A numerical solution for a soft line elastohydrodynamic lubrication contact problem with sinusoidal roughness using the Chebyshev polynomials

A sinusoidal roughness model for the elastohydrodynamic problem of a low elastic modulus semi-infinite solid is investigated numerically. Both pressure and surface deformation are expanded in terms of the Chebyshev polynomials of the first kind T-n(x), and hence the governing equations are reduced to a finite set of non-linear equations using the orthogonality property of T-n(x). The influences of the elasticity parameter and the rough surface parameters, such as roughness amplitude, wavelength and phase angle, are examined. The obtained results show good agreement with existing results for a smooth model, and similar characteristics to those reported for a rough elastic layer.