Implementation of a Finite Element Deformation Model Within an Elasto-Hydrodynamic Lubrication Numerical Solver for a Ball in Socket Tribopair

Abstract

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.

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“…P denotes the contact pressure in megapascals (MPa) units, while K w represents the wear coefficient. A set of wear coefficients was collected by Wang et al 37 The current wear coefficient, K w , on the sliding contact between SS316L and UHMWPE varies between 1 × 10 −7 mm 3 /Nm 38 and 1 × 10 −6 mm 3 /Nm. 39…”

Prediction of ball-on-plate friction and wear by ANN with data-driven optimization

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“…Many other implementations [12,13], including the finite element method (FEM) and boundary element method (BEM) have also been proposed in recent years. Many tribological problem have been successfully modelled by means of FEM, such as contribution of elastohydrodynamics effect on friction [14], the influence of deformation model on the elasto-hydrodynamic lubrication modeling [15], application of FEM friction model for a problem of metal forming [16]. However, numerical modelling is not only computationally expensive due to its iterative nature, but also less reliable and correct than expectations because constants and parameters associated with the complicated mathematical equations as well as the boundary conditions are often poorly specified a priori.…”

Is It Possible to Create an “Ideal Endoprosthesis” for an “Ideal Total Hip Replacement”?

“…However, to develop adequate models of friction and wear, it is necessary to take into account the real nature of the friction pair surface lubrication, which in general is not an easy task. In addition, such models should be built taking into account the similarity of artificial and complex natural human synovial joints, in which biological, hydrodynamic and tribological phenomena occur [66], as well as depending on the type of human motor activity [67]. But even when the above conditions are met, estimates of material wear made on the basis of modeling turn out to be very inaccurate.…”