A semi-analytical approach to the elastic loading behaviour of rough surfaces

Xiaogang ZHANG; Yali ZHANG; Zhongmin JIN

doi:10.1007/s40544-019-0320-4

Friction 2020, 8(5): 970-981 https://doi.org/10.1007/s40544-019-0320-4

Research Article |

Open Access | Issue | Published: 05 December 2019

A semi-analytical approach to the elastic loading behaviour of rough surfaces

Show Author's Information Hide Author's Information Xiaogang ZHANG^¹, Yali ZHANG^¹(

), Zhongmin JIN^{¹^,²^,³}

1 School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China

2 School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China

3 Schoolof Mechanical Engineering, University of Leeds, Leeds LS2 9JT, UK

Keywords:

surface roughness, real contact area, interfacial stiffness, normal contact stiffness

Cite this article:

ZHANG X, ZHANG Y, JIN Z. A semi-analytical approach to the elastic loading behaviour of rough surfaces. Friction, 2020, 8(5): 970-981. https://doi.org/10.1007/s40544-019-0320-4

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Abstract

The elastic loading behaviour of rough surfaces is derived based on the physical understanding of the contact phenomena, where the pressure distribution is analytically obtained without any negative values or convergence problems, thus the evolution of the contact behaviour is obtained in a semi-analytical manner. Numerical results obtained by the proposed approach facilitate the understanding of the contact behaviour in the following aspects: 1) the ratio of contact area to load decreases with an increase in real contact area; 2) normal approach-load relationship is approximated by an exponential decay under relatively small loads and a linear decay under relatively large loads; and 3) average gap shows an exponential relationship with load only in moderate load range.

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A semi-analytical approach to the elastic loading behaviour of rough surfaces

Show Author's information Hide Author's Information Xiaogang ZHANG^¹, Yali ZHANG^¹(

), Zhongmin JIN^{¹^,²^,³}

1 School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, China

2 School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China

3 Schoolof Mechanical Engineering, University of Leeds, Leeds LS2 9JT, UK

Abstract

Keywords: surface roughness, real contact area, interfacial stiffness, normal contact stiffness

References(24)

[1]

V A Yastrebov, G Anciaux, J F Molinari. Contact between representative rough surfaces. Phys Rev E 86(3): 035601 (2012)

Google Scholar

[2]

B N J Persson. Elastoplastic contact between randomly rough surfaces. Phys Rev Lett 87(11): 116101 (2001)

Google Scholar

[3]

O Ben-David, S M Rubinstein, J Fineberg. Slip-stick and the evolution of frictional strength. Nature 463(7277): 76-79 (2010)

Google Scholar

[4]

A Ovcharenko, G Halperin, I Etsion, M Varenberg. A novel test rig for in situ and real time optical measurement of the contact area evolution during pre-sliding of a spherical contact. Tribol Lett 23(1): 55-63 (2006)

Google Scholar

[5]

S Hyun, L Pei, J F Molinari, M O Robbins. Finite-element analysis of contact between elastic self-affine surfaces. Phys Rev E 70(2): 026117 (2004)

Google Scholar

[6]

R Buczkowski, M Kleiber, G Starzynski. Normal contact stiffness of fractal rough surfaces. Arch Mech 66(6): 411-428 (2014)

Google Scholar

[7]

R Pohrt, V L Popov. Normal contact stiffness of elastic solids with fractal rough surfaces. Phys Rev Lett 86(10): 104301 (2012)

Google Scholar

[8]

J R Barber. Bounds on the electrical resistance between contacting elastic rough bodies. Proc Roy Soc Lond Ser A: Math, Phys Eng Sci 459(2029): 53-66 (2003)

Google Scholar

[9]

W J Pan, X P Li, L L Wang, N Guo, J X Mu. A normal contact stiffness fractal prediction model of dry-friction rough surface and experimental verification. Eur J Mech - A/Solids 66: 94-102 (2017)

Google Scholar

[10]

X Shi, A A Polycarpou. Measurement and modeling of normal contact stiffness and contact damping at the meso scale. J Vib Acoust 127(1): 52-60 (2005)

Google Scholar

[11]

R Q Wang, L D Zhu, C X Zhu. Research on fractal model of normal contact stiffness for mechanical joint considering asperity interaction. Int J Mech Sci 134: 357-369 (2017)

Google Scholar

[12]

J F Archard. Elastic deformation and the laws of friction. Proc Roy Soc Lond Ser A: Math, Phys Sci 243(1233): 190-205 (1957)

Google Scholar

[13]

J A Greenwood, J B P Williamson. Contact of nominally flat surfaces. Proc Roy Soc Lond Ser A: Math, Phys Sci 295(1442): 300-319 (1966)

Google Scholar

[14]

A W Bush, R D Gibson, G P Keogh. The limit of elastic deformation in the contact of rough surfaces. Mech Res Commun 3(3): 169-174 (1976)

Google Scholar

[15]

A W Bush, R D Gibson, T R Thomas. The elastic contact of a rough surface. Wear 35(1): 87-111 (1975)

Google Scholar

[16]

X F Tian, B Bhushan. A numerical three-dimensional model for the contact of rough surfaces by variational principle. J Tribol 118(1): 33-42 (1996)

Google Scholar

[17]

J A Greenwood, C Putignano, M Ciavarella. A Greenwood & Williamson theory for line contact. Wear 270(3-4): 332-334 (2011)

Google Scholar

[18]

M H Müser, W B Dapp, R Bugnicourt, P Sainsot, N Lesaffre, T A Lubrecht, B N J Persson, K Harris, A Bennett, K Schulze, et al. Meeting the contact-mechanics challenge. Tribol Lett 65(4): 118 (2017)

Google Scholar

[19]

W Manners, J A Greenwood. Some observations on Persson’s diffusion theory of elastic contact. Wear 261(5-6): 600-610 (2006)

Google Scholar

[20]

R W Carpick. The contact sport of rough surfaces. Science 359(6371): 38 (2018)

Google Scholar

[21]

K L Johnson. Contact Mechanics. Cambridge (UK): Cambridge University Press, 1987.

[22]

I A Polonsky, L M Keer. A fast and accurate method for numerical analysis of elastic layered contacts. J Tribol 122(1): 30-35 (2000)

Google Scholar

[23]

I A Polonsky, L M Keer. A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques. Wear 231(2): 206-219 (1999)

Google Scholar

[24]

B N J Persson. Contact mechanics for randomly rough surfaces. Surf Sci Rep 61(4): 201-227 (2006)

Google Scholar

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Acknowledgements

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Publication history

Received: 21 March 2019

Revised: 10 June 2019

Accepted: 28 July 2019

Published: 05 December 2019

Issue date: October 2020

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Acknowledgements

The authors acknowledge the financial supports by the National Key Research and Development Program of China (2016YFF0204305), the National Natural Science Foundation of China (51775460 and 51905456), and the China Postdoctoral Science Foundation (2019M653836XB).

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