The Effect of Web Permeability and Side Leakage on the Air Film Height Between a Roller and Web

1998 ◽  
Vol 120 (3) ◽  
pp. 559-565 ◽  
Author(s):  
K. S. Ducotey ◽  
J. K. Good
Keyword(s):  
Constant Pressure ◽  
Separation Distance ◽  
Foil Bearing ◽  
Pressure Region ◽  
Entrained Air ◽  
Web Quality ◽  
Air Film ◽  
Roller Radius ◽  
The Web ◽  
Web Tension

Air entrained between a web and roller can cause a loss in traction that can affect web quality. The entrained air causes an air layer to form which separates the web from the roller. Insufficient traction exists at this point and an idler roller will be unable to be driven by the web. Other applications, however, such as newsprint moving around a turnbar, require complete clearance. An equation for predicting the air film height between a permeable web and roller was developed using foil bearing theory. The separation distance (h) between the roller and web is a function of the roller radius (R), web tension (T), air viscosity (η), summation of the web and roller velocities (U), and the web permeability (α). The air film height was found to decrease linearly around the circumference (θ) of the roller in the constant pressure region. Therefore, the air film height can be expressed simply as, h=0.643R[(6ηU)/T]2/3−2[(αT)/U]θ The slope of the air film height is a function of the web/roller velocity, web tension, and the permeability of the paper. A correction factor for side leakage was also incorporated into the result.

Predicting Traction in Web Handling

1999 ◽  
Vol 121 (3) ◽  
pp. 618-624 ◽  
Author(s):  
K. S. Ducotey ◽  
J. K. Good
Keyword(s):  
Piecewise Linear ◽  
Film Theory ◽  
Simple Algorithm ◽  
Squeeze Film ◽  
Web Handling ◽  
Linear Solution ◽  
Foil Bearing ◽  
Air Film ◽  
Roller Radius ◽  
The Web

A simple algorithm has been developed for predicting traction in web handling applications. Minimal traction exists when the minimum air film height between the roller and web is greater than three times the rms roughness of the two surfaces in contact. Classical foil bearing theory modified for permeable surfaces is used to determine the air film height. A piecewise linear solution using squeeze film theory is also used to account for side leakage. The minimum air film height is a function of web tension, web and roller velocity, air viscosity, web width, web permeability and roller radius. The algorithm is applicable for permeable and nonpermeable webs. Values obtained from the algorithm can be used to predict if sufficient traction is available between the web and roller for a given set of physical and operating parameters. Traction values can also be used as input for winding, wrinkling, and spreading models.

Improvement of Web Spacing and Friction Characteristics by Two Types of Stationary Guides

2000 ◽  
Vol 123 (3) ◽  
pp. 509-516 ◽  
Author(s):  
Hiromu Hashimoto ◽  
Haruyasu Nakagawa
Keyword(s):  
Hydrostatic Pressure ◽  
Friction Coefficient ◽  
Hydrodynamic Pressure ◽  
Back Surface ◽  
Gaussian Distributions ◽  
Reflected Light ◽  
Experimental Apparatus ◽  
Entrained Air ◽  
The Web ◽  
Web Tension

In this paper, two types of stationary guides are presented to improve the web spacing characteristics; hybrid hollow porous guide for maintaining the sufficient web spacing and grooved guide for removing the entrained air. In the hybrid hollow porous guide, the pressurized air is added to the lubrication air flow between web and guide from inside the guide. Then, the web spacing characteristics are improved by the hybrid effects of hydrodynamic pressure due to web movements and hydrostatic pressure due to pressurized added air through the guide. The relations between web spacing and web velocity are measured under various supply pressures. Moreover, the relations between web spacing and web tension are examined. The contactless optical sensor, which can measure the variation of the quantities of reflected light from the back surface of web according to the variation of web spacing, is used to obtain the web spacing under various conditions. In the grooved guide, the method for the estimation of web spacing by using the concept of equivalent spacing between web and guide is presented, and the web spacing is measured by the same experimental apparatus used in the case of hollow porous guide. From the calculated and measured results obtained, the effectiveness of two types of guides on the web spacing is clarified. Finally, based on the assumptions of Gaussian distributions of asperities, the simple relations to predict the friction coefficient between web and guide surfaces are formulated, and the variation of friction coefficient with velocity is shown for various values of web tension.

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 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.

scholarly journals A Sign of Things to Come: Predicting the Perception of Above-the-Fold Time in Web Browsing

2021 ◽  
Vol 13 (2) ◽  
pp. 50
Author(s):  
Hamed Z. Jahromi ◽  
Declan Delaney ◽  
Andrew Hines
Keyword(s):  
Web Application ◽  
Web Applications ◽  
State Of The Art ◽  
Influencing Factor ◽  
The State ◽  
Experimental Result ◽  
Web Page ◽  
To Come ◽  
Web Quality ◽  
The Web

Content is a key influencing factor in Web Quality of Experience (QoE) estimation. A web user’s satisfaction can be influenced by how long it takes to render and visualize the visible parts of the web page in the browser. This is referred to as the Above-the-fold (ATF) time. SpeedIndex (SI) has been widely used to estimate perceived web page loading speed of ATF content and a proxy metric for Web QoE estimation. Web application developers have been actively introducing innovative interactive features, such as animated and multimedia content, aiming to capture the users’ attention and improve the functionality and utility of the web applications. However, the literature shows that, for the websites with animated content, the estimated ATF time using the state-of-the-art metrics may not accurately match completed ATF time as perceived by users. This study introduces a new metric, Plausibly Complete Time (PCT), that estimates ATF time for a user’s perception of websites with and without animations. PCT can be integrated with SI and web QoE models. The accuracy of the proposed metric is evaluated based on two publicly available datasets. The proposed metric holds a high positive Spearman’s correlation (rs=0.89) with the Perceived ATF reported by the users for websites with and without animated content. This study demonstrates that using PCT as a KPI in QoE estimation models can improve the robustness of QoE estimation in comparison to using the state-of-the-art ATF time metric. Furthermore, experimental result showed that the estimation of SI using PCT improves the robustness of SI for websites with animated content. The PCT estimation allows web application designers to identify where poor design has significantly increased ATF time and refactor their implementation before it impacts end-user experience.

Modeling of Web Slip on a Roller and Its Effect on Web Tension Dynamics

2005 ◽  
Author(s):  
Ramamurthy V. Dwivedula ◽  
Prabhakar R. Pagilla
Keyword(s):  
Numerical Computation ◽  
Dynamic Models ◽  
Simple Approach ◽  
Roller Surface ◽  
Perfect Adhesion ◽  
The Web ◽  
Web Tension

This paper considers the effect of web slip over the rollers on the span tension dynamics. In classical development of the web span tension dynamics, it is assumed that there is strict adhesion between the web and the surface of the roller and thus, there is no slip-page between the web and the roller. As a result of this assumption, effect of tension disturbances in downstream spans on the upstream span tension is precluded. However, in practice, perfect adhesion between the web and roller surface is seldom achieved and tension disturbances propagate upstream also. Though web span tension dynamic models that include slippage between web and roller are proposed, these models rely to a great extent on numerical computation of slip arc angles and are prohibitively complex to be of practical use. This paper proposes an alternative, simple approach for developing web span tension dynamics to include the effect of web slip.

Advanced Optimization of Industrial Large-Scale Roll-to-Roll Systems Under Parametric Uncertainties

2012 ◽  
Author(s):  
J. Frechard ◽  
D. Knittel
Keyword(s):  
Young’S Modulus ◽  
Large Scale ◽  
Young's Modulus ◽  
Robust Design Optimization ◽  
Parametric Uncertainties ◽  
Optimization Approach ◽  
Roll To Roll ◽  
Polymer Metal ◽  
The Web ◽  
Web Tension

In industrial plants some parameters can not be evaluated properly or they are varying with time. These parametric uncertainties has to be taken into account during the design process of industrial systems. In this work, the developped optimization approach is applied on an industrial roll-to-roll sytem. Such systems are commonly used to handle materials as polymer, metal, paper and textile. The key challenge is to move the web at the expected speed while maintaining the web tension in an acceptable range around its reference. Moreover, the Young’s modulus of the web is difficult to evaluate and it is varying with time due to temperature and moisture variations. This paper deals with the web tension controller synthesis on a large-scale roll-to-roll system with uncertain Young’s modulus. To synthesize web tension controllers, an H∞ approach is applied and adapted to the system with parametric uncertainties using multi-objective robust design optimization.

A Contribution to the Thermal Modeling of Bump Type Air Foil Bearings: Analysis of the Thermal Resistance of Bump Foils

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Andreas Lehn ◽  
Marcel Mahner ◽  
Bernhard Schweizer
Keyword(s):  
Thermal Resistance ◽  
Thermal Contact ◽  
Applied Pressure ◽  
Analytical Formula ◽  
Base Plate ◽  
Air Gaps ◽  
Foil Bearings ◽  
Foil Bearing ◽  
Air Film ◽  
Good Agreement

A detailed analysis of the effective thermal resistance for the bump foil of air foil bearings (AFBs) is performed. The presented model puts emphasis on the thermal contact resistances between the bump foil and the top foil as well as between the bump foil and the base plate. It is demonstrated that most of the dissipated heat in the lubricating air film of an air foil bearing is not conducted by microcontacts in the contact regions. Instead, the air gaps close to the contact area are found to be thin enough in order to effectively conduct the heat from the top foil into the bump foil. On the basis of these findings, an analytical formula is developed for the effective thermal resistance of a half bump arc. The formula accounts for the geometry of the bump foil as well as for the surface roughness of the top foil, the bump foil, and the base plate. The predictions of the presented model are shown to be in good agreement with measurements from the literature. In particular, the model predicts the effective thermal resistance to be almost independent of the applied pressure. This is a major characteristic property that has been found by measurements but could not be reproduced by previously published models. The presented formula contributes to an accurate thermohydrodynamic (THD) modeling of AFBs.

scholarly journals Cloud-Spacing Effects upon Entrainment and Rainfall along a Convective Line

2018 ◽  
Vol 57 (8) ◽  
pp. 1865-1882 ◽  
Author(s):  
Daniel H. Moser ◽  
Sonia Lasher-Trapp
Keyword(s):  
Thermodynamic Characteristics ◽  
Local Environment ◽  
Separation Distance ◽  
Convective Rainfall ◽  
Cumulus Clouds ◽  
Spacing Effects ◽  
Cloud Development ◽  
Cumulus Congestus ◽  
Entrained Air ◽  
New Generation

AbstractCumulus clouds modify their immediate surroundings by detraining their warm, humid updrafts. When clouds are closely spaced, this conditioning of the local environment may alter the properties of the air entrained by neighboring clouds and slow their dilution. This effect has not been quantified, nor has its importance been determined for influencing the amount of convective rainfall from a system of neighboring clouds. Here, a series of idealized numerical simulations, which are based on an observed line of precipitating cumulus congestus clouds, is performed using increasingly smaller cloud spacing to investigate how cloud proximity may alter entrainment, cloud development, and convective rainfall. For clouds of radius R, which is approximately 1 km in these simulations, distances between updraft centers from 4R through 9R are tested. Over this range, the initial clouds all exhibit negligible differences in the directly calculated entrainment rates and in the thermodynamic characteristics of the entrained air. Instead, for cloud separation distances of less than 6R, the subcloud inflow is increasingly disturbed, limiting initial cloud depths and slowing updraft speeds and precipitation onset. Ultimately, however, these same cases produce a new generation of clouds that are stronger and produce more rainfall than for all other cases. The smaller cloud separation distance allows precipitation outflows from the initial clouds to meet and force new, stronger cloud updrafts. For this second generation of clouds, their entrained air is slightly more humid, but the stronger updrafts and ingestion of residual ice and precipitation from earlier clouds appear to be most important for enhancing their rainfall.

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