Surface roughness has a significant effect on the contact properties of heavy loaded contact pairs like gears,bearings,cams,etc.The friction coefficient depends on the anisotropy of surface roughness under heavy-loading working conditions.Measured surface roughness can be decomposed into a series of sinusoidal waviness with different waviness and amplitude.Hence,a sinusoidal waviness was considered to simulate surface roughness and a transient elastohydrodynamically Lubricated (TEHL) point contact model was proposed.A robust multi-level method with innovative constructions of the coarse grid was developed to solve the convergence problem of rough surface lubrication contacts.Influence of surface roughness anisotropy on the friction coefficient was investigated.Simulation results reveal that the surface roughness anisotropy influences surface deformation through variations of the pressure as well as oil film thickness distributions,thereby affecting the friction coefficient.An empirical formula was proposed to quantify the effects of surface roughness anisotropy on the friction coefficient.It indicates that the transition from the full film to mixed lubrication not only depends on the working condition parameters like load and speed,but also depends on the surface roughness anisotropy.