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.
Issue Section:
Technical Papers
1.
Hertz
, H.
, 1882, “On the Contact of Elastic Solids
,” J. Reine Angew. Math.
0075-4102, 92
, pp. 156
–170
.2.
Greenwood
, J. A.
, and Williams
, J. B.
, 1966, “Contact of Nominally Flat Surfaces
,” Proc. R. Soc. London, Ser. A
1364-5021, 295
(1442
), pp. 300
–394
.3.
Johnson
, K. L.
, 1985, Contact Mechanics
, Cambridge University Press
, Cambridge, UK
, Chap. 8.4.
Maugis
, D.
, 1999, Contact, Adhesion and Rupture of Elastic Solids
, Springer-Verlag
, Berlin, Germany
, Chaps. 3–4.5.
Chen
, Y. H.
, Polonsky
, I. A.
, Chung
, Y. W.
, and Keer
, L. M.
, 2002, “Tribological Properties and Rolling-Contact-Fatigue Lives of TiN∕SiNx Multilayer Coatings
,” Surf. Coat. Technol.
0257-8972, 154
(2–3
), pp. 152
–161
.6.
Veprek
, S.
, Mukherjee
, S.
, Karvankova
, P.
, Männling
, H. D.
, He
, J. L.
, Moto
, K.
, Prochazka
, J.
, and Argon
, A. S.
, 2003, “Hertzian Analysis of the Self-Consistency and Reliability of the Indentation Hardness Measurements on Superhard Nanocomposite Coatings
,” Thin Solid Films
0040-6090, 436
(2
), pp. 220
–231
.7.
Tayebi
, N.
, and Polycarpou
, A. A.
, 2005, “Reducing the Effects of Adhesion and Friction in Microelectromechanical Systems (MEMSs) Through Surface Roughening: Comparison Between Theory and Experiments
,” J. Appl. Phys.
0021-8979, 98
(7
), p. 073528
.8.
Sari
, O. T.
, Adams
, G. G.
, and Muftu
, S.
, 2005, “Nano-Scale Effects in the Sliding and Rolling of a Cylinder on a Substrate
,” ASME J. Appl. Mech.
0021-8936, 72
(5
), pp. 633
–640
.9.
Shi
, X.
, and Polycarpou
, A. A.
, 2005, “An Elastic-Plastic Hybrid Adhesion Model for Contacting Rough Surfaces in the Presence of Molecularly Thin Lubricant
,” J. Colloid Interface Sci.
0021-9797, 290
(2
), pp. 514
–525
.10.
Burfler
, H.
, 1959, “Theorie der rollenden Reibung
,” Ing.-Arch.
0020-1154, 27
, pp. 207
–247
.11.
Carter
, F. W.
, 1926, “On the Action of a Locomotive Driving Wheel
,” Proc. R. Soc. London, Ser. A
1364-5021, 112
, pp. 151
–157
; more detail description can be found in Chap. 12 of (33).12.
Muskhelishvili
, N. I.
, 1953, Some Basic Problems of the Mathematical Theory of Elasticity
, 3rd ed., P. Noordhoff
, Groningen
, Chaps. 17–19.13.
Achenbach
, J. D.
, Keer
, L. M.
, Khetan
, R. P.
, and Chen
, S. H.
, 1979, “Loss of Adhesion at the Tip of an Interface Crack
,” J. Elast.
0374-3535, 9
(4
), pp. 397
–424
.14.
Dugdale
, D. S.
, 1960, “Yielding of Steel Sheets Containing Slits
,” J. Mech. Phys. Solids
0022-5096, 8
(2
), pp. 100
–104
.15.
Johnson
, K. L.
, Kendall
, K.
, and Roberts
, A. D.
, 1971, “Surface Energy and Contact of Elastic Solids
,” Proc. R. Soc. London, Ser. A
1364-5021, 324
(1558
), pp. 301
–342
.16.
Derjaguin
, B. V.
, Muller
, V. M.
, and Toporov
, M.
, 1975, “Effect of Contact Deformations on Adhesion of Particles
,” J. Colloid Interface Sci.
0021-9797, 53
(2
), pp. 314
–326
.17.
Hughes
, B. D.
, and White
, L. R.
, 1979, “Soft Contact Problems in Linear Elasticity
,” Q. J. Mech. Appl. Math.
0033-5614, 32
, pp. 445
–471
.18.
Barquins
, M.
, 1988, “Adherence and Rolling Kinetics of a Rigid Cylinder in Contact With a Natural Rubber Surface
,” J. Adhes.
0021-8464, 26
(1
), pp. 1
–12
.19.
Baney
, J. M.
, and Hui
, C.-Y.
, 1997, “A Cohesive Zone Model for the Adhesion of Cylinder
,” J. Adhes. Sci. Technol.
0169-4243, 11
, pp. 393
–406
.20.
Chen
, S. H.
, and Gao
, H. J.
, 2006, “Non-Slipping Adhesive Contact of an Elastic Cylinder on Stretched Substrates
,” Proc. R. Soc. London, Ser. A
1364-5021, 462
(2065
), pp. 211
–228
.21.
Spence
, D. A.
, 1968, “Self Similar Solutions to Adhesive Contact Problems With Incremental Loading
,” Proc. R. Soc. London, Ser. A
1364-5021, 305
(1480
), pp. 55
–74
.22.
Hasebe
, N.
, and Qian
, J.
, 1999, “Fundamental Solution of a Circular Rigid Punch Problem for a Half Plane
,” Eng. Anal. Boundary Elem.
0955-7997, 23
, pp. 841
–846
.23.
Hasebe
, N.
, Okumura
, M.
, and Nakamura
, T.
, 1989, “Frictional Punch and Crack in Plane Elasticity
,” J. Eng. Mech.
0733-9399, 115
, pp. 1137
–1149
.24.
Borodich
, F. M.
, and Keer
, L. M.
, 2004, “Contact Problems and Depth-Sensing Nanoindentation for Frictionless and Frictional Boundary Conditions
,” Int. J. Solids Struct.
0020-7683, 41
(9–10
), pp. 2479
–2499
.25.
Borodich
, F. M.
, and Keer
, L. M.
, 2004, “Evaluation of Elastic Modulus of Materials by Adhesive (No-Slip) Nano-Indentation
,” Proc. R. Soc. London, Ser. A
1364-5021, 460
(2042
), pp. 507
–514
.26.
Mossakovskii
, V. I.
, 1954, “The Fundamental Mixed Problem of the Theory of Elasticity for a Half-Space With a Circular Line Separating the Boundary Conditions
,” J. Appl. Math. Mech.
0021-8928, 18
, pp. 187
–196
.27.
Kim
, K. S.
, McMeeking
, R. M.
, and Johnson
, K. L.
, 1998, “Adhesion, Slip, Cohesive Zones and Energy Fluxes for Elastic Spheres in Contact
,” J. Mech. Phys. Solids
0022-5096, 46
(2
), pp. 243
–266
.28.
Greenwood
, J. A.
, and Johnson
, K. L.
, 1998, “An Alternative to the Maugis Model of Adhesion Between Elastic Spheres
,” J. Phys. D
0022-3727, 31
(22
), pp. 3279
–3290
.29.
Johnson
, K. L.
, and Greenwood
, J. A.
, 1998, “An Adhesion Map for the Contact of Elastic Spheres
,” J. Colloid Interface Sci.
0021-9797, 192
(2
), pp. 326
–333
.30.
Yao
, H.
, and Gao
, H. J.
, 2006, “Mechanics of Robust and Releasable Adhesion in Biology: Bottom-up Designed Hierarchical Structures of Gecko
,” J. Mech. Phys. Solids
0022-5096, 54
(6
), pp. 1120
–1146
.31.
Needleman
, A.
, 1987, “A Continuum Model for Void Nucleation by Inclusion Debonding
,” ASME J. Appl. Mech.
0021-8936, 54
(3
), pp. 525
–531
.32.
Hao
, S.
, Liu
, W. L.
, Moran
, B.
, and Olson
, G. B.
, 2003, “A Hierarchical Multi-Physics Constitutive Model for Steels Design
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 193
(17–20
), pp. 1865
–1908
.33.
Barber
, J. R.
, 2003, Elasticity
, 2nd ed., Kluwer Academic
, Dordrecht, Netherlands
, Chap. 12.34.
Hamaker
, H. C.
, 1937, “The London—Van Der Waals Attraction Between Spherical Particles
,” Physica (Amsterdam)
0031-8914, 4
(10
), pp. 1058
–1072
.35.
Kogut
, L.
, and Etsion
, I.
, 2004, “A Static Friction Model for Elastic-Plastic Contacting Rough Surface
,” ASME J. Tribol.
0742-4787, 126
, pp. 34
–40
.Copyright © 2007
by American Society of Mechanical Engineers
You do not currently have access to this content.
