An asperity-based mathematical model for the boundary lubrication of nominally flat metallic contacts

H. Zhang, L. Chang

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


A mathematical model is presented to study the boundary lubrication of nominally flat metallic contacts. It is developed on the basis of the Greenwood-Williamson model, incorporating key aspects of boundary lubrication in asperity contacts. Four variables are used to describe the asperity contact, including micro-contact area, pressure, interfacial shear stress and flash temperature. Furthermore, three probability variables are used to define the interfacial state of an asperity junction that may be covered by the lubricant/additive molecules adsorbed on the surface, protected by a chemical film, or in direct contact with no boundary protection. Governing equations for the seven asperity-level variables are derived based on first-principle considerations of the asperity deformation, frictional heating and kinetics of boundary films. These equations are solved simultaneously to determine the asperity interfacial state and calculate the contact variables. The asperity-level solutions are then integrated to formulate the boundary-lubrication model at the system level with statistical descriptions of the surfaces. Results are presented and analysed including system friction behaviour, surface separation and real area of contact, and the state of boundary lubrication for various operating conditions and surface roughness. Some potential applications of the model are described. The model and the modelling concepts may provide a framework for future boundary-lubrication analysis, incorporating research advances in contact mechanics, tribochemistry and other related fields.

Original languageEnglish (US)
Pages (from-to)1-19
Number of pages19
JournalLubrication Science
Issue number1
StatePublished - Jan 2008

All Science Journal Classification (ASJC) codes

  • Surfaces, Coatings and Films
  • Materials Chemistry


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