Transient elastohydrodynamic point contact analysis using a new coupled differential deflection method Part 1: Theory and validation

The paper presents a transient analysis technique for point contact elastohydrodynamic (EHL) lubrication problems using coupled elastic and hydrodynamic equations. Full coupling is made possible by use of a novel differential deflection formulation. The way in which the differential deflection is incorporated into the overall solution method for a point contact is discussed. A range of spatial and temporal discretization methods are incorporated and compared. The method is validated under transient conditions by a detailed comparison with published work produced using a different, independent method incorporating a moving roughness feature. A comparison of the results with different discretization methods leads to the conclusion that spatial central differencing with a Crank-Nicolson temporal discretization is the most effective finite difference scheme, and this is generally equivalent to the finite element discretization given in detail in the paper. A comparison of the results produced for moving rough surfaces suggests that the finite element formulation is preferred.