Numerical simulation of a lubricated hertzian contact problem under imposed load

Durany, J.; García, Guillermo; Vázquez, Carlos

doi:10.1016/s0168-874x(01)00097-x

Cited by 17 publications

(11 citation statements)

References 5 publications

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“…For the numerical solution of the ε dependent problems and their corresponding homogenized one, we propose the characteristics method adapted to steady state problems to deal with the the convection term combined with a finite element spatial discretization. These numerical techniques has been already successfully used in previous papers dealing with hydrodynamic aspects (see [8,9]), and elastohydrodynamic aspects (see, for instance, [10,11]). …”

Section: Numerical Resultsmentioning

confidence: 99%

Micro-roughness effects in (elasto)hydrodynamic lubrication including a mass-flow preserving cavitation model

Bayada¹,

Martin²,

Vázquez³

2006

Tribology International

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Section: Numerical Resultsmentioning

confidence: 99%

Micro-roughness effects in (elasto)hydrodynamic lubrication including a mass-flow preserving cavitation model

Bayada¹,

Martin²,

Vázquez³

2006

Tribology International

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“…This approach for the hydrodynamic part has been already succesfully used in previously treated elastohydrodynamic problems [2,15]. On the other hand, the mixed formulation allows the use of P 1 finite elements to approximate u n+1 and Λ n+1 , although a bubble function has to be chosen in order to perform an appropriate approximation of η n+1 (see [13], for further details).…”

Section: Numerical Solution Of the Coupled Problem Without Imposed Loadmentioning

confidence: 99%

Mathematical analysis and numerical simulation of a Reynolds-Koiter model for the elastohydrodynamic journal-bearing device

2002

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Abstract. The aim of this work is to deduce the existence of solution of a coupled problem arising in elastohydrodynamic lubrication. The lubricant pressure and concentration are modelled by Reynolds equation, jointly with the free-boundary Elrod-Adams model in order to take into account cavitation phenomena. The bearing deformation is solution of Koiter model for thin shells. The existence of solution to the variational problem presents some difficulties: the coupled character of the equations, the nonlinear multivalued operator associated to cavitation and the fact of writing the elastic and hydrodynamic equations on two different domains. In a first step, we regularize the Heaviside operator. Additional difficulty related to the different domains is circumvented by means of prolongation and restriction operators, arriving to a regularized coupled problem. This one is decoupled into elastic and hydrodynamic parts, and we prove the existence of a fixed point for the global operator. Estimations obtained for the regularized problem allow us to prove the existence of solution to the original one. Finally, a numerical method is proposed in order to simulate a real journal-bearing device and illustrate the qualitative and quantitative properties of the solution.Mathematics Subject Classification. 35R35, 74K25, 76D03, 76D08.

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“…For numerical purposes, the solution of the free boundary problem associated to the Elrod-Adams cavitation model (see ( [1,2], for details) is obtained by means of a duality method applied to a maximal monotone operator, and a finite element spatial discretization ( [3,6], and references therein). The energy equation in the lubricant film is solved with first order finite element schemes due to the simple upwinding used for convective terms.…”

Section: Introductionmentioning

confidence: 99%

Some aspects of lubrication in heavy regimes: Thermal effects, stability and turbulence

Durany

Pereira–Pérez

Varas

2014

Mathematics and Computers in Simulation

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In this work, a combination of numerical methods applied to thermohydrodynamic lubrication problems with cavitation is presented. It should be emphasized the difficulty of the nonlinear mathematical coupled model involving a free boundary problem, but also the simplicity of the algorithms employed to solve it. So, finite element discretizations for the hydrodynamic and thermal equations combined with upwind techniques for the convection terms and duality methods for nonlinear features are proposed.Additionally, a model describing the movement of the shaft is provided. Considering the shaft as a rigid body this model will consist of an ODE system relating acceleration of the center of gravity and external and pressure loads. The numerical experiments of mechanical stability try to clarify the position of the neutral stability curve.Finally, a rotating machine for ship propulsion involving both axial and radial bearings operating with nonconventional lubricants (seawater to avoid environmental pollution) is analyzed by using laminar and turbulent inertial flows.

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Numerical simulation of a lubricated hertzian contact problem under imposed load

Cited by 17 publications

References 5 publications

Micro-roughness effects in (elasto)hydrodynamic lubrication including a mass-flow preserving cavitation model

Micro-roughness effects in (elasto)hydrodynamic lubrication including a mass-flow preserving cavitation model

Mathematical analysis and numerical simulation of a Reynolds-Koiter model for the elastohydrodynamic journal-bearing device

Some aspects of lubrication in heavy regimes: Thermal effects, stability and turbulence

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