A thermal model for elastohydrodynamic lubrication of rough surfaces

This paper reports on the development of a thermal model that can be used to analyze transient elastohydrodynamic lubrication (EHL) of rough surfaces. The thermal domain is composed of three sub-domains, including the film region and the two bounding solids with the thermal boundaries placed inside the solids at which the temperature variation is insignificant. The irregular and time-varying sub-domains, primarily due to the presence and motion of rough surfaces, are mapped onto rectangular and time-invariant sub-domains so that numerical methods can be easily applied. A control-volume approach is taken to formulate the interfacial conditions between the lubricant film and the bounding solids. Finally, a computational algorithm is developed to calculate the temperature field in high-Peclet-number EHl contacts. The calculation yields results that are shown to be meaningful and consistent through extensive evaluations. A substantial amount of numerical results will be presented in a companion paper.