Effects of Surface Roughness and Additives in Lubrication: Generalized Reynolds Equation and its Application to Elastohydrodynamic Film

Abstract

To study the effects of surface roughness and additives in lubrication, a generalized form of Reynolds equation is derived by taking into account the roughness interaction zones adjacent to the moving rough surfaces as sparsely porous matrices and purely hydrodynamic film of micropolar fluid characterizing the lubricant with additives. A particular, one-dimensional form of this equation is used to study these effects on the elastohydrodynamic (EHD) minimum film thickness at the inlet, between two rough rollers. It is shown that for the low permeability of the roughness zone, the EHD film thickness increases as the mean height of the asperities increases, whereas for the high permeability it decreases. The EHD film thickness is also found to increase with the concentration of the additives and the molecular size of the particles. These results are in conformity at least qualitatively, with various experimental and theoretical investigations, cited in the paper.

A pad roughness model for the analysis of lubrication in the chemical mechanical polishing of a silicon wafer

“…Figure 4 shows the relationship between the average height of the pad roughness zone and the thickness of the fluid film for various concentrations of roughness asperities. The average concentration of roughness asperities is defined as ηa η 1 2 , which roughly reflects the effect of the asperities concentration of the pad surface on the fluid flow beneath a silicon wafer [12]. From figure 4, ha = 0 implies that a pad possesses a smooth surface.…”

“…However, in the other two zones, the rotations are inhibited because of the influence of the roughness, asperities and the porous structure of the pad. Hence, Brinkman equations and Darcy's law, respectively employed to character the slurry flow in the pad roughness zone and in the porous layer zone, are applicable [11,12].…”

“…The effects of pad roughness and porosity on slurry flow are considered according to the Brinkman equations [12]. The flow equations in the pad roughness zone −h a z < 0 can be written as follows:…”

“…In this paper, a three-dimensional model under the light load conditions, based on the micropolar fluid theory, Brinkman equations and Darcy's law [11][12][13], is established. In this model, the effects of pad roughness and some important parameters on slurry flow between the pad and the wafer are taken into account.…”

Effects of couple stresses and surface roughness on the film thickness of heavily loaded rollers

“…The boundary conditions for pressure associated with equation (44) are given by Sinha et al (1987): Equation 117 Equation 118 where h m is the minimum film thickness.…”