Hydrodynamic Analysis of Journal Bearings with Structural Inertia and Elasticity by a Modal Finite Element Method

A General Finite Volume Method for the Solution of the Reynolds Lubrication Equation with a Mass-Conserving Cavitation Model

“…In the presence of irregular geometries and meshes, the finite element method (FEM) is the most widespread method employed for the numerical solution of the Reynolds equation [1][2][3][4][5][6][7], especially due to its great flexibility to deal with distorted elements (interpolation and shape functions). However, when mass conservation is contemplated in the fluid-film cavitation modeling by the imposition of the so-called JFO (Jakobsson, Floberg and Olsson) conditions [8][9][10], the solution of the modified diffusion-convection Reynolds equation (see, e.g., the p À h Elrod-Adams model [11,12]) is not straightforwardly accomplished with the FEM formulation.…”

On the development of advanced techniques for mixed-elastohydrodynamic lubrification modelling of journal and sliding bearing systems.

“…In the presence of irregular geometries and meshes, the Finite Element Method (FEM) is the most widespread method employed for the numerical solution of the Reynolds equation [30,32,35,82,100,128,158,162], especially due to its great flexibility to deal with distorted elements (interpolation and shape functions). However, when mass conservation is contemplated in the fluid film cavitation modelling by the imposition of the JFO conditions (see Section 2.2.2.3), the solution of the modified diffusion-convection Reynolds equation (see p − θ Elrod-Adams model in Section 2.2.3) is not straightforwardly accomplished with the FEM formulation.…”

“…The numerical calculation of the Reynolds lubrication equation together with the Jakobsson-Floberg-Olsson (JFO) complementary boundary conditions for cavitation [87,88,115,160] is not straightforwardly accomplished in such domains, often discretized by unstructured meshes; such complementary conditions aim to ensure the whole mass conservation of the lubricant flow, which are in turn accounted for into the solution by means of the p − θ Elrod-Adams cavitation model [77,78] that defines a modified diffusion-convection Reynolds equation. This solution on irregular grids traditionally uses Finite Element Method (FEM) schemes, which impose difficulties on the discretization process and on satisfying the fluid flow conservation on the moving cavitation boundaries, as well as in providing reliable convergence robustness [30,32,35,82,100,128,158,162]. More recently, a novel FEM formulation that restates the lubrication modelling as a linear complementary problem (LCP) was proposed by [27,93], and an efficient algorithm for the fluid pressure calculation was established by [217].…”