Two-dimensional Hydrodynamic Pad Bearing Design Optimization for Maximum Load Capacity under the Navier Slip Boundary Condition on its Stationary Surface

This work focuses on the influence of the Navier slip/adhesion boundary condition on the hydrodynamic performances of a two-dimensional non-conventional pad bearing. The modified Reynolds equation governing the hydrodynamic behavior of such a bearing, in which the slip condition is assumed to be partially or fully applied on its stationary surface, is established. The effect induced by the convergence ratio, slip coefficient, and slip zone extent and position on the pad bearing’s performances, including load capacity, friction force on the moving surface, and required lubrication flow rate, is evaluated and discussed. The numerical results show that introducing the slip/adhesion condition significantly affects the hydrodynamic performances of a non-conventional pad bearing. Notably, it can support a load even in a divergent configuration or with parallel surfaces. By applying a constrained optimization procedure based on the modified Hooke and Jeeves method, which proves to be highly effective, the optimal values of the convergence ratio, the slip coefficient, and the slip zone extent and position that maximize the load capacity are determined. The optimal slip zone is shaped as a rectangle located at the hydrodynamic contact inlet. A comparative analysis between the optimal non-conventional pad bearing and the conventional configuration is carefully conducted. The impact of the slip/adhesion condition on the slip velocity fields and the flow velocity distribution within the lubricant film is also investigated and discussed. Finally, comparisons with results from the literature confirm the relevance of this study.