Implementation of a finite element deformation model within an elastohydrodynamic lubrication numerical solver for a ball in socket tribopair

In the framework of the elasto-hydrodynamic lubrication simulation algorithms of lubricated tribopairs, a key role is played by the chosen deformation model, since it affects the surfaces’ separation, which guarantees the existence of a thin lubricant film thickness, even when the tribo-system is subjected to high loads. The aim of this article is to merge a finite element deformation model based on linear tetrahedra, previously developed by the same authors, within the Reynolds equation solver in the elasto-hydrodynamic mode, with reference to a generic ball in socket lubricated tribo-system. The main novelty of this research is the implementation of the finite element deformation model, allowing the authors to relate the deformation vector to the pressure one through an influence matrix which takes into account the spherical motion of the ball with respect to the socket. The computer code for the problem–solution was developed in a MATLAB environment and simulated a planar motion condition in terms of eccentricity and angular velocity vectors, in order to calculate the meatus fluid pressure field, surfaces’ separation, shear stress, deformation, and wear depth. The integration over time of the output fields led to the time evolution of the load vector, friction torque vector, and wear volume. Moreover, the lubrication algorithm takes into account the fluid non-Newtonian behavior and the surfaces’ progressive geometrical modification over time due to cumulated wear. The obtained results reproduced the classical elasto-hydrodynamic shapes of the involved quantities, following the meatus minimum thickness predicted by the Hamrock–Dowson model; furthermore, it provided information about the mechanical behavior of the whole bodies belonging to the spherical joint thanks to the finite element deformation model.