A model for analyzing the interfacial conditions of a porous web moving over a cylindrical rigid guide is presented. This problem is different from the classical foil bearing problem due to the fact that the air can diffuse through the porous web itself. A micromechanics model is used to express the web porosity as a function of the fiber volume fraction of the web. Darcy’s law is used to account for the air flow and pressure drop across the web thickness, and a new modified Reynolds equation is derived to model the airflow in the web-guide interface. The porous web is modeled as a moving cylindrically curved beam, and the solid-body contact between the web and the guide is modeled using an asperity compliance function. The governing equations are nondimensionalized and important nondimensional parameters are identified. The coupled nonlinear steady-state system is solved using a modified Newton-Raphson algorithm. The traction characteristics of the web are presented for different porosity levels, asperity height, and compliance. [S0742-4787(99)00102-8]

Issue Section:
Technical Papers
Keywords:
porous materials, paper, air, diffusion, traction, sliding friction, shear deformation, micromechanics
Topics:
Air flow, Equilibrium (Physics), Fibers, Lubrication, Micromechanics (Engineering), Permeability, Pressure, Tension, Traction, Clearances (Engineering), Porosity, Displacement, Belts, Porous materials, Sliding friction
1.
Daly
,
D. A.
,
1965
, “
Factors Controlling Traction Between Webs and Their Carrying Rolls
,”
Tappi J.
,
48
, No.
9
, pp.
88A–90A
88A–90A
, Sept.
2.
Ducotey
,
K. S.
, and
Good
,
J. K.
,
1998
, “
The Effect of Web Permeability and Side Leakage on the Air Film Height Between a Roller and Web
,”
ASME J. Tribol.
,
120
, pp.
559
–
565
.
3.
Gross, W. A., 1980, Fluid Film Lubrication, Wiley, New York.
4.
Hashimoto
,
H.
,
1995
, “
Theoretical Analysis of Externally Pressurized Porous Foil Bearings-Part 1: In Case of Smooth Surface Porous Shaft
,”
ASME J. Tribol.
,
117
, No.
1
, pp.
93
–
102
.
5.
Hashimoto
,
H.
,
1997
, “
Effects of Foil Bending Rigidity on Spacing Height Characteristics of Hydrostatic Porous Foil Bearing for Web Handling Processes
,”
ASME J. Tribol.
,
119
, No.
1
, pp.
422
–
427
.
6.
Mu¨ftu¨, S., and Benson, R. C, 1995, “Modelling the Transport of Paper Webs Including the Paper Permeability Effects,” Advances in Information Storage and Processing Systems–1995, ASME International Mech. Eng. Congress and Exposition, San Francisco, CA, ISPS-Vol. 1, pp. 247–258.
7.
Wang
,
X.
,
1997
, “
Finite Element Analysis of Air-Sheet Interactions and Flutter Supression Devices
,”
J. Comput. Structures
64
, No.
5/6
, pp.
983
–
994
.
8.
Ducotey
,
K. S.
, and
Good
,
J. K.
,
1995
, “
The Importance of Traction in Web Handling
,”
ASME J. Tribol.
,
117
, pp.
679
–
684
.
9.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, England.
10.
Patir
,
N.
, and
Chang
,
H. S.
,
1979
, “
Application of Average Flow Model to Lubrication Between Rough Sliding Surfaces
,”
ASME J. Lubr. Technol.
,
101
, pp.
220
–
230
.
11.
Gutowski
,
T. G.
,
Morigaki
,
T.
, and
Cai
,
Z.
,
1987
, “
The Consolidation of Laminate Composites
,”
J. Compos. Mater.
,
21
, pp.
172
–
188
.
12.
Dave
,
R.
,
Kardos
,
J. L.
, and
Dudukovic
,
M. P.
,
1987
, “
A Model for Resin Flow During Composite Processing. Part 2: Numerical Analysis for Unidirectional Graphite/Epoxy Laminates
,”
Polym. Compos.
,
8
, No.
2
, pp.
123
–
132
.
13.
Lam, R. C., and Kardos, J. L., 1989, “The Permeability and Compressibility and Aligned and Cross-Plied Carbon Fiber Beds During Processing of Composites,” ANTEC ’98, SPE, pp. 1408–1412.
14.
Bruschke
,
M. V.
, and
Advani
,
S. G.
,
1993
, “
Flow of Generalized Newtonian Fluids Across a Periodic Array of Cylinders
,”
J. Rheol.
37
, No.
3
, pp.
479
–
498
.
15.
Bear, J., 1972, Dynamics of Fluids in Porous Media, Dover, New York.
16.
Tichy, J. A., 1994, “A Porous Media Model for Thin Film Lubrication,” ASME J. Tribol., 94-Trib-3.
17.
Bujurke
,
N. M.
,
Patil
,
H. P.
, and
Bhavi
,
S. G.
,
1990
, “
Porous Slider Bearing with Couple Stress Fluid
,”
Acta Mech.
,
85
, pp.
99
–
113
.
18.
Mu¨ftu¨
,
S.
, and
Cole
,
K. A.
,
1999
, “
The Fluid/Structure Interaction in Supporting a Thin Flexible Cylindrical Web with an Air Cushion
,”
J. Fluids Structures
,
13
, No.
6
, pp.
681
–
708
.
19.
Mu¨ftu¨
,
S.
, and
Benson
,
R. C.
,
1996
, “
A Study of the Cross-Width Variations in the Two Dimensional Foil Bearing Problem
,”
ASME J. Tribol.
,
118
, pp.
407
–
414
.
20.
Rabinowicz, E., 1995, Friction and Wear of Materials, Wiley, New York.
21.
Wu
,
Y.
, and
Talke
,
F.
,
1996
, “
The Effect of Surface Roughness on the Head-tape Interface
,”
ASME J. Tribol.
,
118
, No.
2
, pp.
376
–
381
.
22.
Greenwood
,
J. A.
, and
Williamson
,
J. B. P.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc. London, Ser. A
,
295
,
300
–
319
.
23.
Rice, B. S., Cole, K. A., and Mu¨ftu¨, S., 1999, “An Experimental and Theoretical Study of Web Traction Over a Nonvented Roller,” Proceedings of the Fifth Int. Web Handling Conference, Oklahoma State University, Stillwater, OK, June.
Copyright © 2000
 by ASME
You do not currently have access to this content.