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Research Papers

On the Contact of Curved Rough Surfaces: Contact Behavior and Predictive Formulas

[+] Author and Article Information
Ali Beheshti

Department of Mechanical and
Industrial Engineering,
Louisiana State University,
2508 Patrick Taylor Hall,
Baton Rouge, LA 70803

M. M. Khonsari

Department of Mechanical and
Industrial Engineering,
Louisiana State University,
2508 Patrick Taylor Hall,
Baton Rouge, LA 70803
e-mail: Khonsari@me.lsu.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 29, 2014; final manuscript received August 22, 2014; accepted manuscript posted August 28, 2014; published online September 24, 2014. Assoc. Editor: Taher Saif.

J. Appl. Mech 81(11), 111004 (Sep 24, 2014) (15 pages) Paper No: JAM-14-1235; doi: 10.1115/1.4028426 History: Received May 29, 2014; Revised August 22, 2014; Accepted August 28, 2014

The statistical microcontact models of Greenwood–Williamson (GW), Kogut–Etsion (KE), and Jackson–Green (JG) are employed along with the elastic bulk deformation of the contacting solids to predict the characteristics of rough elliptical point contact such as the pressure profile, real area of contact, and contact dimensions. In addition, the contribution of the bulk deformation and the asperity deformation to the total displacement is evaluated for different surface properties and loads. The approach involves solving the microcontact and separation equations simultaneously. Also presented are formulas that can be readily used for the prediction of the maximum contact pressure, contact dimensions, contact compliance, real area of contact, and pressure distribution.

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Figures

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Fig. 1

Elliptical point contact of a rough flat surface and smooth ellipsoid

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Fig. 2

Normalized pressure distribution for relatively smooth and rough surfaces at W¯ = 1.5 × 10−4, Γ = 0.0053, Ω = 0.015, and D = 5 (κ = 2.89) based on (a) and (b) GW and (c) and (d) KE and JG models—a¯R and b¯R are the dimensionless contact half length and half width defined in Sec. 4.3.1

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Fig. 3

Normalized pressure distribution for very rough surface at W¯ = 1.5 × 10−4, Γ = 0.0053, Ω = 0.015, and D = 5 (κ = 2.89) based on (a) GW and (b) KE, and JG models

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Fig. 4

Normalized pressure distribution at low and high loads for σ¯ = 1 × 10−4, Γ = 0.0053, Ω = 0.015, D = 5 (κ = 2.89), and ψ = 2.9 based on (a) and (b) GW and (c) and (d) KE and JG models

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Fig. 5

Real area of contact for (a) smooth and (b) rough surfaces at Γ = 0.0053, Ω = 0.015, and D = 5 based on Hertzian, GW, KE, and JG models

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Fig. 6

Real area of contact based on Hertzian, current simulations and results of Cohen et al. [38]

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Fig. 7

Contact radius based on Hertzian, current simulations and experimental results of Kagami et al. [30]. (a) Smooth steel ball on rough copper plate and (b) smooth steel ball on rough steel plate B.

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Fig. 8

Contact compliance based on Hertzian, current simulations and experimental results of Kagami et al. [30]. (a) Smooth steel ball on rough copper plate and (b) smooth steel ball on rough steel plate A.

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Fig. 9

Contact compliance based on Hertzian, current simulations and results of Li et al. [36] (σ¯ = 3.9 × 10−4, β¯ = 2.18 × 10−2, ψ = 5)

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Fig. 10

Total deformation (compliance), asperity deformation and bulk deformation at the center of the contact as a function of applied load for Ω = 0.015 and D = 5

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Fig. 11

Pressure profile based on the numerical calculation and approximated pressure distribution function (a) XZ plane and (b) YZ plane

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