Refined solutions of thermal lubrication problems generally require fine mesh and many iteration steps. To solve these difficulties, Elrod and Brewe [1–2] proposed an efficient algorithm based on the use of Lobatto point quadrature. Within this approach, the unknown temperature across the film is written in a series of Legendre polynomials. Over the years, the deterministic EHL approach has been widely applied, however, the probabilistic EHL methodology is still used when the main interest of the engineer is directed toward computations of bulk properties. This paper presents an application of the Lobatto point quadrature within a probabilistic EHL algorithm for the computation of the load supported by the fluid, the elastically deformed asperities and the plastically deformed asperities in a mixed EHL contact with either isotropic of non-isotropic roughness.

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