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A Two-Scale Approach for Lubricated Soft-Contact Modeling: An Application to Lip-Seal Geometry

DOI: 10.1155/2012/412190

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We consider the case of soft contacts in mixed lubrication conditions. We develop a novel, two scales contact algorithm in which the fluid- and asperity-asperity interactions are modeled within a deterministic or statistic scheme depending on the length scale at which those interactions are observed. In particular, the effects of large-scale roughness are deterministically calculated, whereas those of small-scale roughness are included by solving the corresponding homogenized problem. The contact scheme is then applied to the modeling of dynamic seals. The main advantage of the approach is the tunable compromise between the high-computing demanding characteristics of deterministic calculations and the much lower computing requirements of the homogenized solutions. 1. Introduction Compliant contacts, most commonly known as soft-contacts, are very common in nature (e.g., cartilage lubrication, eye-eyelid contact) and technology (e.g., tires, rubber sealings, adhesives). It has long been stated that the friction and fluid leakage characteristics of wet soft-contacts are strongly related, among the other factors, to the local interactions occurring at the contact interface [1–5]. In the case of randomly rough surfaces, the basic understanding of the role played by the asperity-asperity and fluid-asperity interactions, occurring over a wide range of roughness length-scales, has been largely investigated and debated in the very recent scientific literature [6–12]. Given the (usual) fractal nature of random roughness, a number of interesting phenomena have been highlighted, as for example, the viscous-hydroplaning [6], the viscous flattening [9–15], the fluid-induced roughness anisotropic deformation [10, 11], the local [10, 11] and global [8, 16] fluid entrapment, and many others. The way to deal with random roughness contact mechanics, despite being nontrivial and suffering of a certain description fragmentation, is however well described in the current scientific literature. On the other side, nowadays bio-inspired research [17, 18], together with the widely-spreading practice of surface engineering [19], is showing the many (mainly unexplored) opportunities offered by the physical-chemical ordered modification of surfaces in order to tailor targeted macroscopic contact characteristics, such as adhesion and friction. Bio-inspired adhesive research [20] is probably the best state of the art example of such research trend. However, investigating the combined effect of, let us say, quantized roughness and fluid action has not equally attracted the scientific


[1]  D. B. Hamilton, J. A. Walowit, and C. M. Allen, “A theory of lubrication by micro-irregularities,” Journal of Basic Engineering, vol. 88, p. 177, 1966.
[2]  K. T?nder, “Mathematical verification of the applicability of modified Reynolds equations to striated rough surfaces,” Wear, vol. 44, no. 2, pp. 329–343, 1977.
[3]  D. Dowson, “Modelling of elastohydrodynamic lubrication of real solids by real lubricants,” Meccanica, vol. 33, no. 1, pp. 47–58, 1998.
[4]  B. N. J. Persson, Sliding Friction: Physical Principles and Applications, Springer, 2000.
[5]  K. L. Johnson, Contact Mechanics, Cambridge University Press, 1985.
[6]  B. N. J. Persson and M. Scaraggi, “On the transition from boundary lubrication to hydrodynamic lubrication insoft contacts,” Journal of Physics Condensed Matter, vol. 21, no. 18, Article ID 185002, 2009.
[7]  B. N. J. Persson, “Fluid dynamics at the interface between contacting elastic solids with randomly rough surfaces,” Journal of Physics Condensed Matter, vol. 22, no. 26, Article ID 265004, 2010.
[8]  B. Lorenz and B. N. J. Persson, “Leak rate of seals: effective-medium theory and comparison with experiment,” European Physical Journal E, vol. 31, no. 2, pp. 159–167, 2010.
[9]  B. N. J. Persson and M. Scaraggi, “Lubricated sliding dynamics: flow factors and Stribeck curve,” European Physical Journal E, vol. 34, p. 113, 2011.
[10]  M. Scaraggi, G. Carbone, B. N. J. Persson, and D. Dini, “Lubrication in soft rough contacts: a novel homogenized approach—part I,” Soft Matter, vol. 7, pp. 10395–10406, 2011.
[11]  M. Scaraggi, B. N. J. Carbone, and D. Dini, “Lubrication in soft rough contacts: a novel homogenized approach—part II—discussion,” Soft Matter, vol. 7, pp. 10407–10416, 2011.
[12]  M. Scaraggi, G. Carbone, and D. Dini, “Experimental evidence of micro-EHL lubrication in rough soft contacts,” Tribology Letters, vol. 43, no. 2, pp. 169–174, 2011.
[13]  C. J. Hooke and C. H. Venner, “Surface roughness attenuation in line and point contacts,” Proceedings of the Institution of Mechanical Engineers, Part J, vol. 214, no. 5, pp. 439–444, 2000.
[14]  C. J. Hooke and K. Y. Li, “Rapid calculation of the pressures and clearances in rough, elastohydrodynamically lubricated contacts under pure rolling—part 1: low amplitude, sinusoidal roughness,” Proceedings of the Institution of Mechanical Engineers Part C, vol. 220, no. 6, pp. 901–913, 2006.
[15]  C. H. Venner and A. A. Lubrecht, “An engineering tool for the quantitative prediction of general roughness deformation in EHL contacts based on harmonic waviness attenuation,” Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, vol. 219, no. 5, Article ID J03804, pp. 303–312, 2005.
[16]  M. Scaraggi and B. N. J. Persson, “Time-dependent fluid squeeze-out between soft elastic solids with randomly rough surfaces,” Tribology Letters, vol. 47, no. 3, pp. 409–416, 2012.
[17]  H. Gao, X. Wang, H. Yao, S. Gorb, and E. Arzt, “Mechanics of hierarchical adhesion structures of geckos,” Mechanics of Materials, vol. 37, no. 2-3, pp. 275–285, 2005.
[18]  B. Bhushan, “Bioinspired structured surfaces,” Langmuir, vol. 28, no. 3, pp. 1698–1714, 2012.
[19]  E. Stratakis, A. Ranella, and C. Fotakis, “Biomimetic micro/nanostructured functional surfaces for microfluidic and tissue engineering applications,” Biomicrofluidics, vol. 5, no. 1, Article ID 013411, 2011.
[20]  G. Carbone, E. Pierro, and S. N. Gorb, “Origin of the superior adhesive performance of mushroom-shaped microstructured surfaces,” Soft Matter, vol. 7, no. 12, pp. 5545–5552, 2011.
[21]  M. Varenberg and S. N. Gorb, “Hexagonal surface micropattern for dry and wet friction,” Advanced Materials, vol. 21, no. 4, pp. 483–486, 2009.
[22]  E. Buselli, V. Pensabene, P. Castrataro, P. Valdastri, A. Menciassi, and P. Dario, “Evaluation of friction enhancement through soft polymer micro-patterns in active capsule endoscopy,” Measurement Science and Technology, vol. 21, no. 10, Article ID 105802, 2010.
[23]  M. Scaraggi, “Lubrication of textured surfaces: a general theory for flow and shear stress factors,” Physical Review E, vol. 86, Article ID 026314, 2012.
[24]  M. Scaraggi, “Textured surface hydrodynamic lubrication: discussion,” Tribology Letters, vol. 48, no. 3, pp. 375–391, 2012.
[25]  R. F. Salant, “Modelling rotary lip seals,” Wear, vol. 207, no. 1-2, pp. 92–99, 1997.
[26]  R. F. Salant, “Theory of lubrication of elastomeric rotary shaft seals,” Proceedings of the Institution of Mechanical Engineers, Part J, vol. 213, no. 3, pp. 189–201, 1999.
[27]  M. Hajjam and D. Bonneau, “Elastohydrodynamic analysis of lip seals with microundulations,” Proceedings of the Institution of Mechanical Engineers, Part J, vol. 218, no. 1, pp. 13–21, 2004.
[28]  M. Hajjam and D. Bonneau, “Influence of the roughness model on the thermoelastohydrodynamic performances of lip seals,” Tribology International, vol. 39, no. 3, pp. 198–205, 2006.
[29]  S. R. Harp and R. F. Salant, “An average flow model of rough surface lubrication with inter-asperity cavitation,” Journal of Tribology, vol. 123, no. 1, pp. 134–143, 2001.
[30]  J. de Vicente, J. R. Stokes, and H. A. Spikes, “The frictional properties of Newtonian fluids in rolling—sliding soft-EHL contact,” Tribology Letters, vol. 20, no. 3-4, pp. 273–286, 2005.
[31]  B. J. Hamrock, Fundamentals of Fluid Film Lubrication, McGraw-Hill, 1994.
[32]  B. N. J. Persson, “Theory of rubber friction and contact mechanics,” Journal of Chemical Physics, vol. 115, no. 8, pp. 3840–3861, 2001.
[33]  B. N. J. Persson, “Relation between interfacial separation and load: a general theory of contact mechanics,” Physical Review Letters, vol. 99, no. 12, Article ID 125502, 2007.
[34]  B. N. J. Persson, N. Prodanov, B. A. Krick, et al., “Elastic contact mechanics: percolation of the contact area and fluid squeezeout,” European Physical Journal E, vol. 35, p. 5, 2012.
[35]  N. Patir and H. S. Cheng, “An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication,” Journal of Lubrication Technology, Transactions of ASME, vol. 100, no. 1, pp. 12–17, 1978.
[36]  N. Patir and H. S. Cheng, “Application of average flow model to lubrication between rough sliding surfaces,” Journal of Lubrication Technology, Transactions of ASME, vol. 101, no. 2, pp. 220–230, 1979.
[37]  C. Putignano, L. Afferrante, G. Carbone, and G. P. Demelio, “A new efficient numerical method for contact mechanics of rough surfaces,” International Journal of Solids and Structures, vol. 49, no. 2, pp. 338–343, 2012.


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