Simulation of mixed lubrication of rigid plain journal bearing by finite difference method with a skewed discretisation mesh

Numerical simulation of lubrication of journal bearing often uses a rectangular discretisation mesh. Steady-state mixed hydro-dynamic lubrication of rigid plain journal bearing is investigated by using finite difference form of Patir-Cheng average Reynolds equation under Reynolds boundary condition. Two kinds of non-orthogonal discretisation meshes, i.e., helix mesh and symmetric herringbone mesh are considered respectively. Three difference schemes, i.e.: 1) central finite difference; 2) second order upwinding; 3) a new central finite difference considering the film thickness at the projected positions from the nodes of neighbouring rows; are used to difference the shear induced flow term (i.e., Couette term). The effectiveness of the three schemes is discussed using the skewed discretisation mesh by comparing theoretical predictions of load with that found in the literature for smooth lubrication using the rectangular discretisation mesh. The effect of the skewed angle of mesh on the predicted parameters such as load, friction coefficient, attitude angle and maximum pressure is investigated for both smooth and rough surfaces. It is found that generally these schemes may provide a reasonable satisfactory solution. However, when symmetric herringbone mesh is used, a larger relative deviation is found as the skewed angle is larger and the eccentricity ratio is smaller.