ARTICLE
Determination of contact pressure distribution on frictionless rough surfaces using an optimisation approach: a one-dimensional study
,

,

More details
Hide details
1
Department of Mathematics, State University of Santa Catarina, Joinville, Brazil

2
Department of Mechanical Engineering, Federal University of Technology – Parana, Curitiba, Brazil

3
Department of Mechanical Engineering, Polytechnic School of the University of São Paulo, Brazil

Submission date: 2023-03-20

Final revision date: 2023-04-27

Acceptance date: 2023-04-27

Online publication date: 2023-06-29

Publication date: 2023-07-31

Corresponding author
Marco Antonio Luersen

Department of Mechanical Engineering, Federal University of Technology – Parana, Curitiba, Brazil

Journal of Theoretical and Applied Mechanics 2023;61(3):573-583

KEYWORDS
TOPICS
ABSTRACT
Determining pressures and stresses that arise when mechanical components come into con- tact is crucial for analysis of surface-related failures. In real situations, determining contact pressure and stress distributions is challenging and depends on several factors, such as load, material properties and surface characteristics. This paper describes the determination of contact pressure on rough surfaces using a one-dimensional approach. Elastic, frictionless, unilateral, normal contact between a rough surface and a smooth surface is considered. Lin- ear elastic half-space theory is used, and the contact pressure distribution is obtained by solving an associated optimisation problem. Results are given for a virtual wavy profile and two engineering roughness profiles.

REFERENCES (19)
1.
Barber J.R., 2018, Contact of rough surfaces, [In:] Contact Mechanics. Solid Mechanics and its Applications, Springer, 250, 329-394.

2.
Bemporad A., Paggi M., 2015, Optimization algorithms for the solution of the frictionless normal contact between rough surfaces, International Journal of Solid and Structures, 69-70, 94-105.

3.
Byrd R.H., Hribar M.E., Nocedal J., 1999, An interior point algorithm for large-scale nonlinear programming, SIAM Journal on Optimization, 9, 4, 877-900.

4.
Cottle R., Pang J., Stone R., 1992, The Linear Complementarity Problem, Philadelphia: Society for Industrial and Applied Mathematics.

5.
Fu S., Kor W.S., Cheng F., Seah L.K., 2020, In-situ measurement of surface roughness using chromatic confocal sensor, Procedia CIRP, 94, 780-784.

6.
He X., Liu Z., Ripley L.B., Swensen V.L., Griffin-Wiesner I.J., Gulner B.R., McAndrews G.R., Wieser R.J., Borovsky B.P., Wang Q.J., Kim S.H., 2021, Empirical relationship between interfacial shear stress and contact pressure in micro and macro-scale friction, Tribology International, 155, 106780.

7.
Hills D.A., Nowell D., Sackfield A., 1993, Mechanics of Elastics Contacts, Butterworth-Heinemann.

8.
Jackson R.L., Green I., 2006, A statistical model of elasto-plastic asperity contact between rough surfaces, Tribology International, 39, 9, 906-914.

9.
Johnson K.L., 1985, Contact Mechanics, Cambridge University Press.

10.
Josso B., Burton D.R., Lalor M.J., 2002, Frequency normalized wavelet transform for surface roughness analysis and characterization, Wear, 252, 5-6, 491-500.

11.
Nocedal J., Wright S.J., 2006, Numerical Optimization, New York: Springer, 2a ed.

12.
Persson B.N.J., 2006, Contact mechanics for randomly rough surfaces, Surface Science Reports, 61, 4, 201-227.

13.
Rey V., Bleyer J., 2018, Stability analysis of rough surfaces in adhesive normal contact, Computational Mechanics, 62, 1155-1167.

14.
Sushun K., 1995, The existence of the solution for linear complementary problem, Applied Mathematics and Mechanics, 16, 7, 683-685.

15.
Venner C.H., 1991, Multilevel solution of the EHL line and point contact problems, PhD Thesis, University of Twente, Enschede, The Netherlands.

16.
Wang J., Zhu D., 2020, Interfacial Mechanics: Theories and Methods for Contact and Lubrication, New York: CRC Press, 1st ed.

17.
Weber B., Suhina T., Junge T., Pastewka L., Brouwer A.M., Bonn D., 2018, Molecular probes reveal deviations from Amontons’ law in multi-asperity frictional contacts, Nature Communications, 9, 1, 888.

18.
Zhang F., Liu J., Ding X., Wang R., 2019, Experimental and finite element analyses of contact behaviors between non-transparent rough surfaces, Journal of the Mechanics and Physics of Solids, 126, 87-100.

19.
Zhao J., Vollebregt E.A.H., Oosterlee W.C., 2014, A full multigrid method for linear complementarity problem arising from elastic normal contact problems, Mathematical Modelling and Analysis, 19, 2, 216-240.

 eISSN: 2543-6309 ISSN: 1429-2955