A New Singularity Treatment Approach for Journal Bearing Mixed Lubrication Modeled by the Finite Difference Method With a Herringbone Mesh

Abstract

Steadystate mixed hydrodynamic lubrication of rigid journal bearing is investigated by using a finite difference form of the Patir–Cheng average Reynolds equation under the Reynolds boundary condition. Two sets of discretization meshes, i.e., the rectangular and nonorthogonal herringbone meshes, are considered. A virtualmesh approach is suggested to resolve the problem due to the singularities of pressure derivatives at the turning point of the herringbone mesh. The effectiveness of the new approach is examined by comparing the predicted load with that found in the literature for a smoothsurface case solved in the conventional rectangular mesh. The effects of the skewness angles of symmetric and asymmetric herringbone meshes on the predicted parameters, such as load, friction coefficient, attitude angle, and maximum pressure, are investigated for smooth, rough, and herringbonegrooved bearing surfaces. It is found that the new approach helps to improve the computational accuracy significantly, as demonstrated by comparing the results with and without the treatment of the pressure derivative discontinuity although the latter costs slightly less computational time.