On the Numerical Accuracy of Rough Surface EHL Solution

Numerical solution of rough surface elastohydrodynamic lubrication (EHL) is of great importance. In recent years, research efforts have been focused on deterministic modeling, because it is proven to be capable of predicting detailed contact and lubrication characteristics based on measured three-dimensional machined surface topography in a wide range of operating conditions. The accurate calculation of roughness derivatives, ∂S/∂X and ∂S/∂T, is found to be crucial for numerically solving EHL problems, especially if machined roughness with high-frequency components is involved. When discretized rough surfaces are employed, one may have to handle three different discretization grids, one for the stationary solution domain of the Reynolds equation and the other two for the moving rough surfaces in contact. Two numerical ways can be employed to fulfill the computation of ∂S/∂X and ∂S/∂T. One is to interpolate the topographic heights into the solution domain grid and then conduct the derivation calculations there. The other is to do derivations first in the surface grids and then interpolate the obtained derivatives into the solution mesh. In order to compare these two ways based on an accuracy analysis, a transverse sinusoidal rough surface is exploited and the effects of mesh spacing, differential scheme, interpolation method, and roughness wavelength on numerical errors of ∂S/∂X and ∂S/∂T are investigated. It is found that the appropriate way to minimize the errors is to ensure that the surface grids are considerably denser than that of the solution domain and to conduct derivation calculation first on the surface grids. A densified surface mesh may lead to a great reduction in numerical errors without causing any significant increase in the computing time. Densification of the solution domain mesh, on the other hand, is more difficult because it would result in a large increase in computational burden. It is also found that high-order differential schemes and interpolation methods are helpful to improve accuracy. Large roughness wavelengths lead to smaller numerical errors, but roughness amplitude has no influence on numerical accuracy.