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Research Papers

Frictional Energy Dissipation in Spherical Contacts Under Presliding: Effect of Elastic Mismatch, Plasticity and Phase Difference in Loading

[+] 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 Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 4, 2014; final manuscript received November 4, 2014; accepted manuscript posted November 10, 2014; published online November 19, 2014. Assoc. Editor: Nick Aravas.

J. Appl. Mech 82(1), 011005 (Jan 01, 2015) (11 pages) Paper No: JAM-14-1467; doi: 10.1115/1.4029020 History: Received October 04, 2014; Revised November 04, 2014; Accepted November 10, 2014; Online November 19, 2014

Behavior of friction at material interfaces is inherently nonlinear causing variations and uncertainties in interfacial energy dissipation. A finite element model (FEM) of an elastic–plastic spherical contact subjected to periodic normal and tangential loads is developed to study fundamental mechanisms contributing to the frictional energy dissipation. Particular attention is devoted to three mechanisms: the elastic mismatch between contacting pairs, plastic deformations, and phase difference between the normal and tangential fluctuations in loading. Small tangential loads simulating mild vibrational environments are applied to the model and resulting friction (hysteresis) loops are used to estimate the energy loss per loading cycle. The energy losses are then correlated against the maximum tangential load as a power-law where the exponents show the degree of nonlinearity. Exponents increase significantly with in-phase loading and increasing plasticity. Although increasing elastic mismatch facilitates more dissipation during normal load fluctuations, it has negligible influence on the power-law exponents in tangential loading. Among all the configurations considered, out-of-phase loading with minimal mismatch and no plasticity lead to the smallest power-law exponents; promising linear frictional dissipation. The duration the contact remains stuck during a loading cycle is found to have a predominant influence on the power-law exponents. Thus, controlling that duration enables tunable degree of nonlinearity and magnitude in frictional energy dissipation.

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Figures

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Fig. 1

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

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Fig. 2

Mesh for different normal preloads

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Fig. 3

Dimensionless energy dissipation as a function of Q1# for periodic in-phase loading for obliquity, P1#/Q1# = 0.8 and P1# = 0.2

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Fig. 4

(a) Periodic out-of-phase loading cycle in PQ-space for phase, ϕ = π/2, P1# = 0.2 and Q1# = 0.2, and (b) snapshots of the contact showing the stick and slip region at various points in the loading cycle

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Fig. 5

(a) Periodic out-of-phase loading cycle in PQ-space for phase ϕ = π/2, P1# = 0.2 and different values of Q1#, and (b) corresponding % time the contact is in forward slip, reverse slip, and stick

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Fig. 6

(a) Plot of % energy dissipation during forward slip, reverse slip, and stick for phase ϕ = π/2, P1# = 0.2 and different values of Q1#, (b) snapshots of the contact in the forward slip region at points with Δ marker in the loading cycle in Fig. 5(a) and (c) snapshots of the contact in the reverse slip region at points with “ο” marker in the loading cycle in Fig. 5(a)

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Fig. 7

Dimensionless energy dissipation as function of Q1# for phase ϕ = π/2, P1# = 0.2

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Fig. 8

Power-law exponent, n versus phase difference ϕ for P1# = 0.2 and in Ref. [15]

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Fig. 9

(a) Hysteresis loop due to tangential loading for P1# = 0.2, Q1# = 0.2, and Dundurs' constant, η = 0.7 and (b) dimensionless energy dissipation due to tangential tractions as a function of Q1# for P1# = 0.2, ϕ = π/2 and different values of Dundurs' parameter, η

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Fig. 10

Total dimensionless energy dissipation as a function of Q1# for P1# = 0.2, ϕ = π/2 and different values of Dundurs' parameter, η

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Fig. 11

(a) Dimensionless energy dissipation due to tangential tractions as a function of Q1# for P1# = 0.2, ϕ = π/2, E/Y = 250 and different dimensionless mean preload values, (b) power-law exponent, n versus dimensionless mean preload, Po* for P1# = 0.2, ϕ  = π/2, and E/Y = 250

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Fig. 12

Dimensionless energy dissipation as a function of tangential fluctuation amplitude for dimensionless normal preload, Po* = 2 and Po* = 3

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Fig. 13

Material behavior map for a material with E/Y ratio 250 and adhered contact subjected to tangential oscillations only

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Fig. 14

Power-law exponent, n versus preload fluctuation amplitude, P1#, for ϕ = π/2 and η = 0.07

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