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Research Papers: Contact Mechanics

Perfectly Elastic Axisymmetric Sinusoidal Surface Asperity Contact

[+] Author and Article Information
S. Saha

Department of Mechanical Engineering,
Auburn University,
Auburn, AL 36849
e-mail: szs0118@auburn.edu

Y. Xu

Department of Mechanical Engineering,
Auburn University,
Auburn, AL 36849

R. L. Jackson

Department of Mechanical Engineering,
Auburn University,
Auburn, AL 36849
e-mail: jacksr7@auburn.edu

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received July 13, 2015; final manuscript received October 30, 2015; published online February 15, 2016. Assoc. Editor: James R. Barber.

J. Tribol 138(3), 031401 (Feb 15, 2016) (7 pages) Paper No: TRIB-15-1261; doi: 10.1115/1.4031994 History: Received July 13, 2015; Revised October 30, 2015

This work presents a finite element (FE) study of a perfectly elastic axisymmetric sinusoidal-shaped asperity in contact with a rigid flat for different amplitude to wavelength ratios and a wide range of material properties. This includes characterizing the pressure required to cause complete contact between the surfaces. Complete contact is defined as when there is no gap remaining between two contacting surfaces. The model is designed in such a way that its axisymmetric and interaction with the adjacent asperities are considered by the effect of geometry at the base of the asperity. The numerical results are compared to the model of curved point contact for the perfectly elastic case (known as Hertz contact) and Westergaard's solution. Once properly normalized, the nondimensional contact area does not vary with nondimensional load. The critical pressure required to cause complete contact is found. The results are also curve fitted to provide an expression for the contact area as a function of load over a wide range of cases for use in practical applications, such as to predict contact resistance. This could be a stepping stone to more complex models.

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References

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Figures

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Fig. 1

Three-dimensional view of the surface of the sinusoidal asperity at Δ = 0.5 mm and λ = 2 mm

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Fig. 2

Schematic of a sinusoidal asperity loaded with a rigid flat

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Fig. 3

Mesh convergence test for different number of elements and comparison with Hertz (Eq. (14)) and Westergaard equations (Eq. (16))

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Fig. 4

Gradual change in the shape of spherical and sinusoidal asperities from initial contact to complete contact

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Fig. 5

A 2D axisymmetric mesh at contact region of a sinusoidal asperity against a rigid flat (λ = 2 mm and Δ = 0.01 mm)

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Fig. 6

Dimensionless area as a function of dimensionless contact force for Young's modulus of 50 GPa at Δ/λ of 0.005 and Poisson's ratio of 0.20

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Fig. 7

Three-dimensional view of the periodic sinusoidal surface at Δ = 0.5 mm and λ = 2 mm (not characterized in this work)

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Fig. 8

(a) Contact area as a function of average contact force for different Young's modulus at Δ/λ of 0.005 and Poisson's ratio of 0.20; (b) contact area as a function of average contact force for different Poisson's ratios at Δ/λ of 0.005 and Young's modulus of 50 GPa. (c) Contact area as a function of average contact force for different amplitude to wavelength ratios (Δ/λ) at Young's modulus of 50 GPa and Poisson's ratio of 0.20.

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Fig. 9

(a) Dimensionless area as a function of dimensionless contact force for different Young's modulus at Δ/λ of 0.005 and Poisson's ratio of 0.33. (b) Dimensionless area as a function of dimensionless contact force for different Poisson's ratios at Δ/λ of 0.005 and Young's modulus of 50 GPa. (c) Dimensionless area as a function of dimensionless contact force for different amplitude to wavelength ratios (Δ/λ) at Young's modulus of 100 GPa and Poisson's ratio of 0.33.

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Fig. 10

Comparison of FEM results with fitted equation at Young's modulus of 50 GPa, Poisson's ratio of 0.20, and amplitude to wavelength ratio of 0.005

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