Multiscale simulation scheme by using a finite-difference derivative framework for lubrication surface

To exactly describe lubrication problems modeling micro-scale influence in rough lubricated contact is un-avoidable. In this study a novel computational scheme for lubricated problem is presented based on two-scale homogenization method, which facilitates solving the two-scale problem. Homogenization model of mass fluxes is implemented at the micro-scale domain, and represents the influence of surface topography. A linearization method is developed to derive finite derivatives of mass fluxes at the micro-scale domain defined by scale separation. The key strength of the proposed procedure is the finite difference derivative coupling which represents the lubricated problem inclusive of the effect of surface topography. The effectiveness of the proposed multiscale scheme is validated by comparing with the deterministic method. The numerical results show that increasing topography amplitude can improve the performance of journal bearing in terms of load carrying capacity and friction coefficient.