Finite element treatment of soft elastohydrodynamic lubrication problems in the finite deformation regime

Abstract

Soft elastohydrodynamic lubrication (EHL) problem is studied for a reciprocating elastomeric seal with full account of finite configuration changes. The fluid part is described by the Reynolds equation which is formulated on the deformed boundary of the seal treated as a hyperelastic body. The paper is concerned with the finite element (FE) treatment of this soft EHL problem. Displacement-based FE discretization is applied for the solid part. The Reynolds equation is discretized using the FE method or, alternatively, the discontinuous Galerkin method, both employing higherorder interpolation of pressure. The performance of both methods is assessed by studying convergence and stability of the solution for a benchmark problem of an O-ring seal. It is shown that the solution may exhibit spurious oscillations which occur in severe lubrication conditions. Mesh refinement results in reduction of these oscillations, while increasing the pressure interpolation order or application of the discontinuous Galerkin method does not help significantly.

Finite deformation effects in soft elastohydrodynamic lubrication problems

“…The formulation presented below follows our earlier work on the soft-EHL problems [13,19] and on the mass-conserving cavitation model [20]. In the present paper, the formulation is further developed for the case of non-planar contact.…”

“…As a remedy, the Couette shear stress in Eq. (19) can be multiplied by a term ð1 ÀλÞ so that the shear stress is reduced in the cavitation zone (for λ40). However, as shown in Section 4.1, this has a negligible effect on the predicted overall friction coefficient.…”

“…Following the approach developed in [13,19], the present coupled problem is solved monolithically for all unknowns. The basic unknowns of the solid deformation subproblem are the displacements, and the corresponding discrete finite-element equations are derived by assuming that the surface traction t is given.…”

“…In the present paper, the general framework [13,19,20] is further developed and is applied to study finite-deformation effects in soft-EHL. Specifically, in Section 3, the formulation is extended to the case of non-planar contact, and the related issue of the choice of the domain on which the Reynolds equation is solved is discussed in detail.…”

“…A general, fully-coupled nonlinear framework for modelling of soft-EHL problems in the finite deformation regime has been developed in [13,19]. In that approach, deformation of the solid is modelled using the finite element method which allows to consistently treat material nonlinearities and finite configuration changes.…”