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Research Papers: Contact Mechanics

Effect of Roughness on Frictional Energy Dissipation in Presliding Contacts

[+] Author and Article Information
Deepak B. Patil

Department of Mechanical Engineering,
University of Wisconsin–Madison,
1513 University Avenue,
Madison, WI 53706

Melih Eriten

Department of Mechanical Engineering,
University of Wisconsin–Madison,
1513 University Avenue,
Madison, WI 53706
e-mail: eriten@wisc.edu

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received January 2, 2015; final manuscript received July 17, 2015; published online August 31, 2015. Assoc. Editor: Mircea Teodorescu.

J. Tribol 138(1), 011401 (Aug 31, 2015) (14 pages) Paper No: TRIB-15-1003; doi: 10.1115/1.4031185 History: Received January 02, 2015; Revised July 17, 2015

A finite element model (FEM) is used to investigate the effect of roughness on the frictional energy dissipation for an elastic contact subjected to simultaneous normal and tangential oscillations. Frictional energy losses are correlated against the maximum tangential load as a power-law where the exponents show the degree of nonlinearity. Individual asperity is shown to undergo similar stick–slip cycles during a loading period. Taller asperities are found to contribute significantly to the total energy dissipation and dominate the trends in the total energy dissipation. The authors' observations for spherical contacts are extended to the rough surface contact, which shows that power-law exponent depends on stick durations individual asperity contacts experience. A theoretical model for energy dissipation is then validated with the FEM, for both spherical and rough surface contacts. The model is used to study the influence of roughness parameters (asperity density, height distribution, and fractal dimension) on magnitude of energy dissipation and power-law exponents. Roughness parameters do not influence the power-law exponents. For a phase difference of π/2 between normal and tangential oscillations, the frictional energy dissipation shows quadratic dependence on the tangential fluctuation amplitude, irrespective of the roughness parameters. The magnitude of energy dissipation is governed by the real area of contact and, hence, depends on the surface roughness parameters. Larger real area of contact results in more energy under similar loading conditions.

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Figures

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Fig. 1

(a) FEM of a rigid flat plate on a deformable sphere and (b) close-up of mesh near contact

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Fig. 2

(a) FEM of a rigid flat plate on a patterned surface with 25 asperities and (b) close-up of mesh near contact at the asperities

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Fig. 3

Periodic out-of-phase loading cycle in PQ-space for phases: ϕ = π/2, P1# = 0.15, and Q1# = 0.2

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Fig. 4

Snapshots of the contact showing the stick and slip region for phases: ϕ = π/2, P1# = 0.15, and Q1# = 0.2 at various points in the loading cycle shown in Fig. 3: (a) at point B, (b) at point C, (c) at point D, and (d) just before point A

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Fig. 5

Dimensionless energy dissipation as function of Q1# from rough surface FEM with multiple asperities in contact for P1# = 0.15 and phase ϕ = π/2

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Fig. 6

Comparing dimensionless energy dissipation (as function of Q1#) from spherical FEM and from PCB model for P1# = 0.2 for (a) phase 0 and (b) phase ϕ = π/2

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Fig. 7

Snapshot of the contact in the forward slip at a point with maximum tangential load and decreasing normal load in PQ loading cycle for P1# = 0.2, Q1# = 0.2, and phase, ϕ = π/2 for spherical FEM

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Fig. 8

Normal compliance versus normal load for d/R = 0.7 for FEM with multiple asperities in contact and comparison with CEP model

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Fig. 9

Comparing dimensionless energy dissipation (as function of Q1#) from rough surface FEM with single asperity in contact and from PCB model for P1# = 0.15 for (a) phase 0 and (b) phase ϕ = π/2

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Fig. 10

Snapshot of the contact in the forward slip at a point of maximum tangential load and decreasing normal load in PQ loading cycle for P1# = 0.15, Q1# = 0.2, and phase, ϕ = π/2 for rough surface FEM with single asperity in contact

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Fig. 11

Comparing dimensionless energy dissipation (as function of Q1#) from rough surface FEM with multiple asperities in contact and from PCB model for P1# = 0.15 for (a) phase 0 and (b) phase ϕ = π/2

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Fig. 12

Snapshot of the contact in the forward slip at a point with maximum tangential load and decreasing normal load in PQ loading cycle for P1#  = 0.15, Q1#  = 0.2, and phase, ϕ = π/2 for rough surface FEM with multiple asperities in contact

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Fig. 13

An example power spectral density plot

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Fig. 14

Dimensionless energy dissipation as function of Q1# for P1# = 0.2, phase ϕ = π/2 and for different fractal dimensions on (a) log–log plot showing power-law dependency and (b) linear plot

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Fig. 15

Normal compliance versus normal load for different d/R values

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Fig. 16

Dimensionless energy dissipation as function of Q1# for P1# = 0.2, phase ϕ = π/2 and for different asperity densities on (a) log–log plot showing power-law dependency and (b) linear plot

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Fig. 17

Power spectral density for different asperity densities

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Fig. 18

Different asperity height distributions: (a) normal distribution, (b) sine distribution, (c) Weibull distribution, and (d) uniform distribution

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Fig. 19

Normal compliance versus normal load for (a) different asperity height distribution and (b) for normal and uniform distribution at high normal load

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Fig. 20

Dimensionless energy dissipation as function of Q1# for P1#  = 0.2, phase ϕ = π/2, and d/R = 1.5 for different asperity height distributions on (a) log–log plot showing power-law dependency and (b) linear plot

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