A new approach of coupling multibody dynamics and fluid dynamics is developed to model hydrodynamic lubrication of spherical clearance joints with thin fluid film and relative multidirectional motion. The model accounts for dynamics motion of articulating components as well as both squeeze- and wedge-film actions of the synovial fluid. Multibody dynamics methodology is employed to derive the motion equations and Reynolds equation governs the fluid dynamics. The finite difference method is utilized to discretize the governing equation of lubricant and the multi-grid method augments computational efficiency to acquire outcomes employing a Gauss–Seidel relaxation scheme. Fluid–structure interaction is incorporated into the methodology using a partitioned formulation embedded in a high-order Runge–Kutta time integrators for integrating the nonlinear equations of the coupled system over time of interest. A demonstrative example of total hip arthroplasty is considered and the developed model is assessed against outcomes available in the literature. The effect of initial conditions on the pressure, film thickness and dynamics of the lubricated spherical joint is analyzed and discussed. It is illustrated that maximum fluid pressure is undergone by the hip implant at the first walking cycle of movement due to an unstable state, which is strongly dependent upon the initial condition. Finally, the approach presented in this research work is a robust dynamic model to study hydrodynamic lubrication of spherical joints.

中文翻译：

---

耦合多体动力学和流体动力学以建模润滑球形接头

开发了一种将多体动力学与流体动力学耦合的新方法，以模拟具有薄流体膜和相对多向运动的球形间隙关节的流体动力润滑。该模型考虑了关节运动的动力学运动以及滑液的挤压和楔膜作用。采用多体动力学方法来导出运动方程，而雷诺方程则控制流体动力学。有限差分法用于离散化润滑剂的控制方程，而多网格法则提高了计算效率，从而采用了高斯-赛德尔松弛法来获得结果。使用嵌入在高阶Runge-Kutta时间积分器中的分区公式将流固耦合纳入方法中，以便在感兴趣的时间内积分耦合系统的非线性方程。考虑全髋关节置换术的一个示例，并根据文献中可用的结果评估已开发的模型。分析并讨论了初始条件对润滑球形接头压力，膜厚和动力学的影响。示出了由于不稳定状态，髋植入物在运动的第一步行周期经历最大流体压力，该不稳定状态强烈地取决于初始条件。最后，在这项研究工作中提出的方法是一个鲁棒的动力学模型，用于研究球形接头的流体动力润滑。