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.

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.

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.

The Importance of Traction in Web Handling

1995 ◽  
Vol 117 (4) ◽  
pp. 679-684 ◽  
Author(s):  
K. S. Ducotey ◽  
J. K. Good
Keyword(s):  
Coefficient Of Friction ◽  
Film Surface ◽  
Root Mean Square Roughness ◽  
Mean Square ◽  
Web Handling ◽  
Traction Coefficient ◽  
Static Coefficient Of Friction ◽  
Air Film ◽  
Static Coefficient ◽  
The Web

An experimental study shows that the traction coefficient of friction (μT) is a function of the predicted air film height, the roller and film surface roughness, and the static coefficient of friction between the web and roller. The traction coefficient shows a noticeable decrease as the air film height becomes greater than the equivalent root mean square roughness of the web and roller and also becomes less dependent on the static coefficient of friction.

A comparison of squeeze-film theory with measurements on a microstructure

1993 ◽  
Vol 36 (1) ◽  
pp. 79-87 ◽  
Author(s):  
M. Andrews ◽  
I. Harris ◽  
G. Turner
Keyword(s):  
Film Theory ◽  
Squeeze Film

Characterization of Nonlinear Rattling Behavior of a Gear Pair Through a Validated Torsional Model

2021 ◽  
Author(s):  
Ata Donmez ◽  
Ahmet Kahraman
Keyword(s):  
Piecewise Linear ◽  
Nonlinear Behavior ◽  
Severity Index ◽  
System Response ◽  
Gear Pair ◽  
Computationally Efficient ◽  
Linear Solution ◽  
Set Up ◽  
The Impact ◽  
Gear Rattle

Abstract Dynamic response of a gear pair subjected to input and output torque or velocity fluctuations is examined analytically. Such motions are commonly observed in various powertrain systems and identified as gear rattle or hammering motions with severe noise and durability consequences. A reduced-order torsional model is proposed along with a computationally efficient piecewise-linear solution methodology to characterize the system response including its sensitivity to excitation parameters. Validity of the proposed model is established through comparisons of its predictions to measurements from a gear rattle experimental set-up. A wide array of nonlinear behavior is demonstrated through presentation of periodic and chaotic responses in the forms of phase plots, Poincaré maps, and bifurcation diagrams. The severity of the resultant impacts on the noise outcome is also assessed through a rattle severity index defined by using the impact velocities.

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.

An Investigation of the Squeeze Film Between Rotating Annuli

1970 ◽  
Vol 92 (3) ◽  
pp. 435-440 ◽  
Author(s):  
C. W. Allen ◽  
A. A. McKillop
Keyword(s):  
Experimental Investigation ◽  
Melting Point ◽  
Liquid Metal ◽  
Decay Rates ◽  
Squeeze Film ◽  
Centrifugal Effect ◽  
Experimental Values ◽  
Free Falling ◽  
Air Film ◽  
Good Agreement

The squeeze film between two plane annuli is examined theoretically and experimentally. The theoretical analysis considers the inertia due to the “centrifugal effect” but neglects all other inertia terms. The experimental investigation is by means of a free-falling spinning rotor which is decelerated by the squeeze film. Fluids examined are kerosene, SAE 10 oil, and a low melting point liquid metal. Good agreement between the predicted and actual decay rates is obtained for kerosene but that for the oil and liquid metal is only fair. The theoretical and experimental values of film thickness are in good agreement. The results for the liquid metal suggest the possibility of a thin air film between the rotor and the liquid metal.

scholarly journals The Performance Effects of Squeeze Film Stiffness on Non-Resonate Interferometric Inertial Sensors

2007 ◽  
Author(s):  
Maximillian A. Perez ◽  
Andrei M. Shkel
Keyword(s):  
Inertial Sensors ◽  
Inertial Sensor ◽  
Film Theory ◽  
Nonlinear Effects ◽  
Squeeze Film ◽  
Nonlinear Frequency ◽  
Reduced Pressure ◽  
Performance Effects ◽  
Film Stiffness ◽  
Kinetic Gas Theory

This paper studies the nonlinear effects of squeeze film stiffening on the performance of a high resolution MEMS nonresonant inertial sensor. It is shown that these effects introduce a surprising dynamic response that extends the operational frequency range of the devices by retarding the resonate response. In addition, this performance advantage will occur without the traditional gain trade-off associated with linear systems of this type. A method is introduced to experimentally characterize the squeeze film stiffness of a passive inertial sensor through the resonant characterization of a Fabry-Pe´rot interferometric accelerometer under reduced pressure. Such passive devices are uniquely suited for the study of squeeze films and, due to the dependence of both the sensitivity and bandwidth on the device structural stiffness, variation of the stiffness with frequency must be considered to accurately predict sensor performance. The characterization confirms established analytical squeeze film stiffness theory in the continuous gas regime for conditions of Knudsen numbers less then one. As the Knudsen number equal to one is approached, it is shown that ideal kinetic gas theory and continuous squeeze film theory converge yielding a simplified stiffness estimate under the resonant response under reduced pressure. These analytical results are used to predict the performance gains due to the nonlinear, frequency dependent total stiffness of the sensor during non-resonant operation.

Predictive Models of Web-to-Roller Traction

2005 ◽  
Vol 127 (1) ◽  
pp. 180-189 ◽  
Author(s):  
Brian S. Rice ◽  
Roger F. Gans
Keyword(s):  
Predictive Models ◽  
Full Range ◽  
Groove Depth ◽  
Squeeze Film ◽  
Asperity Contact ◽  
Process Variables ◽  
Design Variables ◽  
Dimensionless Groups ◽  
Air Film ◽  
Cylindrical Roller

We studied the traction developed between a thin, flexible web and a rotating circumferentially grooved cylindrical roller. We have developed a new two-dimensional analytic model that couples air film pressure, web deflection, and asperity contact to predict traction for circumferentially grooved rollers with arbitrary wrap angles. The entrance effects are incorporated into our new traction model by adapting the squeeze film concept using the distance from the entrance as a surrogate for time. We have verified this model experimentally on a series of 14 rollers and 19 webs. We tested both nongrooved and circumferentially grooved rollers. We showed experimentally that rough, ungrooved rollers that have their low areas unconnected produce significantly lower traction and do not fit the model introduced here. Such rollers should be avoided where traction is important. We introduce dimensionless groups that the roller designer can use to quantitatively assess the interactions of process variables (e.g., speed, tension, etc.) with design variables (e.g., groove depth, groove pitch, roughness, etc.) over the full range of practical wrap angles.

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