Abstract
The numerical prediction of load capacity, stiffness, power loss of hydrostatic journal bearings must be performed for technical applications. In this contribution hydrostatic bearings consisting of porous material are considered. Porous hydrostatic bearings have the advantage that no pressure erosion occurs and that the flow medium can be led homogenously to the gap between shaft and bearing. It is still a problem to design such bearings because the flow in the porous material must be taken into account. There is a simple flow model (SFM) available to calculate quickly the load capacity, stiffness, power loss. This model which is based on the assumption that the flow inside the porous material is axially symmetric works well provided that the eccentricity is small (dimensionless eccentricity e/h0 < 0.5). For large eccentricities — larger than e/h0 > 0.5 the axially symmetric assumption is too strong violated and the results for load capacity, stiffness become inaccurate. Therefore an improved model was developed which is described in the present contribution. This improved model couples the Reynolds equation for hydrodynamic lubrication (REHL) with Darcy Law as it had already been done for the aforementioned fast working SFM. The improved model is not based on the axially symmetric assumption but models the flow completely inside the porous material, i.e. Darcys Law is applied for the porous material without making any assumptions. By the application of the new model, its short name is Full Darcy’s Law (FDL) Model, bearings with high eccentricities can be designed. The application of Darcys Law leads to a Laplace equation for the static pressure distribution in the porous material which is coupled with the REHL. It is described how the resulting equation system is solved by a finite difference method. In this contribution the fast working SFM is described shortly again. The main emphasis lies on the introduction of the FDL-model which needs more computer resources for designing a porous bearing than the SFM. It is explained in detail how the coupling between Darcy Law (Laplace equation) and the REHL is realized. A comparison between the results of both models is shown and the differences are interpreted. Additionally, CFD results are used in order to validate the results of the FDL-model.
