A two-scale homogenization method for modelling the hydrodynamic lubrication of mechanical seals with isotropic roughness was developed and presented the influence of surface topography coupled into the lubricating domain. A linearization approach was derived to link the effects of surface topography across disparate scales. Solutions were calculated in a polar coordinate system derived based on the Elrod cavitation algorithm and were determined using homogenization of periodic simulations describing the lubrication of a series of surface topographical features. Solutions obtained for the hydrodynamic lubrication regime showed that the two-scale homogenization approach agreed well with lubrication theory in the case without topography. Varying topography amplitude demonstrated that the presence of surface topography improved tribological performance for a mechanical seal in terms of increasing load-carrying capacity and reducing friction coefficient in the radial direction. A Stribeck curve analysis was conducted, which indicated that including surface topography led to an increase in load-carrying capacity and a reduction in friction. A study of macro-scale surface waviness showed that the micro-scale variations observed were smaller in magnitude but cannot be obtained without the two-scale method and cause significant changes in the tribological performance.

开发了一种用于模拟具有各向同性粗糙度的机械密封的流体动力润滑的两尺度均质化方法，并展示了耦合到润滑域中的表面形貌的影响。推导了一种线性化方法来链接不同比例尺上的表面形貌的影响。在基于 Elrod 空化算法导出的极坐标系中计算解决方案，并使用描述一系列表面地形特征润滑的周期性模拟的均质化来确定。获得的流体动力润滑方案的解决方案表明，在没有地形的情况下，两尺度均质化方法与润滑理论非常吻合。变化的形貌振幅表明，表面形貌的存在改善了机械密封的摩擦学性能，提高了承载能力并降低了径向摩擦系数。进行了 Stribeck 曲线分析，这表明包括表面形貌导致承载能力增加和摩擦减少。宏观尺度表面波纹度研究表明，观察到的微观尺度变化幅度较小，但如果没有两尺度方法则无法获得，并导致摩擦学性能发生显着变化。这表明包括表面地形导致承载能力增加和摩擦减少。宏观尺度表面波纹度研究表明，观察到的微观尺度变化幅度较小，但如果没有两尺度方法则无法获得，并导致摩擦学性能发生显着变化。这表明包括表面地形导致承载能力增加和摩擦减少。宏观尺度表面波纹度研究表明，观察到的微观尺度变化幅度较小，但如果没有两尺度方法则无法获得，并导致摩擦学性能发生显着变化。