Average MEMT-Field Reynolds Equation for Rough-Surface Lubrication with Application to Electric Polarization

Abstract

Lubrication in electrically driven systems involves coupled mechanical and electromagnetic effects, and the presence of surface roughness further complicates flow transport and pressure generation. In this paper, an average MEMT-field Reynolds equation is developed by extending the Patir–Cheng average-flow framework to incorporate electric and magnetic body-force effects. Flow factors are defined to describe flows driven by field-induced body forces under roughness effect, while hydrodynamic pressure and field induced contributions are treated separately. Electric polarization in dielectric lubricants is used as a representative mechanism to examine whether the field-induced transport requires flow factors distinct from the classical Patir–Cheng flow factors. By analyzing the analogy between the electric polarization potential and the hydrodynamic pressure, and solving corresponding flow-factor model problems, the electric-polarization flow and shear stress factors are equivalent to the Patir–Cheng pressure-flow and shear-stress factors if the polarization potential gradient is independent of local roughness. The lubrication performance of journal bearings is then evaluated using the average flow model to investigate the effects of surface roughness and electric polarization. The results show that surface roughness modifies electric-polarization lubrication with a strong dependence on roughness orientation and bearing geometry. Longitudinally oriented roughness enhances the pressure buildup caused by electric polarization, whereas transversely oriented and isotropic roughness tend to reduce it. The proposed framework provides a general approach for studying lubrication subjected to coupled effects of multifield and engineered rough surfaces.