Abstract
An analytic solution of the full incompressible unaveraged Reynolds equation is obtained by regular perturbation expansion for the case of a finite width bearing with transverse roughness. Results show that the unaveraged pressure is first influenced by the roughness statistics at the 0 (ε2) level and is negligibly affected by the details of the roughness distribution. Through second order effects, it is shown that the closure assumption utilized by Christensen and To̸ender in developing their theory for striated roughness effects on incompressible lubrication is correct. That is, for transverse roughness [h = h(x)], h3 and ∂P/∂y are statistically independent. Due to the linearity of the incompressible Reynolds equation, it is likely that a similar approach can be used for the study of fully three-dimensional roughness effects on lubrication in order to reveal the detailed relationship between clearance and pressure.
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