Load-Carrying Capacity of the Lubricating Film in the Gap Between Surfaces Textured by Hemispherical Pores

2. General Model And Governing Equations

The study is carried out for a mechanical system with two opposing surfaces divided by a lubricating film. The upper surface is moving and an lower surface is fixed. Both surfaces have equidistantly situated (with period) hemispherical pores of radius. The model geometry and coordinate system are shown in Figure 1.

Figure 1.

Two opposing surfaces with 3 x 2 hemispherical pores; rectangular pore cells, the coordinate system and the relative location of the surfaces at the initial time

In this model both the pore, with radius r₀, and the outside of the pore surface constitute the rectangular pore cell with dimensions 2r₁. Since the pores are arranged regularly, their relative positions are constantly repeated; therefore, we assume that only one of the pore cells, called the control cell, can be studied.

For a lubricating film bounded by a pair of the surfaces covered with pores, the Reynolds equation reads:

All variables in Equation(1) are dimensional; p is the pressure in lubricating film, Pa; x, z – coordinates, m; t – time, sec; h – lubricating film thickness, m; u- velocity of the lower surface, m/sec; and µ is dynamical viscosity of lube, Pa·sec.