A generalized compressible Reynolds lubrication equation with bounded contact pressure

A new modified Reynolds equation is derived based on physical principles for rarefied gas for compressible and extremely thin layer gas lubrication. For the one-dimensional problem, theoretical analysis and numerical simulation are employed to show that the new equation does not predict an unphysical unbounded pressure singularity in the limit of contact between the bearing surface and the moving surface. We also show the same is true for other existing models with higher than first order slippage correction, which introduce additional diffusion terms that are functions of the spacing with similar order to that of the convection terms. These developments remove the ambiguity of some previously published analyses and correct prior erroneous statements that all existing generalized Reynolds equation models predict nonintegrable singular pressure fields in the limit of contact. The asymptotic analysis also supplies a means for deriving the needed additional boundary condition at the boundary of a contact region. For the two-dimensional problem, we show by numerical analysis that there are also no unbounded contact pressure singularities for the new model and other models with corrections higher than first order, and that the singularity is weaker than in the one-dimensional case for these lower order correction models due to the cross diffusion effect introduced by the additional dimension.