Analytical solution of Reynolds equation under dynamic conditions

The flow in the clearance heavily influences the lubrication performance of journal bearing. Therefore, it is important to study the flow mechanism in journal bearing. As known, the pressure distribution in bearing clearance can be described with Reynolds equation. In this paper, unsteady form of Reynolds equation was simplified and nondimensionalized at first, based on certain assumptions. Then, the equation was solved with regular perturbation method, obtaining the analytical solution. At the end, the results of our work were compared with the results of infinitely short journal bearing model, Vignolo etal. (Approximate analytical solution to Reynolds equation for finite length journal bearings. Tribol Int 2011; 44: 1089-1099), and numerical simulations. The comparison implies that our results show more coincidence with the numerical results in a wider range.