Kinematics of transverse real roughness in elastohydrodynamically lubricated line contacts using Fourier analysis

A model is presented that facilitates prediction of the transient solution for the pressure and film thickness in an elastohydrodynamically lubricated line contact for the case of arbitrary surface microgeometry (roughness) under the assumption of Newtonian lubricant behaviour and small roughness amplitude. In the model the two parts of the transient solution (particular integral and complementary function) are calculated for each Fourier component of a surface real roughness and combined to obtain the complete transient solution. As no time-consuming numerical simulations are required, the computational scheme forms a simple and efficient tool for use in a practical engineering environment. To validate the approach, first simple cases such as single dents and harmonic waviness were considered. The predictions obtained for these cases are compared with the results of full numerical simulations, showing good agreement. Subsequently the results obtained for a realistic roughness profile are presented.