It is reported that a mass-conserving implementation of cavitation for hydrodynamic lubrication model is crucial to avoid errors.However,a significant increase in computational burden would be induced by the mass-conserving treatment of cavitation.In order to solve the hydrodynamic pressure efficiently and accurately,a fast converging numerical approach for calculating the hydrodynamic pressure distribution was proposed by combining Fischer burmsister Newton Schur (FBNS) method and grid refinement(GR) strategy.In this method,FBNS approach is employed to transform the discrete equations of fluid lubrication model into unconstrained equations,so that the equations can be solved using Newton iteration method,the grid refinement strategy is used to take the calculation results of the lubrication model on the coarse grid as the initial value on the fine grid,so as to speed up the convergence speed of the oil film pressure calculation.The converging numerical approach proposed was used to calculate different examples.The results show that compared with the traditional method,with the fast converging numerical approach proposed,the transient problem of the mechanical systems lubricated oil becomes computationally feasible.