Simplified Formulation for Bush, Gibson, and Thomas Model

Abstract

The random process model, also known as the multi-asperity contact model or statistical model, is one of the dominant methodologies for analyzing the contact between nominally flat rough surfaces. In 1975, Bush, Gibson, and Thomas developed a complete random process model (known as the BGT model) assuming that solid–solid contacts occur on the summits of the asperities, which are semi-ellipsoids uniquely described by three random variables (the asperity height and two principal peak curvatures). The Hertzian elliptic contact theory states that the contact area and normal load are implicit functions of the random variables, which results in an original BGT model with a complex formulation. In this study, we used an adapted Hertzian elliptic contact theory to simplify the formulation of the BGT model. The relative contact area to normal load relation predicted by the simplified BGT model perfectly agrees with that of the original formulation. It is anticipated that rough surface contact models with complex asperity interactions can be effectively built under the framework of this simplified BGT model.