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TECHNICAL PAPERS

Hysteretic Friction for the Transient Rolling Contact Problem of Linear Viscoelasticity

[+] Author and Article Information
D. L. Chertok

Springfield Financial Services LLC, 8700 W. Bryn Mawr Avenue, 12th Floor, Chicago, IL 60631e-mail: dchertok@siichi.com

J. M. Golden

School of Mathematics, Statistics and Computer Science, Dublin Institute of Technology, Dublin 8, Irelande-mail: jmgolden@maths.kst.dit.ie

G. A. C. Graham

Applied and Computational Mathematics Program, Simon Fraser University, Burnaby, BC V5A 1S6, Canadae-mail: gac@cs.sfu.ca

J. Appl. Mech 68(4), 589-595 (Sep 27, 2000) (7 pages) doi:10.1115/1.1354622 History: Received October 03, 1997; Revised September 27, 2000
Copyright © 2001 by ASME
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References

Tabor,  D., 1952, “The Mechanism of Rolling Friction,” Philos. Mag., 43, pp. 1055–1059.
Hunter,  S. C., 1961, “The Rolling Contact of a Rigid Cylinder With a Viscoelastic Half-Space,” ASME J. Appl. Mech., 28, pp. 611–617.
Morland,  L. W., 1962, “A Plane Problem of Rolling Contact in Linear Viscoelasticity Theory,” ASME J. Appl. Mech., 29, pp. 345–352.
Golden,  J. M., 1977, “Hysteretic Friction of a Plane Punch on a Half-Plane With Arbitrary Viscoelastic Behavior,” Q. J. Mech. Appl. Math., 30, pp. 23–49.
Golden,  J. M., 1979, “The Problem of a Moving Rigid Punch on an Unlubricated Viscoelastic Half-Plane,” Q. J. Mech. Appl. Math., 32, pp. 25–52.
Golden, J. M., and Graham, G. A. C., 1988, Boundary Value Problems in Linear Viscoelasticity, Springer-Verlag, Berlin.
Golden, J. M., and Graham, G. A. C., 1995, “General Methods in Non-Inertial Viscoelastic Boundary Value Problems,” Crack and Contact Problems for Viscoelastic Bodies, G. A. C. Graham and J. R. Walton, ed., Springer-Verlag, Vienna, pp. 103–225.
Golden,  J. M., and Graham,  G. A. C., 1987, “The Transient Quasi-Static Plane Viscoelastic Moving Load Problem,” Int. J. Eng. Sci., 25, pp. 65–84.
Fan,  H. Z., Golden,  J. M., and Graham,  G. A. C., 1995, “The Problem of Several Indentors Moving on a Viscoelastic Half-Plane,” ASME J. Appl. Mech., 62, pp. 380–389.
Golden,  J. M., and Graham,  G. A. C., 1996, “The Viscoelastic Moving Contact Problem With Inertial Effects Included,” Q. J. Mech. Appl. Math., 49, pp. 107–135.
Muskhelishvili, N. I., 1963, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen (translated from the Russian by J. R. M. Radok).
Rabotnov, Yu. N., 1977, Elements of Hereditary Mechanics of Solid Bodies Nauka, Moscow (in Russian).
Moore, D. F., 1993, Viscoelastic Machine Elements: Elastomers and Lubricants in Machine Systems, Butterworth-Heinemann, Oxford, UK.
Atkinson, K. E., 1976, A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind, SIAM, Philadelphia, PA.
Squire, W., 1970, Integration for Engineers and Scientists, American Elsevier, New York.
Chertok, D. L., 1998, “Hysteretic Friction in the Transient Rolling Contact Problem of Linear Viscoelasticity,” Ph.D. thesis, Simon Fraser University, Burnaby, BC, Canada.
de Boor, C., 1978, A Practical Guide to Splines, Springer-Verlag, New York.
Davis, P. J., and Rabinowitz P., 1984, Methods of Numerical Integration 2nd ed., Academic Press, San Diego, CA.

Figures

Grahic Jump Location
Schematic representation of the problem: C(t)=[a(t),b(t)]—contact interval, O—center of the cylinder, R—radius of the cylinder, x0(t)—point of deepest indentation of the half-space, x—current point coordinate, u(x,t)—vertical displacement at x,d(t)—maximum displacement, V(t)— indentor speed, W(t)—total load
Grahic Jump Location
Schematic representation of the discretization procedure for the spatial domain
Grahic Jump Location
Constantly accelerating indentor: V=t. History of contact interval width C, indentor tip shift h and speed V.
Grahic Jump Location
Constantly accelerating indentor: V=t. History of hysteretic friction fH and speed V. The solid lines indicate the transient solution and the broken lines indicate the steady-state solution. The dotted line indicates the speed.
Grahic Jump Location
Alternately accelerating and decelerating indentor with V(t) varying as described by (38). History of contact interval width C, indentor tip shift h and speed V. The solid lines indicate the transient solution and the broken lines indicate the steady-state solution. The dotted line indicates the speed.
Grahic Jump Location
Alternately accelerating and decelerating indentor with V(t) varying as described by (38). History of hysteretic friction fH and speed V. The solid lines indicate the transient solution and the broken lines indicate the steady-state solution. The dotted line indicates the speed.
Grahic Jump Location
History of pressure distribution for an alternately accelerating and decelerating indentor
Grahic Jump Location
Periodically accelerating indentor: V(t)=1+0.9 sin(t). History of contact interval width C, indentor tip shift h and speed V.
Grahic Jump Location
Periodically accelerating indentor: V(t)=1+0.9 sin(t). History of hysteretic friction fH and speed V.
Grahic Jump Location
Periodically varying load: W(t)=1+0.9 sin(t). History of contact interval width C, indentor tip shift h and speed V.W is scaled by a factor of 10 to fit on the graph.
Grahic Jump Location
Periodically varying load: W(t)=1+0.9 sin(t). History of hysteretic friction fH and speed V.W is scaled by a factor of 100 to fit on the graph.

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