Coupling multi-body dynamics and fluid dynamics to model lubricated spherical joints

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.