Elastohydrodynamic Lubrication Modeling by a Cosserat Continuum Theory for Small Polymer Journal Bearings

Abstract

Recent experiments have shown that the elastic deformation behaviors of a polymeric material are consistent with the Cosserat elasticity under nonuniform deformation at a millimeter scale. Thus, an elastohydrodynamic lubrication model in the framework of the Cosserat continuum theory is proposed to explore the lubrication performance that deviates from the classical elastohydrodynamic lubrication theory for the small polymer journal bearings with millimeter size. The elastic deformation of the bearing sleeve made of polymeric material and the pressure distribution in a lubricating film are obtained through an iterative solution of the equation of the Cosserat elasticity and the modified Reynolds’ equations with considering the boundary slippage. The effect of bearing size and Cosserat characteristic lengths for torsion and bending on the lubrication performance of the small polymer journal bearings is studied using the proposed Cosserat elastohydrodynamic lubrication model. It was found that the small changes in film thickness due to the Cosserat effect can result in large changes in film pressure. The Cosserat characteristic length of bending possesses a significant effect on the lubrication behaviors of the journal bearings, because the size effect is mainly caused by the increased apparent modulus due to the bending elastic deformation of the bearing sleeve. The boundary slip behaviors dependent on the Cosserat characteristic length are also studied using the Cosserat elastohydrodynamic model, and the numerical results show that the Cosserat characteristic length changes the optimal geometric parameters of the slip zone in terms of load carrying capacity for the small polymer journal bearings.