Theoretical Study on Oil Reduction in Porous Oil Bearings With Running Time

本研究的目的是假设一个理论模型来预测多孔径向轴承内的含油量随时间的变化，该多孔径向轴承只在其结构中初始浸渍的油的情况下运行。在轴承间隙中，液-气(油-气)界面由于油膜中的动水压力而发生运动，油膜的运动受含有所谓滤波项的修正雷诺方程的约束，其运动速度可作为“运动边界”问题来求解。在多孔介质中，假设由油和空气组成的两相流动。油、空气的过滤速度服从相对渗透率的达西定律，相对渗透率是局部含油饱和度的函数，非饱和区的毛管压力对其影响很大。通过求解这两个区域的非稳态连续性方程，以及控制轴承间隙内气液界面和多孔介质中油气流动速度的方程，计算了含油饱和度在轴承间隙和多孔介质中的分布。结果表明：(1)启动后，多孔轴承内的含油量急剧下降。之后，随着运行时间的延长，它逐渐减小，并趋于一个恒定值。多孔基质中含油饱和度随时间的变化与常规实验研究的结果定性一致。(2)多孔基质中油的减少主要是由轴承间隙中的油膜压力引起的，而毛细管压力则抑制了多孔基质中的油，使油保持在多孔基质中。(3)轴承间隙中气液界面的表面张力也会影响多孔基质中的含油饱和度，这将有助于石油从多孔基质渗入轴承间隙。

The purpose of the present study is to suppose a theoretical model predicting the time variation of oil content within the porous journal bearings, which operates with only the oil initially impregnated within its structure. In the bearing clearance, the liquid-gas (oil-air) interface is moved due to the hydrodynamic pressure in the oil film, which is governed by the modified Reynolds equation including a so-called filter term, and its velocity is solved as a problem of "moving boundary". In the porous matrix, the two-phase flow consisting of oil and air is assumed. The filter velocities of oil and air are governed by Darcy's law with relative permeability, which is a function of local oil saturation, and they are significantly influenced by the capillary pressure in the unsaturated region. The distributions of the oil saturation both in the bearing clearance and in the porous matrix are calculated by solving the unsteady-state continuity equations for the two regions, and the equations governing the velocities both of the liquid -gas interface in the bearing clearance and of the oil and air flows in the porous matrix.The results are summarized as follows :(1)Oil content within the porous bearings is reduced steeply just after the start of operation. After that, it decreases gradually with the running time and tends to approach a constant value. This time variation of oil saturation in the porous matrix qualitatively agrees with that shown in the conventional experimental studies.(2)Oil reduction within the porous matrix is mainly induced by the oil-film pressure in the bearing clearance, whereas it is suppressed by the capillary pressure, which contnbutes to keeping the oil in the porous matrix.(3)The surface tension at liquid gas interface in the bearing clearance would also influence the oil saturation in the porous matrix and it will contribute to seepage of oil from the porous matrix into the bearing clearance.