On boundary conditions in lubrication with one dimensional analytical solutions

Shuangbiao Liu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


This work summarizes different boundary conditions for the Reynolds' equation, classifies them using mathematical terms, and demonstrates their effects. Various analytical solutions for 2D journal bearings are presented and the rupture location depends linearly on the eccentricity ratio. With a given eccentricity and inlet position, the inlet pressure is uniquely related to the flow rate inside the bearing if the bearing is not starved nor choked. Furthermore, a general analytical solution of a dimpled step bearing is derived and it demonstrates the invalidity of the Reynolds condition for discontinuous geometry. Cavitation appears in intermediate groove depth of this step bearing.

Original languageEnglish (US)
Pages (from-to)182-190
Number of pages9
JournalTribology International
StatePublished - Apr 2012


  • Analytical
  • Boundary conditions
  • Cavitation
  • Lubrication

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Surfaces and Interfaces
  • Surfaces, Coatings and Films


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