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Finite element method for starved hydrodynamic lubrication with film separation and free surface effects

机译：带有膜分离和自由表面效应的缺乏流体动力润滑的有限元方法

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摘要

This paper proposes a numerical method for determining the evolution of lubricant film thickness and pressure in partially and fully flooded regions of a hydrodynamic contact between two non-conformal rigid surfaces. The proposed method accounts for the classical Reynolds equation within the fully flooded region and for film separation with surface tension driven flow in the partially flooded region, while at the same time it resolves the a priori unknown boundary between the two regions. Additionally it deals with transitions between wetted, partially flooded regions to dry regions, where the film thickness is zero. Both pressure and film thickness fields are considered as unknowns to solve for in each time step and they are approximated through quadratic B-spline finite elements. The geometry of the gap between the rigid surfaces delimiting the lubricant is accounted for in the form of a unilateral contact condition. Appropriate complementarily conditions with respect to separation or no penetration and no slip between the lubricant and the rigid surfaces are enforced by means of a weighted residual formulation. (C) 2018 Elsevier B.Y. All rights reserved.
机译：本文提出了一种数值方法，用于确定两个非共形刚性表面之间的流体动力接触的部分和完全淹没区域中润滑剂膜厚度和压力的演变。所提出的方法考虑了完全淹没区域内的经典雷诺方程，并且考虑了部分淹没区域中具有表面张力驱动的流动的膜分离，同时解决了两个区域之间的先验未知边界。另外，它还处理了润湿的，部分浸水的区域到干燥区域之间的过渡，在过渡区域中膜厚度为零。压力场和膜厚场均被视为要在每个时间步中求解的未知数，并且它们是通过二次B样条有限元近似的。限定润滑剂的刚性表面之间的间隙的几何形状以单侧接触状态的形式解决。借助加权的残留配方，可以实现有关分离或无渗透以及润滑剂与刚性表面之间无滑动的适当补充条件。 （C）2018年Elsevier B.Y.版权所有。

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