Rolling Contact Between Rigid Cylinder and Semi-Infinite Elastic Body With Sliding and Adhesion

[+] Author and Article Information
S. Hao

Department of Mechanical Engineering,  Northwestern University, Evanston, IL 60208suhao@northwestern.edu

L. M. Keer

Department of Mechanical Engineering,  Northwestern University, Evanston, IL 60208l-keer@northwestern.edu

J. Tribol 129(3), 481-494 (Jan 22, 2007) (14 pages) doi:10.1115/1.2736431 History: Received April 02, 2006; Revised January 22, 2007

Based on a hybrid superposition of an indentation contact and a rolling contact an analytical procedure is developed to evaluate the effects of surface adhesion during steady-state rolling contact, whereby two analytic solutions have been obtained. The first solution is a Hertz-type rolling contact between a rigid cylinder and a plane strain semi-infinite elastic substrate with finite adhesion, which is a JKR-type rolling contact but without singular adhesive traction at the edges of the contact zone. The second solution is of a rolling contact with JKR singular adhesive traction. The theoretical solution indicates that, when surface adhesion exists, the friction resistance can be significant provided the external normal force is small. In addition to the conventional friction coefficient, the ratio between friction resistance force and normal force, this paper suggests an “adhesion friction coefficient” which is defined as the ratio between friction resistance force and the sum of the normal force and a function of maximum adhesive traction per unit area, elastic constant of the substrate, and contact area that is characterized by the curvature of the roller surface.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

A rolling contact system with a normal force P, a tangential force Q, and a moment Mappl applied on the central axial line of the roller, where P induces additional moment MP since the system is not symmetric. By varying the magnitudes and directions of P, Q, and Mappl, one obtains different cases of rolling contacts that can be classified into three categories: (1) free rolling:Mappl=0,Q=0; (2) scratching: Mappl+MP+RQ=0 and ω=0; (3) ω≠0 and 0<{∣RQ∣+∣Mappl∣}, which is termed “constraint rolling” in this paper.

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Figure 2

(a) Hierarchical structure of a tribological process, the right most is the contact/sliding between an iron substrate and a TiN particle at (001) surface, the details of this analysis can be found in the Sec. 4.1 of (32); (b) relationship between adhesion energy, surface energy, and the definition of λN0 for JKR-type adhesion

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Figure 3

(a) Models of adhesion contact between elastic bodies; (b) proposed adhesion contact model for the rolling contact

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Figure 4

Solution strategy of the rolling-contact with JKR adhesion; superposition of roller indentation (a) and adhesion rotation (b)

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Figure 5

Two solutions for indentation contact at P=0

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Figure 6

The solutions of (a) the average transverse surface contact strain εav vs Poisson’s ratio at small normal load; (b) the rotation angle Δω vs Poisson’s ratio at small normal load; (c) the evolution of εav when normalized load P¯ increases; (d) the evolution of Δω as P¯ increases

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Figure 7

Comparison between rolling and nonrolling solutions for the normal stress and shear stress: (a) normal stress; (b) shear stress; (c) illustration of the deformation

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Figure 8

The solved normal pressure and shear stress distributions in contact-stick zone, varying with applied normal load: (a) the stresses plotted in the {Xi} coordinate system for the case of T0∕G=0.01, small applied normal load; (b) the stresses plotted in the {t} coordinate system for the case of T0∕G=0.15 under moderate normal load

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Figure 9

The solved rolling-stick friction coefficient 37 against normalized load under different JKR adhesion

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Figure 10

The relationship among maximum adhesion T0, total normal compression force P, and the corresponding resultant moment M, where T¯0=T0∕(6G), P¯=P∕(RG), M¯=M∕(RbG), and b=1 for the plane strain

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Figure 11

Geometric relationship between stick-rotation angle Δω and displacement increments



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