Abstract
Elastohydrodynamic lubrication, or simply soft lubrication, refers to the motion of deformable objects near a boundary lubricated by a fluid, and is one of the key physical mechanisms to minimise friction and wear in natural and engineered systems. Hence it is of particular interest to relate the thickness of the lubricant layer to the entrainment (sliding/rolling) velocity, the mechanical loading exerted onto the contacting elements, and properties of the elastic boundary. In this work we provide an overview of the various regimes of soft lubrication for two-dimensional cylinders in lubricated contact with compliant walls. We discuss the limits of small and large entrainment velocity, which is equivalent to large and small elastic deformations, as the cylinder moves near thick or thin elastic layers. The analysis focusses on thin elastic coatings, both compressible and incompressible, for which analytical scaling laws are not yet available in the regime of large deformations. By analysing the elastohydrodynamic boundary layers that appear at the edge of the contact, we establish the missing scaling laws - including prefactors. As such, we offer a rather complete overview of physically relevant limits of soft lubrication.
Highlights
The introduction of a viscous liquid within the narrow gap between two moving bodies prevents solid–solid contact, reduces friction, minimises wear and allows precise motion control; a process known as lubrication
Pioneering work was done by Dowson & Higginson (1959, 1966) and Hamrock & Dowson (1977), where the complexity of the interaction between deformation and flow led to numerical stability problems at large deformations
Many studies aimed at the derivation of empirical formulas for film thickness prediction under steady conditions from the numerical solutions
Summary
The introduction of a viscous liquid within the narrow gap between two moving bodies prevents solid–solid contact, reduces friction, minimises wear and allows precise motion control; a process known as lubrication. Since the realisation of the essential coupling between deformation and flow for film formation, the study of elasto-hydrodynamic lubrication in engineering (tribology) has been established as a separate field of research. More complex time-varying and extreme operating conditions, such as higher loads and higher temperatures, lead to increased deformation and thinner films, which calls for a better understanding and improved prediction capability for engineering and design. Complex cases of contact geometries with time-varying loading conditions, roughness moving through the contact, contacts with very limited lubrication supply, grease lubricated contacts and coated surfaces are considered, see Wang & Zhu (2019). In spite of the plethora of problems studied and results presented, the fundamental understanding of the physical phenomena and the appropriate scaling laws have developed only relatively slowly.
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