Research Papers: Applications

Wrap Pressure Between a Flexible Web and a Circumferentially Grooved Cylindrical Guide

[+] Author and Article Information
Tugce Kasikci

Department of Mechanical Engineering,
Northeastern University,
Boston, MA 02115
e-mail: tugce.kasikci@gmail.com

Sinan Müftü

Fellow ASME
Department of Mechanical Engineering,
Northeastern University,
Boston, MA 02115
e-mail: s.muftu@neu.edu

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received March 30, 2015; final manuscript received November 25, 2015; published online March 11, 2016. Assoc. Editor: Mircea Teodorescu.

J. Tribol 138(3), 031101 (Mar 11, 2016) (8 pages) Paper No: TRIB-15-1097; doi: 10.1115/1.4032136 History: Received March 30, 2015; Revised November 25, 2015

Contact mechanics in wrapping a thin-shell (tape/web) around a grooved cylindrical surface (roller) under tension is investigated. The problem is analyzed along the axial direction of the roller, and the effects of wrap-angle tape/web motion are neglected. Equations of equilibrium admit analytical solutions, but the problem is nonlinear due to the unknown nature of contact area. The tape bends into the grooves and makes contact over the lands. Three distinct contact states describe the interaction of the tape/web with respect to the lands. Nondimensional analysis shows that contact state depends on the width of the groove and the land, and the nondimensional belt-wrap pressure only modulates the amplitude of the deflected profile.

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Fig. 1

Cross-sectional diagram of a grooved roller, and the definitions of the land–groove pair and the symmetry planes. Note that when (Γ=0), the tape lays flat and contact pressure is zero.

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Fig. 2

Contact states for (Γ > 0): (a) CS-1, contact along groove edges, (b) CS-2, contact along groove edges and center of the land, and (c) CS-3, contact along groove edges and on the land

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Fig. 3

Nondimensional force check for reaction, pull-down, and foundation forces

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Fig. 4

Deflection profiles for the same belt-wrap pressure values Γ  = 0.005, 0.05, 0.11, 0.16, and 0.2 for different land and groove width (L¯L,L¯G) values: (a) (0.5, 1), (b) (1, 1.5), and (c) (1, 0.5). The geometric variables cause the transition from CS-1 to CS-3, but not the nondimensional belt-wrap pressure.

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Fig. 7

Predicted deflection profiles for dimensional roller parameters

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Fig. 6

Effects of different groove (L¯G) and land width (L¯L) values on (a) half-contact width a¯, (b) inner shear force V¯i, (c) corner shear force V¯c, and (d) contact force per length q¯ and pull-down force per length Γa¯. The results are obtained for Γ=0.01. Note that black, red, and blue lines indicate CS-3, CS-2, and CS-1, respectively.

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Fig. 5

Effect of groove width on deflection profiles for constant values of land width (L¯L  = 0.5) and belt-wrap pressure (Γ = 0.01). (a) The belt-wrap pressure that is applied over a large groove width is able to counteract the belt-wrap pressure acting over the land giving rise to CS-1. (b) and (c) If the design has a smaller groove width, the contact states 2 and 3 are expected to develop.




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