On boundary conditions in lubrication with one dimensional analytical solutions

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.

► Boundary conditions for Reynolds equation are discussed in a systematic fashion.
► Rupture location in the Cameron-Wood solution is linear to eccentricity ratio.
► With given eccentricity and inlet position, inlet pressure ties to flow rate.
► For a dimpled step bearing, intermediate film thickness triggers cavitation.