situation of transient EHL film collapse has been analyzed. The aim is to observe the effect of variation of maximum Hertzian pressure (PH) on transient behavior of EHL film thickness (H).The analysis is based upon classical Reynolds equation considering time variation. The simulation results pertaining to EHL film thickness calculated using linear pressure-viscosity relationship have been compared for different values of load. It has been observed that film thickness reduces with increase in load. Similar results are obtained using exponential pressure-viscosity relationship and compared with those for linear pressure-viscosity. The EHL equations are solved by discretizing Reynolds equation and load equilibrium equation along with other equations using Newton-Raphson technique with the help of a computer code.

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.

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.

A Numerical Algorithm for Determining the Traction Between a Web and a Circumferentially Grooved Roller

2000 ◽  
Vol 122 (3) ◽  
pp. 578-584 ◽  
Author(s):  
K. S. Ducotey ◽  
J. K. Good
Keyword(s):  
Reynolds Equation ◽  
Air Entrainment ◽  
Contact Theory ◽  
Asperity Contact ◽  
Governing Equations ◽  
Web Handling ◽  
Plate And Shell ◽  
Variable Mesh ◽  
Air Film ◽  
Theoretical Results

Air entrainment can become a significant problem in a web handling process line. The development of an air film between a roller and web can cause a reduction in traction. This can cause a velocity difference between the web and roller and may also cause guiding problems. Roller grooving is a common method to reduce the effects of the air entrainment to improve traction. A traction simulation model for circumferentially grooved rollers has been devised. The model is based on classical plate and shell theory, the Reynolds’ equation, and asperity contact theory. The governing equations are solved in an iterative scheme using a finite difference method with a variable mesh. Theoretical results are experimentally verified. [S0742-4787(00)02203-7]

Rough Air-Soft Elastohydrodynamic Lubrication

2013 ◽  
Vol 420 ◽  
pp. 30-35
Author(s):  
Khanittha Wongseedakaew ◽  
Jesda Panichakorn
Keyword(s):  
Surface Roughness ◽  
Film Thickness ◽  
Modulus Of Elasticity ◽  
Contact Region ◽  
Elastohydrodynamic Lubrication ◽  
Multilevel Methods ◽  
Inlet Temperature ◽  
Film Pressure ◽  
Air Inlet ◽  
Air Film

This paper presents the effects of rough surface air-soft elastohydrodynamic lubrication (EHL) of rollers for soft material under the effect of air molecular slip. The time independent modified Reynolds equation and elasticity equation were solved numerically using finite different method, Newton-Raphson method and multigrid multilevel methods were used to obtain the film pressure profiles and film thickness in the contact region. The effects of amplitude of surface roughness, modulus of elasticity and air inlet temperature are examined. The simulation results showed surface roughness has effect on film thickness but it little effect to air film pressure. When the amplitude of surface roughness and modulus of elasticity increased, the air film thickness decreased but air film pressure increased. However, the air inlet temperature increased when the air film thickness increased.

DDC Lubrication: A New Concept in Tribology

1992 ◽  
Vol 114 (1) ◽  
pp. 181-185 ◽  
Author(s):  
K. To̸nder
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Gap Function ◽  
Upper And Lower Bounds ◽  
Roughness Effects ◽  
Cavity Depth ◽  
Roughness Amplitude ◽  
Previously Treated ◽  
The Mean ◽  
Expansion Scheme

A new lubrication concept is presented, Deep Disconnected Cavities. It differs from the lubrication of microcavities, previously treated by other authors, by the deepness of the cavities. The validity of Reynolds’ equation and nonturbulent conditions are assumed. By a Taylor expansion scheme, it is shown that the roughness effects are expressible in terms of roughness factors modifying the Reynolds equation, similar to those proposed by Patir and Cheng (1978). Unlike those established for ordinary roughness, the DDC factors are independent of local film thickness and roughness amplitude (cavity depth), and may therefore be used to modify standard hydro-dynamic parameters. By a different mathematical approach, involving upper and lower bounds on the various hydrodynamic quantities, it is found that Reynolds’ equation and all the other hydrodynamic expressions may be written just as for smooth surfaces, with the following modifications: 1. The film thickness should be expressed by the minimum gap function, and not by the mean gap function. 2. There are, in general, three effective viscosities, lower than the physical one, two of which are associated with the x and y directions respectively and appear in the modified Reynolds equation as well as in the flow terms. The third one appears only in the expression for shear stress.

The Effects of Baseplate Warpage and Skew on the Configuration of a Spinning Flexible Disk

1994 ◽  
Vol 116 (3) ◽  
pp. 514-520 ◽  
Author(s):  
R. Y. Wu ◽  
G. G. Adams
Keyword(s):  
Radial Direction ◽  
Reynolds Equation ◽  
Total Response ◽  
Axisymmetric Solution ◽  
Small Deviations ◽  
Close Proximity ◽  
Flexible Disk ◽  
Air Film ◽  
Axisymmetric Configuration ◽  
State Configuration

The behavior of a flexible disk, spinning in close proximity to a warped/skewed stationary baseplate, is investigated. The governing partial differential equation for the disk deflection is coupled to the Reynolds equation of the air film. Four warped/ skewed baseplate configurations are modeled. The effects of baseplate warpage and skew on the steady-state configuration of the disk are determined by investigating small deviations away from the axisymmetric configuration of the disk corresponding to a perfect baseplate. Exponential Fourier series expansions in the circumferential direction, along with finite differences in the radial direction, are used. Numerical results are determined and compared for various values of the angular velocity and initial thicknesses of the air film. Among the three warpages considered, the saddle warped baseplate provides the largest change in disk deflection whereas the spherically warped baseplate gives the smallest change. The total response of the disk is obtained by superposition of the deflection change caused by the warped/skewed baseplate and the deflection obtained from the axisymmetric solution.

scholarly journals Lubrication Analyses of Cam and Flat-Faced Follower

Lubricants ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 31 ◽  
Author(s):  
Hazim U. Jamali ◽  
Amjad Al-Hamood ◽  
Oday I. Abdullah ◽  
Adolfo Senatore ◽  
Josef Schlattmann
Keyword(s):  
Film Thickness ◽  
Pressure Distribution ◽  
Surface Deformation ◽  
Numerical Study ◽  
Point Contact ◽  
Radius Of Curvature ◽  
Operating Cycle ◽  
Essential Step ◽  
Parabolic Shape ◽  
Principal Factors

The principal factors that affect the characteristics of contact problem between cam and follower vary enormously during the operating cycle of this mechanism. This includes radius of curvature, surface velocities and applied load. It has been found over the last decades that the mechanism operates under an extremely thin film of lubricant. Any practical improvement in the level of film thickness that separates the contacted surfaces represents an essential step towards a satisfactory design of the system. In this paper a detailed numerical study is presented for the cam and follower (flat-faced) lubrication including the effect of introducing an axial modification (parabolic shape) of the cam depth on the levels of film thickness and pressure distribution. This is achieved based on a point contact model for a cam and flat-faced follower system. The results reveal that the cam form of modification has considerable consequences on the level of predicted film thickness and pressure distribution as well as surface deformation.

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