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

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

Leonid Burstein (ORT Braude College of Engineering (Retired), Israel)
DOI: 10.4018/IJSEIMS.2021070101
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The load support of a lubricating film that separates the surfaces textured by identical equidistant spaced hemispherical pores was investigated. Two-dimensional time-dependent Reynolds equation is solved numerically for different pore-radius-to-gap and cell-dimension-to-pore-radius ratios and for different relative pore positions of opposite surfaces. The results are compared with the data obtained for the case when only one of the opposite surfaces is covered with pores. The obtained data show a maximum in the carrying capacity of the lubricating film when the cell-to-pore-radii ratio is approximately equal to two, in the case of two opposite surfaces with pores. At small pore radii and with increasing cell dimensions, the load support of two surfaces with pores is much greater than in the case of one surface with pores. This behavior reverses with increasing pore diameter. The presented analysis and the provided MATLAB programs are applicable for mechanisms having rubbing mechanical parts with surfaces covered with pores.
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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 periodIJSEIMS.2021070101.m01) hemispherical pores of radiusIJSEIMS.2021070101.m02. 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.

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