A new elastohydrodynamic lubricated spherical joint model for rigid-flexible multibody dynamics

In a unified global coordinate system frame, a new elastohydrodynamic (EHD) lubricated spherical joint model for flexible multibody dynamics is proposed. The proposed joint can be further used to model the human gait artificial hip joints. To mesh the flexible spherical socket of the joint, an isoparametric fifteen-node pentahedron finite element with global nodal position coordinates is introduced. The element elastic forces and their Jacobians are derived using a continuum mechanics approach. The ball within the spherical joint is assumed to be rigid, and it is described using the absolute nodal coordinate formulation reference node (ANCF-RN). The spherical joint lubricant pressure is obtained by solving the Reynolds' equation using the successive over relaxation (SOR) algorithm. To address the lubrication interface non-conformance problem that exists between the lubricant grid and the socket inner surface node grid, a novel lubricant finite-difference grid rotation scheme is introduced. The assembled equations of motion for the constrained rigid-flexible multibody system with a large number of degrees of freedom are solved using the generalized-alpha algorithm. Finally, four numerical examples are studied to validate the proposed EHD lubricated spherical joint model. Some numerical results are also verified using the commercial software ADINA.